axle torque distributions in 4wd tractors

Journal of Terramechanics, Voi. 18, No. 3, pp. 157-167~ 1981. Printed in Great Britain. Pergamon Press Ltd. @ 1981 International Society for Terrain Vehicle Systems.

0022-4898/811030157-11 $02.00/0

A X L E T O R Q U E D I S T R I B U T I O N S I N 4 W D T R A C T O R S

M. KHALID* and J. L. Stan'.~

Summary--Performance of a four-wheel drive (4WD) tractor can he optimized by controlling the power distribution between the front and rear axles. This paper proposes an automatically controlled hitch system to adjust the vertical force on each axle and thereby control the axle torques. Factors affecting the functional relationship hetween axle torque ratio and hitch position were examined experimentally using a 1/5.7 scale model 4WD tractor. The relationship hetween axle torque and hitch position was affected by the initial static weight distribution, the vvrtical and horizontal drawbar loads and traction or soil conditions. Traction efficiency was not affected by the axle torque ratio.

INTRODUCTION

O~nMIZINO traction performance and minimizing drive train wear in four-wheel drive (4WD) tractors is a major problem. Examination of manufacturers ' specifications for 4WD tractors indicates that different criteria are being used in their design. Static weight distribution, power-to-weight ratio, tractor dimensions, provision for dual tires, etc., vary from manufacturer to manufacturer as reflected in Nebraska Tractor Test results.

Performance of a 4WD tractor can be optimized by controlling the power distribution between the front and rear axles. This in turn can be controlled by varying either or both of the axle speeds and/or torques. Research has indicated that different front and rear axle speeds result in 'push-pull ' and hence vibration and shaking of the tractor [l, 2]. This dictates that the axles should be driven at the same speed and the torque distribution should be varied to achieve optimum performance. Further, if the torque distribution can be controlled, wear and cyclic overloading of drive train components should be decreased.

Axle torque is determined by the horizontal soil reaction against the tire which in turn is primarily a function of the vertical soil reaction against the tire. The vertical soil reaction can be controlled by varying the position of the implement line of pull with respect to the tractor. The latter can be controlled by adjusting the location of the hitch point with respect to the vehicle. Knowing the proper torque split between the front and rear axles for a given mode of operation, the corresponding hitch point

*Assistant Professor, Department of Agricultural Engineering, King Faisal University, AI-Hasa, Saudi Arabia.

~'Professor, Department of Agricultural and Chemical Engineering, Colorado State University, Fort Collins, Colorado 80523, U.S.A.

157

158 M. KHALID and J. L. SMITH

(~/~~ (rr/rR)c

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r-c-1 ×, o I IIT-- RI t

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FiG. 1. Hitch location control system.

{TrlT~),~ ~--

location can be found. In addition, the desired torque split can be maintained with a corresponding reduction in drive train wear.

Under a particula r soil strength condition and static weight distribution, the axle torque ratio is:

,f(p)_ TF TR

where TF = torque on front axle

T R == torque on rear axle

p =- hitch point location.

The func?tion,f(p ), can be determined experimentally, and an automatic hitch system (Fig. 1) can .be designed to maintain the desired value of TF/TR. With the system, the hitch point location can be automatically adjusted to produce opt imum preformance. The purpose-of this research was to examine the variables which affect f(p), and to determine the effect of axle torque distribution on traction efficiency.

DESIGN AND INSTRUMENTATION OF THE MODEL

The model (Fig. 2) was scaled to the prototype by a factor of 5.7. Specifications are listed in Table 1. A three-phase, one horsepower(0.75 kW)gear-motor provided power for both axles. Power to the axles was transmitted through a series of chains run through 90 ° angles so only the driving torque was transmitted to the axles and chain tension forces were eliminated. Strain gages on tubular supoprt members were used to measure horizontal and vertical forces on the axles. Axle torques were measured by strain gages mounted on spokes of the sprockets which transmitted power to each axle. The axles were long enough to permit use of either single or dual tires. Weights could be placed directly above each axle to obtain the desired static weight distribution.

The drawbar force transducer measured the vertical and horizontal components

TRACTOR AXLE TORQUE DISTRIBUTIONS 159

FIG. 2. Scale model 4WD tractor.

of the drawbar load. An essentially constant horizontal component of the drawbar load was.applied through a cable-weight assembly and the vertical component of the drawbar load was applied by adding weights on the hitch point. The position of the hitch point could be adjusted both horizontally and vertically. Axle speed was measured by microswitches located on the front axle.

