LIBRARY
Michigan State
University

 

 

This is to certify that the

dissertation entitled
SPECTRAL ANALYSIS FOR OPTIMAL DESIGN OF A
VARIABLE ECCENTRICITY TRUNK SHAKER HARVESTER SYSTEM
presented by

Henry A. Affeldt Jr.

has been accepted towards fulfillment
of the requirements for

Doctor of Philosophy degreein Agricultural Engineering

 

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SPECTRAL ANALYSIS FOR OPTIMAL DESIGN OF A

VARIABLE ECCENTRICITY TRUNK SHAKER HARVESTER SYSTEM

BY

Henry Albert Affeldt Jr.

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

in
Agricultural Engineering

Department of Agricultural Engineering

1987

SPECTRAL ANALYSIS FOR OPTIMAL DESIGN OF A

'VIfliIABLE ECCENTRICITY TRUNK SHAKER HARVESTER SYSTEM

BY

Henry Albert Affeldt Jr.

Date: I? ”747 fig?

Approved: M— KW

Major Professor

Approved: gd’éw /< 6W

Director of Research i

Approved: WW

Department Chairman

 

ABSTRACT

SPECTRAL ANALYSIS FOR OPTIMAL DESIGN OF A
VARIABLE ECCENTRICITY TRUNK SHAKER HARVESTER SYSTEM

BY
Henry A. Affeldt Jr.

Until the advent of mechanical harvesting in commercial
cherry orchards of Michigan in the mid-1960's, the normal
productive life of trees exceeded 40 years. Annual bark
(damage from trunk shaker harvesting had shortened orchard
life to 15-20 years maximum by the mid-1980's. A dynamic
analysis of a trunk shaker was needed to affect a shaker
redesign and to establish physiologically safe operating
procedures. A method to nondestructively monitor possible
changes in tree growth resulting from mechanical harvesting
was also needed.

A C—clamp, fixed-eccentricity trunk shaker was
instrumented with transducers to measure instantaneous
acceleration and position. A frequency-domain analysis
technique was developed to obtain displacement from
acceleration and compare with other events. Peak
displacements during start-up and shut-down of the shaker
vibration were found to be associated with destructive
stress levels in the bark.

A fixed-eccentricity mass on a harvester was exchanged
for a controllably variable eccentric mass. Starting and

stepping transients that involved excessive displacement and

 

 

 

Henry A. Affeldt Jr.

StreSSes were successfully eliminated with this design, even
thoth the steady—state displacement remained equal to that
Of tile fixed-eccentricity design. Several multi—mass,
fiXEd—eccentricity designs are presented which could also
reduce the trunk damage.

A spectral analysis package was developed to compare
prx>file changes in trunk perimeters with time. Bandwidth,
Fcnarier analysis, and invariant moments appear to indicate
bark damage permeathn1(internal and external damage can be

differentiated), and level of infection.

”in—
\~—_ (/1

To my wife Karen
my mother June
my sister Tara
my father Henry Sr.

United in Time and Space,

Through Love, Sacrifice and Understanding,
We have sought Knowledge,
And learned the Questions.

ACKNOWLEDGMENTS

The author would like to express his deepest gratitude
to the following persons and organizations for their
contribution to this study:

To Dr. John B. Gerrish, my Major Professor, for his
professional guidance, immortal support and incomparable,
eccentric prescriptions for problem solving purveyed
throughout the epoch of this graduate program.

To my Director of Research, Dr. Galen K. Brown
(Research Leader, Fruit and Vegetable Harvesting, U.S.
Department of Agriculture), for his unsurpassing, inimitable
professionalism, logic, and dedication.

To my Guidance Committee, Dr. Clark J. Radcliffe
(Associate Professor Mechanical Engineering), Dr. Steven W.
Shaw (Assistant Professor Mechanical Engineering), and Dr.
Clyde L. Burton (U.S. Department of Agriculture, Assistant
Professor Botany and Plant Pathology) for their time,
auspicious counsel, and professional collaboration.

To USDA Mechanical Engineering Technician Richard
Wolthius, MSU Electronic Technicians Joe Clemens and Sidney
Ehlert, MSU Horticultural Specialist Nancy M. Schulte-Pason,
arui Graduate Students Thomas A. Each and Ghassan Al-Soboh

“’fun each contributed many hours of valuable assistance,

e:<perience, and seasoning to the project.

_/

To cherry growers David and Philip Friday and the
Friday Tractor Company (Hartford, MI) for their cooperative
spirit and contributions of equipment which made this
project feasible.

To the Agricultural Research Service, U.S. Department
of Agriculture for subvention (Research Engineer Recruitment
and Development Program) and continued aspirations for the
agricultural foundations of these United States.

To my mother June, my sister Tara, and the orchestra
of family and friends whose unabated love, confidence, and
understanding have been an important and never ending source
of strength and encouragement.

To my wife Karen, a highly unique and fluorescent
spirit, who brought a wondrously enchanting love,
exhilaration, and placid mystery into my once harmonic

orbit.

 

 

 

 

LIST OF

LIST OF

CHAPTER

1.

TABLE OF CONTENTS

TABLES I I I I I I I I I I I I I I I I I I I

FIGURES I I I I I I I I I I I I I I I I I I

INTRODUCTION . . . . . . . . . . . . . . . .

General Information . . . . . . . . .
.1 Physics and Physiology. .
.2 Importance - Tree Fruit Statistics. .
.3 A Timely Goal . . . . . . .
.4 Objective of this Research. . . . . .

LITERATURE REVIEW. . . . . . . . . . . . . .

Historical Prelude. . . . . . . .
Chronology of Tree Shaker Design.
Root Damage . . . . .
Tree Injury - Prelude . .
Tree Vibration. . . . . .
Shaker Clamps . . . . . .
Modeling. . . . . . . .
Tree Injury — Bark. . . .

at i

Bark Damag

Suggestions for Eradic ng
Trunk Shape Analysis.

emu-00.no-

NNNNNNNNN

LOCDNO‘U'IPWNH

TRUNK SHAPE ANALYSIS - FOURIER AND CORRELATION

3.1 Tree Trunk Profile Measurement. . . . .
3.2 Geometric and Linear Profile Plots. . .
3.3 Bandwidth and Historic Shape Indicators
3.4 Fourier Continuum and Cross-Correlation
3.5 Comment . . . . . . . . . . . . . . . .

SPECTRAL CHARACTERIZATION OF SHAKER PATTERNS

Commercial Trunk Shaker Design. . . . .
Instrumentation for Vibration Sensing
Displacement Tests. . . . . . . . .

Frequency Domain Analysis . . .
Displacement Results. . . . . .

Trunk Shaker Analysis . . .
Need for Shaker Redesign. . .

#999999
I I I I I I I
\IO‘lU’IDwNH

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PAGE

ix

189

CHAPTER

SI

6.
7.
8I

SHAKER REDESIGN AND EVALUATION . . .

with One Mass. . . . . . . .
Displacement Results
with Variable Eccentricity .

Design Performance . . . . .

U101 U1 U! 0101
mm D (.0 NH

. Potential in Future Designs . .
SUWARY I I I I I I I I I I I I
CONCLUS I ONS I I I I I I I I I I I I I

RECOMMENDATIONS FOR FUTURE RESEARCH.

BIBLIOGRAPHY. I I I I I I I I I I I I I I I

vi

On the Prospect of Mode Evasion .
Modified Shaker: Variable Eccentricity

Evaluation of Variable Eccentricity

Theoretical Extension to Two Masses

PAGE
191
191
215
227
248
249
252
253
256
258

261

 

LIST OF TABLES

TABLE PAGE

1.1 Total 1985 U.S. cherry production. (National
Agricultural Statistics Service, 1986). . . . . . 7

1.2 Nutritional composition of fresh raw cherries.
(weStWOOd’ 1978) I I I I I I I I I I I I I I I I I 9

1.3 Cherry tree productivity categorized by tree
age. (Fouch, 1986) . . . . . . . . . . . . . . . 11

2.1 Tree characterization and tree shaker inputs
for several tree fruits (O'Brien et al., 1983). . 39

2.2 Comparison of radial stress causing browning
at cambium and tangential stress causing bark
failure for varies species and varieties.
(Cargill et al., 1982). . . . . . . . . . . . . . 55

2.3 Classical methods of describing particle shape. . 62
3.1 Geometric shape indicators of standard geometric
shapes (All measurements in mm unless noted
otherWise) I I I I I I I I I I I I I I I I I I I I 99
3.2 Geometric shape indicators of cherry tree trunk
profiles (All measurements in mm unless noted
otherwise, listed in size categories in order
of damage). . . . . . . . . . . . . . . . . . . . 100
3.3 Moment invariants for standard geometric shapes . 103
3.4 Moment invariants for tree trunk profiles . . . . 103

3.5 Normalized Fourier coefficients for3standard
geometric shapes (coefficient * 10 ) . . . . . . 117

3.6 Normalized Fourier coefficients for small trunk
profiles (coefficient * 10 ) . . . . . . . . . . 118

3. 7 Normalized Fourier coefficients for medium trunk
profiles (coefficient * 10 ) . . . . . . . . . . 118

3.63 Normalized Fourier coefficients for large trunk
profiles (coefficient * 10 ) . . . . . . . . . . 119

vii

 

TABLE PAGE

4.1 Linearized spring and damping coefficients for
a C-clamp eccentric mass inertial trunk shaker
for cherries. . . . . . . . . . . . . . . . . . . 132

4.2 Linearized spring (k) and damping (C)
coefficients and natural frequencies (wn for
Montmorency cherry trees. . . . . . . . . . . . . 133

4.3 Theoretical damping ratios for a C-clamp
eccentric mass trunk shaker . . . . . . . . . . . 135

5.1 Free displacement at shaker clamp and tree
displacement resulting from fixed-mass and
variable-eccentricity shaker designs (15-16 Hz,

6.5 cm, fast mass engagement) . . . . . . . . . . 240

viii

LIST OF FIGURES

FIGURE
1.1 Michigan cherries: total production.
(Michigan Dept. of Agriculture; 1985, 1986)
1.2 Michigan cherry trees of bearing age.
(Michigan Dept. of Agriculture; 1985, 1986)
2.1 A pictorial register of tree fruit harvester
innovationI I I I I I I I I I I I I I I I I
2.2 The three modes of oscillation of a fruit.
(Cooke and Rand, 1969). . . . . . . . .
2.3 Methods of measuring the diameter of non-
spherical particles (Stockham, 1977). . . . . .
3.1 Tree trunk profile contour tracer . . . . . .
3.2 Block diagram of profile data calibration
3.3 Profile calibration from periphery trace. . . .
3.4 Inequality of centroids with a least squares
best fit circle procedure . . . . . . . . . . .
3.5 Standard geometric shapes referenced in profile
analYSiSI I I I I I I I I I I I I I I I I I I I
3.6 Tree trunk shape/area analysis - trunk
prOfile 11I I I I I I I I I I I I I I I I I I I
3.7 Tree trunk shape/area analysis - trunk
prOfile A I I I I I I I I I I I I I I I I I I
3.8 Tree trunk shape/area analysis - trunk
prOfile ZSI I I I I I I I I I I I I I I I I I I
3.9 Polar map of standard geometric shapes.
3.10 Polar map of tree trunk profile 11. . . .
-3.ll. Polar map of tree trunk profile A . . . .
3.LL2 Polar map of tree trunk profile ZS. . . . .

ix

PAGE

10

18

37

61
66
70

71

75

79

80

81

82
84
86
87
88

F I GURE PAGE

3.13 One year' s radial change in trunk profile —
trees 10,11 and 12 . . . . . . . . . . . . . . 90

3.14 One year's radial change in trunk profile —
trees A, B and C. . . . . . . . . . . . . . . . . 91

3.15 One year's radial change in trunk profile —
trees N and 2S. . . . . . . . . . . . . . . . . . 92

3.16 Cherry tree trunk cross sections: a) shaker
damage b) bark compression . . . . . . . . . . . 94

3.17 Cherry tree trunk cross sections: a) contour
rejuvenation b) staining . . . . . . . . . . . . 95

3.18 Spectral content of a standard rectangular
profile . . . . . . . . . . . . . . . . . . . . . 107

3.19 Spectral content of a standard elliptical
profile . . . . . . . . . . . . . . . . . . . . . 108

3.20 Spectral content of a standard circular
profile . . . . . . . . . . . . . . . . . . . . . 109

3.21 Spectral content of trunk profile 11. . . . . . . 110
3.22 Spectral content of trunk profile A . . . . . . . 111

3.23 Spectral content of trunk profile ZS. 112

3.24 Change in spectral content — trunk 11 . . . . . . 114

3.25 Change in spectral content - trunk A. 115

3.26 Change in spectral content - trunk ZS . . . . . . 116

3.27 Cross-correlation of the time—spaced frequency
spectra of trunk 11 . . . . . . . . . . . . . . . 121

3.28 Cross-correlation of the time—spaced frequency
spectra of trunk A. . . . . . . . . . . . . . . . 122

3.29 Cross—correlation of the time—spaced frequency
spectra of trunk 28 . . . . . . . . . . . . . . . 123

4.1 Dimensioned C-clamp trunk shaker showing
accelerometer and proximity sensor locations.
(All measurements in mm . . . . . . . . . . . . . 127

4.2 C-clamp trunk shaker harvester for cherries
mounted on a Hydro—84 International Tractor . . . 128

 

FIGURE

4.3

4.4

Sensor locations on a cherry trunk. . . . .

Angular velocity of inner mass during a 15—16 Hz
free shake when both masses are operating .

Angular velocity of outer mass

during a 15-16

free shake when both masses are operating .

Angular velocity of outer mass
free shake with only the outer

Angular velocity of inner mass
free shake with only the inner

Angular velocity of inner mass

during a 15—16
mass operating

during a 15—16
mass operating

during a 15—16

Hz

Hz

6.5 cm tree shake when both masses are operating.

Angular velocity of outer mass during a 15—16 Hz
6.5 cm tree shake when both masses are operating.

Angular velocity of outer mass

15- 16 Hz 6. 5 cm tree shake with only the outer

mass operating. . . . . . . .

Angular velocity of inner mass

15— 16 Hz 6. 5 cm tree shake with only the inner

mass operating. . . . . . . .

Angular velocity of inner mass

during a
during a

during a

15—16 Hz 11.0 cm tree shake when both masses are

operating . . . . . . . . . .

o o o n o n o

X and Y motion at shaker clamp with both masses
operating 15—16 Hz in free shake. . . . . .

X—Y planar motion at shaker clamp with both
masses operating 15-16 Hz in free shake . . .

X and Y motion at the tree with both masses

operating 15—16 Hz on a 6.5 cm

X—Y planar motion at the tree with both masses

operating 15—16 Hz on a 6.5 cm

X and Y motion at shaker clamp

tree . . . .

tree . . . . .

with a single

inner fixed-mass at 15—16 Hz in free shake.

X-Y planar motion at shaker clamp with a single
inner fixed-mass at 15-16 Hz in free shake.

Spectral content of vibration with a single inner

fixed—mass at 15—16 Hz in free

xi

shake. . . .

PAGE

137

150

151

152

153

154

155

156

157

158

161

163

164

165

167

169

FIGURE

4.20

PAGE

Spectral content of vibration when free shaking
at 15—16 Hz with both fixed—masses operating. . . 170

X and Y motion at the tree with a single inner
fixed-mass at 15—16 Hz on a 6.5 cm tree . . . . . 171

X—Y planar motion at the tree with a single inner
fixed-mass at 15—16 Hz on a 6.5 cm tree . . . . . 172

Spectral content of vibration when shaking
a 6.5 cm tree at 15—16 Hz with a single inner
fixed-mass. o o o o o n o o a o o o o o u o o a a 173

Spectral content of vibration when shaking
a 6.5 cm tree at 15-16 Hz with both fixed-masses
operating . . . . . . . . . . . . . . . . . . . . 174

X and Y motion at the tree with a single inner
fixed—mass at 15—16 Hz on a 16.5 cm tree. . . . . 176

X—Y planar motion at the tree with a single inner
fixed—mass at 15-16 Hz on a 16.5 cm tree. . . . . 177

Spectral content of vibration when shaking a
16.5 cm tree at 15-16 Hz with a single inner
fixed—mass. . . . . . . . . . . . . . . . . . . . 178

X displacement and frequency spectra at the tree
with both fixed-masses operating 15—16 Hz on an
11.0 cm tree. . . . . . . . . . . . . . . . . . . 179

Free shake test: a) one mass operational
b) two masses operational . . . . . . . . . . . . 181

Free shake pattern with two masses operational:
a) test one b) test two. . . . . . . . . . . . . 182

Single mass oscillator: a) free body diagram
b) resulting X and Y motion c) resulting planar
motion. I I I I I I I I I I I I I I I I I I I I I 183

Two mass oscillator: a) free body diagram
b) resulting X and Y motion c) resulting planar
motion. . . . . . . . . . . . . . . . . . . . . . 184

Amplitude and phase of a linear, second order
system. . . . . . . . . . . . . . . . . . . . . . 187

Geometry of rigid body motion a) relative motion
b) force and torque . . . . . . . . . . . . . . . 193

 

FIGURE PAGE

5.2 Single oscillator shaker excitation (a) in free
space (b) actin forces (c) force and moment
polygons at CG gd) force and moment polygons off
the CG. . . . . . . . . . . . . . . . . . . . . . 195

5.3 Two oscillator shaker excitation (a) both at CG
(b) other than CG (c) general force and moment
polygons. . . . . . . . . . . . . . . . . . . . . 198

5.4 Three oscillator shaker excitation (a) general
configuration (b) force and moment polygons and
(c) dynamic balance analysis. . . . . . . . . . . 202

5.5 Three oscillator shaker excitation (a) simplest
configuration (b) force and moment polygons . . . 203

5.6 Three oscillator shaker excitation (a) linear
configuration (b) force and moment polygons . . . 205

5.7 Three oscillator shaker excitation (a) physical
configuration (b) force and moment polygons
(c) trigonometric balance . . . . . . . . . . . . 207

5.8 Four oscillator shaker excitation (a) linear
configuration (b) force and moment polygons . . . 209

5.9 (a) Modern potential trunk shaker control panel
(b) Couple free 'double mass' shaft . . . . . . . 211

5.10 Four oscillator shaker excitation with a balanced
force distribution about the tree (CR). . . . . . 213

5.11 Linear (X) motion at shaker clamp with fixed mass,
free shake, 15-16 Hz: a-outer mass only,
b—inner [(1853 only 0 o o o o o o o o o o o o o o o 218

5.12 Linear (X) motion at the tree with fixed mass,
6.5 cm tree, 15-16 Hz: a-outer mass only,
b-inner mass only . . . . . . . . . . . . . . . . 219

5.13 Linear (X) motion at shaker clamp with both fixed
masses operating 15-16 Hz: a-6.5 cm tree,
b_free Shake. o o o o o o o o o o o o o o o o o o 220

5.14 Variable-eccentricity shaker mass with positive
contrOI I I I I I I I I I I I I I I I I I I I I I 222

5.15 Variable eccentric mass design: (a) top view
(b) exploded view . . . . . . . . . . . . . . . . 223

5.16 Hydraulic circuit used for controlling mass
position in variable-eccentricity testing . . . . 226

xiii

FIGURE

5.17

Eccentric rod velocity and position when shaking
a 6.5 cm tree using fast engagement of
eccentricity. . . . . . . . . . . . . . . . . . .

Eccentric rod velocity and position when shaking
a 6.5 cm tree using slow engagement of
eccentricity. . . . . . . . . . . . . . . . . . .

Angular velocity of mass rotation for a 15—16 Hz,
6.5 cm tree shake with fast engagement of
eccentricity. . . . . . . . . . . . . . . . . .

Angular velocity of mass rotation for a 15—16 Hz,
6.5 cm tree shake with slow engagement of
eccentricity. . . . . . . . . . . . . . . . . . .

Angular velocity of mass rotation for a 15—16 Hz,
6.5 cm tree shake with fixed-eccentricity . . . .

X and Y motion at shaker clamp with variable-
eccentricity, fast engagement at 15—16 Hz in free
shake . . . . . . . . . . . . . . . . . . . . .

X—Y planar motion at shaker clamp with variable—
eccentricity, fast engagement at 15—16 Hz in free
shake . . . . . . . . . . . . . . . . . . . . . .

X and Y motion at the tree using variab1e~
eccentricity, fast engagement at 15-16 Hz on a
6.5 cm tree . . . . . . . . . . . . . . . . . . .

X and Y planar motion at the tree using variable-
eccentricity, fast engagement at 15—16 Hz on a
6.5 cm tree . . . . . . . . . . . . . . . . . . .

X and Y motion at shaker clamp with variable—
eccentricity, fast engagement at 15—16 Hz on a
6.5 cm tree . . . . . . . . . . . . . . . . . . .

X and Y planar motion at shaker clamp with
variable-eccentricity, fast engagement at 15—16
Hz on a 6.5 cm tree . . . . . . . . . . . . . . .

Spectral content of vibration when shaking a
6.5 cm tree at 15—16 Hz with conventional fixed—
eccentricity. . . . . . . . . . . . . . . . . . .

Spectral content of vibration when shaking a
6. 5 cm tree at 15- 16 Hz with fast engagement of
eccentricity. . . . . . . . . . . . . . . . .

PAGE

229

230

231

232

233

235

236

237

238

242

243

244

245

FIGURE

5.30

5.31

PAGE

Oscillator induced 'shift' and 'drift' on shaker
motionI I I I I I I I I I I I I I I I I I I I I I 247

Shaker design extension to two variable eccentric
OSCillatOrs I I I I I I I I I I I I I I I I I I I 250

XV

CHAPTER 1

VINTRODUCTION

Fruit and nut production around the world continues to
be a costly, long term investment for growers (Brown, 1980).
The onset of industrialization combined with problems in
labor management and production economics has forced growers
to mechanize crop production, harvesting and processing.
Countries such as the U.S., Japan, Australia, New Zealand,
Israel, South Africa, the Socialist Block Countries, Canada
and many countries in South America currently have programs
to mechanize labor-intensive fresh market crops. Improved
means by which production can be made more efficient and
reliable are necessary to meet the demands of the
competitive world food markets and the 4,917 million people
therein (United Nations, 1986).

Tree fruits have been mechanically harvested since the
early 1920's (Abildgaard, 1923) but mechanization actually
began with the development of the eccentric powered cable
limb shaker for walnuts in 1946 by J. P. Fairbanks (O'Brien
et al., 1983). Since that time, there have been extensive
efforts to mechanize the harvest of the world's multitude of
fruit and nut crops, thereby realizing increases in labor

and economic efficiency. An unwanted side effect of

mechanization evolved, however; bark damage at the point of
shaker attachment. The clamping and shaking forces from
vibrating shake-and-catch harvest systems are transmitted to
the tree limb or trunk through the bark and cambium causing
subsequent fruit release onto a catching surface below.
Worldwide, grower's have expressed concern as to the
potential role dynamic shaker loading may play in internal
tree damage and subsequent tree decline, particularly in
younger orchards.

In Michigan, for instance, commercial cherry growers
who mechanically harvest estimate 20-30% annual decline of
cherry trees in some orchards (Brown, 1982). Until the
advent of mechanical harvesting, manual cherry orchard
productive life exceeded 40 years. Commercial orchard life
degenerated to 30 years in the late 1960's and finally to
15-20 years with today's trunk shakers (Burton et al.,
1986).

Trunk damage alone can result in the death of many
trees, particularly young trees subjected to annual shaking.
Mechanical harvesting, however, may simply initiate decline,
presenting an opportunity for the infectious cankers or
predisposing the tree to other stress factors such as cold
injury, nematodes, borers, viruses, fungi, bacteria, etc.

USDA undertook an engineering analysis of a
representative commercial inertial shaker in order to
determine basic dynamic behavior which may be correlated to

fruit harvesting success and bark strength failure. This

information is mandatory for design of a mechanical shaker
which will cause minimum tree (bark) damage. It may also be
of value in indicating the range of basic tree properties as
limits for future harvester designs.

This research describes the hardware and methodology
employed to characterize the dynamic behavior of an inertial
trunk-shaking harvester clamped to different sizes of trees.
The analysis of the data highlights a new criterion for
shaker design. Subsequently, a new mechanical vibratory
tree shaker is designed, built and tested. Finally, a

method for studying the long term effect of shaking on tree

trunk profiles is presented (spectral analysis).

1.1 Physics and Physiology

 

The first limb shakers transmitted forces in a linear
reciprocating motion, practically devoid of any lateral
forces on the tree when the clamps were correctly attached
perpendicular to the limb. Due to the greater speed, lower
harvest cost and lower labor requirement offered by trunk
shakers, however, trunk shakers were adopted in the early
1960's. The trunk shakers applied large forces in epicyclic
patterns such as cycloids, hypocyloids, cardioids, N-leaved
roses and spirals. These patterns are quite efficient at
fruit removal when transmitted at proper design frequency
and amplitude for a given crop. Compared with limb shakers,
the compressive, tangential and longitudinal forces
associated with epicyclic trunk shakers are usually greater,

the motion is non-linear and hence, some lateral forces

 

 

 

become apparent.

Research on cherry bark strength indicates that cherry
tree bark is easier to damage than apple or peach tree bark
in both longitudinal and tangential directions (Diener et
a1, 1968). The adoption of the epicyclic trunk shaker
patterns also brought about obvious bark damage to the
trees. Potential causes of bark damage include operator
error, carrier slip, improper shaker and clamp adjustments,
improper machine maintenance, inadequate orchard maintenance
and poor choice of harvest date, harvest practice or
production practice, and clamping and shaking forces too
high or too low (Cargill et al., 1982).

By itself, bark damage from these and other causes
would not be deleterious to tree production. Insect attack
and fungus cankers often infect the damaged area, however,
spreading and quickly causing premature tree decline (Devay
et al., 1965). Fungal spores can be transported from tree
to tree by shaker pads from diseased trees to healthy,
undamaged plantings.

Damage can be greatly affected by the condition of the
cambium at harvest. During periods of rapid growth and
irrigation when the cambium is moist, the cell interiors and
intercellular spaces become filled with liquid. Cell walls
are thinner (Bukovac, 1984). When shear stress is applied,
the bark slips easily over the wood. When the moisture
content decreases or Fall dormancy sets, cell walls become

thicker and less elastic and intercellular spaces lose their

 

 

 

liquid content (Priestley, 1930); the occurrence of slip is
greatly reduced under these conditions (Fridley et al.,
1970).

Rain and irrigation during periods of rapid growth
increase the tendency for the bark to slip. Thus, cherry
trees harvested in June and July are more susceptible to
damage than peach, plum or apple trees which are harvested
later. Bark damage that occurs as torn or split bark
(visible) has been studied for the past 20 years. Research
has been conducted to determine the limits on cherry bark
strength and how to eliminate bark damage (Diener et al.,
1968; Brown et al., 1982). Excessive clamping forces which
were found to crush bark and internal tree tissues have been
identified in the static, nonvibratory state (Frahm et al.,
1983).

Responding to the recommendations of researchers, some
manufacturers have redesigned clamp pads with increased
contact area; larger pads transmit shaking forces at lower
pressures (Brown et al., 1986). Forces transmitted by
shakers have been studied; recommendations have resulted for
stroke and frequency to remove fruit and minimize tree
damage (Fridley and Adrian, 1960). Procedures on operations
and maintenance of both machine and orchard have been
suggested by other researchers (Brown et al., 1982; Cargill

et al., 1982).

1.2 Importance : Tree Fruit Statistics

 

 

 

Mechanical trunk shaker harvesters are employed to some
extent throughout the U.S. and abroad for apples, apricots,
olives, peaches, pears, plums, prunes, cherries and citrus
(Brown, 1980). Frequently, over 50% of the total labor
required for these crops is dedicated to the harvesting
process. Production quantity and a short harvest season
often mandate the use of mechanical harvesting in some
crops, especially in countries where hand labor is not
available or affordable.

The soil condition, drainage, elevation, and climate
combine to make the counties bordering Lake Michigan host to
some of the most productive cherry orchards in the world.
In 1985 Michigan ranked first in the nation in production
value of tart cherries; Michigan ranked second in production
value for sweet cherries (Table 1.1). Seventy—seven percent
(100,000 tonnes) of the nation's tart cherries, worth 52.4
million dollars, are produced in Michigan along with 23%
(28,000 tonnes) of sweet cherries worth 15.5 million
dollars.

