Tractive characteristics of radial ply and bias ply tyres in a California soil

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1 See discussions, stats, and author profiles for this publication at: Tractive characteristics of radial ply and bias ply tyres in a California soil Article in Journal of Terramechanics December 1988 Impact Factor: 1.42 DOI: / (88) CITATIONS 20 READS authors, including: Dvoralai Wulfsohn Dayenu Ltda 79 PUBLICATIONS 836 CITATIONS SEE PROFILE W.J. Chancellor University of California, Davis 77 PUBLICATIONS 426 CITATIONS SEE PROFILE All in-text references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. Available from: Dvoralai Wulfsohn Retrieved on: 09 May 2016

2 Journal ofterramechanics, Vol. 25, No. 2, pp , Printed in Great Britain / Pergamon Press Plc ISTVS TRACTIVE CHARACTERISTICS OF RADIAL PLY AND BIAS PLY TYRES IN A CALIFORNIA SOIL D. WULFSOHN*, S. K. UPADHYAYA* and W. J. CHANCELLOR* Summary--Four tyres ( , 18.4R38, , 14.9R28) were tested using the UCD single wheel traction tester. Each tyre was tested at two different inflation pressures and three different vertical loads at each inflation pressure. All tests were conducted in a well tilled Yolo loam soil. A dimensional analysis procedure was used to design and analyse the experiment. Two models were considered: (A) using inflation pressure as a variable, and (B) using tyre deflection as a variable. The effect oftyre type, tyre size, tyre inflation pressure and dynamic load on (1) net traction ratio at 20% slip and (2) average tractive efficiency in the 0-30% slip range were investigated using an ANOVA technique. An estimate of the possible energy savings due to the use of radial ply tyres instead of bias ply tyres in California agriculture was made. a,c,a',b',c" A b B b C C~ CRR Cs c~ d D (3/I41)2o G h H J k k K l m,m~y,m,~,d Nsey P P r r' 5 5' So l T NOTATION Traction equation coefficients, dimensionless Contact area [L 2] Tyre unloaded section width [L] Track width [L] Constant in traction equation for data with slip offset, dimensionless Cone index [FL -2] Wismer-Luth wheel numeric, dimensionless Coefficient of motion resistance, dimensionless Soil cohesion [FL -2] Coefficient of traction, dimensionless Tyre outer diameter [L] Net traction IF] Net traction ratio at 20% slip, dimensionless Cone index gradient, dimensionless Tyre unloaded section height [L] Gross traction IF] Shear deformation [L] Generic term for traction constant, dimensionless Rate constant, dimensionless Soil shear modulus [L] Contact length ILl Mobility numbers, dimensionless Sand tyre numeric, dimensionless Inflation pressure [FL -2] Normal pressure [FL -2] Rolling radius [L] Unmodified experimental rolling radius [L] Slip, dimensionless Unmodified experimental slip, dimensionless Slip offset, dimensionless Tyre construction type, dimensionless Torque [FL] *Department of Agricultural Engineering, University of California, Davis, CA 95616, U.S.A. lll

3 112 D. WULFSOHN, S. K. UPADHYAYA and W. J. CHANCELLOR TE (TE)0-30 Va Vt w X ~,/3,~,~',/3',~' 6 0 p 7" OO Tractive efficiency, dimensionless Average TE over 0-30% slip range, dimensionless Actual forward velocity [LT -I] Theoretical forward velocity [LT t] Dynamic load [F] Distance along track [L] Constants in generalised Wills traction equation, dimensionless Tyre deflection ILl Soil dry moisture content, dimensionless Soil dry bulk density [FT2L-4I Shear stress [FL-2I Soil angle of internal shearing resistance, dimensionless Rotational velocity [T -I] INTRODUCTION A WIDE range of agricultural operations are carried out using tractors to provide pull and propulsion. Over the past few decades tractor sizes have increased steadily. As tractors increase in power, the main limitations to performance are limitations of the traction device (wheels or tracks) imposed by the terrain over which they operate. The power efficiency of pneumatic tyres ranges from about 90% when operating on concrete to less than 50% when operating in loose or sandy soils [ 1-5]. A conservative estimate of the annual fuel loss due to the poor tractive efficiency (ratio of drawbar power to axle power) of agricultural tractors in the U.S. alone is 575 million litres [2]. Since the drawbar is the most commonly used power outlet of agricultural tractors, the ability to provide draft to pull various types of implements is a primary measure of a tractor's effectiveness. The tractive efficiency (TE) with which the pull is achieved is also of importance. REVIEW OF LITERATURE Factors influencing tyre performance The tractive characteristics ofa tyre depend on the type and condition of the soil, the tyre physical parameters, and tyre loading. Traction is obtained from forces transmitted through the soil-tyre interface. Experimental evidence indicates that the soil has a greater influence on the traction capabilities than the tyre design features (e.g. [6]). On pavement, vehicles can develop high pulls; but when operating on soil, they may develop only a fraction of the pull they develop on pavement because of the adverse soil conditions [7]. However, within a given soil type and condition, tyre design has a significant effect on the tractive performance. Gill and Vanden Berg [2] showed traction curves demonstrating the relative effect of soil conditions (concrete, silty clay, sand) and tyre design on the performance of two pneumatic tyres: a radial ply tyre with narrow rim and no lugs, and a typical agricultural tractor tyre. The data indicated that, except on concrete, performance was affected much more by traction conditions than by the tyre design changes. The effect of soil type and condition on tractive performance is complex and interrelated with the other parameters (dynamic load, tread configuration, inflation pressure etc.). Tread design has considerable influence on the performance of off-road tyres. Lug height, lug spacing and lug shape have been shown to affect performance [8-11]. Lug angle and lug width were shown to have negligible effect on performance in studies by Taylor [12] and Reed and Shields [8]. In soft cohesive soils the main physical effect of lugs is to increase the effective tyre radius, since the spaces between the lugs tend to clog with soil [13]. In dry frictional soils treads tend to degrade tyre performance, particularly at high slip rates. On firm dry surfaces smooth tyres seem to develop as much drawbar pull as lugged tyres.

