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thesis entitled

A Computer Aided Modeling and Performance
Analysis of a Variable Eccentricity Tree
Shaker Mechanism

presented by

Farzin Khorasanizadeh

has been accepted towards fulfillment
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Masters degree in Agricultural Engineering

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MSU Is An Affirmative Action/Equal Opportunity Institution
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A COIVIPUTER AIDED MODELING AND PERFORMANCE
ANALYSIS OF A VARIABLE ECCENTRICITY
TREE SHAKER NIECHANISM

By

Farzin Khorasanizadeh

A THESIS

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

MASTER OF SCIENCE

in
Agricultural Engineering
Department of Agricultural Engineering

1988

ABSTRACT

A COMPUTER AIDED MODELING AND PERFORMANCE
ANALYSIS OF A VARIABLE ECCENTRICITY
TREE SHAKER MECHANISM

By

Farzin Khorasanizadeh

Shake and catch harvesting of tree crops in commercial orchards is now
practiced on a world wide basis to meet today’s high volume market demand for
these products with more efficiency in fruit removal and less cost. Recent study
results on Michigan’s mechanical cherry harvesting operations have emphasized
the need for development of improved machinery to reduce mechanical damage
to trees, and increase efficiency in fruit removal. A new inertia type shaker
concept has been developed with strong potentials to reduce tree damage by
means of variable eccentricity and increase shake transfer ability by means of a
sliding tail weight, for better fruit removal. A dynamic analysis of this shaker
was needed to find sensitive parameters eflecting its operation and the nature of

such effects.

The operating conditions of the shaker were simulated by modeling a rigid
body version of the mechanism using ADAMS, an advanced mechanism analysis
program. The simulated tree displacements were analyzed for variations in
several model parameters. Critical parameters effecting overall shaker

performance were found to be: shaker weight and the location of its center of

 

mass, eccentric mass housing position, tail weight and its location. The graphic
simulations of the shaker mechanism gave excellent insights to the general
behavior of individual shaker parts under dynamic conditions. Performance
trends of the shaker have also been established under varying parameter
conditions. The results and the existing model can assist in further design

optimization of the shaker mechanism.

Dedication

 

To my father, Mohammad Ali Khorasanizadeh, my mother, F atemeh
Sadeghi, and my youngest sister, Sadaf, who are so far away but closer than

ever in my heart.

ii

Acknowledgments

I thank my father, Mohammad Ali Khorasanizadeh, my mother, F atemeh
Sadeghi, my sisters, F iruzeh, Sepideh, Sadaf, and my brother-in-law, Dr.
Kourosh Danai for providing me with an abundance of unconditional love,

support, and encouragement at all times.

I would like to take this opportunity to express my special gratitude to
Dr. Gary R. Van Be, my major professor, for his professional guidance,
constructive comments for the preparation of this work, and his personal concern

and advise.

I wish to thank Dr. Thomas A. Esch (former Agricultural Engineering

graduate student) for his cooperation and assistance throughout this study.

I would also like to thank Dr. Larry J. Segerlind (professor Department
of Agricultural Engineering) and Dr. Joseph E. Whitesell (Associate professor
Department of Mechanical Engineering) for serving on my graduate committee
and for their constructive comments and suggestions for the completion of this

work.

iii

 

 

Table of Contents

List of Figures .................................................................................... vi

List of Tables ...................................................................................... ix

Chapter 1: Introduction ...................................................................... 1

1.1 - Cherry Production .......................................................................... 3

1.2 - Tree Damage .................................................................................. 8

1.3 - Computer Modeling ........................................................................ 9

1.4 - Objectives of this study .................................................................. 10

Chapter 2: Review of Literature and Research .............................. 11

2.1 - Mechanical Harvesting Methods ..................................................... 11

2.2 - Tree Damage .................................................................................. 14

2.3 — Shaker-Tree Vibrations ................................................................... 19
Chapter 3: The Variable Eccentricity Shaker And The

Computer Model .............................................................. 25

3.1 - Conventional Shaker Design ........................................................... 25

3.2 - Single Degree of Freedom Shaker System ....................................... 28

3.3 - The Variable Eccentricity Shaker ................................................... 33

3.4 - Computer Modeling ........................................................................ 39

3.4.1 - Modeling Procedure .............................................................. 39

3.4.2 - Model Assumptions .............................................................. 41

3.4.3 - Model Definition ................................................................... 43

Chapter 4: Model Response and Evaluations ................................. 48

4.1 - Shaker Model .................................................................................. 48

4.2 - Variation of Shaker Housing Mass ................................................. 56

4.3 - Variation of Eccentric Mass Rotating Frequency ............................ 61

iv

 

4.4 - Variation of The Position of The Eccentric mass Housing ............. 66

4.5 - Variation of The Tail Weight Mass ................................................ 71
4.6 - Variation of The Position of The Tail Weight ............................... 77
4.7 - Evaluation of The Results .............................................................. 81
Chapter 5: Conclusions ...................................................................... 88
Chapter 6: Recommendations ........................................................... 90
Appendix A: ADAMS Code of The Model ..................................... 92
Appendix B: Experimental Shaker Data ......................................... 97
Appendix C: Single Degree of Freedom Models ............................ 101
List of References ............................................................................. 108

 

List of Figures

Figure Page
1.1 United States Total Tart Cherry Production (1986) ................................... 5
1.2 United States Total Sweet Cherry Production (1986) ................................. 5
1.3 Michigan Utilized Tart Cherry Production (1982-1986) .............................. 6
1.4 Michigan Utilized Sweet Cherry Production (1982-1986) ............................ 7

3.1 Single degree of freedom vibrating system excited

by an unbalance rotor ................................................................................. 29
3.2 Frequency ratio vs. amplitude and phase angle of

a single degree of freedom vibrating system ................................................ 32
3.3 Top view of the C shell variable eccentricity

concept ........................................................................................................ 34
3.4 Phase angle configuration of four eccentrics for

zero resultant force ...................................................................................... 35

3.5 Phase angle configuration of four eccentrics for

maximum resultant force ............................................................................ 36
3.6 The Variable eccentricity shaker ................................................................. 38
3.7 The variable eccentricity shaker ADAMS model ......................................... 46
3.8 The variable eccentricity shaker model in motion ....................................... 47
4.1 Shaker model reference frames .................................................................... 52
4.2 Steady state X displacements during free shake .......................................... 53
4.3 Steady state Y displacements during free shake .......................................... 54
4.4 Steady state XY displacements during free shake ....................................... 55
4.5 Variation of shaker mass Free shake ........................................................ 58
4.6 Variation of shaker mass Small tree shake ............................................... 59
4.7 Variation of shaker mass Large tree shake ............................................... 60

4.8 Variation of the rotating frequency of the

eccentric masses Free shake ...................................................................... 63

Figure Page

4.9 Variation of the rotating frequency of the

eccentric masses Small tree shake ............................................................ 64
4.10 Variation of the rotating frequency of the

eccentric masses Large tree shake ............................................................ 65

4.11 Variation of the position of the mass housing

Free shake .................................................................................................. 68
4.12 Variation of the position of the mass housing

Small tree shake ......................................................................................... 69
4.13 Variation of the position of the mass housing

Large tree shake ......................................................................................... 70
4.14 Variation of the tail weight mass Free shake ............................................ 73
4.15 Variation of the tail weight mass

Small tree shake ......................................................................................... 74
4.16 Variation of the tail weight mass

Large tree shake ......................................................................................... 75
4.17 Effect of tail weight mass on its displacement

Large tree shake ......................................................................................... 76
4.18 Variation of the position of the tail weight

Free shake .................................................................................................. 78
4.19 Variation of the position of the tail weight

Small tree shake ......................................................................................... 79
4.20 Variation of the position of the tail weight

Large tree shake ......................................................................................... 80
4.21 Close-up top view of model mass housing in motion .................................. 82

4.22 Closeup top view of the model shaker housing

in steady state motion ............................................................................... 83
4.23 Trace of center of mass point of model eccentrics

and tree center at start of a steady state shake

cycle ........................................................................................................... 84

vii

Figure Page

4.24 Trace of model shaker housing corner points,

tree center, and center of rotation of the

eccentrics for a full shake cycle .................................................................. 85
B.1 Experimental shaker X displacements at 15 Hz

(150 mm tree) ............................................................................................ 97
B.2 Experimental shaker Y displacements at 15 Hz

(150 mm tree) ............................................................................................ 98
B.3 Experimental shaker X displacements at 10 Hz

(Free shake) ............................................................................................... 99
B.4 Experimental shaker Y displacements at 10 Hz

(Free shake) ............................................................................................... 100
0.1 Fortran simulation of a single degree of freedom

harmonic oscillator .................................................................................... 102
C2 ADAMS simulation of a single degree of freedom

harmonic oscillator .................................................................................... 103
0.3 IMP simulation of a single degree of freedom

harmonic oscillator .................................................................................... 104

viii

List of Tables

Table Page

4.1 Tree physical characteristics for model input .............................................. 50

i2:

Chapter 1

Introduction

Mechanical shaking of several orchard fruit and nut trees has proven to be
the most efficient and economical method of harvesting, mainly because it
exhibits a very high ratio of output to input when conducted properly. Shake-
and-catch harvesting systems have now become a necessity for growers in order
to reduce the high cost of manual labor while meeting today’s high volume
market. Although a large variety of fruits are presently mechanically harvested
throughout the world, cherry production has perhaps benefited the most from
the introduction of this method because of the relatively higher number of fruit
(cherries) per tree. Michigan cherry growers, the leading producers of tart
cherries in the United States, adopted the shakers in the late 1960’s and now use
them annually to harvest over 95% of the state’s tart and sweet cherries (Brown
et al., 1982 and 1987). As a result of the extensive use of these machines,
mechanical damage has prevailed as a major threat to the productivity and

health of the bearing cherry trees. Mechanical damage is now the major cause of

tree decline (loss of vigor and yield, resulting in earlier replacement of the
orchard) in orchards of all ages throughout the state. Damage is caused by
excessive static and dynamic pressures applied to the tree when clamping to the

trunk and during the actual shaking operation.

Injury due to clamping has been extensively studied and safe pressure
ranges have been recommended to eliminate overclamping (Brown et al., 1984).
Clamp pads have also been improved to limit shear and compressive stresses,

decreasing the amount of damage to the tree bark.

Excessive dynamic forces during tree vibration, however, are due to the
design nature of the existing shaker models. Recent experiments on the dynamic
response of a typical shaker, commonly used in Michigan for harvesting cherries,
have shown that the shaker experiences a magnification of shake amplitude,
referred to as gallop, for a short period (approximately 1 to 2 seconds) during
"start-up" and "shut-down" (Afleldt et al., 1987). The steady state shake occurs
between these periods and delivers desired stroke for fruit detachment. Shaker
gallop creates excessive dynamic forces that exert high compressive stresses due
to clamp arm movement, and shear stresses from clamp slip on the bark. Gallop
is caused during the short periods when the shaker eccentric masses are brought
up to desired frequency and when shut down to rest. The rotating frequency of
the eccentric masses passes through the natural frequency of the shaker-tree
system and creates a desirable condition for unstable, resonant amplitudes that

are limited by high system damping exerted by the tree.

The Agricultural Engineering Department at Michigan State University has
developed a new concept for shaker design that eliminates the gallop problem.
The shaker is equipped with four eccentric masses and a rotation phasing
mechanism that provide a controlled variable eccentricity. A heavy sliding

concrete block (tail weight), placed at the tail of the shaker, also resists shaker

tail movement thus reducing shear stress on the bark.

The shaker system was modeled using ADAMS (Automatic Dynamic
Analysis of Mechanical Systems, version 5.2) on a VAX-11/750 computer, to
analyze its dynamic response and examine parameters for design optimization.
Model input variable parameters were shaker mass, tail weight, eccentric mass
housing position, tail weight position, and eccentric mass rotating frequency.
The simulations gave good qualitative results in predicting shaker behavior

under free shake and tree shake conditions.

1.1 - Cherry Production

Cherries are generally produced in the tart and the sweet varieties, most of
which are marketed for processing, with a small quantity provided for fresh
market. Cherries are of high nutritional value and are ideal for processing.
Processed cherries are mainly used for the production of juice, jam, jelly, ice
cream, dessert toppings, and wine. Some processed cherries are marketed frozen.
The United States is one of the largest producers of cherries in the world, second
only by a small margin to the Federal Republic of Germany. In the US ,
Michigan is the largest producer of tart cherries with 85,000 tons of total
production in 1986, and is ranked third for sweets with 20,000 tons of total
production in 1986 (Figures 1.1 and 1.2)(United States Agricultural Statistics,
1987). The utilized tart and sweet cherry production in Michigan in 1985 was at
its highest since 1982. The total production data refer to the quantity of fruit
harvested plus quantities which would have been acceptable for fresh market or
processing but were not harvested or utilized because of economic or other
factors. The utilized production refers to the amount sold plus the quantities
used on farms and quantities used in storage. There was a decline in production

in 1986 (28% for tarts and 35% for sweets) which was mainly due to early

season frosts and heavy rains at harvest. Figures 1.3 and 1.4 show the trend of
cherry production in Michigan between 1982 and 1986 (Michigan Agricultural
Statistics, 1987).

