Measuring soil properties to predict tractive performance of an agricultural drive tire

Pergamon

Journal of Terramechanics, Vol. 31, No. 4, pp. 215-225, 1994

Elsevier Science Ltd Copyright © 1994 ISTVS Printed in Great Britain. All rights reserved 0022-4898/94 $7.00+0.00

0022--4898(94)00012-3

MEASURING SOIL PROPERTIES TO PREDICT TRACTIVE PERFORMANCE OF AN AGRICULTURAL DRIVE TIRE SURI T H A N G A V A D I V E L U , * R. T A Y L O R , t S. CLARK~ and J. S L O C O M B E ~

Summary--The coefficient of traction for a 9.5-16 R-1 bias ply tire was measured and compared with predictions using equations developed by Janosi and Hanamoto [Proc. 1st Int. Conf. on Mechanics, p. 707-736 (1961)]; Wismer and Luth [J. Terramechanics 10, 49-61 (1973)] Gee-Clough et al. [J. Terramechanics 15, 81-84 (1978)] and Brixius [ASAE Paper No. 87-1622 (1987)]. For the soft soil condition, with a cone index of 120 kPa, Gee-Clough's equation predicted the coefficient of traction better, but predictions using the Brixius equation were better for soil with a cone index of 225 kPa. An experimental device was developed to simultaneously measure the horizontal and vertical stress-strain relationships of soil. The use of resultant stress from the experimental device data failed to show any improvement in coefficient of traction prediction over using the cone index. The resultant of the normal and shear stress from the experimental device data did not adequately represent the soil properties involved in terrain-vehicle mechanics. INTRODUCTION Theoretical analysis of soil-vehicle interaction is complicated because of the nonhomogeneous, anisotropic and inelastic nature of soil. Therefore, empirical methods are used widely to define the stress-strain relationship of soil for predicting off-road vehicle performance. Tractive performance predictions generally are based on stress-strain relationships of soil using soil cohesion (c), soil-soil friction angle (q~), and sinkage parameter (k) or the strength of soil usually measured as cone index (CI). Bekker [1] adopted the M o h r - C o u l o m b theory of soil failure to develop equations to predict the rolling resistance of and traction developed by pneumatic tires. Janosi and H a n a m o t o [2] developed tractive force prediction equations based on stress-strain relationship of soil for the case of uniform pressure distribution under the tractive device. Wismer and Luth [3] developed equations to predict tractive performance of pneumatic tires using CI and tire parameters. Brixius [4] developed tractive performance prediction equations for bias ply tires operating in cohesive-frictional soils also based on soil strength (CI) and tire parameters. Witting and Alcock [5] developed a single-wheel tester to establish traction conditions of topsoil by measuring the maximum transferable torque under known axle loads. They found that tractive performance prediction using soil parameters like bulk density and/or soil water content was more accurate than the standard Wismer and Luth [3] equations. For prediction equations to be effective, the terrain and traction device parameters

*Postdoctoral Research Associate; tAssistant Professor; ~tProfessor. Department of Biological and Agricultural Engineering, Kansas State University, Manhattan, KS 66506, U.S.A. 215

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need to be identified and measured accurately. Terrain-vehicle mechanics involves both horizontal and vertical stress-strain relationships of soil. The horizontal load of off-road vehicles is balanced by soil thrust, and vertical load is balanced indirectly by motion resistance [6]. Therefore, the soil properties used in traction prediction must represent both horizontal and vertical stress-strain relationships, so the loading conditions of the vehicle and of the device measuring soil properties should be as similar as possible. Several devices have been used to measure properties describing stress-strain behavior of soil for use in predicting tractive performance of off-road vehicles. Yong et al. [7] compared different devices, such as cone penetrometer, shear-vane, sinkage plate, shear plate and shear annulus, on the basis of the vehicle-terrain mechanics they simulate. They observed that slip involved in the vehicle-terrain mechanics, obtained from shear strength determinations, is not simulated by these devices. The cone penetrometer is still being used widely for the reasons of simplicity and ease of use, although the adequacy of cone index in representing all soil properties relevant to tractive performance prediction of off-road vehicles is questionable. Wittig and Alcock [5] concluded that cone index is an unreliable parameter to use in classifying the strength of topsoil because of the inherent variability of cone penetrometer measurements. Vehicle traction is dependent upon both the vertical and horizontal stress-strain relationships of soil, whereas cone index is largely a measure of the vertical stress-strain behavior of soil. A device to measure the horizontal and vertical stress-strain behavior of soil is therefore essential in predicting tractive performance of vehicles.

