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THE POWER DISK PERFORMANCE EVALUATION

- DISK TRAJECTORY SIMULATION AND SIDE FORCE STUDY

presented by

HAIBO GUO

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THE POWER DISK PERFORMANCE EVALUATION
- DISK TRAJECTORY SIMULATION AND SIDE FORCE STUDY

By

Haibo Guo

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

1987

 

THE POWER DISK PERFORMANCE EVALUATION
- DISK TRAJECTORY SIMULATION AND SIDE FORCE STUDY

By

Haibo Guo

APPROVED BY:

MAJOR PROFESSOR: 2/4?va fi'szzé“ AZ M 2/1987
Thomas H Burkhardt

DEPARTMENT CHAIR . ;' (”a 44/973,41987

Donald M Edwards

ABS TRACT

THE POWER DISK PERFORMANCE EVALUATION
-- DISK TRAJECTORY SIMULATION AND SIDE FORCE STUDY
By
Haibo Guo

Primary tillage is a basic requirement in agricultural production. The power
disk, as and alternative tillage implement, needs to be evaluated both theoreti-
cally and experimentally. The computer simulation method was employed to
simulate the disk blade trajectories and a predeveloped data acquisition system
was used to collect field test data. The side force, rear furrow wheel vertical
force, ground speed, tillage depth and soil moisture content were measured.

The theoretical simulation results showed that the power disk worked in the
slipping condition. Given the gang angles of 26' to 34' and the ground speeds of
2 to 8 km/hr, the disk slippages were between 52.79% and 89.11%. The abso-
lute velocity of the disk blade, with the amplitudes between 1.098V and 2.835V,
was always greater than the implement ground speed (V).

The experimental and statistical analyses indicated that there was a linear
relationship between the side force and the ground speed. The simple linear
model could be used to express this relationship. The rear vertical force

increased as the ground speed increased. The gang angle had little effect on

either the side force or the rear vertical force.

This work is dedicated to the memory of my father.

I miss him very much.

iv'

ACKNOWLEDGEMENTS

The author wishes to sincerely thank Dr. Thomas H Burkhardt for serving
as his major professor and for helping him to develop the skill and confidence to
meet the challenge of the future.

Special thanks go to Dr. Robert H Wilkinson, committee member, for his
timely and critical advice throughout the research and Dr. Larry J Segerlind,
committee member, for his guidance during the author’s graduate study in the
department.

The author extends his appreciation to Suzanne NeSmith for her help in the
preperation of this text, Milton Mah for his assistance during the research and
Kiyohide Aiba for his cooperation of the study.

Many thanks are due to the faculty, staff and graduate students of the
Department of Agricultural Engineering for their help of the graduate study,
Albert H Case center for the use of their computer facility and Toyosha Com-
pany, Ltd, Japan for their financial support of this study.

The author wishes to express his gratitute to the people and the government
of the People’s Republic of China for the opportunity and the support to pursue

further studies.

Finally, thanks to his mother and other family members for their love and

their great encouragement.

TABLE OF CONTENTS

CHAPTER PACE
LIST OF TABLES .......................................................................................... viii
LIST OF FIGURES ........................................................................................... ix
1 INTRODUCTION .......................................................................................... 1
2 LITERATURE REVIEW ............................................................................... 3
2.1 SIDE FORCE ......................................................................................... 3
2.2 MOTION TRAJECTORIES OF THE CUTTER ................................... 5

3 OBJECTIVES .............................................................. _. ................................. 3
4 IMPLEMENT, INSTRUMENTATION AND EXPERIMENT ..................... 10
4.1 IMPLEMENT ...................................................................... - ................. 10
4.2 INSTRUMENTATION ......................................................................... 10
4.3 EXPERIMENT ..................................................................................... 11
4.3.1 EXPERIMENT DESIGN ............................................................. 11

4.3.2 EXPERIMENT PROCEDURE .................................................... 15

5 DYNAMIC SIMULATION OF DISK BLADE .............................................. 20
5.1 REFERENCE SYSTEM ....................................................................... 20
5.2 SLIPPINC DISK ................................................................................... .23
5.2.1 DEFINATION OF SLIPPACE .................................................... 23

5.2.2 TRAJECTORIES OF MOTION OF DISK POINT ..................... 23

5.3 VELOCITY DISTRIBUTION SIMULATIONS .................................... 33
5.3.1 DERIVATION OF EQUATION .................................................. 36

5.3.2 VELOCITY DISTRIBUTION IN KY, xz AND YZ PLANES ..... 39

5.3.3 VELOCITY DISTRIBUTION IN ROTATION ............................ 42

5.4 ABSOLUTE VELOCITY ...................................................................... 47

vi

6 SHDE FORCE STUDY ................................................................................. 53

6.1 SIDE FORCE MEASUREMENT ......................................................... 53
6.1.1 STRAIN GAUGE LOCATION AND WHEATSTONE

BRIDGE ....................................................................................... 53

6.1.2 CALIBRATION ........................................................................... 54

6.2 FIELD TEST RESULTS AND DISCUSSIONS .................................... 61

6.2.1 SIDE FORCE .............................................................................. 61

6.2.2 ACCURACY IN SIDE FORCE MEASUREMENT ..................... 62

6.2.3 REAR FURROW WHEEL SETTINGS ....................................... 68

6.2.4 DESIGN MODIFICATIONS ........................................................ 70

6.2.5 REAR VERTICAL FORCE ........................................................ 71

6.3 REGRESSION ANALYSIS OF SIDE FORCE ............... 74

6.3.1 REGRESSION WITH BINARY VARIABLES ............................. 74

6.3.2 SIMPLE LINEAR REGRESSION ................................................ 78

7 CONCLUSIONS AND RECOMMENDATIONS .......................................... 82

7.1 CONCLUSIONS ................................................................................... 82

7.2 RECOMMENDATIONS ......................... ' .............................................. 83

APPENDDC A POWER DISK SPECIFICATIONS ......................................... 85

APPENDDC B POWER DISK FIELD TEST RECORD SHEETS 86

APPENDDC C SOIL DATA ............................................................................ 89

APPENDDC D COMPUTER PROGRAM - MOTION .................................... 91

APPENDIX E COMPUTER PROGRAM - PLOT3.VXYZ .............................. 97

APPENDDC F CALIBRATION RAW DATA AND COMPUTATIONS ...... 106

APPENDIX C SIDE FORCE DATA ............................................................ 108

APPENDDI H REAR VERTICAL FORCE DATA ....................................... 110

BIBLIOGRAPHY ............................................................................................ 112

v11

LIST OF TABLES

TABLES P AGE
4.3.1 Layout of the field test ........................................................................... 13
5.2.1 All possible speeds in X1 direction .......................................................... 28
5.2.2 Slippage simulation results ..................................................................... 32
5.3.1 Velocity simulation results ...................................................................... 41
6.3.1 Regression results with binary variables..................._, .............................. 77
6.3.2 Regression results with one variable ....................................................... 8O
C.1 Soil data ................................................................................................... 90
F.1 Calibration raw data and computations ................................................. 107
C.1 Side force data ........................................................................................ 109
H.1 Rear vertical force data ........................................................................... 111

viii

LIST OF FIGURES

FIGURE PAGE
4.2.1 Instrumentation layout ........................................................................... 12
4.3.1 Hitching method ..................................................................................... 17
4.3.2 How to measure width and depth ........................................................... 17
4.3.3 Soil sampler and soil can ........................................................................ 19
4.3.4 Cone penetrometer .................................................................................. 19
5.1.1 Reference coordinate systems .................................................................. 21
5.1.2 0X2Y2Z2/0X1sz, coordinate systems ...................................................... 21
5.1.3 Disk movement ....................................................................................... 22
5.2.1 Disk working conditions ......................................................................... 25
5.2.2 Disk trajectories in three conditions................................ ...................... 26
5.2.3 Illustration of p and 0 ............................................................................. 29
5.2.4 Disk trajectory with slippage of 88.63% ................................................. 33
5.2.5 Disk trajectory with slippage of 77.25% ................................................. 33
5.2.6 Disk trajectory with slippage Of 65.88% ................................................. 34
5.2.7 Disk trajectory with slippage Of 54.51% ................................................. 34
5.2.8 Disk trajectory with slippage of 52.79% ................................................. .35
5.2.9 Disk trajectory with slippage of 89.11% ................................................. 35
5.3.1 Disk tangential speed .............................................................................. 36
5.3.2 Coordinate rotation about X2 ................................................................. 37
5.3.3 Coordinate rotation about Zl ................................................................. 38
5.3.4 Velocity distribution in planes ................................................................ 40
5.3.5 Tangential Speed component in X direction ............................................ 42
5.3.6 Effect Of gang angle on V, ...................................................................... 44

ix

5.3.7
5.3.8
5.3.9
5.4.1
5.4.2
5.4.3
5.4.4
5.4.5
5.4.6
5.4.7
5.4.8
6.1.1

6.1.2
6.1.3
6.1.4
6.1.5
6.1.6
6.2.1
6.2.2
6.2.3
6.2.4
6.2.5
6.2.6
6.2.7
6.2.8
6.2.9

Effect of gang angle on V, ...................................................................... 44

Efl'ect of ground speed on V, .................................................................. 45
General velocity distribution in rotation ................................................ 46
Effect of gang angle on magnitude of V... ............................................. 49
Eflect of gang angle on 1.. .............................................. ....................... 49
Effect Of gang angle on '7 ........................................................................ 50
Effect of gang angle on 6 ......................................................................... 50
Effect of ground speed on magnitude of V... ......................................... 51
Effect of ground speed on 1 .................................................................... 51
Effect of ground speed on 7 .................................................................... 52
Effect of ground speed on 6 ..................................................................... 52

Rear view of the rear wheel showing side force and

rear vertical force .................................................................................... 55
TOp view Of the rear wheel shaft and hub .............................................. 55
Strain gauge arrangement and Wheatstone bridge ................................. 56
Calibration layout .................................................................................. 57
Rear shaft free body diagram ................................................................. 60
Three resultant forces ......................................................... _ .................... 60
Relationship between side force and ground speed ................................ 63
Relationship between regular side force and ground speed ..................... 64
Relationship between regular side force and gang angle ......................... 65
Ideal hitching .......................................................................................... 66
Hitch containing side force ..................................................................... 66
Hitch producing side force ...................................................................... 67
Rear shaft position ................................................................................. 67
Incorrect rear wheel setting .................................................................... 69
Correct rear wheel setting ....................................................................... 69

6.2.10 Flange on the rear wheel arm ............................................................... 70

6.2.11 Relationship between vertical force and ground speed .......................... 72
6.2.12 Relationship between vertical force and gang angle .............................. 73
6.3.1 Linear regression analysis plot ................................................................ 81

x1

CHAPTER 1

INTRODUCTION

Machinery plays an important role in the agricultural production system.
Among all implements used in tillage, planting, harvesting and transportation,
tillage machines require the highest tractor drawbar power. It is well known
that the tractor engine can do more than pull. It has a relatively low efficiency
of 60-65% considering the power transmission between tires and soil (Soehne,
1963). A power rotary tiller, as an alternative tillage implement, transfers the
engine power directly through the PTO shaft and an insignificant transmission

loss occurs.

The power driven rotary tiller is capable of performing the tillage work

because of (Soehne, 1963):

1. the mixing of organic matter and manure into the soil;
2. the preparation Of a seedbed for vegetables;

3. the breaking of meadows; and

4. spring tillage on heavy soils to avoid many after-tillage Operations.

Nartov (1966) said that disk implements easily overcame diflerent types of Obsta-

cles in the forms of stumps, roots, stones and fallen timber residuals. The disk

rarely clogged with grass and sod-bush plants, and soil did not stick to it.

