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This is to certify that the

dissertation entitled

Analysis of Front Mounted Three-Point Hitch
Geometry On Front-Wheel Assisted Tractors

presented by
Milton Mintsong Mah

has been accepted towards fulfillment
of the requirements for

Ph.D. degree in Agric. Engr.

 

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Major professor

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ANALYSIS OF FRONT MOUNTED THREE-POINT HITCH
GEOMETRY ON FRONT-WHEEL ASSISTED TRACTORS

By

Milton Mintsong Mah

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

in
Agricultural Engineering

Department of Agricultural Engineering

1990

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ABSTRACT

ANALYSIS OF FRONT MOUNTED THREE-POINT HITCH GEOMETRY
ON FRONT-WHEEL ASSISTED TRACTORS

By
Milton Mintsong Mah

Front-wheel assisted (FWA) tractors have been used for providing
more drawbar pull, higher power, and better field efficiency than two-wheel
drive tractors. An FWA tractor equipped with front mounted implements
can increase tractive forces from the tractor's front wheels. The front
implement serves as ballast to aid vehicle stability and eliminates the need
to carry front weights. As a result tractor power is better utilized.
However, the front mounted hitch systems should have an impact on the
tractor's performance. The general goal of this research was to develop
theoretical and experimental means to determine the extent to which the
performance of an FWA tractor with front and rear hitches can be
improved by adjusting hitch configurations, ballast ratios, and implement
dimensions.

A mathematic model was developed to describe the geometries of
front and rear three-point hitches. The tractor's dynamic load distribution
was calculated using the hitch geometries and the forces applied to the
hitches. Finally, two equations published in the ASAE Yearbook were used
to predict the pull developed by the tractor wheels and the tractive efficiency.
These equations were coded into a computer program which could be used
in two modes. The data analysis mode was used to analyze experimental
data to predict tractive efficiency which would be difficult or impossible to

measure with instruments. The simulation mode was used to predict the

effects of changing hitch dimensions, ballast ratios, and implement
dimensions on the tractor's dynamic load distribution.

The field experiment results lead to the conclusion that using an
average value of soil cone index to predict pull developed by the tractor's
wheels was not adequate. The sensitivity test of cone index revealed that the
variation of cone index greatly influenced the predicted value of tractor pull.
There are opportunities for improving tractor performance on loose soil.
The simulation results showed that dynamic load distribution was affected
by the adjustment of most front three-point hitch dimensions. On the other
hand, most of the rear hitch dimensions had no effect on dynamic load
distribution. The dynamic load ratio changed proportionally to the change
of ballast.

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ACKNOWLEDGMENTS

I would like to express my sincere appreciation to all of those people
who provided encouragement and assistance throughout my graduate
program. I would like to extend a special thanks to the following
individuals:

* Dr. Thomas Burkhardt, my major professor, for his personal and
professional guidance throughout the duration of my program.

* Dr. John Gerrish, member of my guidance committee, for his
innovative suggestions during the implementation of testing instruments.

* Dr. Robert Wilkinson and Dr. Ronald Rosenberg, members of my
guidance committee, for their professional contribution to my studies.

* Ford New Holland, Inc., for supplying the plowing system used in
this research and for their financial support during the research period.

* The Universidade Federal de Vicosa, Brasil, for their financial
support during the first part of my program.

* The Conselho Nacional de Desenvolvimento Cientffico e Tecnologico
(CNPq), Brasil, for their financial support during the first part of my
program.

* My brother and sister, Marcos and Gamin, for their financial and
moral support during my program.

* My friend, Dr. John Goeschl, for his suggestion and assistance
during the writing of this dissertation, which greatly improved the

readability of this dissertation.

* Last and the most, to my beloved wife, Carina, for her unlimited

encouragement and personal sacrifice, so that I could complete this study.

 

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TABLE OF CONTENTS

LIST OF TABLES ............................................................................. xi
LIST OF FIGURES ........................................................................... xii
1. INTRODUCTION ........................................................................ 1
2. LITERATURE REVIEW ............................................................... 6
2.1 Effects of tire design, inflation pressure, loading, and soil
properties on tractive efficiency .......................................... 7
2.1.1 Rigid wheel theory .................................................. 8
2.1.2 Pneumatic wheel theory .......................................... 8
2.1.3 Pneumatic wheel performance ................................. 9
2.2 Comparisons of 2WD, 4WD, and FWA tractor
performance .................................................................... 12
2.2.1 Soil bin tests of multiple wheel passes ....................... 12
2.2.2 Performance of 2WD vs 4WD tractors ................... l ..... 13
2.2.3 Performance of 2WD vs FWA tractors ....................... 13
2.3 Configuration optimization studies in 4WD and FWA
tractors ............................................................................ 17
2.4 Attempts to design and test real-time adjustable hitches ....... 20
2.5 Summary ........................................................................ 21
3. GOALS, OBJECTIVES, CONSTRAINTS AND ASSUMPTIONS ........ 23
3.1 Goals ............................................................................... 23
3.2 Objectives ......................................................................... 23
3.3 Constraints ...................................................................... 24
3.4 Assumptions .................................................................... 25

vii

 

 

6F

 

4. MATHEMATIC MODEL ............................................................... 29

4.1 Kinematical analysis ........................................................ 29
4.1.1 Reference position and sign conventions for the

tractor ................................................................... 29

4.1.2 Sign conventions for the front and rear hitches and
implements ............................................................ 29
4.1.3 Mechanism for the rear three-point hitch .................. 30
4.1.4 Mechanism for the front three-point hitch ................. 36
4.2 Analysis of chassis mechanics ........................................... 42
4.3 Predictions of performance ................................................ 48
4.3.1 Predictions of slippage ............................................. 48
4.3.2 Predictions of tractive efficiency ................................ 49
5. SIMULATION MODEL ................................................................ 51
5.1 Program structure and model inputs .................................. 51
5.2 Data analysis mode ........................................................... 55
5.3 Simulation mode .............................................................. 57
6. FIELD TESTS .............................................................................. 61
6.1 Plowing system ................................................................ 61
6.1.1 Tractor .................................................................. 61
6.1.2 Implements ...................................................... . ..... 61
6.1.3 Static weight and rolling radius ............................... 64
6.2 Data acquisition system ..................................................... 66
6.2.1 Three-point hitch dynamometer ............................... 66
6.2.2 Strain gages - application and cautions ..................... 68
6.2.3 Torquemeter on the front wheel drive shaft ................ 69
6.2.4 Other sensors ......................................................... 69

viii

6.2.5 Signal processing, computer, and power source.... ..... 71

6.3 Sensor calibration ............................................................. 72
6.3.1 Three-point hitch dynamometer ............................... 72
6.3.2 Torquemeter .......................................................... 75
6.3.3 Other sensors ......................................................... 75
6.4 Computer software ........................................................... 75
6.4.1 Data collection program .......................................... 75
6.4.2 Data processing program ........................................ 76
6.5 Field operation ................................................................. 77
7. RESULTS AND DISCUSSION ....................................................... 82
7.1 Special considerations regarding the results of field
experiments ..................................................................... 82
7.1.1 Soil cone index and other soil properties .................... 82
7.1.2 Slippage measurements and estimations .................. 84
7.1.3 Total pull, predicted and measured ........................... 85
7.1.4 Sensitivity test of cone index on predicted pull ............ 89
7.2 Comparison of field results with other studies ...................... 92
7.2.1 Relationship between total (average) slip and total
pull ....................................................................... 92
7.2.2 Relationships between dynamic load ratio,
slippage, and TE ..................................................... 95
7.3 Simulation results ............................................................ 97
7.3.1 Effects of hitch dimensions ...................................... 98
7.3.2 Effects of implement dimensions ......................... - ..... 105
7.3.3 Effects of tractor ballast ........................................... 105

7.3.4 Practical considerations in the application of
simulation data ...................................................... 108

ix

 

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APP
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8. CONCLUSIONS ........................................................................... 110

8.1 Field experiments ............................................................. 110

8.2 Simulations ..................................................................... 111

9. RECOMMENDATIONS ................................................................ 113
9.1 Improved measurements of soil properties ..................... l ..... 113

9.1.1 Possible measurements of CI in each test area ........... 113

9.1.2 Develop some means of measuring CI in those
cases where the soil is disturbed by a front
implement before passage of the front wheels ............. 113

9.1.3 Develop some means of measuring CI in the tracks
after passage of the front wheels ............................... 114

9.1.4 Possible development of techniques to measure soil
parameters such as cone index while the tractor is

in motion during a field test run ............................... 114

9.2 Improved measurements of wheel slippage and rear axle
torque .............................................................................. 115

9.3 Determine ideal dynamic load distribution for FWA

tractors ............................................................................ 115
APPENDIX A. ASAE Standard Definitions ......................................... 116
APPENDIX B. Simulation program and input templates ...................... 118
APPENDD( C. Front axle pivot force and power distribution to axles ...... 133
BIBLIOGRAPHY ............................................................................. 136

 

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Table 2.1

Table 6.1
Table 6.2
Table 6.3
Table 7.1

Table 7.2

Table 7.3

Table B.1
Table 3.2
Table B.3

LIST OF TABLES

Rear wheel slippage summarized from tests "CTT436S"

and "CTT436T" of Mueller & Freer, 1986 .............................. 19
Specification of tractor tires ................................................ 62
The weight distribution of tractor with plows attached .......... 64
Tires' rolling radii, unloaded radii, and section widths ......... 65

Average, standard deviation, and range of cone index
measurements ................................................................. 83

Average slippage in the right (measured) and left
(estimated) wheels running respectively on the soil

surface and furrow during opposite direction runs ............... 85
Average of total pull as predicted from individual wheel

data and as measured from hitch forces .............................. 86
Tractor parameters template ............................................. 131
Implement parameters template ........................................ 132
Working condition parameters template .............................. 132

xi

 

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Figure 1.1
Figure 3.1

Figure 3.2

Figure 4.1

Figure 4.2

Figure 4.3

Figure 4.4
Figure 4.5

Figure 4.6

Figure 4.7

Figure 4.8

Figure 4.9

Figure 4.10

Figure 4.11
Figure 5.1
Figure 5.2

LIST OF FIGURES

Front and rear mounted, reversible moldboard plows ......... 3
Position of upper link pin at the front three-point hitch

before the implement reaches steady working state ............ 27
Position of upper link pin at the front three-point hitch

after the implement reaches steady working state .............. 27
Geometry of rear three-point hitch, with plow in
transportation position .................................................... 31
Geometry of rear three-point bitch, with plow in

penetration position ........................................................ 32
Geometry of rear three-point hitch, with plow in

working position ............................................................. 33
Effective lower link length ............................................... 36
Geometry of front three-point hitch, with plow in
transportation position .................................................... 37
Geometry of front three-point bitch, with plow in

penetration position ........................................................ 38
Geometry of front three-point hitch, with plow in

working position ............................................................. 39
Forces acting on the rear three-point bitch and the

virtual line of pull ........................................................... 43
Forces acting on the frent three-point hitch and

implement ..................................................................... 44
Forces acting on the tractor ............................................. 46
Dynamic load distribution on tractor rear wheels ............... 47
Block diagram of simulation program .............................. 52
Flow chart of parameter handling routines ....................... 54

xii

Figure 5.3
Figure 5.4

Figure 6.1
Figure 6.2
Figure 6.3

Figure 6.4
Figure 6.5
Figure 7 .1
Figure 7.2
Figure 7.3
Figure 7.4

Figure 7.5
Figure 7.6
Figure 7.7
Figure 7.8

Figure 7.9

Figure 7.10

Figure 7.11

Figure 7.12

Figure 7.13

Figure 7.14

Flow chart of the simulation program operating in the

data analysis mode ......................................................... 56
Flow chart of the simulation program operating in the
simulation mode ............................................................ 58
Overview of tractor with front and rear mounted plows ....... 63
Configuration of data acquisition system hardware ............ 7O
Strain gages calibration set up: a) simulating the

horizonral forces, b) simulating the vertical forces ............. 74
Flow chart for the field data analysis program ................... 78
Measurement of plowing width and depth ......................... 80
Measured pull vs predicted pull in sandy soil ..................... 87
Measured pull vs predicted pull in silty-clay soil ................ 87
Averaged, measured pull vs predicted pull in sandy soil ..... 90
Averaged, measured pull vs predicted pull in silty-clay

soil ................................................................................ 90
Sensitivity test of CI on predicted pull in sandy soil ............. 91
Sensitivity test of CI on predicted pull in silty-clay soil ......... 91
Pull prediction using variable cone index in sandy soil ....... 93
Pull prediction using variable cone index in silty-clay

soil ........................................................................... _ ..... 93
Averaged slip vs measured pull in sandy soil ..................... 94
Averaged slip vs measured pull in silty-clay soil ................ 94
Averaged slip and TE vs front axle load ratio in sandy

soil ................................................................................ 96
Averaged slip and TE vs front axle load ratio in silty-clay

soil ................................................................................ 96
Front axle load ratio vs front lower link point X-

coordinate ...................................................................... 99
Front axle load ratio vs rear lower link point X-

coordinate ...................................................................... 99

xiii

Fig.
Fig1
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Figu
Figu

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Figure 7.15

Figure 7.16

Figure 7.17

Figure 7.18

Figure 7.19

Figure 7.20

Figure 7.21
Figure 7.22
Figure 7.23
Figure 7.24
Figure 7.25
Figure 7.26
Figure 7.27

Figure C.1

Figure C.2

Figure C.3

Figure 0.4

Front axle load ratio vs front lower link point Y-

coordinate ...................................................................... 100
Front axle load ratio vs rear lower link point Y-

coordinate ...................................................................... 100
Front axle load ratio vs front upper link point X-

coordinate ...................................................................... 101
Front axle load ratio vs rear upper link point X-

coordinate ...................................................................... 101
Front axle load ratio vs front upper link point Y-

coordinate ...................................................................... 103
Front axle load ratio vs rear upper link point Y-

coordinate ...................................................................... 103
Front axle load ratio vs front lower link length ................... 104
Front axle load ratio vs rear lower link length .................... 104
Front axle load ratio vs front implement mast height .......... 106
Front axle load ratio vs rear implement mast height .......... 106
Front axle load ratio vs front wheel ballast ......................... 107
Front axle load ratio vs rear wheel ballast ......................... 107
Restriction on adjustment of front upper link point Y-

coordinate with moldboard plow ....................................... 109

Front axle pivot force vs front axle load ratio in sandy
soil ................................................................................ 134

Front axle pivot force vs front axle load ratio in silty-clay
soil ................................................................................ 134

Front axle power ratio vs front axle load ratio in sandy
soil ........................................................................... ' ..... 135

Front axle power ratio vs front axle load ratio in silty-
clay soil ......................................................................... 135

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1 . INTRODUCTION

The single axle drive (2WD) tractor has dominated the farm tractor
market for years. Its main advantage has been its versatility in row crop
cultivation, tillage, and utility operations. As farm size increases, larger
and higher powered tractors become more important in tillage operations.
As tractor power increases, it becomes difficult to utilize that power at the
drawbar with conventional 2WD tractors. The four-wheel drive (4WD)
tractor is a popular solution to this problem. Research has shown that the
4WD tractor can improve traction, and can save fuel and time, especially
when operating in poor field conditions.

A variation of 4WD tractor called the front-wheel assist (FWA), is
becoming popular. This tractor is a modified 2WD tractor which is
equipped with a front wheel drive. The front wheel drive can be engaged or
disengaged from the operator's platform. The front wheels are steerable
and are smaller than the rear wheels. This gives the FWA tractor many of
the maneuverability benefits of a 2WD tractor, but with greater traction.
These FWA tractors hold an advantage in pull to mass ratio over the
similarly powered 2WD tractors. They also are more cost effective than the
4WD counterparts.

Advantages of the FWA systems in comparison to 2WD systems
(according to manufacturers) include increased pull, drawbar power, and

fuel efficiency. Also wheel slip, rear tire wear, and soil compaction are

 

 

 

 

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reduced. In addition there is better stability against overturning and the
FWA vehicles have increased drive train life.

Due to the popularity of FWA tractors, researchers have conducted
several investigations of FWA tractor performance. They have studied the
effect of tire size, tire type and other parameters. However, there are very
few studies, if any, about the geometry of the three-point hitch in FWA
tractors.

The geometry of the three-point hitch used in FWA tractors is based
on an ASAE (American Society of Agricultural Engineers) standard. This
standard was primarily designed for 2WD tractors, and it was adopted by
the ASAE in 1959. Since then, there have been ten revisions. Nevertheless,
the design of chassis mechanics for the FWA tractor is different from that
of the 2WD tractor. Consequently, the weight distribution and dynamic
behavior of FWA tractors must be different from those of 2WD tractors.
Thus, the FWA tractor requires a reconsideration of the geometry of the
three-point hitch in order to obtain optimal tractive efficiency.