    
 

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1.2 - Tree Damage

Tree damage due to mechanical shaking is caused by static and dynamic
pressures applied to the tree by the shakers. Excessive clamping pressures and
dynamic forces subject the trunk to high compressive and shear forces that
result in ripping the bark or crushing of the internal cells. When the bark is
damaged insects may carry fungi to the injured area, providing a favorable
environment for fungus development and subsequent cankers that become
parasitic and threaten the life of the tree. Internal damage, not immediately
visible to the naked eye, takes place when the phloem (bark), cambium and
xylem (wood) cells are crushed while leaving the bark intact. When internal cells
are crushed, the flow of fluids that carry nutrients essential to the vitality of the
tree is interrupted. To counteract this trauma, the tree walls off the affected
areas; a defensive maneuver that draws on the energy reserves of the tree. When
these stressful events are repeated for several years, a mature tree becomes

weakened, resulting in reduced growth and a decline in fruit production (Burton

et al., 1986).

Moisture content of the tree due to irrigation or rain has a substantial effect
on the strength of the tree. During wet conditions, cells in the cambial layer
swell and enlarge in the radial direction. The radial walls become thinner and
the cell contents seem to change from a solid to a liquid consistency. As soon as
this stage is reached, the cambial walls can break easily and allow the bark to
slip over the wood during shaking. Cherries, which are harvested early in mid-
summer when the cambium is still highly active, are more susceptible to damage
by mechanical harvesters than fruits harvested later in the season (Fridley et al.,
1970). Researchers, who studied the relation of bark strength to its moisture
content, have recommended that farmers stop irrigation at least two weeks prior

to harvest (Brown et al., 1987).

1.3 - Computer Modeling

Computer based analysis techniques are playing a major role in the
engineering research and design. The availability of increasingly powerful
hardware is allowing timely, cost effective, detailed analyses aiding in the study
of more complex, and efficient machines. Accurate analysis of a mechanism
requires careful mathematical formulation of all possible motion and forces of its
components. Numerical techniques (numerical integration, linear equations
solution, etc.) must also be employed to solve the mathematical model. Although
some recurring analysis problems (such as, Four bar or Slider crank mechanisms)
lend themselves to existing special programs, the majority of dynamic problems
have some unique characteristics or are much more complex that require specific
treatment. As a result, the mathematical formulation becomes highly time
consuming and often requires special expertise in analytical techniques. The
problem is compounded if there are several alternate designs, each requiring a

separate analysis.

The development of sophisticated general purpose dynamic simulation
software combined with today’s effective computer graphics has made the process
of applying dynamic analysis in the design cycle both practical and efiective.
ADAMS (Automatic Dynamic Analysis of Mechanical Systems) is one of the
more capable and developed of the few available mechanism analysis programs.
It performs dynamic analysis of both planar and spatial mechanisms utilizing
the rigid body theory for setting up the characteristic system equations. ADAMS
was chosen for the shaker dynamic analysis because of its availability,

suitability, and research preference due to past experience.

10

1.4 - Objectives of this study

The main objective of this study was to develop a computer model of the
controllable variable eccentricity shaker, developed by Esch (1988), possessing
the actual physical characteristics of the shaker and to be able to simulate it
under dynamic conditions. Two machinery simulation programs, ADAMS
(Automatic Dynamic Analysis of Mechanical Systems) and IMP (Integrated
Machinery Design), were considered for the study. After some preliminary tests
and evaluations, ADAMS was chosen as a more suitable program for this specific
application. The model was written in the program’s code and simulated. The

results were satisfactory since they followed the actual shaker’s behavior closely.

Five parameters were then chosen as model variables. These parameters were

1) Shaker housing mass

2) Rotating frequency of eccentric masses
3) Position of the mass housing

4) Tail weight mass

5) Position of the tail weight.

A number of simulations were conducted with a range values for the above
parameters under free shake and tree shake conditions. For tree shake
conditions, each simulation condition was given approximate stiffness and

damping values for two different diameter trees (63mm and 165mm).

The simulation results were used to predict the variable eccentricity shaker’s

behavior and its sensitivity to changes in the above parameters.

Chapter 2

Review of Literature and Research

2.1 - Mechanical Harvesting Methods

Orchard fruit and nut growers had chosen tree shaking as an alternative to
hand harvesting even before the development of mechanical shakers. The concept
of shaking originated before the 1960’s when farmers found that some tree fruits
could be detached by hitting the primary scaffold limbs with a mallet or a club.
The mallets were about one meter long, and had a hard rubber pad near one end
that contacted the limbs. Hitting the limbs generated a low-amplitude, high
frequency vibration that transmitted to the bearing branches and caused fruit
detachment. However, the use of mallets was laborious, and in larger trees,
workers had the difficult task of climbing up the tree in order to shake the small
top limbs (O’Brien et al., 1983).

Eventually, the need for more efiective methods led to the design of more
sophisticated, mechanically powered devices. Among the first was the cable
shaker developed by JP. Fairbanks (1946) to harvest walnuts. The device

consisted of a cable with a hook at one end attached to an eccentric on a tractor.

ll

 

 

12

The cable would be hooked onto a limb while the tractor backed up to tighten
it. The eccentric would then be activated to impart a shaking motion to the
limb, thus detaching the nuts. Because only a tension force could be exerted by
the cable, the rate at which the limbs returned toward their static position was
determined by their fundamental natural frequency; therefore, the shaking
frequency was limited by the resonant frequency of the limbs. Also, care had to
be taken to avoid too great an initial cable tension, to avoid limb breakage.
Shortly after, boom shakers were developed by replacing the cable with a rigid
boom. The advantages were the elimination of the second man on the tree to
hook the cable and an easier positioning of the shaker relative to the limb. Two
types of boom shakers were developed. The more effective type had a
hydraulically actuated clamp fastened to the boom to enable the grabbing of the
limb and thus applying sustained vibration. By clamping to the tree, the
frequency of the shake was no longer limited by the natural frequency of the
limb, but rather could be varied as desired by adjusting the eccentric. The
eccentric was rigidly supported on the tractor so that, for practical purposes, the
stroke delivered to the limb was equivalent to the stroke of the eccentric. The
other type of boom shaker was equipped with a hard rubber pad instead of a
clamp at the end of the boom. Commonly known as a knocker, it was operated
by placing the pad against a limb and activating the eccentric, thus delivering a

series of pulses to the limb.

Through the years, a variety of new harvesting concepts have been
developed in an attempt to minimize damage to the tree and fruit while
maintaining effective fruit removal rates. Among these are: using pulsating air
blasts on the tree utilizing large, high powered fans; using vibrating multi-
layered combing devices to intrude the periphery of the tree and remove the fruit

by shaking the bushes; and the use of optically activated robot hand pickers.

 

13

The complex design, high manufacturing, operating, and/or maintenance cost of
these concepts have been primary factors in their lack of current acceptance

among growers.

In the early 1960’s, Adrian and F ridley developed the concept of inertia type
shakers. The basic principle behind this type of shaker was that it used an
unbalance inside a housing which was suspended by suspension bars from its
carrier. The two kinds of inertia type mechanisms developed were (1) a pair of
eccentric masses, and (2) a slider-crank mechanism with the slider fixed to the
tree. These shakers soon gained considerable acceptance among the growers
because of their isolation of vibration from their carriers, adaptability to
catching frames, high harvest rates of up to 60 trees per hour, and better

maneuverability in the orchards (O’Brien et al., 1983).

The slider crank device is used on shakers intended to attach to limbs, as it
can be designed in the form of a long slender boom desirable for reaching
primary limbs over the catching surface. It is commonly referred to as the limb
shaker and is ideal for older orchards having larger trees with heavy, willowy
branches which require separate limb shaking. Limb shakers are still being used

in some of Michigan’s older orchards on large sweet cherry trees.

Rotating masses are primarily for shakers designed to attach to tree trunks
and are commonly referred to as trunk shakers. They usually consist of two
eccentric masses set to counter-rotate at slightly different speeds when clamped
to the tree trunk. The speed difference of the masses creates a multi-directional
shake perpendicular to the main axis of the tree. Trunk shakers are ideal for
shaking stiff, smaller trees with three or four scaffolds, because of better
vibration transfer from the trunk to the fruit. Early research on trunk shakers
showed direct clamping to the trunk to be the most efficient method of attaching

the harvester to the tree, mainly because a single attachment is sufficient for

 

l4

shaking the whole tree, thus increasing harvest rates (Adrian and F ridley, 1963).
Trunk shakers have gained popular acceptance among most of Michigan’s
commercial cherry growers since the early 1960’s, and are annually used on over
95% of the tart and sweet cherry trees harvested for processing in this state
(Brown et al., 1982). Today, trunk shakers are also used for harvesting many
other tree crops such as, apples, citrus, peaches, apricots, pears, plums, olives,

nuts, and coffee (Cook and Rand, 1969).

There are many types of catching frames that accompany mechanical
shakers, for collection of the fruit. Four general designs have been used for
catching frames. The simplest configuration is an improvement on canvas laid on
the ground and is commonly called the canvas roll-out. Canvas roll—out frames
are part of a general category of extension-type catching frames. The second
configuration consists of two unit machines. The two units move straight down
the row in unison, one on each side of the tree row. The third is an inverted
umbrella concept, which has a catching surface that is wrapped around each tree.
The fourth is an over-the-row framework, which provides a single machine while
achieving down-the—row movement of a two unit machine (O’Brien et al., 1983).
The catching frames are usually sloped in one direction with a conveyor at the

bottom of the slope to carry the fruit to the carrying pallets.

2.2 - Tree Damage

The adoption of mechanical shakers as a major harvesting practice has
shown a few disadvantages in the past. Tree injury, root damage, improper
design and operation of the machines have caused a considerable amount of tree
decline. Growers’ concern for better crop yields and healthier orchards has
prompted researchers and shaker manufacturers to study mechanical harvesting

methods and equipment in order to better understand their impact on yield and

 

15

tree life.

Tree damage was perhaps first investigated in California where almond
growers used mallets or clubs to knock almonds to the ground (DeVay et al.,
1960). Beating trees with mallets caused a certain amount of bark and wood
injury including crushing and splitting of the bark tissue. Injured portions of the
bark provided entry points and a favorable nutrient medium for certain fungi
elements known as Ceratocystic fambria and Cytospora rubescens. These fungi,
although commonly present in almond orchards, were found to become parasitic
and cause cankers when in contact with injured bark tissues. The cankers
expand rapidly and kill major limbs within three or four years. Ceratocystic
fambria was later found to cause similar canker diseases in mechanically
harvested peach, apricot, prune, and nut trees (DeVay et al., 1965). Later studies

showed that tree bark strength during harvest plays a major role in bark

damage.

Adrian et al. (1965) found that tree barks are at their weakest during the
early months of summer when moisture and cell growth conditions in the
cambial zone increase, and regain strength shortly after July reaching full
strength by the end of September (Fridley et al., 1970). It is for this reason that
mechanical harvesting poses a greater threat to cherry trees. Cherries are among
the few tree crops which must be harvested in the early months of summer when
cambial activity is high, unlike other crops such as apples and nuts which are

usually not ready for harvest until early fall.
Tree damage in general takes on three different forms (Cargill et al., 1982)
1) Damage to the bark at the point of attachment of the shaker clamp.

2) Breakage of large stiff limbs (usually in older orchards previously

harvested with a limb shaker).

16

3) Breakage of small branches, leaves, and other new growth.

Recent orchard management techniques, such as reducing the number of tree
scaffolds to three or four, removing or cutting back of low hanging branches,
stubbing of the willowy branches, and trunk shaking instead of limb shaking
have reduced damage to the upper part of the trees, but bark injury to the

trunk at the point of clamp attachment still remains to be a major problem.

Bark damage is caused by excessive shear or compressive stress or strain
during clamping and shaking of the tree. Fridley et al. (1970) developed a
hydraulic, padded bark tester to apply radial (compressive) and shear stresses to
determine critical bark strengths. Test results indicated that the bark can
withstand about three or four times as much stress applied radially as when
applied tangentially to the limb. They also found that bark moisture content
has a substantial effect on the force required to shear a fruit tree limb. High
moisture content was shown to be associated with low shear strength, and low
moistures with high shear strengths. For high moisture conditions of the bark,
shear strength decreased with increase in radial pressure, while at low moisture,
shear strength increased with increase in radial stress. They suggested that
proper scheduling of irrigation prior to harvest may increase bark strength and
therefore decrease the probability of damage. Seasonal tests also indicated that
bark strength is directly related to the cessation of cambial activity and the
associated shrinkage of cambial cells which takes place as the tree gets ready for

colder weather toward the end of the summer.

