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7/28/2019 An Empirical Model for Tractive Performance of Rubber-Tracks
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Journal of Terramechanics JT05-010
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An Empirical Model for Tractive Performance of Rubber-tracksin Agricultural Soils
Robert Grisso, J ohn Perumpral and Frank ZozProfessor, William Cross Jr. Professor and Head Emeritus, Biological Systems Engineering,
Virginia Tech, Blacksburg, VA and Retired Engineer, John Deere Product Engineering Center,Waterloo, IA, USA
Corresponding Author: Dr. Robert Grisso, Biological Systems Engineering, 200 Seitz Hall(0303), Virginia Tech, Blacksburg, VA 24061-0303, 540-231-6538, FAX: 540-231-3199,[email protected]
Abstract: Mathematical models capable of describing the interaction between the traction
devices and soils have been effective in predicting the performance of off-road vehicles. Such a
model capable of predicting the performance of bias-ply tires in agricultural soils was first
developed by Brixius [1]. When the soil and vehicle parameters are known, this model uses an
iterative procedure to predict the tractive performance of a vehicle including pull, tractive
efficiency, and motion resistance. Al-Hamad et al. [2] modified the Brixius equations to predict
the performance of radial tires. Zoz and Grisso [3] have demonstrated that the use of spreadsheet
templates is more efficient than the original iterative procedure used to predict the performance
of 2WD and 4WD/MFWD tractors. As tractors equipped with rubber-tracks are becoming
popular, it is important that we have the capability to predict the performance for off-road
vehicles equipped with rubber-tracks during agricultural operations. This paper discusses the
development of an empirical model to accomplish this goal and its validity by comparing the
predicted results with published experimental results.
Keywords: Rubber-tracks, Traction Mechanics; Traction Prediction, Traction Model
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INTRODUCTION
Through out the world, farm tractors are used extensively to carry out different agricultural
operations. During the last five decades tractors used in agricultural operations have undergone
many changes. Selected examples of these changes include increased horsepower ratings, tractor
configuration (2WD and 4WD/ MFWD), and use of different types of tractive devices such as
(bias-ply tires to radial tires to rubber-tracks). Production capabilities of these tractors depend
heavily on tractor configuration, type of tractive devices used and terrain conditions. Ability to
predict and optimize the performance of these tractors during field operations has been of great
interest to scientists, manufacturers, and users.
In an effort to meet this need, Zoz [4] developed a set of graphs based on field tests
conducted in three types of soils: firm, tilled and soft or sandy, and on concrete with 2WD
tractors. He demonstrated that the set of graphs developed could be used to predict the drawbar
pull, travel speed, drawbar horsepower and travel reduction of 2WD tractors under different soil
conditions.
Wismer and Luth [5] studied the single wheel behavior in an indoor soil-bin facility. Using
dimensional analysis and the results of carefully planned tests, they developed equations to
predict the pull and tractive efficiency of tractors under different slip when certain conditions are
satisfied.
Similar sets of equations were developed by Zoz and Brixius [6] to predict the performance
of tractors on concrete. Nebraska tractor test results were used to develop these relationships.
Based on these equations, they have also developed a computer program to predict the vehicle
performance on concrete.
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In 1987, Brixius revised the relationships originally developed by Wisner and Luth [5].
Using the data from approximately 2,500 field tests involving 121 soil-tire combinations and
improved curve fitting techniques, Brixius [1] came up with a revised set of traction equations.
In addition to providing better predictions, these equations developed for bias-ply tires, extended
the range of applications. Al-Hamad et al. [2] modified the relationships developed by Brixius to
predict the performance of vehicle equipped with radial tires.
A review of literature has revealed that a great deal of experimental studies have been
conducted to assess the tractive performance of rubber-tracks in different soils and to compare it
with the performance of other types of tractive devices ([8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18,
19, 20, 21, 22, 23, and 24]). However, to our knowledge, only limited studies have dealt with the
development of mathematical models to predict the performance of rubber tracks in agricultural
soils. Upadyaya et al. [8] and Zoz [9] have tested rubber-tracks and developed regression
equations to predict net-traction, motion resistance, and tractive efficiency as a function of travel
reduction or slip. They used regression analysis to minimize data scatter and developed useful
relationships for specific test conditions. The limitation of these relationships, however, is that
they may be useful only for the field and vehicle conditions that existed during the collection of
experimental data. Therefore, the overall objective of this study was to develop an empirical
model specifically to predict the tractive performance of rubber-tracks in a variety of agricultural
soils and to establish its validity by comparing the predicted results with the experimental.