Front mounted three-point hitch systems have recently been
introduced in the United States (Figure 1 .1). An FWA tractor equipped with
front mounted implements can increase tractive forces from the tractor's
front wheels. An article (entitled "Dear Murphy...") in the January 1984
issue of Implement & Tractor noted that a front mounted hitch made by
American owned companies in Europe has been used there for over a
decade. It was also noted that improved traction and reduced slippage on
FWA tractors could result if implements were attached to both front and
rear hitches at the same time.

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Before the introduction of the front mounted three-point hitch, a
tractor could only work with a limited size of fully mounted implement due
to its inability to lift heavy weights. With the front mounted three-point
hitch, a tractor can use two implements at the same time and thus increase
the working efficiency without overloading the hitching capability. The
front implement serves as ballast to aid vehicle stability and eliminates the
need to carry front weights. As a result tractor power is better utilized.

A dual three-point hitch also allows a tractor to work with two
different implements simultaneously. There are numerous possibilities of
using dual implements. For instance, a front mounted sprayer and rear
mounted planter, or a front mounted field cultivator and rear mounted
planter could perform two operations in one field trip. A front mounted
sprayer tank and rear mounted sprayer could better distribute loads to the
rear and front axles. The potential advantages of using dual implements
are reduced working time, increased productivity, reduced fuel
consumption, reduced soil compaction and improved working quality. On
the other hand, some specific implements would provide better working
control for the operator with front mounting. For example, an operator
would rather work with a front mounted row crop cultivator than. with a
rear mounted one, because he could control both tractor and implement
while facing forward. Another example is that front mounted shovels
could smooth tire tracks on rough terrain, thus increasing the tire life and
reducing operator discomfort.

However, the introduction of front mounted three-point hitches has
raised concerns about the tractor and implement design and field operating

system. By all means these new front mounted hitch systems should have

5

an impact on the strength requirements of the tractor's front chassis, as

well as on performance, stability and drivability.

 

 

 

 

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2. LITERATURE REVIEW

Ballast ratios, hitch configurations, dynamic loads, and performance
and many other aspects have been studied in 2WD, 4WD, and FWA
tractors, but the specific problem of front and rear hitch configuration on
FWA tractors has not been addressed in published literature. A theoretical
and practical background for this problem, however, can be drawn from
four major lines of research, plus a fifth subject area related to
instrumentation.

First, the practical and theoretical treatment of motion resistance,
slip, and tractive efficiency (TE) of a given wheel , based on soil properties
(e.g. cone index), tire design, tire inflation, and vertical load, has
progressed to the point of having at least some standards accepted by
American Society of Agricultural Engineers (ASAE). It is important to
note that these principles of individual wheel performance are independent
of tractor design. Second, there are numerous studies comparing the
performance of 2WD, 4WD, and/or FWA tractors. Conflicts in the results
and conclusions of these studies have led to considerable discussion and
experimentation with ballast ratios and peripheral wheel velocity ratios;
conflicting conclusions remain. Third, several studies have been
conducted regarding optimization of ballast and hitch positions on 4WD and
FWA tractors per se, but primarily with rear loads only. Fourth, a few
attempts have been made to develop real-time, computer controlled,

hydraulically adjustable hitches using signals from various transducers to

6

7

adjust dynamic loads to optimize tractive efficiency. A fifth area of
literature regarding the design of instrumentation, computer hardware,
and algorithms necessary to conduct the experiments for the present study
will be discussed in Chapter 6.

Both refereed and non-refereed publications (many of them
presentations at ASAE meetings) are included in the present review
because of the scarcity of published studies in many of these areas,
inconsistencies in the reported results and conclusions of some refereed
publications, and the lack of comprehensive literature citations in many

refereed publications.

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The recognition of energy losses due to motion resistance and drive
wheel slip and their significance for efficient operation of agricultural
tractors has long been recognized. The tractor drawbar predictor chart as
presented in the ASAE Yearbook's Data D230.4 Agricultural Machinery
Management Data, illustrates the penalty for non-optimal slip operation
due to incorrect ballasting and/or drawbar pull for a two-wheel drive
tractor. Excessive ballast reduces slip but also increases motion resistance
of the tractor, thus reducing overall tractive efficiency. Since there is only
limited published data regarding these parameters in FWA tractors, and
essentially none regarding FWA's with front hitches, one must draw upon

other sources of information.

 

 

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2.1.1 Rigidxheelihenm
Barger et a1. (1963) discussed the methodology and developed

equations to theoretically calculate the motion resistance of traction devices.
The equations were based on the dynamic wheel load, wheel size, and
cohesive and frictional properties of the soil. The use of the equations is
limited as the soil properties are difficult to determine accurately. These
concepts and equations with respect to thrust and dynamic weight
relationships for rigid wheels were further developed by Burt & Bailey
(1975), Bailey et al. (1976), and Bailey & Burt (1976).

Later, Bekker (1983) presented methods, tests, and numerical
examples for prediction of design and performance parameters in agro-
forestry vehicles. He presented a simplified expression for calculating the
rolling resistance coefficient, but use of the equation still required values for

soil and tire parameters that were not readily available.

2.1.2 Enenmatimheeuheerx

One of the more simplified expressions for determining motion
resistance of a wheel with a pneumatic tire was developed by Wismer and
Luth (1974). Using dimensional analysis, they showed that the motion
resistance of a towed tire could be predicted from:

F = W [:43 + 0.04] (2.1)
where:

F = towed force, N

W = dynamic wheel load, N

cn = wheel numeric

 

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Cn = CWIbd (22)
b = unloaded tire section width, cm
d = unloaded tire diameter, cm

CI = cone index as defined by ASAE Standard $313.1, N/cm2

While equation 2.1 was used to predict traction characteristics of a
towed wheel with a pneumatic tire on soil, Wismer and Luth (1974) also
developed another equation for the driving wheel.

V5} = 0.75 ( 1 - e '03 °n £5) - (t—f + 0.04) (2.3)
where:

P = driving wheel pull, parallel to soil surface, N

s = wheel slip, decimal fraction

and all other terms were as defined for a towed wheel. Wheel slip

was defined as follows:

Va
8 = l - “v: (2.4)

where:
Va = actual travel speed, km/h
Vt = theoretical travel speed, km/h

2.1.3 Eneumatimheelmrfnmanee

Several factors determine the extent to which a given wheel would
approach optimal, theoretical performance. There are numerous studies
regarding the effects of tire design, inflation pressure, and loading on the

performance of single wheels with pneumatic tires.

 

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10

Only selected samples of some publications will be given here, since
many of these review and cite previous, historically important papers.
Performance effects of standard, commercially available tread designs, for
example, were studied by Taylor (1976). The effects of tire width and
diameter on tractive performance were studied by Dwyer & Heigho (1984).
More recently similar studies of radial tires have led to the tractive
performance predictive equations by Brixus (1987) and by Upadhyaya et al.
(1987). '

Ellis (1977) reported that agricultural tire deflections average about 19
percent under conditions of rated load and inflation pressure for normal
field conditions. He defined the deflection as the ratio of the reduction in
tire section height at ground contact to the undeflected tire section height
measured above the rim flange area. With the increased loads approved
for slow speed operations, tire deflections will approach 25 percent. This
has been found to be about the practical limit for agricultural tires in any
application where normal service life is expected. On the other hand, he
indicated that the dynamic loaded radius was slightly larger than the one
measured statically. When in motion, there was a lifting action due to the
distribution of stresses in the moving tire which resulted an increase of
about 3 to 3.5 percent in the tire section height compared with the static
figure.

Gee-Clough and McAllister (1982) conducted a series of field tests to
evaluate the effects of wheel ballasting on a tractor's power output. They
established a dynamic rear axle load as the optimum value and used as the
reference point throughout their tests. They concluded that power delivered

by the tractor increased as the rear axle load approached its optimum value

bu
its

 

 

 

 

 

11

but the rate of increase decreased when the axle load was at 70% or more of
its optimum value.

Burt and Bailey (1982) reported on efforts to optimize tractive
efficiency while holding net traction constant. They varied the static load
on a 20.8-R38 radial tire throughout the range recommended by the Tire
and Rim Association. They also varied the inflation pressure using 28, 55,
83, and 110 kPa. They compared the tractive efficiency at both 10 and 20%
slip. Results showed that tractive efficiency can be optimized by selecting
the appropriate levels of dynamic load and inflation pressure. The relative
difference in tractive efficiency between optimum and minimum was in the
range of 6 to 10%, depending upon soil conditions.

Burt et a1. (1983) conducted a similar study under field conditions at
the University of Natal, Republic of South Africa. These tests were run at
four levels of inflation pressure at each of four levels of dynamic load. Net
traction was held at 10 kN for each operating condition. Results showed
that the difference in tractive efficiency between the maximum and the
minimum was dependent upon soil condition and tire construction (radial
or bias). The observed difference (i.e. maximum - minimum) ranged from
10 to 21%. They also reported that the maximum tractive efficiency did not
necessarily occur at the minimum level of slip.

Lyne and Burt (1987) developed a computerized system for
determining the dynamic load and inflation pressure for optimum tractive
efficiency under dynamic conditions and within the ranges recommended
by Tire and Rim Association. They affirmed that the tractive efficiency can
be optimized by selecting the proper values of dynamic load and inflation
pressure. The difference between the optimum and minimum tractive

efficiency depended upon the net traction demanded, the soil type, and the

 

 

 

I (k I [k a). a I v I Ii'\l'hl. h . I
0 n r 9 X D. 2. W n 0 Mr O. .1 0 met i Ni
5 .1 D. 2 t. d 0 2 m C d D. 0 1m cm H m m m.

 

 

12

soil condition. Under some operating conditions, they achieved a 30%
increase in tractive efficiency by selecting the dynamic load and inflation

pressure for optimum efficiency.

 

Papers comparing 2WD, 4WD, and/or FWA tractors often discuss
tests with each tractor at different front-to-rear (f/r) ballast ratios or
dynamic loads. Although these studies are not necessarily aimed at

optimization of performance, they offer some information along these lines.

2.2.1 Snflhinjestufmultinlenheelm
Some attempts to predict performance of 4WD tractors have been

made using multiple passes of single wheels. Burt et a1. (1980) used
continuously changing dynamic loads during first and second passes of a
drive wheel over the same track in a soil bin as a means of evaluating
possible tandem wheel drives. They found only limited opportunities for
optimization of f/r load ratios in firm soil but slightly better opportunities in
looser soils. In a later study (Bailey & Burt, 1981) the advantages of some
form of tandem drive over single wheel or dual wheel drives were (shown.
However, since the second passes of the wheel were not linked
mechanically to the first, no possibility for dynamic f/r interactions existed
in these studies, thus the results have limited application to the present

problem.

 

“

r
C

 

13

2.2.2 MW

Introduction of the 4WD tractor led to numerous comparisons which
generally showed an advantage of the 4WD over 2WD under various
conditions. For example, Rackham & Blight (1985) conducted an extensive
review of published papers about the advantage of the 4WD tractors over
2WD. They concluded that on a firm, flat surface, 4WD offers very little
advantage; but as soil conditions become progressively softer so the
usefulness of 4WD increases. Clark (1984) reviewed several papers
comparing the performance of various 2WD and 4WD tractors, then
conducted experiments with a 4WD tractor in the 2WD and 4WD modes
(unfortunately with the same ballast ratio). Nevertheless these results also
confirm that drawbar pull and ground speed were greatly improved (e. g. 60
to 125%) in the 4WD mode, along with a 25% to 57% reduction in fuel use per
hectare. Although TE was not calculated directly, it can be presumed to
have been higher in the 4WD mode. One important point in these and other
results is that different operating speeds may affect the relationships
between unevenness of the ground, variations in pull resistance, and the

oscillation and/or deformation frequencies of the tractor-implement system.

2.2.3 W

The possible advantages of FWA tractors over conventional 2WD
tractors have also been studied by several researchers. Bashford (1984)
presented the results of comparative tests with different drawbar loads on a
FWA tractor operated in the 2WD mode and FWA mode based on the power
loss due to slip and motion resistance. He concluded that, for the tractor

operating in the FWA mode, slip power loss is relatively independent of

 

b2
b2
d1

gea
this

Peri

 

14

ballast distribution. However, with the tractor operating in the 2WD mode,
ballast distribution is very important. On the other hand, the power losses
due to motion resistance as related to vehicle traction ratio are relatively
independent of drive mode and ballast distribution.

Bashford (1984) again studied the effects of two static (ballasted) load
ratios (f/r = 41/59 & 26/74) on the performance of an FWA tractor Operating
in the 2WD and FWA modes, pulling only a rear drawbar load consisting of
another tractor. Tests were performed on two different soil conditions in a
wheat stubble field, one a moderately firm soil condition with the field only
disked, and a looser soil condition following plowing and disking of the
same field. Different ratios of drawbar pull to gross tractor load (Vehicle
Traction Ratios, or VTR) were generated by driving the tractor in different
gears at different engine speeds. The results are summarized below and in
this summary his parameter called Axle Power Loss will be expressed as a
percentage of Total Axle Power (TAP).

Power loss due to Motion Resistance (MR) as a percentage of TAP
was essentially independent of the drive modes and load ratios, but was
different on the two soil conditions. For the firm soil condition it accounted
for approximately 40% of TAP at VTR = 0.1 (these values estimated from
Figures 1 & 2 of Bashford, 1984). It decreased substantially as VTR
increased, but began to level off asymptotically toward a value of
apprmdmately 22% of TAP as VTR approached 0.25. On the looser soil MR
accounted for 48% of TAP at VTR = 0.1, and likewise declined and began to
level ofl' toward a value of approximately 22% of TAP as VTR approached
0.32.

Power loss due to slip as a percentage of TAP was affected by the
drive modes and by ballast ratio in the 2WD mode, but not by ballast ratio in

15

the FWA mode. With the tractor in the FWA mode, slip accounted for
approximately 6% of TAP on both the firm and looser soil, and increased
almost linearly toward approximately 19% of TAP on the firm soil and 24%
of TAP on the loose soil at VTR = 0.35. With the tractor in the 2WD mode
and with a ballast ratio of 26/74 slip began at values of approximately 7 and
8% of TAP and increased to 20 and 28% of TAP on the firm and loose soils,
respectively. Although the values of slip in the 2WD mode were higher
than the corresponding slip when front wheels were powered, the slopes of
the increase in slip with VTR were similar. However, with a ballast ratio of
41/59 in the 2WD mode, slip increased more steeply from 8% of TAP at VTR
= 0.1 to 21% at VTR = 0.3 on the firm soil, and curved non-linearly from 11%
to more than 35% as VTR passed 0.25.

Power converted to Drawbar Pull (DP) as a percentage of TAP (i.e.
Tractive Efficiency) was highest in the FWA mode at all values of VTR and
was independent of ballast ratio. In the firm soil it formed a broad convex
curve from approximately 61% at VTR = 0.1, to a maximum of
approximately 68% of TAP at VTR = 0.27, then declined to 64% at VTR =
0.35. In the 2WD mode with a ballast ratio of 26/74 on firm soil the DP curve
had values uniformly 4% lower than those of the FWA mode for all VTR
values. Changing the ballast ratio to 41/59 on firm soil lowered the initial
value of DP to 52% of TAP at VTR = 0.1, with the maximum DP of 58%
occurred at VTR = 0.22, and caused a steeper decline of DP to 54% while
VTR increased from 0.22 to 0.29. The looser soil condition lowered the VTR
values of all of these curves to maxima of 60%, 56%, and 48% respectively.

This study did not address the issue of dynamic loading. The total
static load was maintained at 5105 Kg, however one is left to assume that

the towed load (i.e. a second tractor) did not add significant static vertical

16

load. No information is given about the rear hitch configuration, thus it is
not possible to estimate how much the dynamic load ratio difi‘ered from the
static ratio over the different values of VTR. Regardless of these
considerations, the results of this study appear to be somewhat in conflict
with the earlier study by Woerman & Bashford (1983) and that of Mueller &
Freer (1986), discussed below.

Kucera et a1. (1985) obtained results which appear to conflict with
other studies of 2WD and FWA tractor performance, especially with respect
to fuel efficiency per hectare. They concluded that when each was operated
at its respective optimal ballast ratio, the 2WD could equal or surpass the
FWA tractor. They also reviewed a number of papers with a wide range of
conflicting results, but cautioned that in many cases the two types were not
optimally configured. While these 2WD vs FWA comparisons do not bear
directly on the present study, they do point out the general lack of a
systematic way of setting, measuring and/or calculating tractor
configurations.

Shell et al. (1986) also compared what they believed were optimally
balanced 2WD and FWA tractors, and reached the opposite conclusion from
Kucera et a1. (1985), namely that fuel efliciency of the FWA was better at all
pull levels tested in three soil types.

Mueller and Freer (1986) presented test comparisons of FWA versus
conventional 2WD CASE-1H tractors. They reported that the FWA tractors
were superior to their 2WD counterparts in pulling performance. An issue
emphasized in that paper was the importance of the proper weight ratio on
FWA tractors and the critical nature of weight ratio to the measured

performance.