Cherries are high in nutritive value (Table 1.2) and
are often used as a supplement to the diet. The primary
market for Michigan tart cherries (95%) is in cherry pie
filling and dessert toppings in frozen market packs. The
remaining tart cherries go into juice, raisins, wine and
jams. Sweet cherries are also mostly processed (90%), the

light varieties being packed for juice, jelly, ice cream and

 

Table 1.1. Total 1985 U.S. cherry production.
(National Agricultural Statistics Service, 1986)

TART CHERRIES

 

 

 

 

 

 

 

 

Total Production Value of Production

1000 t 1000 Dollars (U.S.)
Michigan 100.0 52,395
New York 10.2 5,764
Utah 9 5 4,832
Wisconsin 3.9 1,549
Oregon 2.9 1,560
Pennsylvania 2.7 1,608
Colorado 0.8 390
U.S. 130.0 68,098

SWEET CHERRIES

Total Production Value of Production

1000 t 1000 Dollars (U.S.)
Washington 34.4 36,588
Michigan 28.2 15,500
Oregon 26.4 16,761
California 21.4 24,641
Montana 4.2 2,255
Idaho 2.0 2,065
Utah 2.0 1,624
New York 1.8 1,396
Pennsylvania 0.4 655
U.S. 120.8 101,485

 

frozen products, the remaining 10% going into maraschinos
and fresh market.

Yield per tree depends on factors such as climate,
cultural practice and variety but is generally categorized
by age of the tree (Table 1.3). The yield for tarts in
Michigan was up 5% from 1984 while sweet production was down
6% (Figure 1.1). The 1985 average productivities for

Michigan were 1100 kg/ha (6000 lbs/acre) for tarts and 1285

 

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Figure 1.1

 

Table 1.2. Nutritional com osition of fresh raw cherries*.
(Westwood, 1978 .

 

 

Sour Red Cherry Sweet Cherry
Water (%) 83.7 80.4
Calories (kcal) 58 70
Carbohydrates (g) 14.3 17.4
Protein (9) 1.2 1.3
Ash (9) 0.5 0.6
Fat (9) 0.3 0.3
VITAMINS
V1tam1n A (I.U.) 1000 110
Ascorbic Acid Vitamin C (mg) 10 10
Niacin B-Vitamin (mg) 0.4 0.4
Riboflavin B (mg) 0.06 0.06
Thiamine B1 Img) 0.05 0.05
MINERALS
Pota551um (mg) 191 191
Calcium (mg) 22 22
Phosphorus (mg) l9 19
Sodium (mg) 2 2
Iron (mg) 0.4 0.4

* Based on 100 9 (3-1/2 oz, 110 cherries/lb).

 

kg/ha (7000 lbs/acre) for sweets with a reported 82,300
hectares (33,300 acres; 3.25 million tart trees) and 18,800
hectares (7,500 acres; 625,000 sweet cherry trees) of
bearing age (Figure 1.2). There were 1383 tart cherry
growers and 775 sweet cherry growers in Michigan in 1982;
recently grower numbers have been decreasing and orchard
acreage has been increasing.

Ninety-nine percent of the state's tart cherries are of
the Montmorency variety. For sweet cherries, 31% are the
Napoleon variety; Golds (17%), Schmidt's Biggareau (12%),

Emperor Francis (11%) and other varieties (29%) make up the

 

10

SWEET CHERRY
(millions of trees)

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Table 1.3. Cherry tree productivity categorized by tree age.
(Fouch, 1986).

 

Tree Age (Years) Average Annual Productivity (kg/tree)
4 22
5 33
6 44
7 88
8 132
9 176
10 - 18 176 — 220
19 — 20 176
21 - 22 132
23 110
24 66
25 55
26 44
27 33
28 22
29 + 0

General Classification of Bearing Age:

0 ~ 5 : Non-bearing

6 - 9 : Moderately Bearing
10 - 20 : Prime Bearing

21 - 25 : Rapid Decline

 

rest. Domination of the state's cherry trees by the tarts
(84%), in particular by the Montmorency variety, facilitates
design of mechanized harvesting systems because of the
uniformity of tree size and structure.

Over the past eight years there has been an increase in
the number of bearing trees. This increase will continue as
nearly 50% of the state's tart trees and 30% of the sweets
are currently of non—bearing age. New orchards signal even
greater uniformity in terms of design for reduction of bark

damage. New orchards also make urgent the need to eliminate

12

bark damage and tree decline factors before harvesting
should begin on these younger, more susceptible plantings.
Bark damage leading to tree decline (loss of vigor and
yield) is thought to be caused by excessive shear,
compression stress or strain (Adrian et al., 1965). Limb
shakers may damage one or more scaffolds but damage to the
entire tree can occur when a trunk shaker causes damage.
The flow of nutrients essential to tree vitality is
interrupted when the xylem or phloem cells are damaged. The
tree isolates damaged areas in a two step process to protect
healthy wood and tissue (Santamour, 1986). The speed at
which this process occurs depends on the area damaged and

can determine the spread of decay and loss of tree vigor.

1.3 A Timely Goal

Visible bark damage has practically been eliminated for
operators who accept current recommendations for shakers,
pads, operations, pruning, and irrigation scheduling. Bark
damage from excessive stress or strain may still occur in
the form of cell—crushing which is not visible. The outer
bark periderm on cherry trees is elastic and may hide the
internal damaged areas for several weeks. This damage is
later revealed in the form of open cracks, dead bark
tissues, gummy areas, or abnormal bark growth (Brown et al.,
1984).

Despite continued shaker and pad development and the
adoption of enlightened operating procedures, growers

continue to report some bark damage each year in commercial

 

 

13

orchards (Timm, 1986). Sweet cherry trees are more
susceptible than tarts and young trees are more susceptible
than older plantings. The productive life of mechanically
harvested orchards appears to have decreased from 30 years
to 10-15 years; bark damage may be a significant factor
(Burton et al., 1986). When considering that mechaniCal
shake-and-catch harvest systems are used to harvest over 95%
of all sweet and tart cherries used for processing, this
loss in productivity adds up to 3.0 million tart trees (30
million tree—years of productivity) and 536,000 sweet trees
(5.36 million tree-years of productivity) in 1985 alone for
existing orchards. Significant plantings of new orchards in
the late 1970's and early 1980's (nearly 50% of the state's
tart trees and 30% of the sweet trees in 1982) have made the
elimination of bark damage an economic priority. These new
orchards signify another 1.3 million tart trees and 312,500
sweet trees that will come to bearing age in Michigan
orchards which may be harvested mechanically.

The U.S.D.A. Joint Council on Food and Agricultural
Sciences (1986) lists as one of it's eight top research
priorities for 1988: "to sustain the long term productivity
and profitability of agriculture...Greater emphasis is
needed on integrated farming systems which are based on the
appropriate new and existing production technologies". The
current problem of eradication of hidden bark damage
requires the identification and control of safe limits on

applied pressure and strain from mechanical shake-and-catch

14

harvest systems (Brown et al., 1984). Re—design of current
shaker-pad—tree systems and modification of shaker operating
procedures are just two of the many bio—physic interfaces

that promise to benefit from engineering intervention.

1.4 Objective of this Research

The goal of this research was to analyze the dynamic
displacement response of an inertial fruit tree shaker and
attached cherry trees of varying size. Displacement data
can aid in estimation of stress and strain applied to the
bark. Critical maxima thought to be harmful to tree bark
would be sought. Theoretical analysis and re—design of the
inertial fruit tree shaker based on vibration results may
then provide a key step in minimizing bark damage. A tree
trunk profile analysis method, a possible hidden bark damage
indicator, would be developed and presented for utilization
in future studies. The specific objectives formulated for

the needs of this research investigation were:

1. Collect and analyze dynamic displacement data from
a typical commercial inertial fruit tree shaker and develop

the methodology for required signal analysis processes.

2. Determine peak X and Y displacements of the tree

and shaker for several vibration frequencies and tree sizes.

3. Design, construct, test and evaluate a modified
shaking mechanism based on an analysis of the apparent

vibration anomalies potentially harmful to the bark.

15

4. Develop and test a method for monitoring tree trunk

profile changes over a several year period.

 

CHAPTER 2

LITERATURE REVIEW

The first manual harvesting of a tree fruit is
attributed to Eve (Genesis 3:6). For millennia thereafter,
fruits were harvested manually, requiring much time and
labor. The amount of labor needed for harvesting was
frequently over 50% of the total labor and cost requirements
to raise a specific horticultural crop (Brown, 1980).
Different tree fruits pose different difficulties for manual
harvest. Date palms, for example, grow very tall (9—18 m,
30-60 ft.) and bear fruit at the top where skilled workers
are needed to climb and cut the fruit bunches. Some citrus
fruits like tangerines, lemons and limes, rapidly
deteriorate if the stem is improperly removed from the fruit
during picking. Apple, pear, peach and plum trees require
ladder or platform work; the bulk of these fruits also
necessitates frequent trips to empty the picking sacks.

Cherries, on the other hand, are not bulky, but are
small and vastly abundant within a tree. It requires ten
times as many man-h of labor to pick a tonne of cherries as
are required to pick a tonne of apples, peaches or pears
(Levin et al., 1960).

Most tree fruits also pose the problem of a short

16

17

harvest season and low yield per worker, particularly
cherries (150 h season, 8 man-h per tree: Fridley and
Adrian, 1968). When an orchard is ready to be harvested, a
grower may have only a few days to harvest for prime
quality. Until the late 1960's, the cherry growers in
Michigan could rely on over 45,000 workers, 35,000 of whom
were migrant workers, to meet the harvest need (Levin et
al., 1960; ARS, 1964; Brown, 1980). Public Law (PL) 78,
known as the "Bracero program", which permitted seasonal
migratory workers to enter the United States, was terminated
December 31, 1964. Investors in orchard crops were faced
with the choice of selling out, switching crops, abandoning
the orchards or mechanizing. As the problems of labor
shortage, labor cost, labor unrest, transportation costs,
rough handling and economics accumulated, growers learned
that mechanization could be economical and eliminate many
labor problems while maintaining steady product flow to the

market (Drake, 1983).

2.1 Chronology of Tree Shaker Design

 

 

Mechanical vibratory tree fruit harvesting has seen an
evolution from crude tools to current—day, highly complex
mechanized shakers (Figure 2.1). The concept of these tree
fruit harvesters remains quite simple: to transmit enough
shaking force through the shaker and the clamp to overcome
the inertia of the tree and provide limb acceleration
sufficient to detach the fruit at the stem. This concept

was first employed in hand tools used as knockers and

18

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19

shakers. Stiff trees where low amplitude, high frequency
vibration could remove fruit were found to be good targets
for mallet shakers, especially in the nut groves of
California. A l-m long wooden mallet with a hard rubber
padded tip was used to beat limbs to remove fruit. Bark
damage from this method, however, in conjunction with

Ceratocystis fimbriata canker infestation, caused enough

 

 

harm to nut trees in California that the canker earned the
nickname "mallet wound canker" (Devay et al., 1960).

Long willowy poles have also been used to knock limbs,
thereby jarring the fruit from the stem (Gaston et al.,
1959; O'Brien et al., 1983). Fridley and Adrian (1966)
describe manual limb shaking of prunes with a hook secured
to a long pole. W. F. Rurup actually patented the first
manual "tree shaking device" in 1927 consisting of a spring
loaded metal hook on the end of a rod. Gustafson patented a
similar concept in 1951 with an improved hook guide to shake
nuts from tree limbs. Expectedly, the size of the limb was
limited; weakened branches were easily broken, and workers
quickly tired.

Hand-carried mechanically activated shaking devices
were developed to replace poles in the shaking of small
limbs (Gaston et al., 1959; Russel and Dowling, 1964;
Plummer, 1969). Ferguson (1963) developed a hand held,
spring loaded limb knocker which was activated by a hand
crank. Several hand held motorized designs were based on

the use of a chain saw type power unit with a pitman linkage

20

(Londo, 1965; Au1abaugh, 1965). A manually operated pulley
system on a tractor frame was developed in 1959 to knock
tree limbs for fruit removal (Roberts, 1959). Steingas and
Gaul (1968) developed a portable hydraulic/air cylinder
which had one end ratchet—clamped to a limb with the
opposite end supporting a mass which was reciprocated; the
unit was powered through a flexible hose coupled to a
tractor unit. Watson (1970) had a similar idea with a PTO—
powered pneumatic pump hose-connected to a hand held
rotating motor unit which operated a pitman arm for limb
reciprocation. Most of these hand-held shakers were not
popular, however, due to the low rate of harvest, operator
fatigue, shock transferred to the user, in effectiveness on
large limbs and bark damage.

The next step in tree shaker evolution was changing the
shaker carrier from man to machine. Abildgaard patented the
first completely mechanized fruit and nut harvester in 1923.
A spring loaded hook clamped to a trunk or main scaffold
imparted linear reciprocating motion from a boom driven by a
gasoline powered pitman—crank mechanism mounted on a carrier
below. This was the first patented account of a "trunk
shaker" of sorts. In 1927, Harold Bartlett patented a
hydraulically activated boom shaker harvester (limbs or
trunks) with a two—half tree encircling catching frame.
Berger (1937) moved the standard reciprocating pitman-crank
mechanism to the end of the boom on his design such that

only the shaker head and the trunk or limb were oscillated

21

and not the boom itself. Berger was also the first of the
tree shaker patentees to suggest using some padding at the
tree contact surface to prevent bark damage.

Unfortunately, it took almost a quarter of a century
after these first designs were patented before total
mechanization found general acceptance. The first widely-
noted "pioneering account" of mechanical tree shaking was
published in 1946 by J. P. Fairbank, Extension Agricultural
Engineer, at the University of California, Davis (O'Brien et
al., 1983). Although many earlier designs employed rigid
booms, Fairbank's design (for walnut trees) employed a cable
with a hook at one end which was reciprocated by an
eccentric crank on a farm tractor. The hook was placed over
the limb, tension was applied to the cable. The eccentric
was then started to apply reciprocating, large amplitude
motion to the tree limb. The speed of the shaker was
limited by the natural frequency of the limb, which
accounted for the return stroke of the shake, as the cable
was capable of applying only tension. In 1950, the first
cable shaker was patented by Paul Balsbaugh; it consisted of
a cylindrical housing in which a PTO driven crank attached
to a pitman arm provided reciprocating motion to a cable
attached to a tree. Other reciprocating mechanisms for
cable shaker operation followed, often powered by a tractor
PTO (Johnson, 1951; Avansino, 1953; Hess, 1962).

The boom shakers of the 1920's had been difficult to

maneuver in many orchards due to tree shape and ground

22

conditions. Early models were expensive and were subject to
frequent breakdowns. As a result, cable shakers outsold
boom shakers for many years.

Eventually, however, the rigid boom design of the
1920's began to replace the Fairbanks cable shaker of 1946
in the design evolution (Gould and Gould, 1954). The boom
eliminated the second operator who handled the cable hook.
Two types of boom shakers simultaneously developed. One
type of boom shaker was called a "knocker" and consisted of
a padded member which simply maintained flush contact with
the tree delivering a series of impulses to the tree and
thus still relied on the natural frequency of the tree for
return motion (Jones, 1961; Balsbaugh, 1961; Phelps, 1963).
Knocker designs included eccentric boom bumpers, spring
activated impulsers, and pressurized air cylinder impulsers.
Fridley and Adrian (1966) developed an impulse shaker
consisting of an air-accelerated piston in a tube which
impacted a padded head next to the limb. A spring between
the head and the piston prolonged the impact. Pellerin et
al. (1978) designed a pendulum type of trunk impulse shaker
with a variable mass and drop height.

Pacheco and Rehkugler (1980) developed a spring—
activated impact shaker capable of delivering up to 1151 J
(10,185 in.-lb) energy with an 86.6 kg (191 lb) mass moving
at 516 cm/s (203 in./s). In 1982, Pellerin et a1. designed
a spring activated trunk impact shaker capable of both a

double impact mode (second impact strikes tree in opposite

23

direction of first impact and at a time when the tree
reaches maximum displacement from the first impact) and a
recoil impact mode (tree is pulled toward shaker by a spring
recoil force, then impacted to move away).

The second type of boom shaker simply replaced the
cable with a boom and the hook with a mechanically activated
clamp which could be remotely fastened around a limb by the
tractor operator (Lowe, 1955). The tension-compression
member with clamp had the advantage of allowing the
frequency of vibration to be set by the operator,
independent of the natural frequency of the limb or tree.

The majority of the boom and cable shakers which
provided a linear motion utilized a cam, piston—crankshaft
or pitman—crank drive mechanism. Some innovative deviations
from these designs had arisen, however. Goodwin (1954) used
a linear hydraulic actuator (cylinder) to reciprocate the
boom as fluid was switched in and out of opposing cylinder
sides. Balsbaugh (1963) developed a journaled swash plate
to reciprocate the shaker boom. In a rigid boom limb
shaker, Anderson (1963) used a rotating eccentric to pull a
cable attached to a sliding shaker head for retracting
motion and used a built-in compression spring to provide the
extending motion. Sumner et a1. (1975) used a four bar
crank-rocker mechanism including a flywheel to provide
linear motion at the tree. Khalilian et a1. (1978) added a
spring between the mass and the limb shaker boom to reduce

the maximum force and peak power necessary at frequencies

24

above the second natural frequency (mode) without affecting
limb displacement.

Cherry tree shaker mechanization made its debut in 1958
in Michigan. Levin et a1. (1960) recorded 95% fruit removal
on sour cherry trees with a Gould tractor-mounted,
hydraulically-activated boom shaker designed for West Coast
nut crops. Operation was at 12 - 17 Hz with a 3.8 cm (1.5
in.) stroke for 3-5 s. A bear—hug style clamp with rubber
padding was used. Tart cherry tree bark damage ranged from
no damage to very serious damage depending on clamp slip,
clamp pressure, or deviation from a 900 clamp angle. Sweet
cherry harvest with this same machine caused severe bark
damage due to the violent, long shaking periods required to
remove immature fruit for brining (the maraschino process).

Boom shakers, where the boom was fixed to the carrier,
required the mass of the carrier to be greater than the mass
of the tree, otherwise the carrier would shake more than the
tree due to the reactions. The development of the floating
inertial limb shaker (Adrian and Fridley, 1965) relaxed this
requirement, however, since the suspension of the shaker
from its center of gravity allowed free body motion relative
to the tractor and thus absorbed some of the reactions.

Fridley and Adrian (1960) experimented with a double
eccentric mass boom shaker where masses weighing 2.3 kg (5
lb) were mounted on a common shaft, had 6.4 cm (2.5 in.)
eccentricity, and rotated at 7-18 Hz (400-1100 c/min).

Herbst (1964) patented a boom shaker activated by two

 

25

eccentric masses on the same shaft capable of running in
apposition or opposition. Read's (1965) boom shaker patent
was similar to Fridley and Adrian's model of 1960 actuated
by two eccentric masses on separate shafts rotating
synchronously in opposition to produce linear motion.
Whitfield (1971) designed a pivoted boom shaker activated by
a single rotating eccentric mass.

Fridley (1968) used a crankshaft arrangement to
oscillate a mass thus providing a "linear inertially—
excited" shake. Brandt (1965) developed a general two
eccentric mass vibration generator capable of real-time
phase/velocity indexing between the two masses thus
producing a multidirectional shake. Brandt's was the first
multidirectional vibration generator for inertial shakers.
Two rotating eccentric masses were mounted atop one another
on a common shaft and driven by a common hydraulic motor and
V-belt. Twisting of the V—belt provided reverse rotation
for one mass and different eccentric mass pulley diameters
permitted slight speed differences. Shipley (1970) patented
a plural eccentric mass harvester, each driven by its own
hydraulic motor on a C-clamp frame to provide a
multidirectional shake.

In 1967, Shipley patented a complete multidirectional
trunk shaker design which used two masses in line with the
tree, one on either side of the tree, operated hydraulically
by individual motors on a free hanging suspended body.

Direction of rotation was by hydraulic design, velocity was

26

by hydraulic flow control and eccentricity was adjustable by
manual adjustment of the masses on their eccentric arms.
Fridley and Adrian (1966) produced a multidirectional shake
by placing two masses on opposite sides of a tree, rotating
the masses in the same direction and at the same speed for a
circular translation of the trunk, or rotating the masses in
opposite directions at equal or different speeds to produce
various translational patterns.

Gould and Richter (1969) developed a two mass
hydraulically driven multidirectional trunk shaker with two
masses in line with the tree but adjacent on the same side
of the tree. The masses rotated in opposition and were
chain linked for pattern fixation. This design is claimed
to achieve minimal bark damage with increased shake yield
due to the extra "twisting" of the tree. Savage (1981)
developed a C-clamp shaker that uses two chained eccentric
masses rotating in the same vertical plane but on spaced
axes and synchronized such that a linear horizontal forcing
vector is generated to vibrate the tree.

Gentry (1980) developed a citrus shaker for lemons in
1978 utilizing two rotating masses totaling 114 kg (250 lb)
in a housing weighing 565 kg (1245 lb). The shaker was
attached to trunks up to 40 cm (16 in.) in diameter at
heights of 36 cm to l m (14 - 40 in.) above the ground. The
frequency of shaking was less than 5 Hz (300 c/min).
Debarking of the lemon trunks forced Gentry to switch to

grapefruit; trees which had smoother trunks and tougher

 

 

27

bark.

Trunk shakers usually deliver an output of relatively
high frequency (12 - 40 Hz), short stroke (5 - 20 mm, 0.2—
0.8 in.) and varying pattern (O'Brien et al., 1983). These
parameters can be varied by modifying the relative masses,
the eccentricities, the relative direction of rotation and
the relative speeds of rotation. Overstreet (1969)
developed a three-mass triangular (isoceles) arrangement of
eccentric masses around the tree, which were chain-linked to
provide a circular motion of the trunk shaker and tree.
This design was used in conjunction with a tri—clamp to
effectively transmit forces with minimal bark damage. Fruit
removal is a function of stroke and frequency and is also
influenced by pattern. Inertial shaker stroke can be
approximated by (Adrian and Fridley, 1965):

S = 2*m*r/(Mshaker + Mlimb)

Peak to peak stroke
Eccentric mass of shaker
Eccentricity of shaker
Mshaker = Total mass of shaker

Mlimb = Total mass of limb = 0.2 kg/mm diameter for limbs
= 2.0 kg/mm diameter for trunks

mam
"Inn

The development of the trunk shakers throughout the
1960's saw larger power units transmitting larger forces.
Unrecognized at the time, the general design of some shakers
inherently induced tree damage. Torques generated by
counter-rotating masses induced twisting effects at the pad
which must be absorbed as friction at the tree bark.

Redesigned clamps and pads were necessary to fit the

trunk diameters and allow the bark to survive the increased

 

28

stresses (radial, tangential, longitudinal) imposed on the
trunk. Clamp design (Burke, 1951; Gould, 1962; Gould, 1964;
Gerrans, 1968; Gerrans, 1971), pad design (Gerrans, 1966),
pad lubrication (McEwen, 1965), increased pad contact area
and reduced clamping forces (Edgemond, 1967) have all been
means by which researchers have attempted to reduce shear
and torque transmitted to the tree.

The first tri-clamp pad design was patented in 1969 by
L. B. Overstreet. Three pads comprised the clamp, grasping
the tree approximately 120° apart, via one fixed arm and two
hinged arms; the tri-clamp made for better grip and less
slip within the clamp system. A tri-clamp design by Friday
(1981) incorporates a single hydraulically-driven rotating
mass in each of two arms. These arms pivot about the trunk
so two pads make contact at approximately 1200 and 240° from
the approach angle, and combine with a third stationary pad
at 0°. The forcing vectors developed by the masses are thus
nearly in-line with the tree, although torque may still be a
problem.

To study relative levels of bark damage, two shakers
were utilized by Hedden et a1. (1984) to harvest Valencia
and Hamlin oranges. One shaker provided linear motion, the
other multidirectional motion. Minimal bark damage was
observed in all tests, even for growing Valencia orange
trees when clamping 16.2 cm (6.4 in.) average diameter
trunks at 640 kPa (93 psi) average contact pressure for the

linear shaker and 1215 kPa (176 psi) for the

 

multidirectional shaker.

No obvious trunk damage was apparent when Millier et
a1. (1983) tried a recoil impact shaker for apple harvest.
The linear impact shaker performed better on Y—shaped trees
than did a multidirectional shaker on limbs parallel to the
applied force. Violent action was needed to remove fruit on
limbs perpendicular to the applied force.

With the advent of mechanical harvesting, tree crops
frequently needed pruning or retraining to make the
operations efficient. Tree modification could increase the
speed of harvesting, promote uniform maturity, improve
recovery, decrease product and plant damage and improve
overall economics (Brown, 1980). Often new harvester
designs were based on a particular tree—orchard pruning
configuration, particularly when continuous harvester
designs were being investigated.

Conventional low density orchards (75 — 200 trees/ha)
are presently harvested at acceptable rates with stop-and—go
shaker harvester systems (Tennes and Brown, 1981). Trunk
shakers with self propelled catching frames harvest 60 — 120
cherry trees per h. High density orchards (200 — 400
trees/ha), however, may have lower yield per tree and
therefore necessitate higher speeds for equivalent
volumetric harvest rates. As a result, various continuous
harvesters for tree crops have been designed.

Tennes and Burton (1977) developed a sway—bar shaker

for continuous harvest of tree crops consisting of a pair of

 

30

equi-spaced horizontal bars pivoted at the front end and
powered by two synchronized rotating eccentric masses at the
back end. A roller assembly mounted along each bar formed a
free wheeling contact surface for tree trunks. Tennes and
Brown (1980) expanded upon this design such that the
oscillating sway-bars were combined with a pendulum system
for absorbing vibrations otherwise transmitted to the power
frame. Bark damage was still a problem, however, as the
harvester moved 3 - 6 cm (1 - 2 in.) during each cycle of
the sway bar, causing probable shearing impact on the bark
as discussed by Fridley et a1. (1970).

Peterson and Monroe (1973,1974) developed an automatic
sequencing continuous over-the-row trunk shaker harvester.
Harvest rates were increased 100% on a time basis, reaching
200 trees/h. In 1985, Peterson et al. combined a recoil
impact shaker with an over-the-row sequencing harvester
frame to provide continuous detachment of apple fruits
without some of the apple damage and bark damage problems
associated with compact high-power inertial trunk shakers.

Continuous over-the-row tree harvesters with two
eccentric masses on separate shafts using a scissors type
grasping unit have also been developed by Peters (1980).
Orlando and Fitzmaurice (1981) built an over-the-row
harvester with a vertical scissors—type clamp suspended from
the top of the frame and shaken by a non-positive
oscillatory eccentric pair of masses at the upper end of the

frame. The entire assembly was pivoted by a single axis to

31

alternately impact opposite sides of the trunk.

Gebendinger (1973) created a three mass shaking unit
with all three masses concentric on the same shaft to
prevent twisting of the shaker axis. This effectively was a
two-mass shaker however, as the top and bottom masses
rotated synchronously and were each half the weight of the
middle mass. Westergaard et a1. (1983) discuss a true
three—mass concentric shaft design where the three eccentric
masses would be driven by various combinations of motors and
sheaves to impart a plurality of distinct shaking patterns
to, a tree trunk or limb. Tempkins (1973) developed a
scissors type shaker head pivotally coupled to the distal
end of a transportable boom and having two counter-rotating
masses on a common axis, driven at different angular
velocities by a twisted V-belt; this could develop a 360°
progression of the shaking force vector.

Variable amplitude shakers have been developed to change
the shaking characteristics of the tree, sometimes even
while running. These often consist of adjustable eccentrics
with pitman arms (Harrett, 1963). Fridley (1970) developed
a mechanism to create any desired shaking pattern by having
a variable offset mass on a common shaft with a fixed offset
mass, chain-linked for a fixed phase relationship. Gould
and Richter (1971) used hollow cylindrical shells to vary
eccentricity by varying the amount of flowable heavy matter
(such as BB's, lead shot, etc.) in the cylinder. Because

the amount of unbalance depended on movement of the material

32

in the shell, the moment of inertia was a function of the
shell's rotational velocity during operation. Hood et a1.
(1979) created a unique scissors-type trunk shaker by using
eccentric masses mounted on sun gears which "walked" around
the inside of planet gears. As the eccentricity of the mass
was capable of being offset by the offset of the "walking"
sungear shaft, various shake patterns were realizable.