Three aspects Of tillage operations are of increasing importance on today’s
farms (Young, 1976). They are the need for increasing farmer productivity, the
need for better utilization of energy and the increasing importance of environ-
mental aspects of tillage operations. The power disk has potential to meet the
needs of increasing the productivity in terms of reducing the number of tillage
operations required and for better utilizing energy in terms of reducing the
energy loss in direct transmissions.

Even though the power disk has many advantages, it has not been widely
marketed (Abernathy, 1976). The main problem is that its working quality can
not be always guaranteed. "The disk poorly inverts the slice" (Nartov, 1966).
Therefore the quantitive performance evaluation is necessary. The best disk
working parameters need to be determined. Whether it will be economically
feasible must be figured out.

A joint research efi‘ort with Mr. Kiyohide Aiba was initiated. The ultimate
goal of this joint research was to evaluate the power disk field performance,
investigate the power requirement and study the side force on the implement.
The author focused on the side force and Mr. Aiba emphasized the power
requirement. The hitch forces, PTO torque, ground speed, engine speed and side
force were measured with the aid of an in-field microcomputer-based data

acquisition system.

CHAPTER 2

LITERATURE REVIEW

Many researchers have contributed to the power disk studies. This chapter

provides a review of the more pertinent literature which covers the past efforts

on the experimental and theoretical works.

2.1 SIDE FORCE

The side force (lateral force) has been a special problem in disk tiller studies.
A Considerable amount Of attention was given to the draft forces although the
side force was measured and discussed. Taylor (1967) developed the trailed rig
for measuring a single plow disk forces in three dimensions. The instrumented
disk was carried on an L—shaped subframe which was connected to the main
frame by six links with each link had a strain gauge on it. Six force com-
ponents, depth, distance travelled and time elapsed were measured in an instru-
ment van which followed the rig and was connected to it by‘ cable. Using this
instrument, he designed the factorial experiment to study the forces with four
variables of gang angle (a), tilt angle ()8), ground speed (V) and furrow width
(W) on two different kinds of soil. The major effects on the side force were due

to )9, V and W. They formed a quadratic relationship between the side force and

3

the disk angle. Some linear inteaction effects, such as Wfi, WV and Va on the
side force were shown.

Harrison (1977) conducted split-plot experiment tests. He concluded that the
main efi'ects of disk angle, depth and soil type were SignifiCant for the draft,
vertical and lateral reactions. The main effect of speed was significant only for
the lateral reaction. The first order interaction of the soil type—depth was
significant for draft and lateral reaction. The difference in the draft and the
lateral reaction for the soil types was large. The increase of the tillage depth
increased the draft and the lateral reaction.

At the National Tillage Machinery Laboratory, Gill (1980-1982) conducted a
series of investigations on various parameter effects on disk forces. He used the
dynamometer car to control the disk in order to change one variable continu-
ousely while all other variables were held constant. The data acquisition system
was emplOyed to measure and record the forces, forward speed, rotational velo-
city and disk angle. His results showed that there were nonlinear effects of
width Of cut, depth, disk curvature and gang angle on the side forces. The
ground speed was linear with the side force.

A dynamometric trolly was constructed by Nartov (1985) to determine the
reactive forces acting on the disk in a soil bin. It was a carriage with a moving
part and a mechanism to control the carriage. The suspended disk blade and
base Carriage were connected by six force transducers. Each Of the transducers
sensed a force particularly in the longitudinal, the transverse or the vertical
direction. The disk force in any direction was calculated from the sum of the

sensed forces in the same direction. The data suggested that the maximum

value of the lateral force occured at the disk angle between 30 degrees and 35
degrees. A sharp reduction in the lateral force at small disk angles took place
due to the counter pressure exerted by the furrow wall on the rear side Of the
disk. At large disk angles, the force was reduced as a result of decrease in the
transverse component of normal pressure of the slice on the disk. Also with
increases in the radius of curvature and a reduction in disk diameter, the lateral

force increased marginally.

2.2 MOTION TRAJECTORIES OF THE CUTTER

The power driven rotary disk cutter was described as a tool with the positive
drive by Klenin et al (1985). It performed complex motions. The cutter rotated
about its own axis due to the positive drive from the PTO shaft or the axle of
the driving wheels of the machine while it had the translatory motion with the
machine. The simple generalized cutter rotated in the plane coinciding with the
direction Of implement travel and its trajectory equations for a point on the

cutter were
X = R(% + cos¢) (2.2.1)

Y = Rsin¢ (2.2.2)

where
X - displacement of a point in the X axis;
1’ -— displacement of a point in the Y axis;
R - radial distance from the rotation axis;

414 -- rotating angle;

¢ = wt (2.2.3)

w -- angular velocity;
t -- time interval;

1 - ratio Of tangential velocity and machine ground Speed, that is

x = (2.2.4)

3‘.
V
u -- cutter tangential velocity;
V - implement travel speed.
The trajectory was a cycloid. The shape of the cycloid was governed by the
ratio 1. If 1<1, the cycloid did not have loops, that is, a shortened cycloid. If
1>1, the trajectory was represented by an elongated cycloid.

Nartov (1985) developed a set of equations to describe the unpowered disk
blade movement in three dimensions. These equations are given as Equations
5.2.7, 5.2.8 and 5.2.9 in Chapter 5. When the equations were difierentiated with
respect to t, the velocity of motion for a point on the spherical disk surface in

three axis directions was determined. Nartov gave the expressions as

V, = V — p0(sinflsinasin0 + cosacoso) (2.2.5)
V, = p0(sinacos€ - sinflcosasino) (2.2.6)
V, = p0cosfisin0 (2.2.7)

where
V,, V, and V, - velocity components in X, Y and Z directions;
V -- assembly ground speed;

p -- radial distance from the rotation axis;

o -- rotating angle;

a - disk gang angle;

13 - tilt angle.
The absolute velocity was the sum Of the three velocity vectors in X, Y and Z
directions. The absolute velocity was studied by Nartov. He concluded that the
absolute velocity was minimum at the lowest position of the disk blade. The
maximum velocity occured at the top position with the amplitude of 1.95V.
With an increase in disk angle and with a decrease in the radius, the velocity

amplitude decreased.

CHAPTER 3

OBJECTIVES

The side force is one of the important factors that affect the performance of
a power disk. The research on the single disk using specially developed equip-
ment did not Show the side force problem that occurred during real operations.
A full study Of the side force on the implement helped to find good working
parameters for the implement under various ground speeds and gang angles.

In today’s technology, a computer is a powerful tool for calculation, model-
ing and simulation. The dynamic behavior of a real motion or process can be
approximately simulated. This technique was employed to study the disk mov-
ing trajectories and the velocities.

Specifically the Objectives of this research were to study the relationship of
the side force, ground Speed and gang angle, and to Simulate the disk motion

trajectories and velocity distributions. The following parameters were measured:
1. side force;
2. vertical force on the rear wheel;

3. ground Speed;

engine speed;

tractor front and rear wheel rotation speeds;

tillage depth and width; and

soil data (moisture and cone index).

CHAPTER (I

ILIPLEMENT, INSTRUMENTATION AND EXPERIMENT

4.1 IMPLEMENT

The implement used in this research was a PTO driven disk tiller, called a
power disk. Power is transferred from the PTO shaft to the disk blades through
a centrally located bevel gear box, followed by a roller chain drive. The disk
blades have a Spherical surface. The lower part of the disk blade cuts the soil,

deforms it and then throws the soil in a particular way.

Based on a previous study (Tembo, 1986), the light model F-8OO power disk
had some penetration problems. Therefore, the heavy model F-2806 was used

in this research. Specifications Of the F-2806 disk are listed in Appendix A.

4.2 INSTRUMENTATION

A predeveloped computer on-board data acquisition system (Aiba, 1987;
Tembo, 1986) was used, and the sensors on the rear furrow wheel shaft Of the
power disk for measuring side and rear vertical forces (see Chapter 6 for details)
were added in this research.

All instruments were powered from a 12V DC-12OV AC, 60HZ, 500 watt

Sinusoidal voltage converter, inputted by a 12V DC battery. Force sensors were

10

11

strain gauges with four arm bridges. A commercially available Dickey-john
Tractor Performance Monitor II (DjTPMII) was employed to measure the engine
speed, ground speed and tractor front and rear wheel rotation speeds. A tor-
quemeter between the PTO Shaft and the implement was used to measure the

torque in the PTO shaft.

Once the transducer sensed a signal, it was amplified and sent to an analog-
to—digital converter. A computer (Apple IIe) collected all the digits in its
memory first and then saved them on a floppy disk after one set of data was col-
lected. As shown in Figure 4.2.1, 12 channels were used. Six hundred data
points were collected on each channel at a frequency of 10 data points per

second.

4.3 EXPERIMENT

The experiment was conducted in the field to measure draft forces, vertical
forces, side forces, PTO torque and rpm, ground speed and tractor front and

rear wheel rotation speeds in November, 1986 and September and October, 1987.

4.3.1 EXPERIMENT DESIGN

There were two factors that could be varied on the tractor implement assem-
bly: gang angle and ground speed. The treatments had five gang angle (26, 28,
30, 32 and 34 degrees) and four ground speed (2, 4, 6 and 8 km/hr) combina-
tions so that there would be a possibility of 20 field tests without replications.
Unfortunately tests for some combinations Of ground speeds and gang angles

were not possible because of excessive side force. For the 32 degree gang angle at

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Table 4.3.1 Layout of the field test

 

 

 

 

 

 

 

 

 

 

 

 

Test type Gang angle Ground speed
degree kilometer per hour
2 4 6 8
26 x x x x
28 x x x x
Regular _
30 x x x x
32 x x x
34 x x
28 s d h
Depth control
32 s d h
p 28 x
Hard soil
32 x
28 x x
Unpowered
32 x x
26 x x x
28 x
Short top link
30 x x
32 x

 

 

 

 

 

 

 

Notes: x--the test has been done for the maximum possible depth;
s--the test has been done for a shallow depth Of 11 cm;
d—-the test has been done for a deep depth Of 17 cm;
h--the test has been done for the depth of 17 cm using

hydraulic control.

14

8 km/hr and the 34 degree gang angle at 6 and 8 km/hr, the sway chain of the
left lower link was very tight. This tensile force in the sway chain caused the
side force reading in the rear wheel shaft to be erroneous. There was no tensile
force in this chain for any of the other tests. Therefore seventeen field tests were
conducted. These and the overall field test layout are represented in Table 4.3.1.

In a tillage operation, the depth control is usually expected to meet different
crop requirements. Six tests were performed to investigate the variation of the
drawbar power, PTO power and forces at two different depths (approximately 11
cm and 17 cm). Four out of Six tests used the depth control wheel and the other

two tests utilized the tractor hydraulic system to control the working depth.

Soil condition is another factor that affects the power disk behavior. Most Of
the tests were performed in the same field which had a soil type of sandy loam.
Two tests were conducted on a heavy clay loam soil. It was assumed that the
soil was homogeneous in the same site and the surface was flat, that is, there

was no gradient effect.

When the powered and unpowered disk were compared, it was especially
interesting to see the power requirements in both situations (Aiba, 1987). When
the PTO shaft was disconnected from the power disk, the implement behaved
like a regular unpowered disk. Four tests of this sort were conducted on 28 and

32 degree gang angles, each at 2 and 6 km/ hr.

The first year, the field test was accomplished using a top link length of 715
mm. The next year 777 mm Of the top link length was utilized and a deeper
depth resulted. In 1987, seven tests were conducted in order to study the effect of

the top link length on the working depth and other parameters using 715 mm Of

15

the top link.

4.3.2 EXPERIMENT PROCEDURE

Field tests were performed at the southwestern Side of the Michigan State
University campus farm. Soil was sandy loam with moisture content in the

range of 10-20% (Appendix C).