17

Babacz et a1. (1986) conducted an extensive series of tests with an
instrumented FWA tractor to determine the ballast distribution that led to
the highest tractive efficiency for operation in the 2WD and FWA models. A
subsequent step was to compare tractor performance in these two modes
when operating at optimum ballast distribution. Relative performance
reported for operation in good, intermediate, and poor tractive conditions
showed that the optimum ballast distribution for the FWA mode required
60-64% of the tractor static weight on the rear axle, a result which was in
agreement with what other researchers had found. Felsenstein et a1.
(1987) continued tests similar to those reported by Babacz et a1. They
concluded that the FWA mode with optimum ballast generally

outperformed the 2WD mode. However, the optimization curve is relatively

flat compared to that of 2WD tractors.

 

Murillo-Soto & Smith (1977, 1978) used a 1:10.9 scale 4WD model in a
soil box with sand or clay loam to establish that front to rear (f/r) static load
ratio (i.e. ballast ratio), drawbar vertical position (which affected dynamic
weight transfer), and different f/r wheel peripheral velocities could affect
tractive efficiency. They adjusted the ballast ratio and effective drawbar
height and used an equation established in their 1977 paper to calculate
absolute dynamic weight transfer. The dynamic f/r load ratios were not
measured and are difficult to calculate from their published data since the
absolute total weight of the model was not given.

The primary result of their study was that tractive efficiency

increased as angular velocity of the axle supporting the larger dynamic

18

load was increased. Since the front and rear tires of this test model were
equal in size, the actual f/r ballast ratios and hitch positions for this model
would not likely apply directly to a FWA tractor with its smaller front
wheels. This same problem of comparing results from one tire size to
another occurs in many of the studies discussed below.

Another important observation was that even under ideal conditions
(i.e. 1:1 f/r ratios of load and of angular axle velocities on dry sand) weight
transfer was about 5% lower than theoretical predictions. This discrepancy
increased as the ratios of loads and angular velocities deviated from 1.0,
and was attributed to shaking and vibration (i.e. angular acceleration of the
tractor), front-to-rear oscillations in slippage (i.e. "push-pull" effect), and
desynchronization of the tire lugs. This is suggestive that in addition to
optimizing the sum of slippage and motion resistance, optimal static load
distributions and hitch configurations may improve TE by minimizing
these oscillatory power losses.

Erickson & Larsen (1983) also focused on the problems of oscillations
in f7r load ratios and/or power ratios, and the associated variations in TE
under field conditions. Heavy draft loads increased the oscillation
problems, which became unmanageable under conditions of turning. They
did not confirm the "push-pull" effect suggested by the soil bin model
studies of Murillo-Soto & Smith (1977, 1978), but do confirm that power
losses from oscillatory motion may greatly reduce performance below
theoretical predictions under real operating conditions.

In many other studies only static ballasting was considered, for
example Shell et a1. (1986) used fuel efficiency during field tests to
determine some relationships between total mass (three levels) and ballast

ratios (three levels) in an FWA tractor on three soil types. Their results are

19

suggestive that some of the discrepancies in published optimal ballast
ratios resulted because the ratios used were not properly matched to the
total mass.

Woerman & Bashford (1983) presented TE data for an FWA tractor
[assuming a rear drawbar load] showing an optimal f/r dynamic load ratio
of about 40/60 and optimal f/r wheel peripheral velocity ratio of about 1.03.
TE was improved, and differences in the various tractor configurations
were minimized (i.e. the optimization curves were flattened) when the
tractor was operated at a speed of about 8 M as compared to 4-5 km/h.
This resulted because of a substantial decrease in slip accompanied by a
smaller relative increase in rolling resistance.

Mueller & Freer (1986) used a mechanical front drive (MFD) tractor
(i.e. Case-1H 3594) with an unspecified rear drawbar load. They found that
some ballast ratios resulted in slightly lower amounts of rear wheel slip
than others over a range of drawbar pulls (see Table 2.1). The differences

were more noticeable on the firm soil (i.e alfalfa sod).

Table 2.1 - Rear wheel slippage summarized from tests
"CTT436S" and "CTT436T" of Mueller & Freer, 1986

 

 

 

Soil condition F/R Axle Load Ratio
DP range (lbs)

25/75 30/70 40/60 45/55
Alfalfa sod 16.8 16.7 13.9 15.7
4700 - 10300
Tilled soil 11.9 11.0 12.5 12.9

2900-11300

 

 

Summarizing the above sample studies it is clear that many factors
interact to determine the performance of an FWA tractor. These include
soil and tire properties, total mass, static ballast, dynamic loading, tractor
speed, possibly front-to-rear oscillations, and possibly angular momentum.
One approach to dealing simultaneously with these interactions in real
time is with computer controlled adjustments of various parts. of the
tractor-implement system.

Smith & Khalid (1982) attempted to minimize oscillations in weight
transfer in two scale models (i.e. 1/10.9 and 1/5.7) fitted with computer
controlled hitch systems whose vertical position was adjusted in real time
in response to signals from torque transducers on the front and rear axles.
While these systems did respond as planned by optimizing the f/r division of
power, they concluded (primarily on the basis of other published studies)
that this adjustment would not increase TE, but may reduce uneven wear
on the drive system.

Dodd et a1. (1986) attempted to optimize rear wheel load in a 2WD
tractor using a computer controlled 3-point hitch in which the height of the
upper link position was adjusted hydraulically. Proper angles of the hitch
configuration were maintained by sliding the upper hitch point through an
angled slot which approximated the effect of adjusting the upper link
length. The effect of this adjustment was to alter the virtual hitch point in
response to signals from appropriate load transducers [described in
Reynolds et a1. (1982)] and a mathematical model which included
instantaneous calculations of cone index and optimal loading to improve

TE. Field studies indicated that the hitch responded as expected, but actual

21

field evaluation for improved tractor performance had not been completed.
These authors also mention another study of an automated hitch
adjustment system for 4WD tractors [i.e."McNab (1982)"], but failed to cite
the publication reference. Cowell & Herbert (1988) used a variable-length
upper link to improve the depth control of a fully mounted implement.
However, they did not address the effects of three-point hitch geometry on

tractor's dynamic behavior.

2.5 Summary

Past researchers have focused on several factors which affect tractive
efficiency such as soil types, tire characteristics and inflation pressures,
static ballasting ratios, rear hitch configurations, and the resulting
dynamic loading. Many of these observations were made in the course of
studies designed to compare the tractive efficiency of 2WD with 4WD and/or
FWA tractors. An overview of these studies results in several impressions.

First, it is clear that bitch configurations and ballast ratios affect the
performance (including TE) of 2WD tractors, but considerably less so for
4WD and FWA tractors. Indeed, in optimization studies of 4WD and FWA
tractors the range between the highest and lowest values of TE were only a
few percent, whereas there were greater differences for a given 2WD
tractor.

Second, in comparison tests where each type of tractor was optimally
configured the differences in TE between 2WD and 4WD or FWA tractors
were a few percent smaller. Note, that a 4WD or FWA tractor may have
greater value to the user beyond that of moderately better TE because of

added advantages in plowing speed, implement pulling capacity, or other

22

characteristics relevant to a particular type of farming operation. However,
it does forewarn that the opportunity for optimization of TE by hitch
configurations and/or ballasting in FWA tractors may be limited. ‘

Finally, since none of the publications dealt with combined front and

rear hitches and implements on FWA tractors, a number of questions
remain open, for example:

1) How do the combined front and rear hitches affect dynamic
loading, TE, handling, and other performance characteristics of
FWA tractors in comparison to those with a rear bitch and
implement only?

2) Is the range of opportunity for optimization of a given FWA tractor
with front and rear equipment greater than, the same as, or less
than the same tractor with rear equipment only?

If one finds that there is good opportunity for optimization then:

3) How should the front and rear hitches be configured in general,
and how would this vary with different types of implements, soils
and other factors?

4) How should the tractor be ballasted for optimal TE with front and
rear hitches, and with different implements?

The remaining chapters of this dissertation will address some steps

intended to answer these questions, and hopefully provide the means of

aChieving the best performance from this new type of agricultural tool.

3. GOALS, OBJECTIVES, CONSTRAINTS AND ASSUMPTIONS

3.1 Goals

The general goals of this research are to develop theoretical and

experimental means to:

1) Determine the extent to which the performance, especially tractive
efficiency (TE), of an FWA tractor with front and rear hitches can
be improved by adjusting hitch configurations, ballast ratios, or
other properties of the tractor implement system as outlined in
section 2.5.

2) Provide a basis for attaining whatever optimization is possible.

3.2 Qbiectixcs

The primary objectives necessary to accomplish the above goals are:

1) Develop a mathematical model of an FWA tractor with both front
and rear, three-point hitches. This model, would utilize static
dimensions and properties of the tractor and hitch system, along
with dynamic forces and movements of system components during
field operation, to calculate those parameters, such as dynamic
loads and wheel slippage that are necessary to evaluate
performance, e.g. tractive efficiency (TE).

2) Develop the instrumentation, data acquisition system and software

necessary to obtain the measurement data from field tests, and to

24

develop the software necessary to evaluate that data utilizing the
model from the first objective.

3) Conduct sufficient field tests to determine if the model and
measured parameters are adequate to analyze and predict
performance for this type of tractor system.

4) If the third objective is favorable, then the model and field
measurements will be used to evaluate the potential opportunities
for optimization in this type of tractor system and make specific
recommendations for experiments, modifications, or other

developments to achieve these ends.

3-3 Qanstraints

Several things constrainted the development of this simulation model
in order to maintain the compatibility of the tractor and implements and to
maintain safe working conditions. The constraints were:

1) The simulated geometry of rear three-point hitch had to be
compatible with the ASAE standard for the implements. At
present ASAE standards have not been published for front hitch
geometry, thus in this study the manufacturer's dimensions were
used as a starting point.

2) The dimensions of the simulated rear implement's mast had to
follow the specification of the ASAE standard. The front
implement's mast dimensions have also not been standardized by
ASAE; thus, in this study the front mast dimensions were set the

same as the rear.

25

3) The simulated hitching geometry had to promote soil penetration
for the implements.

4) The hitching geometry had to promote stability at working depth
without excessive penetration.

5) The arrangement of ballast could not violate the working safety
code.

6) The addition of ballast could not cause load beyond the tire
specification.

7) The tractor's weight distribution on both axles, with the addition of
ballast, could not exceed the maximum permissible load, either in
static or in dynamic situation.

8) The tractor's total weight with ballast could not exceed the
specification of Roll Over Protection Structure (ROPS).

3.4 Assumptions

Several assumptions simplified the design procedure and simulation

model:

1) The implement's working depth was assumed constant after it
reached the steady state, regardless of the field conditions.

2) The irregularity on the soil surface was assumed to be negligible.
However, the field inclination was not ignored.

3) The upper link point on the mast of the front implement was an
oval shaped slot which permitted relative motion between the link
pin and the mast. Before the implement reached the working
steady state, the upper link was in tension. The link pin was

assumed to be at one end of the slot (Figure 3.1). However, it was

26

assumed that when the front implement reached working steady
state, the link pin moved to the opposite position (Figure 3.2). With
a proper adjustment of the front three-point hitch and implement,
the front upper link should not experience any load.

4) The rolling radii of tractor wheels were measured with
implements in the raised position. The rolling radii while the
implement was actually working are likely to be slightly smaller.
However, this difference was assumed to be negligible.

5) The difference of rolling radius caused by the field topography was
considered to be negligible.

6) The center of gravity of each wheel ballast was assumed to be at the
center of the wheel.

7) The front axle load was considered to be distributed equally to both
wheels. The difference caused by the in-furrow travel was
considered to be negligible. .

8) The tractor was assumed to be advancing at constant ground speed
when it reached the working steady state.

9) Gibson and Biller (1974) verified how the fuel and hydraulic fluids
affect the location of the center-of-gravity of the tractor. They
concluded that these effects were negligible. Their assumption
was used in this research.

10) The weight of the data acquisition system and the tractor operator
was included in the total tractor weight. However, the weight
difference between different operators was considered to be

negligible.

®\

 

 

 

Figure 3.1 - Position of upper link pin at the front
three-point hitch before the implement
reaches steady working state.

f\

 

 

 

Figure 3.2 - Position of upper link pin at the front
three-point hitch after the implement
reaches steady working state.

28

11) The components of the data acquisition system were spread inside
the tractor cab, with the majority of its weight located behind the
rear axle. The position of the operator seat could be adjusted to fit
the operator's body dimension and driving habit; however, the
position was always over or before the rear axle. Thus, it was
assumed that the total weight of the data acquisition system and
operator acted directly on the rear axle.

4. MATHEMATIC MODEL

4.1 Kinematicalmlxsis

The geometries of front and rear three-point hitches must be
designed so that they could provide conditions for an implement's
penetration, working stability, and in-field manipulation along with
optimal performance. The following model is designed to predict
theoretically how hitch geometry will affect these parameters, and to serve
as a means of evaluating data from field experiments and optimization

tests.

4.1.1 WWW

The reference position used through this dissertation was the
position in which the tractor operator sits on the seat and faces toward the
front of the tractor. In this case, the right-hand side was referred to the
operator's right-hand side and the same rule to the left-hand side.

The tractor's transverse angle was defined as positive when it was
counter-clockwise at the reference position. The tractor's pitch angle

(longitudinal) was defined as positive when the tractor is going uphill.

4.1.2 _ 34!, or '1 '1: o ,t‘ I u :90 ‘:_ ° .1': 2-10 no ‘1! fl; :
The angle of any given link (i.e. upper or lower, front or rear) relative
to the ground is considered positive if the hitch point of the link is. higher

than the link point. The angle between a vertical reference line drawn

29

30

through the lower link point and a line drawn from the lower link point to
the upper point is positive if the latter line slopes away from the vertical line
toward the tractor center. Likewise, the angle of the main longitudinal axis
of an implement relative to the ground is positive if the end of the axis away
from the hitch point is higher than the hitch point.

Note, in the various figures that follow (with the tractor facing left),
these conventions have the effect that positive angles will be oriented
clockwise in the rear hitch system, but will be oriented counterclockwise in

the front hitch system.

4.1.3 Mechmismfcntherearthreezminmmh
There are three working positions for the three-point hitch which

deserve special consideration when designing its geometry. The first
position is that in which the implement is lifted for transportation (Figure
4.1). In this position, the distance between the hitch point and the soil
surface (RHH) must provide sufficient clearance for the implement so that
the tractor can maneuver in the field. The second position is that in which
the implement merely touches the soil surface (Figure 4.2). In this
position, the implement frame angle (4),.) must be positive in order to
promote a penetration force into the soil. The third position is that when
the implement reaches steady working state (Figure 4.3). In this position,
the frame must remain parallel to the soil surface and the frame angle
must be 0° during the working period so that the implement can keep the
working depth constant.

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From Figure 4.1 the following equations can be obtained.

 

 

.,....-1{Rm-I-<I;gR-RLY>} (4...
RLX - RTX
Br = tan'lhiLY + RTY} (4'2)
where:
a, = rear lower link angle relative to soil surface, degrees

RHH = perpendicular distance from rear hitch point to soil
surface, cm

RRR = rear wheel rolling radius, cm

RLY = vertical distance from rear axle center line to rear
lower link point, cm

AD = effective length of rear lower link as shown in Figure
4.4, cm

[3,- = the angle formed by a line connecting the centers of the
rear upper and rear lower link points in relation to a
vertical line through the lower link point, degrees

RLX = horizontal distance from rear axle center line to rear
lower link point, cm

RTX = horizontal distance from rear axle center line to rear
upper link point, cm

RTY = vertical distance from rear axle center line to rear
upper link point, cm

By the sign convention used in this dissertation, the angle [3; shown
in Figure 4.1 is negative, whereas the angle a,- is positive. The diagonal
distance B_D of the rear three point hitch, and the angle formed by the
diagonal line DD and the lower link AD, 5,, can be calculated by analyzing

the geometry of Figure 4.1.

ITI—i

 

 

 

35

 

312:wa +AD2 - 2*AB*AD*cos(90° - a,+ is.) (4.3)

2 2 -
5r = 608'1{W (4.4)

where:

fl = distance from rear lower link point to rear upper link
point, cm

Finally, the rear implement angle, 4),, and the rear upper link angle,
0,, are obtained by the following equations.

7, = cos-1{%IQ— (4.5)
¢r=wr=90°+ar-5r-Yr (4.6)
tyr=90°-y,-(o, (4.7)
B32 + 3122 - £212
0, = cos-llw - \Ilr (4.8)
where:
y, = angle between rear diagonal line and rear implement

mast, degrees

B_Q = rear upper link length, cm

CD = rear implement mast height, cm

0, = rear implement frame angle relative to soil surface,
degrees

00, = rear implement mast angle relative to the line

perpendicular to soil surface, degrees

w, = rear diagonal line angle relative to soil surface,
degrees

0, = rear upper link angle relative to soil surface, degrees

36

[<— Link Width

Effective Link Length __.1 J-

  

 

!= Hitch Width =1

 

 

Figure 4.4 - Effective lower link length

4.1.4 Mechamsmflnthefinntthreemmthrtch

The same three special working positions for the rear hitch also
deserve special consideration when designing the front three-point hitch
geometry (Figures 4.5 to 4.7). However, there are differences due to some
different moving requirements for the front implement.