4 TRACTIVE CHARACTERISTICS OF TYRES 113 However, when traction conditions deteriorate due to the presence of moisture, loose soil, surface vegetation etc., then lugged tyres develop more pull than smooth ones. When surface moisture is very high, even lugged tyres do not develop sufficient traction [14] and traction aids may be needed. Various researchers have compared the tractive performance of radial ply and bias ply tyres. Radial ply tyres were found to obtain significant increases in average pull when run in the 0-30% slip range [15, 16]. The radial ply tyres obtained slight increases in tractive efficiency. A report from the National Swedish Testing Institute for Agricultural Machinery [ 17] claimed higher pull at any given slip for radial ply tyres in all conditions tested except in a very cohesive clay soil. Thaden [18] found that the tractive advantage of radial ply tyres drops off at higher slip values. Gee-Clough et al. [19] and Burt et al. [20] found that the benefits of radial ply construction tended to disappear as tyre inflation pressure increased. Taylor et al [21] compared the tractive performances of a radial ply and a bias ply tyre of the same size and shape in a range of soil conditions. They concluded that the radial ply tyre had its greatest advantages on firm surfaces where most of the soil-tyre deformation took place in the tyre, and that this advantage was gradually lost as the soil became softer, causing more of the total soil-tyre deformation to take place in the soil. Burt et al [20] tested radial and bias ply tyres with various inflation pressures and static loadings in two soil conditions. On the wetter, higher bulk density soil the bias ply attained higher tractive efficiency. The radial ply tyre had a greater mean tractive efficiency on the drier, less dense soil. Hausz [22] stated that the tractive advantages of radial ply tyres over bias ply tyres result from their deflection characteristics and resulting pressure distribution. Radial ply tyres usually yield a larger footprint than the same size bias tyre at the same load and inflation pressure. Even when the footprint of the radial ply tyre is not significantly greater than that of the bias, tests show improved traction for the radial ply tyre. This is because the lugs on the radial ply tyre (near the center of the tread) have a much more uniform pressure distribution on them, and so will bite into the soil more uniformly. Plackett [23] found that radial ply tyres gave a more even distribution of ground pressure than bias ply tyres, with a 15% decrease in the peak value of ground pressure. The importance of contact area geometry was shown by the equations for gross traction developed analytically by Wills [24]. To get higher longitudinal soil displacement (and thus greater traction) for a given contact area, a larger contact length/width ratio is needed. Taylor et al [6] conducted experiments to determine the effects of diameter on the tractive performance of tyres. At the same normal load and inflation pressure, increasing tyre diameter in general led to increased pull and tractive coefficient. Increasing the applied vertical load led to increased pull. Pneumatic tyres showed the greatest benefit from increasing the diameter when the additional vertical load, which the larger tyre is capable of carrying at the same deflection, was added. Moreover, they found that increasing inflation pressure for constant vertical load and diameter led to decreased pull. Dwyer et al [25] tabulated data of predicted values of tractive performance of tyres for different soil conditions. They found that in good traction conditions the drawbar pull developed can be increased by increasing the dynamic load on the driving wheels and that the increase in inflation pressure needed to accommodate the increased load will not lower performance. In poor traction conditions, on the other hand, the increase in pull obtained by increasing the dynamic load needs to be accompanied by increased tyre size to keep the inflation pressure down [26]. Burt et al. [27] investigated the role of both dynamic load and slip on tractive performance. The results of this study showed that at low values of slip, large changes in performance

5 114 D. WULFSOHN, S. K. UPADHYAYA and W. J. CHANCELLOR occurred with small changes in slip. However, at higher slip changes in dynamic load had a greater effect on performance than changes in slip. At constant slip, tractive efficiency increased with increases in dynamic load on compacted soil. On the soils with an uncompacted subsurface, tractive efficiency decreased with increased dynamic load. Input power increased linearly with respect to dynamic load and non-linearly with respect to slip. Output power changed in a non-linear way with respect to changes in either dynamic load or net traction. The empirical modelling of tyre performance The most commonly cited empirical approach to modelling soil-wheel performance evolved from the trafficability analysis of the U.S. Army Engineer Waterways Experiment Station (WES) based on the cone penetrometer technique, which was developed originally to provide a simple means to assess vehicle trafficability and mobility. Freitag [28] extended the approach to predict the tractive performance of treadless pneumatic tyres on soft soils. Two dimensionless ratios based on cone index, termed mobility numbers, one for sand and one for clay, were developed:. ( Cbd ) 6,/2. w G (b d) 3/2 6 M~and' -- W ( T ) (2) where C = cone index, G = cone index gradient, b = tyre unloaded section width, d = tyre outer diameter, W= dynamic load, 6 = tyre deflection, h = tyre unloaded section height. He then empirically correlated tyre output parameters (pull, towed force, torque and sinkage) at 20% slip, to the mobility numbers. Turnage [29] amended Freitag's relationships to account for a wider range of tyre parameters. He introduced a non-linear wheel numeric for clay. c e. ),J2 b )_, M= 7 ( l+ 2d and reported an empirical equation for estimating net traction. Turnage [30] reassessed the original methodology and proposed a new sand-tyre numeric, N~ey, which takes into account the effects of moisture content, compactibility, before-tyre-pass relative density and sand grain median diameter. He reported that the new methodology can accurately predict tyre performance in a wide range of soil types and conditions. Dwyer et al. [31] and Wismer and Luth [32], derived empirical relationships for the tractive performance of tyres on agricultural (cohesive-frictional) soils. Wismer and Luth [32] developed empirical equations for the traction characteristics of towed and driven wheels. The following equation for net traction of the driven wheel was proposed D = 0.75 (1 - e - ~ c0,) _ ( \ W cn (4) I