During the field test, a front wheel assist tractor was used to pull the imple-
ment and the position control of the hydraulic system was employed to control
the implement. The tractor operated on undisked soil (Figure 4.3.1), that is, no
wheel was in the furrow. The implement hitching method with. the tractor is
shown in Figure 4.3.1. This hitching method avoided an excessively wide strip

for the disk blade on the right Side. Parameters measured were as follows:
1. engine speed;

2. ground speed;

3. tractor front and rear wheel rotation speeds;

4. lower link tension forces;

5. lower link vertical forces;

6. top link force;

7. side force;

8. vertical force on the rear wheel; and

9. PTO torque.

To collect one set of data, several steps were followed:

16

EstabliShed width measurement references (Figure 4.3.2). Three reference
posts were set up before each test. The distance from the furrow wall to
the posts was one meter, which was called "BEFORE" in Figure 4.3.2. The
distances between posts in the direction of travel varied due to the different

ground speeds, and as the ground speed increased, this distance should be

longer.

Set the disk gang angle.

Activated the computer to collect data.

Selected the transmission gear speed for the appropriate ground speed.

Set the engine speed at aproximately 2000 rpm so that when the tractor
was in operation, the engine rpm reduced to about 1900 rpm to give a
correct PTO rpm of 540 and the expected ground speed. For higher ground
speeds , the engine speed should be adjusted higher to maintain the engine

working speed at around 1900 rpm.

When all settings described above were ready, disking was started. Once
the tractor has worked at a stable ground speed after a short run, the
RETURN key on the computer keyboard was pressed to start data collec-
tion. It took aproximately one minute to collect one set Of data for 12 chan-
nels on the computer. The computer displayed menu options when it had
finished the data collection. This set of data was saved onto a floppy disk
by choosing the appropriate Option. Steps 7, 8 and 9 were completed while

the data file was being saved.

l7

 

 

 

"‘1 (7774

 

 

44‘

Figure 4.3.1 Hitching method

 

 

 

 

 

wurru J POST

2 _ Ll «=1,

AFTER

 

L BEFORE ‘

" ' -"1 x F?"

I DISKED

 

UNDISKED

DEPTH

P-‘-
\
\

 

FURROW WALL

 

Figure 4.3.2 How to measure width and depth

 

18

7. Measured the width from the furrow wall to the posts again. This width
was called "AFTER" in Figure 4.3.2. The actual working "WIDTH" was

the "AFTER" minus the "BEFORE".
8. Measured the depth using a level and a tape.

9. Measured the hitch angles from the horizontal plane. These angles were

used to compute the hitch draft and vertical forces.

Each time the data acquisition system was turned on, instruments were
zeroed and the computer was initialized. After each half day field test, soil mois-
ture samples, using cans and the soil sampler (Figure 4.3.3), were oollcted. Also,
the cone penetrometer was used to attain the soil cone index (Figure 4.3.4). The
power disk field test record Sheets are presented in Appendix B. They summar-
ized what data needed to be recorded during the field test performance. The soil
conditions that the field test was performed in are shown in Appendix C.

The field test data was recorded in the computer code. After field tests,
work was needed to transfer the Apple II code to the Apple III code using a com-
mercial program, SOSTRAN, and then to do calibration computation which util-
ized the program MASTER (Aiba, 1987) on the Apple III plus computer to get

actual data.

 

Figure 4.3.4 Cone penetrometer

CHAPTER 5

DYNAMIC SIMULATION OF DISK BLADE

The movement of each disk blade is in three dimensions. The computer
Simulation method was employed to study the disk motion characteristics. The
simulation emphasized the disk with parameters of tilt angle (6) = 0", disk
diameter (D) = 710 mm, disk curvature (r) = 680 mm and PTO rotation speed
(11) = 540 rpm. The disk blade was simulated on the circle with a diameter of

710 mm using various gang angles (a) and ground speeds (V).

5.1 REFERENCE SYSTEMS

Nartov (1985) defined three different coordinate systems to study the
kinematics Of a disk blade (Figure 5.1.1). The origin coincided with the center Of
the circular cutting edge of the disk. OX was in the direction of the assembly
movement. OY was in the lateral direction, and OZ was in the vertical direc-
tion. By rotating OXYZ +a degrees about the Z axis, OX,Y,Zl resulted, and then
rotating OX1Y1Z, -6 degrees about the X, axis, 0X2Y2Z2 resulted. OX2 was in the
horizontal direction of the disk motion as it rotated. 0Y2 was along the disk

axis and, 0Z2 was upward along the disk edge (Figure 5.1.2). Since the power

20

 

21

 

Figure 5.1.1 Reference coordinate systems

Za

/‘L
\

 

X1 X:

Z:

O Y1 Y2

 

 

Figure 5.1.2 OX2Y2Z2/0X, 1’12, coordinate systems

22

disk used in the research had a tilt angle of [3 = 0°, OX,Y,Z, was the same as
029132,.

The gang angle (a) was the angle between a horizontal diameter Of the disk
face and the travel direction of the assembly (Figure 5.1.3). As the disk rotated,
it had a tendency to go in the X, direction which was the disk diameter direc-
tion. But the entire implement was hitched to the tractor. The disk movement
from position I to position III could be divided into two parts (Figure 5.1.3).
First, it moved to position II from position I along line I-II. Then it moved per-

pendicular to line I-II along line II-III to arrive at its final position III.

 

 

Figure 5.1.3 Disk movement

23

5.2 SLIPPING DISK

The movement of the disk blade was complicated. The blade rotated about
its own axis while the implement moved along with the tractor at a certain
speed. The blade movement was the combination of the angular rotation

powered by the PTO shaft and the translation movement pulled by the tractor.

5.2.1 DEFINITION OF SLIPPAGE

In the 0X,Y,Z, coordinate system along the line MI in Figure 5.1.3, the disk
had an angular velocity (w) powered by the PTO drive and a forward translation

speed (V,) developed by the tractor pull in the X, direction
V, = Vcosa * (5.2.1)

where
V - assembly ground speed (km/ hr);
0 -- gang angle.
The angular velocity resulted in the maximum tangential peripheral velocity

(V,') on the disk edge

w = Re: (5.2.2)

where
R -- disk radius (m);
w — disk angular velocity (rad/s).
The disk motion was a combination of the translatory motion and the rotary

motion for any point on a disk edge. There were three possible combinations:

24
If the forward speed (V,) was equal to the linear tangential speed (V,' ), that
is,
n=Rw . 62$
the disk was pure rolling (Table 5.2.1);
If the forward speed was greater than the tangential speed,
V, > R0) (5.2.4)

the disk was skidding;

If the forward speed was less than the tangential speed,
V1 < R0) (5.2.5)

the disk was slipping.

These could also be expressed as:

1.

If the disk diameter (D) was equal to the disk rolling diameter (D'), the
disk was pure rolling (Figure 5.2.1);

If the disk diameter (D) was less than the disk rolling diameter (D' ), the
disk was skidding. In this case, it was the same as that the disk was pure
rolling with its rolling diameter (D' );

If the disk diameter (D) was greater than the disk rolling diameter (D' ), the
disk was slipping. In this case, it was the same as that the disk was pure

rolling with the rolling diameter (D' ).

Trajectories of a single point on the disk for these conditions are given in Figure

5.2.2.

 

illustration

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CODCIUtion condition
pure rolling 0,. §
D' :0
v, > R w
skidding or f —‘ ” o. ——
j + —'—M = K
D, >0 K
V1<R U) / V In
slipping or // + £1) = g
D’ <D

 

Figure 5.2.1 Disk working conditions

 

 

 

 

 

A Z1

0
= XI
(a) pure rolling
I) 21
f "‘ ,4"

O

/ \/ = XI

b)skidding
A 21

U

(c) slipping

\

 

Figure 5.2.2 Disk trajectories in three conditions

27

Given
PTO speed (11) = 540 rpm.

Gear ratio = %—i—;— from PTO shaft to disk axis.

Disk diameter (D) = 710 mm.

Then the disk shaft speed is

10 11
= 540----- = 113.8
"‘ 29 18 ”pm

and the disk angular velocity is

2t
9) =- fi— 2—‘233—8 an 11.917 rad/a

The tangential speed of the disk cutting edge is
v: = Rw 0$11917 = 4.23 m /3 (5.2.6)

On the otherhand, Table 5.2.1 gives all possible V, values for our field tests
in units of m/s. These ground speed were used not only in this research, but are
reasonable for tillage Operations. Therefore, it was true that Equation 5.2.5 was
always satisfied when the tabular values were compared with 4.23 m/s, the
result Of Equation 5.2.6. Since this condition was met in all cases, the power

disk worked in the slipping condition for all of our fielf tests.

28

Table 5.2.1 All possible speeds in X, direction

 

 

 

 

 

 

 

 

 

 

 

GROUND SPEED (km / hr) 2 4 6 8
GROUND SPEED (m/s) 0.5556 1.1111 1.6667 2.2222
GANG ANGLE (degree) V1 SPEED (m/s)

26 0.4993 0.9987 1.4980 1.9973
28 0.4905 0.9811 1.4716 1.9021
30 0.4811 0.9623 1.4434 1.9245
32 0.4711 0.9423 1.4134 1.8846
34 0.4606 0.9212 1.3817 1.8423

 

 

 

 

 

 

 

5.2.2 TRAJECTORIES OF MOTION OF DISK POINT

An interactive program, MOTION, written in FORTRAN (Appendix D), was
used to Simulate motion trajectories for a point on disk edge given different gang
angles and ground speeds. Point coordinate equations for any point on a disk in

the OXYZ system, given by Nartov (1985), were as follows

X = Vt + (V r2 — (D/2)2 — V r2 - p2)cosfisina + pcosOSinfisina — psinocosa (5.2.7)

Y = (V r2 — (D /2)2 — V r2 — p2)cos,6cosa + pcosflsinficosa + psin95ina (5.2.8)
Z = (V r2 — (D /2)2 — V r2 — p2)sinfi — p cosOcosfl (5.2.9)

where
t -- time (s);
r -- disk curvature (m);
p -- SiIn ulating point’s radial distance form rotation axis (In);
0 -- Simulating angle rotated from the bottom of the disk clockwise

(rad) as shown in Figure 5.2.3; and

29

 

 

 

Figure 5.2.3 Illustration Of p and 0

0:6)! (5.2.10)

The representation of the disk trajectories was in the 0X,Y,Z, coordinate
system (Figure 5.1.1 and Figure 5.1.3), where the disk was rotated in X, direc-
tion. The~ coordinate point equations in the 0X,Y,Z, system were Obtained by
rotating XYZ +a degrees about the Z axis, that is, multiplying the vector (X Y
Z] by the matrix Operator (Rogers, 1976)

cosa sine: 0
-sma cosa 0

0 0 l

The resulting equations are

X, = Vtcosa - psinfi (5.2.11)
Y, = Vtsina + (W — thosfi + pcosOSinfi (5.2.12)

Z, = (V r2 - (D/2)2 — V r2 — p2)sinfi — pcosOcosfi (5.2.13)

30

Some simulation results are presented in Figure 5.2.4 through Figure 5.2.9
where the vertical movement is Z, of Equation 5.2.13 and the horizontal move—
ment is X, of Equation 5.2.11. All of results are in the slipping condition. The
more the disk point trajectory overlaps, the more the disk slips. The percentage
of slippage varies with gang angle and ground speed. The percentage of slippage

was defined (Zhou, 1980) as

 

s—s
SL1P%= ‘S 100 (5.2.14)
t

where
S, -- theoretical distance the disk moved;
S - actual distance the disk moved.
As the disk was rotated one entire rotation in the X, direction and D = 0.71

In, the theoretical distance is
S, = IrD = «6.71 = 2.23 m (5.2.15)

Since the disk implement was hitched to the tractor, it could move only along at
the ground speed (V) of the tractor. The distance that the implement moved at
speed (V) was the actual distance. This distance was simulated by using the
program MOTION. Part of the simulation results are listed in Table 5.2.2. Disk
trajectories with various slippages are shown in Figure 5.2.4 to Figure 5.2.9. In
one rotation, the theoretical distance (3,) was the same, and the actual distance
(S) varied with gang angles and ground speeds. By using Equation 5.2.14, disk
slippages were calculated. Table 5.2.2 showed that with a gang angle of 26' to
34' and ground speed of 2 to 8 km/hr, the disk slippages were varied from

52.79% to 89.11%.