M A T E R I A L S AND M E T H O D S An experimental device (ED) was fabricated to simultaneously measure the vertical and horizontal stress-strain behavior of soil. It was designed to be simple, easy to use, and provide data that could be used in existing traction prediction equations. The ED is a modified cone penetrometer with two rectangular vanes welded 180° apart along the slant edge of the standard cone (Fig. 1). The vanes provide a twisting action that shears the soil in contact while the cone is pushed into the ground, thereby providing a measure of both vertical and horizontal stress-strain behaviors of soil. The ED was attached to a shear graph in place of the shear head for recording the normal and shear stress. A study was conducted to compare different traction prediction equations and determine if the predictions were improved by using the ED data. Experiments were conducted in a soil bin 9 m long and equipped with a soilprocessing carriage and an instrumented test carriage. Carriage movement was controlled by a winch mechanism driven by a hydraulic motor. The processing carriage had a roto-tiller, levelling blade, and compaction drum. The test carriage contained a hydraulic power unit to drive a pneumatic tire and was instrumented to record pull, input torque, and tire and test carriage speeds. Speed was measured by pulse counters mounted on the axles of the wheel and test carriage. Tests were conducted with a 9.5-16 R-1 bias ply tire carrying a 4 kN axle load on two different soil conditions of five slip levels. The specifications of the test tire are listed in Table 1. Soil was prepared for each test by tilling the top 0.19 m, levelling and passing the compaction drum twice to create the first soil condition

Measuring soil properties to predict tractive performance

217

Fig. 1. The modified ASAE standard cone mounted on a shear graph to simultaneously measure the normal and shear stress of soil. Table 1. Specifications of the 9.5 × 16 Firestone traction field and road tire used for testing Tire parameter

Value

Section width, b (m) Overall diameter, d (m) Deflection, 6 (m) Section height, h (m) Lug angle, (deg)

0.24 0.85 0.02 0.21 23

(CI = 120 kPa) and six times for the second soil condition (CI = 225 kPa). Wheel speed was held constant at approximately 1.34 m/s, while the test carriage speed was varied to create different slip levels. A n IBM PC-XT equipped with Omega Engineering, Inc. DAS-16 and ComputerBoards, Inc. CIO-CTR05 data acquisition boards was used to record data. Voltage signals for the torque and pull load cells were amplified with Calex MK-160 bridge conditioning cards and recorded at a frequency of 100 Hz by the DAS-16. The pulse signals from optical encoders for the

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tire and test carriage speeds were counted by the CIO-CTR05 for 2.5 s for each test. This arrangement yielded 250 readings for torque and pull for each test, which were averaged to obtain a single value. Tire and test carriage speeds were determined from the number of pulses counted during the 2.5 s interval. Soil properties were measured for each condition tested. Soil-cohesion (c) and soil-soil friction angle (~0) were determined from shear graph data. The sinkage parameters (kc and k~) were determined from plate sinkage data obtained by pressing 0.1 and 0.12 m square plates into the soil while measuring force with an Alphatron 9 kN capacity load cell and sinkage with a Celesco 0.75 m range position sensor. The CI for each soil condition was determined using an ASAE standard cone with the above mentioned load cell and position sensor for a depth of 0.15 m. The experimental device was used with a shear graph calibrated for simultaneous application of torque and normal force. The vertical and horizontal stress-strain relationships were recorded for each condition over depths of 0.125 and 0.075 m for the first and second soil conditions, respectively. Soil property measurements were replicated three times for each soil condition and slip level tested. The average values used for tractive performance predictions are shown in Table 2.