In a more recent study, Brown et al. (1982) developed another bark tester to
apply both clamping pressure (compressive) and shear stress to cherry trunks.
The tester was equipped with electrical transducers to provide force and
displacement signals and a magnetic tape recorder to record signals for later

analysis. Obvious bark injury occurred for clamping pressures exceeding 1,034

17

kpa (150 psi) for sweet cherry barks and 2,412 kpa (350 psi) for tart cherry
barks during the pressure tests, under stable moisture conditions. Shear tests

also agreed with these pressure limits.

Proper selection of clamp pads also has a great effect on the amount of
damage subjected to the bark. Shaker manufacturers have redesigned their
clamp pads to increase the contact surface during clamping for a better
distribution of clamp and shake forces. Today, common pad systems consist of
two molded cylindrical rubber pads, each covered by two layers of belting. Each
pad is wrapped with one layer of belting to form a sling that holds the pad in
place. The second layer or flap is usually placed over the sling and contacts the
tree. A lubricant is applied between the two pads to reduce shear forces

transmitted to the bark by the shaker.

Frahm et al. (1983) evaluated mechanical properties of four different
varieties of clamp systems commonly used in Michigan and measured peak
contact pressures under the pads to determine their relationship to bark damage.
Contact pressure was measured by a miniature pressure transducer that was
sequentially moved on a grid pattern across the pad contact areas while clamped
on steel pipes, to simulate pressures in the bark due to clamping. A computer
program normally used to draw topographic maps was then used to plot
pressure contours under the pad. An average peak contact pressure of 2,067 kpa
(300 psi) was chosen from previous research (Brown et al., 1982) as a criterion
for pad evaluation. Manufacturer’s recommended clamping forces were used for
each pad. The pressure contour maps showed that peak pressures on all pads
exceed the contact pressure limit of 2067 kpa. Two of the pads exceeded the
value on approximately 35% to 50% of the contact area, while the other two
exceeded the pressure limit on only 15 to 20% of the contact area.

Recommendations were made to reduce clamping forces to limit contact pressure.

18

For some of the pads, the suggested clamping force to limit peak pressures to

2,067 kpa were about half the manufacturer’s recommended values.

Dynamic compressive and shear stresses on the bark during shaker
operation was studied by (Brown et al., 1984). A Friday C-clamp trunk shaker
with a standard pad was used to shake instrumented steel pipes in the
laboratory. Tests showed that static compressive stresses increased during the
start—up and the shut-down period of the shaker. For example, a static
compressive stress of 1,137 kpa (165 psi) on a 165 mm (6.5 in.) diameter pipe,
resulting from a clamping force of 18,237 Newtons (4100 lbs.), increased to 1,654
to 2,067 kpa (240 to 300 psi) at start-up when the shaker operated at 900 rpm.
The increase in compressive stress due to dynamic pressures suggests that it is

another source of bark damage.

Timm and Brown (1985) conducted detail static dynamic friction tests to
identify possible changes in flap belting and lubrication choices that would
minimize shear force transmission. Two different machines were developed for
estimating the relative static and dynamic forces existing between two lubricated
surfaces. Static friction, the characteristic of the belting surface to resist the
start of sliding, was estimated using a static friction machine. Dynamic friction,
the resistance of the belting surface to slide at high velocity, was estimated using
a dynamic friction machine. Three different beltings (Polymate 135 Polyurethane
COS, Polymate 135 Nitrile COS, and conventional Neoprene) and five different
lubricants (Modoc gear lubricant, light bearing grease, food grade grease, Crisco
shortening, and Silicone spray) were tested. The results of both static and
dynamic tests showed that Nitrile or Polyurethane belting with any of the
lubricants had the lowest friction between smooth surfaces, and thus reduce
shear force transmission to the bark better than Neoprene belting. Field

observations narrowed down the lubricant choices to spray Silicone because of

19

easy application, easy cleaning (resulting in less dirt build up), less heat build

up, and longer operation hours before lubrication.

2.3 - Shaker-Tree Vibrations

An inertia type mechanical shaker basically acts as a vibrating exciter
which, when attached to a tree or a limb, must transmit necessary forces to
overcome its inertia. When a limb or a tree is excited, it transmits motion
throughout its length and fruit is detached when its acceleration is large and/or
if the fruit-stem system has gone through a sufficient number of stress cycles.
Researchers have studied the dynamics of tree shaking by utilizing a number of
mathematical and numerical methods to come up with a better understanding of
the shaker-tree vibrational characteristics and determine optimum conditions for
effective fruit removal. An optimum system has been defined as one that causes
effective fruit removal in the least time, with minimum power, without
developing prohibitive forces as determined by bark strengths (Adrian and
Fridley, 1963).

Adrian and F ridley (1962) devel0ped the first mathematical model of an
inertia shaker-tree system. The single degree of freedom model represented the
tree and the shaker as a single mass, constrained by linear stiffness and viscous
damping and excited by a sinusoidally varying force. An expression for the
approximation of the stroke delivered by the shaker was derived from the

equation of motion to be

2mr

S =
Mshaker + Mlimb

 

where
S = displacement of the limb

m = mass of unbalance ( eccentric )

20

r = eccentricity
Mum = mass of limb

M = mass of shaker

shaker
Test results indicated that within the common frequency range, the calculated
stroke from the above equation varied about 25% from the actual displacements
in the field. Expressions for required power and torque were also derived, but did
not correlate well with the actual values because they did not account for the
torque required to overcome friction.

Halderson (1966) used the following equation for work done by a

harmonically varying force upon a harmonic motion of the same frequency to

approximate the work done by a mechanical harvester

W = 7’ ,
2P0 X0 smgb

 

where
W = work/cycle
P0 = maximum applied force
X0 = peak to peak displacement
d) = phase angle between the applied force and the resulting

displacement

The maximum work occurs when the force is 90 degrees ahead of the motion, a
component of force in phase with displacement does no work. Assuming that
the force applied to the tree varied sinusoidally, the power applied was

determined by

WN

HP = ——
33000(12)

21

where N is the vibrating frequency. Actual phase angles were obtained by
simultaneously recording force and displacement through the use of an
oscillograph strain indicator. For larger power transmissions, the actual phase
was found to be at or very close to 90 degrees. Theoretically, a shaking force
leads the displacement by zero degrees when vibrating a pure spring, and leads it
by 90 degrees when vibrating a pure dashpot, and by 180 degrees when vibrating
a pure mass (Thompson, 1981). This shows that almost all the energy applied to

the tree is dissipated by damping.

Lenker and Hedden (1968) used a vector method in a similar manner to the
analysis of alternating-current circuits, to derive an equation for limb
displacement of a limb shaker. A dimensionless form of the equation was plotted
from which the effect of a change in shaker or limb properties could be
determined. They concluded that a light boom weight was desirable, but that

compromises must be made since the boom weight could not be made zero. An

m
unbalance mass to boom mass, (———u—), ratio of 0.5 to 1.0 was theoretically shown
mb

to greatly increase shaker effectiveness.

Fruit-stem dynamics have also been modeled and studied to determine ideal
shake frequencies for detachment. The fruit-stem system generally has three
degrees of freedom, which may be described as a pendulum mode (motion of the
fruit and stem about the supporting branch), a tilting mode (motion of the fruit
about its own axis, perpendicular to the axis of the stem), and a twisting mode

(motion of the fruit about the axis of the stem)(Diener et al., 1969).

Cook and Rand (1969) formulated a linear, three degree of freedom model of
the fruit-stem system. They found that maximum instability occurs when the
frequency of the support (branch) motion is twice the natural frequency of the

system in the planar (pendulum and tilting) modes. The natural frequency of

 

22

each fruit, however, is dependent on its individual mass, radius, and stem
length; which indicates that apples, for example, have a lower natural frequency
than cherries because of their shorter stem length and larger mass. Therefore, a

higher range of shake frequency is needed to detach cherries.

The introduction of finite element methods in the 1970’s prompted
researchers to use the numerical techniques to develop more complex models to
study the tree and fruit vibrations. Yung and Fridley (1975) used a finite
element approach to develop a computer model of a complete tree system. A
complete tree system was considered as a combination of three portions: (a) a
tree structure which consisted of tree trunk, limbs, secondary branches, and
larger branches, (b) the fruit and stems, (c) the leaves and twigs. The finite
element modeling allowed the use of six generalized coordinates (three
translational and three rotational) and incorporation of elastic properties into
the system. The steady state results of forced vibration of the model correlated
fairly well with previous experimental test results on models made of steel bars
to study vibrational behavior of branched cantilever beam systems. Upadhyaya
et al. (1981) developed another finite element model to predict the dynamic
behavior of a fruit bearing limb impacted at its base. Their model was also
verified to be fairly accurate when compared with simpler tests and with

experimental results.

Recent studies have concentrated more on the vibrational characteristics of
existing machines through field tests. Affeldt et al. (1984) analyzed the dynamic
displacement of an eccentric-mass trunk shaker relative to the trunk of a cherry
tree and analyzed results to determine the relationship of relative displacements
to bark damage. A Friday C—clamp eccentric-mass trunk shaker and a cherry
tree trunk were set up with accelerometers to detect their planar my motion. The

signals from the sensors were amplified and then channeled through an analog-

23

to—digital acquisition unit. The displacement data was later plotted versus shake
time. The plots showed larger than expected amplitudes during the two to three
seconds of "start-up" and "shut-down" of the shaker operation. These unexpected
transient amplitudes are referred to as shaker gallop. Gallop, which is induced by
very large and complex acceleration patterns upon mass engagement, may cause
potential damage to the tree in the form of tangential or longitudinal pad slip or
radial impact. A probable cause of gallop was attributed to the passage of the
shake frequency through the lower natural frequency of the shaker-tree system,
that could cause resonance in the absence of damping. With the presence of large
damping forces in trees, the passage over the natural frequency merely causes

higher than steady state amplitudes.

Gallop was actually first noticed by Gould et al. (1971). In a patent request
they reported that: "With the use of a solid mass bob of fixed inertia in an
eccentric-mass trunk shaker, there is an interim period when the shaker is not up
to normal operating speed which is unstable and in which the operator and the
apparatus are subjected to uncomfortable asynchronous shaking motion, which
is not particularly effective as a harvesting motion." To eliminate the problem,
they developed a variable inertia weight bob in which the moment of inertia
rapidly increased as a function of its rotating speed during its initial acceleration
from rest and rapidly decreased during deceleration. The bob was a shell-like
structure which contained a mass of flowable heavy matter (such as oil) and a
suitable amount of metal pellets such as BB’s or lead shots. By partially filling
the cavity, the moment of inertia and the eccentricity at rest had relatively low
values, whereas when the bob was rotated and the metal pallets moved outward,
the moment of inertia and the eccentricity increased in proportion to the
redistribution of mass from portions adjacent to the axis of rotation to regions

more remote within the bob.

 

24

Al Soboh (1986) developed a rigid body model of a Friday C-clamp shaker
using a mechanism design program called IMP (Integrated Machinery Program).
Parameters such as eccentric mass acceleration, weight, and starting phase angle
between masses were used as variables to determine conditions that limit gallop.
Although the model was not successful in simulating clamped shaker-tree
conditions, some results were obtained for free shake conditions. The simulation
results indicated that for a starting phase angle of 255 degrees between the
masses, "start-up" gallop was eliminated. This could be due to the fact that the
rest position of the center of gravity of the shaker system with the masses at
this relative angular position is closer to the dynamic center of gravity during
shaker operation. Therefore, the shaker would not have to position itself about
the dynamic center of gravity when started. Although this hypothesis agrees
better with a 180 degree phase angle between the masses, other parameters such
as the shaker housing center of mass location could count for the 255 degree
phase angle simulation results. The shut down conditions could not be simulated

due to model limitations.

Afleldt (1987) developed and installed a controlled eccentricity mass housing
unit on a Friday C-clamp shaker to eliminate gallop. The unit consisted of a C-
shaped shell filled with molten lead and a hydraulic cylinder assembled on a
circular plate, mounted on a central shaft (Figure 3.3). The unit allowed
achieving high rotation frequencies at zero eccentricity. Eccentricity was then
created by extension of the hydraulic cylinder. The design, while correcting the
gallop problem, required high speed rotation of the hydraulic cylinder in action
that was complicated and required expensive components (cylinder, seals,

bearings, etc.).