31

As the slippage of the disk blade increased, the wear of the blade increased
due to the friction between the soil and the disk blade. According to the simula-
tions, a high ground speed resulted in low slippages which are benificial to the
disk blade wear and also to the productivity. On the other hand, it was
observed from the field tests that the disking quality was not good enough at the
ground speed of 8 km/ hr and the PTO speed Of 540 rpm. The tillage quality
was improved at lower ground speeds. Basically if the parameters of the ground
speed, the gang angle setting and the PTO speed are considered, there will be a
Optimum combination among them to result in the less disk wear, good working
quality and high productivity. This optimation needs more theoretical simula-

tions and more field test evaluations.

Table 5.2.2 Slippage simulation results

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Gang angle Ground speed Actual distance Theoretical distance Slip
degree km/ hr m m %
2 0.263283 2.2305308 88.20
26
4 0.526567 76.39
6 0.789850 64.59
8 1.053133 52.79
2 0.253685 2.2305308 88.63
30
4 0.507369 77.25
6 0.761053 65.88
8 1.014737 54.51
_ 2 0.242850 2.2305308 89.11
34
4 0.485699 78.22
6 0.728548 67 .34
8 0.971398 56.45

 

 

 

 

 

 

VERTICAL MOVEMENT (M)

VERTICAL MOVEMENT (kl)

33

 

.0
4:.

.0
U
I

.0
N
I

.0
A
l

.0
o
I

--O.l ~
~o.2—J

_O.3.-J

 

\
\_. \v/ .J/

_l____L._I.___ I l g 4......

 

-O.4

. I 'T I r 7 I T 1 T T— I— r 7
-0.-<‘r—0.3-0.}0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

HORIZONTAL MOVEMENT (M)

1
1.0

GANG ANGLE 30 DEGREES, GROUND SPEED 2 KAI/HR

Figure 5.2.4 Disk trajectory with slippage of 88.63%

 

0.4
0-3—
0.2—
0.1-4
o.oJ
—o.1~
43.2.4

-O.3-4

 

-O.4

. T I
-—O.4 —0.2 0.0

I

\.
\.

\1.

‘1 1 “ I _‘ I

I ‘ I f T 7
0.2 0.4 0.5 0.8 1.0

HORIZONTAL MOVEMENT (u)

J_._..._l_..__.l..___1.___1___l-___l

GANG ANGLE 30 DEGREES, GROUND SPEED 4 KIA/HR

Figure 5.2.5 Dsik trajectory with slippage of 77 .25%

VERTICAL MOVEMENT (M)

VERTICAL MOVEMENT (M)

34

 

0.4‘v'~--v----’--r '[--v-"-*1--r--1~Pr-r-‘r—*1~';r-‘v--—‘ -v- r r T w

21"»‘7‘ - ”""\ j
0.3- / \f/
0.1— f/ I/ J
I‘ . / l l
..o.1- { I l 3:}

--O.2—I ‘
7031 k. K/ j!

r r T T' T fif‘l
—-O.4-—0.2 0.0 0.2 0.4- +70 6 O 8 1.0 1.2 1. 4 1. 6 1.8 2.0
HOP IZONTAL MOVEMENT (M)

GANG ANGLE .30 DEGREES, GROUND SDEED 6 KM/HR

.—

 

 

1
.0
,x

-1

 

Figure 5.2.6 Disk trajectory with slippage of 65.88%

 

0.4 fi— I—j—. 7" 1 I T I I I Y—‘fi T 7' ‘ I

0.3—
0.2-

C.1-I

_J

l

0.04

—O.1—I f/ '1

--O.2~ ‘

-0.3—.

 

 

 

’70-4' VfiTfit'firf

-0.3-0.1O.1'1030.507.0971.11'l131.51.7192.1 232.5
HORIZONTAL MOVEMENT (I..)

GANG ANGLE 30 DEGREES, GROUI 1D SPEED 8 K‘A/HR

Figure 5.2.7 Disk trajectory with slippage of 54.51%

VERTICAL MOVEMENT (1V1)

VERTICAL MOVEMENT (M)

O 4“--1-r fi—l—he

0.3-
0.2-
0.1-

0.0—1

 

~O.1-

 

 

—0.2-

_0_3_

 

1

\L

35

fl"m"‘1’:fi*"flj
\K \ I

l

1

 

1

l

 

 

J

 

 

-O.4

macs—0101030507091113151/19217'325

HORIZONTAL MOVEMENT (M)

GANG ANGLE 26 DEGREES, GROUND SPEED 8 KM/HR

Figure 5.2.8 Disk trajectory with slippage of 52.79%

 

 

 

HORIZONTAL MOVEMENT (M)
GANG ANGLE 34 DEGREES, GROUND SPEED 2 KLI/HR

Figure 5.2.9 Disk trajectory with slippage of 89.11%

 

36

5.3 VELOCITY DISTRIBUTION SIMULATIONS

5.3.1 DERIVATION OF EQUATION

Any point on the rotating disk had an angular velocity (w) and radius (p).

Its linear tangential speed (V,) was expresed as

v, = pw (5.3.1)
where

p - radius of a disk point from the rotation axis (m);

w -- disk angular velocity (rad/s).
By employing the reference systems described earlier, velocity components for a

disk point in the 0X2 Ygz2 system (Figure 5.3.1) produced by I.) were

V” = —p wcoso (5.3.2)
V” = 0 (5.3.3)

V,2 = pwsino (5.3.4)
20

 

Figure 5.3.1 Disk tangential speed

37

Rotating the vector [Vfl Vyg Vfl] fl degrees about the X2 axis (Figure 5.3.2), that

is, multiplying the velocity vector in OXZYQZ2 reference by a matrix Operator

(Rogers,1976), V“, V“, 1;, resulted

 

1 0 0
[V,, v,, 14,]: m, V,2 v,21[o cosfi sinfl] (5.3.5)
0 -—sin,6 cosfi
2., ‘
I 21
fl
3 ):)

p
/

 

.Figure 5.3.2 Coordinate rotation about X2

Similarly, rotating the vector [V81 V“ V21] -a degrees about the Z1 axis (Figure

5.3.3), that is, multiplying the velocity vector in 0X,Y,Z, reference by a matrix

operator, V“, V“, V,l resulted

(5.3.6)

sina cosa 0

IV: Vy Vzl = 1V3! V11 V11] 0 l

cosa -sina 0]

 

Replacing V,,, V“ and V,l by using Equations 5.3.6, 5.3.5, 5.3.4, 5.3.3 and 5.3.2,

Equation 5.3.6 became

38

 

Figure 5.3.3 Coordinate rotation about Zl

V, = -pw(sinfisinasiuo + cosacosO) (5.3.7)
V” = pw(sinozc056 — sinflcosasinfl) (5.3.8)
VI = pwcosfisino (5.3.9)

The above equations were resulted only from the disk blade rotations. The
assembly ground speed (V) also contributed to the velocity vector [V, V, V,].
Since V was in the X direction, it only increased the magnitude of the V,. When
both the linear speed and rotation velocity were considered, that is, add V into

Equation 5.3.7, the equation became
V, = V — pw(sinflsinasin0 + cosacosO) (5.3.10)

Equations 5.3.10, 5.3.8 and 5.3.9 had a form similar to those derived by Nartov

(1985)

39

5.3.2 VELOCITY DISTRIBUTION IN KY, XZ AND YZ PLANES

Equations 5.3.10, 5.3.8 and 5.3.9 describles the disk velocities in three dimen-
sions. Using these equations, computer simulations were made with the program
MOTION. A computer program PLOT3.VX'YZ (Appendix E) was used to plot
the simulation results in the planes. Figure 5.3.4 is a typical plot output from
the computer. It showed that velocity distributions in both XZ and YZ planes
were ellipses and in the XY plane the distribution was a straight line. The
ellipse in the YZ plane was symetric about the origin, and the ellipse in the X2
plane was symetric about the X axis.

A disk blade was rotated clockwise starting at the lowest point A and went
through points B, C, D, E, F and back to point A, as shoWn in the upper left
corner of Figure 5.3.4. The velocity started with V, =-- 0 at point A. When the
blade rotated to point B, V, became zero. At points 0, D, E and F, V,, V,, V,
and V, were equal to zero respectively. And finally the blade returned to its ori-
ginal position, point A, where V, = 0. Table 5.3.1 shows that V, and V, are
equal to zero at points A, C, D, and E. For point B in the table, its value is
negative and the value just below it is positive. There is a transient point of
zero between these two points where V, is zero, which should be point B exactly.
This can be seen from Figure 5.3.4 clearly. The same story is for point F where
its values go from the positive to the negative.

A, C, D and E became the points of interest because they were located on
axis. Point B and F were denoted because the component Vm/Vp, of the disk
tangential velocity (Rw) was equal to the assembly ground speed (V) (Figure

5.3.5).

40

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2
B .——C-I~---
7.1
I)
C 0 E
x1 0
B r
A .
DISK BLADE 1";‘--——__.L_.~-
E
_— D .“ —-—-
_,., --------- “x,
C l 0 "II E O
1‘ - .?
__'._____.-__ _ _ .-' »_, .1 C(12)
. I 1‘ -' II(r)
"-\‘\._ .._.’f I" "
'-.___‘_ _..—-"‘.. .
""-—-—-r_—=—r___..
A A

Figure 5.3.4 Velocity distributions in planes

Table 5.3.1 Velocity sumulation results

romrr V,

A

I"

A

4.662450
4.638608
4.496792
4.427617
4.331610
4.209203
4.061626
4.889902
4.696339
4.479418
4.243780
4.990222
4.720670
4.437177

4.141901

0.162911

0.474939

0.791810

1.111110
1.430410
1.747281

2.059309

2.364121

2.669398

2.942890

3.212442

3.466002

3.701639

3.917661

4.112123
4.283847
4.431424
4.663732
4.64 9839
4.719014
4.760731
4.774672
4.760732
4.719016
4.649840
4.663734
4.431426
4.283860
4.112126
3.917663
3.701641
3.466006
3.212446

2.942894

2.669400

2.364126

2.069312

1.747286
1.430413
1.111114
0.791812
0.474944
0.162914
4.141897
4.437176
4.720666
4.990219
4.243777
4.479416
4.696337
4.889901
4.061624
4.209202
4.331608
4.427616
4.496791
4.638608
4.562460

41

V9
2.115157
2.107108
2.083023
2.013085
1.987698
1.916984
1.831780
1.732035
1.020305
1.195012
1.359597
1.213205
1.057579
0.893905
0.723127
0.647444
0.367294
0.184349
0.000001
4.184347
0307293
0517112
0.723120
4.898903
4.067578
4.213201
4.369696
4.195012
4.020301
4.732035
4.831780
4.916983
4.987598
4.043086
4.083024
2107109
2115158
2.107109
4.083024
4.043086
-1.987599
-1.910985
4.831781
4.732037
4.020300
4.195013
-1.359599
-1.213205
4.067581
4.893905
4.723428
0517111
0307295
.0. 181319
0.000002
0.181317
0.307291
0.517112
0.723121
0.893903
1.057577
, 1.213203
1.359595
1.195011
1.020303
1.732035
1.831779
1.910983
1.987597
2.013085
2.083023
2.107108
2.115157

V.