TABLE I. SPECIFICATIONS OF THE MODEL

Total weight* 1500 Newtons Wheel base 53.3 cm Rolling radius 14.9cm No slip speed 38.0 cm/s Static weight distribution 38.0 cm/s Static weight distribution

% weight on front axle 50 75 to

% weight on rear axle 50 25 62

Location of center of gravity,* ~ static weight distribution

Height above ground surface 29.1 cm Distance rearward of front axle 21.3 cm

Moment of inertia* about C.G., 62 3-~ static weight distribution 18.11 N-m-s e

*Not scaled.

! 60 M. KHALID and J. L. SMITH

RESEARCH FACILITIES

The soil bin facility at the Agricultural Engineering Research Center, Colorado State University, consists of three indoor soil bins having three different soils, i.e. clay loam, silt and coarse sand. The main carriage on the soil bins includes soil preparation equipment and a hydraulically operated ASAE Standard soil cone penetrometer. An asphalt strip was added to evaluate performance of the model of a hard surface.

The data acquisition and reduction system consists of strain amplifiers and strip chart recorder, and an analog tape recorder, A/D converters and a digital computer.

RESULTS AND DISCUSSION

Axle forces Experimental relationships between the dynamic vertical load on each axle and the

horizontal load pulled by that axle are shown in Figs. 3, 4 and 5 for asphalt, dry sand and clay loam, respectively. The dynamic vertical loads on the axles were varied by changing the static weight distribution and drawbar position. A vertical drawbar load equal to 30 ~o of the horizontal drawbar load was also used on the tests con- ducted in sand and clay loam. Note that corresponding data points are located symmetrically on each pair of curves. For example, the data points which occur on the extreme left end of the curves for the front axle correspond to the points on the extreme right end of the curves for the rear axle. The total drawbar load thereby remains constant for each set of curves.

Referring to Fig. 3, with the tractor pulling a load equal to 38 ~ of its total weight (P/W ~ 0.38), the load pulled by each axle was not affected by the dynamic load on the axle. However, the rear axle exerted a larger portion of the total drawbar load than did the front axle. As the tractor pulled greater total drawbar loads (P/W increased), definite relationships were defined between the dynamic load on each axle and the load pulled by that axle, but the rear axle always pulled slightly more than the front axle.

~200 Z

g ~ooo

~ 800

~ 6 0 0 _ _ D ~1

~ 4O0

g 2oo N , - -

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Y A F ron t ax le J ~ ' "

o Reo~ ox,e ~C2", ~/~/ . . . . P / W - 0 . 6 0

p / w . o38 ~ / - ~ / w . o . ~ ~ . e .

~,~:~ ~_ ~ o . ~ ~ - ~

2 0 0 4 0 0 6 0 0 8 0 0 1000 1200 1400 1600

D y n a m i c v e r t i c a l l oad on a x l e , N

FIG. 3. Relationship between dynamic axle loads on asphalt.


Z

0 0

400

300

200

I00

I I 0 200 400 600 800 1200

Dynomic verticol Iood on the axle,

/~ Front axle o Rear axle

. . . . P / W = 0 . 2 2 ~ P/W=O. 12

~ I ~ I I I ~ I ~ I000

N

FIG. 4. Relationship between dynamic axle loads on dry sand.

The experimental results on asphalt were influenced by two factors. First, for low drawbar loads, the wheel slippage was not sufficient to develop the total potential friction force between the wheels and asphalt. Thus the load pulled by each axle was independent of the dynamic load on the axle. The friction force was more fully developed as the total drawbar load increased and the wheel slippage increased.

The second factor influencing the results on asphalt was that the rear tires were slightly larger than the front tires. With half of the total tractor weight on each axle, the measured rolling radii of the front and rear tires were 14.77 and 14.97 cm, respectively. At low drawbar loads and slippage, the set of tires having the larger peri- pheral speed (larger rolling radius) exerted the greater horizontal force. The effect of rolling radius decreased as the total drawbar load and wheel slippage increased. The

1200

Z ~000

, ; - -

8 0 0

~ 600

• 400

o~ 200

.~ Front axle o Rear axle

. . . . P/W=O.53

~ P / W = O . 2 9

-

I I I I I I I :~00 4 0 0 600 800 IO00 1200 14OO 1600

Dynamic vertical load on the ox le , N

FIG. 5. Re la t ionship between dyrmmic axle loads on clay loam.