 

Chapter 3

The Variable Eccentricity Shaker
And The Computer Model

3.1 - Conventional shaker design

Today’s most commonly used cherry shakers are multi-directional, inertia
type units that operate using two eccentric masses on a single or separate shafts
driven by separate variable displacement hydraulic motors. The masses counter-
rotate at slightly different speeds to create a multi directional shake pattern. The
shaker body is suspended using suspension bars with bushings used at both ends
to prevent vibration transfer to the support frame. The crude geometry and
design of these shakers limit their performance to an extent where their desirable
shake for one range of trees may not be effective for another. They also induce
unacceptable damage to tree barks causing tree decline. Although experienced
operators have learned to operate and modify shakers to fit their needs while
reducing the damage to the trees, there are still a few problems which originate

from the nature of their design and cannot be eliminated by modifications.

25

26

Major problems associated with almost all multi-directional, inertia type shakers

are 2

Gallop - Gallop is a term referred to higher than normal amplitudes
of shake at the "Start-up" and "Shut-down" periods of operation and
is considered as the major cause of tree damage in mechanical
harvesting. These initial and final deviations from desired amplitudes
have been observed in recent studies conducted on shakers (Afl'eldt et
al., 1984). The large forces that cause gallop result in high stresses and
strains at the cambium zone of the tree. While proper pads and clamp
pressures reduce the amount of injury, invisible damage in forms of
internal cell crushing still occur.

Probable causes of gallop can be attributed to the following which are

fixed characteristics of inertia type shakers :

1) The shaker natural frequency is low due to high mass and
relatively low stiffness over the natural frequency of the shaker, or
the lower natural frequency of the shaker-tree system when
clamped. This causes resonant shake amplitudes at lower "start
up" and "shut down" rotating frequencies of the shaker eccentric

masses.

2) As the shaker shuts down, the masses stop at a random position,
with an unknown phase angle in between. This results in a
randomly displaced shaker center of mass at the end of each
shake. As the succeeding shake starts, the masses accelerate about
the previous center of mass for a short period until the steady
state is reached, by which time the shake will be about the actual

center of mass of the shaker. In this short period the shake center

27

moves a distance close to the gallop amplitude. The same action
happens at shut-down as the the masses stop at random positions

and the center of mass is displaced.

b) Fixed amplitude - The shake amplitude (stroke) of the shaker is

fixed, unless the eccentric masses are replaced with heavier (for a larger
stroke) or lighter (for a smaller stroke) ones. This requires the time

consuming task of disassembling the shaker.

Random shake pattern - Cherry orchards are not uniform in tree
shapes and sizes. This is especially true in case of older orchards or
previously mechanically harvested ones. Irregular tree growth in these
orchards is common and is usually caused by insect attacks, disease,
and injury due to mechanical harvesting. These trees have uneven fruit
yield and may require more shake time in one direction than others.
Also, lateral shaking forces face reaction from stiff trees that act at the
suspended shaker tail, resulting in a lower force transfer in that
direction. This causes an uneven elliptic pattern with lower amplitudes
in the lateral direction which results in less fruit removal from the sides
of the tree. The reaction forces also cause displacements at the shaker
tail, causing a radial movement about the tree which results in shear

forces between the clamp and the bark surfaces.

 

28

3.2 - Single degree of freedom shaker system

In order to illustrate general vibrational behavior of a shaker, a single
degree of freedom system is considered and analyzed here. The system is a
spring loaded, viscously damped mass excited by a rotating machine that is
unbalanced, as shown in figure 3.1 . The unbalance is represented by an eccentric
mass m with eccentricity e that is rotating at an angular velocity w. Letting .1:
be the displacement of the nonrotating mass (M — m) from the static

equilibrium position, the displacement of m is
x + e sin cut

The equation of motion is

2
(M—m)fi+mF(at+esinwt)=—ka:-c:t
t

which, when differentiated, can be rearranged to

M25+crt+kx=(mewz)sinwt

The complete solution to the above differential equation is the combination
of the homogeneous and the particular; or otherwise known as the transient and

the steady-state solutions, respectively
:1:(t) = :r,(t) + 3:380)
The transient solution is given by
xt(t) = Xle—gw“ sin( V 1 —— g2 cunt + 9251)

where
X1 and (151 are achieved by introducing initial conditions.

k = spring stifiness

con = ’\/:—k_= natural frequency of the undamped oscillation
m

//

29

/////////L/

 

 

 

 

 

 

 

 

 

.M

m

 

 

Figure 3.1 - Single degree of freedom vibrating system excited by an unbalanced

rotor

30

c = damping coefficient
cc = 2m co, = critical damping

c . .
g” = — = damping ratio

CC

The steady state solution is given by

= 6 sin w — rt
33.93“) V(k — mm?)2 + (cw)2 ( t )
where

w = frequency of the exciting force

43 = the phase of displacement with respect to the exciting force

CCU

k—mtu2

45 = tan"1

When reduced to a nondimensional form, the steady state equations take the

following form

 

 

 

 

 

 

 

 

 

w 2
MX_ (wt)
me (ll-(5)2]; 2%" IF
2d )
45=tan"l n
1—1“)2

C0,,

Plots of the above equations (Figure 3.2) show that for small frequency
ratios of less than 1.0 the inertia forces are small which means that the shake
forces are approximately equal to the spring force and are spent in overcoming
the stiffness of the system. When the frequency ratio equals 1.0, the inertia force

gets larger and becomes balanced by the spring force. At this point, called

31

resonance, the displacement amplitude of the system becomes dependent on the
amount of damping present in the system. At frequency ratios of greater than
1.0, the damping has little eflect on the displacement amplitude and a stable
shake in achieved. A shake frequency greater than the natural frequency of the

system is ideal for shaking trees because of its stability.

The equation of motion was programmed in FORTRAN using zero initial
conditions for x and a}. The displacement results of the program were compared
with identical systems programmed with ADAMS and IMP, to verify program

accuracies. The program codes and results are presented in appendix C.

 

32

|80°

         
 

3.0

Phase angle 45
L0
0
O
l
l
l
l
l

 

2~0 0 1.0 2.0 3.0 4.0 5.0

(1.)
Frequency rClllO an

in
me

0 1.0 2.0 3.0 4.0 5.0
' Frequency r0110 “5’"

Figure 3.2 - Frequency ratio plot vs. amplitude and phase angle of a single

degree of freedom vibrating system

33

3.3 - The Variable Eccentricity shaker

The shaker was designed and built at the department of Agricultural
Engineering, Michigan State University. The following criteria were considered as
objectives:

1) To eliminate gallop.

2) To have variable eccentricity for a broad range of shaking forces.

3) To transfer shake effectively in all directions.

4) To control shake direction.

The objectives were achieved by introducing the following design changes into a

multi-directional, inertia type shaker concept:
1) Four eccentric masses to allow phase angle control during operation.

2) A phasing mechanism to control phase angle between masses during

operation.

3) A weight at shaker tail for effective shake transfer in the lateral

direction.
4) Separate drive to control shake direction.

As previously discussed, the galloping problem is attributed to: (a) The passage
over the natural frequency of the system while masses speed up to shaking
frequency, and (b) Random resting angular position (phase angle) of the masses.
As shown in the previous section, the resultant eccentricity is one of the main
parameters in control of the sinusoidal shake force. Conventional inertia type
shakers develop the force by increasing frequency, from zero, to the desired
value. This causes large excitations at periods when w=wn. However, with
variable eccentricity it is possible to achieve shaking frequency with eccentricity
set to zero ( zero resultant force ) and then move eccentricity up to full or

desired value, creating shake force. This had been proven to eliminate gallop

34

when Affeldt (1987) installed a variable eccentricity mass housing unit on a
Friday C-clamp shaker. The unit consisted of a C-shaped shell filled with molten
lead, and a hydraulic cylinder assembled on a circular plate, mounted on a
central shaft (Figure 3.3). The C shell is free to pivot to an open position,
extending eccentricity, or to a closed position (zero eccentricity) with the motion
of the hydraulic cylinder. To create a full shake period with no gallop, the
cylinder is extended from a retracted to an open position after the housing is at

shaking frequency. Retracting the cylinder before shutting down also eliminates

end gallop.

 

Figure 3.3 - Top view of the C shell variable eccentricity concept

35

A simpler alternative was implemented in the variable eccentricity shaker
with the use of four eccentric masses. Figure 3.4 shows a four mass configuration
with a position and angular velocity combination that results in zero force and
moment about its center, providing that the rotational axes of the masses are

fixed and are all symmetric relative to the center.

 

Figure 3.4 - Phase angle configuration of four eccentrics for zero resultant force.

In the position shown, the force from each counter rotating pair is equal and
opposite in direction to the other. When the upper pair accelerate downward, the
force created cancels with the equal force from the upward acceleration of the

lower pair since the acceleration and the physical property of both pairs is the

 

36

same. In this condition, the resultant moment about the center is also zero.
When the phase angle between the pairs is decreased from 180 degrees, the
created force from each pair add, producing a resultant force at the center.
Maximum force is achieved at a zero phase angle between the pairs which has a
magnitude of 4me 012. The rotation of this configuration about the center

distributes the force in all directions (Figure 3.5).

 

Figure 3.5 - Phase angle configuration of four eccentrics for maximum resultant

force.

37

A mass assembly and a phasing mechanism have been developed for the
shaker that permit control of the phase angle between two pair of masses. Four
eccentric, pie shaped, molten lead masses on four separate shafts were fitted
between two circular plates. The masses were paired. Within each pair, the
masses were chained in reverse order to counter-rotate at the same speed. Both
pairs were chained around a central shaft that supported the mass assembly.
With the help of a phasing mechanism, placed in the chain connection of one of
the masses and the drive motor, it is possible to vary the phase angle between
the two pairs, when masses are engaged. A single hydraulic motor has been used
to drive both pairs. The central shaft (mass housing) is belt driven by a side
motor on the top of the shaker housing. The rotation of the mass housing

creates a multi-directional shake.

Figure 3.6 shows a view of the variable eccentricity shaker. The block at the
tail is made of poured concrete and is free to slide on the aluminum tubing. The
tube is bolted to the shaker housing. The concrete block (referred to as the tail
weight) acts as a reaction force when clamped to a tree and resists tail
movement. It is also expected to increase shake amplitude in y direction.
Conventional multi-directional shakers create a smaller shake in y direction

resulting in an elliptical shake pattern instead of a circular pattern.

Figure 3.6 —

38

 

The variable eccentricity shaker

39

3.4 - Computer Modeling

The variable eccentricity shaker mechanism was modeled using ADAMS.
The program allows the user to design a closed or open loop mechanism and
simulate its motion for a dynamic or a kinematic analysis. It employs the rigid
body theory for creating the equations of motion and setting up the mechanism
geometry. A brief explanation of the program’s language and scope is included to

familiarize reader with the modeling process.

3.4.1 - Modeling Procedure

To model a mechanism using ADAMS, it must first be "broken down" into
its individual links or rigid bodies that are termed PARTS. The user must
choose and locate a reference frame for each part with respect to a global
reference frame. The coordinates of the parts key points are called MARKERS.
These are points such as the center of mass and joint positions relative to the
local reference frame. The PART statement defines the inertial properties of a
part, its position, orientation, and velocity. The parts can have any shape or size
and are the only model elements that can have mass, although they may be

massless under certain circumstances.

MARKERS are points with fixed location and orientation with respect to
the local part reference frame. They should be used to define any point that is
significant to the analysis or display of the model. For example, they can be used

to :
l) Designate the center of mass of a part.

2) Indicate the position and orientation of a reference frame with respect

to which the moments of inertia are specified.

3) Define position and orientation of a joint.

40

4) Denote force action and reaction points.
5) Specify points for request, and graphics output.

6) Provide other reference frames for resolving the components of vector

quantities such as velocities.

After the definition of all link characteristics, the user must define the
connections between parts using the JOINT statement. The joint statement
describes a combination of constraints on the motion of one part relative to the
other, such as translational, revolute, cylindrical, universal, spherical, planar,
rack and pinion, and screw joints. Each part must be connected to at least one
other by including a marker from each, in a joint statement. Constraint
combinations other than those available with joint statements can be defined
using a joint primitive or a JPRIM statement. A GEAR statement is also
available to simulate the constraints of a spur, helical, bevel, or a planetary gear

pair. GEAR connects the motion of a pair of joints.

Mechanism motion, velocity and acceleration with respect to simulation
time must be defined by the MOTION statement. The MOTION statement is
user programmable and can define a set of complex translational or rotational
motions within a joint. The program solves for the applied forces and torques to
create the specified motions, in the execution mode. It also solves for reaction
forces (between constrained markers) and inertia (or d’Alembert) forces. Other

applied forces must be defined using the following statements :

FIELD, and SFORCE - Linear or non linear translational or torsional force

between two markers.