6 TRACTIVE CHARACTERISTICS OF TYRES 115 where D = net traction, W = dynamic load, s = slip, and C, = (Cbd/W). Tractive efficiency was calculated using the equations for gross traction and motion resistance as 1.2/Cn TE = [ 1-0.-~--e -k'-s~') ] (1- s). (5) Dwyer et al. [31 ] used equation (3) to examine the results of field tests on a range of tractor tyres at different loads and inflation pressures in various field conditions. Empirical equations were developed relating the coefficient of traction at 20% slip, the coefficient of rolling resistance, maximum tractive efficiency, coefficient of traction at maximum efficiency, and slip at maximum efficiency to the wheel mobility number. Later, these results were re-analysed [33] and the mobility number related to three performance parameters: coefficient of rolling resistance, CRR, maximum coefficient of traction, (Cx)... and a rate constant, k, defined by CT ---- (CT)max(1-e-k s). (6) Leviticus and Reyes [34], Clark [35], and Ashmore et al. [36] proposed more generalised forms of the Wismer-Luth model. To account for the effects of dynamic load, Ashmore et al. [36] introduced a dimensionless ratio describing the dynamic load on the tyre as a percentage of the tyre's rated load as a modelling variable. The predictive traction equations in most common use today, are those given in the ASAE Standards [1]. These empirical equations are limited to bias ply tyre performance with 20% tyre deflection, in the range of soil conditions for which they were developed. Therefore, the effect of tyre dimensions, inflation pressure and soil shear properties are not explicitly included. The applicability of these equations for tyres in California soil conditions is not known. OBJECTIVES The objectives of this study are: (1) To investigate the tractive ability of various agricultural tractor tyres operating in a California soil with respect to tyre type (radial versus bias ply), tyre geometry (such as its overall diameter, section width) and tyre loading (axle load, inflation pressure). (2) To develop quantitative relationships between the tyre performance (net traction, torque quotient, slip) and the tyre and soil parameters. EXPERIMENTAL DESIGN Tyre performance depends on tyre geometry, on the physical properties of both the tyre and the soil, and on the loading applied. The pertinent soil-tyre variables are presented in Table 1. Cone index is assumed to represent soil type (e.g. clay, sand) and condition (e.g. bulk density, moisture content etc.). Tyre geometry is represented by the section width and roiling radius. The zero conditions used are zero net traction when slip of the tyre is zero on the test surface. Although both inflation pressure and tyre deflection are included in Table 1, only one of the two terms is required to describe tyre stiffness. In our study we have developed two models: (A) Using tyre inflation pressure as a variable, and (B) Using tyre deflection as a

7 116 D. WULFSOHN, S. K. UPADHYAYA and W. J. CHANCELLOR TABLE 1, PNEUMATIC TYRE--SOIL SYSTEM VARIABLES Variable Symbol Basic dimension Soil: Cone index C [FL-2I Tyre: Section width b [LI Overall diameter d ILl Rolling Radius r [k] Inflation pressure p [FL-2] or Tyre deflection 8 ILl System: Dynamic load W IF] Net Traction D IF l Torque T [FL] Slip s [ ] variable. Model B is expected to be more general because the tyre deflection not only accounts for inflation pressure, but possibly includes the influence of tyre construction type (radial or bias ply). Model A In this study we planned to use the single wheel traction tester developed at the University of California, Davis [37]. The single wheel tester allows vertical load and either draft or slip to be controlled. The system outputs are torque and either slip (draft controlled) or net traction (slip controlled). These parameters are not independent, leading to two coupled equations describing the functional relationships between the variables. T=f(W, D, p, b, d, r, C, s) (7) D=g(W, T,p, b, d, r, C, s). (8) Using dimensional analysis the following pi terms were selected: (i) Cbr/W (ii) pbr/w (iii) D/W (iv) T/rW (v) b/r (vi) b/d (vii) s giving the following functional relationships: T/rW = f (D/W, pbr/w, b/r, b/d, Cbr/W, s) (9) D/W = g (pbr/w, b/r, b/d, Cbr/W, T/rW, s). (lo) By conducting controlled tests it is possible to evaluate the above relationships. In our experiments the value of b/dwas similar for all tyres (about 0.2). For a given test the values of Cbr/W, pbr/w and b/r are all constant. Thus, we can establish the relationships T/rW = f ~ (D/W, s) (11) D/W = f2 (T/rW, s). (12)

8 TRACTIVE CHARACTERISTICS OF TYRES 117 These equations are coupled, so we can derive T/rW and D/W as functions of slip alone: T/rW =f3 (s) (13) D/W =f4 (s). (14) Once the relations in equations (13) and (14) have been established, the data can be analysed as follows. Consider all tests which, for a given value of b/r, have the samepbr/wratio. Any change in the traction coefficients will be caused by variation in Cbr/W. Similarly, if there are tests in which Cbr/Wis constant, then any changes in the traction coefficients depend on pbr/w. In this way we should be able to determine the effect of these parameters on the tractive performance of the tyre. Model B Another approach is to characterise the tyre by its deflection characteristics. Using the single wheel tester we can find the relationship between tyre deflection and loading (vertical load, inflation pressure) for a given tyre (i.e. given construction type and geometry). Let 6 be the deflection of the tyre. 6 =f(tyre stiffness, loading) =f(b, r, t, p, W) (15) where t = tyre construction type. For a given inflation pressure, 6 is expected to vary linearly with vertical load. Thus, we expect the relationship to be of the form 6 =f' (b, r, t,p) W (16) where f' (b, r, t, p) represents the effective tyre stiffness. This approach would simplify the analysis since 6 incorporates stiffness related tyre terms. We now need to establish the functional relationships T=f(6, C, b, r, at, D, W, s) D=f(6, C, b, r, d, D, W, s) (17) (18) or, in dimensionless form T/rW=f (6/b, r/b, d/b, D/W, Cbr/W, s) D/W=f (6/b, r/b, d/b, T/rW, Cbr/W, s). (19) (20) The development of these relationships would follow the same methods as in the first analysis technique. TEST PROCEDURE Experiments were conducted in a heavily tilled Yolo loam soil. Four tyres were tested: an 18.4R38, , 14.9R28 and All were 8 ply rating except the small radial tyre