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18OO


1 5

1 3

I I

.£

I-- 0 9 - -

0 7 - -

PIW =0.~,0

6 CT=I5 Nlcm z

o CI=30 Nlcm z

t3 CI=45 Nlcm z

05 [ I 0 5/15 I0130 15/45

Hitch position, cm

FIG. 6. Relationship between hitch position and axle torque split in. clay loam soil with P/W = 0.40, and vertical component of the drawbar load equal to 30% of the

horizontal component of drawbar load.

position of the curves for the front and rear axles was reversed by mounting the larger tires on the front axle.

The behavior of the tractor on dry sand, as shown in Fig. 4, was similar to that on asphalt. This was due to that fact that in dry sand, as on asphalt, the front and rear tires experienced nearly the same tractive surface or soil characteristics.

In clay loam, as shown in Fig. 5, the rear axle always pulled considerably more load than the front axle. This occurred even when the tractor was pulling large loads and the slippage was high. Placing the larger tires on the front axle decreased the separation between the curves, but the rear tires still pulled more load in these test conditions. Thus, in addition to the two factors discussed above for asphalt and dry dry sand, the separation between the curves for front and rear tires was also influenced by the different traction conditions experienced by each set of tires. The rear tires always followed in the tracks of the front tires. Since the front tires com- pacted the soil, the rear tires developed a greater horizontal force.

Axle torque splits The effect of hitch position on the axle torque ratio is shown in Figs. 6, 7 and 8.

In these figures, a drawbar position of 5/15 designates a position 5 cm above the

TRACTOR AXLE TORQUE DISTRIBUTIONS

1.5

163

. - -

O

g

FIG. 7.,

13 -

0 .9 -

0 7 -

0.~ 0

P / W = 0 . 4 8

", C I = 2 0 N / c r n ~

o C I = 3 0 N / c m z

c] C I = 4 0 N / c m 2

I . ! 5 /15 10/15 15/15

H i t c h p o s i t i o n , cm

Relationship between hitch position and axle torque split inclay loam soil with P / W = 0.48. No vertical drawbar load:

ground and 15cm behind the rear axle. Figure 6 was obtained with 75 % of the static tractor weight on the front axle and a vertical drawbar load equal to 30 % of the horizontal drawbar load. Figures 7 and 8 were obtained with 62 % of the static weight on the front axle and no vertical drawbar 16ad. All eight tires used on the tractor had the same rolling, rodius with half of the static weight on each axle. With this range of conditions, the front axle at times developed more horizontal force than the rear axle. Thus the torque ratio ~was greater than one in some tests.

The axle torque ratio indicates the torque split between the front and rear axles. Note, however, that with an axle torque ratio of 0.6 and equal axle angular velocities, 37. % of the total power or torque is transmitted through the front axle and 62.5 % is transmitted through the rear axle.

Undisturbed soil strength, as indicated by the cone penetrometer~ had a negligible effect on the axle torque ratio. The main factors influencing the torque ratio were the drawbar force and hitch position. Increasing the magnitude of the horizontal drawbar fore. e and/or adding a vertical drawbar force increased the sensitivity of the axle torque ratio to hitch position. These effects were anticipated based on simple


15

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13,

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E o 0 9

0 7

P / W = 0 . 6 2

6 C I = 2 0 N / c m z

o C I = $ O N / c m 2

o C I = 4 0 N / c m 2

O 5 I t 5/15 10/15 ~5/t5

Hi tch pos i t ion, cm

Relationship between hitch position and axle torque split in clay loam soil with P/W = 0.63. No vertical drawbar load.

80

70

60

50

40 0.5

FIG. 9.

A

P / W - O . 4 0

o C I = 4 5 N l c m ~ o C I , ~ O N / c m z ~ C I . 1 5 N / c m ~

I 0 t 5 2 0

T o r q u e r a t i o , T F / T R

Relationship between axle torque ratio and traction efficiency in clay loam soil with P / W = 0.40.

T R A C T O R AXLE T O R Q U E D I S T R I B U T I O N S 165

80

u . _

70 -

60 -

50

4 0 0.6

F m , 10.