Rubber-Track Mechanics
In many respects, the mechanics of the rubber-tracks and wheel systems are very similar, and
a brief discussion of mechanics of rubber-tracks is included in this section. A more detailed
review of the same is available in Zoz and Grisso [3]. Figure 1 shows the forces on a rubber-
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tracks system. The torque input (T) to the axle develops a gross thrust (GT). Part of the gross
thrust is used to overcome the motion resistance (MR). The remainder is the net traction (NT) or
pull available for useful work.
Though there are similarities between tires and rubber-tracks, the dynamic load distribution
on rubber-tracks is significantly different. For example, the location of the dynamic load
resultant (eh) depends on the static weight distribution, the design of the suspension system
supporting the bogie wheels, and the vehicle weight transfer characteristics [7].
To maximize the tractive performance and to minimize the soil disturbance, ideally the
pressure distribution on a rubber-track should be uniform and, the dynamic weight distribution in
the front and rear should be equal. The dynamic weight distribution on rubber-tracks depends on
factors such as static weight, tractor dimensions, location of center of gravity, angle and the
magnitude of pull. Unlike in the case of tires, both the magnitude and uniformity in dynamic load
distribution are important during the testing of rubber-track systems.
Traction Equations for Rubber Tracks
Since our goal was to develop a traction model with the capability to predict the rubber-track
performance in a variety of agricultural soils and for different track systems, we decided to
modify the following original equations developed for tires by Brixius[1]. Brixius expressed
GTR (Gross Traction Ratio) and MRR (Motion Resistance Ratio) as a function of mobility
number (Bn) and wheel slip (s). He determined the dimensionless numbers in the equations
using a curve-fitting technique and the following are the generalized equations he developed:
( )( )
+
+
=
db
2K1
h
1K1
W
dbCI
nB (1)
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4C
s3
Ce1n
B2
Ce1
1C
Wr
TGTR +
=
= (2)
nB
s6
C
4C
nB
5C
W
MMRR
++== (3)
MRRGTRW
NTNTR == (4)
Where,Bn Mobility numbers CI Cone Indexb unloaded tire section width d unloaded tire diameterr tire rolling radius tire deflectionh tire section height W Dynamic load on the tractive devicess Wheel slip M motion resistanceNT Net traction or pull NTR Net traction ratio
T Axle Torque
Equations 1-3 include six coefficients (C1-C6) and two tire constants (K1 & K2). These
constants and coefficients may change depending on the type of tractive devices. For bias-ply
tires, values of C1, C2, C3, C4, C5, C6, K1, and K2 are 0.88, 0.1, 7.5, 0.04, 1.00, 0.5, 5 and 3,
respectively [1].
Zoz [25] created a Lotus 1-2-3template for Brixius equations. This template helped the
users to predict the performance of tractors or different configurations equipped with bias-ply or
radial tires in different agricultural soils.
As radial tires became popular, there was interest in models capable of predicting
performance of tractors equipped with radial tires. Al-Hamed et al. [2] modified the Brixius
equations to meet this need. Using experimental data and curve fitting techniques, a new set of
coefficients C1 thru C6 and K1 & K2 to represent the radial tires was generated. They are 0.88,
0.08, 9.5, 0.032, 0.90, 0.5, 5 and 3, respectively.
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When spreadsheet use, became more common, Zoz and Grisso [3] employed the spreadsheet
for predicting the tractive performance of tractors. This spreadsheet has the capability to handle
tractor configuration, bias-ply, radial tires, and different agricultural soil conditions.
Recognizing the advantages of pneumatic tires and tracks, more and more farm tractors are
now being equipped with rubber-tracks. Even though field studies have been conducted to
compare the performance of rubber-tracks and MFWD tractors in different soils [11 and 12], to
date very little has been done to develop a mathematical model to predict the tractive
performance of rubber-tracks.
In order to develop a generalized model for rubber-tracks, first we used a trial and error
procedure to determine the values of the coefficients (C1 C6) and constants (K1 and K2) for
rubber-tracks. Using the test data collected with rubber-tracks in different soils, we determined
the coefficients and constants that provided the best fit and developed the following
relationships:
a) Gross-traction-slip,
b) Motion resistance-slip, and
c)Tractive efficiency-slip
For comparison purposes, the values of the constants and coefficients for bias-ply tires, radial
tires, and rubber-tracks are included in Table 1.