9 118 D. WULFSOHN, S. K. UPADHYAYA and W. J. CHANCELLOR which had 10 ply rating. The two smaller tyres are of a size usually used on the front axle of a front wheel assist tractor. Each tyre was tested at two inflation pressures and at three vertical loads within each inflation pressure. The tests were designed in an attempt to obtain several constant values of the dimensionless ratiopbr/w--within the limitations of loads that can be applied to any given tyre at a given inflation pressure, Tests were fully randomised between tyres and between applied vertical loadings within tyres as shown in Fig. 1. % ~ W2 WI t tit " I to Wl,#. "1~ t ~Ir ~'~.~ I I i I I,oo I'-. / ",-.. / 1 W3 ii II '~% WI * Number of test t W3>W2 >Wl Each segment : 30 FIG. 1. A typical layout of the field experiment. Preliminary field tests using the single wheel tester indicated that the tyres should be tested in a constant draft or a constant slip mode, or a combination of the two to obtain meaningful results (less scatter in the experimental data). The test procedure used was as follows: The first few test runs were conducted in a slip-control mode. The first run was conducted with slip set to near zero, and for each of the next few runs, slip was increased successively to produce higher drafts. The remaining runs were conducted in draft-control mode, such that draft output was increased by fixed increments each run, up to the maximum power capability of the traction tester. An average value of slip was calculated for each run. This procedure allowed tests to be conducted over the maximum possible slip range for a given tyre within the capabilities of the traction tester. Tests were conducted at a forward speed of 2 km/h. After every test run the tyre test stand was pivoted about the rear support wheels by an angle of about five degrees so as to stand over an undisturbed stretch of soil. Thus, each test area occupied a sector of approximately 30 (see Fig. 1). The input torque, dynamic load,

10 TRACTIVE CHARACTERISTICS OF TYRES 119 net traction, actual and theoretical forward speeds (giving slip) were recorded on a digital data acquisition system and processed using a microcomputer. For each tyre at each inflation pressure, two sets of readings of variation of cone penetration resistance with depth were taken so that the cone index of the soil could be determined. Each set contained six readings taken at approximately equidistant positions along the test track. In addition, a neutron probe strata gauge was used to get density and moisture data in the test locations. Five sets of bulk density readings were obtained at depths of 50, 100 and 150 mm. Values of moisture content in the top 75 mm were also measured. DATA ANALYSIS TECHNIQUE The experimental data were analysed using a non-linear regression technique to obtain the best fit values of the coefficients (a, c) in a generalized form of the Wismer-Luth traction equation, D -- = a(l -e-c~). g, (21) Note that equation (21) assumes by definition zero net traction at zero slip. During the field tests zero slip was not necessarily achieved, causing the traction data to be offset along the slip axis. In this case the net traction can be described by where D -- = a(1 - e -cts'+~ )) W S" ~- S - S O (22) (23) and So is the offset from true zero slip. Equation (22) can be rewritten as where D = a(1 - e... e -c ~') = a(1 -/~ e -c s,) W (24) /~= e-cs0 (25) A nonlinear regression program was written which uses an iterative scheme during curve fitting to determine the coefficients a, b and c. The slip offset, so was computed from equation (25) and used to correct the experimental slip data to obtain the true slip. Since we have the true slip values, s, and the values of the coefficients a and c (21), is completely described. Once the slip data have been corrected the program then determines the rolling radius (at zero slip) as follows: Slip can be expressed as I.'t - Va rto-va Va S vt r to r to (26)

11 120 D. WULFSOHN, S. K. UPADHYAYA and W. J. CHANCELLOR Similarly, the uncorrected slip, s', is given by s,=l_ Va r' co (27) where r' is the unmodified rolling radius. Combining equations (26) and (27) and rearranging the terms, we can determine the corrected rolling radius v,, = (1 - s) r o~ = (1 -s')r'co (28) Therefore r' 1 - s r 1 - s' (29) r=r' ( l-s',~ 1 - s ~ (30) and at zero unadjusted slip r = r'/(1 - s). (31) In effect the program determines the "true rolling radius" that is specific to the tyre for a given loading and soil condition. The torque data behaved in a similar fashion to the net traction data except that, unlike net traction, input torque is not zero at zero slip because of tyre motion resistance and the zero condition used (i.e. zero net traction when slip is zero on the test surface). Therefore, the torque data were analysed using a similar non-linear scheme to obtain the best fit values of the coefficients in the equation T -a'(1 -b'e -C'~) rw (32) where s is the corrected or true slip. Equations (21) and (32) were then used to predict the tractive efficiency (TE) as follows: TE= D va x 100 ToJ W (1 - s)" 100 (33) a (1 - e -cs) a' (1 - e-c'9 (1 - s) x 100.

12 TRACTIVE CHARACTERISTICS OF TYRES 121 EXPERIMENTAL RESULTS Table 2 summarises the soil and loading conditions for the tyres tested in the tilled Yolo loam soil. The rolling radii given are those determined by the analysis program as described above. The soil physical conditions shown are for the top 150-mm layer. The soil was low in moisture, with low dry bulk density and cone index values. These values indicate that the soil was overtilled giving poor traction conditions. TABLE 2. EXPERIMENTAL CONDITIONS Tyre Dynamic load Inflation pressure Rolling radius Soil physical conditions W p r C p e (kn) (kpa) (m) (kpa) (kg/m 3) (%) 18.4R R , , , , , , , , ll , , , , , , , , Notes: C = cone index; p = dry bulk density at depths of 50, 100, and 150 ram*; 0 = dry basis moisture content* *Obtained using neutron probe. Usually reliable as a relative indicator of density and moisture content. The predicted traction equation parameters are given in Table 3. Figures 2 and 3 show typical plots of experimental and predicted (D/W), (T/rW) and TE vs slip. From these figures and the R 2 values reported in Table 3 it is clear that the experimental data fit equations (21) and (32) very well.

13 122 D. WULFSOHN, S. K. UPADHYAYA and W. J. CHANCELLOR TABLE 3. TRACTION PARAMETERS OBTAINED STATISTICALLY, BY FITTING EXPERIMENTAL DAIA TO STANDARD EQUATION FORMS Tyre Test Inflation Dynamic date pressure load (1986) (kpa) (kn) Net traction equation Torque equation a c R ~ a" b' c' R R38 10/ , , ,0896 0, (/ /7 14.9R28 10/ / , (/ , , Note: Net traction equation: D/W = a( I-e-"s); Torque equation: T/rW = a'.( 1-b'.e-'"~); s = slip in % DISCUSSION Analysis of traction performance parameters In order to compare the tractive characteristics of different tyres with varying inflation pressures and dynamic loads, the following parameters were investigated: (1) Maximum tractive efficiency (TE) and the slip at which it occurs; (2) Average TE over the 0-30% slip range; and (3) D/W at 20% slip. The values of these parameters are given in Table 4. The results for the large tyres ( , 18.4R38) show that at the lower inflation pressures, increasing the dynamic load led to increased maximum net traction ratios. At the higher inflation pressures, the tyres developed similar maximum D/W values at all three dynamic loads tested. The small tyres ( , 14.9R28) showed a markedly inferior performance in this soil condition. Maximum values of D/W were mostly in the order of 0.3 as opposed to about 0.4 for the large tyres. Peak tractive efficiencies were in the 35% to 50% range. The radial ply tyre achieved higher peak TE's. Generally the peak values of TE occurred at higher