The steady state working position still requires a 0° frame angle for
the front implement (Figure 4.7). However, the angle (bf at the penetration
position (Figure 4.6) must be negative so that there is a penetration angle on
the implement. The requirement for transportation is the same as the rear

hitch (Figure 4.5).

37

scammed £383,383... E 303 35 £33 353-833 38¢ .«o @88on - m6 88E

 

 

 

8%:on 838.5809 E 339 £35 £32 33353:... 38¢ no .388on .. $4. 383

 

 

39

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40

From Figure 4.5 the following equations can be obtained.

 

 

af= sin'1{FI-IH - (EH - FLY)} (4.9)
FLX - FTX
Bf = tam'lh‘LY + FTY} (4'10)
where:
(if = front lower link angle relative to soil surface, degrees

FHH = perpendicular distance from front hitch point to soil
surface, cm

FRR = front wheel rolling radius, cm

FLY = vertical distance from front axle center line to front
lower link point, cm

EH = efl'ective length of front lower link as shown in Figure
4.4, cm

[if = the angle formed by a line connecting the centers of the
front upper and front lower link points in relation to a
vertical line through the lower link point, degrees

FLX = horizontal distance from front axle center line to front
lower link point, cm

FTX = horizontal distance from front axle center line to front
upper link point, cm

FTY = vertical distance from front axle center line to front
upper link point, cm

By the sign convention used in this dissertation, the angle Bf shown
in Figure 4.5 is positive, and the angle (If is also positive. The diagonal
distance EH of the front three point bitch, and the angle formed by the
diagonal line EH and the lower link EH, 5f, can be calculated by analyzing

the geometry of Figure 4.5.

41

 

EH.= «JEEZ +EH2 - 2*EE*EH*cos(90° - a“ Bf) (4.11)
2 2 -
where:

E = distance from front lower link point to front upper link
point, cm

Finally, the front implement angle, (bf, and the front upper link
angle, 0f, are obtained by the following equations.

 

7r= c08'1{-E—H—22%:—fi& (4.13)

¢f=wf=90°+af-0f-‘Yf (4.14)

‘i’f= 90° ’ “if" 03f (4.15)

Of = cos‘1{E22:EE—G%2Efigfl- - w (4.16)
where:

'Yf = angle between front diagonal line and front implement

mast, degrees
F_G = front upper link length, cm
(211 = front implement mast height, cm

(pf = fiont implement frame angle relative to soil surface,
degrees

(of = front implement mast angle relative to the line
perpendicular to soil surface, degrees

\Vf = front diagonal line angle relative to soil surface,
degrees

0f = front upper link angle relative to soil surface, degrees

4.2 Analxsisnfchassiamechanics

The location of the center of resistance CR is fixed for a given
implement at a certain working condition. The direction and magnitude of
the soil resistance force also are fixed.

The Figure 4.8 shows forces acting on the rear of the tractor. With
input of three forces, T,, V, and C,, and the upper link pitch angle 0,, the
virtual pull point VP, can be determined. At the same time, the direction of
the soil resistance force is also determined.

For the front three-point hitch, knowing three forces, Tf, Vf and Cf,
and the angle 0f (Figure 4.9) is not enough to determine the virtual push
point. However, these four inputs along with front three-point hitch
geometry provide a means of calculating tractor dynamic load.

The initial model for load distribution is based on the tractor's
longitudinal plane, assuming that there is no sideways roll. Analyzing
Figure 4.10, an equation relating forces perpendicular to the soil surface
can be obtained:

R, + Rf= W*cos0g + V, + Vf- C,*sin0, - C(isinef (4.17)
where:

R, = dynamic load on rear axle, N

Rf = dynamic load on front axle, N

W = tractor weight, N

0g = ground slope at tractor travel direction, degrees
V, = vertical force acting on rear lower links, N

Vf = vertical force acting on front lower links, N

C, = axial force acting on rear upper link, N

Cf = axial force acting on front upper link, N

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45

0,, 0f = as defined in Section 4.1.3 and 4.1.4, degrees
The sum of moments about point C can be obtained from Figure 4.10.
The equation 4.18 is derived based on the convention that clockwise
moments are positive and counter-clockwise are negative. Since the forces
acting on the links were defined as positive for tensile force and negative for
compressive force, the signs in the equation must agree with this

definition.

R,*BASE - V(*(EH*cosaf + FLX + BASE) - T,*FHH

- Cf’icos0f*(F_G*sin0f + FTY + FRR) +

Cfsin0f*(E_G*cosOf + FTX + BASE) -

W*cosOg*CGX + W*sin0g*(CGY + RRR) -
C,*sin0,*(DQ*cos0, + RTX) + C,*c080,*(BD*sin0,

+ RTY + RRR) + T,*RHH + V,*(AD*cosa, + RLX)

= 0 (4.18)

where:
BASE = tractor wheel base, cm

CGX = horizontal distance from the tractor's center of gravity
to tractor's rear axle, cm

CGY = vertical distance from the tractor's center of gravity to
tractor's rear axle, cm

The remaining symbols used in equation 4.18 are described in

Sections 4.1.3 and 4.1.4.

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47

Thus, R, and Rf can be calculated by equations 4.17 and 4.18. After
the calculations, the rear axle is rotated to the actual working condition
where one wheel is in the furrow, and thus is lower than the other which is
on unplowed ground (Figure 4.11). The resulting load distribution to the
lower and higher wheels, R,1 and R,h, will then be calculated by equations
4.19 and 4.20. However, the front axle load is evenly divided between the two
front wheels due to the action of the pivot point where the front axle is

attached.

 

 

 

 

 

 

4
FWD
Rrh J—
l~— L1. _+__ L. _~.
l$ L er

Figure 4.11 - Dynamic load distribution on tractor rear wheels

48

L}, W*sin03*CGY

 

 

 

 

 

R,1 = R, * —L_ + L (4.19)

Rrh = R.r * if} - Waksmfifm (4.20)
where:

L = \lTread2 - FWD2 (4.21)

L}, = g L + RRngEAWD (4.22)

L] {EL - “151.2521“ (4.23)

03 = tractor's roll angle

_ - 1{__FW_P_}
" 3m Tread
Tread = tractor's rear wheels tread, cm

FWD = front implement working depth (Figure 4.7), cm

The optimal three-point hitch geometry should promote a certain

R,/Rf ratio in order to obtain the best tractive efficiency for an FWA tractor.

If this condition is not met, the geometries of both front and rear three-point

hitch should be redesigned until the optimal R,’Rf ratio is obtained.

4.3 W

4.3.1 W
The equations above can be used to calculate the dynamic load on the

front and rear wheels for any given combination of hitch configuration and

static weight distribution. Thus, the first aspect of performance, namely

 

’

49

slippage (s) of each wheel on a soil with a given value of cone index (CI),

can be calculated for given values of pull by equation 4.24.

S = fich— ln 1307152 (4.24)
' “ 0°75'(ii+‘c"_+°'°4)
n

 

where:
on = wheel numeric, defined in Section 2.1.2
P = pull delivered by the wheel, N
R = dynamic load on the wheel, N
4.3.2 W

The second aspect of performance, namely tractive efficiency (TE) for
the tractor must now be calculated in a stepwise manner on a per wheel
basis. Using the calculated values of slippage for each wheel from equation
4.24, an individual TE for each wheel can be calculated using equation 4.25.

{ % + 0.04 }
TE = 1 - 1 - .
( 8) 0.75 (1 - e'0-3 cn s) (4 25)

 

Based on the individual values of TE, the power delivered to each

wheel (HP) can be calculated by equation 4.26.

a:
PTEV (4.20)

 

HP:

where:

HP = input power to each wheel, kw

V = tractor's advance speed, m/sec

Finally a value of tractive efficiency (TEt) for the tractor can be

obtained as a quotient of the sum of the power developed by the 'wheels

AFII

 

50

(2‘. PW) and the sum of input powers to the wheels (2‘. HP) as shown in

equation 4.27.

_ EP*V
'ZHP

 

TEt (4.27)

5. SIMULATION MODEL

The equations described in Chapter 4, along with appropriate
solution procedures and the usual input/output subroutines have been
incorporated into a computer program. Appendix B shows the Pascal-like
pseudo code of this program. The logic of this program is outlined in the
flow charts presented in the subsequent sections. The computer code is

written in such a way that the model can be used in two different modes.

5.1 W

A block diagram showing the interactions of the main subroutines is
illustrated in Figure 5.1. The main routine is designed to serve as an
interface between users and the model. With a main option menu shown
on the computer output device (usually it is the monitor screen), the user
would initiate the selection of option by typing an appropriate number.
After the validation of option selected, the corresponding subroutine would
be initiated.

There are six options available in the program. Three are devoted to
the input, retrieval, editing, and saving of tractor and implement
parameters and the field working conditions. The fourth option is used to
analyze field test results and the fifth one is used for optimizing the tractor
performance. The last option handles the finalization of program execution

and exiting of the program.

51

52

 

 

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53

The logic for the input, retrieval, editing, and saving of the input
parameters is illustrated in Figure 5.2. Since the handling of data
regarding the tractor, the implements, and the working conditions have
similar logic, they are presented in one flowchart.

The input parameters for either the data analysis or simulation
mode can be entered into the model either as templates (Tables B.1, B.2, and
B.3 in Appendix B), or as step-by-step keyboard entries in response to
interactive statements presented by the program in the same order as those
of the templates seen in the tables mentioned in this paragraph. The
templates have an advantage that they can be set up in any text editing
program (e.g. a word processor), stored as text files, and then loaded into
the model from memory or disk, usually this is faster than the step-by-step
keyboard entry. The stepwise keyboard entry, however, minimizes the
likelihood of typographic errors, especially those which might affect the
data column positions which are critical to FORTRAN data handling. In
either way it is possible to change the value of a given parameter by

invoking the editing subroutines.

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55

The input parameters are clustered in three sets, each with its own
template or keyboard entry subroutine. The first of these, listed in Table
B.1, includes the dimensions and static weight distribution of the tractor
and dimensions of the hitches. The second set, listed in Table B.2,
represents the implement dimensions. The third set, listed in Table B.3,
includes the working conditions such as working depth, ground speed, type
of soil and cone index, along with the forces acting on the three point
hitches. This arrangement makes it easy to enter each set of data with
different combinations of tractors, implements, and working conditions in
a modular fashion for analysis of experimental data and especially for

simulation runs.

5.2 Detainalxsimodc

The computer program can be used to analyze experimental data to
calculate values of some parameters, especially performance parameters
such as dynamic load and TE, which would be difficult or impossible to
measure with instruments. A flow chart showing the logic of the program
operating in the data analysis mode is illustrated in Figure 5.3.

In this mode, one would measure the values of input parameters
such as tractor dimensions, static weight distribution, hitch dimensions,
implement dimensions, and soil properties. Then experiments would be
conducted in which forces acting on the hitches and motion of the tractor
and wheels, as well as the implement's working depth would be measured
and recorded. These input parameters and experimental data would then

be used to calculate the values of dynamic load and TE.

 

l

 

 

calculate
front and rear axles
dynamic loading

 

 

 

 

 

result file name/

 

calculate individual
wheel pull force

 

 

 

 

 

 

 

 

results
call tractor, calculate total
implement, and pull force
working condition

 

handling routines

 

 

 

 

 

calculate TE

 

calculate implement

 

 

working depth

 

 

 

save results

 

 

 

 

 

calculate
three-point hitches
working geometry
return
main

 

 

Figure 5.3 - Flow chart of the simulation program operating
in the data analysis mode

57

5.3 Sinnflationmodc

The model can also be used as a type of simulation or optimization
model to predict the consequences of changing such parameters as
dimensions of hitch components, static ballast, and implement
dimensions. A flow chart showing the logic of the program operating in
the simulation mode is illustrated in Figure 5.4. As in the case of the data
analysis mode, one would begin by entering all of the measured tractor and
implement dimensions, desired implement working depth, tractor's static
ballast, along with field conditions such as ground slope.

Since experimental data are not being used in the simulation mode,
one must enter a set of values for the forces acting on the hitch. Unlike the
situation with drawbars where forces transferred to the tractor can be
predicted from hitch position and implement pull, the interactions between
an implement and a three point hitch are much more complex than the
interaction when a drawbar is used. Although the resultant forces applied
to a three-point hitch by an implement can be predicted using empirical
equations (see ASAE Data D230.4), the analytical decomposition of force
components applied to each link can not be done easily. The reason is that
forces acting on each link and the center of resistance of implement are
functions of three-point hitch geometry, which represents a non-linear
relationship between components. Thus some experience is necessary to
help the selection of appropriate values. For example, the force components
used in this simulation were selected from the field test data to present
three different loading modes. Once these values are entered the model will
calculate front and rear upper link lengths and dynamic load on each

wheel.

 

 

 

 

tractor model /

r—no

3'68

 

if

call tractor,
implement, and
working condition
handling routines

L

compute front and
rear three-point
hitches working
geometry

l

compute front and
rear upper link
lengths

 

 

 

 

 

 

 

 

 

 

 

 

 

compute dynamic load I

 

     

within

 

 

compute implement
penetration condition

 

 

 

- n o permissible

load ?

     
 

is

compute dynamic
load distribution

 

 
     

show simulation
results

 

 

return
m ai n

Figure 5.4 - Flow chart of the simulation program operating
in the data simulation mode

59

Before the simulation, a target value of dynamic load distribution
ratio must be selected based on previous experience or the results from
other research projects which would result in maximum TE. The
calculated dynamic load distribution ratio can then be compared with this
value. If the calculated dynamic load distribution ratio would not likely
result in maximum TE, then a selected input parameter could be changed
interactively and a new set of values of dynamic load calculated. This
would be repeated until the calculated value of dynamic load distribution
ratio approached the selected target value.

However, the effects of front and rear three-point hitch geometry on
dynamic load distribution are not only functions of the hitch dimensions,
but also functions of how the forces are applied on the hitch. It would
require a great amount of knowledge about these functions to implement an
algorithm to decide mathematically how the parameters should be changed
during the simulation in order to approach the preset dynamic load
distribution. Since the implementation of this algorithm is not possible at
this moment due to insufficient knowledge about these functions, the
simulation process must be done one iteration at a time and the user must
make judgements about which parameter should be changed for the next
iteration. Some simulation results are discussed in Chapter 7 regarding
this concern. Automated simulation for optimization would be possible
only after more detailed research. Also note that the model does not predict
values of TE directly because there appears to be no adequate model to
Predict slippage from soil properties and dynamic load. When the model is
used in the experimental analysis mode the values of slippage are obtained

from experimental measurements of tractor and wheel motion, thus the

60

Equations 4.24 and 4.25 can be used to predict the values of tractor wheel
pull and TE.

6. FIELD TESTS

6.1 2mm
An FWA tractor equipped with a conventional rear three-point bitch

and a front mounted three-point hitch was used for the field tests. Two fully

mounted, reversible moldboard plows were used for the experiments.

6.1.1 mm

The tractor used in this research was a Ford1 agricultural tractor,
model 7610, with fiont wheel assist. The nominal PTO power of this tractor
was 64.1 kW (86 hp). In addition to a standard rear mounted three-point
hitch, the test tractor came equipped with a front mounted three-point
hitch. The front hitch was manufactured by Ransomes Company of
England and imported to the United States. Table 6.1 shows the size of
tractor tires, the tire inflation pressures used during the field tests, and the
rated permissible loads at corresponding pressure published by the Tire

and Rim Association (1986).

6.1.2 Imnlsmcnta

The implements used for the field test were two reversible moldboard
plows. They were made by the same company that made the front hitch.
Each plow had three bottoms with the nominal cutting width of 35.6 cm (14

 

1Trade names are used in this dissertation solely to provide specific information.
Mention of a product name does not constitute an endorsement of the product by the author to
the exclusion of other products not mentioned.

61

62

inches). The only difference between these two plows was in the mounting
frame. One was designed for conventional mounting on the rear hitch of
the tractor, the other was for front hitch mounting. Both frames were

designed to allow addition or reduction in the number of bottoms.

Table 6.1 - Specification of tractor tires

 

 

. . Inflation Pressure Permissible Load
Tire Slze kPa (psi) N (lb)
Rear 18.4-34.6, 6 ply 111 (16) 22100 (4960)
Front 136-24, 6 ply 152 (22) 13200 (2960)

 

The front plow was mounted so that its angular position could be
moved, from the center line of the tractor during transport, to an offset
angle toward the right or left of center for plowing. With the front gage
wheel running in the previous furrow, the last bottom would leave a new
furrow for the tractor wheels. The rear plow was mounted in the
conventional way. With either the right or left tractor wheels running in
the furrow, the front bottom of the rear plow should cut beginning from the
furrow edge. Figure 6.1 shows an overview of the tractor with two plows

mounted in working position.