The following are the modified relationships for predicting the tractive performance of
rubber-tracks:
+
=
TL
TW61
5
CI/0.698-e-1W
TLTWCI
nB (5)
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( )DWI0.03s17e1n
B0.025e11.10GTR +
= (6)
( ) ( )n
B
s0.5
DWI
0.03
DWI0.7
n
B
1.75MRR
++
= (7)
( )sGTR
NTRTE
= 1 (8)
Where, TW and TL are track width and track length respectively.
Since the dynamic weight ratio (DWR), the ratio between dynamic loads on the rear and
front, play a significant role in the overall performance of rubber tracks, it is necessary to express
the coefficients C4 and C5 in terms of dynamic weight index, DWI, and,
( )( )
+
=
1DWR
1DWR0.7ABS1DWI (9)
The tractive efficiency is its maximum when the DWI reaches it maximum value of one.
DWI is maximum when the weight distribution is equal in the front and the rear (DWR =1).
The values for C4 and C5 shown in table 1 are assuming equal weight distribution in the front and
rear.
Validation of the Model
The validity of the model developed was examined by comparing the predicted and
experimental results. Net Traction Ratio (NTR), and tractive efficiency (TE)-slip relationships
were developed for 44 cases based on field tests [9, 13, 14, and 15] conducted in sandy loam, silt
loam, clay and clay loam soils under tilled and untilled conditions and in subsoiled sandy loam
with four different track widths (406, 457, 635, and 813 mm) and compared against predicted. In
order to assess the closeness between the two, the Pearson Correlation Coefficients and the
Average absolute differences at 30 different track slips in the range of 1-30% were determined
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and the average for each of the 44 cases considered is presented in table 2. High correlation
coefficient and low absolute difference values indicate good agreement between the predicted
and experimental results except in clay soils.
In order to further illustrate the agreement between the predicted and experimental results,
the NTR and TE were plotted as a function of track slip for four different cases (Fig. 2). Curves
for two different track widths 813 mm (case 44), and 406 mm (case 40) are shown in Fig. 2a.
As expected wider track widths provided better performance in terms of net traction developed
and tractive efficiency. Even though case 44 provided high correlation coefficient and low
absolute difference values for both NTR and TE, the model seems to under predict the NTR at
higher track slips.
Figure 2b compares the performance of 406 mm rubber-track in untilled (case 9) and tilled
(case 5) sandy loam. In general, there is good agreement between the predicted and experimental
results. As expected the track performance in untilled soil with higher CI is slightly better than in
tilled soil with lower CI value. The maximum tractive efficiencies (TEmax) in both cases
occurred at slips between 6-7 percent. The predicted TEmax values are 0.831 and 0.815 for
untilled and tilled soils, respectively.
To further illustrate the validity of the model, we determined the maximum tractive
efficiencies from predicted and experimental results and the corresponding net traction and track
slip values at TEmax and plotted these ratios against each other as shown in Fig. 3 for each of the
44 cases in Table 2. The fact that most points for all three ratios clustered around 1:1 line, once
again illustrates very good agreement between predicted and experimental results.
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Model Application
The model developed can be used effectively for a number of different applications. Figure 4
is included to demonstrate one such use. The horizontal and vertical axes of this figure represent
Net Traction Ratio and traction performance ratios such as TE and track slip, respectively. Plots
include predicted TE, and slip curves for different mobility numbers. For a given mobility
number (Bn), the figure provides the information on the maximum TE possible and the
corresponding Net Traction ratio and track slips at which the vehicle has to operate to obtain
these ratios. For example, for Bn=40, to attain a maximum TE and a Net Traction ratio of 0.43
the vehicle must operate at a track slip of approximately 7.1%. In the same soil (which provided
a Bn value of 40), if higher TE and NTR are desired, one could select wider and or longer track
to provide a higher Bn number. This model together with the spreadsheet [3] will provide the
user the flexibility to determine the influence of different parameters on Bn values and develop
similar performance curves quickly for different Bn values. This model can also be used
effectively to compare the performance of vehicle with rubber-tracks or tires and for conducting
parametric studies as illustrated in Zoz and Grisso [3].
Conclusion
An empirical model to predict the tractive performance of vehicles equipped with rubber-
tracks has been developed. Comparison of predicted and experimental results shows that the
model developed is effective in predicting the performance of rubber-tracks during agricultural
operations.