BUSHING - Massless bushing with linear stiffness and damping.

41

SPRINGDAMPER - Massless spring and /or damper with linear properties.

AC CGRAV - Gravitational effect.

The program has three modes of simulation; Static, Kinematic, and
Dynamic. Simulation time and output steps must be specified for a mechanism
undergoing motion. Desired simulation results in forms of displacement, velocity,
acceleration, or force, must be predefined in the code using REQUEST
statements. In addition to the above statements, complex motions, forces, and
requests can be defined by using FUNCTION statements, or by assigning a user
written subroutine to the model code file. The output of the program is in
tabular form that can also be plotted in ADAMS’ postprocessor. The
postprocessor is utility provided to view the requested results in a graphical
form, and to graphically simulate the model with respect to time (ADAMS user’s
manual 5.2, 1987).

3.4.2 - Model Assumptions

The actual shaker has almost no displacements in the vertical 2 direction,
therefore, the shaker-tree system was modeled in a two dimensional :ry frame.

Assumptions made for modeling and analysis were:

1) System is a combination of rigid links and joints.

2) The restoring force is proportional to displacement for both the shaker

and the tree.

3) Damping is viscous (linearly proportional to velocity).

42

The simple pendulum theory was used to determine the shaker and the tail
weight’s restoring force to avoid drifting problems. The rate of the restoring

force and the damping coefficient can be defined as

and
c = 2§\/k—nT
where

m - total mass of the shaker or tail weight.
1 - length of the hanger chains.
5' - damping ratio.

9 - gravitational constant

 

43

3.4.3 - Model Definition :

The shaker was integrated into nine parts (Figure 3.7). The names and

definitions are as follows:

Part 1 : Ground (global reference frame)

Part 2 : Tube - connection between shaker housing and tail weight.
Part 3 : Tail weight.

Part 4 : Shaker housing.

Part 5 : Mass housing.

Part 6 : Mass #1.

Part 7 : Mass #2.

Part 8 : Mass #3.

Part 9 : Mass 76%.

Trees was modeled as a pair of springs and dampers connected to the clamp

position of the shaker housing. There are seven joints linking the above parts :

JOINT/11 : PLANAR - Connects the mechanism to ground (part one) through
part three. Since rigidity is assumed, one planar joint is sufficient

to connect the entire system to ground.

JOINT / 22 : TRANSLATIONAL - Connects parts three and two. It allows only
one translational degree of freedom between parts which
constrains the block for all movements relative to the shaker, but

sliding along the long axis of the tube.

JOINT/ 33 : REVOLUTE - Connects parts four and five. It acts as the central

shaft connecting the mass housing to the shaker allowing one

JOINT /44 :

JOINT /55 :

JOINT /66 :

JOINT /77 :

44

degree of rotational freedom about a vertical axis parallel to the

shaft.

REVOLUTE - connects parts six and five. It acts as a vertical

shaft connecting the eccentric mass one to the mass housing.

REVOLUTE - Connects parts seven (mass two) and five (mass
housing).
REVOLUTE - Connects parts eight (mass three) and five (mass
housing).

REVOLUTE - Connects parts nine (mass four) and five (mass

housing).

In addition to the joints, two JPRIMs rigidly connect the tube to the shaker

housing.

There are five sources of motion in the mechanism. All the moving

components are modeled to be driven independently :

MOTION/1 :
MOTION/2 :
MOTION/3 :

MOTION/4

MOTION/5 :

on joint/ 33, Rotational. Mass housing motion.
on joint/ 44, Rotational. Mass one motion.

on joint/ 55, Rotational. Mass two motion.

: on joint/ 66, Rotational. Mass three motion.

on joint / 77 , Rotational. Mass four motion.

Motions are defined by a polynomial function, using its first term to create

constant velocity.

7:
Function = goof ( t-—-t0 )
J-

45

with
t = time
a1 = speed

Function = speed * time

Mass one and mass two are in one pair and masses three and four in another.
Masses are assigned to counter-rotate with the same speed within each pair.
Figure 3.6 shows a simple view of the model and figure 3.7 shows a short period

of simulation. ADAMS code of the model is provided in appendix A.

46

 

Figure 3.7 - The variable eccentricity model

47

 

Figure 3.8 - The variable eccentricity shaker model in motion

Chapter 4

Model Response and Evaluations

4.1 - Shaker Model

An initial model of the shaker was set up with approximate physical
characteristics of the shaker at a rotating mass frequency of 13.3 Hz (800
rev/ min) and a mass housing speed of 50 rev/ min. Each eccentric had a mass of
21.6 kg (47.6 lbs) at an eccentricity of 70 mm (2.8 in’.). The model response to

variations in several parameters were studied under three conditions:

1) Free shake
2) small tree shake

3) Large tree shake

Trees were modeled as pure linear stiffness and viscous damping applied at the
clamp point of the shaker model. Two spring and damper sets were used for the

x and y direction, which at one end connected to the clamp point and at the

48

49

other end connected to points on the ground reference frame. Values for tree
masses were obtained from experimental data presented by Al-Soboh (1986). The
following equation, used for determining the average mass of trees, is a

regression fit through a scatter plot of tart cherry tree diameters vs. their mass

Y = 1.05mi)?-628

2.54

where
Y = tree mass (kg)

X = tree diameter (cm)

Average tree stiffness and damping ratios were obtained by Esch and Afleldt
(1986) by performing pull tests on a number of tart cherry trees. The static
displacements for specific applied forces were recorded and used for
determination of tree stiffness. Subsequent displacements, after release of the
trees, were also recorded to find the displacement rate of decay for a logarithmic
decrement approach to determine damping ratios for each tree. Given mass (m),
stiffness (k), and damping ratio (5'), the following equation has been used to find

tree damping coefficients (c) for input to the shaker model

c =2§Vkm

Values used for tree models are presented in Table 4.1.

50

Table 4.1 - Tree physical characteristics for model input

 

 

 

 

Tree diameter mm(in. ) 63 (2.5) 165 (6.5)

Average mass (kg) 11.5 144.0
. N

Average stiffness ( ) 12.7 657.9
mm

 

Average damping ratio (5‘) 0.1 --

 

 

 

 

Average damping coefficient 2.4 62.0 est.

 

 

51

Parameters assumed to have nonlinear effect on shaker displacements were

chosen as model variables. These were:
1) Mass of the shaker housing
2) Rotating frequency of eccentric masses
3) Position of the eccentric mass housing
4) Tail weight mass
5) Position of the tail weight

The parameter values were varied in the neighborhood of the original values
taken from the actual shaker, to determine their individual effects on shaker
behavior. Requested results from the model simulations were .7: and y
displacements of the clamp location where, in cases of tree shake, stiffness and
damping was applied. The steady state portion of the outputs were used for
measuring peak to peak amplitudes. Figure 4.1 shows the reference frame in
which displacements were measured, and shaker orientation with respect to this
reference frame. Figure 4.2 and 4.3 are a: and y plots of the base model steady
state response versus time, respectively. Figure 4.4 is an illustration of the :1: vs.
y plot of the same simulation. Real plots of shaker behavior at the clamp
position are actually smoother but, to reduce simulation time, a lower rate of

definition (output steps) was used in running the models.

fl XdlSp.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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4.2 - Variation of shaker housing mass

The effect of shaker housing mass on shaker displacement was investigated
by performing five simulations, with a different shaker mass and moment of
inertia for each run while keeping other variables constant. Exact input values

for masses and moments of inertia were:

1) M=293 kg (650 lbs) I I I =45.0,125.0,160.0 kg.m2

zz’ yy’ 22

2) M = 315 kg (700 lbs) 1,2,13,31,12, = 48.0 , 134.0 , 173.0 kgm2
3) M = 337 kg (750 lbs) 1,2,1” ,I,, = 51.0 , 144.0 , 185.0 kg.m2

4) M=360 kg (800 lbs) I I I =55.0,154.0,198.0 kg.m2

zz’ yy’ ea

5) M = 383 kg (850 lbs) 1mg, ,I,, = 58.0 , 164.0 , 210.0 kgm2

In free shake simulations, the :1: and y amplitude curves were close, for
practical purposes and declined in a relatively linear rate as the shaker housing
mass increased (Figure 4.5). When a small tree was introduced, the amplitude
curves followed approximately the same decline with increase in shaker housing
mass (Figure 4.6). However, tree shake simulations resulted in smaller
amplitudes in the y direction than the x direction, with the greatest difference in
shaking the large tree model. Shaker housing mass variations, within the range
of study, did not have as much an effect on displacement amplitudes when

shaking the large tree model (Figure 4.7).

Shaker housing mass effects displacements by absorbing a portion of the
force created by the masses to overcome its own inertia. A decrease in the ratio
of unbalance mass to shaker mass results in a higher rate of energy spent for
shaker displacement. In this study, the variation of the ratio, although not

significant (0.2-0.3), indicated that a higher unbalance to shaker housing mass

57

ratio results in a more effective transmission of shake amplitude to the tree. The
weight of the hardware (that is hydraulic motors, shafts, chains, bearings, and
housing structure material), however, limits the possibility of increasing the

unbalance to shaker mass ratio.

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4.3 - Variation of eccentric mass rotating frequency

Figures 4.8, 4.9, and 4.10 illustrate the effect of change in rotating mass
frequency on shake amplitudes during free shake, small tree, and large tree
shakes, respectively. Five different frequencies were simulated with the following

specific values:

1) 3.3 Hz (200 rev/min)
2) 6.7 Hz (400 rev/ min)
3) 10 Hz (600 rev/min)
4) 13.3 Hz (800 rev/min)

5) 15 Hz (900 rev/min)

Common frequencies for effective fruit removal are between 13 and 15 Hz. The
above range was specifically considered to find approximate locations where the

frequency ratio is equal to one.

For free shake simulations, increase in frequency from 3.3 Hz had little effect
on steady state displacement amplitudes. This is due to the low natural

frequency ((1),) of the shaker, that allows its motion to enter into the steady

 

w ). During tree shakes, the stiffness of
n

state phase at lower frequency ratios (

the tree contributes to increase the total natural frequency of the shaker-tree
system. In small tree shakes, it appears that the natural frequency of the
shaker-tree system model was somewhere between 6.7 and 10 Hz. The curves in

Figure 4.9 show that during this period the shake frequency passed through the

w =1, and entered steady state motion when at
n

 

resonant frequency ratio, where

10 Hz. The high damping coefficient of trees limit resonance which might

otherwise cause extreme amplitudes.

62

The large tree shake simulation curves show that system natural frequency
is much higher than the operating frequency range of 13-15 Hz since amplitudes
continue to increase within this range. This phenomena is one of the main
reasons that shaker damage is usually higher in smaller trees, and is due to the
fact that more resonant amplitudes are likely to be created while shaking smaller
trees. The variable eccentricity shaker eliminates this problem by reaching
desired shake frequency at no resultant eccentricity (therefore, no shake forces)
and instantly shifting to full or desired eccentricity, "jumping over" and avoiding

resonant frequencies.

 

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4.4 - Variation of the position of the eccentric mass housing

The a distance between the mass housing (center of shake forces) and the
clamp point was varied to study shake force proximity effects on displacement
magnitude differences in the a: and y directions. The a: direction amplitudes
naturally stayed the same in all simulations since the variation of the mass
housing distance to the clamp, within the simulated range, should only effect the
y component of the applied forces. The actual shaker mass housing is located at
approximately 0.75 m (40 in.) from the clamp point. In all simulations, the
shaker housing, the tail weight, and the connecting tube’s center of mass were
located at 0.6 m (24 in.), 2.9 m (115 in.), and 2.8 m (112 in.) from the clamp
point, respectively. Therefore, the resultant x component of the shaker center of
mass, excluding the eccentric masses, remained at 1.4 m (56 in.) from the clamp

point.

In free shake simulations, the :1: and y amplitudes were approximately
uniform at a mass housing distance of 1.0 m. Amplitudes in the y direction
increased as the housing position moved closer toward the clamp point (Figure
4.11). In small tree shakes, the y amplitude curves followed free shake results

closely, but with a lower rate of increase as the distance was reduced (Figure

4.12).

In large tree conditions, the y direction amplitudes were about 6 mm
smaller than amplitudes in the a: direction, at a mass housing distance of 1.0 m
from the tree (Figure 4.13). Amplitudes in the y direction increased as the mass
housing distance to tree was reduced, and came close to the a: amplitudes at a

distance of 0.4 m (8 in.).

Theoretically, the most effective location for force application is at the
center of the clamp where trees are grabbed. This, however, is not totally

possible with the variable eccentricity shaker due to existence of the four masses

67

and geometrical limitations associated with them. Therefore, the mass housing
is positioned between the resultant center of mass of the shaker and the clamp,
so that the total weight of the shaker can oppose the y component of the
reaction forces from the tree, restricting rotational movement of the shaker
about the tree’s vertical axis and also result in more uniformity in the a: and y

amplitudes.