0263 600558 .800 98 39¢ 55 5000.5 mo B03005 - H6 0.89m

 

 

 

 

 

 

 

 

 

64

6.1.3 Statiumightandmllinaradms

The tractor and plows were weighed on a platform scales. The
tractor with front bitch and the operator weighed 44200 N (9940 lb). The
rear plow with 3 bottoms weighed 10100 N (2260 lb). The front plow with 3
bottoms weighed 11600 N (2600 lb), but was reduced to 9250 N (2080 lb) when
one of the bottoms was removed. Table 6.2 shows the tractor total weight
and static load distribution on both axles with the three-bottom plow
attached to the rear hitch and the two or three-bottom plow attached to the
front hitch. Note that the removal of one bottom from the front plow

drastically reduced the front axle load.

Table 6.2 - The weight distribution of tractor with plows attached

 

no plows 3 fi'ont x 3 rear 2 front x 3 rear

 

Rear axle load, N (lb) 26900 (6040) 33200 (7460) 37300 (8380)
Front axle load, N (lb) 17300 (3900) 32000 (7200) 25600 (5760)
Total weight, N (lb) 44200 (9940) 65200 (14660) 62900 (14140)

 

The tractor wheels' rolling radii were measured in the field with
implements and data acquisition system mounted. The plows were lowered
but without cutting the soil. To prevent wheel slippage, the tractor was
towed by another tractor at the lowest speed possible. The values were
obtained by measuring the linear distance covered by 10 revolutions of the
front and rear wheels respectively. Then the rolling radii could be

calculated easily by the following equation:

r = 261; (6.1)
where:

r = rolling radius, cm

L = distance covered by 10 revolutions, cm

Table 6.3 - Tires' rolling radii, unloaded radii, and section widths

 

3 front x 3 rear 2 front x 3 rear

 

 

cm (inch) cm (inch)
Rear Front Rear Front
On Land 79.5 (31.3) 57.2 (22.5) 78.5 (30.9) 57.9 (22.8)
In Furrow 76.5 (30.1) 56.6 (22.3) 75.7 (29.8) 57.2 (22.5)
Unloaded 82.7 (32.6) 60.5 (23.8) 82.7 (32.6) 60.5 (23.8)
Sect. Width 46.7 (18.4) 34.5 (13.6) 46.7 (18.4) 34.5 (13.6)

 

The measurement was made in two different situations: one with two
wheels running in an 8-inch deep furrow, the other with the wheels
running on unplowed land. The results are presented in Table 6.3 along
with unloaded tire radii and section widths which were specified in the Tire
and Rim Association Yearbook (1986). Note that the difference between the
rolling radius of the in furrow rear wheel and that of the on land rear
wheel is significant due to the weight shifting caused by the shift of

tractor's center of gravity toward the furrow side. However, the front

66

wheels don't display this difference because of the action of pivot point
where the front axle is attached. The small difference is caused by the
weight of front axle and wheels.

6.2 W

A microcomputer based data acquisition system designed to meet
Objective 3.2.2 was developed and mounted on the tractor. There were 15
sensors used on the plowing system to monitor the tractor's engine speed,
ground speed, front and rear wheels rotational speed, front drive shaft
torque, and forces acting on the front and rear three-point hitches. The
signal from each sensor was supplied to an appropriate channel of a signal
conditioner, then to one of 16 channels of an A113 analog to digital (AID)
converter, and the digital information was then recorded by a computer as
outlined below. Many components developed for this system were utilized
and tested in another study in conjunction with Tembo (1986), thus details
of these components were presented therein. Note that the sensors used to
measure forces acting on the front three-point hitch were the same type as
those used on the rear three-point hitch, thus they were calibrated by the
same procedure as described in Tembo's thesis and had the same
measuring accuracies. Also, the sensor used to measure the torque on the
front drive shaft had the same property as the one used to measure the PTO
torque by Tembo.

62.1 W
A series of investigations was undertaken to find the best suited

three-point hitch dynamometer for this research. In the past, the majority

67

of three-point hitch dynamometers developed by several researchers
consisted of two subframes, one of which attached to the tractor and the
other to the implement. The two frames were connected by a transducer
capable of measuring forces between them, (Devine and Johnson, 1979;
Langwisch and Frisby, 1976; Johnson and Voorhees, 1979; Kendall, et a1.
1984). Although this type of dynamometer was interchangeable among
different tractors, it had the disadvantage of adding additional weight to the
tractor hitch if it was constructed to withstand loads from large
implements. This type of dynamometer also extended the implement
rearward, thus altering the tractor's operating characteristics. These
disadvantages made this type of dynamometer incompatible with the main
objective of this project, which was to analyze the tractor dynamic weight
distribution under normal operation with rear and front mounted
implements. A

Hoag and Yoeger (1974) described an extended ring load cell
transducer which measured a vertical and axial force. Luth et a1. (1978)
described the use of this transducer mounted in the lower draft links of a
three-point hitch so as not to alter the original hitch geometry. Bandy et a1.
(1985) adapted Luth's idea and constructed a dynamometer at Texas A&M
University. They cut off the original lower links. An adapter bracket was
welded to each link. An extended ring load cell was bolted to each bracket
and the original telescoping link from each lower link was welded to the
load cell. This dynamometer had the advantage of maintaining the
original three-point hitch geometry, as long as we assumed that the
alignment of link and bracket was perfect after welding. However, the
interchangeability of this dynamometer was limited to those tractors with
equal dimensions at the lower links.

68

In order not to alter the original hitch geometry, the ability to
interchange between different tractors had to be sacrificed. Thus, the above
type of dynamometer was selected for this research. To simplify the
construction process and to avoid any inaccuracy in fabrication, it was
decided that the strain gages would be applied directly to the original lower

links.

6.2.2 WW
The surfaces of the telescoping parts of the lower links of the rear

three-point hitch were milled so that the adjacent faces were perpendicular
to each other and the opposite faces were parallel to each other. Because
the telescoping link system was not a symmetrical, straight beam, the
neutral axis could not be determined geometrically. A stress coating was
used to determine the neutral axis.

The upper link had one set of strain gages, and each lower link had
two sets of strain gages. Each set had four strain gages forming a full
Wheatstone bridge. The advantages of full bridges are higher sensitivity
and guaranteed temperature compensation. However, the lead wires must
have the same length so that no error is caused by the difference in the wire
resistance.

One Wheatstone bridge on each lower link was set to measure the
force parallel to the center line of the tractor. The other bridge on each
lower link was used to measure the force perpendicular to the link. There
was one Wheatstone bridge on the rear upper link to measure the axial

force. Signals from these 5 Wheatstone bridges were passed through

69

appropriate channels of the signal conditioner to channels 1 - 5 of the A113
A/D converter.

The front upper link had the same configuration and single
Wheatstone bridge as the rear upper link. The front lower links were bolted
to a rigid frame which could move vertically by the activation of a hydraulic
cylinder but could not move laterally. The two links were machined to have
parallel surfaces. Two full Wheatstone bridges were attached to each link
to function the same as those on the rear links. Signals from the front 5
bridges were conditioned and supplied to channels 10 - 14 of the A113 AID

converter.

62.3 W

A set of four strain gauges forming a single Wheatstone bridge on the
front wheel drive shaft were connected to a combined voltage to frequency
(V/F) converter and FM transmitter which, along with rechargeable
batteries, were embedded in an aluminum ring on the drive shaft. The FM
receiver and frequency to voltage (F/V) converter were mounted inside the
tractor cab where the voltage output of the FN converter was connected to
channel 15 of the A113 A/D converter.

62.4mm
Other sensors, some of which utilized signals from a Dickey john

Tractor Performance Monitor 11 (DjTPMII, described in detail in Tembo,
1986), are summarized as follows where Channel numbers refer to specific

channels of the A113 A/D converter as shown in Figure 6.2.

70

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Engine speed in revolutions per minute (RPM) [Channel 6] was
obtained from the frequency signal generated by the DjTPMII RPM sensor
fitted between the existing mechanical drive sender and the tachometer
cable. The signal was processed through an M1080, 10KHz F/V converter
and was read by the A113 A/D converter.

Ground speed, [Channel 7] was obtained from signals generated by
the DjTPMII radar unit, processed through an M1080 F/V converter, and
also read on the A113 A/D converter.

To measure front and rear wheel angular velocities (RPM), sprockets
were mounted on the axle hubs just inside the right front and right rear
wheels. Cylindrical pole piece magnetic pickups (Wabash Inc.) were
mounted on brackets and positioned near the periphery of each sprocket.
The brackets were very rigid to avoid variations in the distance between the
magnetic pickups and the sprockets, and thus minimize noise in the
signals. As the wheels turned, the passing of the sprocket teeth and gaps
past the magnetic pickup caused an alternating signal whose frequency
was proportional to the wheel RPM. These signals were processed through
M1080 F/V converters, and the voltage supplied to Channels 8 & 9 of the
A113 A/D converter.

6.2.5 W

The signal conditioner, A/D converter, computer, battery power
source, and their mounting inside the tractor cab are described in more
detail by Tembo (1986). An FM telemetry receiver was added to the system
to receive signals from the torquemeter (see 6.2.3). One important point

was that each component was chosen to meet the objectives of system

72

flexibility, documentation, high volume and high speed data storage,
durability, and compactness. Because of the ruggedness of the units
chosen only moderate precautions regarding enclosure (a plastic film
around the Apple 11 computer) and vibration resistant mounting (e.g. foam
plastic padding in wooden box) in the tractor cab was necessary. Special
care was taken to provide a stable source of electrical power during
operation. This was accomplished by using a high quality 1 2VDC-1 20VAC,
60HZ, 500 watt sinusoidal voltage converter powered from a 12VDC free-
floating ground battery, disconnected from the tractor charging system
during operation. This precaution of disconnecting the battery prevented
the possibility of electrical spikes or noise (e.g. from engine RPM
fluctuations) from reaching the data acquisition system. More importantly
it also prevented the possibility of current leakage from the transducers to
the tractor ground. Also, during tractor operation, all data was stored in
the RAM memory of the computer, thus avoiding possible errors and

damage in the disk drives (see section 6.4 below).
6.3 Sansoncalihmtion

6.3.1 WW
Details of procedures to calibrate the Wheatstone bridges on the three

point hitches are given in Tembo (1986), however several key points are
summarized here. As illustrated in Figure 6.3a the horizontal load was
applied to each link (i.e. front & back, upper & lower) by a hydraulic
cylinder which was carefully aligned so that the force was applied parallel
with the tractor center line to simulate the longitudinal draft. The output of

73

each axial Wheatstone bridge was then correlated to that of a Chatillon
HCL hydraulic tensiometer (John Chatillon and Sons). Because the links
are not exactly symmetrical nor straight some vertical forces may be
generated, and because there is a cross-bar between the right and left lower
links some forces may be transferred across to the opposite link. Thus,
output from the axial sensor of the opposing link and from the vertical
sensors of both the loaded and opposite links were also recorded to evaluate
these "cross signals".

When vertical loads were generated in each of the lower links by the
test tractor's hydraulic system, the angle of the link was not necessarily
exactly horizontal (see Figure 6.3b). Thus, the link angle with respect to
horizontal was recorded along with the outputs of the axial and vertical
sensors and the Chatillon tensiometer. Again, the axial and vertical
sensor "cross signals" from the opposing link were also recorded. An
additional precaution was exercised with the front lower links which were
bolted to a frame that induced stress in the links. After calibration, the
bolts were not tightened or loosened since this would alter the induced
stresses.

The possibility of "cross signals" being generated by lateral or side
forces was tested, and were found to be negligible.

74

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75

6.3.2 12110119111919):
One end of the tractor drive shaft (approximately 210 cm long) was

fixed in a vice, and the other end was supported on a stand with a free
turning roller perpendicular to the shaft. The surface of the roller was
smooth and hard, thus the fi'iction between the shaft and support was
considered negligible. A 91 cm long torque arm was fastened to the free end
of the shaft, 9 series of weights was added. and the output of the
torquemeter was recorded. Also, as each weight was added the angle of the
torque arm changed slightly, so the angle of the arm with respect to a
horizontal line through the center of the shaft was measured in order to

calculate the effective arm length and true applied torque.

6.3.3 (21119119115023

The primary signals for engine RPM, ground speed, and wheel RPM
were in the form of frequencies which, especially in the case of the RPM
measurements, were based on mechanical action and thus not in need of
calibration. However, each of the FN converters was calibrated by
supplying known frequencies from an accurate signal generator, and

measuring the voltage output of the converter.

6.4 Qamputansaflwara

6.4.1 Datamllacfianmzram
The data collection program, developed for an Apple IIe
microcomputer, was designed to occupy as little memory as possible since

the data were stored temporarily in RAM memory during each

76

experimental run of the tractor. It was important not to use the disk drive
during tractor operation to avoid the introduction of noise, data loss, and
possible damage to the drive because of mechanical vibration.

The program was also user friendly, and informative, so that the
operator knew what the computer was doing at each step. At the beginning
of each run the operator could enter the number of data sets to be collected
and the interval at which the computer would query the A113 AID
converter, ranging from 0.05 ms to 1 8. When the tractor reached steady
state operation during an experimental run the operator could initiate the
data collection procedure with a single keystroke. After each experimental
run the program was continued by the operator to verify the data and thus
the functionality of the sensors before the data were recorded on a fl0ppy
disk. The 12-bit digital data were stored as an ASCII file in order to provide

transferability to other computers for analysis.

6.4.2 Warm

Data from the field experiments were processed in two steps. First,
the data (still in 12-bit digital form) were transferred from disks through an
Apple IIe connected directly to a Macintosh computer by a BASIC program
written specifically for this purpose. A second program written in
FORTRAN 77, with proposed FORTRAN 8x extensions was used to convert
the 12-bit digital data into real numbers representing the voltages sent from
the signal conditioner to the A113 AID converter. These voltage values were
then converted by the appropriate calibration equations to represent the

parameter measured by each sensor. These parameter values then were

77

stored on disks for later analysis and interpretation by the simulation
model.
The steps in these data transfer and analyses are represented in the

following flowchart. (Figure 6.4)

6.5 W
All of the tests were conducted on the Michigan State University

farms for two seasons. The field used during the first season (1986
Summer) consisted of a sandy soil with an average cone index of 45 N/cmz,
ranging from 38 to 70. The field used during the second season (1987
Summer) consisted of silty-clay soil with an average cone index of 90 N/cm2,
ranging from 70 to 176. Cone index was randomly sampled in 30 locations
in that area of each field where several runs were to be conducted.
Moisture content, measured in random samples from the second field,
ranged from 7% to 12%, dry base. Both fields were relatively flat with
average slopes (longitudinal and lateral to the plowing runs) averaging no
more than 1°, with occasional longitudinal slopes up to 4° during portions

of some runs.

 

# of data files

 

 

 

data file name

I open data file I

raw data

 

 

 

convert digital
data to
analog data

 

 

 

 

calculate primary
results using
calibration equations

 

 

 

 

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calculate derived ~
results using
primary results

1

I statistic summaryW

< save resultsi

l

decrement # of
data file

#ofdatafile=0?

 

 

 

 

 

 

   

Figure 6.4 - Flow chart for the field data analysis program

79

In addition to the fifteen variables monitored by the data acquisition
system, the tillage depth and width of the front and rear plows were
measured after each run, along with pitch angles of the tractor and six
links. Tillage depth for the rear plow was determined at three positions
along the length of the run, by placing a level on the surface of unplowed
ground adjacent to the furrow, and measuring the distance from the lower
side of the level to the bottom of the furrow (Figure 6.5). Because the rear
plow cuts and covers the furrow formed by the front plow, tillage depth for
the front plow could be determined only in that portion of the front furrow
which remained between the front and rear plows when the tractor was
stopped. Tillage width at three positions along the plowing run was
determined as the distance from the new edge of plowed ground to three
respective pre-set stakes minus the distances of the previous run (Figure
6.5).

The field tests were designed to measure the effect of varying ground
speed, different soil conditions, different combinations of front and rear
plow bottom numbers, and the impact of upper link length on the
implement's draft, power requirements, and overall field performance.
The parameters were varied in the following order:

1) four different ground speeds with other conditions fixed

2) three front bottoms versus two front bottoms

3) different rear and front upper link lengths, in order to obtain

different tensile or compressive forces in the upper link

A total of 36 tests for the 1986 season and 24 tests for the 1987 season
were conducted. Plow adjustment and hitch geometry, except rear and

front upper link lengths, were kept constant.

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81

At the beginning of each run, with the tractor in position, the data
collection program was initiated to the "stand-by" condition, then the
plowing run was started. When the tractor's forward speed and plowing
conditions were steady, the data collection procedure was executed. The
program was set to collect all 15 channels of data at 0.1 second intervals for
a total of 500 data sets, thus 50 seconds of plowing time. During the run,
data were stored only in the RAM memory of the computer to avoid
operating the disk drive while the tractor vibration might disturb its
operation. When the data collection was completed, the operator was
signaled by the monitor and the tractor was stopped. The data could then be
quickly checked, channel by channel on the monitor, and then stored on

disk. The measurements of tillage parameters, as described above, were

then taken.