14 TRACTIVE CHARACTERISTICS OF TYRES , Experimentot D/W *,, Experimentot T/rW e,, Experirnentot. TE e-, Preclictecl. D,/W, ":, Predictecl ' T/rW.... *:,Predict eel TE 08 t 07 1!,I = i I F- g 03 O2 i o, " ; ",b ",g " 2'o " g " 3'o ".~s " ~ " &' " 5b " gs " 6o Stip (%) FIG. 2. Traction characteristics of tyre with 13.6 kn dynamic load and 110 kpa inflation pressure in Yolo loam soil. slip values for the small tyres than for the large tyres. For the large tyres the peak TE was attained at approximately 10% slip. The maximum TE for the small tyres occurred on average at about 14% slip. The maximum TE occurred sometimes at slightly lower slip values for the higher loadings and at slightly greater slip at low loads. Tables 5 and 6 give the results of a two way analysis of variance (ANOVA) performed on the parameters (1) average TE over 0-30% slip range, (TE)0_30, and (2) D/W at 20% slip, (D/W)20, respectively. The tyres (18.4R38, , etc.), dynamic load level (low/medium/ high) and the level of inflation pressure (low/high) were treated as factors in these additive models. The results of the ANOVA show that the physical tyre differences and the dynamic load significantly influence (TE)o-30 and the value of(d/w)20. A Duncan's multiple range test was performed to detect the differences between the three factors. The analysis for (TE)0_30 indicates that the large tyres performed better than the small tyres, and that radial ply tyres had superior performance. The large tyres developed significantly higher (D/W)2o than the small tyres. Although there was a significant difference between the large radial and bias ply tyres, the small tyres formed a homogeneous group. In both these analyses, increased dynamic load led to better performance. Moreover, inflation pressure had no effect on either (TE)0-30 or (D/W)2o. In view of this, an analysis of variance was performed for (TE)0-30 and (D/W)2o where the two levels of inflation pressure were considered as replications, and the tyre-load interaction was included as a factor (Tables 7 and 8). The results for both these analyses showed that there was no interaction between the physical tyre features and load.

15 124 o81 D. WULFSOHN, S. K. UPADHYAYA and W. J. CHANCELLOR x, Experimental D/W +., Experimental T/rW v.. Experimental TE e', Predicted D/W m:, Predicted llrw *;. Predicted TE O7 06 Cl O2 OI 5 I ~ SLip (*Io) FIG. 3. Traction characteristics of 14.9R28 tyre with 12.7 kn dynamic load and 205 kpa inflation pressure in Yolo loam soil. Implications for energy use In our experiments, the large radial tyres achieved an average tractive efficiency of 27.23% vs 25.37% for the large bias ply tyres, over the 0-30% slip range*; an increase of 6.8%. It is of interest to determine the implications of this in terms of energy savings. To estimate the energy savings which would arise by using machinery equipped with radial ply tyres rather than bias ply tyres, the following assumptions were made: (a) The annual energy use in California agriculture amounts to million barrels of oil equivalent [38]; (b) of this, 17.7% represents energy used in field operations [38]; (c) half of this energy (i.e. approximately 9% of the total) was consumed in performing field operations in tilled soil conditions; (d) the reported energy data was for power units equipped with bias ply tyres; (e) rear wheel drive tractors are used for field operations; and (f) the data for the tilled Yolo Loam condition is typical for other tilled California soils. Thus, we have: Energy saved = = 0.29 million barrels of oil equivalent. In December 1986 the cost of crude oil was $11.11/barrel [39], so a 6.8% increase of (TE)0_30 amounts to a saving of approximately $3 million per annum! This is a conservative estimate since it uses a very low crude oil price. *These are very low because of the poor traction conditions.

16 TRACTIVE CHARACTERISTICS OF TYRES 125 Statistical analysis: model A The values of the experimental dimensionless parameters (pi terms) used in both models A and B for analysing the traction coefficients (a, c, a', b', c') are given in Table 9. The results of the analysis aimed at relating the traction equation coefficients to the dimensionless parameters are given in Table 10 (For the complete analysis refer to ref. [40]). Based on these results, a multiple linear regression analysis was performed to relate a given traction coefficient with the dimensionless terms which significantly influence that parameter, The "best" fit equations based on a high correlation coefficient and significant slopes are given in Table 11. Statistical analysis: model B In the second model considered, the tyres were characterised by their deflection characteristics. Instead of inflation pressure, p, tyre deflection, ts, was used as a variable. It was hoped that this would allow the pooling of the radial and bias ply data. TABLE 4. SUMMARY OF TRACTIVE CHARACTERISTICS OF THE TEST TYRES IN YOLO LOAM SOIL CONDITION Tyre Inflation Dynamic Tractive efficiency (%) D/W pressure load at 20% (kpa) (kn) Maximum Average over slip 0-30% slip Value Slip (%) 18.4R R l I

17 126 D. WULFSOHN, S. K. UPADHYAYA and W. J. CHANCELLOR TABLE 5. ANALYSIS OF VARIANCE OF TRACTION PARAMETER. AVERAGE TE OVER 0-30% SkIP RANGE. FOR TEST TYRO: IN YOLO LOAM SOIL Source of Sum of Degrees of Mean Computed variation squares freedom square f value Tyre "* Inflation Load "* Error Total Homogeneous subsets predicted by Duncan's multiple range test+. Tyre$ T3 T4 T1 T2 treatment means ,23 Inflation pressure PI P2 treatment means I... i Loadll WI W2 W3 treatment means TABLE 6. ANALYSIS OF VARIANCE OF TRACTION PARAMETER, D/W A1 20% SLIP, FOR TEST TYRES IN YOLO LOAM SOIk Source of Sum of Degrees of Mean Computed variation squares freedom square f value Tyre "* Inflation Load ** Error Total Homogeneous subsets predicted by Duncan's multiple range testt. Tyre$ T3 T4 T 1 T2 treatment means I... I Inflation pressure P1 P2 treatment means I... I Loadll WI W2 W3 treatment means **significant at 1% level. t I... I indicates homogeneous subset. STI = , T2 =- 18.4R38, T3 = , T4 = 14.9R28. PI = low inflation pressure; P2 = medium inflation pressure; P3 = high inflation pressure. llwl = low load; W2 = medium load; W3 = high load.