The simulation curves here indicate that a mass housing position suitable
for causing equal a: and y amplitudes in shaking small trees may not be
sufficient to do the same in shaking larger trees, or vise versa. As illustrated by
plots of Figure 4.12 and 4.13, a mass housing a: distance from clamp of 1.0 m,
for shaking the small tree model, and 0.4 m, for shaking the large tree model,

are suitable for creating equal a: and y amplitudes.

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4.5 - Variation of the tail weight mass.

The mass of the tail weight is a determining factor in positioning the a:
component of the resultant center of mass of the shaker. Its value was varied to
examine its effect on the y amplitude of the shake. Since the tail weight is free,
for practical purposes, to slide on the tube in the a: direction, its physical
characteristics do not effect the :2: component of the shake amplitude. The

simulated mass values for the tail weight were:
1) 90 kg (200 lbs)
2) 112 kg (250 lbs)
3) 158 kg (350 lbs)

4) 180 kg (400 lbs)

An increase in the mass value from 90 kg resulted in an increase in the y
amplitude of the shake for free shake and small tree shake simulations. The a:
and y amplitudes became uniform within the range of 160-180 kg for the tail
weight mass (Figure 4.14 and 4.15). In shaking the large tree model, a lower rate
of increase in y displacements was noticed as the tail weight weight mass varied

in the simulated range (Figure 4.16).

The results indicate a relatively low sensitivity of shaker displacement to
the mass of the tail weight for larger trees, in a 90 kg (200 lbs) range. A mass of
160—180 kg is sufficient for uniformity in the :1: and y amplitudes in shaking only
small trees whereas, for larger trees, a much larger mass (perhaps in the 300 kg
range) is needed. A larger mass value was not simulated because, although
sufficient for amplitude uniformity in both directions, it would create much

higher y direction displacements in small tree shakes.

 

 

72

The mass of the tail weight, however, has a great effect on shaker rotational
movement about the tree’s vertical axis when shaking a large tree (Figure 4.17).
A tail weight mass in the 160—180 kg range reduces its motion in the y direction
during operation leading to less rotational shaker movement about the tree, thus

decreasing shear stresses between the bark and the clamp pads.

 

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4.6 - Variation of the position of the tail weight

The present position of the tail weight in the variable eccentricity shaker is
approximately 2.9 m (115 in.) from the clamp point, in the a: direction. During
initial shaker tests, the reinforced aluminum tubing experienced resonance at
operating shake frequencies of 13.3-15 Hz (800-900 rev/min) for tail weight
distances higher than 2.9 111. Therefore, unless the tube is replaced by a stronger
member, the tail weight cannot be positioned farther than 2.9 m from the clamp
point. In the simulations, the distance between the tail weight and the clamp

point was reduced to observe their respective effects on shaker displacement.

In free shake and small tree shake simulations, a tail weight position of 2.9
m from the clamp point was sufficient for uniformity in the a: and y
displacements (Figure 4.18 and 4.19). The 31 displacement amplitude curves
declined as the tail weight was moved closer to the clamp point. This trend was
also evident in shaking the large tree model, with the exception that a tail
weight distance of higher than 2.9 mifrom the clamp point is needed for

uniformity in the a: and y shake amplitudes (Figure 4.20).

The tail weight location relative to the clamp point is another factor in
positioning the resultant center of mass of the shaker. The results here indicate
that a more effective shake is achieved by placing the tail weight at farther
distance from the clamp for large trees, than for small trees. Orchard tree
spacings, however, dictate the allowable shaker length. A larger shaker length
also limits its own maneuverability between trees. Therefore, compromises have
to be made, based on experimental tests, between the mass of the tail and its
distance from clamp for a more uniform shake in both a: and y directions and

better shaker maneuverability.

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4.7 - Evaluation of the results

Although displacements from the variable eccentricity shaker experimental
tests (obtained by Esch in the fall of 1987, presented in Appendix B) were higher
than the ones displayed by the ADAMS model, the simulation results were in

qualitative agreement with the actual shaker results.

General shaker dynamic behavior is illustrated in Figures 4.21 to 4.24.
Figure 4.21 shows a close-up view of the mass housing for a short period after
engagement. Figure 4.22 is a top view of the shaker housing with masses in
motion for about 0.5 seconds of steady state simulation time. Figure 4.23 shows
the trace of the center of mass of the eccentrics and the center of tree at the
start of a steady state shake cycle. A complete steady state shake cycle is
illustrated in Figure 4.24, while tracing corner points of the shaker housing, tree
center, and the center of rotation of the eccentrics. The graphic illustrations of
the model behavior are in agreement with expected actual shaker behavior which

gives confidence to the model as a tool to predict overall shaker behavior.

The tests of the shaker showed a fairly uniform shake in the a: and y
direction of about 40 mm during free shake at a 10 Hz operating frequency. In
tree shake tests, however, the y amplitudes recorded were higher than
amplitudes in the x direction. This is attributed to a larger shaker tail weight
than initially estimated for model input. Also, the tests were conducted in fall
when trees had lost a substantial amount of their leaves, resulting in a lower
system damping and increasing the possibility of resonant excitations. Leaves
count for a large portion of tree damping due to air drag. The damping data
used for modeling had been gathered in the summer months when trees had a

full load of leaves.

 

 

82

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 4.21 - Close-up top view of the model mass housing in motion

83

 

 

 

 

 

 

 

 

 

 

 

Figure 4.22 - Close-up top view of the model shaker housing in steady state

motion

84

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 4.23 - Trace of center of mass of model eccentrics and tree center at start

of a steady state shake cycle

85

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7 .

   

 

Figure 4.24 - Trace of model shaker housing corner points, tree center, and

center of rotation of the eccentrics for a full cycle

86

The variations among the simulated and experimental results can also be
attributed to the rigid body formulation of the shaker mechanism by ADAMS.
The actual shaker structure is not as perfectly rigid as theoretically assumed by
the model. This is specifically true in the case of the aluminum tubing which
connects the tail weight to the shaker. The relative elasticity (compared to a
rigid member) allows nonlinear vibrations within the tube, caused by reaction
forces from the tail weight, that could very well be responsible for amplification

of tree displacements in the y direction.

An overview of the this study leads to the following deductions about the

variable eccentricity shaker’s behavior:

 

1) Total mass of the shaker (excluding the mass of the eccentrics) effects tree
shake amplitudes by absorbing a portion of the forces created by the
rotating masses to overcome its own inertia. A relatively higher ratio of
unbalance (eccentric) to shaker mass should result in a more effective
transmission of shake to the tree. This ratio is, however, limited due to
space limitations for eccentric masses and the weight of hardware used in

shaker assembly and power transmission.

2) Eccentric mass rotating frequencies of 10 Hz and higher are above the
natural frequency of the shaker and a shaker-small tree system. Therefore,
for smaller trees, operating the shaker at the 10 Hz neighborhood should,
for practical purposes, result in the same shake amplitudes when operating
at the common (13-15 Hz) frequencies. For larger trees, a high natural
frequency of the shaker-tree system (well over the common operating
frequency), due to high tree stiffness, allows the increase or reduction of

shake amplitude by varying the eccentric mass frequency.

3) The mass housing position on the long axis of the shaker, relative to the

clamp point, has a substantial effect on the magnitude of displacements in

87

the y direction. A shorter distance between the mass housing and the clamp
is needed for creating uniform shake amplitudes in the x and y direction in
shaking larger trees. If the distance was to be minimized ,the shaker would
be suitable for creating uniform amplitudes in large tree shakes, but would
result in higher y amplitudes in small tree shakes. In this case decreasing
resultant eccentricity would create the desired 31 amplitude, but would at

the same time reduce x amplitudes, resulting in an ineffective shake in the a:

 

direction.

At this time, space limitations in the shaker housing prevent the mass

housing from being moved any closer to the clamp.

 

4) The tail weight mass and its position relative to the clamp are
interchangeable parameters for varying the y direction shake amplitudes.
The variation of these parameters have the same type of effect as does the
position of the mass housing. Increasing tail weight mass, or its distance to
the clamp, does help in creating uniform a: and y amplitudes in large tree
shakes but, on the other hand, causes larger y amplitudes in small tree
shakes. Adjustment of the tail weight position is a practical solution to

tailor to different tree sizes.

In this study, only two tree diameters were considered while orchards consist
of a variety of tree sizes, each having a different stiffness and damping. This
would require more than one adjustment in the tail weight position during

harvest .

A larger mass, or a longer distance from the clamp, of the tail weight also

reduces shaker tail movement which results in less shear stress.

1)

Chapter 5

 

 

Conclusions

The ADAMS model of the variable eccentricity shaker mechanism was
successful in predicting its behavioral characteristics and its response to

variations in the following parameters:
Shaker housing mass
Rotating frequency of the eccentric masses
Position of the mass housing
Tail weight mass

Position of the tail weight

Variations existed among the simulated and the experimental results of
shaker operation that were attributed to the linearity and rigid body

assumptions in modeling.

The variable shake force capability obtained by adjusting the phase angle

88

3)

4)

89

between two pair of counter-rotating eccentric masses is a successful method

to achieve a wide range of shake amplitudes.

Unless the center of shake forces in both a: and y direction is positioned at
the center of the clamp, shakers will always create a non-uniform shake
pattern. The sliding tail weight introduced in the variable eccentricity
shaker does help in creating a uniform shake but, to achieve this, its

position must be adjusted for different tree sizes.

Shaker housing mass should be minimized for a more effective transfer of

inertia forces created by the eccentric masses.

Chapter 6

Recommendations

Field tests should be conducted in the harvest season to validate the the

trends in shaker behavior presented in this study.

More field experimental tests are needed to determine suitable tail weight
mass and position for a uniform shake in all directions on several common

tree sizes.

At present, the tube connecting the tail weight to the shaker is too weak
and does not support the tail weight as rigidly as desired. It should be
replaced with a stronger member to allow positioning of the tail weight at

further distances from the shaker.

A mechanism should be designed to allow the sliding of the tail weight in
the field. This would lead to a quicker adjustment to achieve a uniform

shake for different tree sizes in the orchard.

The existing ADAMS model of the shaker should be used in conjunction

90

 

91

with more accurate tree and shaker physical properties to support

experimental results of recommendation one.

Appendix A

ADAMS Code of The Model

 

92

Shaker (2-D)

RUN 0N ADAMS l! 11:! ( DYNAMIC PROBLEM )
( SHAKER WITH FOUR MASSES )

( PART IDENTIFICATION )

pant/1,cnouun
MARKER/101,9P-BSO,600,250
MARKER/102,9P-850,600,—250
MARKER/103,9P-3100,600,600
MARKER/104,9P-3100,600,-600
nanxaa/105,qp-3700,3oo,o
MARKER/106,9P-822,300,0,REULERsO,2700,0
MARKER/107,9P-4200,300,0
MARKER/108,9P-3700,300,500

 

:11: EXTRA GROUND ran DAMPER suppoar:l
MARKER/109,9P-8SO,300,750
Hansen/110,99-1aso,300,250
Hansen/111,99-aso,300,-750
MARKER/112,QP-1350,300,-250
usaxsa/a13,qp-3100.3oo,1100
MARKER/114,QP-3600,300,600
MARKER/115,9P-3100,300,-1100
MARKER/116,9P-3600,300,-600
MARKER/117,9P-2300,300,550
MARKER/118,9P-1800,300,1050
usaxsa/119,qp-2aoo,300,-550
MARKER/120,9P-1800,300,-1050

 

3!!! T083 1!!!

Paar/2.xass-22,CM-203,Iuazos.Ipuo,6E6,o
,Qo-o,3oo,o,REULER=o,o,o
MARKER/201,QP-0,0,0,REULER=900,90Q,0
MARKER/202,QP=822,0,0,REULEau9oo,900,o
MARKER/203,9P-9oo,o,o
MARKER/204,9P-1800,0,0

2!!! BLOCK MASS 11:!