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7. RESULTS AND DISCUSSION

7.1. we: 09:0: 2 H: o..1° a: 1‘:.: o 1' o 'QO‘UU‘J :

Before reporting and interpreting the results of field experiments in
this study, it is useful to summarize certain points established in previous
chapters. First, the review of published literature (Chapter 2) indicated
that the relationships between dynamic load distribution, slippage, pull,
and TE are very important in comparisons or optimization of tractor
performance.

Second, two of these parameters (i.e. dynamic load distribution and
TE) must be calculated stepwise on a per-wheel basis from appropriate
equations (Section 4.2). During the course of these calculations, individual
values at each wheel for dynamic load, pull, TE, and horsepower, must be
calculated using measured values of tractor and hitch dimensions, static
load, forces acting on the hitches, tractor speed, wheel numeric (which
depends in part on soil cone index), and slip.

Third, the tractor's wheel motion was not measured simultaneously

on all wheels during each experiment as discussed below.

7.1.1 Saflmnaindaxandnthauoilmaemgs

Measurement of cone index was conducted in a manner that several
measurements of cone index were made to a depth of 15 cm (6 inches) with

a standard instrument at random positions in the test area of each field.

82

 

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83

The average values, standard deviations, maximum values, and minimum

values are shown in Table 7.1.

Table 7.1 - Average, standard deviation, and range of cone
index measurements. (See also Section 6.5)

 

Average Std. Dev. Maximum Minimum

 

Sandy Soil 45 10.5 70 38
Silty-Clay 90 33.1 176 70

 

Note: 30 values of cone index were collected for each type of soil

There are several possible consequences of both the variability and
the method of these measurements.

First, the cone index used in the calculations for each run was
assumed to be the average value for the whole field. Considering the
variability of these measurements in different parts of the field the
calculations involving the wheel numeric (e.g. Equations. 4.21 and 4.22) for
any given run could be considerably different from the actual conditions.

Second, the maximum value of force during penetration of the
instrument was recorded, regardless of whether that maximum was
reached at the top, middle, or bottom of the 6 inches stroke. A general
impression during these measurements was that maximum force was
reached toward the bottom of the stroke in the sandy soil, but near the top of
the stroke in the silty soil which was somewhat crusted. Thus the value of
CI may have been correct for wheels on the silty soil surface, but overvalued
for wheels on the sandy surface. However, since the front plow cut to a

depth of approximately 8 inches, the cone index of the soil under wheels in

 

 

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84

the furrow might have been overvalued for the silty furrow, and

undervalued for the sandy furrow. A sensitivity analysis of possible effects

of these variations and assumptions regarding cone index will be shown in

Section 7.1.4.

 

Wheel motion was measured only on the right front and right rear
wheels as described in Section 6.2.4, and the amount of slippage in each of
these two wheels was calculated using Equation 2.4. The amount of
slippage in each left wheel was calculated as an inverse function of rolling
radii of these wheels. The geometric inputs (including the lateral
inclination resulting from the wheels on one side running in the furrow)
and force transfer equations of the model are believed to closely predict the
dynamic load distribution. However, considering the possible problems of
applying average values of cone index to the soil surface and furrow, the
estimation of slippage in the left wheels, based on the measured behavior of
the corresponding right wheels, is subject to question (Table 7.2).

Note that the measured slippage of the right wheels was higher on
the surface of the sandy soil than in the furrow, and was lower on the
surface of the silty-clay soil than in the furrow. These measured slippage
patterns are consistent with the suggested variation of cone index
measurements as a function of soil depth discussed in Section 7.1.1.
However, this discrepancy should be canceled by the opposing runs in each

test and thus in the final averages.

 

 

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85

Table 7.2 - Average slippage in the right (measured) and left (estimated)
wheels running respectively on the soil surface and furrow
during opposite direction runs.

 

 

 

Right wheels Left wheels Avg. slip
(measured) (estimated) (R+L)/2
Sandxfiail
Surface 0.147 Furrow 0.143 0.145
Furrow 0.132 Surface 0.136 0.134
5'“ _ l S .1
Surface 0.116 Furrow 0.118 0.117
Furrow 0.147 Surface 0.150 0.148

 

Note: each test consisted of two runs, one in a direction that the right
wheels running in the furrow, and the other in the opposite
direction with the left wheels running in the furrow.

Fortunately, there are several ways to either minimize or evaluate
the potential effects of these averaged soil properties, along with possible
effects of longitudinal and lateral slope, on the calculation of slippage and
pull and TE. First, these effects were minimized as much as possible by
including two runs of opposite direction in each test. Secondly, certain
intermediate calculations can be checked against independently obtained
experimental results (e.g. Section 7.1.3). Third, sensitivity analyses can be
used to evaluate the amplitude of variations in the final calculations caused

by variations in any given parameter (e.g. Section 7.1.4).

7.1.3 W

One means of evaluating the effects of estimated slippage and/or cone

index is to note that a predicted value of total pull can be obtained by

Ri
0n
Ri}

in

 

 

86

summing the calculated horizontal force or "pull" exerted by each wheel
(Equation 4.21 rearranged). This predicted value of total pull can then be
compared with the total pull determined from the measured hitch forces.
Such comparisons of predicted and measured pull in individual runs on
sandy and silty soils are illustrated respectively in Figures 7.1 and 7.2, in
which S denoted that right wheels (instrumented) are on the land surface,
and F in the furrow.

The averages of the data shown in the above two figures are

summarized in Table 7 .3.

Table 7.3 Average of total pull as predicted from individual wheel data and
as measured from hitch forces

 

Sandy Soil Silty-clay Soil

 

Predicted Measured Predicted Measured

 

Right Wheels 16100 12000 23500 23100
on surface
Right Wheels 14400 15400 27100 20400

in furrow

 

87

 

25

measured pull, kN
H N
on c

H
O

 

40

co
O

measured pull, kN

N
O

10

0

surface

 

 

 

predicted pull, kN

S - Instrumented wheels on surface

25

measured pull, kN
H w
or o

H
C

 

 

 

 

 

10 15 20 25
predicted pull, kN

F - Instrumented wheels in furrow

Figure 7.1 - Measured pull vs predicted pull in sandy soil

 

0

 

surface

 

 

 

10

30
predicted pull, kN

20

measured pull, kN

40

S - Instrumented wheels on surface

 

 

 

10

 

 

40

30
predicted pull, kN

20

F - Instrumented wheels in furrow

Figure 7.2 - Measured pull vs predicted pull in silty-clay soil

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88

In sandy soil with the right wheels on the surface, predicted pull is
higher than the measured pull in nearly all runs (Fig. 7.1-S) and thus in
the average (Table 7.3). This is consistent with the high values of slip, and
the suggestion that cone index is lower at the surface of the sandy soil.
With the right wheels in the furrow the relationship between predicted and
measured pull varied from run to run (Figure 7.1-F), but the average
predicted pull was nearly the same as measured pull (Table 7.3). These
results are also consistent with the suggestion that the maximum force
recorded during measurement of cone index occurred near the bottom of
the stroke near the level of the furrow.

In silty soil the relationships of predicted and measured pull with the
right wheels on the surface versus in the furrow are reversed from those of
the sandy soil (Figure 7 .2 and Table 7.3). Again, these results are
consistent with the suggestion that cone index of the furrow is lower than
that of the crusted surface of the silty-clay soil.

In both cases it should be noted that some of the measured slippage
during a given run may have included brief periods when the wheels began
to spin, and thus would not have been following the mathematical
relationship between dynamic load, spin, and pull (i.e Equation 4.21). This
tendency of wheels to spin in places where actual cone index was lower
than the average would have exaggerated the apparent differences between
opposite direction runs. It is less likely that this particular source of
variability would have cancelled in the two runs within each test.

Given the above considerations, and the fact that slip has a non-
linear effect on the calculated or predicted value of pull, it is not surprising
that there remain some differences between predicted and measured pull

even when the opposing runs are combined into a single value for each test

 

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89

(Figures 7.3 and 7.4). Specifically, the predicted values continue to be

somewhat higher than the measured values.

7.1.4 WW
Finally, the extent to which variations of cone index, above and below

the average, might influence the calculated values of pull is illustrated in
Figures 7.5 and 7.6. In both cases the measured value of pull from 10
selected tests are plotted as closed diamonds, and the corresponding
predicted pull based on the appropriate average C1 are plotted as open
circles. Then, new values of predicted pull were calculated using values of
CI which were 33% lower (open squares), 50% greater (closed squares), and
100% greater (open diamonds) than the average CI.

Note that the standard deviation, maximum, minimum, and range
of the actual CI measurements (see Table 7.1) were similar to the 33% to
50% variations used in this sensitivity test. Thus the observed variations in
the relationship between predicted and measured pull are well within the
range that might be expected based on the variability of CI within the areas
of the field tests. Nevertheless, problems in the variability of CI in test fields
and its effects on slip and pull are common to many other studies (e.g. see
variations in pull with time in Figure 7 of Shell & Fox, 1986). Thus, the
results of this study should be comparable to others.

2-— :--l u..11-111t| 2v— .::nu malpCI

 

measured pull, kN

measured pull, kN

 

 

 

 

25
20 -
O 00
o
o

15 - 0 °

0 00 o

o
o

00 o

10 - o
0
° averaged pull
5 l l I
5 10 15 20 ' 25

predicted pull, kN

Figure 7.3 - Averaged, measured pull vs predicted pull in sandy soil

 

 

 

 

40
30 - A

A

A ‘ A
A A
20 -
A ‘ A
A averaged pull
10 l l
10 20 3O 40

predicted pull, kN

Figure 7.4 - Averaged, measured pull vs predicted pull in silty-clay soil

pull force, kN

pull force, kN

4O

30

20

10

40

3O

20

10

 

 

—a— CI = 30 + CI = 68 —°'_ measured

—°— CI=45 —°_ CI=90

Figure 7.5 - Sensitivity test of CI on predicted pull in sandy soil

 

 
 
   

CI=60
—°— CI=90

+ C1 = 135
'_°—‘ CI = 180
'—'*— measured

1 l l l l l l l l I

 

Figure 7.6 - Sensitivity test of CI on predicted pull in silty-clay soil

 

r1

in<

 

92

Figures 7.7 and 7.8 illustrate the influence of cone index on the
calculated values of pull. The values of predicted pull used to plot Figures
7.3 and 7.4 were calculated by the use of averaged cone index for both in-
furrow and on-surface wheels. However, different values of cone index
were used for each wheel while calculating the values of predicted pull in
preparation of Figures 7.7 and 7.8. The criterion of variation was based on
the discussion presented in Section 7.1.1. In sandy soil, the cone index used
for in-furrow wheels was the average measured value (i.e. 45), while on-
surface wheels used a smaller cone index (i.e. 30). On the other hand, the
measured cone index (i.e. 90) was used for on-surface wheels and the
reduced value (i.e. 60) was used for in-furrow wheels in silty-clay soil. The
results show that the modification has brought the values of the predicted

pull closer to those of the measured pull.

 

Total or average slippage in all types of tractors increases with
increased pull. This relationship in the present study is illustrated in
Figures 7.9 and 7.10 on sandy and silty-clay soils respectively. These
results are of the same magnitude and slope as those reported in other
studies of 4WD or FWA tractors (e.g. Meuller & Freer 1986, Wismer & Luth
1972), and have comparable or even less variability (e.g. Wismer & Luth

1972, Bashford, 1984).

measured pull, kN

measured pull, kN

20

15

10

40

30

20

10

93

 

 

° sandy

 

l l l

 

10 15 20 25
predicted pull, kN

Figure 7.7 - Pull Prediction using variable cone index in sandy soil

 

 

10

A averaged pull

 

20 30 40
predicted pull, kN

Figure 7.8 - Pull prediction using variable cone index in silty-clay soil

total slip

total slip

0.20

0.16

0.12

0.08

0.04

 

0.00

0.20

0.16

0.12

0.08

0.04

0.00

 

 

 

 

 

'- O
- 0 total slip
f slip = 0.0060*pull + 0.0593, R2 = 0.526
a l n l 1 l 1 l n J
8 10 12 14 16 18
measured pull, kN
Figure 7.9 - Averaged slip vs measured pull in sandy soil
A total slip
- slip -_- 0.0066*pull - 0.0152, R2 = 0.583
1 L l 1 J 1 l L l j I
18 20 22 24 26 28 30

measured pull, kN

Figure 7.10 - Averaged slip vs measured pull in silty-clay soil

 

‘_

ei

0b

 

7.2.2

 

A major objective of this study was to determine the extent to which
performance of an FWA tractor with front and rear implements could be
optimized by adjustments affecting dynamic load distribution ratio. The
relationships of slippage and TE with dynamic load distribution ratio on
sandy and silty-clay soils are illustrated respectively in Figures 7.11 and
7.12.

In the case of the sandy soil there was little change in slip as a
function of front load ratio, however, TE increased from about 0.52 to 0.68 as
front load ratio increased from 0.2 to 0.4. This magnitude of optimal TE at a
front dynamic load ratio of 0.4 in FWA tractors, especially on loose soils, is
consistent with essentially all of the published studies. Although no
attempt to measure or calculate rolling resistance is being made in this
study, it is possible that the 0.4/0.6 f/r load ratio results the best distribution
within this experiment's range, and thus a reduction in total rolling
resistance and an increase in TE.

In the case of the silty-clay soil there appears to be little change in
either slippage or TE. Again, this is consistent with other published
observations, and may result because there is less opportunity to minimize
rolling resistance on firmer soils.

Finally, the apparent limited opportunity for optimization in this
tractor system (i.e. :t 15%) is not surprising since similar values were found
in other studies. Furthermore, the front/rear implement system may act to
stabilize the tractor (i.e. prevent oscillations) and thus improve

performance in the field.

total slip and TE

total slip and TE

 

 

0.8 P
0 Q
0 0
0.6 - 0 o
0
0° 3%
o 0
0 TE

0‘4 __ 2 total slip
0.2 - o

. . Q.: . O.
0.0 I I I I I

0.0 0.1 0.2 0.3 0.4 0.5

front axle load ratio

Figure 7.11 - Averaged slip and TE vs front axle load ratio in sandy soil

 

 

0.8 r-

O O O o

0 Q9 0 00
0.6 -
0 TE
0.4 - 2 total slip
0.2 -
o. O

’ o o ’ .3.

0.0 I I I I I
0.0 0.1 0.2 0.3 0.4 0.5

front axle load ratio

Figure 7.12 - Averaged slip and TE vs front axle load ratio in silty-clay soil

'1

pr

di

V8

th

tr.

0t

0'

CO

CO

 

7.3 Simulatianxaanlts

Throughout all of the published studies, and to some extent in the
present study, the f/r load distribution has been emphasized as a possible
means of optimizing tractor performance. The exact value of f/r load
distribution for optimal tractor performance is not known, and clearly
varies from one set of working conditions to another. Therefore the
following simulations are aimed only toward determining the sensitivity
and trends of f/r load ratios resulting from the varied parameters, rather
than attempting to optimize TE or other aspects of tractor performance.

In the following simulations many of the input parameters (i.e
tractor and implement dimensions and weights and working conditions)
were similar to those used in the field studies. However, since implements
other than plows might be used in other field studies, the simulations were
run with three different sets of values for the forces acting on the front and
rear three-point hitches. These three sets of forces were chosen to generate
either tension loading, neutral loading (i.e. almost no loading), or
compression loading on the upper links. Then with each set of loading
conditions, simulations were conducted by varying the value of a selected
hitch dimension, implement dimension, or tractor ballast. Each selected
parameter was varied in seven increments; namely, 0.7, 0.8, 0.9, 1.0, 1.1,
1.2, and 1.3 times the original value of that parameter used in the field
tests. All other parameters were held constant during the seven
simulations at each of the three loading conditions.

The hitch dimensions to be varied in the simulations were the X- and
Y-coordinates of the lower and the upper link points of the front and rear
hitches, the front and rear lower link length. The implement dimensions

t0

lt

‘P

 

 

98

to be varied were the front and rear mast heights. The front and rear wheel

ballasts of the tractor were also varied.

7.3.1 Efiicctuflhitchjimaasians
The first set of simulations was designed to determine the effects of

the lower link point X-coordinates of the front and rear hitches on. the f/r
load ratio (reported as front axle load ratio). In each case, increasing the
value of X moves the lower link point away from the tractor. Figures 7.13
and 7.14 illustrate that this parameter in the rear hitch has little or no
effect (Fig 7.14), while increased values in the front hitch greatly increase,
moderately increase, or slightly decrease f/r load ratio when the upper link
is in tension, neutral, or compression loads respectively.

The second set of simulations (Figures 7.15 and 7.16) illustrates that
varying the lower link point Y—coordinate of either the front or rear hitches
has little or no effect on f/r load ratio.