Brown and Perkins (1967) used a light weight, hand—
carried hydraulically powered eccentric mass C-clamp
vibrator for successful and complete fruit removal from date
palm bunches with a 3 s shake.

Tree fruit harvester mechanization improvements over
the past 25 years have reduced 65 man-h of hand picking per
hectare down to 4 and 8 man—h per hectare for mechanized
harvest of tart and sweet cherries, respectively.
Improvements in tree shaking and other fruit removal methods
will undoubtedly continue as technology advances in sensors,

controls and actuators.

2.2 Root Damage

 

Bukovac (1983) suggested that shaking with "unnecessary
force" may result in "breaking of roots, interfering with
conduction systems and doing other harm which is not so
apparent". The use of plant growth regulators which would
loosen fruit and increase removal rate may prevent an
operator from shaking extra hard and long, thereby stressing

the tree and causing premature orchard death.

33

Early experiments by Levin et al. (1960), however,
found no adverse affects on cherry root systems when limb
shaking to harvest fruit. Halderson (1966) also found that
root movement during trunk shaker harvesting ceased
approximately 15.2 cm (6 in.) below the soil surface and did
not appear to cause root or tree decline.

Beljakov et a1. (1979) found no adverse effect on tree
growth either with only an insignificant number of roots
severed (less that 0.05% of the roots by weight of diameter
0.1 cm (0.04 in.) or smaller) when sweet and sour cherries,
peaches and plums were trunk shaken. An eccentric mass
trunk shaker clamped 20 cm (7.9 in.) above the ground
operating at 15 — 18 Hz with 2.4 — 3.0 cm (1.0 — 1.2 in.)
strokes was used.

Lyons and Yoder (1981) found that 7.6 - 12.7 cm (3 — 5
in.) diameter peach trunks which were poorly anchored had
deeper crown roots and were susceptible to breakage by wind
and shaking.

More recently, however, Brown et a1. (1984), in
attempts to find a nondestructive, convenient method of
detecting hidden bark damage, suggest that increased
ethylene production found in samples taken beneath trunk
shaken cherry trees may result from injury to the root
system, though this has not yet been verified. The question
of root damage from mechanical harvesting and its effect on

tree decline is still under inquiry.

 

 

34

2.3 Tree Injury : Prelude

 

Tree damage generally occurs in three different forms:
1) damage to the bark at the point of shaker attachment, 2)
breakage of large stiff limbs, and 3) breakage of small
branches or detachment of leaves and other new, young growth
(Cargill et al., 1982). The authors list 19 possible
factors that can result in bark damage, much of which can be
serious.

Breakage of large limbs generally results from
excessive stroke length, shaking at a natural frequency or
shaking for a long period of time. Weak, grafted or low-
crotched trees are most susceptible. Breakage of small
limbs results from high frequency vibration. Long periods
of shake are likely to magnify the damage.

Bark damage normally occurs as a total stripping of the
bark from limbs or trunk or as a separation of the bark from
the cambium (Brown et al., 1982). The latter can seldom be
detected except by trained personnel. Tapping of the bark
for presence of a hollow sound is one method used to detect
internal damage; other more sophisticated methods of
detecting hidden bark damage have also been investigated
(Brown et al., 1984). Neglected bark damage combined with
adverse winter weather, insect and disease attack, poor
nutrient supply from the soil, improper use of growth
regulators or poor irrigation practices can cause rapid
orchard decline. Diener et al. (1968) found that the amount

of bark damage accumulated by a limb or trunk is determined

35

by the bark properties, the radius of the limb or trunk, and
the resistive forces of the shaken object.

Preventing bark damage is of prime importance with
today's harvester which clamps to a tree trunk. Ironically,
Sturos and Erickson (1977) of the USDA Forest Service use a
compression debarking device consisting of two stiff rollers
which squeeze wood samples in order to intentionally
separate the bark. The adverse effect of poor tree clamping
mechanisms on bark damage has reinforced concern over what

is happening in Michigan orchards.

2.4 Tree Vibration

 

Fruit detachment is the prime objective in shake—
harvesting. Much work has been done to study fruit
detachment. When shaking is used for fruit detachment,
efficiency depends on the pull force required to remove the
fruit (the lower the better), the fruit mass (the higher the
better), the location of the fruit on the tree structure,
and the stem length (the shorter the better). For example,
pull force for Windsor sweet cherries never gets as low as
that for Schmidt's sweet cherries while Windsor cherries
seldom get as large as Schmidt's; thus Windsors are more
difficult to shake harvest.

Since mechanical shakers are attached to the tree trunk
or limb, factors like the limb's natural frequency,
efficiency in transmitting vibration, damping effect of the
leaves, damping effect of the fruit, mass of the limb and

direction of vibration are important. With inertia shakers,

 

36

the mass of the shaker and its parts must also be
considered. Adrian and Fridley (1958) concluded that the
four variables affecting fruit removal were: 1) the
frequency of shake, 2) the length of the stroke, 3) the
force/weight ratio required to remove the fruit, and 4) the
number of limber fruit bearing hangers in the tree.

Cooke and Rand (1969) describe the three important
modes of vibration for a fruit (Figure 2.2). Instability
and fruit-stem resonance have been important in creating
high stress for fruit detachment. However, limb
characteristics are very important in successful vibration
transmissibility (Fridley and Yung, 1975).

Coffee, cherries and macadamia nuts are easily removed
because the stiff tree structure allows excitation of
resonant frequencies at the fruit—stem interface. Olives,
however, are more difficult to remove because the flexible
stem and branch act as vibration absorbers, isolating the
fruit from the excitation.

At low frequencies, fruit tends to detach by failure of
the stem or branch near the fruit, leaving a variable length
stem or branch attached to the removed fruit. The stem may
also be pulled or broken from the fruit causing a stem—tear
or similar damage at the area of stem attachment. At high
frequencies, the inertia of the fruit causes it to remain
stationary and stem failure normally occurs at an abscission
layer between the stem and fruit or the stem and branch. In

the cherry industry, excitation of the pendulum mode (low

37

23.1.... 8 do

200: 9.3.2:...

 

 

Rome .Ucdm .090 mxooov
contozfimo mo mono: motor. of. m

.m 9.39...

moo: 053:. moo: 233.03.;

 

 

38

frequency) provides sweet cherries with stems for
maraschinos and fresh market, excitation of the tilting mode
(higher frequencies) provides stemless cherries for
processing.

High frequencies (25 — 40 Hz) and short strokes (20 -
25 mm, 0.8-1.0 in.) have been proven most effective at fruit
removal when the tree structure and fruit attachment are
relatively rigid (O'Brien et al., 1983). Low frequencies
(1.5 - 6.0 Hz) and long strokes (100 — 125 mm, 4.0-5.0 in.)
have been found superior for long branched and willowy trees
that hang down under the load of the fruit (Table 2.1).

Kronenberg (1964) found the detachment force of fruit to
decrease as the fruit ripened. The difference between the
force 10 days before harvest and that on the traditional
picking day varied according to the equation:

Y = -48°X + 428

9 — Number of days before harvest
Detachment force, 9

Where: X
Y

Ripe cherries detached without stems whereas unripe cherries
detached with stem.

Discovery of satisfactory frequency and stroke for
fruit removal has provided researchers with the following
empirical means by which to estimate fruit removal for
cherries, prunes, olives and macadamia nuts (Markwardt et
al., 1964; Halderson, 1966; Fridley and Adrian, 1960, 1966;
.Fridley et al., 1971; Peterson et al., 1972):

Percent Removal = 100°(l - exp(-ksawb))

39

 

 

 

 

 

Table 2.1 Tree characterization and tree shaker inputs for
several tree fruits (O'Brien et. al., 1983).
Typical Input to Tree
Tree Shaker Frequency Stroke
Crop Character Utilized (Hz) (mm)
Apricots l Trunk 15-30 12-8
Limb 10—20 40—25
Almonds 1 Limb 15-20 40-25
Trunkz 15-25 12—8
Apples 2 Limb 10—20 40—35
Trunk 15—25 12—8
Prunes 2 Trunk 15-25 14—10
Limb 10-20 40—25
Walnuts 3 Limb 7—16 50—30
Trunk2 15—20 14—10
Pecans 3 Limb 10—16 50—35
Trunk2 15—20 14-10
Peaches 3 Trunk 15—25 16—12
Red Tart
Cherries 3 Limb 10—15 40—30
Trunk 10-24 40-20
Sweet
Cherries 4 Limb 10—20 60-35
Trunk2 12—24 16-12
Olives 5 Limb 20-35 75-50
Oranges 5 Limb 1.6-6 125—100
Trunk 10—15 16—12

 

 

l A rating of 1 indicates a stiff tree structure and fruit

stem;
stem.

5 indicates willowy structure and long flexible

2 In large trees, multidirectional trunk-type shakers are
mounted on booms and used to shake major scaffold

branches.
Source:

Bruhn, 1969.

 

Where: Constants a, b,

S
(I)

Unfort

frequency does not necessarily increase fruit removal

and k have been tabulated

Stroke delivered to the limb, mm

Shaking frequency, Hz

unately, however,

increasing either

stroke or

since

40

increasing the frequency may decrease the stroke or the
effective vibration transmission through the limbs to the
fruit stem (Fridley and Adrian, 1966; Fridley et al., 1971).
In fact, Diener et a1. (1969) found limb transmission
efficiencies (ratio of end of limb stroke to shaker stroke)
ranging from 25-130%.

Direction of shake influences removal of fruits and has
had a significant role in shaker design. McLaughlin et al.
(1976) found that vertical shaking on apple limbs removed
16% more fruit than horizontal shaking for a 1 s period.
Lenker and Hedden (1968) used a variable stroke, variable
frequency FMC hydraulic cylinder (square wave) inertia
shaker and a crank—type inertia shaker to harvest Pineapple
and Valencia oranges. They found that more fruit in
Pineapple oranges were removed with smooth limb shaking
action than with the square wave.

Shaking patterns can be present on some machines; on
others there is an undefined continuous change of motion
either by design or from the operator's controls. Shaking
frequency and shaking force are related by the square of the
frequency. Increasing the frequency on any shaking pattern
requires more power. This frequency increase requires both
higher hydraulic system flow rate and pressure, resulting in
excessive clamping pressure between the pad and bark on
inachines where the shaking and clamping circuits are
interconnected. Force transmission of most shaking patterns

can also cause excessive radial stress, tangential stress or

41

longitudinal stress on the bark due to reactive forces at
the clamp.

Direction of shake has more influence on fruit damage
than on fruit removal. Pellerin et al. (1979) state that
minimum damage occurs when fruit is removed by several short
bursts rather than longer, more intense shaking. Fruit tend
to move very little before detaching and falling straight
down when shaking by impact shakers (Upadhyaya et al.,
1981a).

Fruit detachment is complicated by the existence of
combined tension, bending and shear stresses at the stem
(Alper and Foux, 1976). As the angle at which tension is
applied increases, bending and shear stresses on the stem
increase while tension stress decreases. Desired shaking
characteristics (frequency, stroke, direction) to get the
proper stress combination for removal of a particular fruit
are difficult to optimize due to the vibration
transmissibility. Fruit remaining attached to trees after
shaking are commonly hanging on limber fruiting branches
near the tree surface.

Fridley and Adrian (1960) conducted studies to
determine the power and optimal frequency of vibration of
prune trees such that fruit removal was high but fruit and
tree damage was avoided. Vibrations at the natural
frequency of the fruit, which would be the most efficient in
terms of power, were difficult to transmit through the

branched tree structure because of the damping by leaves and

42

the collision of limbs. Vibrations at the natural frequency
of a limb caused both limb and fruit damage. Attempts to
vibrate prune tree limbs at the natural frequency indicated
that selection of the proper natural frequency was dependent
on the stroke required to remove the fruit at that
frequency, the power required and the resulting tree and
fruit damage (Fridley and Adrian, 1960). As expected,
minimum force and power were needed to vibrate a tree when
clamping was at an anti—node and shaking speed was at a
natural frequency. Less power was needed with longer
strokes and lower frequencies. Tree and fruit damage tended
to increase as stroke or frequency increased, although the
stroke effect was more predominant.

Alper et a1. (1976) studied the effect of frequency and
the point-of—force application on resultant amplitudes at
the points of fruit suspension and at the zone of force
application on orange trees. Vibration amplitudes in a
shaken branch at points of fruit suspension were found to
increase as the force application point was moved further
from the main branching point. Vibration amplitudes at
points of fruit suspension remained the same with and
without attached fruit. With multidirectional trunk
shakers, Berlage and Willmorth (1974) found that the nodes
and antinodes of a vibrating limb move along the limb as
frequencies change, thus preventing dead spots with zero

displacement.

Halderson (1966) found the first resonant frequency of

43

a vibrating tart cherry tree to be very low (e.g. 50 c/min).
Bruhn (1969) found that, except at very low values, changing
applied frequency and amplitude had little effect on cherry
fruit removal unless the combination resulted in a change in
acceleration. Accelerations in the outer fruiting zone of
the tree exceeded those applied to a trunk or limb base in
all cases. These conclusions were confirmed by Tennes and
Brown (1981) in over—the-row apple harvesting tests with a
sway bar shaker.

The response of each individual tree to vibration and
damage is different, and can vary from orchard to orchard as
well. The force and power required to shake trees varies
with stroke and frequency of shake, type of shaker, position
of tree attachment, limb or trunk size and tree species
(Fridley and Adrian, 1966). As expected, force was found to
be proportional to the stroke and to the square of the
frequency. Power was proportional to the square of the
stroke and the cube of the frequency. Power for increasing
trunk displacement was proportional to the square of the
ratio of the increased displacement to the original
displacement (Cargill et al., 1982). Limb shakers operating
with hydraulic motors typically average 8 kW (11 Hp) while
trunk shakers require 30 to 40 kW (40 - 54 Hp) (O'Brien et
al., 1983).

Hoag et al. (1971) studied the damping properties of
almond tree limbs. They found a log decrement of 0.0667 to

0.1015 when limb moisture content was near the saturation

 

44

point of fiber (30%). External damping due to limbs moving
through the air was nonlinear and proportional to the
velocity squared. Air drag on vibrating olive tree limbs
could be described by a constant drag coefficient of 1.5;
the leaf area turned out to be important. With leaves
removed, external damping was negligible unless limb
velocities were very high.
2.5 Shaker Clamps

The most likely
shaker attachment.

radial forces from

transmitted through
damper and spring.
vibrational energy
imposed on the bark

pad does not slip.

clamping pressure too low, observable scarring of the

or excessive shear

slipping action
action (radial).
pressure
pressure also
force increment),
belt-system
large peak contact

shaking.

(tangential or

On the other
can crush or split the bark.
stiffens pads (smaller
reduces internal pad flex,

slip but a very stiff pad system

 

point of tree injury is at the point of

Here, longitudinal, tangential and

epicyclic pattern trunk shakers are

a pad which must act as a cushion,

The pad must be firm enough to conduct

so that excessive stresses are not

yet conform to the trunk such that the

If pad contact area is too small or

bark

stress may result, observable as a

longitudinal) or beating

hand, excessive clamping

Excessive clamping

pad deflection per

and reduces

can generate

pressures and large torques during

45

Brown et a1. (1982) found peak pressures between the C-
clamp pad and the bark of 2345 kPa (340 psi), 3450 kPa (500
psi) and 4140 kPa (600 psi) on an 11 cm (4.5 in.) diameter
trunk when clamping at manufacturer's recommended pressures.
Results indicated that all current commercially utilized
pads developed pressures that exceeded the suggested limit
when clamped at the manufacturers recommended circuit
pressure. Reducing circuit pressure to limit peak pad
contact pressure was not possible on some pad designs
because tree contact area became insufficient. Contact area
on limbs of 50-165 mm (2.0-6.5 in.) diameter ranged from
5000-25000 mm2 (8-39 in.2) per pad for pads that were
acceptable relative to peak pressure and shake transmission.
Frahm et al. (1983) suggested 2070 kPa (300 psi) as an
ultimate bark pressure under a pad since the average
ultimate compressive strength of tree bark was found to be
2415 kPa (350 psi) on sour cherry trees and 1035 kPa (150
psi) on sweet cherry trees. Zero compressive failure is
preferred under shaker pads but a practical limit of 15% of
the pad area is stated as reasonable without necessitating
pad redesign (Brown et al., 1986).

Bark injury is usually caused by excessive tangential
or radial stresses at the cambium under the clamp (Fridley
and Adrian, 1966). The stresses at which the cambium is
damaged increase with age, decrease with cell turgidity and
increase from spring to fall (Fridley et al., 1970).

Cambial failure from compressive stress (radial) was

 

46

initiated at lower pressure on sweet cherries (1000 kPa, 145
psi) than on tart cherries (2310 kPa, 335 psi). Shear
strength ranged from 350-700 kPa (50-100 psi) and should be
assumed to be the lower value of 300 (43 psi) to eliminate
shear damage. Bark strain at failure ranged between 4.5°
and 11.60 and should be limited to 5° for design purposes
(Brown et al., 1982). Bark damage is also more likely to
occur during morning operation since the trees experience
diurnal moisture fluctuations, having greater moisture in
the cambium during the morning (Burton et al., 1986).

Early padding in shaker experiments consisted of cloth,
belting or rubber wrapped around a tree attachment point
when clamping circuit pressure was 8280 kPa (1200 psi)
(Levin et al., 1960). Pads have been formed as hollow
tubes, bags filled with sand or ground nutshells (Martin,
1968; Brandt, 1967), solid rubber pads with small holes
drilled parallel to the tree trunk axis (Kilby, 1972),
preformed clamp jaws and rubber pads, belting mounted on
spring and universal joint assemblies (Brandt, 1964) and
other conforming materials (Brandt, 1985). Adrian and
Fridley (1963) suggested pads in the form of sacks filled
with magnetic particles and oil or viscous fluid. Flat
belts on parallel rollers and bolts placed in trees were
also investigated. Pool and Steingas (1969) employed
"bouncing putty", a non-Newtonian silicone fluid, on their
shaker head to conform to tree shape and prevent bark damage

(luring force transmission. Pool (1971) filled airtight

47

pouches with a combination of silicone putty, tire carcass
discs and air to clamp to the tree. Savage (1971) took
another approach and used a hydraulically manipulated chain
to clamp firmly around the tree to prevent slip during
shake. Most manufacturers now place a flap over the clamp
pad with lubrication between to provide a slip surface,
thereby limiting shear stresses during cherry harvesting.

Affeldt et al. (1984) observed a shaker pad relaxation
effect, a change in contact pressure distribution of the pad
around the tree after a settling time. Settling time may
complicate the ability to maintain adequate contact force
for vibration transmission.

The Friday Tractor Company (1982) utilized a commercial
"tri-clamp" composed of three pads 120° apart which
completely surrounded the tree. An eccentric mass on each
side of the shaker was centered in-line with the tree. This
design is claimed to prevent slip between the bark and pads
and to direct all forces to the center of the trunk to
minimize torque on the bark.

Research by Burton et al. (1986) indicated, however,
that after four years of mechanical harvesting, 58% of the
trunks in a 9 year-old tart cherry orchard had moderate-to-
severe trunk damage regardless of whether the Friday tri-
clamp system or experimental reduced pressure pad systems
were used to clamp to the trees. A low-pressure scissors-
clamp kit was developed in 1985 for further testing for

trunk damage control. In 1986, this kit resulted in almost

48

zero damage on 6.5 cm (2.6 in.) diameter trunks, whereas the
tri-clamp severely damaged 20% to 90% of the trunks. The
low—pressure kit appears to eliminate the damage experienced
with previous clamp systems (Brown, 1986).

Timm (1986) compared three beltings and five lubricants
to study the static and dynamic friction properties and
their relation to bark damage. Static and dynamic friction
forces were greater for neoprene-lubricant combinations than
for either polyurethane or nitrile—lubrication combinations.
Polyurethane belting had a lower nominal intermittent
operating temperature compared with nitrile, and delaminated
under high clamping pressure and long shaking periods.
Silicone spray was a better lubricant than Modoc oil, light
bearing grease, food grade grease or Crisco shortening due
to its tenacity, easy application, easy cleanup, low
friction, and minimal heat and dirt buildup. Furthermore,
the nitrile belting combined with the silicone spray
lubricant was found by researchers and growers to produce
minimal visible bark damage.

The optimal clamp pad system should have adequate
contact area to limit peak radial pressures, exert only
radial forces upon the tree (to eliminate tangential and
longitudinal bark stresses) and efficiently transmit shaking
motion from the shaker to the tree. A properly designed pad
can minimize bark damage due to peak pressures. Even the
best pad, however, will not eliminate tree damage caused by

improper operation, thus highlighting the need for both good

49

design and good operator training.

Some designs have come about as alternatives to
clamping the tree with pads. Adrian et a1. (1965) attempted
to reduce shaker clamp injury to fruit and nut trees by
using permanent style installed fasteners in trees for
shaker attachment; the idea was to transmit shake force
directly to the structural wood. Fasteners included lag
screws, eye hooks and nut and bolt arrangements. Shaking
force transmission was adequate to remove fruit but problems
with initial installation, screws pulling out, screws
bending, tree gumming, structural failure and decay offset
any advantages. Coblentz (1973) developed several types of
permanent tree frames and fasteners to which the shaker
could be attached each season for fruit removal by shaking.
These included frames bolted to a group of limbs, eyehooks
bolted to individual tree limbs, spring loaded C-clamps and

multiconnector C-clamp hardware.

2.6 Modeling

Experimental study has provided a basic understanding
of the forced vibration of fruit trees but details required
by engineers to design shakers or by growers to make optimum
use of shakers are difficult to obtain experimentally.
Therefore, many researchers have attempted to model the
shaker *and a typical tree utilizing various mathematical
analysis methods. Alper et al. (1976) found good
correlation when modeling dynamic forces and displacements

of a shaken fruit suspension twig. Optimal removal of fruit

 

50

occurred at 10 Hz (600 c/min) with a 30 mm (1.2 in.) stroke
using minimum power.

Phillips et a1. (1970) used finite element analysis to
study a branched system consisting of a straight primary
limb with straight lateral branches all having viscous,
proportional damping. Hoag et al. (1970) also used finite
element analysis for a branched system where the elements
could be arranged to create curved branches. A Rayleigh-
Ritz procedure was used to find the undamped mode shapes and
natural frequencies. Hutchinson et a1. (1970) found that
nonlinear damping gave better predictions than linear or
viscous damping. Most of these methods used lumped mass
systems.

Cooke and Rand (1969) developed a linearized three
degree-of—freedom model of a fruit-stem system excited by
sinusoidal periodic horizontal and vertical planar
displacements. Dynamic instability and modal shapes were
inferred from the coupled nonhomogeneous Hill's equations
allowing prediction of frequency conditions for fruit
separation or detachment with, or without, the stem
attached. Results indicated that the greatest dynamic
instability of the fruit occurred at a drive frequency twice
the natural frequency when the upper stem underwent small,
planar elliptical displacements.

Ghate and Rohrbach (1980) used a transfer matrix
technique with lumped parameters to account for the

generalized structural geometry and interdependence of

51

bending, longitudinal and torsional vibrations when solving
for vibrational characteristics of a continuous structure
having a rigidly fixed base, a fork with two branches, and
an arbitrary geometric configuration. The model accurately
predicted response of an aluminum forked structure and was
subsequently applied to blueberry cane vibrations.

Yung and Fridley (1975) used finite element analysis
and a consistent mass matrix (mass not lumped) to model
coffee and olive trees bearing fruit. Their model used
truncated conical segments which formed a trunk and two
branches supporting fruits. Natural frequencies, mode
Shapes, dynamic internal stress, and vibration response of
the complete tree structure correlated well with the steady-
State forced vibration of a similar steel model.

Moini et a1. (1980) also used a consistent mass finite
element model to simulate cone harvesting in the forest
industry, modeling the limbs and branches as truncated
conical beams and the fruit as short circular beams with
concentrated masses at the end. Leaves and twigs were
treated as distributed loads along corresponding elements.

Analytical studies of tree vibration have supported the
concept of shaking at several frequencies to develop a
multitude of vibrations throughout the tree, as the
Structural variation from tree-to-tree has not permitted the
designation of any one optimum frequency or range of

frecInencies for shaking (Liang et al., 1971; Hussain et al.,

19'75). Analysis shows the waveshape is important: high

52

,ffzrequency components account for more fruit detachment and
potentially more damage to the bark.

Transient analysis using finite elements has been
conducted for impact shakers with good correlation between
experimental and analytical results (Upadhyaya et al.,
1981a; Upadhyaya and Cooke, 1981b).

Upadhyaya and Cooke (1981) used a finite element model
t:c> study the transient response of a limb impacted on its
Ilricieerside at 90° to its vertical inclination. They found
‘tlléit: impacting the limb transversely was superior to
impacting the limb in any other direction. The optimal
direction for branch inclination in Y-shaped open center
trees was 450-60o from horizontal for a transverse impact
frTDnn below. The percent of harvested apples having a stem
EN11.1_ (rather than an intact stem or stem and spur) was
dependent on stem—spur angle of attachment, spur-limb angle
()f' attachment, impact direction, and stem physical
properties.

Upadhyaya et al. (1981c) were able to show that a
Sillfljple one—degree-of—freedom model adequately represented
the impact response of a tree and concluded that physical
properties relevant to design of impact harvest equipment

((iYUiamic mass, damping coefficient, spring stiffness and
Yoking's modulus) could be obtained from a pendulum test.
Themechanical energy loss may be as high as 40-50% and must

be accounted for when attempting to impact harvest tree

fruits.

53

2.7 Tree Injury : Bark

 

Cherry bark consists of a thin, nonliving outer
periderm, a large, spongy, nonfunctioning phloem in the
center and a thin, functioning phloem next to the cambium.
Phloem cells have their long axis in a longitudinal
( ‘reertical on the trunk) direction, whereas periderm cells
Pléi‘fe their long axis in the tangential (horizontal on the
tLIrtlnk) direction. This gives cherry bark its characteristic
ggz°eearter strength in the longitudinal direction. The
periderm consists of dead cells encrusted with waxes; the
waxes lubricate the tissue allowing slippage between cells
(Esau, 1965). The periderm on cherry trees is elastic and
can hide compression damage to the phloem, xylem and cambium
for several weeks.

When cells are crushed, cell liquids are freed and
Small cracks usually occur in phloem (bark) tissue. Damaged
bark often separates from the wood (xylem) interrupting the
flow of vital nutrients. Hairline cracks in the bark tissue
fCDITn, then air enters and oxidizes cambial tissues turning
‘t11enn brown quite rapidly (Adrian and Fridley, 1963; Adrian
est al., 1965). Insects and disease, can then enter and
infect the damaged tissue, slowly spreading to healthy
tiSsue and causing tree death. Devay et al. (1960) describe
the canker attack as a depression in the infected tissues,
acCOmpanied by the production on an orange frothy gum.

P . . . .
womonas syringae, a serious bacterial canker d1sease of

 

Stone fruits in Michigan, is almost identical to C.

— E

f imbriata, except that it is active only when the tree is

’1

dormant and early in the spring months; at other times it is

 

inactive (Devay et al., 1960). _E:._ syringae is normally more
infectious to young trees (4 to 8 years old), and is rarely
found in the older orchards.

Live canker fungi spread rapidly as soil moisture and
insect activity increase. The first few weeks after
irrigation in an orchard is the time when fungus development
is most pronounced. Continued trunk shaker damage to the
tree base can spread spores and mycelial fragments of
diseased tissue to healthy trees, causing tree death within
a few years.

The strength of fruit tree bark has been studied by
researchers trying to develop design parameters for
m€3C111anical harvest systems (Table 2.2). Fridley et a1.
(1970) found the bark strength of prune, peach, apricot,
allIlond and olive trees to be directly related to seasonal
faCltors such as moisture content and cambial activity. When
the moisture and cambial activity are high, the bark
StI‘ength is low and the bark "slips" easily. "Slip" is the
Separation of the bark from the wood at the cambial zone
(Cargill et al., 1982).

Diener et al. (1968) found the periderm strength of
Cherry bark to be highest in the tangential direction
perpendicular to the vertical axis of the tree. Phloem
StI'er‘lgth was greatest in the longitudinal direction,

parallel to the long axis of its cells and weakest in the

 

 

55

 

Comparison of radial stress causing browning at
cambium and tangential stress causing bark
failure for various species and varieties
(Cargill et. al., 1982).