Paar/3.xass=1ao,cunaoo,In-soo
,IP-loae,1026,636,Qc=822,300.o
MARKER/3OO,QPIO,O,O,REULER=900,900,0
MARKER/301,QP-28,0,-250
MARKER/302,99-o,0,0,REULaaco.27on,o
MARKER/303,QP--222,125,450
MARKER/304,9P--222,125,-450
MARxER/305,QP-278,125,-225
MARKER/306,QP-278,125,225
MARKER/307,9P-278,-125,225
MARxER/308,QP-278,-125,~225
MARKER/309,9P--222,-125,-450
MARKER/310,9PI-222,-125,4SO
MARKER/311,9P-28,0,250
MARKER/312,99-278,0,0,REULERn9oo,900,0
MARRER/313,QPI-222,O,O,REULER=9OD,90D,O

:11: saaxna 111:
PART/4,MASSI4OS,CM-4O3,IM-403,IP=SSEG,19886,15486

.90-1800,300,0
MARKER/401,9P-0,0,0 TUBE

 

93

MARKER/402,9P-9oo,0,0,REULERn0,27on,o MASS HOUSING
MARKER/403,QP-1300,0,0 CLAMP
MARKER/404,QP-1900,0,0 TREE
MARKER/405,QP-1300,150,-600 HANGERS -—>

MARKER/406,QP-1300,150,600
MARKER/407,9P-O,150,-5$O
MARKER/408,9P-O,150,550
MARKER/409,QP-1900,150,—400
MARKER/410,9P-1300,-150,-600
MARKER/411,9P-1300,-150,6OO
MARKER/412,99-1900,150,400
MARKER/413,9P-O,-1SO,-550
MARKER/414,9P-O,-150,550
MARKER/415,9P-1300,150,—400
MARKER/416,9P-1300,150,400
MARKER/417,9P-1900,-150,400
MARKER/418,99-1300,-150,400
MARKER/419,9P-1900,-150,—400
MARKER/420,QP-1300,-150,—4OO
MARKER/421,9P-1300,150,-350
MARKER/422,9p-1aoo,-1so,-350
MARKER/423,QP-1900,150,-350
MARKER/424,QP-1900,—150,—350
MARKER/425,9P-1300,150,350
MARKER/426,9P-1300,-150,350
MARKER/427,9P-1900,150,350
MARKER/428,9P-1900,~150,350
MARKER/429,9P-1300,0,-22S,REULER=9OD,90D,O
MARKER/430,9P-1300,0,225,REUL3R=9OD,90D,O
MARRER/431,QP-1600,-1so,o,aEULER=o,27on,o '

3!!! MASS HOUSING !!!!!

PART/5,MASS=1,CH=SO4,IPBO,O,0

,QG-2700.300.0
MARKER/500,9P-17S,O,175,REULER=O.27OD,O M1
MARKER/501,99-175,0,-175,REUL3R=0,27OD,0 M2
MARKER/502,9PI-17S,O,17S,REUL3R=0,27OD,O M3
MARKER/503,QP--l75,0,-175,REULER=O,27OD,O M4
MARKER/SO4,QP-0,0,0,REULER=O.270D,O SHAKER
MARKER/505,QP-20,0,0

MARKER/506,QP--20,0,0

MARKER/507,QP-0,0,2O

MARKER/509,QPIO,-15O,0,REULER=0,27OD,0

2!! HASSl ll!

Paar/6,Mass-21.6,CM=602,IP=0,0,0
.QG-2875,3oo,175,REULER=0,2700,0
MARKER/601,9P-0,0,0
MARKER/602,9P-70,0,0
MARKER/603,9P-1oo,4o.o
MARKER/604,9P-100,-40,0
MARKER/605,9P-0,0,SO
MARKER/606,QP-100,40,SO
MARKER/607,9P-100,-40,50

2!!! MASS2 !!!!

PARI/7,Mass-21.6,cM-702,1M=702,IP=o,o,o
.QG-2875,300,-17S,REULER=O,2"OD,O
MARXER/7Ol,QPIO,O,O
MARKER/7OZ,QPI7O.O,O
MARKER/703,9P-100,40.0
MARKER/704,9P-100,-40,0

 

94

MARKER/7OS,QPIO,O,SO
MARKER/706,QP-100,40,50
MARKER/707,QP-100,-40,SO

l!!! MASS3 1!!!

Paar/8,Mass-21.6,CM=802,19:0.0,0
.QG-2525.300,17S,REULER=O,27OD,1800
MARKER/801.9?-0,0,0
MARKER/802,9P-70,0,0
Masses/803,9pcloo,4o,o
MARKER/804,99-100,—40,0
MARKER/805,9P-0,0,50
MARKER/806,9P-100,40,SO
MARKER/807,9P-100,-40,50

:11: MASS4 l!!!
Paar/9,Mass-21.6,CM=902,19:0.0,0
.QG-ZSZS,300,-17S,REULER=O,2"0D,1800
MARKER/901,QP-0,0,0
MARKER/902,9P-70,0,0
MARKER/903,9P-100,40,0
MARRER/SO4,QPI1OO,-4O,O
MARKER/905,9P-0,0,50
MARKER/906,9P-100,40,SO
MARKER/907,9P-100,-40,50

( JOINT IDENTIFICATION )

JOINT/ll,I-302,J-106,PLANAR

!! BLOCK-TUBE !!
JOINT/99,II202,J=300,IRANS
I! TUBE-SHAKER 2!

JPRIM/101,I-204,J-401,AIPOIN2
JPRIM/102,I-204,J-401,0RIENTATION

l! SHAKER-HOUSING ::
JOINT/110,1-402,J=504,aav

I! HOUSING—MASSES 1:
JOINT/111,I-SOO,J-601,REV
JOINT/112,I-SOl,J-701,REV
JOINT/113,1-502,J-801,anv
JOINT/114,1-503,J-901,REV

( Monous, a spnp's )

( MASS ASSEMBLY e 50 RPM )
MOTION/1.JOINT=110,ROTATIONAL,FUNCTIONsPOLY(TIME,0,0,3OOD)

( MASSES counrsn—aorama @ 800 RPM )
MOTION/2,JOINT-111,ROTATIONAL,FUNCTIONcPOLY(TIME,0,0,48000)
Morton/3,JOINT-113,30ramIONhL,FUNCrIOM-Ponx(TIME,0.0.48000)

MOTION/4,JOINT-112,ROT,FU-POLY(TIME,0,0,-4BOOD)
MOTION/5.JOINT-114,ROT,FUIPOLY(TIME,O,0,-48000)

95

COUPLER/1,JOINCS=112,111,SCALES=1,1
COUPLER/2,JOINTS=114,113,SCALES=1,1

2!! TREE STIFFNESS 1!.

11 SPRINGDAMPER/1,I=107,J=404,TRANS,C=300,K=SOO

11 SPRINGDAMPER/2,I=108,J=404,Taaus,c=300,x=soo
SPRINGDAMPER/3,I=109.J=311,TRANS,C=10,K=34,L=500 (10.88)
SPRINGDAMPER/4,I=110,J=311,TRANS,C=O.S,K=2.75,L=500
SPRINGDAMPER/s,1:111,J=301,Tnans,c=1o,xa34,L=soo
SPRINGDAMPER/6,I=112,J=301,TRANS,C=O.5,K=2.75,L=500
SPRINGDAMPER/7,I=113,J=406,TRANS,C=1,K=5.0,L=SOO (17.6)
SPRINGDAMPER/8,I=114,J=406,TR3NS,C=1,K=S.O,L=SOO
SPRINGDAMPER/9,I=115,J=4OS,TRANS,C=1,K=5.0,L=SOO
SPRINGDAMPER/10,I=116,J=40$,TRANS,C=1,K=S.0,L=$OO

11 SPRINGDAMPER/11,I=117,J=403,TRANS,C=4.05,K-17.6,L=500

11 SPRINGDAMPER/12,I=118,J=403,TRANS,C=4.05,K=17.6,L=500

I! SPRINGDAMPER/13,I=119.J=407,?RANS,C=4.0S,K=17.6,L=500

11 SPRINGDAMPER/14,I=120,J=407,TRANS,C=4.05,K=17.6,L=500

( OUTPUT RSQUESCS )

REQUEST/1,0ISPLACSMEMTS,1:404,J=105
REQUEST/2,DISPLACEMENTS,I=300,J=106

( GRAPHICS )

GRAPHICS/1,0Urfl303,304,305,306,303,310,309,304,309,308
,305.308,307,306.307,310

GRAPHICS/2,0UTB4O7,408,4O6,405,407,413,414;408,414,411
,406.411,410.405,410,413

GRAPHICS/3,CYL,CM-201,L=1800,RAD=62,SIDES=10
GRAPHICS/4,CIRCLE,CM=504,RADn380

GRAPHICS/5,00T-601,603,604,601,605,606,603,606,607,604,607,605
GRAPHIcs/6,our=701,703,704,701,7os,706,703,706,707.704.707.705
GRAPHIcs/7,our=801,803,804,801,805,806,803,806,807.804,807,805
GRAPHICS/8,0UT=901,903,904,901,905,906,903,906,907,904,907,905
GRAPHICS/9,00T-SOS,506

GRAPHICS/10,00TBSO7,508
GRAPHIcs/11,ours4os,409,415,420,419,409,419,410,405,421,423
GRAPHIcs/12,our=406,412,416,418,417,412,417,411
GRAPHIcs/13,our=421,422.424.419.424,423,409
GRAPHICS/14,0UT=425,426,428,417,428,427,412,427,425
GRAPHIcs/15,crL,CMa429,L=600.3AD=125,SIDES=5
GRAPHICS/16,CYL,CM=430,L=600.3AD=125,SIDES=5
GRAPHICS/17,CYL,CH:431,L=300.RAD=100,81DES=10
GRAPHICS/18,C!L,CM=509,L=300.RAD=40,SIDES=10

GRAPHICS/19,01RCLB,CH-312,BAD=100
GRAPHICS/20,CIRCLE,CM-313,RAD=100

GRAPHICS/21,ch,CM=601,L=50,RAD=5
GRAPHICS/22,C!L,CM=701,L=50,RAD=5
GRAPHICS/23,C!L,CM=801,L=50,RAD=S
GRAPHICS/24,0!L,CM-901,L=50,RAD=5

(MUST HULT. BY 25 BEFORE USE)
GRAPHICS/69,SPDP,I=;05,J¢402,DA=O.2,DBRO.3,DC=O.3
,LA-0.3,LB=0.3,LC=O.35,LD=0.35,COILs-6

GRAPHICS/79,5PDP,I=;06,J-402,DA=0.2,Dsno.3,Dc=o.3
,LAsO.3,LB=O.3,LC80.35,LD=O.3S,COILs-6

 

96

( SYSTEM & CONTROL PARAMETERS )

ACCGRAV/GC=1000,JGRAVI-9807
I! DEBUG/DUMP,EPRINT,VERBOSB,DOF
OUTPUT/REQSAVE,GRSAVE,FIXED,TELETYPE

END

 

Appendix B

Experimental Shaker Data

 

 

__LO
_<l‘
_N
_O
-(I)
i
g —
$—
%_ _0
"j —<r
—C\l
5% _
l . l I l I l I 1 I I I O
Q o O O O O
.. N — r I?

(ww) iNZ—lWEJOV’ldSlG ><

Figure B.1 - Experimental shaker X displacement at 15 Hz (150 mm tree)

O
”'1’

TIME (sec)

98

 

 

 

__LO
_<,.
: __C\I
3 __O
_: “00
; L
W
—4% a...”
ifi “0
5f
f
fim ..
é h—d.
773:,_J_ "‘
E;
E ~01
i
E L
I I l I I I I I I I I I I l O
O O O O O O O O O '

(ww) INEWEIQWCISIG I

Figure B.2 - Experimental shaker Y displacement at 15 Hz (150 mm tree)

TIME (sec)

99

 

 

 

 

 

 

 

 

+9
2:
2e.
le
__: : _
-0
‘3 __q.
- --N
S _.
‘IIIII I I I I 11 0
93385320092???
I

(UM) INEIWZIOV‘IcISIG x

O
"I

Figure B.3 - Experimental shaker X displacement (Free shake)

TIME (sec)

 

100

 

 

 

 

 

 

16

I4

12

 

 

l l I I I I I
0 LO LO 0 LO 0 LO Q
r”) N v- v- I T

-15-

I l
O O
N ‘T’

ww) .LNEIWZ—IOWdSICI I

1
LO
‘7’

O
"F

Figure BA - Experimental shaker Y displacement (Free shake)

TIME (sec)

 

 

Appendix C

Single Degree of Freedom Models

101

Simple oscillators were modeled using ADAMS, IMP, and a Fortran program of
the equations of motion. The results of ADAMS and IIVIP followed the Fortran
model results, as well as each other’s, quite closely. The accurate performance of the

simple models indicate an initial confidence in both ADAMS and MP for further,

more complex modeling of the shaker.