RESULTS AND DISCUSSION

Experimental data Wheel slip was determined from the carriage and test wheel forward speeds recorded using pulse counters. Wheel slip and coefficient of traction (CT--ratio of pull to axle load) are plotted for the two soil conditions in Figs 2 and 3. A non-linear model of the form given in equation (1) was fitted to the slip and coefficient of traction data using the Marquardt's method in the SAS NLIN procedure [8]. The estimate (Pexp = {aexp, bexp, Cexp}) and confidence interval of each parameter for the model fitting the experimental data are shown in Table 3. The fitted model showed good agreement with the experimental data for both soil conditions (Table 3). P - a ( 1 - e bs)- c, W

(1)

where P/W is the coefficient of traction; P is drawbar pull (kN); W is dynamic weight (kN); s is wheel slip (decimal); and a, b and c are model parameters. Table 2. Average

soil and mobility parameters calculated for each soil condition

Soil parameter Cone Index, CI (kPa) Soil cohesion, C (kPa) Soil-soil friction angle, ~ (deg) Sinkage parameter, kc Sinkage parameter, k¢ Sinkage exponent, n Resultant stress, R (kPa) Wheel numeric, Cn Mobility number, Bn Mobility number, M

measured/

Condition No. 1

Condition No. 2

120.0 6.3 18.3 2.1 4.7 1.4 170.5 8.5 8.7 1.7

225.0 14.5 23.8 1.9 9.2 1.8 325.0 17.2 17.6 3.1

Measuring soil properties to predict tractive performance •

0.4

Actual

Soil condition 1 • ......

T i r e 9.5-1 6

....... ••

0.3

C 0

•

219

A•

Fitted Brixius Wis. & Luth G e e Clough Janosi

0

.m

I0.2 Q ," 0 0

•

.7

j

0.1

0

. . . . . . )..

0.0

0

10

20

30

40

Wheel s l i p

Fig. 2. Regression curves of the experimental and predicted data for soil condition 1 (CI = 120 kPa). •

0.6

Soil condition 2 ...... ....

Tire 9,5-1 6

.......

0.5 .- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

C 0

Actual Fitted Brixius Wis. & Luth G e e Clough Janosi

0.4 I.-

"6

03

fJ

0.2

0,

/¸¸¸11//

0.0 0

5

10

15

20

25

30

Wheel slip

Fig. 3. Regression curves of the experimental and predicted data for soil condition 2 (CI = 225 kPa).

Tractive performance predictions The coefficient of traction of the test tire was predicted with standard soil parameter estimates using equations (2-5) developed by Janosi [3], Wismer and Luth [3], Gee-Clough [9] and Brixius [4], respectively. The same nonlinear model (1) was fitted to the predicted data and the estimates of the model parameters for each data set (Ppre = {apre, bpre, Cpre}) a r e shown in Table 3. Regression curves for the experimental and predicted data are plotted in Figs 4a-c and 5a-c. The prediction equations were evaluated based on two criteria: (1) the estimates of model parameters ({apre, bpre, Cpre}) falling within the 95%

S. Thangavadivelu et al.

220

Table 3. Estimate of model parameters for the experimental and predicted values of coefficient of traction for the test tire using C! and RES for the two soil conditions Data set

Estimates of model parameters

Re

a

b

c

0.44 [0.04, 0.84] 0.27 0.37 0.26 0.41 0.74 0.75 0.43

-27.73 [-44.96, -10.50] -11.61 -9.84 -13.96 -13.96 -1.88 -2.55 -3.38

0.16 [-0.25, 0.56] 0.23 0.16 0.00 0.00 0.24 0.18 0.00

0.87

- 11.86 [-14.23, -9.49] -8.77 -8.34 -28.65 -28.65 -3.03 -4.88 -2.84

0.03 [-0.03, 0.09] 0.12 0.09 0.00 0.00 0.14 0.11 -0.01

0.98

Soil condition No. 1 (CI = 120 kPa, R = 170 kPa) Experimental [*] Brixius (CI) Brixius (R) Gee Clough (CI) Gee Clough (R) Wismer and Luth (CI) Wismer and Luth (R) Janosi