Table 2 . 2

 

 

Radial Stress Tangential Stress

C rap and Variety

 

 

 

(kPa) (kPa)
Apricots, Tiltonl 1 5500-6200 1720-1830
Apricots, Blenheim 5500-6200 1480-1690
Peaches, Dixon 4830-5500 1380-1590
Almonds, Non Pariel 3800-4140
Almonds, Peerless 3800-4140
Prunes, French 4140-5170 1000-1210
Prunes, French 4830-6210 1310-1720
01 ives 3450-4140 960-1100
Cherries, Tartz 2410 550-690
Cherries, Sweet2 1030 410-480

*

Trees approximately 6 years old; other trees tested were

 

 

mature.
Source: Brown et. a1, 1982; trees approximately 4 years
old.

tangential direction. The periderm could elongate five—to-

Six times that of the phloem in the tangential elongation

before rupture. These facts indicate that tangential shear
St-I‘ess or strain from shaker torsion or clamp pressure can
cause the phloem underneath to rupture without periderm
r11pture, thus concealing the hidden damage.

failure on sweet

Brown et al. (1982) studied bark

Cherry and sour cherry. Sweet cherry bark was damaged about

twice as easily as tart cherry bark on equal diameter trees.

The bark of young cherry trees (up to 8 cm (3 in.) trunk
diameter) damaged more easily than the bark of older trees
and was more likely on 4-8 year-old trees than on 10—20

56

year-old trees. Contact pressure limits, subject to
Ixtcaisture content and cambial activity, were accepted as 1035
kPa (150 psi) and 2415 kPa (350 psi) for sweet and sour
cherry trees, respectively.

Adrian et al. (1965) found that tangential shear
failure in fruit and nut trees always resulted in complete
bark failure. Cambial browning was initiated by average
dynamic stresses which were only 75% of average static
stresses which caused browning. This indicates that
acceptable average static clamping pressures may be much too
high to prevent tree damage in a dynamic state.

Cherries are harvested earlier in the growing season
than most other fruit crops; cambial activity and moisture
Content are very high and the bark is very susceptible to
Slip. In addition, variations in use of trickle irrigation,
“Se of growth regulators, location, climate, soil, and

production methods may adversely affect bark strength.

2.8 Suggestions for Eradicating Bark Damage

 

The success of a shake harvesting system depends on
faCtors such as age and structure of the tree, cultural
practices, equipment, operator care and supervision.
Adjusting the shaker properly, proper pruning of the trees
to accommodate the shaker, employing attentive operators,
and avoiding canker infected areas on trees were all

Significant factors in maintaining orchard vitality.

Proper design of shaker pads (Adrian and Fridley,

 

57

1 963), proper clamping pressure and maintaining
perpendicularity at the point of shaker attachment have all
been valuable suggestions (Brown et al., 1982).

Prevention and control of Ceratocystis fimbriata canker

 

by avoiding bark injury, shaving away bruised bark tissue,
dressing wounds with an appropriate fungicide (Cerano, for
example), surgically removing and dressing internal wounds
and severing infected limbs or scaffolds have been promoted
by Devay et a1. (1965). Diseased tissue should be
immediately collected and burned.

One of the current odious tasks facing researchers is
the nondestructive detection of bark damage. At present,
detection of hidden bark damage is possible only through
deStructive tests that are subjective. Either sections of
bark are removed for visual inspection or the tree is cut
down and the trunk sectioned for inspection (Brown et al.,
1984; Santamour, 1986).

Nondestructive methods of detecting hidden damage have
been investigated by Brown et al. (1984); the methods
in(Zlude electrical resistance measurements, infrared
thermography, ultrasound spectrum analysis, scanning
electron microscopy (SEM), and energy dispersive X-ray
spectrophotometry (EDS). None of these methods were both
nondestructive and effective in the field. EDS analysis of
Cote samples revealed an accumulation of K and Ca and a
deCI‘ease in P in damaged tree tissue; the test was somewhat

destructive and time consuming.

 

58

2.9 Trunk Shape Analysis

 

Proper training of operators, better designs for clamp
pads, safe recommended pressures for clamping, stopping
irrigation prior to harvest and checking fruit for maturity
level prior to harvest are all means by which recognizable
bark damage has been reduced (Brown et al., 1982; Frahm et
a1 -, 1983). Bark damage that is not visible may still occur
during trunk shaker harvesting. Damage is currently
evaluated by assessing the delayed decline symptoms of the
tree: loss of yield, bark splitting, insect and disease
infestation, dead branching structures, and decay spots.

Many trees never show signs of decline when damage is
minor or occurs only once. A young tree can segregate a
WOuncled area from undamaged tissue (Santamour, 1986).
FiI‘St, a chemical barrier is set up to limit the spread of
decay, then the cambium develops a decay resistant wall to
protect new growth in the wood. Some tree species are more
Su(Icessful than others at this process and individual trees
amOrig a species may also vary. Stressful events requiring a
healing process draw heavily upon the energy reserves of the
tree. If wounded annually for several years, a mature tree
can become weak, develop poor growth patterns, and decline
in fruit productivity.

Santamour's work indicated that growth rates in the
tree may vary within a zone depending upon the degree of
reCOvery undertaken to prevent decay. Therefore, even

though the conventional signs of decline may never surface,

59

the shape of a tree limb or trunk may change within the
clamp attachment region during the seasonal growth period.

Because trunk shakers are designed to shake mature

trees, most growers have delayed starting mechanical
harvesting operations in their new orchards until the tree
trunks were at least 13 cm (5 in.) in diameter: about 9
years old. In recent years, however, because of economic
incentives and lack of labor, growers have begun to
mechanically harvest trees of trunk diameters as small as 5
cm (2 in.) (tree about 4 years old). These young trees are
particularly susceptible to trunk damage (Burton et al.,
1986). Young trees (3-6 years old) suffering major wounds
015’ a series of lesser wounds may never realize their full
PFOduction capacity.

Nondestructive continuous measurements of
Circumferential growth on stems of woody plants utilizing a
S"train gage dendograph have been conducted by Burger et al.
(1982). Light and temperature controlled growth chambers
prOvided the environment for experimental young trees. Data
cot‘related well with young tree growth and could provide a
ltleans to estimate the effects of environmental changes in
these and other growth factors as a means for following
orChard progress.

The shape of a tree trunk, particularly when young, is
rather smooth and circular. As age increases, the bark
beCOmes rougher. Tree limbs which are undamaged are still

nearly circular to elliptical in older trees and are usually

60

expressed by an average diameter. Kenworthy (1974) reports
that tart cherry trees may exhibit terminal shoot growth
from less than 25 cm (10 in.) to more than 46 cm (18 in.)
with corresponding changes in shoot girth, depending on tree
vigor. The peripheral shape of a trunk would only be a
planar number so other means are needed to classify the tree
trunk shape and express shape changes over time.

Means to classify trunk shapes that vary between
circular and elliptical may be similar to investigations in
the literature on microscopic particle size analyses.
Classical methods to classify particle shapes are revealed
in Table 2.3.

Stockham (1977) demonstrates some of the means by which
nonspherical particles can be expressed (Figure 2.3). The
most common is the area-projected—diameter: the diameter of
a Perfect circle with equal area. Martin's diameter is the
mean length of a line, parallel to the fixed direction of
scan, that divides the particle profile into two equal
arefis. Ferets' diameter is the mean length between two
tangents on opposite sides of the particle profile,
per£>€2ndicular to the fixed direction of scan. The maximum
hori~zontal intercept is the longest diameter from particle
edge to edge in the direction of scan. The perimeter-
prOj ected-diameter is the diameter of a perfect circle with
the Same perimeter.

Hausner (1966) has displayed a set of common general

Shapes described by an elongation factor X, a bulkiness

61

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UPable 2.3 Classical methods of describing particle shape.

 

.7

 

 

 

 

jAJJthor (Year) Parameter Formula
(:11rray (1951) Roundness RD=Object Area/Circle Area
fiéausner (1966) Elongation X X=Length/Width
Bulkiness Y Y=Area/(Length-Width)
Surface z Z=Perimeter /(12°6°Area)
C3zraf (1966) Form Factor FF=Area/Perimeter2

Duda and Hart
(1973) Thinness Factor TF=4°n°FF

Segerlind and

We inburg (1973) Shape by
Harmonics Fourier Transforms

Stockham (1977 ) Area
Projected

Diameter D=2°(Object Area/100’5
Perimeter
Projected
Diameter D=Object Area/n
Martin's
Diameter D: A1 = A2 || Scan
Feret's
Diameter D: Dist. Between
Tangents || Scan
Maximum
Horizontal
Intercept D: Maximum D II Scan

Sites and
Delwiche (1985) Invariant
Moments See Reference

\

facrtxar Y, and a surface factor Z. When X = l, the particle
is equiaxed; when Y = l the particle fills the rectangle and
When 2 = l, the particle is spherical and smooth. Clarenburg
(1966) suggested that the side lengths of a rectangle, a and

b' in.Hausner's description could be symmetrically reduced

¥ _ - __ __

 

 

63

1:0 equal the area 'A' of the particle thus eliminating the
IIGEd for 'A'. 'Y' would then become unity and thus
superfluous.

Curray (1951) described the roundness of an object
1;:5ing the measured projected area and the smallest
<::ircumscribing circle. Graf (1966) separated objects based
(>11 the 'form factor' which creates a distribution for
ssealected objects such as circles even when triangles and
treactangles exist in the same field.

Similarly, Duda and Hart (1973) defined the roundness
c>f' near-circular objects by a property known as the thinness
ratio 'T', a dimensionless property independent of the
obj ect's size, which was used by Parrish and Goksel (1977)
111 attempts to design an automated robotic harvesting
machine for apples. The maximum 'T' value is l which occurs
fCJr’ a perfect circle. As the object's shape changes, 'T'
decreases.

Segerlind and Weinberg (1973) classified various types
0f sgrain kernels using a Fourier series expansion of the
radial distance from the two dimensional center of gravity
to “the grain kernel periphery. The first ten harmonics of
eacll grain kernel shape were calculated and statistically
CQmQDEared. Interspecies discrimination among relatively
difEEeerent kernels resulted in only 1% error but intraspecies
disClrimination resulted in an error range of ll-25% when
Utilsizing only ten harmonics.

Sites and Delwiche (1985) utilized various vertical,

 

 

— V
64

horizontal and central moments of inertia combined with area

and perimeter for feature extraction as the means for

locating tree fruit for robotic harvesting. As machine
vision becomes more popular, many algorithms will become
available for shape analysis of real world objects (Sarkar,

1984).

CHAPTER 3
TRUNK SHAPE ANALYSIS - FOURIER AND CORRELATION

3.1 Tree Trunk Profile Measurement

In 1985, peripheral shape of nine Montmorency cherry
trees, located at the Michigan State University
Horticultural Research Orchards, were measured for profile
analysis. These trees were first trunk shaken in 1983.
Circumferal traces of tree trunks were first made in
September 1985 before experimental trunk shaker harvesting
tests. Successive corresponding measurements were made on
the same trees in September 1986.

A perimeter measuring device designed and constructed
by the USDA Plant Pathology and Agricultural Engineering
teams at Michigan State University was utilized to perform
the measurements. The contour tracer (Figure 3.1) consisted
Of a toroidal aluminum table (a), hinged on one side (b),
with a spring loaded clasp opposite (c). The device
encircled the tree (d). Three adjustable legs (e) allowed
Positioning and leveling. A leveling bubble (k) ensured
cOnsistent alignment. A sliding pointer (f) mounted on the
t'Eible's rail border (9) consisted of a teflon pen carrier

”1) precisely fitted with an aluminum cam-follower (i) at

its head.

65

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67

The height of shaker clamp attachment at harvest time
on each of the nine trees was marked with indelible white
tree paint. Each tree was also marked for magnetic north as
a reference and alignment point for the following year's
measurements.

The contour tracer was centered, leveled, and clamped
around each tree at shaker clamp height. A pre—cut,
toroidal—shaped piece of paper was aligned on pins (1) on
the table and taped onto the contour tracer table. A pen
(j) was inserted into the teflon pen carrier (h) until the
point made contact with the paper. Light downward pressure
was applied to the pen as the follower (f) was moved around
3600 of the tree's perimeter to trace the profile of the
tree trunk at this height. The largest of the nine sample
trees outgrew the contour tracer size and was therefore not
measured in 1986.

Each trace was identified by orchard, row and tree
number. Magnetic north, as marked on the tree, was also
labeled correspondingly on the paper trace. The two halves
of the paper trace were then removed from the table, taped
together, and stored for later analysis.

Accuracy in following the tree profile was estimated to
be i 1 mm (: 0.04 in.) on smooth trees and t 2 mm (x 0.08
in.) on rough bark trees due to the width of the pointer tip
"filtering" the valleys in rough bark. The cam radius of
curvature (p(t) = 5 mm, 0.20 in.) was slightly larger than

the average radius of curvature of valleys on rough tree

68

bark (p(t) = 2—3 mm, 0.08-0.12 in.). This radius was
selected to provide a continuously smooth motion in tracing
tree bark. Narrower tipped cams (small radius of curvature)
had a tendency to lodge in tree bark abnormalities, thus
shifting the burden of accuracy to the operator's dexterity.
Repeatability in measurements was approximately 1 1 mm (:
0.04 in.).

Accuracy in realigning the measuring table in 1986 to
the magnetic north mark made on the tree in 1985 was
estimated to be i 3°. This was also the repeatability in
realignment. Repeatability in vertical alignment was
estimated at i 5 mm (1 0.20 in.).

It should be noted that the accuracy of measurements on
some smooth trees decreased in 1986 due to severe damage
resulting from intense shaking tests in 1985 which caused
the bark to deform. This introduced measurement error of
valleys in the bark not previously a factor with smooth
bark. Expected overall profile measurement tolerance was
found to be i 2 mm (i 0.08 in.) on rough bark trees, a
figure I chose to accept.

In the laboratory, a transparent acetate overlay
containing 360 radial lines emanating from the center (10
resolution) provided equally spaced polar coordinates for
digitization and analysis of the near—circular tree
profiles. Each profile trace was visually centered under
the transparent acetate grid and taped onto a Tektronix 4954

Graphics Tablet (1080 mm x 880 mm, 42.5 in. x 35 in.). The

69

graphics tablet was connected to a Prime 750 Mainframe
located in the MSU Engineering Computing Facility via a
Tektronix 4014 Graphics Terminal. The points at which each
radial line intersected the periphery were digitized
starting at north as 0° and proceeding 360° ccw back to
north. The first point was redigitized along with one point
directly north of the periphery for a total of 362 points.
These last two points provided computer identification of
magnetic north in the data. Digitized values were put into
an IBM AT Personal Computer for disk storage and analysis.

The block diagram for the data preparation phase of the
shape analysis project is shown in Figure 3.2. In the
calibration phase, digitized data were converted from
digitizing tablet coordinates to paper trace measurements
via multiplication by a simple ratio. Calibration was then
necessary to convert from paper trace measurements into
actual tree profile values by adjusting the radial lengths
from the profile center to each digitized coordinate to
compensate for the constant radial offset of the measuring
table's cam follower (Figure 3.3) determined from the
equation:

Cam Radius (mm) = (HOLE - l) * 25 + 58.5

The trace radius for each digitized point was:

 

Radiustrace (mm) = / (xi - xc)2 + (Y1 — Yc)2
for i = 1,2,...360

Where:

xcenter
C center

0
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X Y- = (X,Y) coordinates of the ith digitized

i' 1 .
data p01nt of the trace
The uncorrected area was calculated using the survey
area coordinate method (Brinker and Wolf, 1984) as follows:

X: * Y

X1 Y1 SUMpos f 1 * i+l
X2 Y2 SUMneg - X1+l Yi
xn Yn AREA = (SUMpos — SUMneg)/2

Area-projected-radius (APR) is often used to define near-
circular particles and is defined as the radius of a circle
with area equal to the object area under consideration. The

area—projected-radius of the trace is then:

 

APRt = /FTrace Area / n
Where:

APRt = Area-projected—radius of trace
The corrected profile radius for each point is then:

Radius = Radiustrace - Lengthcam

COI‘I’GCt

And the corrected (x,y) profile coordinates which give the

corrected profile radius are then:

 

Xi—correct = Xi * APRt ' Lengthcam
APRt
Yi-correct = Yi * APRt - Lengthcam

 

APRt
The valid profile area was then recalculated using the
survey area coordinate method. Profile area (Ap) and
profile radii (APRp) were compared with hand measured
estimates.

The profile center was defined utilizing a least

squares fitting procedure, i.e., the point which minimized

73

the sum of squares distance from all the Circumferal points
(Kasa, 1975).

Letting (Xi'Yi) represent the x,y coordinates of the
ith measured data point, N the number of data points
(lgiiN), (XC,YC) the coordinates of the center, and R the
radius of the circle, the least squares error criterion for

locating the center is:

N
E (Ri — R)2 = min

 

i=1
Where: 2 2
R1 = /(xi -xc) + (Yi —Yc)
for N33

This expression is not easy to solve analytically.
Consequently, Kasa (1975) uses a modified least squares
error criterion defined as:
N
(Riz — R2)2 = min
i=1
This form presents no analytic difficulties and can be
written in the form:
N
H = Z [(Xi - XC)2 + (Yi - YC)2 - R2]2 = min
i=1
A best fit circle is then found by searching for the

unknowns XC, Y and R.

c

Since the sum u is a second—order function of XC and YC
without constraints, the extrema can be simply evaluated by
setting derivatives of u equal to zero. Taking derivatives

with respect to XC, YC, and R, setting them equal to zero,

and simplifying, the new variable C can be introduced to

 

74

linearize resulting equations:

_ 2 _ 2 _ 2
C - R Xc YC

Resulting equations appear as (all summations are over i=1

to N): 2 2
XCZZXi + YCZZYi + CN = z<xi + Yi )

2 _ 3 2

xczzxi + Yczzxiyi + czxi — 2(xi + XiYi )

2 _ Z 3

xc2zxiyi + YCZZYi + czvi — 2(xi Yi + Yi )

Introducing the matrix DM and the vectors EM and QM

respectively:

2£xi 22Yi N
DM = 22x12 zzxigi zx
ZEXIYi ZZYi ZY
2(xi2 + Yiz)
EM = 2(Xi3 + XiYiZ)
2(Xi2Y + YiR)

We can write:

and solve:
QM = DM“ * EM
by the classical Gauss or other appropriate method.

If R from Kasa's solution was within 2% of APRt, then
the geometric center found from Kasa's equations was
accepted. If not, this meant that the tree trace was not
bilaterally symmetric and hence, the center of the tree
trace would not correspond to the center of a best fit
circle through its coordinates (Figure 3.4). Therefore, a
least squares error criterion was used to iterate through
the profile to find the best center:

E = ((Xi — XC)Z + (Y1 ‘ YC)Z)2 = min
irrespective of R

 

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The geometric profile center calculated by either
method does not necessarily correspond to the tree's center
of mass, however, due to density variations in material
content.

Once calculated, the center of a tree profile plot
could be translated to any desired X,Y location for further

analysis via:
Xnew = xold _ xtranslate

Ynew = Yold " Ytranslate
Where (xtranslate'Ytranslate) usually equal (XC,YC) in order
to center profiles at (0,0). For uniformity, all centers
were subsequently translated to (0,0) for plotting and
analysis.

Rotation was also performed to align the profile on the
plot as desired. The angle of rotation 6 could be specified
by the user or it could be calculated so as to set magnetic
north at the top of the plot according to the routine:

AX

X - X
AY 361 c

Y361 ‘ Yc
e = ARCTAN(AY/AX)

Rotation was accomplished by matrix multiplication:

QM = DM * RM

Where:
QM is the N*3 output matrix of rotated X,Y values
DM is the N*3 input matrix of nonrotated X,Y values
RM is the 3*3 rotation matrix:
cos(6) sin(9) 0
RM = -sin(9) cos(6) 0
-Xc(cos(6)-l)+YCsin(e) —XC(sin(e)-1)-Yc(cos(6)-l) l

Rotation was necessary in the 1986 profile data in

 

77

order to increase the accuracy (and repeatability) of
alignment of plots with magnetic north. A time domain
cross—correlation procedure was used on the 1985 - 1986
profile plan to determine a rotation angle for best

alignment as follows:

1 ‘1,1

$12(C) = ———— ' f fl(¢)f2(¢+C) d¢
¢1 ¢=0

or in discrete formulation:

1 ¢1

W12(C) = ———— ° 2 f1(¢)f2(¢+(C-l))
¢l ¢=0

C = l...Cl

This provided the required angle of rotation of the 1986
plot which would provide best alignment with the 1985 plot.
Assuming accurate directional traces on each years profile
plot, this would improve alignment repeatability to t 0.5°
from magnetic north.

Now that successive profiles are calibrated and
aligned, multiple shape discriminators can be calculated.
The perimeter (needed for several shape discriminators) was

calculated as:

LA)
01

9
P (Hun) = Z /((Xi+l—Xi)2 + (Yi+l-Yi)2)
i=1

 

 

+ /(Xl—XN)Z + (Yl—YN)2

3.2 Geometric and Linear Profile Plots
Much work has been devoted to image analysis and shape
discrimination. Unfortunately, most of this work has been

targeted towards keeping similar shapes in the same category

—: 3" . ‘4'
.lyu:

 

 

78

(rectangles, ellipsoids, circles: Figure 3.5). This
presents a problem in trunk profile analysis because, while
it is clear that successive annual profiles will have
similarity, my goal is to identify those small differences
which may provide indicators of tree deformation and damage.

Tree shapes have received little attention as
indicators of damage. In a first attempt to make small
discriminations in shape, the simplest methods of
discrimination were approached - observation of the
geometric profile plots produced by the digitization and
calibration procedures of Section 3.1. Three of the nine
tree profiles analyzed were selected as examples for what
follows. Tree 11 (Figure 3.6) has a small trunk (dia<100
nun, 4.0 in.), Tree A (Figure 3.7) has a medium trunk (100
nun<dia<150 mm, 4.0-6.0 in.) and Tree 25 (Figure 3.8) has a
large trunk (150 mm<dia, 6.0 in.). Plots are not to—scale.
Dashed lines indicate a circle of area equal to that of the
Cc>rresponding trunk profile (Area—projected-radius circle).

Tree 11 in 1985 had a nearly circular cross section.
If! 1986, after having been shaken once in 1985, the shape
Ilas become less circular, having a radius smaller than APR
iri the SW and NE octants and a radius larger than average in
tile NNW and SE octants. Visual inspection of this tree
irldicates no external damage except for a slightly scuffed
bark patch in the WSW sector.

Tree A appeared to have some slight malformation in

1985; visual inspection in 1985, however, failed to reveal

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83

any external damage. The 1986 profile shows drastic changes
in shape; in addition severe bark splitting, bark folding,
and decay can be seen.

Tree ZS also showed some malformation in 1985. Visual
observation revealed slight external bark scuffing in the
NNE sector. The 1986 profile appears to amplify the profile
distortion observed in 1985. In general, the periphery is
similar to 1985 except for slight bark protrusion in the NE
quadrant, possibly the result of splitting. This tends to
agree with 1986 observations; minor external change has
taken place except for uniform radial growth.

Profile plots were subsequently linearized by
transforming from Cartesian coordinates to polar coordinates
and plotting the radius from the calculated geometric center
(rersus the angular displacement from magnetic north

(positive CCW). This plot transformation appears as:

Xi=9i.
Yi = Rad1us(ei)
e = o...3so° ccw

This provides a means to observe and compare the
IIrofile perimeter in 1985 with that in 1986. Difference
kNatween successive annual plots indicates a radial change in
SIIape for the growth period. It also provides a means for
ePValuating the circularity of the profile each year. For
example, a linearized perfect circle would map to a perfect
S‘traight line, y=R, assuming the geometric center of the
‘3ircle was accurately calculated (Figure 3.9).

More importantly, however, this method also provides a

84

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85

check on the accuracy of the previously calculated geometric
center of the profile. For example, if the profile was a
perfect circle but the calculated geometric center was not
the true geometric center, then the polar transformation
would reveal a cycloid. This is not to be confused with
actual perimeter malformations in non-circular profile
plots, however.

Figure 3.10 is a linearization of the Tree 11 profile
for 1985 and 1986. As shown, the calculated geometric
centers are accurate. In 1985, Tree 11 was nearly a perfect
circle. By 1986, however, some change in shape had
occurred. Low magnitude changes with no sharp peaks may
indicate internal cell damage causing redirected radial
Igrowth without visible external damage.

Tree A (Figure 3.11) shows minor non-circularity (via
ruonlinearity) in 1985 with drastic shape changes in 1986.
'Phe sharp changes correlate with visual observation of
Eixternal bark damage. Valleys in the plot indicate decay or
exxposed wood. Peaks correlate with bark protruding due to
Ss>litting and peeling.

Tree ZS (Figure 3.12) exhibits a tri-lobed shape in
15385; by 1986 little more than radial growth has taken
Eilace. The jagged look of the 1986 data seems to indicate
SCnne bark scuffing and an increase in "rough bark". The
fact; that the two valleys do not show growth proportionate
withthe peaks may indicate slight internal damage.

The differences between 1985 and 1986 linearized

86

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89

profiles are shown in Figures 3.13 — 3.15. These plots
provide an assay of radial growth among trunks of the same
size class. If a perfectly circular tree has grown
uniformly from 1985 to 1986, then a straight line would be
expected at a Y-axis value equivalent to the measured radial
growth. Deviation from a straight line indicates less
growth (valleys) or more growth (peaks) than the average.
Note the vertical axes are broken so that minor fluctuations
will be emphasized.

Of the three small trees, Tree 11 appears to have
developed most uniformly. Slight lack of growth is visible
on the sw (900+) and NE (2700+) sides of the tree. This
Inappens to reflect the clamp location for the 1985 and 1986
liarvests.

Tree A (Figure 3.14) shows drastic changes at the SW
( 900+) and NE (2700+) quadrants agreeing both with location
<>f clamping for the 1985 and 86 seasons as well as the
Krisibility of external bark damage.

Tree ZS (Figure 3.15) clearly shows two areas of
aniform growth and two areas of superior growth, differing
-r13dially by approximately 5 mm (0.20 in.). The fact that

titlese two valleys are very close to 180° apart agrees well

VWith the hypothesis that slight internal damage at clamping

53(311nts may have caused slight redirection in growth with no

EBJ'K‘lzernal markings.

The preceeding data indicate that degeneracy of

<2 ' .
1rcular shape occurs to varying extents as these trees

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93

grow; the common causal agent appears to be trunk-shaking.
Profile peaks above the mean difference may indicate bark
protrusion and callus development while valleys below the
mean difference may indicate compressed bark, decay areas,
or dead wood. The trees in this test were shaken more
severely than may be typical in commercial operations.

Live control trees were not available for profile
analysis but several control cross sections of disected
Montmorency cherry trees are shown in Figures 3.16-3.17.
These cross sections indicate that trees generally take on a
near-circular shape when young and continue to maintain the
shape of the previous year's growth ring as they mature
(Figures 3.16a, 3.16b). Shape can be influenced, however,
13y factors other than shaker damage such as wind, light
intensity and direction, pruning, and staking. These
:factors change the fiber stress level and/or distribution of
galant growth regulators which, in turn, change the growth
Ciistribution (pattern) of new cells.

Damage to trunks can often change the shape of the
tlrunk when associated with splitting, pealing, and cracking.

'Iqle tree healing process will then tend to reshape trunks to
‘tlne predamage growth ring profile as shown in Figure 3.17a.
SSlight shaker damage may often become exhibited by a thin,
Ciéirk-stained arc or by stain pockets (Figure 3.16a, 3.17b).
£31161ins may show up as patches, patches which extend towards
tlllfié heartwood but stop short, or patches that extend all the

Vvéi}? to the heartwood (Figure 3.17b). Stains are often

AIIIIIIl-n...

 

94

 

(b)

FIgure 3.16 Cherry tree trunk cross sections:
a) shaker damage b) bark compression.

 

95

 

(b)

Figure 3.17 Cherry tree trunk cross sections:
a) contour rejuvenation b) staining.

96

evidenced with shaker damage and usually accompany decay.
Decay, however, does not necessarily accompany staining.
The physiological initiation, makeup, and activity of stains
are not yet understood (Burton, 1987).