F=mew
1.0 kg

IE
ll

102

 

P
U1j'rrljjlIUITIUIIUFT'ITT‘TVUSlIUUITITIr F

 

 

I- I-

I— 4—9 ho
'—

- <; I

I. f : Pm

' D "

~ _ ‘ Pm

 

 

j
A '
f

 

 

 

 

 

 

- ‘ I
" ‘ I‘
I: Im—
II II
I-I-x

 

 

 

T -
4
c 1 - Fortran Model

tf'ljl'I'
T?
51

 

 

 

0.20

r
‘—
IVUVIIfiTIIIrIlTITrlru1I1IIU1l11I1'I1r1 ‘
ID 0 ID 0 IO 0 IO 0
F: v': Q 0. 0. I“: F. 0!
° ° ° ° ‘7’ ‘I’ ‘I’ ‘I’

(w) IuaweooIdsIQ

103

 

 

 

 

 

 

 

 

 

._
I l I I I I I r I I I r IT! I I 1 I I l I I I ' I I r U l‘r U—' '1 I h T N
.. .8
.. -0)
LP
.. -0
,..
_ _Ix
F
I— - - (_‘o
P
_ IO
L!-
I. “ _ b¢
F

~ +
- _n
F

b b
I... - LN
- 1-

I- I-
F
.. _0
F

I- I-
0"UF'AY—I'rltUIUITTTVITUVIIVUIITIUTlrITT m

0 IO 0 In C

"Q «I 02 02 0. o '- 9 3

o o o o .— .- .—' «3 .1

I I I I l I I I I

(w) iuewaooldsgg

104

03.2%.
can; 0.0"...
38: n3. - S
08:.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

‘Tl(Ilirl‘jerITiilIIlrS!IUlIliiithfit

 

PFPI—n—Ppbbnpr—n—nlblp

rh PIE

FN ON Or we hp or mp .vw mu— N— w— Ow a
b—pbP~.I—IbP-bL-bbhb—IFLouo—vl
T
m
“.05..
n
./ ) wot...

In

C!

F
l

c

9

F
l

mad...

00.0...

and...

firq'TITIr‘IT'UUUUITWIIITU

 

 

omdl

(w) iuewaomdsgq

00000

10

105

PROGRAM RorMASS (FORTRAN)

REAL A,B,D,E,F,G,PHI.PHIl

REAL w,x,wu,c,cca,x1.n,n1,r,P

REAL MASS,RMAss,xNUM.anM,2ErA

REAL TERHI,TERM2,TERH3,TERM4

REAL x(50)
OPEH(UNIT-1,FILE='DISP.DAT',STATUS=’NEW’)

PRINT*,’ENTER SPRING STIFFNESS :'
READ*,K

MASS -1

RMAss-o.2

WN . SQRT(K/MASS)
CCR - 2*MASS*WN
PRIHT*,’WN,CCR'
PRINT*,WN,CCR

PRINT*,'ENTER SPEED OF ROTOR (RAD/SEC):’
READ*,W

PRINT*,’ENTER DAMPING COEFFICIENT :’
READ*,C

PRINT*,'ENTER SIMULAHION TIME (SEci):I
READ*,T

PRINT*,'ENTER NUMBER OF OUTPUTS DESIRED:’
READ*,N1

E -1
ZETA - C/CCR
A - 0*w
a - K-MASS*W*W
PHI . ATAN(A/B)
a . SIN(PHI)
D - COS(PHI)
P - RMASS*E*W*W
e . SQRT(1-ZETA*ZETA)
PHIl - ATAN(G/(ZETA—{W/(WN*TAN(PHI)))))
x1 - (F*H)/(SIN(PH:1)*SQRT(B*B+A*A))
M - T/Nl
I-o
no 10 Pao,T,N
I-I+1
X(I) - o
TERMl - (SIN(W*P-PHI))*F
TERM2 = SQRr(E*E+AwA)
TERMB . SIMIPM11+G«WN~P)
TBRM4 - EXP(-ZETA*WN*P)
x<1) - (X1*TER&4*TSRH3)+(TERM1/TERM2)

WRITE(1,*),P,X(I)
CONTINUE
END

 

106

UMEALANCED ROTOR ( ADAMS )

PART/1,6ROUND
MARKER/101,9P-0,0,0,REULER=JBDD,QOD,9OD
MARKER/102,QP--O.1,0.1,0
MARKER/103,9P-O.1,0.1,0
MARKER/104,9P-0,0.1,0

PART/2,MASS=1,CM:201,Qe=0,-1.o
.IP=0,0,28-5,REULER=180D,SOD,9CD
MARRER/201,gP-0,0,o
MARKER/202,9P-o,o,o
MARRER/203,gP-0,-o.os,o
MARKER/204,9P-o,-o.os,o.os
MARKER/205,9P-o,o.os,0.05
MARKER/206,QP=o,o.os,o

JOINT/11,I=201.J=101.TRANS

GRAPHICS/1,our=102,103
GRAPHIcs/2,our=203,204,205,206,203

SFORCE/1,I=201,J=101,TRANSLBQIONAL,ACTIONONLY
.FUNCTIONISHF(TIME,O,3,3,0,0}

SEE: P-A*SIN(wx-PMI) P-TRIRD,w—POURTM
FORCE/44,I=20l,J=104,GFORCE,C=6,K=10,L=l

REQUEST/1,DISPLACEMENT,I=201.38101

AcccRAv/Gc=1,JeRAv=-9.81
ANALYSIS/BRR-lOE-S _
EXECUTION/END-ZO,STEPS=100
OUTPUT/REQSAVE,GRSAVE

END

107

SYSTEM-SPDP ( I MP )

REMARK: JOINT DEFINITION

PRISM(BASE,NMT)=PRJ
DATA PRISMIPRJ)=o,o,o;o,s,o;o,o,1

REMARK: GRAPHICS

POINT(WHT)=P101,P102,P103,P104,P101
DATA POINT(P101,ABS)=-O.5,-0.5,0
DATA POINT(PIOZ,ABS)=-O.5,0.5,0
DATA P01NT(P103,AES)-o.s,o.5.o
DATA POINT(P104,ABS)-O.5,-0.5,0

POINT(WHT)=P105
DATA POINT(9105,ABS)=0,0,0

POINTIBASE)=P106,P107
DATA POINT(PlOG,ABS)=-l,1,0
DATA POINT(P107,ABS)=1,1,0

POINT(BASE)-P108
DATA P01NT(P108,ASS)=0,1,0

POINT(BASE)-P110

SPRING(P108,P105)=SP
DAMPERIP108,P105)-DP

DATA SPRING(SP)-1o,1

DATA DAMPER(DP)=6
VALUE(F)-3*SIN(3*TIME)
PORCEIPlos/P108,P105IsPDsa
DATA FORCB(PUSH)=F

UNIT MAss-1.o

DATA MASS(NRT,PRJ)=1;0,0,0

DATA GRAVITY=O,-9.81,0
FIND DYNAMICS

ZERO SPRING=0.00000001
remark ZERO ZERO=0.0000001
ZERO POSITION-0.0000001
ZERO INERTIA-0.0000001
DATA TIME-20.0.0001,0.2
LIST poaition(PRJ)

RETURN

 

LIST OF REFERENCES

LIST OF REFERENCES

ADAMS User’s Manual, Version 5.2. 1987. Mechanical Dynamics Inc., Ann
Arbor, MI.

Adrain, P. A. and R. B. Fridley. 1963. Shaker Clamp Design as Related to
Allowable Stresses of The Tree Bark.

ASAE Paper No. 63-121. American Society of Agricultural Engineers, St. Joseph,
MI 49085.

Adrian, P. A. and R. B. Fridley, 1965. Dynamics and Design Criteria of Inertia-
Type Tree Shakers.

Transactions of ASAE 8(1):12-14

Adrain, P. A., R. B. Fridley, and Coby Lorenzen. 1962. Forced Vibration of a
Tree Limb.

ASAE Paper No. 62-154. American Society of Agricultural Engineers, St. Joseph,
MI 49085.

108

109

Afieldt, H. A. 1987. Spectral Analysis for Optimal Design of a Variable
Eccentricity Trunk Shaker Harvester System.

Ph.D. Dissertation. Michigan State University, E. Lansing, MI 48824.

Affeldt, H. A., G. K. Brown, J. B. Gerrish, and C. J. Radcliffe. 1984.

Microcomputer Detection of Dynamic Displacements within Trunk Shaker Pads.

ASAE Paper No. 84-1067. American Society of Agricultural Engineers, St.
Joseph, MI 49085.

Al-Soboh, G. 1986. A Simulation Study of the Displacement Behavior of a Trunk
Shaker System during Cherry Harvest.

Ph.D. Dissertation. Michigan State University, E. Lansing, MI 48824.

Brown, G. K., J. R. Frahm, R. L. Ledebuhr, and B. F. Cargill. 1982. Bark
Damage when Trunk Shaking Cherry Trees.

ASAE Paper No. 82-1557. American Society of Agricultural Engineers, St.
Joseph, MI 49085.

Brown, G. K., J. R. Frahm, L. J. Segerlind, and B. F. Cargill. 1986. Bark
Strength and Shaker Pads vs Cherry Bark Damage During Harvesting.

Transactions of ASAE 30(5):1266-1271

Brown, G. K., L. J. Segerlind, P. L. Richey. 1984. Bark Stress Caused By Trunk
Shaker Displacements.

ASAE Paper No. 84-1066. American Society of Agricultural Engineers, St.
Joseph, MI 49085.

Burton, C. L., N. L. Schulte—Pason, G. K. Brown, and D. E. Marshal. 1986.
Influence of Mechanical Harvesting on Cherry Tree Decline.

ASAE Paper No. 86-1559. American Society of Agricultural Engineers, St.
Joseph, MI 49085.

110

Cargill, B. F., G. K. Brown, and M. J. Bukovac. 1982. Factors Affecting Bark
Damage to Cherry Trees by Harvesting Machines.

Michigan State University, CES, AIES Bulletin No. 471.

Cook, J. R. and R. H. Rand. 1969. Vibratory Fruit Harvesting: A Linear Theory
of Fruit Stem Dynamics.

Journal of Agricultural Engineering Research 14(3):195-209.

DeVay, J. E., W. H. English, F. L. Lukezic, and H. J. O’Reilly. 1960. Mallet
Wound Canker of Almond Trees.

California Agriculture 14(8):8-9.

DeVay, J. E., F. L. Lukezic, W. H. English, W. J. Moller, and B. W. Parkinson.
1965. Ceratocystic Canker of Stone Fruit Trees.

California Agriculture 19(10):2-4.

Diener, R. G., J. H. Levin, and R. T. \Nittenberger. 1969. Relation of Frequency
and Length of Shaker Stroke to the Mechanical Harvesting of Apples.

ARS 42—148. US. Department of Agriculture.

Esch, T. A. 1987. Personal Communications.

Ph.D. Graduate Student in Agricultural Engineering. Michigan State University,
E. Lansing, MI 48824.

Frahm, J. R., G. K. Brown, and L. J. Segerlind. 1983. Mechanical Properties of
Trunk Shaker Pads.

ASAE Paper No. 83-1078. American Society of Agricultural Engineers, St.
Joseph, MI 49085.

Frahm, J. R., L. J. Segerlind, G. K. Brown, and J. R. Clemens. 1984.

Instrumentation for Bark Strength and Shaker Pad Pressure Determination.

ASAE Paper No. 84-1569. American Society of Agricultural Engineers, St.
Joseph, MI 49085.

111

Fridley, R. B., G. K. Brown, and P. A. Adrian. 1970. Strength Characteristics of
Fruit Tree Bark.

Higardia 40(8):205—223.

Gould, R. D. and J. E. Richter. 1971. Variable Inertia weight for Tree Shaker.
US. Patent No. 3,564,825.

Halderson, J. L. 1966. Fundamental Factors in Mechanical Cherry Harvesting.
Transactions of ASAE 9(5):681-684.

Lenker, D. H. and S. L. Hedden. 1968. Optimum Shaking Action for Citrus Fruit
Harvesting.

Transactions of ASAE 11(3):347-349.

Michigan Department of Agriculture. 1987.
Michigan Agricultural Statistics. P.O. Box 20008, Lansing, MI 48901.

O’Brien, M., B. F. Cargill, and R. B. Fridley. 1983. Principles and Practices for
Harvesting and Handling Fruits and Nuts.

AVI Publishing Co., Inc. Westport, CT.

Timm, E. J. and G. K. Brown. 1985. Minimizing Shear Force Transmission in
Trunk Shaker Pads.

ASAE Paper No. 85-1563. American Society of Agricultural Engineers, St.
Joseph, MI 49085.

Upadhyaya, S. K., J. R. Cooke, and R. H. Rand. 1981. Limb Impact Harvesting,
Part I: Finite Element Analysis.

Transactions of ASAE 24(4):856—863.

US. Department of Agriculture. 1987. US. Agricultural Statistics.

112

Yung, C. and R. B. Fridley. 1975. Simulation of Vibration of Whole Tree Systems
Using Finite Elements.

Transactions of ASAE 18(3):475-481.

   

 

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