The third set of simulations indicates that varying the front upper
link point X-coordinate moderately decreases, has no effect, or moderately
increases f/r ratio when the upper link is in tension, neutral, or
compression loads respectively (Figure 7.17). Nevertheless the effect of
changing this parameter in the rear hitch is opposite to that of the front
hitch (Figure 7.18).

front axle load ratio

front axle load ratio

 

 

 

 

 

 

 

 

 

 

 

 

0.40
+ tension
—"'— neutral
—'— compression
0.35 -
0.30 - '—__.——-—I—I——I-——I———I
0.25 ‘ ‘ '
30 40 50 60 70
front lower link point X-coordinate, cm
Figure 7.13 - Front axle load ratio vs front lower link point X—coordinate
0.40
+ tension
—"_ neutral
—l— compression
0.35 -
“Wm
0.30 - I———I———-I——I——-I-——'I—'I
0.25 i l 1
6 8 10 12 14

Figure 7.14 - Front axle load ratio vs rear lower link point X-coordinate

rear lower link point X-coordinate, cm

100

 

 

—a— tension
"—’— neutral

—"_ compression

0
0
0

 

I I I I I

 

0.40
.2
g 0.35 -
h
'6
Q
.2
O)
1
Q
4.?
= 0.30 ~
43
0.25
12

14

16 18 20 22 24 26

front lower link point Y-coordinate, cm

Figure 7.15 - Front axle load ratio vs front lower link point Y—coordinate

 

 

 

 

 

 

 

0.40
“-5— tension
—°— neutral
—'— compression
O
33 0.35 r-
In
'3 EI-————n I a a—a—a
O
0 c 4 ¢ ¢ ¢ t c
‘E
0
.0 .
g 0.30 - I———-I I a I———I———I
‘H
0.25 ' 1
15 20 25 30

rear lower link point Y-coordinate, cm

Figure 7.16 - Front axle load ratio vs rear lower link point Y—coordinate

front axle load ratio

front axle load ratio

100

 

0.40

0.35 -

0.30 -

 

—-a— tension
—’— neutral

—'_ compression

0
o
0
o
o

I I I I I

 

 

0.25
12

Figure 7.15 - Front axle load ratio vs front lower link point Y-coordinate

14

16 18 20 22 24
front lower link point Y-coordinate, cm

26

 

0.40

0.35

T

0.30 *-

 

0

0

—°— tension
—°—— neutral

—‘l— compression

0
0
0
<5

I I

0

 

 

0.25
15

Figure 7 .16 - Front axle load ratio vs rear lower link point Y-coordinate

20 25

rear lower link point Y-coordinate, cm

30

front axle load ratio

front axle load ratio

101

 

0.40
—a— tension
—‘— neutral
—'— compression
0.35 -

W

A A A A A A A
' V ' V V V V

 

 

 

0.25 ‘
30 40 50

front upper link point X—coordinate, cm

60

Figure 7.1 7 - Front axle load ratio vs front upper link point X-coordinate

 

0.40
+ tension
—"— neutral
—'— compression
0.35 -

‘P
0
0

0.30 r- m

 

 

 

0.25 L J I I
20 25 30 35 40

rear upper link point X-coordinate, cm

45

Figure 7.18 - Front axle load ratio vs rear upper link point X-coordinate

102

The most dramatic effects are observed in the fourth simulation,
where increasing the front upper link point Y-coordinate greatly increases,
has no effect, or greatly decreases f/r ratio respectively with the upper link
in the tension, neutral, and compression modes (Figure 7.19). However,
little or no effect occurred when the rear upper link point Y-coordinate was
varied (Figure 7.20)

Substantial effects were also obtained in the fifth set of simulations,
in this case resulting from changes in both the front and rear hitch
dimensions. Increasing the front lower link length greatly increased,
moderately increased, or slightly decreased f/r ratio respectively in the
tension, neutral, and compression modes of the upper link (Figure 7.21).
Increasing the rear lower link length caused a great decrease, moderate
decrease, and slight decrease in f/r load ratio with the rear upper link in

the tension, neutral, and compression modes respectively (Figure 7.22).

103

 

 

 

 

 

 

 

 

 

 

 

0.40
—'_ tension
—‘— neutral
compression
.0
fa 0.35
1:
an
.2
i
+3
5 0.30
cL‘"
0.25 I L I L I I
35 40 45 50 55 60 65
front upper link point Y-coordinate, cm
Figure 7.19 - Front axle load ratio vs front upper link point Y-coordinate
0.40
_9_ tension
—‘_ neutral
—'— compression
.2
43 i-
E 0.35
“U “Wow
3
i t t e ¢ ¢ ¢ ¢
‘5’ 0.30 - .____'_____________..___——.————-—-——'
ch
0.26 Al I I I
10 12 14 16 18

rear upper link point Y-coordinate, cm

Figure 7.20 - Front axle load ratio vs rear upper link point Y-coordinate

104

 

 

 

 

 

100

 

 

0.40
—“_ tension
—*—' neutral
—"'— compression
0
a 0.35 _ /
In
a:
a
'2 A“/.
i - v
a.)
8 0.30 - m
cf:
0.25 I J I I I
40 50 60 70 80 90
front lower link length, cm
Figure 7.21 - Front axle load ratio vs front lower link length
0.40
‘—""n_ tension
—°— neutral
—l— compression
0
'5‘ _3 .
'u
a
.2
i
E 0.30 - m
4':
0.25 I 1 I I I

 

 

60 70 8O 90 100 11 0

rear lower link length, cm

Figure 7.22 - Front axle load ratio vs rear lower link length

120

105

7 .32 WW

Only one of the implement dimensions, namely mast height, can be
readily changed by an operator, since each implement is designed by the
manufacturer to achieve its particular operating conditions. Also, the
range of adjustment in this parameter is limited by ASAE Standards.
Nevertheless it is interesting to simulate the effects of this parameter and
find that increasing the front implement mast height has a pattern of
greatly decreasing, not affecting, or greatly increasing f7r ratio respectively
with the upper link in the tension, neutral, or compression modes (Figure
7 .23). On the other hand, increasing the rear implement mast height has
the effects of moderately increasing, not affecting, or moderately decreasing
f/r load ratio respectively with the rear upper link in the tension, neutral, or

compression modes (Figure 7.24).

7.3.3 Was];

Finally, tractor ballasting has been frequently used in 4WD and FWA
as one way of achieving desired f/r dynamic load ratios. The following
simulations confirm the obvious expectation that adding front ballast
increases f/r dynamic load ratio (Figure 7.25), and adding rear ballast

decreases f/r ratio (Figure 7.26) regardless of upper link loading mode.

106

 

 

0.40
‘45— tension
—’— neutral
—'— compression
.2 "
g 0.35 - U
I-
a U
a
O n
l—
g of c c t t
*3
g 0.30 .-
e:
0.25 L L I I

 

 

 

50 60 70 80 90
front implement mast height, cm

Figure 7.23 - Front axle load ratio vs front implement mast height

100

 

 

 

 

 

0.40
+ tension
—‘_ neutral
'—"_ compression
.0
g 0.35 . M/
I-
1:
fl
.9.
o c c c c c 4'
“i
a
‘5
O 0.30 '-
d:
0.25 I L I I
40 50 60 70 80

rear implement mast height, cm

Figure 7.24 - Front axle load ratio vs rear implement mast height

90

front axle load ratio

front axle load ratio

107

 

0.40

0.35

 

0.30 —E— tension
—‘— neutral

 

—'— compression

0.25 , ‘ '
0 2 4

front wheel ballast, kN

Figure 7.25 - Front axle load ratio vs front wheel ballast

 

 

0.40
—a_ tension
_'°— neutral
—'_ compression
0.35 r-

 

0.30

 

 

0.25 ~ 1 ‘
0 2 4

rear wheel ballast, kN

Figure 7.26 - Front axle load ratio vs rear wheel ballast

108

7.3.4 ' z. H:0‘ .. 00:1 a- :.oo.:_ u . :‘g. o. h. ..

Attempts to use these simulations to achieve a particular desired f/r
load distribution must take into account such practical considerations as
the effects that adjustments in hitch configuration would have on the
orientation of the implements. In the case of the moldboard plow, altering
the hitch geometry could have negative effects on one or more of the three
orientation requirements for transport, entry, and normal operation of the
plow (see Constraints #3 and #4 in Section 3.3, also discussions in Section
4.1.3 and 4.1.4).

An example of such practical limitations is illustrated in Figure 7.27
(same simulation data as Figure 7.19). In this case the shaded area
indicates those values of front upper link point Y-coordinate which would
result in the plow having an upward angle while the plow were being
lowered into operating position. This would prevent normal entry of the
plow into the ground. Similar considerations would have to be applied to
the other parameters, and all of these limitations might be different for

different implements.

front axle load ratio

109

 

0.40 .
\\\ “—9— tension
—*— neutral

'—'— compression

0.35

.A _
\\\\‘-‘ '7 - ( V '

0.30

 

0.25 k I I I I

 

 

35 40 45 50 55 60 65
front upper link point Y-coordinate, cm

Figure 7.27 — Restriction on adjustment of front upper link point
Y—coordinate with moldboard plow

70

8. CONCLUSIONS

The following conclusions were drawn based on the field tests and

simulation results.

8.1 Wm

8.1.1.

8.1.2.

8.1.3.

8.1 .4.

Measurements of soil cone index by the standard technique,
especially if the values are averaged together for the whole test
area, may not be adequate for use in the type of field
experiments in this study. Equally important is the fact that
the presence of a front implement such as a plow or cultivator
presents a special case where the wheels on one side of the
tractor may run in a soil condition different from the
measured CI.

Measurements of slippage in only two of the 4 drive wheels
(with estimation of slip in the other two) are also less than
desirable for a rigorous analysis of tractor performance.
Despite the considerations in conclusions 8.1.1 and 8.1.2 of
present section, the relationships between slippage and pull
are reasonable in magnitude and curve shape as compared
with results of other published studies.

The relationships between TE and f/r dynamic load ratio on
loose and firm soils are also consistent with other studies.

Specifically, on loose soil there are some opportunities for

110

111

optimization (i.e. apparent optimum f/r ratio near 0.4/0.6), but
a nearly flat response on firm soil may limit the opportunity for

optimization in these conditions.

8.2 Simulations

8.2.1 .

8.2.2.

8.2.3.

8.2.4.

8.2.5.

8.2.6.

Adjustments of all front hitch dimensions, except the lower
link point Y-coordinate, had moderate to substantial effects on
f/r dynamic load ratio when the upper link was in either
tension or compression load, but little or no effects when there
was no load on the upper link.

Adjustments of rear hitch dimensions have little or no effect on
f/r dynamic load ratio, except rear lower link length.
Adjustment of front implement mast height has dramatic
effects on f/r dynamic load ratio. Adjustment of rear
implement mast height has moderate effects on F/R load ratio.
The known effects of adjusting front and/or rear ballast are
confirmed by these simulations. The f/r dynamic load ratio
changes proportionally to the change of ballast.

Some practical limitations in the range of adjustment in some
dimensions must be observed since these adjustments also
may change the orientation of the implements, and thus
interfere with various aspects of their operation. This must be
done on an implement by implement basis.

Overall, the simulations pinpoint several parameters such as
front lower link point X—coordinate, front upper link point X-

and Y- coordinates, front and rear lower link lengths, front

112

implement mast height, and front and rear wheel ballast
whose adjustment alone or in combination could be used to
achieve a desired f/r dynamic load ratio, thus the model has

good potential for practical application.

9. RECOMMENDATIONS

9.1 W

9.1.1 W
Variability in the value of CI in different areas of a given field could

first be established by the random sampling method. In those cases where
the standard deviation exceeds 10% in soils where penetration is relatively
uniform with depth, or 15% in soils with crusts or other distinct layers,
then, according to the sensitivity analysis of this parameter, one should
sample the specific area of each test, and use those local values of CI in the
analyses of data.

C O .
91,2.- '70.:0u- u'aqzo u'q;_q¢° quoz' :_:‘: .g' ‘ ‘u
C O
o: . p'op :, you un‘u‘ 9’0 ‘ o;:::_°'o ‘3' .0; I1.“

This task will not be easy because the only means of making such
measurements is after the tractor has stopped at the end of each run,
leaving a short length of furrow or tillage between the rearmost part of the
front implement and the front wheel. In the case of the plow used in these
studies such measurements would have been nearly impossible because
components of the plow extended back over this area obstructing the use of
the penetrometer. Assuming that some means were developed to achieve
this measurement, it would have the weakness of sampling only a small

portion of soil at the end of the run. Another alternative is to measure CI in

113

114

the furrow from the rear implement after each test and on the surface
before each test. This measurement would be an improvement over the

method used in these studies.

0 C ‘
9,.13I- Ioouu' u':_,¢:o ".:_: so) 1 g' 1; $31; o:,.::_H o

thsfmntJMhssls
This problem is similar to that of 9.1.2, since only a short length of

front tire track remains between the front and rear wheels at the end of the

run .

 

The ideal solution to both of the above problems would be a continual
measurement of soil properties in front of all of the wheels while the tractor
is in motion during the tests. At present there are no ASAE methods for
this purpose, and apparently no formal proposals to develop such
instrumentation. Perhaps this is because the value of such measurements
has only become more noticeable in the types of tests conducted in these
studies and other recent studies of 4WD and FWA tractors. Indeed, an
examination of many recent publications reveals variabilities in calculated
values of slip, pull, and/or TE which could be entirely accounted for by
variations in actual CI in the test fields.

Mechanical devices (e.g. some type of knife blade being pushed
through the soil in front of each wheel) are likely to be extremely
troublesome. Thus one might consider some form of acoustic or radar

reflectivity.

115

9.2 no . -. u-:_: '0‘; : . . y“ : ~sz uo -:, :_.; - .ow

The addition of wheel motion measurements on all driving wheels is
primarily a matter of installing additional sprockets, sensing devices,
signal processing channels, and data acquisition capability of the types
already in use. It is quite possible that wheel motion sensors on all wheels
would greatly minimize the need for more elaborate soil property
measurements, since slippage would not have to be estimated in
unmeasured wheels. This addition would be relatively easy, however in the
case of the present instrumentation system it would require at least one
more channel of signal processing electronics since none of the other
measurements could be deleted.

Addition of torquemeters (i.e. Wheatstone bridge type of strain gage)
to the rear axles would be highly desirable, but extremely difficult because

they are enclosed in housings and immersed in oil. The same

consideration applies to the rear driveshaflz.

 

The above improvements in measurement of soil properties and
instrumentation would make it possible to obtain rigorous analyses of field
performance, and thus determine the ideal load distributions for the
conditions and implements tested. The same data could also be used for
further validation and development of the model. If a better relationship
between soil properties, dynamic load, and slippage could be established by
these or other studies, then the model could be used to predict and optimize

tractor performance over a wide range of conditions.

APPENDICES

APPENDIX A

ASAE Standard Definitions

1) Ballast : Mass that can be added or removed for the purpose
of changing total load or load distribution. (ASAE Standard:
ASAE 8296.3)

2) Dynamic load : Total force normal to the reference plane of
the predisturbed supporting surface exerted by the traction or
transport device under operating conditions. This force may
result from ballast and/or applied mechanical forces. (ASAE
Standard: ASAE $296.3)

3) Hitch point : The articulated connection between a link and
the implement. For geometrical analysis, the hitch point is
established as the center of the articulated connection between a
link and the implement. (ASAE Standard: ASAE 8217.10)

4) Implement frame length : The distance between lower hitch
point and the farthest supporting point of the implement away
from the hitch point.

5) Implement height : The distance between lower hitch point
and the lowest point of implement while it is at working position.

6) Link point : The articulated connection between a link and
the tractor. For geometrical analysis, the link point is
established as the center of the articulated connection between a
link and the tractor. (ASAE Standard: ASAE $217.10)

7) Load transfer : The change in normal forces on the traction
and transport devices of the vehicle under operating conditions,
as compared to those for the static vehicle. (ASAE Standard:
ASAE 8296.3)

8) Mast height : The perpendicular distance between the upper
hitch point and common axis of the lower hitch points. (ASAE
Standard: ASAE S217.10)

9) Motion resistance : Force required in the direction of travel to
overcome the resistance from the supporting surface and the
internal resistance of the device. (ASAE Standard: ASAE $296.3)

116

117

10) Static load : Total force normal to the surface plane of the
predisturbed supporting surface exerted by the traction or

transport device while stationary with zero net traction and zero
input torque. (ASAE Standard: ASAE 8296.3)

11) Vehicle traction ratio : Ratio of the drawbar pull of the vehicle
to the gross vehicle load. (ASAE Standard: ASAE 8296.3)

12) Tractive efficiency : Ratio of output power to input power.
The output power is the product of net traction and forward
velocity of a traction device. The input power is the product of
input torque and angular velocity of the driving axle of a traction
device. (ASAE Standard: ASAE $296. 3)

13) Travel reduction : One minus travel ratio. Travel ratio is
defined as the ratio of distance traveled per revolution of the
traction device when producing output power to the rolling
circumference under the specified zero conditions. (ASAE

Standard: ASAE 8296.3)

14) Working depth : The distance between soil surface and the
lowest point of implement while it is at working position. The
irregularity of soil surface is ignored.