Slight changes in trunk shape may be caused by
compression of the large phloem cells between the vascular
and cork cambium layers (Figure 3.16b). These cells are
larger and less rigid than most other bark cells and hence,
are more likely to fail under stress. If damaged, these
cells cannot provide passage of sugars from the leaves to
the roots for over-winter storage. During a food shortage,
available energy is allocated in a hierarchical manner with
fruit yield and new shoot growth having lesser priority than
maintenance of existing structure. Postwinter rejuvenation
may also be inhibited by a nutrient shortage such as this.

Food shortage may reduce winter cold hardiness. Thin,
dark growth rings often signify temperature or moisture
extremes beyond a tree's physiological tolerances. Over a
period of several years, periodic damage may accumulate and
become a significant factor in the tree decline episode.

Having mathematically identified shape changes that
were confirmed by visual observation, further more complex
indicators for shape discrimination were investigated to

find a convenient accurate index for bark damage.

3.3 Bandwidth and Historic Shape Indicators
Several geometric indices were calculated for the tree

Ebrofile plots in an attempt to identify bark damage and

97

discriminate between external and internal damage. Some of
these methods are used in digital image processing and have
been converted for this application. Area and perimeter
have already been calculated for the profiles. These two
properties are invariant to rotation and translation and are
considered good indicators of "multiple" versus "non—
multiple" objects.

The area-projected-radius, as previously mentioned, is
calculated for a shape as the radius of a perfect circle

having the same area as the shape under investigation:

 

APR (mm) = / Profile Area (mmz) / n
A similar parameter, the perimeter-projected-radius is
the radius of a perfect circle having the same perimeter as
the shape under investigation:
PPR (mm) = Perimeter (mm) / 2n
A 'bandwidth' factor was defined for this application

as:
BW (mm) = Max Radius - Min Radius

Where:

 

Max. Rad. (mm) Max ( /fi(Xi — XC)2 + (Yi - YC)2 )

 

Min. Rad. (mm) Min ( / (xi — xc)2 + (Y1 - YC)2 )
i = l...N
'Percent bandwidth' can then be defined as:
% BW = BW (mm) / APR * 100
Compactness, CPR, (Agin, 1976) is a dimensionless

feature that is invariant to translation, rotation, and size

63nd has been used to distinguish "single fruit" objects from

98

"noise objects". It is defined as:
CPR = Area / Perimeter2

The thinness ratio, TR, was defined by Duda and Hart (1973)

as:
TR = 4n * CPR

Finally, Curray (1951) identified an object's roundness

(RDNESS) as:

RDNESS = Object Area / Circle Area

Where:

Calculated Area in the shape

Object Area
Area of a circumscribing circle about the

Circle Area

 

shape
= n * RLONG2
Where:
RLONG = LONG DIA. / 2
And:
LONG DIA. = MAx I f(x(ei)—XC)2 + (Y(Gi)-YC)2

 

+ J'(X(ei+180)-XC)2 + (Y(ei+180)-YC)2 ]
9i = O...180

Shape indicators for standard geometric figures are
giwren in Table 3.1. Application of these methods to the

trwee trunk profiles results in the data of Table 3.2.
Elongation, a measure of length to width ratio, is
inVariant to translation but only semi—invariant to rotation
‘thén defined as the minimum moment of inertia divided by the
maJ'liimum moment of inertia (Gonzales and Wintz, 1977). Since
r0tlation is important when defining damage areas on tree
prOfile plots, the rotation-sensitive elongation factor was

nc’t calculated. However, a more in-depth moment approach

ILaES been used to calculate shape descriptors invariant in

99

 

Table 3.1 Geometric shape indicators of standard geometric
shapes (All measurements in mm unless noted

otherwise).

 

 

 

2 MIN. MAX. LONG

Profile AREA (mm I APR RAD. RAD. PERIM DIA.

RECTANGLE 7200.0 44.6 30.0 60.0 360.0 120.0

ELLIPSE 4897.0 39.5 30.0 52.0 262.1 104.0

CIRCLE 8481.9 52.0 52.0 52.0 326.5 104.0
BW %BW PPR CPR TR RDNESS

 

RECTANGLE 30.1 67.7 52.2 0.0580 0.7290 0.5568
ELLIPSE 22.0 55.6 41.7 0.0713 0.8956 0.5773
CIRCLE 0.0 0.0 52.0 0.0796 1.0000 1.0000

 

translation, rotation and size. Gonzales and Wintz (1977)
define seven invariant moments which combine to reveal
features for object classification where the features are
composed of second and third order moments divided by an
area factor defined as [(moment's order/2)+l].

A moment of order (p + q) is defined for a two

dimensional continuous function f(x,y) of an image as:

m (D
m = f f xpyq°f(x,y) dx dy
pg —00 —00

p,q = O,l,2,...
The center of gravity of an object can then be determined
from:
E = mIo / m00 I = m01 / m00
The central moments are expressed as:
m 0

= f f (x — §)p(y - §)q'f(X,y) dx dy

-00 -®

uPq

 

100

Table 3.2 Geometric shape indicators of cherry tree trunk
profiles (All measurements in mm unless noted
otherwise, listed in size categories in order of

 

 

 

damage).
* 2 MIN. MAX. LONG
Profile ED AREA LEE 1 APR RAD. RAD. PERIM DIA.
11-1985 1 1487.1 21.8 21.0 22.0 137.9 44.1
11-1986 2 4306.8 37.0 35.9 37.8 234.5 75.2
12-1985 1 1749.3 23.6 22.7 24.0 150.1 48.0
12-1986 3 3927.6 35.4 33.4 36.9 225.2 72.4
10-1985 2 1739.5 23.5 23.1 23.8 148.5 47.5
10-1986 5 4048.7 35.9 32.7 38.0 229.6 75.0
C-1985 1 10348.5 57.4 54.3 60.2 367.9 119.1
C-1986 3 15006.8 69.1 65.8 74.2 445.5 143.3
B-1985 2 10734.7 58.5 56.8 60.0 369.4 118.7
B-1986 4 16622.2 72.7 68.6 75.1 467.8 149.3
A-1985 2 9771.7 55.8 54.3 57.2 353.9 114.1
A-1986 5 15985.0 71.3 65.3 78.8 461.9 151.0
N-1985 1 20399.0 80.6 78.3 82.6 510.0 164.6
N-l986 2 28074.8 94.5 90.6 97.8 599.1 193.9
28-1985 1 16981.1 73.5 70.7 75.2 464.4 149.1
2S-l986 3 22443.3 84.5 80.1 87.7 535.5 173.2
E! %BW PPR £35 25 RDNESS
11-1985 1.0 21.9 0.0783 0.9833 0.9754
11-1986 2.0 37.3 0.0783 0.9840 0.9692
12-1985 1.3 23.9 0.0777 0.9763 0.9678
12-1986 3.5 1 35.8 0.0775 0.9736 0.9534
10-1985 0.7 23.6 0.0789 0.9913 0.9823
10-1986 5.3 1 36.5 0.0768 0.9655 0.9156
C-1985 5.9 1 58.5 0.0765 0.9610 0.9284
C-1986 8.4 1 70.9 0.0756 0.9501 0.9299
B-1985 3.1 58.8 0.0787 0.9888 0.9708
B-l986 6.5 74.5 0.0759 0.9544 0.9493
A-l985 3.0 56.3 0.0780 0.9802 0.9560
A-1986 13.5 1 73.5 0.0749 0.9414 0.8931
N-1985 4.3 81.2 0.0784 0.9854 0.9581
N-1986 7.2 95.4 0.0782 0.9828 0.9507
2S-1985 4.5 73.9 0.0787 0.9893 0.9720
28-1986 7.6 85.2 0.0783 0.9835 0.9524

* Estimated Damage: l-(No Visible Damage), 3-(Moderate

visible damage, no cracking or peeling), 5-(Severe visible
damage, cracking, peeling, or sapping).

101

which, in format for digital processing becomes:

”pq = g 5 (x - §)p(y - §)q°f(x,y)

After expansion and simplification, the central moments to

order 3 can be summarized as:

1100 = m00 u11 = m11 ‘ 7m10

u10 = 0 L130 = m30 ‘ 3$11120 + 2m10i2

u01 = 0 L112 = m12 ‘ 27mm ‘ 32“02 + 272mm
u20 = m20 ‘ §m10 1121 = m21 ’ 232m11 ‘ §m20 + ZEZm01
u02 = m02 ‘ 7m01 u03 = m03 ' 3§m02 + 2372mm

The normalized central moments are defined as:

= Y
npq upq / H 00
y = ((p + q)/2) + l p+q = 2,3...

Where:

From the above second and third order moments, a set of
seven moments (01), invariant to translation, rotation and
size, are defined as descriptors for the continuous region:

‘ n20 + n02
ll’2 = (“20 ‘ “02)2 + 40211

e
H
I

$3 = (030 — 3012)2 + (3021 + T103)2
¢4 = ("30 + “12)2 + (021 + ”03)2

w = (n - 30 )(n +n )[(n +n )2 - 3(n +n )2]
5 + %9021 ‘1003)?%21 $2003)?9(n332+ 012 2 21(02g3+ 003)21
$6 = (0&0 ‘ 002)[(n30 + 012)2 - (021 + 003)2]
+ n11(030 + n12””21 + “03)

$7 = (3n 2 ‘ n30)(n 0 + n12)[(n + 012)2 - 3(0 1 + 003)21
+ (3n21 - n03>in21 + n03>[§?n30 + 012)2 - inZI + n03)2]
The function f(x,y) is defined as a continuous image

function over the region of scan. In the case of profile

E>lots, this function must be defined since only the profile

102

boundary is stored in the data. Two methods are available
to do this. The first consists of plotting the boundary on
a screen and then filling the boundary regions by varying
levels of contrast (grey tones). F(x,y) is then defined as
the screen area in pixels. The value of f(x,y) for each
iteration is dictated by the grey level of the pixel at
(x,y).

In the case where the image is not too complex, it may
be easier to analytically define image boundaries and then
check to see if each (x,y) lies within. This second method
was used with the profile plots by converting the Cartesian
coordinates (x,y) of the boundary to polar coordinates (R,0)

and scanning an area which is known to include the largest

profile. A value f(xs,ys) = 1 is returned if the scan
coordinate (xs'Ys) = (Rs,es) lies inside the minimum profile
radius Rmin or f(xs,ys) = 0 if (xs,ys) = (Rs,es) lies

outside the maximum profile radius Rmax’

If the scan coordinate lies "in the bandwidth" between
Rmin and Rmax' the angle as is used to find the two boundary
points (xs_1,ys_l) and (xs+l'Ys+l) which border (xs,ys). A
linear interpolation is then performed between (xs-l'Ys-l)

and (Xs+l'Ys+1) to determine a "virtual boundary radius"

(Rvirtual) at 05. The scan radius RS is then compared to
Rvirtual to determine relative internal or external
location. The number of calculations using this method is

thereby dependent on the bandwidth.

The standard geometric shapes have moments as shown in

103

 

Table 3.3 Moment invariants for standard geometric shapes.

Moment (Log)

 

 

 

 

___Pr°f i 19 19. £1 12 1413 14 19.5 16 1'47
RECTANGLE 0.120 0.885 6.174 7.021 14.251 7.923 13.800
ELLIPSE 0.132 0.859 5.520 6.525 12.621 7.205 12.720
CIRCLE 0.196 7.276 6.666 9.769 17.890 13.407 0.000
Table 3.4 Moment invariants for tree trunk profiles.

Moment (Log)

___Pr°f i 19 12 £1 12 23 114 is 16 17
11-1985 0.196 4.085 4.589 9.140 15.983 11.272 15.779
11-1986 0.196 3.553 4.330 8.122 14.117 10.463 14.126
12-1985 0.196 4.274 4.998 8.805 15.706 10.942 15.706
12-1986 0.196 3.803 3.611 6.521 11.376 8.424 11.573
10—1985 0.196 3.984 3.806 6.875 12.086 8.942 12.666
10-1986 0.194 2.621 3.568 6.042 10.622 7.360 10.746

C-1985 0.195 2.869 3.338 6.722 11.732 8.235 11.826
C-1986 0.195 3.319 2.900 6.355 11.529 8.671 11.364
B-l985 0.196 3.870 3.579 7.232 12.557 9.411 13.065
B—l986 0.196 3.405 5.416 7.516 14.182 9.219 13.935
A-1985 0.196 3.477 3.924 7.669 13.634 9.752 13.473
A—l986 0.195 3.726 3.820 5.601 10.736 7.465 10.426
N-1985 0.196 3.091 4.743 7.855 13.939 9.432 14.194
N—1986 0.195 3.072 4.164 6.683 12.995 8.911 12.120
28-1985 0.196 3.704 3.656 7.173 12.589 9.510 12.749
2S-1986 0.195 3 162 3.703 6.582 11.562 8.363 11.981

Table 3. Application of these seven invariant moment

equations to the tree profiles reveals the data of Table

3.4.

These results show that first moment 01 is
practically invariant for a set of profiles of near
circularity. From 1985 to 1986, 02 tends to decrease for

104

all profiles except for A and C which are the two profiles
with the largest perimeter "bumps" from bark distortion.
From inspection of the profile plots, 04 - $7 tend to
decrease for all three example trunks (11, A and ZS)
proportional to the amount of shape change. With further
data, 02 and 04 may provide adequate indication of direction
and magnitude of shape change. 01 alone seems to be
inadequate for separation of similar shapes. 02 and $6, in
combination with perimeter measurements, have been used to
separate single objects from multiple objects of the same
shape and may provide an indicator of "bumps" on trunk
perimeters. Therefore, a combination of $1, 02, and 07 may
provide a bark damage envelope upon which judgement can be

based.

3.4 Fourier Continuum and Cross-Correlation

Pattern recognition techniques have often been based on
the Fourier series expansion of the linearized functions
such as Figures 3.10, 3.11 and 3.12 (Ehrlich and Weinberg,
1970). The Fourier series coefficients contain information
about an object's shape and thus can be used for
identification. I wrote a discrete Fourier transform
program to calculate the Fourier coefficients of the
periphery radius of the tree profiles about their center of

gravity in the form (Segerlind and Weinberg, 1973):

on G)

R(0) = R0 + Z An°cos(n0) + Z Bn°sin(n0)
n=1 n=1

l 211’
Where: R0 = ——— ° 1 R(0) d6

2n 0
l 2'"

An = ——— : f R(8)°Cos(n0) d0
n 0
l 211'

Bn = ——— ° I R(0)'sin(n0) d0
0 0

The polar form is employed since the profile radius is a
function of the angle about the center of gravity from a
select reference line. Peripheral points are mapped to
polar coordinates and the values of An and Bn for each value

are calculated from the discrete form:

N _ .
R(k) = —1— - z R(0)°e hike/N
N 0=1
Then the expansion becomes:
co
R(0) = R0 + X Rn-Cos(n6+¢n)
n=1
Where: Rn = An2 + an
and: ¢n = Arctan (En/AN)

The RO term in the series identifies the average radius
while the RH terms identify added "bumps" superimposed on
the average radius properly placed by their corresponding
phase.

The number of points needed to evaluate the Fourier
series coefficients must be at least twice the number of the
highest desired harmonic. Utilizing the acetate grid with
l0 spaced radials, 360 points were collected, providing data

for the zeroth through the 179th harmonics. The zeroth

106

harmonic gives a centered circle with an area equal to the
total area, the first harmonic is a offset circle, the
second is a figure eight, the third a trefoil and so on.
Frequency spectra for the standard geometric shapes are
shown in Figures 3.18-3.20. Note from Figure 3.20 that some
digital numerical error is evident around 0.001 to 0.005
magnitude. Values above 0.01 are considered accurate.

Figures 3.21 - 3.23 show the spectral content of Trunks
11, A, and 2S, respectively. The data are not normalized;
therefore, differences in the projected area between
profiles for the same trunk are apparent as the zeroth
harmonic. Frequencies at the low end of the spectrum
represent slower changing shapes and are more reliable than
frequencies at the higher end where vision, dexterity, and
digital numerical error begin to play an important role in
frequency decomposition.

Figure 3.23 reveals that Trunk ZS did not significantly
change shape from 1985—1986. Referring back to Figure 3.8,
this agrees with visual observation. Significant magnitude
Changes in the low frequency spectral content of Trunk 11
and Trunk A would, however, indicate significant shape
changes.

The profile of Trunk 11 shows significant Changes up to
approximately the 40th harmonic whereas Trunk A has an
obvious extension up to about the 100th harmonic. Referring
to the profile plots, Trunk A has significant shape changes

with sharp valleys and peaks. High frequencies are

107

 

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113

developed from rapidly Changing signals. Since Trunk A was
observed to have external damage and Trunk 11 had none, it
may be possible to distinguish frequencies which identify
external from internal damage.

Figures 3.24 to 3.26 reveal the ratio of frequency
spectra for the sample profiles. Values for frequencies
having original spectral contents above 0.01 are considered
accurate. Trunk ZS, which had very little change is shape,
shows a low spectrum ratio for the two years. Trunk 11,
which had a gentle change in shape, shows a significant peak
at about the 7th harmonic with significant area of change
from the 2nd to the 15th harmonics. Trunk A, on the other
hand, presents its gradual peak at about the 12th harmonic

with important side peaks at the and

I

harmonics. Area change extends from the 2nd to the 80th

over the other two samples.

With evidence of frequency decoding in these plots, the
first 20 harmonic frequency coefficients (Rl'RZO) of each
profile plot were normalized by dividing by R0 to eliminate
the projected area differences. Frequency coefficients are
tabulated in Table 3.5 for the standard geometric shapes and
in Tables 3.6—3.8 for tree trunks.

A low value for the first harmonic in all profiles
indicates that the origin was located at the centroid of the
profile. As symmetry decreases, the odd harmonics increase
in amplitude. The second harmonic is generally associated

with elliptical shaping, therefore as circularity decreases

114

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117

Table 3.5 Normalized Fourier coefficients for3standard
geometric shapes (coefficient * 10’ ).

Shape Identification

 

 

Harmonic RECTANGLE ELLIPSE CIRCLE
1 0.00 0.00 0.00
2 161.16 130.41 0.00
3 0.00 0.00 0.00
4 18.10 8.65 0.00
5 0.00 0.00 0.00
6 42.52 1.15 0.00
7 0.00 0.00 0.00
8 18.11 0.00 0.00
9 0.00 0.00 0.00
10 6.03 0.04 0.00
11 0.00 0.00 0.00
12 12.82 0.00 0.00
13 0.00 0.00 0.00
14 6.03 0.00 0.00
15 0.00 0.00 0.00
16 2.92 0.00 0.00
17 0.00 0.00 0.00
18 6.02 0.00 0.00
19 0.00 0.00 0.00
20 2.92 0.00 0.00
due to tree damage, the second harmonic increases. A change
in shape from circular to elliptical tends to increase even
harmonics.

Cracks, which often show up in shear damage, usually
occur one per tree. This appears to relieve enough strain
in the bark to prevent a second crack. A crack has the
effect of adding frequency content to the lst harmonic and

the higher harmonics, particularly the 3rd_7th.

Young trees which are of particular interest to
commercial growers in terms of investment, longevity, and
productivity are more adversely affected by severe shake
harvesting than older, tougher trees. From the normalized

frequency spectra of the young trees, it appears that in all

118

Table 3.6 Normalized Fourier coefficignts for small trunk
profiles (coefficient * 10' )

Trunk Identification

 

 

 

Harmonic 10-1985 10-1986 11-1985 11-1986 12-1985 12-1986
1 0.98 1.06 0.50 0.80 0.37 0.38
2 1.55 19.86 4.98 7.44 4.41 5.09
3 2.57 9.02 0.75 2.88 1.84 7.50
4 2.12 4.00 0.64 1.56 2.09 7.66
5 0.22 4.02 0.11 1.64 0.44 0.77
6 0.87 2.52 0.09 2.50 0.65 0.64
7 0.82 2.63 0.43 2.47 0.43 1.83
8 0.82 3.21 0.49 0.58 0.41 1.74
9 0.31 1.93 0.14 0.85 0.26 2.63

10 0.50 1.65 0.19 0.61 0.18 2.06
11 0.31 0.68 0.21 0.36 0.51 1.83
12 0.42 1.31 0.35 0.85 0.88 1.23
13 0.18 0.58 0.05 0.11 0.35 0.16
14 0.42 1.17 0.12 0.30 0.33 0.33
15 0.36 1.33 0.26 0.29 0.37 0.91
16 0.26 0.40 0.21 0.29 0.23 0.69
17 0.33 0.63 0.09 0.35 0.41 0.63
18 0.22 0.39 0.14 0.16 0.13 1.11
19 0.14 0.38 0.18 0.29 0.40 0.55
20 0.11 0.38 0.15 0.32 0.07 0.51

Table 3.7 Normalized Fourier coefficients for medium trunk
profiles (coefficient * 10’ ).

Trunk Identification

 

 

 

 

 

 

Harmonic A-l985 A—1986 B-1985 B—l986 C—1985 C-1986
1 0.21 0.23 0.44 0.28 0.31 0.30
2 7.85 5.25 4.23 7.65 13.92 6.42
3 3.63 9.15 5.90 0.79 7.63 13.26
4 0.55 8.40 3.74 6.53 5.05 2.47
5 0.55 5.59 1.82 3.33 4.50 4.77
6 2.03 10.84 0.42 2.94 2.01 3.24
7 1.54 4.23 0.29 0.97 1.04 4.05
8 1.05 7.64 0.26 2.00 0.46 4.46
9 1.43 4.88 0.30 1.16 2.32 3.44

10 0.39 1.49 0.55 2.50 2.04 2.37
11 0.08 3.49 0.35 1.61 1.89 2.63
12 0.34 1.51 0.53 2.01 0.12 2.44
13 0.27 3.35 0.60 0.42 2.32 2.63
14 0.24 2.16 0.34 1.98 0.33 2.24
15 0.15 1.00 0.37 1.95 1.90 0.66
16 0.24 1.82 0.47 0.99 1.21 2.18
17 0.12 0.63 0.33 1.25 2.65 1.04
18 0.57 1.48 0.32 0.89 1.28 0.94
19 0.06 0.59 0.28 0.72 0.08 0.20
20 0.32 0.27 0.08 0.06 0.94 0.12

119

Table 3.8 Normalized Fourier coefficients for large trunk
profiles (coefficient * 10‘ )

Trunk Identification

 

 

Harmonic NAN—1985 NAN—1986 28-1985 28—1986
1 0.26 0.36 0.45 0.16
2 10.77 11.40 5.63 10.61
3 2.35 6.17 7.04 8.30
4 1.65 3.68 3.11 5.17
5 1.81 2.20 0.84 0.92
6 0.80 1.49 2.18 1.42
7 1.17 2.77 0.93 1.73
8 0.78 1.99 0.50 0.39
9 0.63 1.53 0.65 0.43
10 0.70 1.02 0.49 0.59
11 0.23 0.31 0.07 0.19
12 0.12 0.35 0.29 0.38
13 0.18 0.08 0.56 0.42
14 0.24 0.08 0.30 0.65
15 0.26 0.14 0.22 0.26
16 0.20 0.09 0.24 0.21
17 0.11 0.35 0.32 0.26
18 0.18 0.26 0.08 0.12
19 0.19 0.14 0.10 0.52
20 0.13 0.16 0.09 0.24
cases, both circularity and symmetry have decreased
the second year of shaking. This indicates that
harvesting may be causing tree damage and hence,
redirection of growth.
Small trees tend to exhibit most of their shape

(frequency) Change in the low harmonics (2nd_4th) indicating

gradual, smooth shape changes. This may result from the

fact that although the tree is smaller than a mature tree in

relation to the magnitude of shaking force, the young tree

puts up less mechanical resistance to vibration and hence,

is more susceptible to internal damage. Furthermore, in

young trees, the bark system is more sensitive to

compression and shear failure. Older trees, on the other

120

hand, exhibit a greater resistance to shaking and thus, with
an equivalent clamping pressure induce more energy
dissipation at the clamp pad-tree interface and thereby
invite greater external damage via splitting and stripping.
Older trees therefore display their shape (frequency) Change
more conspicuously at the higher harmonics.

Frequency shifting was investigated in order to
determine the similarity between the two profiles from year
to year. Cross-correlation of the frequency spectra of the
two profile plots for each tree was calculated as follows:

012(0) = ——£— ° ?1 fl(w)f2(w+0) d0
01 w=0

In digital form, this appears as:
1”12(0) = i— ' (£1 fl(w)f2(w+0)

01 w=0
Cross-correlation plots are shown in Figures 3.27 -
3.29. The high values are at w=0 for all plots indicating
that for the most part, frequency distribution within a
profile remains the same. However, a comparison of the
figures reveals that as Change in shape decreases, the peak
around 0:0 becomes narrower. Trunk 28 for example, changes
very little in shape, which evidences a sharp narrow peak in
the cross-correlation plot. Trunk A on the other hand,
changes shape significantly and reveals a wide peak near

w=0. Therefore, changes in profile may also be revealed in

cross-correlation plots.

121

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124

3.5 Comment
Although this was a preliminary investigation, the
methods presented in this chapter for analysis of tree trunk
profiles have suggested some indicators of tree damage.
Bandwidth, invariant moments, and frequency decomposition
seem particularly suited to analyze the problem. Further
experiments should be conducted with many tree sizes and a
set of experiment controls to compare statistically the
effects of wind, light, pruning, and staking, as well as

shaker damage, on tree trunk shape.

The implementation of all of these techniques is quite
tedious due to the effort required for digitization and
processing. Advances in current technology, however, such
as minicomputer imaging systems and dedicated coprocessors
would make this type of analysis fast and simple. Laser
optic systems capable of performing Fourier transformations
optically are another possible mechanism by which this could
be simplified. Advances in image processing equipment will

surely aid in an endeavor of this nature.

 

CHAPTER 4

SPECTRAL CHARACTERIZATION OF SHAKER PATTERNS

Direct clamping of a mechanical shaker to a tree trunk
has proven to be a very effective method of harvesting
cherries (at least in the short run). High—powered machines
currently harvest 60-100 trees/h. In recent years, orchard
life expectancy has decreased from 30 years in the late
1960's to 15 to 20 years currently (Burton et al., 1986).
The shaking of young trees (4 to 8 years of age), with trunk
diameters as small as 5 cm (2 in.), is believed to
contribute to this degeneration. Bark stripping, bark
splitting, and cell damage in the phloem and cambium layers
resulting from excessive shear, radial or tangential
stresses induced by undesirable dynamic shaking patterns are
all suspected causes of tree decline. Excessive relative
displacements between the trunk and shaker may provide an
indication of excessive transient dynamic stresses.

Real-time vibrations of a commercial trunk shaker and a
cherry tree were analyzed and characterized according to
shake pattern. Sensors and signal conditioning devices
provided representation of X and Y accelerations of the tree
and shaker, and the positions of the rotating masses.

Waveforms were digitized, calibrated and

125

126

characterized in both time and frequency domains.
Accelerations were integrated twice to give absolute
displacements at the trunk shaker and the tree.
Integrations were performed in the frequency domain rather
than in the time domain because the time domain integrations
were unstable and dominated by low frequencies.

Resulting patterns revealed extreme displacement
transients during shaker start-up and shut-down resulting
from passage through a low natural frequency in the system.
Low frequency shaker tests confirmed this resonance
phenomenon. Elimination of potentially high transient

stress necessitates shaker redesign.

4.1 Commercial Trunk Shaker Design

 

A C-clamp fixed-eccentric mass inertial trunk shaker
was obtained from the Friday Tractor Co. (Hartford, M1) for
characterization of the real-time dynamic behavior of
shaker-tree vibrations (Figure 4.1). The total mass of the
shaker was 635 kg (1400 lb) including two 40 kg (88 lb)
semi-circular unbalanced rotating masses. The radius of
each mass was 17.1 cm (6.75 in.). Each mass was attached to
a shaft, chain-driven by its own 2.8 L/s (44 gpm) 10,345 kPa
(1500 psi) counter-rotating Vickers hydraulic vane motor.

The shaker was mounted on a 2250 Mount—O-Matic loader
frame of a 42 PTO kW (56 PTO Hp) Hydro-84 International
Tractor (Figure 4.2). A frame was constructed to suspend
the shaker at the three points recommended by the

manufacturer. Rubber bushings on both ends of the three

127

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129

suspension bars isolated shaker vibrations from the tractor.