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References
[1] Brixius, WW. Traction prediction equations for bias-ply tires. ASAE Paper No. 871622. St. Joseph,MI: ASAE, 1987.
[2] Al-Hamad, SA, Grisso RD, Zoz FM, Von Bargen K. Tractor performance spreadsheet for radial tires.Computers and Electronics in Agric, 1994:10(1):45-62.
[3] Zoz, FM, Grisso RD. Traction and Tractor Performance. ASAE Distinguished Lecture Series #27. St.Joseph, MI: ASAE, 2003.
[4] Zoz, FM. Predicting tractor field performance. Trans. ASAE, 1972:15:249-255.
[5] Wismer, RD, Luth HJ . Off-road traction prediction of wheeled vehicles. ASAE Paper No. 72619. St.Joseph, MI: ASAE, 1972.
[6] Zoz, FM, Brixius WW. Traction prediction for agricultural tires on concrete. ASAE Paper 79-1046,1979.
[7] Corcoran, PT, Gove DS. Understanding the mechanics of track traction. In Proc. Int'l Conference onSoil Dynamics, 4:664-678, 17-19 June. Auburn, AL: Auburn University, Office of ContinuingEducation, 1985.
[8] Upadhyaya, SK, Chancellor WJ , Wulfsohn D, Glancey JL. Sources of variability in traction data.J.Terramechanics, 1988:25(4):249-272.
[9] Zoz, FM. Rubber and tire tractive performance. SAE Technical Paper Series 972731. Warrendale,PA: SAE, 1997.
[10] Culshaw, D. Rubber tracks for traction.J. Terramechanics, 1988:25(1): 69-80.
[11] Shell, LR, Zoz FM, Turner RL. Field performance of rubber rubber and MFWD tractors in Texassoils. In Rubber and Tire Traction in Agricultural Vehicles, 65-73. SAE SP-1291. Warrendale, PA:SAE, 1997.
[12] Turner, RJ, Shell LR, Zoz FM. Field performance of rubber rubber and MFWD tractors in southernAlberta soils. In Rubber and Tire Traction in Agricultural Vehicles, 75-85. SAE SP-1291.Warrendale, PA: SAE, 1997.
[13] Bashford, LL, Kocher MF. Rubbers vs tires, rubbers vs rubbers, tires vs tires. Applied Engng in Ag,1999:15(3):175-181.
[14] Esch, JH, Bashford LL, Von Bargen K, Ekstrom RE. Tractive performance comparisons between arubber rubber track and four-wheel-drive tractor. Trans. ASAE, 1990:33(4):1109-1115.
[15] Upadhyaya, SK, Rosa UA, Josiah MN, Koller M. Effects of rubber width and grouser wear on thetractive characteristics of rubber-tracked vehicles. Trans. ASAE, 2001:17(3):267-271.
[16] Okello, JA, Dwyer, M.J , Cottrell, FB. The tractive performance of rubber tracks and a tractor drivingwheel tyre as influenced by design parameters.J. agric. Engng Res. 1994:59(1):33-43.
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[17] Okello, JA, M Watany, DA Crolla. A theoretical and experimental investigation of rubber trackperformance models.J. agric. Engng Res. 1998:69(1):15-24.
[18] Okello, JA. Prediction and experimental validation of the field tractive performance of a rubbertrack. J. agric. Engng Res. 194:59(3):163-171.
[19] Marsili, A, Servadio, P, Pagliai, M, Vignozzi, N. Changes of some physical properties of a clay soilfollowing passage of rubber- and metal-tracked tractors. Soil and Tillage Research, 1998:49(2):185-199.
[20] Blunden, BG, McBride, RA, Daniel, H., Blackwell, PS. Compaction of an earthy sand by rubbertracked and tyred vehicles.Australian Journal of Soil Research 1994:32:1095-1108.
[21] Dwyer, MJ; Okello, JA; Scarlett, AJ. Theoretical and experimental investigation of rubber tracks foragriculture.J. Terramechanics, 1993:30(4):285-298.
[22] Ma ZD, NC Perkins. Modeling of track-wheel-terrain interaction for dynamic simulation of trackedvehicle systems. Proceedings of the 1999 ASME Design Engineering Technical Conferences
September 12-15, 1999, Paper DETC99/VIB-8200, Las Vegas, Nevada
[23] Rahman, A, Yahya, Mohd. Zohadie, Wan Ishak and Desa Ahmad. Design parameters optimizationsimulation of a prototype segmented rubber track vehicle for Sepang peat in Malaysia.AmericanJournal of Applied Sciences 2005:2(3): 655-671.