0.000000
0. 368696
0.734686
1.094886
1.446863
1.787808
2.116167
2.426409
2.719193
2. 99 1284
3.240609
3.465271
3.663660
3.833967
3.976196
4.086170
4.166046
4.214217

4.230314
4.214217
4.166047
4.086171
3. 976197
3.833968
3.663661
3.466272
3.240611
2.991%6
2.719196
2. 426411
2.116169
1.787811
1.446856
1.094888
0.734689
0.368699

0.000003

4.368694
4.734684
4.094884
4.446851
4.787806
4.116166
4.426407
4.719193
4.991284
4.240608
4.466271
4.663669
4.833968
4.976196
4.086171
4.166047
-4.214218
4.230316
-4.214218
-4. 166049
-4.086172
-3. 976199
4.833969
4.663663
4.466274
4.240613
4.991287
4.719199
4.426412
4.116162
4.787812
4.446868
4.094889
4.734692
4.368700
4.0(XJOO5

NOTE
Vz =0

V,=-o

 

 

Z

 

 

 

 

 

 

Figure 5.3.5 Tangential speed component in X direction

5.3.3 VELOCITY DISTRIBUTION IN ROTATION

Velocity distributions were affected by the change of the gang angle and

ground speed. Since the disk tilt angle (,8) was equal to zero in this research, the

Equation 5.3.8 became

V11 : pwsinacose (5.3.11)

Similarly Equation 5.3.9 became

Vl = pwsinB (5.3.12)

The change of gang angle (01) did not alIect V“ and changing the ground speed
had no effect on either V, or V,. For all of the tests, V, had the same distribu-
tions in any one disk rotation (Figure 5.3.9). V, remained the same distributions
for the same gang angle even though the ground speeds varied (Figure 5.3.6).

Increasing the gang angle increased the velocity in the Y axis for positive Vy and

43

decreased the velocity for negative V,. V, remained at zero for 0 == 90' and o =
270' as demonstrated in Figure 5.3.6. Increasing the gang angle at a given
ground speed decreased the velocity in the X axis for positive V, and increased
the velocity for negative V,. V, remained at zero for o = 90' and 270‘ (Figure
5.3.7). The velocity in the X direction was also affected by the ground speed.
When the the ground speed (V) was increased, V, was increased (Figure 5.3.8).
Figure 5.3.9 gives the general distributions of V,, V, and V, in two rotations
of the disk blade. The working part of the disk was located on the lower part of
the disk (the arc CBAF E of Figure 5.3.4) in between the angles 0' to 90° and
270' to 360'. In Figure 5.3.9, the working part of the disk was between 360' to
450' and 270' to 360'. The lower front part of the disk, at an angle of 270' to
360', cut and moved the soil, and the lower rear part at an angle of 0° to 90°
moved and threw the soil. In Figure 5.3.6, it was demonstrated that V, was
always positive for the lower part of the blade. V, was negative and became
slightly positive as ground speed increased, and V, was negative for the lower
front part and positive for the lower rear part of the disk blade (Figure 5.3.9).
Therefore, the lower front part of the disk cut the soil, moved it backward, to
the right and some what lower. The lower rear part of the disk moved the cut

soil upward, to the right and backward.

Vy (W8)

44

 

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3 5 H GANG ANGLE - 26 DEG

' o—o GANG ANGLE - 30 DEG
3.0 H GANG ANGLE - :54 DEG

2.5

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—2.o~ J
-2.5— ~
+ 4
“3-0 v i v r w T ' T ' 7 Y r fl I v
0 90 180 270 360 450 540 630 720
THETA (DEG)
Figure 5.3.6 Effect of gang angle on V,
r _I v I Y r 7 I —' I '7 l '— l 1
7-l x—x GANG ANGLE - 25 DEG j
j H GANG ANGLE - 30 DEG
54 H GANG ANGLE - 34 DEG ’j
1
A J
m .
\ '1
1‘ 1
V
" 3
>

   

 

 

 

'6 90 150 ' 2% T séoffisofi‘fi 550T 5:30 :30
THUA (DEG)
GROUND SPEED 4 KM/HR

Figure 5.3.7 Ellect of gang angle on V,

Vx (M / S)

45

 

10.0-

v I ' l ' I ' I —' I II VI ' T
H GSP - 2 KM/HR
H 05? - 4- KM/HR
a—a GSP - 6 KM/HR
H GSP - 8 KM/HR

  

fl v ' r v r l

90 123D F70 $60 450 540 6:50 .
THETA (DEG)
GANG ANGLE 3O DEGREE

Figure 5.3.8 Elicct of ground speed on V,

.l-:..l.1..l.J_L4 1.1.14.1 1.1.1.1 .l.

46

 

 

 

 

-5- H GSP a 3 KM/HR
451 H GSP = 2 KM/HR

 

 

Vy (W5)
0 -* N
1 l 1 J

 

 

 

_2_
.1
_3_«
45
4.0
3.5
5.0
2.5
2.0
A 1.5
U) 1.0
3 0.5
0.0 ,
V -0.5 90 1
g -1.0
-1.5
-2.0
-2.5
-3.0
—3.5
-4.0
-4.5

Figure 5.3.9 General velocity distribution in degrees of rotations

 

47

5.4 ABSOLUTE VELOCITY

Given Equations 5.3.10, 5.3.8 and 5.3.9, the magnitude of the absolute velo-

city vector of a disk point in three dimensional space is

V... = V Vf+ V,2+ V} (5.4.1)

Its direction can be determined from the direction cosines

V.

06.

cos). =-

 

(5.4.2)

V
c057 =- ——!— (5.4.3)
V».

V.
c035 =- 37: (5.4.4)

where
A -- angle between vecter V... and X axis (rad);
'1 -- angle between vector V... and Y axis (rad);
6 -- angle between vectro V... and Z axis (rad).

The simulation using the above equations and the program MOTION,
showed that the magnitude of the (absolute velocity vector varied from 2.4 m/s
up to 6.3 m/s. A was in the range of 20' to 150°, 7 was between 40' and 120',
and 6 varied in the largest range from 5° to 180‘. The results also proved that
the variation of gang angle and ground speed had the influence on the vecter of
absolute velocity.

From the simulation result plots in Figure 5.4.1 to Figure 5.4.4, the gang
angle did not have much effect on the magnitude and the direction of the abso-

lute velocity. The change of gang angle influenced the '7 values slightly more

48

than for the others.

The ground speed had more ellect on both the magnitude and direction.
Figure 5.4.5 shows that as the ground speed increased, the magnitude varied
largely. When the ground speed was at 2 km/hr, the magnitude of the absolute
velocity varied from 3.76 to 4.72 m/s. As the ground speed increased up to 8
km/hr, the manitude varied from 2.56 to 6.25 m/s, given the gang angle of 36".
The I value shifted up when the ground speed went higher (Figure 5.4.6). The
ground speed also affected 7 and 6 as indicated in Figure 5.4.7 and Figure 5.4.8.

Nartov (1985) reported that the maximum amplitude of the absolute velocity
equalled 1.95V for the unpowered disk implement. In this study of the power
disk, it proved that the absolute velocity, with the minimum amplitude of
1.098V and the maximum of 2.835V, was always greater than the ground speed

given the range of gang angles between 26° and 34" and ground speeds between 2

km/hr and 8 km/hr.

LAMBDA (DEGREE)

ABSOLUTE VELOCllY (M/S)

3.5

 

49

 

l'l'l'l’l'l’l

'I'I'I'I'I'I’
,. H GANG ANGLE- 26 DEG ~
H GANG ANGLE-I .30 DEC
H GANG ANGLE-34 DEC

 

 

 

0 V 50 '160'1507260250‘350'350'400v45rofi550'550506550766
THEIA (DEGREE)
GROUND SPEED 2 KM/HR

Figure 5.4.1 Effect of gang angle on magnitude of V...

 

 

  

I

'"I'I'I'I'I'I'I'I'I'I'I'l'
H GANG ANGLE-26 DEG ?

H GANG ANGLE - 30 DEC
H GANG ANGLE - 34 DEC

i
l l l l l l l I I l l 1 ‘1

 

 

 

0

1 5b '100'150200125030055040545050055066075501700
' THETA (DEGREE)
GROUND SPEED 2 KM/HR

Figure 5.4.2 Effect of gang angle on >.

GAMMA (DEGREE)

DELIA (DEGREE)

 

 

 

 

 

 

 

.matdrtea;ae'o‘acr"""w '.
150_ H GANG ANGLE - :50 DEG _
‘ a—a GANG ANGLE - 34 DEC ‘
413:}. '
a" ..
- w
KR;
1ol'lfi'T'IEI‘I‘T'I'I'I'I'T‘T'j
O 50 100150 200 250 300 .350 400 450 500 550 600 650 700
THUA (DEGREE)
GROUND SPEED 2 KM/HR
C
Figure 5.4.3 Eflcct of gang angle on 7
220 rvavI'I'I'I‘I'I'I'I'I'l'l
< H GANG ANGLE — 26 DEG
200- H GANG ANGLE - 30 DEG
‘ a—a GANG ANGLE - 34 DEG
180-
160-
140—
120-
100-
A
80-
60-
40-
204
0

 

 

0 . 5'0 '100'1505602501300350460450560550500550765
THETA (DEGREE)
GROUND SPEED 2 KM/HR

Figure 5.4.4 Effect of gang angle on 6

 

 

51

 

 

 

 

  
 
 

 

aij'fiI'I'I I I I I
.HGSP~2KM/HR ' I '

A :a—o esp-4KM/HR

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U) .

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26'SIO'T'I'I'I'I'I'I'I‘I‘I'I'I‘fi—

100150200250300350400450500550600650700

THETA (DEGREE)
GANG ANGLE 26 DEGREE

Figure 5.4.5 Effect of ground speed on magnitude of V...

LAMBDA (DEGREE)

190—
170-
1501
130$

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110-

d

90-

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70-

q

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.

 

 

10

 

0 ' 5'0 '100'150200250500'350‘450'450'500550'500655700

THEIA (DEGREE)
GANG ANGLE 26 DEGREE

Figure 5.4.6 Effect of ground speed on )s

GAMMA (DEGREE)

DELTA (DEGREE)

 

 

 

 

 

180 .— fi . . r . a fi T r A . a T
. Ins—air GSl’ -'2 Kill/HR 1 j T r r E ‘ ' T.
160- H CSP :- 4 KM/HR
H 05? - 6 KM/HR -
' H 05? - 8 KM/HR *
140— —
120— .1
100- J
80-1 -—l
j r i
so A..- a;
40 >
ZOTTI‘fifiI'T‘IfiYrIfiY‘TfiT‘iijl‘lE
0 50 100150 200 250300 .350 400450500550 600 650700
THETA (DEGREE)
GANG ANGLE 26 DEGREE
Figure 5.4.7 Ellect of ground speed on 7
220 vwvfifiIfiIr'Ivfi'fiIrIfiIvfi'T'II—r
H GSP - 2 KM/HR
200 4 H GSP .- 4 KM/HR ‘4
180-4 H GSP - 6 KM/HR J
J H GSP - 8 KM/HR " .1
150- .11 ~
1 '4? "
140~ a: a
'1

 

 
 

:llijlnl

 

 

 

IrrI—II*III'IRITI'Tv—IvIfiRIET
0 50 100 150 200 250 300 350 400 450 500 550 600 650 700

THETA (DEGREE)
GANG ANGLE 26 DEGREE

Figure 5.4.8 Effect of ground speed on 6

CHAPTER 6

SIDE FORCE STUDY

The side force is one of the key problems that should be considered during
power disk design and study. It is generated by the reaction of the spherical

disk in cutting the soil, deforming the slice, moving the soil along the disk and

throwing it to one side.

6.1 SIDE FORCE MEASUREMENT

6.1.1 STRAIN GAUGE LOCATION AND WHEATSTONE BRIDGE

Previous researchers have developed many different kinds of equipment to
study the reactions of a single disk blade, and a few of them have studied an
entire commercial implement. In this research, an attempt was made to put
strain gauges on the implement directly.