18 TRACTIVE CHARACTERISTICS OF TYRES 127 TABLE 7. ANALYSIS OF VARIANCE OF TRACTION PARAMETER, AVERAGE TE OVER 0-30% SLIP RANGE. FOR TEST TYRES IN YOLO LOAM SOIL, WHEN THE TWO LEVELS OF INFLATION PRESSURE ARE CONSIDERED AS REPLICATIONS Source of Sum of Degrees of Mean Computed variation squares freedom square fvalue Tyre "* Load "* Tyrex load Error Total Homogeneous subsets predicted by Duncan's multiple range test. Tyre* T3 T4 TI treatment means T Loadt Wl W2 W3 treatment means **Significant at 1% level. *TI = , T2 = 18.4R38, T3 = , T4 = 14.9R28. twl = low load; W2 = medium load; W3 = high load. TABLE 8. ANALYSIS OF VARIANCE OF TRACTION PARAMETER, D/W AT 20% SLIP. FOR TEST TYRES IN YOLO LOAM SOIL. WHEN TWO LEVELS OF INFLATION PRESSURE ARE CONSIDERED AS REPLICATIONS Source of Sum of Degrees of Mean Computed variation squares freedom square f value Tyre "* Load ** Tyre x load Error Total Homogeneous subsets predicted by Duncan's multiple range test. Tyre* T4 T3 T2 treatment means T Loadt Wl W2 W3 treatment means **Significant at 1% level. *T1 = , T2 = 18.4R38, T3 = , T4 = 14.9R28. twl = low load; W2 = medium load; W3 = high load. In order to quantify the relationship between tyre load and deflection, a load-deflection test was conducted with the tyre at seven levels of inflation pressure. A multilinear regression was conducted between the tyre deflection, the vertical load and the tyre pressure for the tyre. The resulting expression~ 8 = XW- 1.35X10 -~ X (Wp) (34) :~The units are 8 (m), W(kN),p (kpa).

19 128 D. WULFSOHN, S. K. UPADHYAYA and W. J. CHANCELLOR has a correlation coefficient of Different constants would be expected for each tyre depending on size and construction type. The tyre deflection, therefore, can be completely explained by the vertical load and pressure. The traction coefficients can be expressed by the relationship k=f ( Cbr b b W ' r ' 6 ) (35) TABLE 9. VALUES OF DIMENSIONLESS RATIOS USED tn ANALYSES Tyre Inflation Dynamic 7r terms pressure load (kpa) (kn) pbr/w Cbr/W b/r ( 6/b )-I 18.4R R , t , , (I TABLE 10. RELATIONSHIPS BETWEEN TRACTION COEFFICIENTS AND PI TERMS Traction Cbr/W pbr/w b/r coefficient a no no yes c no yes no a' no yes no b' no yes yes c' no yes no

20 TRACTIVE CHARACTERISTICS OF TYRES 129 TABLE l 1. SELECTED RESULTS OF ANALYSIS USING TYRE INFLATION PRESSURE AS AN INDEPENDENT VARIABLE Traction Parameter Radial ply Bias ply Coeff. Intercept Slope R 2 Intercept Slope R 2 a b/r "* "* c pbr/w "* "* a" pbr/w ** ** b/r ** ** b' pbr/w * (gbr/140 (b/r) 1.040t c' pbr/w ** "* **Significant at 1% level. *Significant at 5% level. ~'Significant at 10% level. where k = traction coefficient (a, c, etc.). Various dimensionless terms incorporating t5 other than (~/b) were attempted (e.g. (r/d)-l); however, of these only the term (b/8) was found to correlate with the traction coefficients. From the previous analysis it is known that (Cbr/BO is not important. Therefore, only combinations of the terms (b/r) and (b/ts) were analysed. Various combinations of these two parameters were investigated. The proposed "best" relationships are summarised in Table 12. Three criteria for selection were used: (1) high correlation coefficient; (2) level of significance of coefficients (slopes); (3) magnitude of the coefficients. When two or three models had similar correlation coefficients, the model which led to similar coefficients between radial ply, bias ply, and combined data with all coefficients significant, was selected. In some circumstances this may have resulted in the selection of a model with a slightly lower R 2 value if the latter criteria were better satisfied. TABLE 12. SUMMARY OF STATISTICAL ANALYSIS OF TRACTION CONSTANTS USING TIRE DEFLECTION AS A CHARACTERISTIC (MODEL B) Traction Parameter Combined data Radial ply Bias ply Coeff. Intercept Slope R 2 Slope R 2 Slope R 2 ~/(b/~5) 0.397** ** 0.266t a x/(b/ts)'(b/r) ** ** * x/(b/8) 0.604** 0.674** ** b' x/(b/~)'(b/r) "* "* "* a' x/(b/6)'(b/r) ** ** "* c x/(b/8)'(b/r) ** "* * c' x/(b/8)'(b/r) ** ** * **Significant at 1% level. *Significant at 5% level. tsignificant at 10% level.