A separate PTO-driven hydraulic system mounted on the
rear of the tractor powered the shaker drive motors. A 35
tooth sprocket on the PTO stepped up the pump driven speed
2.7:1 to a 13 tooth sprocket on a Hydreco hydraulic gear
pump. A 150 L (40 gal) reservoir, equipped with a return
line oil filter and master shut off valve, was mounted above
the PTO and pump. Hoses of 1.9 cm (0.75 in.) ID distributed
fluid from the pump to a flow divider for equal allocation
to continuously variable, pressure-compensated flow control
valves controlling each shaker drive motor. Separate valves
regulated oil flow to each shaker drive motor such that the
angular velocity of each mass could be independently
selected. A 45 tooth motor sprocket then stepped up mass
velocity by chain driving an 18 tooth sprocket on the mass
shaft.

A double acting 8 cm ID x 61 cm stroke (3 in. x 24 in.)
hydraulic cylinder activated the C-clamp for trunk gripping.
Cylinder pressure was derived from the tractor's hydraulic
system. At 12,415 kPa (1800 psi), the hydraulic system
could provide 0.4 L/s (6.3 gpm) at 1500 engine r/min and 0.7
L/s (11.0 gpm) at 2200 engine r/min. Clamping pressure was
set at 4,830 kPa (700 psi) in a separate circuit; the
clamping pressure was unaffected by operation of the shaker
motor drives.

Two cylindrical rubber pads (19 cm OD, 8 cm ID, and 55

cm long, 7.5 in. x 3.0 in. x 21.5 in.) were fastened in

130

support slings in the clamping jaw. A lubricant was applied
to each sling per manufacturer's recommendations; the sling
was then covered with an attached rubber flap prior to
shaking to reduce shear force on the tree bark by providing
a slip surface between the sling and flap.

During Operation, the loader frame tilt mechanism was
used to set the shaker perpendicular the the trunk at the
point of tree attachment (thereby minimizing shear forces).
Clamping pressure for shaking 6.5 cm (2.5 in.) to 16.5 cm
(6.5 in.) diameter trunks was set at 4,830 kPa (700 psi) as
recommended by Frahm et a1. (1983) and monitored on the
hydraulic system with a 10,345 kPa (1500 psi) pressure gage.
Clamping circuit check valves prevented clamp movement
during shaking (Affeldt, 1984).

During shaking, engine speeds of 1500 and 2200 r/min,
corresponding to pump outputs of 1.9 L/s (30 gpm) and 2.5
L/s (40 gpm), respectively, at 10,345 kPa (1500 psi)
provided shake frequencies of 9-10 Hz (560-600 c/min) and

14-15 Hz (840—900 c/min) according to the design equation:

' — *
FreQuency (Hz) = [Engine R/MIN 100] 0°4

 

60

Engine and PTO r/min were monitored on the tractor
tachometer.

I needed the engineering parameters for the trunk shaker
in order to analyze the tree—shaker system. The shaker
center of gravity (shown in Figure 4.1) was found by

balancing the machine on the tip of a 5 cm x 5 cm (2 in. x 2

131

in.) piece of angle iron on two orthogonal axes (Affeldt,
1984).

Spring and damping coefficients for the three-point
shaker suspension design were found by testing (Esch, 1986).
A rectangular, rigid steel test frame was constructed around
the trunk shaker body and attached to the tractor loader
frame which supported the shaker. One side of the test
frame was then attached to a vertical steel girder in the
engineering machine shop to provide absolute rigidity. The
shaker (suspended from the loader frame in its operating
position) could then move with no vibration feedback from
the loader frame.

Spring coefficients for the shaker were found by
applying a force to the shaker body in one of the three
directions X, Y, or 0, and measuring the corresponding
displacement (Table 4.1). The point of force application on
the shaker for each directional test was selected as the
point which, when force was applied, caused motion only in
the desired direction. A Linear Variable Differential
Transformer (LVDT), mounted between the rigid test frame and
the shaker, provided an electric signal proportional to
shaker displacement. A 2.2 cm ID x 7.6 cm stroke (0.875 in.
x 3 in.) 48,275 kPa (7000 psi) hydraulic cylinder, also
mounted between the rigid frame and the shaker body,
equipped with a pressure transducer provided a signal
proportional to cylinder pressure.

Transducer signals were collected in an Analogic Data

132

 

Table 4.1 Linearized spring and damping coefficients
for a C—clamp eccentric mass inertial trunk
shaker for cherries.

 

 

 

 

Direction Masses Installed Masses Not Installed
Damping (C) Spring (K) Spring (K)
(%) (N/mm) (N/mm)
X 0.18 86.0 70.4
Y 0.16 153.2 137.2

 

6000 Waveform Analyzer (Analogic Data Precision, Danvers,
MA) for calibration. Pressure signals were converted to
forces via multiplication by the appropriate cylinder inside
area. Data were plotted as force versus displacement with
the slope equal to the suspended shaker spring constant.
Calculations revealed linear spring constants of 86.0 N/mm
(490 lb/in.) in the X direction and 153.2 N/mm (875 lb/in.)
in the Y direction with small displacements of 7.6 cm (3.0
in.) about the shaker's equilibrium point. For larger
displacements, spring coefficients became nonlinear.

The same system was used for determination of the
damping ratio (C). The hydraulic cylinder was equipped with
a quick release mechanism. The shaker was displaced to a
maximum position in the desired test direction (X, Y, 8),
then released instantaneously to allow free swing.
Displacement traces from the LVDT provided data for
determination of damping ratios via the Logarithmic

Decrement Method.

133

 

Table 4.2 Linearized spring (K) and damping (C)
coefficients and natural frequencies (wn) for
Montmorency cherry trees.

 

Tree Diameter (cm)

 

 

Property 6.5 11.0 16.5

K (N/mm) 12.7 144.5 657.9
C (%) 0.12 na na
wn (r/s) 2.8 na na

na: not available

 

A similar procedure was used to obtain the spring and
damping coefficients for several cherry trees of different
sizes (Table 4.2). The higher spring coefficients of larger
trees made determination of damping coefficients unreliable
with the equipment utilized.

Damping ratios for the shaker appeared constant over
the displacement range tested. Cherry tree shakers normally
operate at less than 3.8 cm (1.5 in.) peak-to-peak
displacement. Since spring and damping coefficients were
linear over this range in laboratory testing, a linear,
second-order, lumped mass vibration model was used to
compare spring and damping coefficients found in the
laboratory with values calculated from free (unloaded)
shaker displacement traces:

X = x + e°sinwt
d2

(M—m)k + m -- (x + e°sinwt) = - Kx - Ci
dtz

134

Mi + Ci + Kx = (mew2)sinwt
Where:
Mass of shaker
Mass of rotating unbalance
Shaker damping property
Shaker spring property
Eccentricity of rotating unbalance

03:05::
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The general solution is:
X(t) = Xle'Cwnt°sin(/l-;2 wnt +¢l) +

mew2°sin(wt - ¢)

 

 

/ (K — Mw2)2 + (Cw)2

 

 

Where:
w = Natural system frequency (rad/s)
C = C/Cn = C/2mwn = Damping Ratio
Cw 2C(w/wn)
Tan¢= :
K - sz l - (w/wn)z

The resonant amplitude is then:

 

 

 

 

2
ME = (w/wn)
me /(1 - (w/wn)2)2 + (26(w/wn))2
Therefore:
(me/M)
x = --—— = x
2C res
And:
me
X: =XSS
M
Finally:
Xss
C1 =
2Xres

Data for theoretical calculations are shown in Table 4.3.
Table 4.3 shows close agreement with the actual
coefficients for free shake. Very little change from free

shake to tree shake was observed; this indicates that in a

135

 

Table 4.3 Theoretical damping ratios for a C-clamp
eccentric mass trunk shaker.

 

Shake Condition Damping Ratio

 

 

 

C1 C2 C3 Cave
Free Shake 0.19 0.22 0.18 0.20
6.5 cm Trunk 0.25 0.25 0.27 0.26
11.0 cm Trunk 0.22 0.25 0.19 0.22
16.5 cm Trunk 0.25 0.30 0.33 0.30
dynamic state, the shaker appears to dominate. Tree

properties tend to have little effect on the shaker
vibration possibly because of the large mass of the shaker
body and rotating masses in comparison with the effective
mass and stiffness of the tree.

Finally, the center of rotation of the shaker (shown in
Figure 4.1) was found by locating the coordinates of the
node where no X or Y displacement occurred during torsional
vibration. This center of rotation is greatly displaced
from the shaker center of gravity due to the force
distribution in the suspension bars created by the
suspension system. The center of rotation with the tree
suspension

attached may likely differ from this free

rotation point.

4.2 Instrumentation for Vibration Sensing

 

Three accelerometers, two at one location and one at a

third, were strategically placed on both the trunk shaker

136

and a tree in order to characterize planar motion (X, Y, 0)
in real time. On the shaker, two accelerometers were placed
at the base of the pad on the shaker frame (Figure 4.1) to
detect X and Y motion (A5, A6) while a third was placed at
the shaker center of gravity to detect X motion (A4). A
fourth sensor (A3) was placed in the Y direction at the
shaker center of gravity to verify corresponding signals.

Two 0.8 cm (0.3 in.) diameter holes were drilled
radially in each tree trunk 900 apart and 46 cm (18 in.)
above the ground plane. A single X axis accelerometer was
placed in one hole while a 16 cm3 (1 in.3) aluminum block
was mounted in the second hole with an X and Y accelerometer
attached (A0-A2, Figure 4.3).

Sunstrand (Sunstrand Data Control, Inc., Redmond, MA)
accelerometers were used in all tests. The accelerometers
had natural resonant frequencies of 40 kHz, well above the
shaker vibration range, and time constants of 20 us,
providing frequency response of 0.02 to 5000 Hz with 5%
underestimates at the low frequency end and 5% overestimates
at the high frequency end. With an expected shaker—tree
response spectrum of 0.1 to 30 Hz (complex vibration of two
15 Hz rotating masses), the transfer function of these
sensors for this application was almost exactly 1.0. The
acceleration range was i 250 g (1 g = 9.8 m/sz) with i l %
amplitude linearity.

Calibration of accelerometers was accomplished by

constructing a vibration table consisting of a 40 oz (1135

137

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g) magnet loud speaker firmly mounted onto a laboratory
frame. A test accelerometer was mounted onto the speaker
along with with a calibrated (National Bureau of Standards
(NBS) traceable) accelerometer of the same frequency
specifications. The speaker was driven by a frequency
generator capable of generating white noise. The driving
signal was band-limited from 0 to 100 Hz.

Output signals from the two accelerometers were fed
into a Hewlett Packard 5423A Structural Dynamics Analyzer
through an HP 54410A A/D Converter. Spectra for each signal
were calculated and then the transfer function, in magnitude
and phase, was derived between the two. This provided a
calibration reference to the NBS-traceable standard for all
test accelerometers.

Since the vibration amplitude of the speaker was very
small in comparison with vibration amplitude of the
mechanical shaker, the accelerometers were also calibrated
in a separate test for output voltage per unit displacement
by mounting them on a swash-plate driven, reciprocating
plunger (Affeldt, 1984). Plunger displacement was 1.09 cm
(0.43 in.) at an operating frequency of 11.3 Hz (676 c/min).
The signal output was amplified with a Piezotron Coupler or
a Kistler Model 503 charge amplifier, then integrated twice
by hardware integrators. Displacement signals were recorded
on the Data 6000 and analog tape recorders for reference and
calibration.

Proximity sensors (PSA & PSB, Figure 4.1), operating on

139

electromagnetic induction principles, were mounted to
monitor frequency and angular position of each eccentric
mass. A steel gear was mounted on each shaft to cause the
flux changes in the magnetic field necessary for sensing by
the nearby coil. Each gear had one tooth removed. This gap
was aligned with the radial position corresponding to the
center of mass of the rotating mass, thereby providing a
reference mark to determine mass position in the output
data.

Proximity sensor pulse shape was uniform except at the
gap where an extra half pulse was produced. Pulse voltage
was proportional to angular shaft velocity and was adjusted
by changing the gap between the sensor head and the gear
teeth. Mass position at any time was determined by counting
the pulses since the last reference pulse and referring this
to the number of teeth on the particular gear in use. The
more teeth on the gear, the higher the angular resolution.
Because of waveform analyzer speed and memory limitations,
the pulse frequency was limited to 25% of the digitizer
frequency (Nyquist demands at least 50%), thereby limiting
the number of teeth.

Two LVDT's were available for vibration sensing along
with the accelerometers. LVDT's are more accurate at low
frequencies and would therefore complement the accelerometer
response as verification. These sensors were connected to
measure displacement in both the X and Y Cartesian

directions on the tree (Figure 4.3). The LVDT's were just

 

140

below and vertically aligned with the X and Y accelerometer
sensors to directly record trunk displacement. In free
shake tests, a small 5 cm x 10 cm (2 in. x 4 in.) board was
placed in the clamp, to which all tree sensors were
attached. A Daytronic Model 300C amplifier with a type 61
module provided a 3 V excitation for the LVDT. Output
voltage was linearly proportional to rod displacement on the
i 0.025 cm (i 0.010 in.) scale and ranged from i 40 mV DC.

Planar motion of the tree (X,Y) made it necessary to
modify the attachment mechanism of the LVDTs such that
"crosstalk" caused by motion perpendicular to the LVDT's
sensing direction would be minimized. This was accomplished
by constructing a frame around each LVDT to which the back
end of the LVDT slide rod could be attached via a light
spring (Figure 4.3). This spring provided tension on the
rod to pull it away from the trunk and eliminate binding.
The front end of the rod was then fitted with a 3.0 cm (1.2
in.) long 0.2 cm (0.08 in.) diameter spring which provided
no flexure in the longitudinal direction but maximal
deflection in the lateral direction. By preforming the
spring with a small vertical bend, "crosstalk" from motion
perpendicular to the desired sensing direction was
minimized.

Finally, displacement was recorded simultaneously
through a high—speed photography system (Marshall, 1986). A
matrix of high intensity light emitting diodes (LED's)

strategically located at points on the tree and harvester

141

was filmed at high speed from a stationary camera during
shaking. Developed film was then projected frame-by—frame
onto a screen with a movie camera, imaged onto a color
monitor, and digitized to record the position of each LED as
a function of time in order to trace the motion of the
shaker with time. In analyzing the data, this provided an
excellent check on lower frequency vibrations not limited in
accuracy by film speed, optic distortion, LED point source
dimension, or imaging resolution.

Three Piezotron couplers provided a current source and
amplified the accelerometer signals on the tree. Six
Kistler Model 503 charge amplifiers coupled the
accelerometer signals from the shaker. All direct and
amplified transducer signal carrier lines were connected to
recording devices. A four and a fourteen channel Racal
Instrumentation Tape Recorder (Racal Recorders Inc., Covina,
CA) were used to record accelerometer and mass position
sensor signals. These instruments provided a bandwidth of
DC to 5000 Hz on a tape speed setting of 190.5 mm/s (7.5
in./s) with a signal-to-noise ratio of 48 dB at 0.35% P-P
Flutter and i 0.2% tape speed inaccuracy. An Analogic Data
6000 Waveform Analyzer was capable of recording another four
channels of data at 100 kHz and storing data on a floppy
disk. During most field tests, recording equipment was
stationed in an air—conditioned van which provided
protection from dust and temperature effects.

A Vanner Model 80—500 (12 VDC to 120 VAC, 60 Hz, 500 w)

142

voltage inverter was connected to the van battery to provide
120 VAC instrument power (Vanner Corp., Columbus, OH).
Ground potential was obtained through a #12 stranded copper
wire clamped to a galvanized steel rod driven 76 cm (30 in.)
into damp soil at a distance of 1.5-2.5 m (5-8 ft.) from the

van.

4.3 Displacement Tests

 

Displacement tests were conducted on Montmorency tart
cherry trees in the Michigan State University Horticultural
Orchards. All trees were in the same general location and
were presumed to have the same soil base. Nine trees were
shaken, each at 1500 shaker r/min and then at 2200 shaker
r/min. These speeds provided individual mass frequencies of
9 and 16 Hz. The actual vibration transmitted to the tree
was a complex combination of frequencies.

Three trees of 6.5 cm (2.5 in.), three of 11.0 cm (4.5
in.), and three of 16.5 cm (6.5 in.) trunk diameter at clamp
height were selected for testing. The shaker clamp was
positioned orthogonal to the tree trunk at 25 to 30 cm (10
to 12 in.) clamp height according to common practice and was
closed with the tree centered in the pads. Clamping
pressure was 4,830 kPa (700 psi). The pad slings and flaps
were greased prior to each test series. A test at each
engine speed was also conducted for free shake (no tree in
the clamp).

The following were recorded: date, engine r/min, tree

identification data, clamp height above soil surface and

143

accelerometer location with respect to the trunk center and
the soil surface.

All amplifiers were zeroed before each test. The LVDT
slide rods were centered for zero readout. The desired
engine speed was obtained and the data recorders were
initialized. After 1 to 2 s, the operator was signaled to
begin the shake. A shake lasted 3 to 6 s. The operator was
then signaled to end the shake; there were 2 to 3 s of shut
down data at the end of the acquisition period.

Data were recorded on magnetic tape and floppy disk.
While data were being stored on the floppy disk, the LVDT's
were rezeroed and the shaker body was propped with blocks to
prevent vertical clamp slippage on the tree due to hydraulic
system relaxation. The process was repeated for each tree
such that all instrument settings and clamping pressures
were the same at the start of every run.

Data digitized into the Data 6000 Waveform Analyzer
were Collected at a speed of 500 Hz over a 16.4 5 trial
period for a total of 8192 (28) points per waveform. This
point count was significant for the Fourier Transforms used

in the data analysis.

4.4 Frequency Domain Analysis

 

In the laboratory, acceleration and LVDT data were
transferred from magnetic tape to the Analogic Data 6000
Waveform Analyzer for digitization and storage on a floppy

disk. The LVDT data were calibrated directly in the memory

144

of the Data 6000 using the appropriate linear calibration
equation, then plotted using a Hewlett Packard 7475A
plotter.

Mass position data on magnetic tape were also digitized
in the Data 6000 as well as transferred to the input port of
a 16 channel 12 bit analog-to-digital converter (Interactive
Structures, Inc.) for digitization into an Apple III
minicomputer. Although the Data 6000 is capable of
digitization rates up to 10 MHz, memory limitations (14
kbytes per channel) prevented capture of long, high
frequency waveforms. The Apple III can digitize up to 20
kHz with memory allocations up to 256 kbyte. Digitized
proximity data were then transcribed to floppy disk for
later retrieval and analysis.

Proximity sensor data existed in the form of sinusoidal
pulses over the period of the test with interspersed half
pulses resulting from the missing tooth indicator of the
mass' center of gravity. For analysis, a UCSD (University
of California, San Diego) Pascal program was written to
convert pulse data to frequency by converting the time
between pulses into frequency, averaging frequency over one
half mass revolution if the frequency was within 10% of the
desired operating frequency, and storing/presenting output
as frequency versus time with markers identifying the points
at which the mass center of gravity passed the proximity
sensor. If frequency was not within 10% of the desired

operating value, no averaging was performed. Instead,

145

frequency was plotted directly with the assumption that a
rapidly changing start-up, shut—down, or disturbed zone of
operation of prime interest was occurring.

Time domain integration of accelerometer data on the
Data 6000 Waveform Analyzer produced unrealistic results for
displacements because integrated low frequencies masked the
higher frequency shaker vibration of interest. To
circumvent this problem, frequency domain analysis of the
accelerometer data was performed on an IBM PC AT. Data 6000
floppy disks were IBM format compatible although file
headers and data were stored in a non-standard binary—coded
integer format. I wrote a Microsoft Pascal program
(Microsoft Corp., Bellevue, WA) on an IBM PC AT to read a
Data 6000 data diskette, decode the header and data values,
and restore the information in ASCII format. Data were then
suitable for normal programming access.

I also wrote a Spectral Analysis Program in IBM
Professional Fortran (Ryan-McFarland Corp., IBM Corp., Boca
Raton, FL) to read decoded acceleration files, calibrate
data, and convert time domain information into the frequency
domain with a Decimation-In-Time (DIT) Cooley-Tukey Fast
Fourier Transform (FFT) algorithm which uses the discrete
Fourier Transform in a bit-reversed butterfly routine:

A(k) = NE: A(n)°exp_.121mk/N
n=

k 0...N-1

Double integration of time domain data was performed on the

146

frequency domain acceleration data by dividing complex

 

 

 

frequency components by wz:
f(t) = F((D)°ejwto
2n

df(t) . dw

..___. = F(w)°e3wt°jwo
dt 2n

df(t) .

g(t) = ---- where g(t) = G(m)oert.
dt 2.”

G(w) = jw°F(w)

Therefore:
G(w)

 

F(w) =
jw

Then, with the data:
A(k) = Aei‘”t = Acoswt + isinwt = c + di
k = 0...N-l
“0 = (2" * fsampling)/N
w = mo * k
X(k) = A(k)/(oz
k = l...N-l
Integration of the zero frequency is simply integration of a
constant (DC):
A(k) = Aeiet = Acoset + iAsinet = c + 0i
X(k) = c * t2
and was not performed since any DC in the data was a result
of amplifier bias. The DC was thus zeroed out in the
frequency domain since integration would allow it to
obliterate the higher displacement frequencies of interest.

The boundary conditions for double integration were as

 

147

!
"1.) ;

follows: .
x(0) 0 x(0 0
X(w) 0 x(0° 0

vv
II II

Low frequencies resulting from amplifier drift (often
exponential with a very long period) obscured true data and
were filtered by modifying the frequency sequence with a
Hanning (cosine squared) Window:

fit 1 2nt T

w(t) = cos ——— = ———°(l + cos -——) for ltl : -—-

T 2 T 2
= 0 elsewhere
The Fourier Transform of the Hanning Window is then:
T sin nf

T
—'—-—'[l/(l-(fT)2)]
2 nfT

W(f) =

Cutoff frequencies used in the filtering process were
determined by comparing the frequency content of the
contaminated acceleration signal with an uncontaminated
acceleration signal from another sensor and with the LVDT
displacement traces. LVDT's were very accurate at low
frequency response and were reliable as a standard for
comparison.

Convolution of a time domain sequence for filtering
purposes transforms into a frequency domain multiplication.
Therefore, by multiplying the frequency domain acceleration
data with the Fourier Transform of the window function, time
domain filtering results:

A(n) = A(k) * W(f)

N—l
Z a(k)°w(n—k)
k=0

148

Initial filtering in some displacement traces indicated

an insufficient frequency filter weighting. Therefore, the
acceleration data (originally 8192 points) were doubled in
number by linearly interpolating a midpoint between every
two successive data points. All other factors remaining the
same, the resolution doubled, the filter weighting thereby
changed, and the filtering process for these waveforms was
significantly more effective.

Although this process appears to contradict the Nyquist
theory, the error introduced is small when the waveform is
periodic and repeatable. The sacrifice made is in accuracy
of peaks and areas of rapidly changing signal, which may be
drastically over or under-estimated. Here, where the
waveform is known and verifiable, the application of this
method provides the weighting necessary for data filtering.

An Inverse Fourier Transform was performed to transform
the data back into the time domain by reprocessing data
through the same FFT routine with the sign of the exponent
reversed and dividing final coefficients by N:

N-l .
Z X(k)'exp12"nk/N
n=0

X(n) = -l-
N
k = 0...N—l
Final displacement data were plotted as X versus time, Y
versus time, and X versus Y; the latter of which provided a
planar view of the tree or shaker vibration pattern.

Piezoelectric accelerometers are more accurate at

higher frequencies and the LVDT is more accurate at lower

"9. 2

149

frequencies. Therefore, linear X and Y displacement traces
of the tree derived from acceleration data were compared

with LVDT traces for verification.

4.5 Displacement Results

 

Excessive displacements occurring during the transient
start—up and shut—down phases of shaker operation have been
referred to as shaker "gallop". Gallop is an unintended
magnification of shaker displacement beyond the design,
operating, safe, or steady—state limits. This motion is
normally but not necessarily transmitted to the tree in an
observable fashion. By analysis of the dynamics of shaker
and tree, gallop and its causes may be identified and
controlled or eliminated.

The rotating masses of the shaker tended to come up to
speed in about 0.35 s in these tests, and to overshoot or
"gallop" as shown in Figures 4.4—4.12. This is typical of
an underdamped second order linear system and can be modeled
by a system where C < 0.707. Overshoot may result from
loading of the hydraulic pump with the full inertia of the
masses. This loading is transmitted to the power source
(the tractor) which relies on the governor to bring the
engine speed back to steady-state. Shut-down of mass
rotation required 2 to 3 s and often exhibited a gallop at
about 1.5-2.0 Hz rotating frequency, possibly due to low
natural modes of the shaker and tree resulting in a
"beating" or "frequency pulling" phenomena.

Figure 4.4 and 4.5 show the inner and outer rotation

150

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when both masses are operating in a conventional fixed-mass
shaker. These plots exhibit the overshoot and oscillation
(1-2 Hz) to steady-state as might be expected when full
power is suddenly applied to both masses, again loading the
power source. Note that although the inner mass shuts down
quickly, the outer mass continues to run for 1.5-2.0 5
longer. Figures 4.6 and 4.7 display fixed-mass rotation
when only one mass operates during a shake. Overshoot is as
large or larger than with both masses operating, and
settling to steady-state is more rapid. This most likely
results from the elimination of the second mass which acts
as an absorber (filter) of energy peaks. Again, at low
frequency, the outer mass tends to hit a low resistance
state and extend the period of rotation.

Figure 4.8 and 4.9 show the inner and outer mass
rotation when both masses are operating in a conventional
fixed-mass shake of a small 6.5 cm (2.5 in.) tree. These
plots correspond well with the free shake data of Figures
4.4 and 4.5, though absolute overshoot and oscillation to
steady-state differ slightly, possibly due to the response
of the hydraulic pump loading and circuit flow divider.
Slight unsmoothness on the downslope end of rotation tends
to indicate that the masses were periodically absorbing
extra energy and speeding up slightly. This could be the
result of an inertial phasing action resulting from energy
input from the tree-shaker system displacements on shut—

down. As will be shown, shut—down displacements are quite

160

nonuniform.

Single mass operation in Figures 4.10 and 4.11 do not
exhibit this 'energy pickup' by the masses in the shut-down
period, although the outer mass still exhibits a free-
wheeling period at the tail. Figure 4.12 is evidence of an
extreme case of mass oscillation when an 11.0 cm (4.5 in.)
tree is shaken. Displacement response from this tree may be
interfering with the inertia of the rotating masses as they
tend to settle to steady-state.

When attached to the tree, it was observed that
displacement maxima normally occurred during start-up and
shut-down of the shaking mechanism, probably because the
forcing of vibration coincided with the lowest natural
frequency of the tree and/or that of the shaker. The lowest
natural mode of the shaker was found to be 1-2 Hz in both X
and Y directions. Harmonic magnification of system
displacement can result in potentially destructive reactive
forces. When passing through these low frequencies,
fluctuating shaker displacements may require unusual
reactive forces by the tree. These vibrations were evident
in shut-down, possibly due to the forces synchronizing at
system resonance.

Figure 4.13 shows X and Y linear displacement plots for
a conventional fixed-mass shaker in free shake when both
masses are operating. Transients on start-up, resulting
from sudden power application, overshoot steady—state values

by 50% or more. Oscillation in both the X and Y directions

 

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require several cycles to settle. Frequency of this
oscillation envelope is about 1-2 Hz; the same as the first
natural mode of the shaker. Transients often reach 30 mm
(1.2 in.) amplitude while steady—state is usually about 10—
15 mm (0.4-0.6 in.). Though start—up transients may result
from a sudden power transfer from the masses to the shaker
inertia, the shut-down transients appear to occur as a
result of low first natural modes of vibration of the shaker
and tree, combined with some phasing of the masses.
Displacement on shut—down tend to decay, then increase to
potential maximums of 50 mm (2.0 in.). These shut—down or
resonant phenomena normally occur at frequencies around 1.0—
2.0 Hz often starting to build up while at 3.0—4.0 Hz.
Double—peaked maxima and zero displacement values indicate
rapid changes in shake direction and can be seen in the
planar X-Y plot of Figure 4.14. Shut-down, with both masses
operating, may impose significant stress and strain in tree
bark as a result of these amplitude and direction changes.