[24] Sandu, C, Freeman, JS. Connectivity algorithm for an extended rubber-band track model.HeavyVehicle Systems, A Series of the Int. J. of Vehicle Design, 2002:9(4):334355.
[25] Zoz, FM. Predicting tractor field performance (updated). ASAE Paper No. 871623. St. J oseph, MI:ASAE, 1987.
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Captions:
Table 1. Comparison of constants and coefficients in the generalized traction model for bias-plytires, radial tires, and rubber-tracks.
Table 2. Comparison of predicted and experimental results from 44 cases with a range of soil and trackwidth conditions.
Figure 1. Rubber-tracks drive nomenclature and mechanics.
Figure 2. Comparison of predicted (lines) and experimental (symbols) Net Traction Ratio and TE Sliprelationships. (a) Effect of track width on track performance in wet untilled loam soil (Solid &Diamonds - 813 mm ; Dash & Square - 457 mm.) (b) Effect of soil condition on theperformance 406 mm rubber track (Solid & Diamond - untilled soil with CI =1.31 MPa; Dash& Square - tilled soil with CI =1.10 MPa)
Figure 3. Predicted and experimental performance ratios plotted against each other.
Figure 4. Tractive Efficiency and Slip curves for three Mobility Numbers as a function of Net TractionRatio.
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Table 1. Comparison of constants and coefficients in the generalized traction model for bias-plytires, radial tires, and rubber-tracks.
Coefficients &Constants
Bias-Ply TiesBrixius [1]
Radial TiresAl-Hamad et al. [2]
Rubber-tracks
K1 5 5 5
K2 3 3 6C1 0.88 0.88 1.10C2 0.10 0.08 0.025C3 7.5 7.0 17.0C4 0.04 0.03 0.03
1C5 1.0 1.20 1.75
1C6 0.5 0.5 0.5
1DWR is assumed to be one.
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Table 2. Comparison of predicted and experimental results from 44 cases with a range of soil and trackwidth conditions.
Case Bn TW TL CI
mm mm MPa TE NTR TE NTR
1 Sandy Loam Subsoi led 46.3 406 2261 1.00 0.997346 0.999905 0.0472663 0.02014116
2 Sandy Loam Subsoi led 56.1 635 2261 1.00 0.996561 0 .99798 0 .0282443 0.04510789
3 Sandy Loam Subsoi led 61.0 813 2261 1.00 0.994104 0.999924 0.0285734 0.02813827
4 Sandy Loam Subsoi led 46.3 406 2261 1.00 0.997324 0.997768 0.0335123 0.04185892
5 San dy Lo am Till ed 49.0 406 2261 1.10 0.998363 0.996981 0.0129518 0.03853785
6 San dy Lo am Till ed 59.3 635 2261 1.10 0.950108 0.980163 0.0113751 0.06809252
7 San dy Lo am Till ed 64.6 813 2261 1.10 0.999352 0.999738 0.0104614 0.03490425
8 San dy Lo am Till ed 49.0 406 2261 1.10 0 .975066 0.99996 0.009508 0.04693027
9 Sandy Loam Un til led 54.7 406 2261 1.31 0.990594 0.996663 0.0063653 0.02009918
10 San dy Lo am Un til led 66.1 635 2261 1.31 0.978403 0.9994 0.0097118 0.01749651
11 Sandy Loam Un til led 72.0 813 2261 1.31 0.994029 0.999663 0.0093409 0.01409025
12 Sandy Loam Un til led 54.7 406 2261 1.31 0.998466 0.996467 0.0094774 0.03528276
13 Silty L oam Till ed 35.9 457 2261 0.34 0.951008 0.942627 0.0218614 0.16603619
14 Silty L oam Till ed 36.6 635 2261 0.45 0.78922 0.991682 0.0300104 0.15334806
15 Silty L oam Till ed 35.5 635 2261 0.40 0.913543 0.925394 0.0758524 0.08257325
16 Silty L oam Till ed 44.1 813 2261 0.34 0.682614 0.991732 0.0367875 0.07466717