It was considered that the side force generated by the working disks was bal-
anced by the rear furrow wheel. Therefore, two forces, the side force (SDF) and
the vertical force (VTF), existed against the rear furrow wheel (Figure 6.1.1).

Both forces were assumed to act on the the lowest point of the wheel’s rim circle.

53

54

The side force and the vertical force produced tension and a bending moment on
the shaft. The strain gauges were put on the rear furrow wheel shaft to measure
these two forces. This shaft was manufactured with the length of 125 mm and
was extended up to 270 mm (Figure 6.1.2) during the research. Therefore there
was enough space for the strain gauges.

Two gauges were put on the top and the bottom of the shaft separately, and
two on each side of the shaft. The top and bottom gauges formed a four arm
Wheatstone bridge to measured the bending moment and the side gauges formed
the other bridge to measure the tension. The Wheatstone bridge circuit and

gauge arrangement are shown in Figure 6.1.3.

6.1.2 CALIBRATION
The calibration was carried out with two tractors. One of the tractors was
hitched with the power disk so that the implement could be moved easily. The
other tractor supplied a. hydraulic power. The layout of the calibration is given
in Figure 6.1.4. The rear furrow wheel shaft was affixed to 'a large post to
prevent any movement of the power disk while external forces were applied. The
horizontal force, which was produced mainly by the two way hydraulic cylinder,
was read from the hyraulic dynamometer. The chain hoist gave the vertical
force read from the 500 pound spring scale. Both forces applied to the bolt holes
on the hub. The strain gauge responses were recorded by the computer in the
data acquisition system. The calibration raw data and their computations are

listed in Appendix F.

55

strain gauges -——-—-—— 6
3!: L‘
I} i

312
SDF

 

12

VT 1“

Figure 6.1.1 Rear view of the rear wheel showing

side force and rear vertical force

 

 

 

 

 

 

 

Figure 6.1.2 Top view of the rear wheel shaft and hub

56

tension bending

left right top bottom

R? ll l 33 Hal—“M --—-——-———- R‘
Hie—~47? [mums E3 Eng.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

power

 

reading

 

 

 

L
K

 

 

Figure 6.1.3 Strian gauge arrangement and Wheatstone bridge

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To compute the calibration equations, the rear shaft free body diagram was
considered (Figure 6.1.5). P, was split into two components, the vertical force
(V,) and the horizontal force (H,) giving the angles of 45, and ¢2. Then the three
forces of P2, H, and V, were moved to the strain gauge point and combined as the
vertical force (V), the horinzontal force (H) and the bending moment (M) when
the dimensions of x’s and y’s were known (Figure 6.1.6). Therefore the bending
gauges, that is, the top-bottom gauges, could only sense the moment (M) and
the side gauges responsed to the forces of H and V. The first order linear equa-

tions were obtained
CH13 = —150.883+0.195621H+0.310272V (6.1.1)
CH14 = 62.44379-7.99175M (6.1.2)

where
CH13 - channel 13 computer reading (mv);
CH14 -- channel 14 computer reading (mv);
H - horizontal force (lbs);
V - vertical force (lbs);
M -- bending moment (lbs-mm).
from statistical analysis. The coficients of determination for each of the equa-
tions were 0.980 and 0.998, respectively.
In the field tests, it was assumed that the side force (SDF) and the vertical
force (V TF) acted on the circle of the rear wheel rim (Figure 6.1.1). Given 2,, 22,

y, and y2, the relationships between H, V and M and SDF and VTF were

H = SDF (6.1.3)

59

V = VTF (6.1.4)
M = 0.234565DF—0.13265 VTF (6.1.5)

where
SDF - side force;
VTF -- vertical force.
Substituting the above equations into Equations 6.1.1 and 6.1.2, the strain gauge

responses to the forces of SDF and VTF were determined
CH13 = -150.883+0.195021SDF+0.310272 VTF (6.1.6)
01714 = 02.44379—1.87454493DF+10001050 VTF (6.1.7)

where
SDF -- side force (lbs);

VTF - vertical force (lbs).

These two equations could be expressed in a matrix form

[CH13]_ [ 0.195021 0.310272 SDF] + [—150.883 (6 1 8)
01114 ‘ —l.8745449 1.0001050 VTF 02.44379 ° '

Solved for SDF and VTF, and changed the force unit from pounds to Newtons

SDF]: [5.9912813 4.7535299“ CH13+150.883 (6 1 9)
VTF 1 5941570 1.1055095 CHM—62.44379 ° -

where
SDF -- side force (N);
VTF - vertical force (N).
Equation 6.1.9 was the one that was used in the program MASTER to do cali-

bration computations (Aiba, 1987 )

00

1),

31:1
311 Pt

 

 

it! (fil

Figure 6.1.5 Rear shaft free body diagram

 

1 V
\fi 11
M \

Figure 6.1.6 Three resultant forces

61

6.2 FIELD TEST RESULTS AND DISCUSSIONS

Using the method and the instrumentation just discussed, the side force and
the vertical force were measured and calculated. Appendix G lists all side force
data with their extremes (the minimum and the maximum) and Appendix H

gives the rear vertical force data.

6.2.1 SIDE FORCE

Figure 6.2.1 ploted all side force data versus the ground speed. Each point
of Figure 6.2.1 represents the average of 600 data points for a single test. Clearly
there was a trend that as the ground speed increased, the side force also
increased. For the regular tests where only gang angle andground speed were
varied, the results showed in Figure 6.2.1 were closely related. For the tests with
additional variables, such as soil type and depth control, that is, where more
than two variables were varied, the side force results were lower than the regular
ones. This implied the new variables affected the side force. The results using
the depth wheel to control the working depth were a lot lower than the regular
results because the depth wheel absorbed part of the side force. The other vari-
able effects were not clear because there was not enough data to investigate.
Therefore only the regular results where the ground speed and the gang angle
were varied are discussed in the rest of the chapter.

The regular test side force results versus the ground speed for different gang
angles are shown in Figure 6.2.2. The side force was linear with the ground
speed. At each gang angle setting, the linear relationship between the side force

and the ground speed was slightly different from the others. The side force was

62

highest at the 30' gang angle. Figure 6.2.3 presents the relationship between the
side force and the gang angle for different ground speeds. For a given speed, the
side force was almost constant as gang angle changed. The figure clearly indi-
cated that the side force increased as the ground speed increased, but gang angle

had little, if any, influence on side force.

6.2.2 ACCURACY IN SIDE FORCE MEASUREMENT

The data acquisition system worked well throughout the research. The sys«
tem gave high linear responses which were indicated by the coefficients of deter-
mination (0.980 and 0.998) in calibration regressions.

There were two things about the implement gang angle settings realized after
completing the field tests which resulted in inaccuracy in the side force measure-
ment. One was that the relative positions of the implement about the tractor
varied according to the gang angle settings and thereby the three point hitch
may absorbed some of the side force. If the relative position between the tractor
and the implement was ideal and the top link was parallel to the travel direction
and the lower links contained the side force in the same magnitudes but the
opposite directions (Figure 6.2.4), there would be no hitching effect. This relative
implement position varied due to the change of the gang angle. When the imple-
ment swung to the left relatively (Figure 6.2.5), the hitch would absorb some
side force. Therefore the measured side force from the rear shaft was less than
the actual force. On the other hand, when the implement swung to the right
(Figure 6.2.6), the hitch would produce some side force. The side force measured

was larger than the actual side force. It was observed that the implement

63

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Figure 6.2.4 Ideal hitching

 

 

 

 

 

 

 

Figure 6.2.5 Hitch containing side force

 

 

 

 

 

 

Figure 6.2.6 I-Iitch containing side force

 

 

Figure 6.2.7 Rear shaft positions

68

rotated and the rear wheel moved to the right at low gang angle settings and to
the left at high gang angle settings.

Second was the rear furrow wheel position. As the gang angle was changed,
the rear shaft position varied also. In position I (Figure 6.2.7), the side force was
measured more accurately. At another gang angle setting, the rear shaft was

like position H. In this case, only part of the side force was measured.

6.2.3 REAR FURROW WHEEL SETTINGS

The rear furrow wheel is very important because its settings can influence
the power disk behavior. Since the rear shaft was not straight (Figure 6.1.2), the
rotations about the shaft center line and the furrow wheel arm resulted in
dramatically different working depths, rear disk cutting paths and high rear
vertical forces.

The relative position of the rear wheel settings was described by the wheel
scraper welded on the shaft (Figure 6.1.2). Incorrect settings resulted in a shal-
low depth, a wrong rear disk path and a tight sway chain for the left lower link
of the three point hitch. Figure 6.2.8 demonstrates one bad setting where the
scraper is horizontal. The rear wheel cut the upper portion of the furrow wall
which was not subjected to the total side force reaction and the maximum work-
ing depth was only about 10 cm. After many tests, another setting was found
(Figure 6.2.9) where the scraper was in the vertical position and the rear wheel
shaft was aproximately 50' from the horizontal plane. The rear wheel cut the
lower corner of the furrow wall which would produce enough reaction to keep

the sway chain loose. This setting also resulted in a deeper ”working depth with

69

 

Figure 6.2.8 Incorrect rear wheel setting

 

Figure 6.2.9 Correct rear wheel setting

70

the maximum of 30 cm. At this setting, the scraper did not function well and a

large amount of soil fell onto the rear wheel. The scraper needed to be placed

horizontally to avoid this soil accumulation.

6.2.4 DESIGN MODIFICATIONS

In order to set the rear furrow wheel properly, three design modifications
were made. The first modification was that the rear shaft was extended from 125
mm up to 270 mm. The primary purpose of the extension was to make the rear
wheel adjustable laterally to the left and the right. Later it was found that this
extension also provided plenty of space to put strain gauges on the shaft.

A flange was put on the rear wheel arm to make the shaft rotation about the
arm possible (Figures 6.2.8 and 6.2.10). This adjustment toward the rear wheel
settings was as important as the rear wheel scraper rotation about the rear shaft
center line: A good setting was a combination of these two rotations. For
example, the rear wheel setting worked well while the scraper was rotated verti-

cally and the rear shaft was rotated 50' from the horizontal plane.

 

 

 

 

Figure 6.2.10 Flange on the rear wheel arm

71

The rear wheel rim was on the right hand side of the rear wheel as the power
disk was manufactured. During the field tests, this rim position did not work
well in reaction to the side force. Alternatively the rear wheel was rotated 180‘
and then put on so that the rim faced in the other direction as shown in Figure

6.1.1, and it worked better. This was the third modification.

6.2.5 REAR VERTICAL FORCE

While the side force information was collected, the rear vertical force was
also measured. Figure 6.2.11 presents how the vertical force is related to the
ground speed. It is obvious that the rear vertical force increased as the ground
speed increased with two exceptions. The slope of the vertical force was less
than that of the side force which meant the vertical force variation was less.
The two high vertical force points at 2 km/hr with the gang angles of 26° and
28' resulted from another rear wheel setting. At these ground speed and gang
angles, the sway chain of the right lower link of the three point hitch was tight.
The rear wheel setting was readjusted as the rear shaft was aproximately 30°
from the horizontal plane and the scraper was in the vertical position. (At this
rear wheel setting, the sway chain was loose. Figure 6.2.12 indicates that the
vertical force was not related to the gang angle when the two high value points

which resulted from another rear furrow wheel setting were removed.

72

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74

6.3 REGRESSION ANALYSIS OF SIDE FORCE

Regression analysis is a modern technique that helps to study the relation-
ship among variables more deeply and accurately. Based on the previous discus-
sions, the regular side force test results had a linear relationship with the ground

speed, which could be expressed using the model
1’ = 1,, + b,X (6.3.1)

where
Y - side force;
X - ground speed;
be, 6, - parameters to be estimated.
and the gang angle did not have much effect on the side force. Statistically it
was interesting to investigate the linear relationship and use the statistical state-

ment to comment on the ground speed and gang angle effects.

