Measurement of forces acting on 4WD-4WS tractor tires during steady-state circular turning in a rice field

Pergamon

Journal of Terramechanics, Vol. 32, No. 5, pp. 263-283, 1995 Published by Elsevier Science Ltd Copyright © 1996 ISTVS Printed in Great Britain. All rights reserved 0022-4898/95 $9.50+0.00 0022--4898(95)00021-6

MEASUREMENT OF FORCES ACTING ON 4WD-4WS TRACTOR TIRES DURING STEADY-STATE CIRCULAR TURNING IN A RICE FIELD H. ITOH*, A. OIDA t and M. YAMAZAKI *

Summary--Three directional forces on tractor tires, the normal forces, lateral forces and thrusts, were measured during steady-state circular turning in a rice field. The tested tractors were a four-wheel drive, four-wheel steering (4WD-4WS) and a four-wheel drive, two-wheel steering (4WD-2WS) tractor. The measured forces were analyzed with the measured slip, side slip angle and the turning radius of the tractor center of gravity. The results were compared with the results derived from the same experiments on a paved road. It was then presented that a clear, tight corner braking phenomenon occurred in the case of the 2WS tractor, in spite of its turning radius being larger than that of the 4WS tractor. The lateral forces on the tires did not act to the inside of the turn either on the paved road or the rice field. Through analysis, it became clear that the 4WS system could supply a smoother and more efficient turn than the 2WS system. Copyright (~) 1996 ISTVS. Published by Elsevier Science Ltd.

INTRODUCTION The turning motion of a vehicle on soft soil is governed by the forces acting on its tires and an implement which contacts the ground. The forces acting on the vehicle tires should be investigated first to realize efficient and successful farm operations in the rice field. Of course many researchers have analysed the forces acting on a tire-soil interface by using single wheel testers, but there are very few studies in which the forces on actual vehicle tires are measured, especially normal and lateral loads on soft soil. In this paper, the results of the measured three directional forces acting on the tires of both the 4WD-4WS and the 4WD-2WS tractors in a rice field during a steady-state turn are shown. The forces are analysed in relation to the slip and the side slip angle of the tires and the turning radius of the tractor center of gravity in a similar way to that described in a previous report [1]. Measurements of the above forces and slips were achieved during steady-state turning by keeping the steering wheel angle and the forward speed constant. The steady-state turn generally shows the fundamental characteristics of a vehicle's turning motion, and the results of measurement in the steady-state turning would be useful in an analysis by a computer simulation. A similar experiment had been done in another rice field [2], but the results shown in this paper were calculated in a different manner.

*Faculty of Biology Oriented Science and Technology, Kinki University, Naga-gun Wakayama 649-64, Japan. Faculty of Agriculture, Kyoto University, Sakyo-ku, Kyoto 606-01, Japan. 263

264

H. I t o h

et

al.

METHOD OF EXPERIMENT

Tested tractor The tested tractor and the procedure of the experiment were the same as had been used in the experiment on the paved road [1]. Figure 1 shows relationships between the steering angles of the tractor tires and the steering wheel angle. The steering system of the tested tractor consists of only links and gears. The steering angle of each tire is then determined by the steering wheel angle. The rear tires of the 4 W D - 4 W S tractor are steered to the same direction as the front tires if the absolute value of steering wheel angle is under 200 ° . On the other hand, the absolute value of steering wheel angle of over 200 ° steers the rear tires to the opposite direction [3]. By disconnecting the rear steering links and fixing the steering angles of the rear tires to zero, a 4 W D - 2 W S tractor was prepared. The experiment was done as follows. The steady-state circular turn was achieved by fixing the steering wheel angle and the shift position of the transmission of the tested tractor. Combinations of one of four steering wheel angles, 250 °, 350 °, 400 ° and 450 °, and one of three ground speeds of 0.41 m/s (3rd gear), 0.91 m/s (5th gear) and 1.92 m/s (7th gear) were selected and each turn was done at full throttle. The above combinations were set in both 4WS and 2WS. Forces acting on the inside tires of a turn were measured in a right turn, whereas forces acting on the outside tires were measured in a left turn because force transducers were fixed only to the right front and rear tires [1].

MEASUREMENT AND DATA PROCESSING Measured forces were as follows: normal load, lateral force, wheel axle torque and axial force of tie rods of the right front and rear tires. As for angles, steering angles of the fifth front and fifth rear wheels and the steering wheel angle were measured. Circumferential speeds of four driven tires and the rear fifth wheel were also measured. F u r t h e r m o r e , after each turn the turning circle diameters of four driven tires were directly measured from their trajectories using a tape measure. In another experiment the tested tractor was pulled straight by another tractor on the same rice field to determine the drawbar pull. The pull was supposed to be the total rolling resistance of the tested tractor. ~

Left "

I

'

Steer

'

"

Right l

"

I

"

'

..........4 -. ~ • .+................i-..