21 130 D. WULFSOHN, S. K. UPADHYAYA and W. J. CHANCELLOR Interpretation of (~) The term x/(b/6) seems to be related to all the traction parameters. It is therefore of interest to interpret the meaning of this parameter. Consider the simplistic model of a tyre deforming shown in Fig. 4. From the geometry we can write (l/2) 2 = (d- 6) 6 d 6 [since d >> 3] l/2,/(d where/---contact length [40]. Thus, d/l ~ 2 xf(d/66) -- = 2 ~ VC(d/b) (36) The term xf(b/6) is proportional to the reciprocal of the contact length. In fact this same relationship can be derived for a toroidal tyre having an elliptical contact area. The model parameters have terms relating to tyre size (b/r) combined with this deflection term.! I- t v I FIG. 4. Simple model of a tyre deforming. Wills traction equation The correlation coefficients associated with the traction coefficients (Tables 11 and 12) indicate that a soil related parameter is missing. Unlike the Wismer-Luth equations [32] the term (Cbr/W) did not relate to the traction coefficients. Wills [24] developed expressions

22 TRACTIVE CHARACTERISTICS OF TYRES 131 for traction due to soil-track interaction using more fundamental soil parameters. He used the integral equation for gross traction proposed by Janosi and Hanamoto [41]: / H= B rdx = Bfo (c~ + P tan 4)) (1 - e -j/k) dx (37) where B = track width, r = shear stress,j = soil deformation beneath the tractive device, 0 = soil angle of internal shearing resistance, K= soil shear modulus and Cs = soil cohesion. The term (cs + P tan ~b) is the Micklethwaite equation for the maximum soil shear strength. If the normal pressure under the contact area is constant, and shear deformation increases linearly from the front of the contact area to the rear, then for a rectangular contact area the gross traction developed becomes K H=(Ac,+Wtan~b) [ 1+ (e -'v/<-l) ] sl (38) where A = contact area, l = contact length. Although the above assumptions are nbt entirely true for soil-tyre interaction we investigated whether our experimental data fitted this form of equation well. We performed an iterative regression technique to develop equations of the form O /3 W T~ o/t l+- (e-'- 1) ] s ~t rw [l+--(e-'/ s l) ] (39) (40) where a,fl,~,a',b',g' are constants. A typical plot of the experimental and predicted curves obtained is shown in Fig. 5. The resulting traction coefficients and correlation coefficients are given in Table 13. The results indicate that the experimental data fit the equation very well. Moreover, the values of the coefficients B and g in the net traction equation are similar to each other at each load level, further supporting the validity of the Wills equation (since both fl and g correspond to K/I). The equation indicates that a shear related soil parameter is required. CONCLUSIONS (1) The regressed traction data fit the following equations for net traction coefficient and torque quotient: D/W= a(1 - e-c0 T/rW = a" (1 - b' e -es) where a, c, a', b', c' are traction coefficients. R 2 values ranged from 0.96 to 0;995. (2) Two models were developed using dimensional analysis to model the traction

23 132 D. WULFSOHN, S. K, UPADHYAYA and W. J. CHANCELLOR 0.8 x,, Experimental. D/W +., Experimental. T/rW o,, Experimental TE, *'.Predicted D/W u:, Predicted T/rW.... *:,,,Predicted TE e It 0. 1 w i..- o5 ~ 04 e- 03, 02. o l 5 I Stip (%) FIG. 5. Traction characteristics of 18.4R38 tyre with 14.2 kn dynamic load and 100 kpa inflation pressure in Yolo loam soil, obtained using Wills [24] traction equation. equations. One model used tyre inflation pressure as an independent variable. This resulted in two equations for each parameter: an equation for radial ply tyres, and an equation for bias ply tyres. The second model used tyre deflection to represent tyre type and inflation pressure. In this model the use of the term ~/(b/6) to represent tyre loading allowed pooling of the bias ply and radial ply data to give one set of equations. This term seems to be proportional to the reciprocal of the contact length. (3) The traction data fitted the Wills [24] equation very well for the cases investigated, with R 2 values ranging between 0.96 and TABLE 13. WILI,S TRACTION EQUATION COEFFICIENTS FOR 18.4R38 TYRE IN YOLO LOAM SOIL Inflation pressure (kpa) Dynamic load (kn) Net traction equation Torque equation Note: , Net traction equation: D/W = a-t1 + B/s (e-s/c-l)] Torque equation: T/rW = c '.[1 + ff/s (e-s/~'-l)] with slip in per cent.

24 TRACTIVE CHARACTERISTICS OF TYRES 133 (4) None of the traction coefficients related to cone index. However, ourr 2 values for a', c, and c' indicate that a soil related parameter is needed. Based on (3) above, that parameter is expected to be soil shear modulus. (5) Two performance characteristics of the Lyres were compared: (1) Average tractive efficiency in the 0-30% operating slip range, and (2)D/Wat 20% slip. It was found that in the tilled Yolo loam soil condition: (a) The large Lyres performed better than the small tyres, (b) The radial ply Lyres performed better than the bias ply tyres, (c) Increased dynamic load led to increased performance, (d) Tyre inflation pressure did not influence performance. (6) The large radial ply tyres resulted in an average tractive efficiency of 27.23%, vs 25.37% for the large bias ply Lyres, over the 0-30% slip range; an increase of 6.8%. On an energy basis, this increase is equivalent to a $3 million per annum saving in California alone. REFERENCES [1] ASAE Standards, Agricultural Machinery Management Data, ASAE Data D American Society of Agricultural Engineers, St. Joseph, MI (1987). [2] W. R. GILL and G. E. VANDEN BERG, SoilDynamics in Tillage and Traction. Agricultural Handbook 316., U.S. Government Printing Office, Washington, D.C. (1968). [3] M.J. DwYERandG. PEARSON, A field comparison ofthe tractive performance oftwo-and four-wheeldrive tractors. J. agric. Engng Res. 21(1), (1976). [4] M.J. DWYER and G. PEARSON, A field comparison of the tractive performance of two-and four-wheel drive tractors. J. agric. Engng Res. 21(1), (1976). [5] H. STEINKAMPF, Problem of power conversion through the driving wheels of large tractors. Grundlagen der Landtechnik 27(5) [NIAE Translation 425] (1977). [6] J. H. TAYLOR, G. E. VANDEN BERG and I. F. REED, Effect of diameter on performance of powered tractor wheels. Trans. ASAE 10(6), (1967). [7] P. A. TAYLOR and N. Y. WILLIAMS, Traction characteristics of agricultural tractor Lyres on hard surfaces. J. agric. Engng Res. 4(1), 3-8 (1959). [8] I. F. REED and J. W. SHIELDS, The effect of lug height and of rim width on the performance of farm tractor tires. Soc. Automotive Engrs J. 58(12), (1950). [9] G. H. VASEY and I. T. NAYLOR, Field tests on tractor Lyres. J. agric. Engng Res. 3(1), 1-8 (1958). [ 10] J.H. TAYLOR, Lug spacing effect on traction performance of pneumatic tires. Trans. Am. Soc. Agric. Engrs 17, (1974). [11] D. GEE-C~UGH~ M. M~A~Is~ER and D. w. EvERNDEN~ Tractive perf~rmance ~f tract~r drive tyres_~. The effect of lug height. J. agric. Engng Res. 22(4), (1977). [12] J. H. TAYLOR, Lug angle effect on traction performance of pneumatic tires. Trans. ASAE 16(1), (1973). [13] M. G. BEKKER, Off-the-Road Locomotion: Research and Development in Terramechanics. University of Michigan Press, Ann Arbor (1960). [14] J. L. SMITH, A study of the effects of wet surface soil conditions on the performance of a single wheel. J. Terramechanics 3(2), 9-24 (1966). [15] G. E. VANDEN BERG and I. F. REED, Tractive performance of radial ply and conventional ply tires. Trans. ASAE., St. Joseph, MI (1962). [16] P.J. FORREST, I. F. REED and G. V. CONSTANTAKIS, Tractive characteristics of radial ply tires. Trans. ASAE 5(2), 108, 115 (1962). [17] National Swedish Testing Institute for Agricultural Machinery, Traktordack, Pirelli Cinturato. Report No. 1663, Ultuna, Uppsala, Sweden (1963). [18] T. J. THADEN, Operating characteristics of radial-ply tractor tires. Trans. ASAE 5(2), (1962). [19] D. GEE-CLOUGH, M. MCALLISTER and D. W. EVERNDEN, Tractive performance of tractor drive tyres--ii. A comparison of radial and cross-ply carcass construction. J. agric. Engng Res. 22(4), (1977). [20] E.C. BURT, P. W. L. LYNE and J. F. KEEN, Ballast and inflation pressure effects on tractive efficiency. ASAE Paper No ASAE, St. Joseph, MI (1982). [21 ] J.H. TAYLOR, E. C. BURT and A. C. BAILEY, Radial tire performance in firm and soft soils. Trans. ASAE 19(6), (1976). [22] F.C. HAUSZ, Traction characteristics of radial tractor tires. Proc. Int. Conf. SoilDynamics, Auburn, Alabama. Vol. 4, pp (1985). [23] C.W. PLACKETT, The ground pressure on some agricultural tyres at low load and zero sinkage. Z agric. Engng Res. 29(2), (1984).