D

O u

0 o u

A

P / W , O , 4 8

o C I , 4 0 N /cm z o C l , 3 0 N / c m z ~ C I , 2 0 N /cm 2

0.8 1.0 1.2

Torque rat io, T F / T R

Relationship between torque ratio and traction etf~ciency in clay loam soil with P / W = 0.48.

chassis mechanics analysis, and the fact that axle torque is primarily related to the frictional component of soil strength (and thus the vertical force between the tires and soil).

Traction efficiency" The axle torque ratio, as shown in Figs. 9, 10 and 11, had no significant effect on

traction efficiency. The primary factors influencing traction efficiency were soil strength and slippage. Since soil strength determines slippage and traction efficiency

80

o

70

60

50

4 0 05

F~G. I1.

0 A

0 0 o g

o ~

A

~ ~

- P / W ' O . 6 2

n c ' r , , 4 0 N/cm 2 o C l - 3 0 N / c m ~ A C Z - 2 0 N / c m z

I

U

I I I IO ~5

Torque ra t i o . T F / T ~

20

Relationship between torque ratio and traction eflk~iency in clay loam soil with P / W ffi 0.62.


IO

08

0¸6

04

02

0 ©

Asphalt

/ Clay loam

• //// _ I o C~=30 N/cm ~

"Dr sand " CI=40 N/era 2 oJ Y / . / ~ C I : 5 0 N lcm z

m . / ~ ~ ~,

O~ 02 03

s~p

F~G, ~2. S f i ~pU~ curves.

is directly related to slippage, the results were approximately as expected. Increas- ing the drawbar load to 62 ~o of the tractor weight decreased the traction efficiency slightly due to increased wheel slippage.

It is interesting to note that neither the position of the drawbar nor the static weight distribution, both of which cause changes in the dynamic vertical forces on the tires, had a significarit effect on overall tra~ction efficiency. Examination of available data indicated a tendency for the traction efficiency to be a maximum with an axle torque ratio of 0.8. However, the maximum traction efficiency was typically less than 2~i, greater than the average value.

The axle torque distribution can be controlled by adjusting the hitch position. However, the traction efficiency will not be improved significantly and the same results could be achieved by properly ballasting and hitching the vehicle for given operating conditions. The major benefit achieved by control of the axle torque distribution would be to provide an equal or predetermined distribution of power between the axles under varying field conditions and/or drawbar loads.

Slip-pull relationships Slip-pull curves for asphalt, dry sand and clay loam are shown in Fig. 12. These

data were obtained with 62~i of the tractor static weight on the front axle. On asphalt, the tractor became unstable (jumped violently) when the total drawbar load was approx. 90°,~, of the total tractor weight. However, by changing the drawbar position and static weight distribution (essentially making the tractor two-wheel drive) the tractor was stable and pulled an even larger drawbar load. in fact, the slippage approached 100% without any evidence of a tendency to become unstable.

Increasing the strength of the clay loam soil, as indicated by the cone index,


decreased the slip of a given drawbar load. These results were expected based on previous experience. Further, the same effect was indicated in the traction efficiency data.

CONCLUSIONS

I. On hard surfaces or dry sand where the front and rear tires experienced nearly identical traction conditions, the portion of the total drawbar load contributed by each axle depended upon the rolling radii of the tires and, with sufficient wheel slippage, upon the dynamic vertical l~ad on the axle. For low drawbar loads and low wheel slippage, the horizontal force on an axle was essentially independent of the vertical force.

2. In compactable soils and with sufficient wheel slippage, the portion of the total drawbar load contributed by each axle depended upon the rolling radii of the tires, dynamic load on the axle, and the increase in soil strength caused by passage of the front tires.

3. Altering the distribution of axle torques did not have a significant effect on traction efficiency.

4. The distribution of axle torques was directly related to and could be controlled by adjusting the hitch position. The major benefit of automatically controlling the axle torque distribution in a 4WD tractor would be to maintain an equal or predetermined distribution of power between the axles.

REFERENCES [l] F. MURI~.Lo-SoTo and J. S. SMITH, Weight transfer in 4WD: a model study. Trans. Am. Soc.

agric. Engrs 20(2), 253-257 (1977). [2] R. MURXLLo-Soxo and J. L. SMIT~, Traction efficiency of 4WD tractors: a model study. Tran~

~4m. Soc. agric. Engrs 21(6), 1051-1053 (1978).

axle torque distributions in 4wd tractors

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