Soil condition No. 2 (CI = 225 kPa, R = 325 kPa) Experimental [*] Brixius (CI) Brixius (R) Gee Clough (CI) Gee Clough (R) Wismer and Luth (CI) Wismer and Luth (R) Janosi

0.36 [0.31, 0.41] 0.47 0.59 0.50 0.59 0.79 0.75 0.46

Bold faced numbers are estimates of model parameters for predicted data falling within the confidence interval of the model parameters for the experimental data. [*]95% confidence interval. c o n f i d e n c e i n t e r v a l o f t h e c o r r e s p o n d i n g m o d e l p a r a m e t e r for the e x p e r i m e n t a l d a t a ({aexp, bexp, Cexp}) and (2) the closeness o f t h e r e g r e s s i o n curves for p r e d i c t e d a n d e x p e r i m e n t a l data.

H=(AC+ P

Wtan(q0)(1-

-0.75(1-

e°3C")-

1(1-e-J)), l

(2)

( 12 + 0.04)),

w

co (3) Cn --

Clbd W

C T = (CT)max(l -(Cr)max = 0.796

e-m), 0.92 M (4)

K(CT)ma x - 4.838 + 0 . 0 6 1 M , M

1

CI bd ~ [ 1 .~ l - - I W ~/---h\l + ( b / 2 d ) )

9

221

Measuring soil properties to predict tractive performance

P - 0.88(1 - e-0AB~)(1 -- e -75s) -W

Bn where

1 + 0.5_._____Ls

(5)

Tl\l + 3(b/d)!

b nominal width of tire; d overall unloaded tire diameter; h section height;

j iol/k; i0 degree of slip; k deformation modulus; 6 tire deflection; soil-soil friction angle; A contact area; Bn dimensionless mobility number; C soil cohesion; CI cone index; Cn wheel numeric; CT coefficient of traction; H traction force; K sinkage parameter; and M mobility number. The Gee-Clough equation (4) predicted coefficient of traction better than the others for the softer soil condition (CI = 120 kPa), with all three parameter estimates (apre, bpre, ¢pre} falling within the confidence interval of the parameter estimates of the experimental data {aexp, bexp, Cexp}. Estimates of the model parameters for the predicted data (Ppre) using the Brixius equation were within the confidence interval of the model parameters for the experimental data (Pe×p) but the regression curve was not close to the experimental data regression curve. Although the regression curves (a)

0.6

0.5

Soil condition 1 Tire 9.5-16

FI'I-I'ED MODEL Brlxlus (Cl) Brlxlus (RES)

Cl = 120 kPa RES = 170 kPa

__o

E "6

0.4

I-

0.3 O

0.2 O

¢3 0.1 //

0.O 0.0

....

0.1

......

•. . . . . . . . . . . . . . .

0.2 Wheel slip

Fig. 4.

Continued overleaf.

0.3

0.4

222

S. Thangavadivelu et al.

(b)

0.6

0.5 t,-

_o 3

Soil condition 1 Tire 9.5-16 CI = 120 kPa RES = 170 kPs

FITTED MODEL Wis. & Luth(CI) Wls. & Luth(RES)

0.4

I-

"6 0.3

5

O O

0.2

0.1

jjt

/

0.0 0.0

jjj

jJ

.//

,,/

/

/

/

0.1

0.2

0.3

0.4

Wheel slip

0.6

(c)

0.5 P o o

Soil condition 1 Tire 9.5-16 CI = 120 kPe RES = 170 kPa

FITTED MODEL Gee Clough(CI) Gee Clough(RES)

0.4

I-

"6 0.3

fJ

_o @

o O

J I ....................................

0.2

0.1

0.0 0.0

///.