17 Si lt y Loam Un til led 37.5 457 2261 0.41 0.945927 0.947026 0.0316202 0.1753590618 Silty L oam Un til led 36.1 635 2261 0.43 0.905658 0.95606 0.0223477 0.13643306
19 Si lt y Loam Un til led 39.4 635 2261 0.57 0.872817 0.985759 0.0372502 0.02778831
20 Si lt y Loam Un til led 46.2 813 2261 0.41 0.958382 0.973264 0.0101703 0.09209565
21 Clay Tilled 53.7 457 2261 1.01 0.820267 0.792466 0.0151746 0.15879987
22 Clay Tilled 39.1 457 2261 0.48 0.60586 0.754862 0.0277168 0.0991268
23 Clay Tilled 51.1 635 2261 0.69 0.797113 0.85587 0.0307369 0.12043289
24 Clay Tilled 44.2 635 2261 0.46 0.828185 0.939957 0.0296629 0.05800577
25 Clay Tilled 68.2 813 2261 1.04 0.936452 0.853057 0.0190983 0.197039
26 Clay Tilled 42.9 813 2261 0.28 0.726106 0.811423 0.0393161 0.07126382
27 Clay Untilled 54.5 457 2261 1.03 0.905086 0.996594 0.0263013 0.03134426
28 Clay Untilled 41.5 457 2261 0.57 0.672038 0.84052 0.0450066 0.11782215
29 Clay Untilled 62.4 635 2261 1.03 0.901489 0.914425 0.0124913 0.11090144
30 Clay Untilled 52.0 635 2261 0.72 0.850327 0.926415 0.0208519 0.06013871
31 Clay Untilled 67.9 813 2261 1.03 0.967229 0.995113 0.0069084 0.09847739
32 Clay Untilled 55.2 813 2261 0.68 0.917268 0.946129 0.0092776 0.05634723
33 Loam Tilled 44.7 457 2261 0.69 0.740461 0.832527 0.0262387 0.07627296
34 Loam Tilled 43.5 457 2261 0.65 0.854858 0.981217 0.0384508 0.06026457
35 Loam Tilled 57.5 635 2261 0.89 0.915002 0.923621 0.010294 0.11262731
36 Loam Tilled 51.1 635 2261 0.69 0.785959 0.758413 0.0169448 0.08446186
37 Loam Tilled 51.3 813 2261 0.56 0.881195 0.930607 0.0165314 0.07695967
38 Loam Tilled 57.5 813 2261 0.74 0.896175 0.905043 0.0106538 0.07261524
39 Loam Untilled 54.5 457 2261 1.03 0.923889 0.997448 0.0232292 0.02364217
40 Loam Untilled 48.7 457 2261 0.83 0.980841 0.999865 0.0255197 0.02022895
41 Loam Untilled 62.4 635 2261 1.03 0.94936 0.988319 0.0088979 0.05442887
42 Loam Untilled 60.3 635 2261 0.97 0.9512 0.99077 0.0095515 0.03012802
43 Loam Untilled 67.9 813 2261 1.03 0.926902 0.981142 0.0176778 0.09050577
44 Loam Untilled 73.1 813 2261 1.17 0.994844 0.998042 0.0068254 0.05062752
Brixius parameters
Soil Conditions
Pearson
Correlation
Average Absolu te
Difference
Experimental cases [9, 13, 14, and 15].
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MR
slrrr
NT T
W1
Va
Wd
GT
W2 W3 W4
W5
Ground LineDh
rt
Vt =Velocity, theoreticalVa =Velocity, actualT =Axle torqueGT =Gross traction (theoretical pull)NT =Net traction (actual pull)
MR =Motion resistance
W =Weight, staticWd =Weight, dynamicslr =Loaded radius, staticrr =Rolling radiusrt =Torque radius
Vt
Va
T
GT
NT
MR
W
Wd
slr
rr
rt
eh
Figure 1. Rubber-tracks drive nomenclature and mechanics.
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(a) Effect of track width on track performance in wet untilled loam soil (Solid & Diamonds - 813
mm ; Dash & Square - 457 mm.)
(b)Effect of soil condition on the performance 406 mm rubber-track (Solid & Diamond - untilledsoil with CI =1.31 MPa; Dash & Square - tilled soil with CI =1.10 MPa)
Figure 2. Comparison of predicted (lines) and experimental (symbols) Net Traction Ratio and TE Sliprelationships.
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Figure 3. Predicted and experimental performance ratios plotted against each other.
Figure 4. Tractive Efficiency and Slip curves for three Mobility Numbers as a function of Net TractionRatio.