6.3.1 REGRESSION WITH BINARY VARIABLES

Since the side force data were obtained at various gang angles, these settings
may affect the linear model 6.3.1 to have different paramenters as seen in Figure
6.2.2. Regression analysis was used to develop a linear relation between the side
force and the ground speed. Binary variable were used to determine whether a
single line would be sufficient or if a series of lines would be necessary because of
different gang angle settings. The reason that the variables were called binary
was that these variables contained binary numbers of 0 and 1. There were five

gang angle settings (26', 28', 30', 32', and 34') and four binary variables were

employed. The following model was considered

75

Y = 60 + 61X + 6221+ 6322 + 6423 + 6524

where

X -- ground speed;

b’s - parameters to be estimated;

Z’s -- binary variables; where

1
Z}: 0
223 {0
l
23: o

l
Z4: 0

H

if gong
others

if gong
others

if gong
othere

if gang
othere

angle =26“

angle 828‘

angle =30’

angle =32°

(0.3.2)

The model 6.3.2 could be decomposed as a set of regression lines if Z’s were

substituted by their values

Y = (b, + 62) + 61X for gang
Y = (b, + 03) + b,X for gang
Y = (b, + 64) + b,X for gang
Y =’ (b, + 65) + b,X for gang

Y=bo+b,X

angle=26°'Z,-él and Zg=Zs=Z4=0
angle=28°' 22:1 and Z,=Z3=Z,=0
angle=30°'Z3=l and Z,=ZZ=Z4=0
angle=32°'Z,=l and Z,=Z2=Z3=0

for gang angler-=34" and Zl=Z2=Z3=Z4=O

(0.3.3)
(0.3.4)
(0.3.5)
(0.3.0)

(0.3.7)

The regression analysis was performed on an IBM PC computer using LOTUS

spread sheet. The results and the ANOVA (ANalysis Of VAriance) table are

given in Table 6.3.1. The coefficient of determination (R2) was 0.902. The

76

Equations 6.3.3 to 6.3.7 became
Y = 3308.418 + 474.080X
Y = 3511.296 + 474.080X
Y = 3736.077 + 474.080X
Y = 3569.583 + 474.080X

Y = 2857.768 + 474.080X

for

for

for

for

for

W’W

gang

gang

947W

9““9

angle =26“

angle =28"

angle =30"

angle =32°

angle =34'

(6.3.8)
(0.3.9)
(0.3.10)
(0.3.11)

(0.3.12)

The above equations have the same slope of 474.080 and different Y axis

intecepts. Therefore they are a set of parallel lines.

 

 

 

The F test
SSE(X) - SSE(X,z,,zzz,,z,)
F= 4
SSE(X,Z,,Z,,Z,,Z,)
11
where

SSE(X) - sum of square of errors using model 6.3.1;

SSE(X,Z,,ZZZ,,Z,) -- sum of square of errors using model 6.3.2.

tested whether there was the gang effect with hypothesis

H. =32=flz=fls=fi4=0

11,: not all flb=0 (h=2, 3, 4)

Since

279627228 - 167035025

F= 4

01322-22.

ll

=l.854

(0.3.13)

77

Table 6.3.1 Regression results with binary variables

 

A

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Y X 21 22 23 Z‘ Y Errors
4414.62 1.93 l 0 0 0 4223.39 191.23
5107.53 3.78 l 0 0 0 5100.44 7.09
5911.06 5.94 l 0 0 0 6124.45 -213.39
6642.06 7.00 1 0 O 0 6626.98 15.08
3779.04 1.94 0 l 0 0 4431.01 -65l.97
5324.65 3.53 0 1 0 0 5184.80 139.85
6924.14 5.52 0 l 0 0 6128.22 795.92
6370.65 6.63 0 l 0 0 6654.45 -283.80
4598.22 1.83 O 0 1 0 4603.64 -5.42
5924.63 3.90 0 0 l 0 5584.99 339.64
6396.28 5.71 0 0 l 0 6443.07 -46.79
6601.29 6.65 O 0 l 0 6888.71 -287.42
4668.67 1.78 0 0 0 1 4413.45 255.22
5053.51 3.58 0 0 0 1 5266.79 -213.28
6253.60 5.75 0 0 0 1 6295.54 -4l.94
3554.85 1.98 0 0 0 0 3796.45 -241.60
4900.87 3.80 0 0 0 0 4659.27 241.60

Regression Output:

Constant 2857 .7 68
Std Err of Y Est 389.679
R Squared 0.902
No. of Observations 17
Degrees of Freedom 11
X ColIicient(s) 474.080 450.650 653.528 878.309 711.815
Std Err of Coef. 54.295 350.926 347.353 348.918 358.458

ANOVA Table
Source of variation SS df MS
Regression 1545638387 5 309127677
Error 167035025 11 151850.02
Total l7l26734.12 l6

 

 

 

 

 

 

78

and
F,,.,,(0.95, 4, 11)=3.30
given the significant level of a=0.05, then
F <F,.u,

It was concluded that there was no significant gang angle effect and the common

line of model 6.3.1 was good enough to fit the test data.

6.3.2 SIMPLE LINEAR REGRESSION

Because statistical statement agreed with the earlier discussion that there
was little gang angle effect, which was
fl2=fl3=fl4=fis=0
the model 6.3.2 reduced as
Y = b0 + 61X
The regression results using the above model plus the ANOVA table is given in
Table 6.3.2. Substituting the estimated parameters, the above equation became

Y = 3337.507 + 500.88X (6.3.14)

with the R2 = 0.837.

By performing the t test

5: 500.88

8(01) 57.128

t

where

bl - estimated parameter;

79

0(61) - estimated standard error of parameter b,.

and

a...“ (0.975, 15)=2.131

given the a level of 5% and
8..., (0.995, 15)=2.947

given the a level of 1%, it was proved that the linear relationship between the

side force and the ground speed was highly significant since
“>4“, (0.995, 15)

and this relationship was expressed by Equation 6.3.14. Figure 6.3.1 presented
the raw data points, the regression line, the 95% confidence band and the error
plots. The confidance band contains most of the data points so that the model
6.3.14 expresses the relationship bewteen the side force and the ground speed

very well. The maxmum positive absolute error is 821.76 (N) and the maximum

negative is -774.42 (N).

I: ml". V _l'."

80

 

A

 

 

 

 

 

 

 

 

 

Table 6.3.2 Regression results with one variable

 

 

 

Y X Y Errors
4414.62 1.93 4304.23 110.39
5107.53 3.78 5230.85 -123.32
5911.06 5.94 6312.75 -401.69
6642.06 ‘ 7.00 6843.69 -201.63
3779.04 1.94 4309.23 -530.19
5324.65 3.53 5105.63 219.02
6924.14 5.52 6102.38 821.76
6370.65 6.63 6658.36 -287.71
4598.22 1.83 4254.14 344.08
5924.63 3.90 5290.96 633.67
6396.28 5.71 6197.55 198.73
6601.29 6.65 6668.38 -67.09
4668.67 1.78 4229.09 439.58
5053.51 3.58 5130.68 -77.17
6253.60 5.75 6217.59 36.01
3554.85 1.98 4329.27 ~774.42
4900.87 3.80 5240.87 -340.00

‘ Regression Out ut:
Constant 3337.527
Std Err of Y Est 431.762
R Squared 0.837
No. of Observations 17
Degrees of Freedom 15
X Coliicient(s) 500.880
_ Std Err of Coef. 577.128
ANOVA Table
Source of variation SS df MS
Regression 1433046185 1 1433046185
Error 279627228 15 186418.15
Total 1712673412 16

 

 

 

 

 

 

 

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CHAPTER 7

CONCLUSIONS AND RECOMMENDATIONS

7.1 CONCLUSIONS
Based on the theoretical, experimental and statistical studies, the

following conclusions can be drawn:

1. The power disk worked in the slipping condition. Given the gang angles of
26° to 34° and the ground speeds of 2 to 8 kin/hr, the disk slippages were
between 52.79% and 89.11%.

2. The disk velocity distributions were ellipses in the XZ and YZ planes and a
straight line in the XY plane. The distributions were affected by the
ground speed and gang angle.

3. The absolute velocity of the disk blade, with the amplitudes between
1.098V and 2.835V, was always greater than the implement ground speed.

4. The gang angle settings had little, if any, ellect on the vertical force.

5. According to Figure 6.2.3, little influence of gang angle settings on the side
force was observed. As discussed in Section 6.2.2, the side force for large
gang angles was underestimated and the side force for small gang angles

was overestimated. Consequently additional tests which fix the power disk

82

1W“

83

position relative to the tractor are necessary to determine the effect of gang

angle on the side force.

The linear relationship between the side force and the ground speed was
established through the experimental and statistical analyses. The statisti-
cal test indicated that this relationship was highly significant and could be

expressed using a simple linear model 6.3.14.

The rear furrow wheel setting was important, and it affected the power disk

behavior dramatically.

The rear vertical force increased as the ground speed increased.

7.2 RECOMMENDATIONS

Further advanced studies of the power disk are necessary. Several topies are

suggested for the future research projects:

1.

Theoretical study of the power disk. A modern computer modeling and
simulation method can be employed to study the power disk, such as disk
blade motion, power requirement and furrow width, at various gang angles,

ground speeds, tilt angles, disk curvatures and PTO speeds.

Further field tests are needed to investigate the gang angle effect on side

force and other factors. The relative position of the implement about the

tractor needs to be fixed in order to detect the gang angle effects.

Full understanding of the rear furrow wheel is a interesting and important

aspect in the power disk research.

 

84

4. The side force needs to be studied with more variables besides the ground

speed and the gang angle, such as the working depth and soil condition.

APPENDICES

 

APPENDIX A

POWER DISK SPECIFICATIONS

MODEL

DIMENSSIONS
OVERALL LENGTH
OVERALL WIDTH
OVERALL HEIGHT

MASS

NUMBER OF DISK BLADE

DRIVING SYSTEM

DISK BLADE DIAMETER

DISK CURVATURE

DISKING DEPTH

DISKIN G WIDTH

GANG ANGLE

WORKING SPEED

APPLICABLE TRACTOR

PTO REVELOTION

HITCHIN G

F 2806

2770 mm
2200 mm
1450 mm
875 kg
6
BEVEL GEAR AND ROLLER CHAIN
710 mm
680 mm
150--3OO mm
1750 mm
25-- 35 DEGREES
3-- 5 km/hr
100--l30 HP
540 rpm

TIIREE POINT IIITCI-I

85

153;: _.

APPENDIX B

POWER DISK FIELD TEST RECORD SHEETS

The following two sheets summarized the data needed during the field test.
The test data sheet was filled out for each test run and the soil condition data

was collected for each half day period.

86

87

POWER DISK FIELD TEST

DATA SHEET

DATE: 1987
FLOPPY DISK NO.:

FILENAME:

 

GEAR/G.SPEED: /

WIDTH & DEPTH (cm)

WORKING WIDTH FORROW WIDTH
. WORKING DEPTH
before after width top middle bottom

 

ANGLES (degrees)

 

3-POINT HITCH

 

GANG ANGLE REAR DISK ANGLE
top link lower left lower right

 

 

 

 

 

 

 

 

NOTES: 1.THIs RUN Is UP/DOWN HILL/FLAT:

2.THE CHAIN Is LOOSE/TIGHT:
3.WORKING QUALITY: GOOD/AVERAGE/BAD,

IF ANY, PICTURE No.: / / / / :
4:RESIDUAL CONDITION: NO/SOME/A L0T,

IF ANY, PICTURE No.: / / / /___;
5:TOP LINK LENGTH: -CM; _
6:LOWER LINK LENGTH: LEFT CM, RIGHT on:
7.0THERS.