0.1

0.2

0.3

0.4

Wheel slip

Fig. 4, (a) Regression curves of the experimental data and data predicted with the Brixius equation using cone index (CI) and resultant stress (RES) for soil condition 1 (CI = 120 kPa and RES = 170 kPa). (b) Regression curves of the experimental data and data predicted with the Wismer & Luth's equation using cone index (CI) and resultant stress (RES) for soil condition 1 (CI = 120 kPa and RES = 170 kPa). (c) Regression curves of the experimental data and data predicted with the Gee-Clough equation using cone index (CI) and resultant stress (RES) for soil condition 1 (CI = 120 kPa and RES = 170 kPa).

for the Wismer and Luth and Janosi equations did not resemble the experimental data curve, some of the model parameter estimates (Ppre) were within the confidence interval of the model parameters of the experimental data (Pexp), because of the wide confidence interval. The confidence interval of Pexp for the second soil condition (CI = 225 kPa) was narrower and very few model parameter estimates of Ppre fell within it. The model parameter estimate that fell in the confidence interval was the constant Cpre, which is of lesser importance than the other two (apre and bpre). The Brixius equation (5) was

Measuring soil properties to predict tractive performance

223

closer to the experimental data than others for this soil condition (CI--225 kPa), even though none of Ppre were within the confidence interval of Pexp.

Predictions using experimental device data The resultant (RES) of the average normal and shear stress recorded using the ED was calculated as an index of horizontal and vertical stress-strain behavior of soil and used in place of cone index in the prediction equations (3-5). The predicted data using the RES from the ED are plotted in Figures 4a-c and 5a-c. In the softer soil condition (CI--120 kPa), using RES improved predictions by the Brixius equation (5). Using RES with the Gee-Clough equation (4) overpredicted coefficient of traction for both soil conditions. In the case of the Wismer and Luth equation, no appreciable improvement in coefficient of traction prediction occurred from using (a)

0.6

0.5

Soil condition 2 Tire 9.5-16 Cl : 225 kPs RES = 325 kPe

......

e. mo

/ / J j/-

0.4

./

./

I-

"6

FITTED MODEL Brlxlus(CI) Brlxlus(RES)

/ J

0.3

....

• ...........

O mtJ

"6

0.2

o O

//

0.1 //

0.0 O.0

" / I

0.1

0.2

0.4

0.3

Wheel slip

(b)

0.6 0.5

Soil condition 2 Tire 9.5-16 CI = 225 kPs RES = 325 kPs

....

j f

0.4

.....'""

/ J

I-

"6

0.3

~

0.2

E

J

0.1 0.0 0.0

J

FITTED MODEL Wls. & Luth(Cl) WIs. & Luth(RES)

..... .~

-

//

///.... " 0.1

0.2 Wheel slip

Fig. 5. Continued overleaf.

0.3

014

224

S. Thangavadivelu et al.

(c)

0.6 j i

/

/

0.5

--ira

/

o

/

0.4

/

i--

/

"6

/ "

_Q _u q) o

. . . . . . . . .

/

C

.m

FITTED MODEL Gee Clough(Cl) Gee CIough(RES)

J

0.3

•

/ /

J

Soil condition 2 Tire 9.5-16 CI = 225 kPa RES = 325 kPa

/

/

0.2 I

0.1

0.0 0.0

/

/ 0.1

0.2

0.3

0.4

Wheel slip

Fig. 5. (a) Regression curves for experimental data and data predicted with the Brixius equation using cone index (CI) and resultant stress (RES for soil condition 2 (CI = 225 kPa and RES = 325 kPa). (b) Regression curves for experimental data and data predicted with the Wismer & Luth equation using cone index (CI) and resultant stress (RES) for soil condition 2 (CI = 225 kPa and RES = 325 kPa). (c) Regression curves for experimental data and data predicted with the Gee-Clough equation using cone index (CI) and resultant stress (RES) for soil condition 2 (CI = 225 kPa and RES = 325 kPa).