25 134 D. WULFSOHN, S. K. UPADHYAYA and W. J. CHANCELLOR [24] B. M. D. WILLS, The measurement of soil shear strength and deformation moduli and a comparison of the actual and theoretical performance of a family of rigid tracks. 3. agric. Engng Res. 8(2), (1963). [25] M.J. DWYER, D. W. EVERNDEN and M. MCALLISTER, Handbook of Agricultural Tyre Performance (2nd. edn.). NIAE Report No. 18, National Institute of Agricultural Engineering, Silsoe, Bedford, England (1976). [26] M. J. DWYER, The tractive performance of wheeled vehicles. J. Terramechanics 21(1), (1984). [27] E.C. BURT, A. C. BAILEY, R. M. PATTERSON and J. H. TAYLOR, Combined effects of dynamic load and travel reduction on tire performance. Trans. ASAE 22(1), (1979). [28] D. R. FREtTAG, A dimensional analysis of the performance of pneumatic tires on soft soils. Tech. Rpt , U.S. Army Corps of Engineers, Waterways Experiment Station, Vicksburg, MS (1965). [29] G. W. TURNAGE, Using dimensionless prediction terms to describe off-road wheeled vehicle performance. ASAE Paper No , ASAE, St. Joseph, MI (1972). [30] G. W. TURNAGE, Prediction of in-sand tire and wheeled vehicle drawbar performance. Proc. 8th. Int. Conf. Soc. Terrain-Vehicle Systems, 1STVS, Cambridge, England, Vol. 1, pp (1984). [31] M.J. DWYER, D,R: COMELY and D. W. EVERNDEN, Field measurement of agricultural tyre performance at the National Institute of Agricultural Engineering. Proc. 4th. Int. Conf. Int. Soc. Terrain-Vehicle Systems, Stockholm, Sweden, Vol. 1, pp (1972). [32] R. D. WISMER and H. J. LUTH, Off-road traction prediction for wheeled vehicles. Z Terramechanics 10(2), (1973). [33] D. GEE-CLOUGH, M. MCALt.IS'rER, G. PEARSON and D. W. EVERNDEN, The empirical prediction ot" tractor-implement field performance.,i. Terramechanics 15(2), (1978). [34] L. 1. LEVITICUS and J. F. REYES, Traction on concrete--i, dynamic ratio and tractive quotient. ASAE Paper No , ASAE, St. Joseph, MI (1983). [35] R. L. CLARK, Tractive modeling and field data requirements to predict traction. ASAE Paper No. 84-1(155, ASAE, St. Joseph, MI (1984). [36] C. ASHMORE, E. C. BURT and J. L. TURNER, Predicting tractive performance oflog-skidder tires. ASAE Paper No ASAE, St. Joseph, MI (1985). [37] S. K. UPADHYAYA, J. MEHLSCHAU, D. WULFSOHN and J. L. GLANCEY, The development of a unique, mobile single-wheel traction testing machine. Trans. ASAE, St. Joseph, MI (1986). [38] W.J. CHANCELLOR, V. CERVINKA, P. K. AV1ANI, N. J. RuPP, N. C. THAI and E. Q. YEE, Energy Requirements for Agriculture in California ( 1978 Data Base), Vol. I. Report, Joint Study by University of California, Davis, and California Department of Food and Agriculture (1981). [39] California Energy Commission, Quarterly Oil Report, Third Quarter (December 1986), [40] D. WULFSOHN, Tractive characteristics of radial ply and bias ply tires in a California soil. Unpublished M.S. Thesis, Department of Agricultural Engineering, University of California, Davis, CA 95616, U.S.A. (1987). [41] Z. JANOSl and B. HANAMOTO, The analytical determination of drawbar pull as a function of slip for tracked vehicles in deformable soils. Paper No. 41, 1st. International Conference on Mechanics of Soil-Vehicle Systems, Torino, Italy (1961).