88

POWER DISK FIELD TEST

SOIL CONDITION

DATE: 1987

WEATHER:

 

SOIL MOISTURES
NO. LAYER CONE INDEX

CAN NO GROSS WEIGHT DRY WEIGHT MOISTURE

MEAN

 

NOTES: 1.DISK DIAMETERS:
1. CM, 2. CM, 3. CM, 4. CM, 5. CM, 6. CM
REAR DISK. CM;

2.0THERS.

APPENDIX C

SOIL DATA

The soil samples and the soil cone index were collected for each half day
period. The soil samples were put in soil cans for the use of determining soil
moisture contents. The cone index was recorded in the soil condition data sheet
shown in Appendix B. Six to ten data were collected for each test day. The

data shown in the following page were the averaged data for each test day.

89

90

Table C.1 Soil data

 

 

 

 

 

 

 

 

 

 

 

 

Average cone index
Date Location Average moisture (top layer)
% N/‘cm2
9/1/87 Collins 16.72 26.67
9[2/87 Collins 12.43 38.42
9/3/87 Collins 12.67 33.17
9/3/87 Dairy barn 13.88 70.68 .
9/9/87 Collins 14.19 33.17
9 / 21 / 87 Collins No data collected due to sudden rain
10/5/87 Collins 16.54 29.98 '

 

Note: Soil at Dairy barn is hard soil.
Its cone index is twice higher than that at Collins.

 

APPENDIX D

COMPUTER PROGRAM - MOTION

This interactive computer program written in FORTRAN was used to study
the dynamics of the power disk. Simulations were done on the Prime 750 com-
puter. The disk trajectories and velocity distributions were simulated by using
this program. The flowchart of the program is given on the following page and

the list of the program follows.

91

92

I’ROC.‘ {AM Howe: mm

l BIKE,

. I
l lN’.l‘lAl.l'/.A'l‘l()N

 

 

 

 

 

 

 

 

 

 

I r
MENU OPTIONS:

 

CIIANCI‘I? GANG ANGLE
'l'll/l‘ ANGLE
DISK CURVA'I'UI‘IIS
l"l‘() Sl’l‘ll'll)
l’()ll\"l' RADIUS

GROUND Sl’l'll'll)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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APPENDIX E
COMPUTER PROGRAM - PLOT3.VXYZ
An interactive computer program written in FORTRAN was used to plot
three dimensional curves and figures on the Prime 750 computer. The plot can

be translated and rotated as desired. Figure 5.3.4 was plotted by using this pro-

gram. The program flowchart and the program list are given as follows:

97

 

 

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APPENDIX F

CALIBRATION RAW DATA AND COMPUTATIONS

The calibration of channel 13 and channel 14 was carried out Successfully in
August 24, 1987. The raw data, their computation results and regression out-
puts are given in the following page. The computations were based on the dis-
cussions in Chapter 6. The regressions were carried out by using LOTUS

software.

106

107

Table F.1 Calibration raw data and computations

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

RAW DATA COMPUTATIONS
CH 13 CH 14 P, P2 H, V, H V M
reading reading lbs lbs lbs lbs lbs lbs lbs-m
55 -482 330 385 329.548 17.271 329.548 402.271 67.928
134 -702 720 380 719.013 37.682 719.013 417.682 95.007
187 -857 1000 377 998.630 52.336 998.630 429.336 114.517
237 -1015 1280 375 1278.246 66.990 1278.246 441.990 134.143
276 -1135 1520 375 1517.917 79.551 1517.917 454.551 151.163
191 -937 1150 380 1148.424 60.186 1148.424 440.186 125.502
141 -791 890 385 888.780 46.579 888.780 431.579 107.642
109 -678 690 387 689.054 36.112 689.054 423.112 93.690
67 -585 500 390 499.315 26.168 499.315 416.168 80.562
35 -471 330 375 329.548 17.271 329.548 392.271 66.771
72 «586 440 405 439.397 23.028 439.397 428.028 78.042
141 -728 710 405 709.027 37.159 709.027 442.159 97.190
212 -927 1050 401 1048.561 54.953 1048.561 455.953 120.839
266 -1040 1260 400 1258.273 65.943 1258.273 465.943 135.616
339 -1239 1660 393 1657.725 86.878 1657.725 479.878 163.173
240 -1042 1310 398 1308.205 68.560 1308.205 466.560 138.930
168 -880 1010 401 1008.616 52.859 1008.616 453.859 118.002
123 -729 730 405 729.000 38.205 729.000 443.205 98.608
91 -624 550 405 549.246 28.785 549.246 433.785 85.843
31 -498 350 406 349.520 18.318 349.520 424.318 71.775
107 -667 530 457 529.274 27.738 529.734 484.738 90.438
171 -846 850 454 848.835 44.486 848.835 498.486 112.785
207 -949 1040 450 1038.579 54.429 1038.575 504.429 125.797
268 -1100 1320 447 1318.191 69.083 1318.191 516.083 145.306
329 -1254 1610 443 1607.794 84.261 1607.794 527.261 165.410
225 -1025 1220 445 1218.328 63.850 1218.328 508.850 137.983
187 -857 910 448 908.753 47.626 908.753 495.626 116.346
122 -700 630 450 629.137 32.972 629.137 482.972 96.720
88 -590 440 450 439.397 23.028 439.397 473.028 83.246
35 -467 230 453 229.685 12.037 229.685 465.037 68.700
CH 13 Regression Output: C11 14 Regrwsion outmit:
Constant -150.883 Constant 62.44379
Std Err of Y Est 12.63132 Std Err of Y Est 11.07110
R Squared 0.980038 R. Squared 0-9977’14
No. of Observations 30 No. of Observations 30
Degrees of Freedom 27 Degrees of Freedom 28
X Coefiicient(s) 0.195621 0.310272 X Coefficient(s) -7.99175
Std Err of Coef. 0.006862 0.079461 Std Err of Coef. 0.071801

 

 

 

 

 

 

 

APPENDIX G

SIDE FORCE DATA

The side force was measured throughout the field tests. Each type of test
was explained in Chapter 4. The gang angle was set before each field test. The
ground speed and the side forces were averaged from 600 data points for each
test. The minimum and the maximum side forces were the extreme points
within the 600 data points. The tillage depth was averaged based on three
measurements for each test.

Most of the tests were free depth control, that is, the implement cut as deep
as possible. In the depth control tests, the depth was controlled by using the
depth wheel or the tractor hydraulic system.

The tests using the depth wheel control and two regular tests for the 26 and
28 degree gang angles at 2 km/hr used a different rear furrow wheel setting.
The rear wheel shaft was 32 degrees from the horizontal plane and the scraper
was at the vertical position, while in the other tests the shaft was 50 degrees.

Two tests were conducted on the hard soil with the cone indix was two times
of that in the other soil condition to investigate the soil type effect.

The rest of two kinds of tests were explained in chapter 4.

108

 

109

Table (3.1 Side force data

 

 

 

 

 

 

 

 

 

Type Gang gangle Ground speed Depth Side force (N)

(degree) (kmjhr) (cm) average minimum maximum

26 1.93 22.90 4414.62 3199.63 5586.69

3.78 29.97 5107.53 3872.39 6499.35

5.94 28.13 5911.06 4718.29 7398.75

7.00 23.97 6642.06 3941.83 8807.46

28 1.94 26.77 3779.06 2951.36 4956.76

3.53 23.80 5324.65 3740.04 7269.79

5.52 28.20 6924.14 4573.45 8532.72

6.63 28.40 6370.65 5094.44 8624.53

Regular 30 1.83 28.60 4598.22 2135.83 6909.93

3.90 26.10 5924.63 4300.88 7807.15

5.71 28.30 6396.28 4830.73 8644.13

6.65 28.43 6601.29 5169.16 8020.65

32 1.78 28.70 4668.67 2952.13 5792.26

3.58 28.80 5053.51 1349.39 6853.42

5.75 27.23 6253.60 4530.36 8384.36

34 1.98 30.10 3554.85 2437.22 5198.80

3.80 29.87 4900.87 3499.11 6529.03

Depth 28 4.17 11.23 2096.25 854.19 3437.61

wheel 3.82 17.77 3682.80 2589.50 4823.89

control 32 4.15 11.27 2249.97 1297.53 3300.12

3.90 17.67 3547.65 2052.36 4571.78

Hydraulic 28 4.02 14.77 3564.07 2053.99 5011.92

depth control 32 4.12 17.27 3630.45 1889.24 5702.40

Hard soil 28 1.58 13.80 3537.10 966.82 5685.51

32 1.64 16.03 3519.47 558.68 7620.69

Unpowered 28 1.75 23.47 4192.02 3062.13 5189.46

5.72 20.10 5265.31 2952.84 7301.46

32 2.26 24.73 4737.71 3434.35 6997.05

5.74 26.10 6095.35 4005.17 7618.93

26 1.60 21.95 3050.91 1413.10 4401.23

3.71 21.47 4897.34 1756.14 8212.83

5.84 21.63 4819.71 2210.22 7411.77

Short 28 3.86 24.03 4856.54 2084.95 8472.06

top link 30 1.90 22.70 3553.56 2500.22 5228.59

1.63 20.30 3724.62 1857.94 6401.53

32 1.70 28.67 5312.71 4029.35 6992.21

 

 

 

 

 

 

 

 

APPENDD{ H

REAR VERTICAL FORCE DATA

The rear furrow wheel vertical force was measured in the same tests where
the side force was measured. The data explainations are the same as the side

force in Appendix G.

110

111

Table 11.1 Rear vertical force data

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Type Gang angle Ground speed Depth Vertical force LNL

Ldegree) (kmjhr) icml averag minimum maximum

26 1.93 22.90 5039.83 3812.67 6512.33

3.78 29.97 2895.57 1996.83 3701.56

5.94 28.13 3491.86 2130.84 6388.87

7.00 23.97 3712.41 2399.57 5255.00

28 1.94 26.77 4565.41 3161.97 6312.15

3.53 23.80 3144.46 1901.94 7542.08

5.52 28.20 3791.36 2624.86 5424.60

6.63 28.40 3933.25 2945.50 4965.09

Regular 30 1.83 28.60 2902.70 1541.98 4307.21
3.90 26.10 3477.41 2188.70 4591.31

5.71 28.30 3586.65 2687.69 4915.30

6.65 28.43 3710.40 2819.63 5196.86

32 1.78 28.70 2636.67 1093.30 3847.00

3.58 28.80 2742.53 1321.56 4160.26

5.75 27.23 3557.25 2177.03 4997.43

34 1.98 30.10 2135.72 1287.80 4905.74

3.80 29.87 2981.76 1785.73 5957.16

Depth 28 4.17 11.23 3123.92 1938.73 7308.63
wheel 3.82 17.77 4630.99 3380.02 5847.73
control 32 4.15 11.27 3230.12 _ 1750.64 4645.27
3.90 17.67 4225.09 2941.82 5409.52

Hydraulic 28 4.02 14.77 2577.40 1792.59 4364.35
deRth control 32 4.12 17.27 2622.88 516.18 6093.31
Hard soil 28 1.58 13.80 2325.83 853.58 3446.96
32 1.64 16.03 2412.02 959.96 4582.26

Unpowered 28 1.75 23.47 2779.73 2034.95 3945.46
5.72 20.10 3017.41 1456.53 4179.80

32 2.26 24.73 3099.09 2308.00 7307.17

5.74 26.10 3775.91 2754.36 4954.99

26 1.60 21.95 2439.67 1167.26 5714.74

3.71 21.47 3090.50 1685.99 5103.54

5.84 21.63 2873.84 1876.50 4211.20

Short 28 3.86 24.03 3120.54 1875.17 7672.27
top link 30 1.90 22.70 2344.15 1316.08 3206.88
1.63 20.30 2874.79 1538.83 4287.46

32 1.70 28.67 3079.87 2111.30 4912.06

 

 

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‘

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