Figures 4.15 and 4.16 exhibit the same phenomena when
shaking a 6.5 cm (2.5 in.) tree, as in commercial operation,
with both masses. With the current shaker suspension
system, X direction displacements occur slightly larger than
Y displacements. The vector sum causes a shake at angles
between +X and +Y. Y motion normally ends prior to X
motion, possibly from the damping in the different
directions of shake.

By observation, the majority of fruit is removed at

163

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start-up and during the high frequency steady—state
operation. Insignificant amounts of fruit are detached
during shut-down, even though displacements reach maximum
values there. This is a key effect which will aid in
elimination of high-stress displacements while maintaining
shaker efficiency. Growers who indicate that stopping and
starting the shaker during harvest results in an increase in
fruit removal are likely observing the effect of a change in
shake pattern resulting from a change in mass phasing.

Displacements of a single inner fixed—mass operating in
free shake are shown in Figures 4.17 and 4.18. Start-up
oscillations (= 1.0 Hz) are more pronounced and take longer
to settle. Shut-down resonance (= 1.0 Hz) is also present
but the sudden change in shake direction, evidenced by
double—peaked maxima and zero displacements in the
progression of shake, are not present, even though the
direction of shake does similarly change as shown in the
planar plot. Frequency content of this free shake is shown
in Figure 4.19 as compared to that with both masses
operating in Figure 4.20.

The single fixed-mass shake of a small tree is shown in
Figures 4.21 and 4.22 with frequency content in Figure 4.23,
as compared to the frequency content with both masses in
Figure 4.24. Contrary to free shake performance, a
transient peak occurs immediately upon start-up.
Oscillatory decay to steady-state is faster. Finally, shake

of a very large tree (16.5 cm, 6.5 in.) is shown in Figures

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4.25 and 4.26 with frequency spectra in Figure 4.27. Start-
up transients are smaller as well as shut-down resonance,
though it appears that resonance may be occurring at a
higher frequency; about 5 Hz. The first natural mode of the
larger tree, with more heartwood, may be slightly higher.
An extreme transient case is shown in Figure 4.28 where a
medium (11.0 cm, 4.5 in.) tree is shaken with both fixed—
masses at 15 Hz. In agreement with the rotating mass plots,
there appears to be a tree size which is capable of inducing
very large shaker transients.

In summary, displacements resulting from fixed—mass
conventional shakers usually involve transient start-up and
shut-down peaks with sudden direction changes. Single mass
operation is similar and appears to be appropriate as a
basis for analysis and design. Removal of fruit occurs
mainly at high frequency steady-state operation and
therefore, should not be significantly affected by presence
or absence of transients; the maxima which may induce

excessive stress and strain in tree bark.

4.6 Trunk Shaker Analysis

 

The Friday C—Clamp trunk shaker, during steady—state
operation, does create an omni—directional displacement
pattern. The individual masses which rotate asynchronously
(they are connected only by the hydraulic system) may start
with any phase difference, but eventually seek a minimum
energy level at which to operate, though they must "beat" in

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masses are operated in free shake (no tree), the resulting
shaker motion is only omni-directional on start-up and shut—
down, otherwise it is linear and appears to be a function of
the suspension system parameters (Figure 4.29 and 4.30).
Note that in Figure 4.29, the patterns are very nearly that
which is expected, even though the shaker properties have
been found to be nonlinear and difficult to analyze. For
example, the one mass operation would appear as in Figure
4.3la with forces:

2
Fn

Ft

m1 : r1 * 0
m1 at

Neglecting the suspension system (spring force Fkr damping
force Fc)' we see that:
2F = Ma = Fn + Ft
A single driving function would appear as in Figure 4.3lb
with resultant planar motion as in Figure 4.3lc. This
occurs simply due to the centrifugal force Fn. If a slight
radial acceleration occurs due to the hydraulic system
(which is very likely), this small force will shift the
circular planar pattern. The restoring force caused by
gravity (a pendulum support system) then acts against the
tangential force Ft and a pendulum oscillation is
superimposed on the planar circular pattern as in Figure
4.29a. Start—up transients likely excite pendulum motion.
Figure 4.29b shows a different phenomenon and relies on
the assumption that without resistive motion of a tree, the

two masses synchronize into a minimum energy state in which

forces begin to cancel as shown in Figure 4.32a with near

 

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185

pure centrifugal normal forces:

2
F = m * r * w

l l l 12
F2 = m2 * F2 * 02

Since ml = m2 and r1 = r2, we can assume that 01 = 02 at
steady—state in free shake. Thus, with the masses in phase,
but rotating opposite, we have a flip—flop effect of the
forcing function as shown in Figure 4.32b with resulting
motion shown in Figure 4.32c.

This shake will therefore be linear with about twice
the amplitude of a one—mass shake. Any tangential
acceleration of the masses will induce some shifting motion.
This again could be induced from the start—up transient
(which reveals itself as an omni—directional shake at the
beginning of Figure 4.29b). This theory agrees with the
data shown in Figure 4.29b. The addition of springs and
dampers from the suspension system will tend to rotate this
line off—phase.

The assumption was made that the masses were in phase.
This does not have to hold. If the masses are 1800 out of
phase, the same result occurs except that the motion will be
shifted 900 to the Y direction (with spring and damping
effects neglected). A force couple or torque will also be
present, however.

Figure 4.30 shows the desired omni-directional response
when shaking a tree. Notice that the motion is actually
cycloid-shaped, thus pushing and whipping the tree to the
side (assuming trunk motion resembles shaker motion). The

current Friday shaker, however, has transient gallop

186

problems presumably due to the low natural frequency of the
system (tree and shaker) which we are required to pass
through to get to wdrive as shown in Figure 4.33.

From previous displacement data, it has been stated
that gallop will reach twice the steady-state displacement
i.e. XM/me = 2.0. From Figure 4.33, we see that this occurs
at about w/wn = l (resonance) where c = 0.25. In fact,
damping ratios found earlier in Table 4.1 agree very closely
with this theoretical value.

The current design then has the problem that the system
natural frequency is too low. As a first look, we see that
the mass of the shaker is much greater than the mass of the
tree for small trees. Therefore, by decreasing the mass of
the shaker or increasing the spring constant of the shaker,
the natural frequency of the shaker could be increased
beyond the drive frequency and thus gallop, which occurs
partially due to resonance, would not occur. With “n =

K/M > 0d, amplitude could be limited.

effective
Unfortunately, however, as trees get larger than 16.5
cm (6.5 in.) diameter, their mass becomes significant and
the system requires an actual multi—degree of freedom
analysis which becomes quite complex and has been attempted
by many researchers with a multitude of approaches.
The normal solutions for resonance problems are to: 1)
move the drive frequency; 2) move the natural frequency; 3)
increase damping; or, 4) power—up through and brake—down

through the resonance point. Other more elaborate schemes

187

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Figure 4.33 Amplitude and phase of a linear,
second order system.

188

exist but are rare and not economical for this application.

The drive frequency cannot be shifted. Previous
researchers in the past 30 years have determined the optimal
stroke and frequency for cherry removal by mechanical
shaking, and it is well above the problematic natural mode.

Shifting the natural frequency has just been discussed
but poses realistic problems in material properties (mass,
strength) as well as problems with different tree sizes.
Not much can be done about the natural frequency of the tree
(about 1 to 3 Hz).

Increasing the damping may help to reduce gallop but
will probably reduce the steady—state value too, simply
dissipating needed energy. A time—varying damper may
potentially permit a high shaker damping ratio on start-up
and shut-down to avoid resonance with a subsequent low
damping ratio during steady-state shake. Undesirably,
however, the shaker carrier would be required to absorb more
vibration during transients.

Power—up and brake-down are simple concepts but
difficult to implement directly with this system. I tried
to power-up through resonance before the system could
respond. However, with all the available tractor power,
there was little evidence that start—up gallop had
dissipated. Brake-down has not been tested directly but
would require strong materials to ensure "braking" of the
masses and not "breaking" of the unit. Braking also

requires a secondary power unit, or energy sink, to rapidly

189

decelerate the rotating masses. Brake-down through

resonance, however, would theoretically reduce bark damage.

4.7 Need for Shaker Redesign

 

 

Vibratory displacement patterns resulting from
mechanical shaking of cherry trees with a fixed—eccentricity
inertial trunk shaker reveals displacement maxima at
transient start—up and shut-down periods. These transient
extremes exceed steady-state amplitudes by as much as 100%
and may impress dynamic stresses and strains not previously
recognized in static analyses. Biological limits of cell
strength in bark and cambium may well be exceeded since
stress and strain from this phenomenon is superimposed on
static clamping pressures.

From an engineering standpoint, the tree acts as a
complex beam, with a stiffness and a damping property. In
the static or motionless sense, a push on the tree causing
displacement creates a force 'Fk' from the spring property
of the tree. If the shaker and tree move, a damping force
is created 'FC', which in a simple sense is proportional to
the velocity of the motion. An inertial force 'Fm' is also
present from acceleration of the shaker and tree masses.
Hence, the sum of these three forces may exceed previous
static compressive force recommendations.

Both the tree and the shaker individually have very low
natural frequencies. During start—up and shut—down then,
with fixed-eccentric masses, both tree and shaker natural

frequencies are encountered. Vibrations in machinery are

190

often eliminated by changing physical prOperties of the
system or by conventional vibration absorbers. Tree
properties, however, are fixed and vibration absorption is
counter to the harvesting process. Therefore, we need a
method of reaching the desired shake frequency while
transferring minimal energy at the critical resonance
frequencies when passing-through. Typical engineering
methods to avoid resonance, as discussed in section 4.6, are
difficult if not unreasonable to implement in this
application. Hence, a new method of getting masses up to
rotational velocity with minimal energy transfer at

resonance, is needed.

CHAPTER 5

SHAKER REDESIGN AND EVALUATION

5.1 93 the Prospect of Node Evasion

Shaking force is the resultant of all forces acting on
the frame of a shaking mechanism. Shaking motion is usually
produced by inertial forces. If the resultant of all forces
due to inertial effects acting on the frame is zero, then no
shaking (linear displacement) is produced. Although linear
shaking forces may sum to zero, there may nevertheless be a
shaking couple (rotational displacement) present. Balancing
the mechanism thus consists of eliminating both the shaking
force and the shaking couple. In most mechanisms, it is
usually not practical to provide a means for completely
eliminating both. In fruit harvesting however, it is
important to eliminate shaking couples at all frequencies
(to prevent torsion on tree bark) and all linear shaking
forces near the low natural frequencies (to prevent
"gallop").

The low natural frequency modes of the tree, the
shaker, and the tree—shaker system cause unstable,
unproductive, and damaging vibrations when the driving force
is oscillating near these same frequencies. A means to

circumvent these vibration "gallops" with minimal economic

191

192

investment and minimal change in design was sought.

The customary methods of altering vibration
characteristics of a mechanism, as mentioned in Section 4.6,
are not practical in this application. Total vibration
isolation is contrary to the shake—harvesting objective and
a power—through resonance method requires an impractical
power source which could potentially damage both the tree
and shaker outside the resonant region.

A more promising approach, therefore, is to isolate
vibration near the low resonance frequencies and deliver
shaking energy near higher shake frequencies. In this
investigation, two methods are discussed to accomplish this
task. The first method involves the concept of vibration
balancing by the phasing of oscillators. The second method
involves changing the eccentricity of a single mass or a

pair of masses.

a; Phasing
Oscillators, or vibration exciters, usually consist of
a fixed—eccentric mass rotating in a plane. The
displacement of a shaker body can be considered as a linear
displacement of some point on the body plus an angular
displacement of the body about this point. For example, if
the acceleration of a point B (Figure 5.1a) is known as AB,

then the acceleration of any other point C is:

A = A + A + A
C B C B C B .
/ normal / tangential

given the angular velocity 0 and the angular acceleration a

 

(a)

(lo)

Figure 5.1 Geometry 01“ rigid body motion
a) relative motion lo) Force
and torque.

194

of the body. Given the body of Figure 5.lb, with G as the
center of gravity and AG the acceleration of G with a known
in magnitude, then a force and torque can be found that must
correspond to produce AG and a as:

F
T

MAG
Ia

where I is the mass moment of inertia of the body about an
axis which passes through G and is perpendicular to the
plane of rotation. A single force F can act at a location h
units from G and replace both the force F and the torque T

where:
T = Fh = Id

h Ia/F

The inertial force is then defined as the reversed
resultant force and the inertial torque is the reversed
resultant torque. By D'Alembert's Principle, an inertial
force and an inertial torque can be added to a body which is
acted upon by a resultant force and a resultant torque to
bring the body to equilibrium. This is a key concept that
will be applied to a system of rotating masses in a shaker
body to avoid low frequency resonance.

A single oscillator can be attached to the center of
gravity G of the shaker body Ms, as shown in Figure 5.2a,
with the shaft rotating at a constant speed “d and a single
concentrated mass m1 at radius r1. This planar analysis
provides the three degrees of freedom (X, Y, 9) which must

be force-constrained and moment-constrained for prevention

of shaking motion. The forces on this rotating mass are

 

195

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196

shown in Figure 5.2b where:
Ft = mat at = 0 when “d = constant
an = Vz/o = (wo)Z/o = wzo
_ _ 2
Fn — ma — mm o
The conditions to balance the shaker body Ms are:

2M = Id = O
ZFi = mai = 0

Neglecting tangential forces, the force vector of a single
oscillator m1 is always directed through G thereby causing
no rotational moment:

F x p = 0 = EM = Ia with F || 9

n
With only one oscillator, however, there is no cancellation
of the forcing vector F and thus, motion is imparted to Ms

through G:
2F = ma- = ma = F ¢ 0

1 n
Rigid body motion, in free space, will then occur unless m =
0 and r = 0. Force and moment polygons for the single
oscillator case at the center of gravity and off the center
of gravity are shown in Figures 5.2 c,d.

Seeking a solution to the vibration "gallop" phenomena
using D'Alembert's Principle, the concept of vibration
analysis for dynamic rigid bodies is extended to multiple
masses ml...mn with multiple radii r1...rn with the
following assumptions:

1) The shaker body lies in planar free space and is
capable of X, Y, and e motion.
are not

2) Oscillator masses ml...m and radii r1...r

n n

necessarily equivalent.

197

3) Oscillator location in the rigid body is not
constrained.

4) The center of gravity of the system can be located
and referenced; the center of rotation is unconstrained,
however.

An arrangement of oscillators is sought which will
provide a configuration in which no motion is imparted to
the body and which can provide a desirable shaking pattern
for fruit removal with proper phasing control above the
resonant frequencies. If all masses are constrained to
rotate at the same r/min, then any phase relationship set up
by the operator will repeat every 2n radians. If masses
rotate in the same direction, a phase difference ¢ between
them will not be a function of time ¢(t) but will remain
constant ¢ = y Vt, even if mi = mj and ri = rj. If m°r
differences exist, they will be evident in the forcing
functions.

The two oscillator system, quite common in shaker
design, yields to two analytic approaches: the first being
the simplest and most obvious Figure 5.3a. Here, both
masses are fastened to the same shaft. By analysis:

2F = miai = 0
Fli - F2cos(l8O—6)i + F2sin(180-9)j = O
Fli + cmosei + Fzsinej = 0
For equilibrium:

-1 or e
0 or 6

TT
11'

i: F + F cose = O cose
j: Fzsine = O sine

For forces to cancel, the phase difference must remain at n

radians Vt and:

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F1 f F2
mlrl ‘ m21‘2
For moments:
*ZMC - Id 0
+ F2 * r2 = 0
But F1 I} r1 I.and F2 || r2 so EM = 0

Therefore, on the same shaft, two oscillators with this
frequency and phase relationship will impart no force or
moment to the platform. For all practical purposes,
however, the tree can be considered to be the center of
rotation. Therefore, moments will occur when the phase # n.
In the more common commercial shaker design, the oscillators
are on separate shafts. By moving the oscillators off the
center of gravity (Figure 5.3b):
Flcosei + Flsinej + cmos(9+¢)i + Fzsin(9+¢)j = O

Flcose + cmos(6+¢)
Flsine + F2sin(9+¢)

II II
0

Balancing and dividing:

tan 9 = tan (e+¢)
Therefore, ¢ = (2n+1)n radians n=0,l... will satisfy this
condition and can be satisfied at every instant only when
both oscillators rotate in the same direction at the same
speed (wd). For moments:

Flsine ° L1 — Fzsin(6+n) ° L = 0 where ¢ =
Flsine ' L1 + FzsinS ‘ L2 = a

Transients can only be zeroed when ¢ = 2nn n=0,l... Since
forces cancel only for ¢ odd and moments cancel only for o
even, then it can be concluded that two oscillators mounted
at separate centers cannot simultaneously prevent both

linear and torsional vibration regardless of the phasing.

 

 

200

If oscillators are rotated counter to one another with
¢ = n and at the same frequency wd, then forces would be
zero Vt but moments would not be zero. In summary, then,

for a two—oscillator body:

¢ = 2m: (1)1 = (02 = (Dd 2F # 0 2M = 0
= (2n+l)fl ml = ”2 = “d 2F = 0 2M # 0
2nn < o < (2n+l)n 2F # 0 EM # O

The force and moment polygons for the two-oscillator case
are shown in Figure 5.3c. It is evident that unless F1 = F2
= F, the force polygon will not close (zero resultant) which
confirms a phase angle of n radians between the functions.
Therefore, the masses must rotate in the same direction at
the same frequency w. with this, moments are shown as:
—Flsinwt°Ll = Fzsinwt°L2
Thus: —L1 = L2
And the only two fixed—mass oscillator system which will
impart no motion to the shaker or tree is where both masses
connect at the same center (trivial case: —L1 = L2 = 0).
Furthermore, as long as both concentric oscillators rotate
in the same direction at w and Emiri = 0 for some t, then no
motion will be imparted to the body Vt (assuming no
acceleration at or other external influences).

This produces a very interesting result. Many
commercial vibratory fruit and nut harvesters incorporate
two fixed-mass oscillators which physically cannot be
located at the desired point of no rotation - the tree. In
spite of mechanical restrictions to rotation, there is the

possibility of moments about the tree, an unwelcome

201

precursor of bark stress and strain. Mechanical
restrictions to rotation seldom exist as most shakers are
vertically suspended by three or four hangers to allow free
motion, limited only by the damping properties of the hanger
bushings and gravity which discourage horizontal and
vertical displacement. These configurations cannot prevent
small amounts of rotation of the heavy shaker and clamp
which easily strain susceptible tree bark during harvesting.

Since a two-oscillator system cannot balance the shaker
body within reasonable physical dimensions, a three-
oscillator system is examined, Figure 5.4a. The force
polygons for a three—oscillator system are shown in Figure
5.4b. The analysis proceeds as follows, Figure 5.4C:

ZF = 0 i: Flcoswt + cmos(mt+¢l) + F3cos(wt+¢2)
' j: Flsinwt + Fzsin(wt+¢l) + F3sin(wt+¢2)

II II
OO

2M = o F sinwt°L — F cos(wt+¢ —90+w )-L +
a F§cos(mt+$2-9ng2)°L3 =10 l 2

Where: ¢l and ¢2 are relative phase angles
$1 and $2 are relative mounting angles

Several three-oscillator scenarios are now possible. By

letting wt + 0:

H‘
0

F1 + F cos¢ + F cos¢ = 0
Fl = _ 2COS$1 — 3COS$2

The trivial case is to let o1 = ¢2 and F1 = F2 = F3 = F as
shown in Figure 5.5. To satisfy moments, L1 = L2 = L3 = 0.
However, as 2F = O for vibration, EM = 0 only about the
oscillator's center of rotation. With a tree attached
physically at some other point on the body, force vectors

would create moments about the tree, that would be damaging

 

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Figure 5.5 Three oscillator shaker excitation
(a) simplest configuration (i0) Force
and moment polygons.

 

204

to the bark.

If ¢1 = ¢2 = n, and F3 = Fl + F2 as shown in Figure
5.6, an interesting configuration arises. With ml = w2 = w3
and L1 = L2 then 2F = 0 and 2M = 0 Vt. In fact, as long as
ml = ”2 = w3 = w and Fl'Ll = F3-L2 with F2 at the center of
gravity and SF = 0, then the system is balanced Vt. The
violation here is that F2 is at the center of gravity which
is the desirable location for the tree.

By examining the general equations and force and moment
polygons, a third balanced three-oscillator configuration
can be determined which is analogous with electrical three-
phase phenomena. Field balance methods require that force
and moment polygons close for dynamic equilibrium. By
examining the moment polygon, we see that if moments are
360°/n out of phase (where n is the number of oscillators)
the polygons will close. Applying this theory to the
general three-oscillator scenario gives:

A¢ = 36OO/n = 120°
_ 00

¢ _
.3 = 1200
$2 = 2400

Having found a desirable set of relative phase angles,
forces can be checked and moments can be used to solve for
relative mounting angles (w):

i: F + F cos¢ + F cos¢ = 0
1 2 1

Any relationship of forces as given above balance the force
field. For simplicity, let Fl = F2 = F3 = F. Moments are

then:

 

 

205

 

 

 

 

 

A 2
F2=mer2w Y
{will
X
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Ms F3=m3r3w3 F1=m1r1wa Shaker
(a)
ii
.Ex 1
a _\
F31 F3l3 . Fll1
mara E» l
m3r3 2 2
.Fe __\
3 M3
Force Moment
(b)

Figure 5.6 Three oscillator shaker excitation
(a) linear configuration (lo) Force
and moment polygons.

206
F °L — F cos(¢ —90+w )-L + F cos(¢ -90—w )‘L = 0
1 l 2 . l l 2 .3 2 2 3
Fl'Ll - F251n(¢1+¢1)°L2 + F351H(¢2‘¢2)'L3 = 0
With the trigonometric identity:
sin(a+B) = sina-cosB + cosa°sin8
Moments become:

F'Ll - F(O.866COSW1 - 0.551n¢1)'L +
F(-6.866cos¢2+0.55inw2)0L3 = 0

Letting L1 = L2 = L3:

cos $1 = —cosw2
sin $1 = -sinw2

In order to cancel moments:

60°

tan w
l 600

0.866/0.5 + *1
tan $2

0.866/0.5 + $2

Therefore, with equal forces generated by the oscillators,
relative mounting angles of 600 will also balance moments
given the above relative phase angles. This third case is
shown in Figure 5.7, indicating balanced forces and moments
when masses are 36OO/n out of phase and remain at that phase
Vt. This configuration does not require a balancing
oscillator at the shaker's center of rotation, thus making
this option particularly suitable for a realistic design. A
violation occurs in this configuration, however; the masses
must rotate in the same direction Vt for balance which will
produce ellipsoidal displacement patterns when the masses
are phased, and thus be void of forcing peaks - an
undesirable and often ineffective shake pattern for fruit
removal. The three in—line design therefore is preferred
for its ability to create good patterns of oscillation,

Figure 5.6.

 

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208

Theoretically, the shaken tree is located at the center
of rotation. This holds true particularly with large trees.
If any one of the three oscillators in the three in—line
design is moved off the center line or changed in rotation
direction, starting forces or torques are generated, either
of which is undesirable. Although two three-oscillator
scenarios have been developed which satisfy different
aspects of the problem, neither one satisfies both force and
moment balance as well as mass counter—rotation for peaked
forcing vectors necessary for effective fruit removal.

The next step, therefore, is to examine a four-
oscillator system as shown in Figure 5.8. The force polygon
closes with the simplest case of F1 + F2 = F3 + F4. Hence,
a "double pair" of oscillators can balance forces. The
moment field also balances about a point '6' with this
scenario. Geometry and direction of rotation allow us to
change the moment vectors without affecting the force
balance. In contrast, with the three—oscillator system,
changing the direction of rotation changes the force
balance, which cannot be corrected by geometry.

The four-oscillator system of Figure 5.8 can be phased
to impart no net motion to the body due to the double pair
of counter—rotating masses. Let:

1800

-w m with o
4 l 4 1800

w3 = -w2 with $3

Where:
w1=w2=w3=w4=w

 

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210

2F = 0:
Flcoswti + F sinwtj + F2cos(wt+¢2)i + F2sin(wt+¢2)j +
F3cos(wt+¢2+ 3)i + F3sin(wt+¢2+¢3)j + F4cos(wt+¢4)i +
F sin(wt+¢ )j = 0
4 4
Substituting the above values and solving for components:

i: Flcoswt - F2cos(wt+¢2) + F3cos(wt+¢2) — F4cos(-wt) = 0
j: Flsinwt + Fzsin(wt+¢2) - F3sin(wt+¢2) - F4cos(wt) = 0

Backsubstituting F1 = F4 and F2 = F3:

2F coswt - 2F cos(wt+¢ ) = O
l 2 2
2Flcoswt = 2F2cos(wt+¢2)

Since F2 = Fn > 0 where F is centrifugal force, then ¢2 =

n
0°. As expected then, F1 = F2. Checking moments:
2Mleft = EMrightz

F sinwt:L + F sin(wt+¢ )-L =
si%(wt+¢ +3 )-L2 + F sin(wt+$ )‘L
F3 2 3 3 4 4 4

Substituting the above values:

Fsinwt-L2 — F3sinwt°Ll = -Fsinwt-Ll + F3sinwt'L2
Therefore, with Fl = F2 = F3 = F4 and L1 = L4 and L2 = L3,
with proper phasing, no net torsional or linear motion will
be imparted to the platform.

With all masses rotating in the same direction, orbital
patterns such as circles, ellipses, hyperboloids, and
cardioids can be produced by proper phasing of the four
oscillators. Orbital patterns are less desirable than
peaked displacement patterns so phasing of counter—rotating
masses would be more effective for fruit removal. A
hypothetical four—oscillator harvest control system is shown
in Figure 5.9a. With two oscillators per shaft, the number
of drive motors is half the number of oscillators. A

"double mass" shaft is shown in Figure 5.9b. The "double

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212

mass" configuration allows two masses on one shaft to act as
a phased pair without a bending couple imposed on the shaft
in the balancing configuration.

Since mlrl = mnrn to cancel both forces and moments, a
four-oscillator design could be arranged as a "double pair"
as long as the pairs of individual masses were spaced
equally about the center of rotation of the platform (e.g.
the tree) as shown in Figure 5.10. At low frequency, the
oscillator masses balance and impart no motion. At the
proper shaking frequency, the masses are shifted out of
phase to produce a peaked oscillation pattern. Although
moments may still exist as in the two—oscillator design,
they are minimized by minimizing L. The important feature
is to avoid "resonant moments" (at low frequencies) by phase
control. A system of 4 separate oscillators would eliminate
all undesirable effects, but be more complex in structure to
manufacture and control.

In summary, a four—oscillator system provides both a
rotating shake pattern with displacement peaks and a force-
moment balance for "gallop" avoidance which can be

controlled by phasing of fixed—mass oscillators.

b; Variable Eccentricity

 

The second method of isolating vibration at low
unstable frequencies and realizing this energy at higher
desirable shake frequencies involves balancing of each
individual oscillator in itself. This balancing can be

performed by physically changing the inertial properties of

 

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214

the oscillator; a concept which will lead to variation of
eccentricity.

The single oscillator generates a force proportional to
its mass (m), rotational velocity (w), and eccentricity (e):

F = mew2

Therefore, changing the force involves changing the mass,
rotational velocity, or eccentricity. Since rotational
velocity has the greatest effect on force because of the
exponent, it would be obvious to vary w. However, zero
force requires zero velocity which requires passing through
low frequencies. This negates the mode evasion strategy,
however.

With rotational velocity fixed, two variables remain
for control of the force vector. Changing the mass involves
a mass transfer to/from the inertial shell. This could be
extended to the concept of engaging a fixed mass with a
clutch between the oscillator and the shaker body such that
even though the oscillator is generating a force, the
isolation clutch prevents this force from being transferred
to the shaker body. These systems involving a mass or force
transfer are difficult to implement, and involve an
alternate absorber for the mass or force being isolated.
This type of design has historically been unpopular and was
not examined in this experiment.

The last variable which can be manipulated is the
eccentricity of the fixed mass. If e20 when w is small,

near the provocative natural resonances, then F20 and no

215

motion would occur. Then, when w is larger, near the
desired shake frequency, e + eforcing and F + Fshake
resulting in a desirable motion, the intolerable transients
having been avoided. Hence, eccentricity was chosen as the
variable upon which to base a new design.