_
‘F—i

 

 

 

118

APPENDIX B

Simulation Program and Input Templates

This appendix lists the Pascal-like pseudo program of simulation
model developed in this dissertation along with three tables of input
parameters used by the simulation model. The pseudo program can be
easily translated into any high level programming language. The input
parameters are listed as three templates which can be used directly as
model input.

The in-line comments (e.g. (* Eq. 4.1 *), (* Fig. 4.1 *)) refer to the
implementation of that piece of code by the use of that particular equations
or figures in the dissertation.

 

119

B1. Esendsuzmgnamnfsimnlannnmodel

program Simulation:
include variable declaration file:
(* *)

procedure Initialization:

begin
GetTracData = false:
GetImplData = false:
GetWorkData = false:
TracDataChanged := false:
ImplDataChanged := false:
WorkDataChanged := false:
finished = false:

input data file path name prefix:
input parameters title:

end:
(* *)
procedure MainMenu (var option);
begin

option := 0:
set up main menu;

while ( option not in [1..5, 9] ) do
beep:
input option:
end of while;
end:
(* *)
procedure SaveTractorData;

begin

input file name:
save parameters to file:
TracDataChanged := false:

end:

(* *)

1%)

procedure TractorDataHandling:

(* *)

 

procedure TractorDataMenu (var option);
begin

option := 0:
set up option menu:

while ( option not in [1..4, 9] ) do
beep:
input option:

end of while:

end;

 

(* *)
procedure InputFromFile:
begin
input file name:
input data from file;

GetTracData := true:

end;

 

(* *)
procedure InputFromKeyboard:
begin
for loop := 1 to # of parameters do
write parameter title[loop]:

input parameter[loop]:
end of for:

 

GetTracData := true;
TracDAtaChanged := true:
end:
(* *)

procedure EditData:
begin
while (not quit) do
for loop := l to # of parameters do

write parameter title[loop]:
end of for:

121

input parameter#:
write parameter title[parameter#]:
write parameter[parameter#]:
input parameter[parameter#]: (* get new value *)
if (new parameter <> old parameter) then
TracDataChanged := true:
end of if
end of while:

end;

(* *)

 

begin (* of procedure TractorDataHandling *)
quit := flase:
while (not quit) do
TractorDataMenu (option);

case option of

1 InputFromFile;

2 : InputFromKeyBoard:
3 : EditData;

4 : SaveTractorData:

9 : quit := true:

end of case:
end of while:
end; (* of procedure TractorDataHandling *)
(* *)
procedure SaveImplementData:
begin
input file name:
save parameters to file;
ImplDataChanged := false:
end:
(* *)
procedure ImplementDataHandling:

(* *)

 

122
procedure ImplementDataMenu (var option);
begin

option := 0:
set up option menu:

while ( option not in [1..4, 9] ) do
beep:
input option:

end of while:

end:

 

 

(* __ __ _- ______ *)

procedure InputFromFile;
begin
input file name:
input data from file:
GetImplData := true:

end;

 

(* *)
procedure InputFromKeyboard;

begin

for loop := 1 to # of parameters do
write parameter title[loop]:
input parameter[loop]:

end of for:

GetImplData = true:
ImplDataChanged := true:
end:

 

(* *)
procedure EditData:
begin
while (not quit) do
for loop := 1 to # of parameters do
write parameter title[loop]:
end of for:

input parameter#:

write parameter title[parameter#]:
write parameter[parameter#]:

123

input parameter[parameter#]: (* get new value *)
if (new parameter <> old parameter) then
ImplDataChanged := true:
end of if:
end of while;

end:

 

(* *)
begin (* of procedure ImplementDataHandling *)
quit := flase:
while (not quit) do
ImplementDataMenu (option);

case option of

1 : InputFromFile:

2 : InputFromKeyBoard:
3 : EditData;

4 : SaveImplementData:
9 : quit := true:

end of case:
end of while:
end; (* of procedure ImplementDataHandling *)
(* *)
procedure SaveWorkingData:
begin
input file name;
save parameters to file:

WorkDataChanged := false:

end:

 

(* *)

procedure WorkingDataHandling:

 

(* *)
procedure WorkingDataMenu (var option);
begin

option := 0:
set up option menu;

 

124

while ( option not in [1..4, 9] ) do
beep:
input option:

end of while:

 

 

 

end:
(* *)
procedure InputFromFile:
begin
input file name:
input data from file;
GetWorkData := true:
end:
(* - *)
procedure InputFromKeyboard:
begin
for loop := 1 to # of parameters do
write parameter title[loop]:
input parameter[loop]:
end of for:
GetWorkData = true;
WorkDataChanged := true:
end:
(* *)
procedure EditData;
begin
while (not quit) do
for loop := 1 to # of parameters do

write parameter title[loop]:
end of for:

input parameter#:

write parameter title[parameter#]:
write parameter[parameter#]:
input parameter[parameter#]: (* get new value *)

if (new parameter <> old parameter) then
WOrkDataChanged := true:
end of if:

125
end of while:

end:

 

(* *)
begin (* of procedure WorkingDataHandling *)
quit := flase;
while (not quit) do
WorkingDataMenu (option);

case option of

 

l : InputFromFile:

2 : InputFromKeyBoard:
3 : EditData:

4 : SaveWorkingData:
9: qutz=tnm:

end of case:
end of while:
end; (* of procedure WorkingDataHandling *)
(* *)

procedure RearUpperLinkLength (var NewLength; WorkDepth);

 

begin
calculate effective rear lower link length; (* Fig. 4.4 *)
calculate rear alpha angle using WorkDepth: (* Eq. 4.1 *)
calculate rear beta angle; (* Eq. 4.2 *)
calculate distance of AB; (* Fig. 4.1 *)
calculate diagonal distance BD; (* Eq. 4.3 *)
calculate rear delta angle; (* Eq. 4.4 *)
calculate rear gamma angle: (* Eq. 4.6 *)
calculate NewLength; (* Eq. 4.5 *)
calculate rear theta angle; (* Eq. 4.8 *)

end; (* of procedure RearUpperLinkLength *)

(* *)
procedure FrontUpperLinkLength (var NewLength; WorkDepth);

begin
calculate effective front lower link length; (* Fig. 4.4 *)
calculate front alpha angle using WorkDepth; (* Eq. 4.9 *)
calculate front beta angle; (* Eq. 4.10 *)
calculate distance of EF; (* Fig. 4.5 *)

 

 

\B—J’J'

 

(*

calculate
calculate
calculate
calculate

calculate

end: (*

126

diagonal distance FH;
front delta angle:
front gamma angle:
NewLength;

front theta angle;

of procedure FrontUpperLinkLength *)

 

*)

procedure CalculateDynamicLoad (forces on hitches;
var wheels dynamic load):

(*

begin

calculate
calculate
calculate
calculate
calculate
calculate

end; (*

front axle dynamic load:

rear axle dynamic load;
effective tread width:

in-furrow rear wheel dynamic load;
on-surface rear wheel dynamic load:
front wheels dynamic load:

of procedure CalculateDynamicLoad *)

 

*)

procedure OptimizeGeometry:

(*

(‘k

 

begin

*)

procedure SimulationMenu (var option);

option := 0:
set up option menu:

while ( option not in [1..4, 9] ) do

beep:

input option:
end of while:

end:

 

function FrontPenetrateAngle (UpperLinkLength)

begin

*)

calculate
calculate
calculate
calculate
calculate
calculate

effective front lower link length;

front beta angle:
distance of EF;
diagonal distance FH:
front delta angle:

front alpha angle with WorkDepth=0.

(* Eq. 4.11 *)
(* Eq. 4.12 *)
(* Eq. 4.14 *)
(* Eq. 4.13 *)
(* Eq. 4.15 *)
(* Eq. 4.18 *)
(* Eq. 4.17 *)
(* Eq. 4.21 *)
(* Eq. 4.19 *)
(* Eq. 4.20 *)
: real:
(* Fig 4.4
(* Eq. 4.9
(* Eq. 4.10
(* Fig 4.5
(* Eq. 4.11
(* Eq. 4.12

 

127

calculate front gamma angle; (* Eq. 4.13 *)
calculate FrontCutAngle; (* Eq. 4.14 *)

end; (* of function FrontPenetrateAngle *)

 

(* Ik)
begin (* of procedure OptimizeGeometry *)

while (not quit) do (* main while loop *)

while (not GetTracData) do
TractorDataHandling:
end of while:

while (not GetImplData) do
ImplementDataHandling:
end of while:

while (not GetWorkData) do
WorkingConditionHandling:
end of while:

 

RearUpperLinkLength (RearUpperLength, WorkDepth);
FrontUpperLinkLength (FrontUpperLength, WorkDepth);

FrontCutAngle := FrontPenetrateAngle (FrontUpperLength);

if (FrontCutAngle >= 0) then
ErrorMessage ('Can not penetrate'):
else

CalculateDynamicLoad (forces on hitches, wheels dynamic load):

if (wheel dynamic load > permissible load) then
ErrorMessage ('Overloading the tires'):
else

output FrontUpperLength, RearUpperLength, FrontCutAngle,
wheel dynamic loads, dynamic load ratio:
end of if:
end of if:

while (option not in [4, 9]) do
SimulationMenu (option);

case option of
1 : TractorDataHandling:
2 : ImplementDataHandling:
3 : WorkingConditionHandling:
4 : :
9 : quit := true:

end of case:
end of while:

end of while: (* main while loop *)

end; (* of procedure OptimizeGeometry *)

128
(* *)

procedure VerifyFieldData:

(* *)

 

procedure CalculateGeometry:
begin
done := false:
UpperLimit := 100:
LowerLimit := l; I

RearUpperLinkLength (CurrentLength, (LowerLimit+UpperLimit)/2);

while (not done) do

 

if (abs(CurrentLength — RearUpperLength) > tolerance) then

if (CurrentLength > RearUpperLength) then
LowerLimit = (LowerLimit+UpperLimit)/2;
else
UpperLimit = (LowerLimit+UpperLimit)/2;
end of if

RearUpperLinkLength (CurrentLength,
(LowerLimit+UpperLimit)/2):
else
rearWorkDepth :
done := true;
end of if

(LowerLimit+UpperLimit) / 2;

done := false:
UpperLimit :8 100:
LowerLimit := 1;

FrontUpperLinkLength (CurrentLength, (LowerLimit+UpperLimit)/2);
while (not done) do
if (abs(CurrentLength - FrontUpperLength) > tolerance) then

if (CurrentLength > FrontUpperLength) then
LowerLimit = (LowerLimit+UpperLimit)/2;
else
UpperLimit = (LowerLimit+UpperLimit)/2;
end of if

FrontUpperLinkLength (CurrentLength,
(LowerLimit+UpperLimit)/2);
else
FrontWorkDepth := (LowerLimit+UpperLimit) / 2;
done := true:
end of if

end; (* of procedure CalculateGeometry *)

('k

(‘k

129

 

*)

var wheels pull, TE);

begin
calculate non—instrumented wheels slip:
calculate wheel numerics; (* Eq.
calculate wheels pull; (* Eq.
calculate TE: (* Eq.
end; (* of procedure EvaluatePerformance *)
*)

 

begin (* of procedure verifyFieldData *)

while (not GetTracData) do

TractorDataHandling:

end of while:

while (not GetImplData) do

ImplementDataHandling:

end of while:

while (not GetWorkData) do

WorkingConditionHandling:

end of while:

while (not done) do

input field data file name:
initialize accumulators to zeros:
CalculateGeometry:

for loop := l to # of data set do

input field data:

procedure EvaluatePerformance (wheels dynamic load, field data:

2.2 *)
4.24 *)
4,25 *)

CalculateDynamicLoad (field data, wheels dynamic load):

EvaluatePerformance (wheels dynamic load, field data,
wheels pull, TE);
accumulators := accumulators + new results:
end of for;
averages := accumulators / # of data set:

output averages:
input option whether done:

end of while:

(* of procedure VerifyFieldData *)

 

*)

130

procedure Finalization (finished):
begin

if (TracDataChanged) then
input option whether save data:
if (WantToSave) then
SaveTractorData:
end of if:
end of if;

if (ImplDataChanged) then
input option whether save data:
if (WantToSave) then
SaveImplementData:
end of if;
end of if:

if (WorkDataChanged) then
input option whether save data:
if (WantToSave) then
SaveWorkingData:
end of if:
end of if:

input whether quit program:
if (quit) then
finished := true;

 

else
finished := false:
end of if:
end; (* of procedure Finalization *)
(* *)

begin (* of main program *)
Initialization:
while (not finished) do
MainMenu (option);
case option of
: TractorDataHandling:
: ImplementDataHandling:
: WorkingConditionHandling:
: OptimizeGeometry:

: VerifyFieldData:
: Finalization (finished):

\DmIbOONI-J

end of case:
end of while;

end. (* of main program *)

131

B2. Modelinnuugmnlalss
Table B.l - Tractor parameters template

 

FORD 7610 2x3

X-coordinate of
Y-coordinate of
rear lower link
rear lower link
X-coordinate of
Y-coordinate of
x—coordinate of
Y-coordinate of

rear lower link point
rear lower link point
length (cm)

width (cm)

rear top link point
rear top link point
front lower link point
front lower link point

front lower link length (cm)

front lower link width (cm)
X-coordinate of front top link point
Y-coordinate of front top link point
the tractor wheel base (cm)

the tractor rear wheels tread (cm)
unloaded rear wheel radius (cm)
unloaded front wheel radius (cm)
rear axle load (Newton) =

front axle load (Newton) =

tractor total weight (Newton)

center of gravity from rear axle (cm)
rear wheel ballast (Newton)

front wheel ballast (Newton)

ballast in front of tractor (Newton)

distance from front ballast to front axle
front ballast height from front axle (cm)

Y—coordinate of center of gravity (cm)
z-coordinate of center of gravity (cm)

number gear

L01
HIl
L02
HIZ
L03
HI3
L04
HI4
L05
HIS
L06
HI6
L07
HI?
L08
HI8

11

OHHHHNNWNWDU‘IONCDKO

.780
.160
.102
.300
.543
.310
.807
.960
.331
.590
.289
.780
.569
.220
.080

.840
rear differential ratio
front differential ratio
rear final drive ratio
front final drive ratio
front drop box ratio

16

II II

23.
15.
.000
.000
.096

.200
.900
.600
.100
.700
.800
.200
.400
.300
.000
.900
.200
.600
.200
.700
.500
.000
.000
.000
.900
.000
.000
.000
.000
.000
.300
.000

790
820

 

 

132

Table B.2 - Implement parameters template

 

no of front bottom = 3

rear mast height = 68.0
rear hitch width = 89.5
rear frame angle phi = 0.0
rear implement height = 73.0
rear clear point = 49.0
rear cut point = 49.0
rear frame angle = 0.0
front mast height = 76.0
front hitch width = 89.0
front frame angle phi = 0.0
front implement height = 73.0
front clear point = 63.0
front cut point = 210.0
front frame angle = 0.0

 

Table B.3 - Working condition parameters template

 

left plowing

ground slope = 0.01
cone index = 45.0
rear roll radius(furrow) = 76.5
rear roll radius(land) = 79.5
rear wheel width = 46.7
rear work depth = 20.0
rear tire perm. load = 22100.0
front roll radius(furrow) = 56.6
front roll radius(land) = 57.2
front wheel width = 34.5
front work depth = 20.0
front tire perm. load = 13200.0

 

 

133

APPENDIX C

Front axle pivot force and power distribution to axles

Figures Cl and C2 show the forces acting on the tractor's front axle
pivot point. Each point in the figures represents the average value of each
test run. There were 500 data set recorded during each test run.

Figures C.3 and 0.4 illustrate the power distribution to the tractor's
front and rear axles. The power delivered to each wheel was calculated by
equations 4.25 and 4.26. The front axle power ratio was obtained by dividing
the sum of the power delivered to the front wheels by total power delivered to

four wheels.

front axle pivot force, kN

front axle pivot force, kN

134

 

 

 

 

 

 

 

 

 

30
o
o
20 003%0 :fi
0 o
00 0° 0
fl 0
00°
10 c
9 sandy
0 .L I I
0.1 0.2 0.3 0.4

front axle load ratio

0.5

Figure C.1 - Front axle pivot force vs front axle load ratio in sandy soil

 

 

 

 

 

 

 

 

 

 

30
A .5
20 A P‘—
A
A A i
A _
10
A silty-clay
o I 1 I A I
0.1 0.2 0.3 0.4

Figure C.2 - Front axle pivot force vs front axle load ratio in silty-clay soil

front axle load ratio

0.5

 

front axle power ratio

front axle power ratio

0.5

135

 

 

0.2

power = 0.204 + 0.482*lood R‘2 = 0.643

I

 

0

 

 

0.1

0.3

front axle load ratio

0.4

Figure C.3 - Front axle power ratio vs front axle load ratio in sandy soil

 

 

 

 

0.5
A
A A A
A
04 A
. ' A
A ‘ A
A
A
0.3 -
A silty-clay
0.2 ‘ l I
0.1 0.2 0.3 0.4

front axle load ratio

Figure 0.4 - Front axle power ratio vs front axle load ratio in silty-clay soil

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