RES instead of CI. Because RES for each soil condition was higher than the corresponding CI, the predictions using RES gave higher coefficient of traction at all slip levels. The coefficient of traction predictions were also compared with the model fitted to the experimental data in terms of the mean absolute difference expressed as a percentage of the mean coefficient of traction for slip levels ranging from 5-25% at 1% increments. The criterion for the predictions to be acceptable was arbitrarily set to +5%. The results are summarized by soil condition for predictions made using CI and RES in Table 4. Using RES improved the predictions by the Wismer and Luth equation (3) for both the soil conditions. The predictions by the Brixius equation (5) showed improvement in the softer soil condition (CI = 120 kPa, RES = 170 kPa). Predictions by Gee-Clough's equation wer.e not improved by using RES over CI for

Table 4. Average absolute differences between observed and predicted values of coefficient of traction for the two soil conditions Prediction equation Brixius Gee-Clough Wismer & Luth Janosi

Parameter CI R CI R CI R C, ~

Soil condition No. 1 0.27 0.15 0.05 0.08 0.32 0.21 0.09

(105.7) (59.1) (18.3) (31.3) (121.9) (79.8) (35.8)

Soil condition No. 2 0.05 0.06 0.23 0.31 0.12 0.05 0.08

(19.7) (25.3) (89.8) (123.1) (47.1) (20.0) (32.7)

Values in parentheses are mean absolute differences expressed as percentages of the mean coefficients of traction (0.26 and 0.25 for soil conditions 1 and 2, respectively).

Measuring soil properties to predict tractive performance

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either soil condition. Although improvements were observed in some of the predictions, none of them fell in the acceptable range because the average coefficients of traction in both soil conditions were low (0.27 and 0.26). CONCLUSIONS For the softer soil condition (CI = 120 kPa), the coefficient of traction prediction with Gee-Clough's equation using CI gave better results and Brixius's equation with CI predicted well for the other soil condition (CI -- 225 kPa). Use of RES instead of CI to predict coefficient of traction failed to show any consistent improvement in the prediction equations. However, predictions by the Brixius equation in the softer soil condition (CI = 120 kPa, RES = 170 kPa) and predictions by the Wismer and Luth equation in both soil conditions were improved by using RES. Although the experimental device measures the horizontal and vertical stress-strain relationships, the resultant of the normal and shear stress does not adequately represent soil properties involved in terrain-vehicle mechanics to predict tractive performance. REFERENCES [1] M. G. Bekker, Theory o f Land Locomotion. The University of Michigan Press, Ann Arbor, MI (1956). [2] Z. Janosi and B. Hanamoto, The analytical determination of drawbar-pull as a function of slip for tracked vehicles in deformable soils. Proc. 1st Int. Conf. on Mechanics of Soil-Vehicle Systems, Torino, Italy, pp. 707-736 (1961). [3] R. D. Wismer and H. J. Luth, Off-road traction prediction for wheeled vehicles. J. Terramechanics 10, 49-61 (1973). [4] W. W. Brixius, Traction prediction equations for bias ply tires. ASAE Paper No. 87-1622. ASAE, St. Joseph, MI 49085 (1987). [5] V. Wittig and R. Alcock, An empirical method of predicting traction. ASAE Paper No. 90-1570. ASAE, St. Joseph, MI 49085 (1990)., [6] M. G. Bekker, Introduction to Terrain-Vehicle Systems. The University of Michigan Press, Ann Arbor, MI (1969). [7] R. N. Yong, A. F. Youssef and E. A. Fattah, Vane-cone measurements for assessment of tractive performance in wheel-soil interaction. Proc. 5th International Society of Terrain Vehicle Systems, Detroit 3:769-788 (1975). [8] SAS Institute Inc., SAS User's Guide: Statistics, Version 5 Edition. Cary, NC: SAS Institute Inc. (1985). [9] D. Gee-Clough, M. McAllister, G. Pearson and D. W. Evernden, The empirical prediction of tractor-implement field performance. J. Terramechanics 15, 81-84 (1978).