Historically, a few shaking devices have been developed
with this concept in mind. Most of them involve a heavy
flowable medium (oil, BB's) which would be transferred from
a balanced position to an unbalanced position by gravity or
centrifugal force. Unfortunately, the transfer occurred at
very low rotational frequencies, too low for this
application. Moreover, there was no positive control of
eccentricity in these designs, as they reacted the same each
time to centrifugal and gravitational forces.

I wanted positive control over eccentricity, with the
possibility of simultaneously controlling the amplitude;
therefore I selected an actuator-controlled, fixed—mass
variable—eccentricity oscillator design. Several methods
were considered for varying the eccentricity (linear,
rotary, inclined—screw). For simplicity of construction and
ease of connection to an external power unit, I selected a
hydraulically controlled fixed—mass pivoted about a primary
rotating shaft from a balanced position (e20) to a fully
unbalanced position (e=max). This system offered the best

potential for meeting the goal of resonant mode evasion.

5.2 Modified Shaker: Variable Eccentricity with One Mass

 

Vibration analysis of a trunk shaker led to the

 

 

216

hypothesis that variable eccentricity may solve the gallop
problem. The Friday C-Clamp commercial trunk shaker (Friday
Tractor Co., Hartford, MI) was modified in design to
accommodate a variable-eccentricity mass.

The Friday Tractor Co. donated a steel mass shell and a
4.92 cm (1.94 in.) diameter steel shaft as used in the
fixed—eccentric mass construction for use in construction of
an experimental variable-eccentricity mass. Only one
variable-eccentricity mass was constructed due to limited
time, cost, and space within the shaker body. The other
mass was pinned with its center of gravity in the —Y
direction using a 2.5 cm (1.0 in.) diameter bolt to prevent
interference from movement during design evaluation testing.
Because only one variable-eccentricity mass could be
developed, conventional shaker tests were conducted at two
different shake frequencies (9 Hz and 15 Hz) on three
different size cherry trees (6.5, 11.0 and 16.5 cm; 2.5,
4.5, and 6.5 in.) as well as in free shake to determine the
effectiveness of individual masses in developing a shake
pattern.

Typical displacement results are shown for free shake
for analysis and design purposes and for shaking small (6.5
cm, 2.5 in.) trees because of the heavy population of young
trees in commercial orchards. Interpretation of X—Y planar
motion plots is difficult. Therefore, results are shown for
x displacement only at the point of tree attachment.

Displacement traces for individual operation of the

 

 

217

inner mass and outer mass in free shake (Figure 5.11) and in
shaking a 6.5 cm (2.5 in.) tree (Figure 5.12) differ very
little from one another in frequency content or response
time. Occurrence of start-up and shut-down resonance for
each treatment were the same within experiments. However,
though a start—up transient occurs when shaking 6.5 cm (2.5
in.) trees with individual masses, the decay to steady-state
time is much shorter. Resonance on shut—down is still
prominent, though decay time from steady-state to zero
displacement also occurs much faster. This results from the
additive damping factor of the tree. This relation between
free shake and tree shake also indicates that part of the
resonance component (1.0—2.0 Hz) occurs due to the shaker
properties. Though tree damping increases the decay rate of
the start-up transient, the low natural frequency of the
tree (2 1.0 Hz) still appears to contribute to the shut—down
resonance. Amplitude of free shake at steady-state reaches
8-9 mm (0.3-0.4 in.) with transients up to 23 mm (0.9 in.).
Steady—state amplitude of a 6.5 cm (2.5 in.) tree shake
remains the same (8-9 mm, 0.3-0.4 in.) with transients still
reaching 20 mm (0.8 in.).

Results of free shake and shake of a small tree with
both masses operating are shown in Figure 5.13. Start-up
and shut—down transients are similar to individual mass
operation in location of occurrence. A beating phenomena is
also present with two mass operation however, evidenced on

shut-down where linear displacements go to zero, then

 

218

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rebound to transient maximums. Surprisingly, however,
transients with two masses operating are greater when
shaking a tree than in free shake; evidence of the
contribution of the low natural modes of the tree to the
beating phenomena.

Since transients are similar in amplitude and frequency
for all treatments, the inner mass was chosen for design
modification. This would provide maximum vibratory input to
the tree with minimum side effect from shaker torsion.

The variable—eccentricity mass, designed to modify
shaker displacement characteristics, is shown in Figure
5.14. A top View and an exploded view are shown in Figure
5.15. Mass 10 in Figure 5.15 is made from a steel shell,
appropriately cut in the center for passage of the vertical
rotating shaft through the proper arc, and fitted with a
hole at each end for the rotary and the hydraulic cylinder
pins. Mass 10 was formed with this curved slot 20 so as to
engage vertical shaft 14 in the closed position as shown in
Figure 5.14. The shell was then filled with molten lead and
cooled. Bottom plate 11 and top plate 12 are welded to
vertical shaft 14. The free end of mass 10 is rotatably
mounted to top plate 12 and bottom plate 11 by shoulder bolt
16 which passes through top plate 12 and fastens into bottom
plate 11. The free end of mass 10 is rotatably mounted to
piston rod 15 by pin 13.

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which are aligned with a rotating union 24 bolted to union

 

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Figure 5.15 Variable eccentric mass design
(a) top view

 

 

224

plate 23 for hydraulic fluid passage. Suitable flexible
hydraulic hoses 25, 26 transmit hydraulic fluid from
vertical shaft 14 to actuator 17.

Operation of a 7.6 cm x 7.6 cm (3.0 in. x 3.0 in.)
hydraulic cylinder 17 rotatably mounted to top plate 12 and
bottom plate 11 by pin 18 extends and retracts piston rod
15, thus pivoting mass 10 about shoulder bolt 16 causing a
change in location of the mass' center of gravity about the
center of rotation of vertical shaft 14. In the retracted
position, the center of gravity of mass 10 plus cylinder 17
is nearly coincident with the center of vertical shaft 14,
thus imparting no unbalance to the rotation. In the
extended position, the center of gravity of mass 10 is
eccentric, unbalancing the rotating mechanism, thereby
generating vibratory shaking forces.

The magnitude of the shaking force can be varied by
varying the position of the center of gravity of mass 10
with respect of the center of rotation of shaft 14. The
amount of piston rod 15 extension controls the amount of
eccentricity, which in turn changes the shaking force and
amplitude. In normal operation, vertical shaft 14 would be
rotating at the desired shaking frequency whereupon
hydraulic cylinder 17 would be controllably engaged and
disengaged to pivot mass 10 about shoulder bolt 16 thus
varying eccentricity and hence, shaking force and amplitude.
Furthermore, the frequency of vibration is controlled by the

velocity of rotation of shaft 14. Various shaker patterns

I a _ a

 

 

225

can be developed by adjusting the number, relative size,
direction, phase, and frequencies of individual masses.

The experimental variable-eccentricity mass was
installed in the shaker body in place of the inside mass
(MB). Slight modification of the shaker box frame was
necessary since the dimensions of the modified mass were
necessarily slightly larger than the fixed mass.

A hydraulic control circuit (Figure 5.16) was assembled
to independently vary eccentricity. A 9 cm x 20 cm (3.5 in.
x 8.0 in.) hydraulic cylinder was mounted in series with
hydraulic actuator 17 as a slave for monitoring the
eccentricity of the variable mass enclosed in the shaker
body. A flow control valve was used to regulate the
velocity of eccentricity engagement providing engagement
velocities from 0.0 to 175 mm/s (0.0 to 6.9 in./s) maximum.
A pressure regulator limited system pressure to 8275 kPa
(1200 psi), as limited by the rotating union design.
Hydraulic pressure was tapped from one outlet of the
auxiliary PTO pump which would normally power the second
rotating mass drive motor.

Initial lab tests indicated that flow and pressure were
adequate for proper operation of the new design; the system
operated satisfactorily for all tests reported.

Sensors, similar to those employed in the unmodified
shaker design, were mounted upon the shaker and subsequently

upon cherry trees to evaluate the modified shaker design.

 

 

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227

5.3 Displacement Results with Variable Eccentricity

Displacement tests of the modified shaker were similar
to tests of the unmodified shaker. Two different engine
speeds (1500 and 2200 r/min) were utilized on each of three
different size Montmorency cherry trees (6.5, 11.0, and 16.5
cm; 2.5, 4.5, and 6.5 in.) as well as in free shake (using a
5 cm x 10 cm board 60 cm long (2.0 in. x 4.0 in. x 24.0 in.)
in the clamp in place of a tree). All tests were conducted
at the Michigan State University Horticultural Research
Orchard.

Instrumentation was the same as that used in the
unmodified shaker tests: an X and Y LVDT on the tree, an X
and Y accelerometer on the tree, an X and Y accelerometer on
the shaker at the shaker-pad interface, and a proximity
sensor at the rotating mass shaft. The operation of only
one mass eliminated the need for the position sensor on the
second mass shaft.

Displacement traces for the modified shaker were
calibrated at low frequency against photographic traces
obtained by Marshall (1986). Initial observation of
photographic displacement traces indicated that torsional
motion with the modified shaker design was minimized.
Therefore, since recorder channels were limited for
transducer input, the X and Y accelerometer at the shaker
center of gravity were eliminated.

A position sensor was not available to monitor movement

of the cylinder controlling the variable—eccentricity mass,

 

 

228

therefore a Schaevitz Model 7LlOVT—Z velocity sensor
(Schaevitz Engineering Co., Pennsauken, NJ), was attached
to the slave cylinder of the hydraulic eccentricity control
circuit. Output was then proportional to the speed of
eccentricity engagement and, after integration, proportional
to main cylinder displacement, and thus, eccentricity via

the approximate calibration equation:
t
e = (f v dt + C) * Cal factor
0

Cal factor = Nonlinear calibration factor accounting for
arcuate movement of mass.

Where: (1 v dt + C)| = 0|
0 t=0 e=0

Typical eccentricity engagement rate and position plots
are shown in Figure 5.17 for shaking of the 6.5 cm (2.5 in.)
tree with fast engagement of variable eccentricity and in
Figure 5.18 for slow engagement of variable eccentricity. A
conventional shake with the single modified mass consisted
of engaging full eccentricity prior to start-up of mass
rotation. Corresponding rotational frequency versus time
plots for the single modified mass are shown in Figures 5.19
(fast engage), 5.20 (slow engage), and 5.21 (conventional
pre—engage). Engaging the mass fast had more effect on
disturbance of rotational frequency than slow engage,
possibly due to the power drawn from the system to maintain
the set frequency. The added effect of the sudden change in
rotational inertia of the mass may have contributed to the

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shake still exhibits overshoot and settling to the desired
shake frequency; evidence that the system still responds
similar to the pre—modified condition. Mass frequency
patterns varied insignificantly with tree size or within
free shake tests.

Data in the field were recorded using the same Racal
four— channel instrumentation tape recorder and a Data 6000
Waveform Analyzer as used in previous tests. Data on the
Racal recorder were later transferred to the Data 6000 for
floppy disk storage. Data were processed as in Section 4.4
with the velocity sensor traces being integrated and
calibrated directly in the Data 6000.

Typical linear X and Y displacement traces at the tree
location of the modified shaker are shown for fast mass
engagement in free shake (Figure 5.22) and for shaking a 6.5
cm (2.5 in.) tree (Figure 5.24). Planar X—Y motion for free
shake is shown in Figure 5.23, with 6.5 cm (2.5 in.) tree
motion exhibited in Figure 5.25. In free shake with the
modified mass, overall amplitudes are approximately
equivalent to the steady—state value of the conventional
shake (8—9 mm, 0.3-0.4 in.). Free shake shows a low
frequency oscillation envelope similar to that of the fixed—
eccentricity data due to the start-up transient, though the
magnitude is only l—2 mm (0.04—0.08 in.) above steady-state;
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pronounced with fast engagement of eccentricity than with
slow engagement due to the greater effect of the inertial
pulse on the natural frequency of the shaker body in the
pendulum mode when moving the mass to its outer, unbalanced
position. Fast engagement was used for subsequent tests,
however, because of the speed desirability in commercial
harvesting operations. In all tests, the low frequency
oscillation in free shake from mass engagement was much
greater in the X direction than the Y due to the respective
natural modes and varied proportionately to the velocity of
mass engagement. However, magnitudes remain very small in
comparison to fixed-eccentricity transients. The X—Y planar
plot exhibits this as an ellipsoid which oscillates (slides)
on a line through its centroid.

When attached to a small tree, X and Y motion starts
linearly and reaches a steady—state value approximately
equivalent to the steady—state of a conventional shake of
equivalent frequency and tree size. No transient or
resonant motion is evidenced on start-up or shut-down with
only minor overshoot (1 mm, 0.04 in.) at mass engagement
evidenced in the X direction; again a result of the fast
mass engagement inertial pulse on the natural frequency of
the shaker-tree system. This overshoot appears to be
proportional to mass engagement and not affected by tree
size, in agreement with the mass frequency versus time
plots. The ellipse of the planar plot of Figure 5.25 is

very uniform, thus requiring a second variable-eccentricity

 

 

240

 

Table 5.1 Free displacement at shaker clamp and tree
displacement resulting from fixed-mass and
variable—eccentricity shaker designs (15—16 Hz,
6.5 cm tree, fast mass engagement).

 

Maximum Displacement

 

 

 

 

Free Shake Tree Shake
X Y X Y
mm mm mm mm
Conventional
Fixed-Mass
a. Both Masses 35 30 52 45
b. Single Mass 38 21 24 23
Modified Variable
Eccentricity Mass
a. Single Mass l6 14 11 ll

 

mass to ensure excitation of different modes of the tree for
fruit removal. Table 5.1 summarizes tree displacements
incurred by both fixed—mass and variable—eccentricity shaker
designs.

From Table 5.1, when a tree is added to the vibrating
single mass system, the displacements generally decrease due
to the damping property of the tree. However, the beating
phenomena of both masses appears in increased displacements
during shut-down from steady-state. Values of 15—25 mm
(0.6-1.0 in.) to peaks of 40—52 mm (l.6—2.0 in.) occur in
the X direction when a tree is shaken. This beating
phenomena, as shown in Chapter 4, appears to become harmonic

with the tree and shaker bodies and attempts to resonate

fifi

 

241

around 1.0—2.0 Hz. A pair of variable-eccentricity masses
then, when retracted prior to cessation of rotation, would
likely avoid these displacements by avoiding beating near
this frequency.

The same characteristics are evidenced at lower,
nonconventional shaking frequencies (lower frequencies used
for testing but not used commercially) indicating that the
variable—eccentricity mass concept avoids the majority of
transient vibration excited at resonant frequencies which
cause excessive displacement and thereby possible excessive
stress in tree bark.

Corresponding displacement motion (X and Y) of the
shaker next to the pad are shown in Figure 5.26. A planar
plot of this motion is shown for shaking a 6.5 cm (2.5 in.)
tree in Figure 5.27. Amplitude of motion is nearly the same
though X motion is slightly larger than that of the tree
(0.5-1.5 mm, 0.02—0.06 in.), possibly because some motion is
being absorbed in pad compression. The overall displacement
pattern of the shaker is thereby ellipsoidal as is the tree
pattern.

Comparison of frequency content of a commercial 15 Hz
fixed-mass shaker on a 6.5 cm (2.5 in.) tree (Figure 5.28)
and a modified variable—eccentricity shaker with fast mass
engagement on the same tree (Figure 5.29) highlights the
broad spectrum of frequencies present in the conventional
method which are exhibited as peak resonant amplitudes and

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ment at 15—16 Hz on a 6.5 cm tree.

 

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246

frequency oscillations not only contribute to peak
amplitudes for high stress levels in the bark, but may also
provide a mechanism for shaker rotation, thereby imparting
highly damaging torsion on tree bark. Variable eccentricity
eliminates this broad band and allows the shake frequency to
be precisely designated.

Justification: "Shift" of the tree-shaker system can be
defined as an initial gross displacement (D.C.) from the
center of rest or steady-state center of oscillation from
which successive oscillatory displacements occur (Figure
5.30). "Drift", on the other hand, can be defined as the
path of a changing, noncyclic center of oscillation. Al—
Soboh (1986) attempted to model the Friday C—clamp shaker
with fixed and variable eccentric inertial driving forces to
develop design parameters. Problems with numerical
stability in his commercial development program prevented
completion of this task. However, in free shake, he found
that at high m and with eccentricity engaged quickly, both
shift and drift were kept small.

Modified shaker tests show that shift and drift were
nearly zero in all cases and were unaffected by velocity of
mass engagement. Shift and drift occurred only near extreme
conditions simulating conventional fixed—mass operation.
Preceeding variable-eccentricity displacement plots are thus
shown only for rapid eccentricity engagement because this
would be a preferred characteristic in commercial operation

for best harvesting time efficiency.

 

247

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248

5.4 Evaluation of Variable Eccentricity Design Performance

 

The variable—eccentric mass provides a new and improved
vibratory actuator for use in shake harvesting fruit and nut
bearing trees in which the eccentricity is positively
controlled or predetermined by physical mechanics between a
balanced condition and a desired maximum unbalanced
condition by means of an actuator controlling an inertial
mass. The amount of eccentricity and resulting range of
shaking amplitudes is controllably varied in a simple, quick
operation. Independence of shaking amplitude and shaking
frequency gives the operator total shake harvesting control.

Since shaking force and frequency are independently
controllable, continuous operation of the primary rotatable
shaft which determines the shake frequency is possible for
the duration of the entire harvest, thereby eliminating the
time and power required for acceleration and deceleration of
the masses at each tree. Furthermore, continuous shaft
rotation reduces component wear due to acceleration forces
and eliminates the need for the operator to reset the shake
frequency at each tree.

The most prominent benefit is the provision by this
design of an improved tree shaking motion eliminating
undesirable and potentially harmful damaging vibrations
during transient frequency operation. Since shaking
frequency is independent of shaking amplitude, undesired low
frequency vibrations are avoided by operating the primary

rotating shaft at a higher frequency prior to the

 

249
introduction of any vibration—generating unbalance.

5.5 Theoretical Extension to Two Masses

 

The variable-eccentricity design was experimentally
tested with one mass but can be theoretically examined for
operation with two masses as shown in Figure 5.31. With one
mass located on either side of the tree, any rotation must
occur about the tree (a valid assumption particularly with
larger trees).

A control system could be constructed to activate the
shaking process by starting with a clamp sensor which
detects the proper tree position in the clamp jaws and
closes the pads around the tree. Both masses would be
counter—rotating at shaking speed with zero eccentricity
during the clamping operation. Eccentricity would be
engaged to start shake, with each mass free wheeling (no
phase control). As resonance frequencies are by-passed by
the variable—eccentricity design, gallop would be avoided.
The desired omni—directional shake with counter-rotating
free wheeling masses would be obtained, then the control
system would stop the shake by shifting eccentricity back to
zero.

The only drawback to this design is the moment about
the tree. By moving the masses to either side of the tree,
however, and positioning the suspension system close to the
masses, the moment arm is small and therefore the moment is
minimized. This configuration also guarantees that the

center of rotation is at the tree with the forcing vectors

 

250

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251

lined nearly through the tree. The moment is a maximum when
the masses are n radians apart as analyzed in Figure 5.3b:

EFX = Mx: F2coswt — Flcos(wt+¢)
ZFY = My: Fzsinwt + Flsin(wt+¢)

Forces are:
R = / F 2 + F 2

x Y
R = /7F22coszwt - 2FlF2coswtcos(wt+¢) + Flzcosz(wt+¢)

 

 

/ + Fzzsinzwt + 2F1Fzsinwtsin(wt+¢) + Flzsin2(wt+¢)

Fl=F2=F by m1e1=m2e2

 

R = / 2F2 - 2F2[—sinwtsin(wt+¢) + coswtcos(wt+¢)]

 

R = / 2F2 - 2F2cos(2wt+¢)
As cosine varies between 0 and t l, the resultant force
vector will be 5 2F and the maximum moment will be 2F-L
Minimizing L, limiting phase shift to : n/2 radians, and
constructing a suspension system to prevent torsional motion
are all means to minimize the presence of torsion about the
tree.

An elliptical motion with no moment could easily be
developed by rotating the masses in phase in the same
direction. In fact, shakers have been developed which
produce elliptical motions, although fruit removal on some
crops is unsatisfactory.

The problems of eliminating gallop and torsion while
maintaining frequency and stroke (pattern) control may
generally be solved with the variable—eccentricity mass.
Unfortunately, with two fixed masses, it is theoretically
impossible in any free suspension configuration (except with

both fixed masses on the same shaft at the center of

252
rotation) to cancel both moments and forces.

5.6 Potential in Future Designs

 

As the current design eliminates many of the problems
associated with most of today's fixed—inertia vibratory
harvesters, further modification of this mass design to
other environments may produce many different shaker
patterns for different applications. Alteration of the
actuator (hydraulic, electric, etc.), the mass motion
(rotational, linear, combined), the primary shaft drive
mechanism (gears, belts, direct drive), the number of
rotating masses per housing, the direction, speed,
eccentricity, and phasing of each of these masses, the plane
of activation (horizontal, vertical, inclined), and the
division of masses within a housing (one main housing or
multiple subhousings) coupled with efficient suspension and
clamp systems gives the designer a free hand to achieve
practically any desired vibration sequence for a particular

need.

 

 

CHAPTER 6

SUMMARY

Dynamic forces imposed on fruit tree bark may be beyond
acceptable physiological limits, thereby adversely impacting
orchard life and harvesting economics. This research
consisted of a three-phase systematic plan to reduce bark
damage inflicted by the dynamic loading of mechanical fruit
tree shaker harvesters. Tests in this research were limited
to a single variety and species: Montmorency Cherry, Prunus
cerasus. This study involved three steps as follows.

Firstly, an instrumentation system was devised to
detect acceleration during shaking on a commercial trunk
shaker. Integration and frequency domain spectral analysis
were employed to derive peak displacements which could be
compared to the tolerable strength of fruit tree bark.
Results indicated that transient vibrations during start—up
and shut-down of shaker masses may well exceed adopted
stress and strain limits even when static clamping forces
are at approved levels.

Secondly, based on the peak dynamic bark loading
results, a controlled variable—eccentricity trunk shaker was
designed, built and tested as one possible method of

restricting dynamic bark loading while maintaining

253

 

 

 

254

harvesting efficiency and economic feasibility. Transient
vibration anomalies present in the original shaker design
were eliminated in the variable-eccentricity design,
meanwhile preserving selected amplitude and frequency
multidirectional shake characteristics.

A preliminary planar kinetic analysis reveals two model
configurations for replacing variable—eccentricity with a
three-mass fixed-eccentricity system for elimination of
start—up and shut—down transients. A four—mass fixed-
eccentricity model is also presented which is completely
controllable in terms of amplitude, frequency, and phasing.

Thirdly, based on the theory that trees
compartmentalize wounded areas, variations with time of tree
trunk profiles were studied in seeking indicators of the
tree's health status. Because a convenient, nondestructive
means of sensing sub-clinical bark damage is currently not
available, several signal analysis methods were investigated
on measured cross—sectional profiles as a means of
nondestructively monitoring the long term effects of trunk
shaker harvesting. Preliminary results indicate that the
change in radial bandwidth of the trunk profile can diagnose
tree damage while a Polar Fourier Analysis may discriminate
between internal and external damage and provide an estimate
of severity. Cross—correlation of time—spaced frequency
signals assisted in detecting profile changes.

The variable-eccentricity design which resulted from

this research may significantly reduce bark damage and

 
 

255

orchard decline, particularly in younger, more susceptible
orchards. Investment in improved shaker designs of this
caliber could provide substantial economic returns,
especially since current day orchards have declined 30-50%
in productive life from 10 years ago and 30-50% of today's

cherry orchards are of nonbearing age.

 

 

CHAPTER 7

CONCLUSIONS

1. Tree displacements caused by a fixed-eccentricity,
multidirectional C-clamp trunk shaker were determined for
cherry tree sizes of 6.5, 11.0, and 16.5 cm (2.5, 4.5, and
6.5 in.) at shaker operating frequencies of 9 Hz and 16 Hz.
Steady—state tree displacements in single mass operation
ranged from 10—12 mm (0.4-0.5 in.). Two mass operation gave
steady—state displacements of 15-25 mm (0.6—1.0 in.).
Amplitudes of gallop were found to exceed the steady-state
amplitudes by as much as 100%. Torsional motion has been
observed to occur, especially during start-up and shut-down

transients.

2. Steady—state tree displacements of 10—12 mm (0.4—
0.5 in.) were developed by a single mass, controllably
variable-eccentricity trunk shaker; the same steady-state
displacement as that in the single mass, fixed—eccentricity
shaker tests. Start-up and shut—down tree gallop were
eliminated with this design. Alternate four—mass, fixed—
eccentricity shaker designs can provide similar independent

positive control of shake amplitude and frequency.

3. Profile bandwidth provides a first time indicator

256

 

 

257

of bark damage, having changed 0.5-2.4% on slightly damaged
trees to maximums of 13.5% on severely damaged trees in one
year. Fourier analysis of the profile, optionally combined
with cross—correlation of time-spaced frequency samples,
revealed that increases in the second or third harmonic were
related to internal or callus damage while increases in
higher harmonics (4th—7th) indicated split or protruding
bark. The combination of invariant moments l, 2, and 7 also
provided indication of tree trunk profile change resulting

from damage.

 

CHAPTER 8

RECOMMENDATIONS FOR FUTURE RESEARCH

l. TREE PROFILE ANALYSIS: Preliminary methods for

 

defining changes in the profile of a cherry tree trunk over
time have been introduced. As image processing equipment
becomes more powerful and available, further algorithms for
object discrimination and shape analysis need to be
investigated. These methods, if integrated into an
experimental design for a period of several years, may
provide valuable insight into the growth and damage response
characteristics of both mechanically harvested and control
trees under a multitude of environmental conditions.
Physiological basics of tree maturation may be revealed
which will aid in future production and harvesting

practices.

2. INJURY DETECTION: A convenient, nondestructive

 

means for evaluating sub—clinical bark damage and/or tree
stress at minute levels needs to be developed in order to
aid research on the effects of orchard production and
harvesting practices. If effective, this means could
provide a critical link in the communication gap between
plant life and humans, thereby providing a daily means by

which to monitor plant and orchard condition.

258

 

 

 

259

3. SENSOR DEVELOPMENT: Sensor packages are needed to

 

detect both mechanical and biological information from trees
(plants) and tree (plant) interaction devices. Sensors are
required to relay basic data on stimuli, plant response to
stimuli, and plant growth to controllers and research
instruments as crucial elements in a strongly needed
integrated feedback system which would help control or

eliminate nonconducive growing conditions.

4. HARVESTER AND CONTROLLER DESIGN: Agriculture, in

 

general, is heading into an age of total auto—mechanization
via microprocessor controlled robots and universal
integration via sensor feedback systems. In agriculture,
harvesting fruits from woody plants is a most important part
of these systems. Harvesters which can efficiently interact
with the biological systems without causing damage are
necessary. The controllable, variable—eccentricity design
of this dissertation needs further development and testing
as one feasible solution to the bark damage dilemma on fruit
trees. Harvesters of this and other designs need further
investigation for their task efficiency and economic
potential. Researchers and inventors are just now beginning
to apply robotics, intelligent controllers, sensors, and
image processing equipment to the harvesting process.
Though adequate sensor technology appears to be the current
limiting factor, basic biological data integrated into
minimum control schemes may provide immediate benefits in

damage reduction potential.

260

5 . SYSTEM MANAGEMENT AND SOFTWARE: Efficient

 

mechanization of the harvesting process and the
implementation of intelligent controllers may require
radical changes in current production and harvesting
practice. Environmental control, pruning techniques, and
genetic engineering may necessitate a 'total systems'
approach to fruit tree management. Efficient, high speed
software will be needed to receive information from sensors,
then process data, activate controllers, and provide
constant information updates on the status of all
operations. New integrated systematic techniques for
growing, pruning, and harvesting need further investigation
as a means of maximizing yield and minimizing adverse

physical or biological intervention.

6. SIGNAL PROCESSING: Sensed information in the

 

biological sciences is seldom clean and clear cut. Often,
the external stimulus or sensor limitations interfere with
the desired signal. As sensors are developed for
agricultural applications, it will become increasingly
necessary to apply advanced electrical and mechanical signal
processing principles in search of new techniques to

decipher the sought out message.

 

 

 

 

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