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:............................. l ~ " r .................. ~ " ~ - -

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.

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.

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................~................,.................~-~4~ .... Front Left Tire "[ Front Right Tire ] Rear Left Tire ~ " Rear Right Tire

.

.

200

400

S t e e r i n g W h e e l A n g l e (°) Fig. I. R e l a t i o n s h i p s b e t w e e n the s t e e r i n g a n g l e s of the t r a c t o r tires a n d the s t e e r i n g w h e e l angle.

Measurement of forces acting on 4WD-4WS tractor tires

265

Experimental apparatus The measuring devices used were almost the same as those in the previous experiment on a paved road [1]. The normal load and the lateral force acting at right angles to the vehicle's longitudinal axis were measured by four extended octagonal ring force transducers fixed to the right front and rear axle housings. The axle torques and the axial forces of the tie rods of the right front and rear tires were measured using a strain gage. The steering angles of the fifth front and fifth rear wheels and the steering wheel angle were measured by rotary type potentiometers. The circumferential speeds of the four driven tires and the fifth rear wheel were obtained by counting the time during one pulse signal generated by the photo interrupter fixed to each tire. A tire chain was fitted to the fifth rear wheel to prevent slip on soft soil.

Data processing The measuring system is also the same as that used in the experiment on the paved road. The data flow diagram is shown in Fig. 2. A part of the recorded digital data in the steady-state turning was processed. Ten points were selected from the extracted data at the same time interval. By processing these data in all channels, the same number of results concerned with the normal load, the lateral force, the thrust, the side slip angle of the measured tires, the forward velocities of four driven tires and turning radii of the center of gravity of the tractor were obtained for each turn. The averages of the instantaneous data written above were then calculated. The circumferential speeds of four driven tires and the rear fifth wheel were also calculated by counting a time during one pulse signal which included the selected point [1].

Verticaland longitudinalforces] of trontand rear tires from L.._ octagonalring ] 8 channels ] Torquesof frontand rear] axles 2 channels ] Tie-r,x:laxial forces ] of frontand reartires 2channels

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266

H. Itoh et al.

C A L C U L A T I O N OF T H E L O C A T I O N OF T U R N I N G C E N T E R The side slip angles and the slips of the four driven tires were calculated from the location of the turning center which was derived from the steering angles of the fifth front and rear wheels [1]. The rotation and steered motion of the fifth wheels were not stable at high speeds and in sharp turns in the rice field. Figure 3 shows the instantaneous location of the turning center in right turns in 4WS in the rice field. The locations are expressed in terms of the X - Y coordinates (the vehicle fixed system) and the origin is the center of gravity of the tested tractor. The locations of the turning center were distributed in a larger range in 7th gear and at the steering wheel angle of over 400 ° than in other gears and steering wheel angles. This tendency was also observed in left turns in 4WS and in left and right turns in 2WS. It was attributed to a lack of precision in the measurement of the steering angles of the fifth front and rear wheels in 7th gear in the rice field. So, the calculation method explained in the previous paper [1] to obtain the location of the turning center could not be adopted in the above cases. The average X - Y coordinates of the location of the turning center in 7th gear were recalculated by using the turning radii of the four driven tires, which were measured using a tape measure. Hence only the average values of the side slip angles and the slips of the tires were calculated for the 7th gear. Figure 4 shows a turning center in the X - Y vehicle fixed system. Steering angles of the driven tires, 71, c~1, are calculated from the measured steering wheel angles [3]. If the coordinates of the turning center are known, Xn, Yn, Xr~ and Y~ in Fig. 4 are easily calculated. (5th gear)

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The Abscissa (m) Fig. 3. Instantaneous location of turning center in right turns in 4WS in the rice field. (Number in legend indicates steering wheel angle.)

Measurement of forces acting on 4WD-4WS tractor tires

267

X(+)

Front left tire

Y(+) RADrl

.c

.

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-~

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~ X

Yrl

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Fig. 4. Location of turning center in the X - Y vehicle fixed system. (RADn--turning radius of front left tire. RADr~--turning radius of rear left tire, Xrn--X directional distance from turning center to rear left tire axle. Yr~--Y directional distance from turning center to rear left tire axle.)

Relationships between the coordinates of turning center and the turning radii of the tires, for example, the left front and rear tires, are given by equation (1). +

= (rc

-

2 +

-

Xc) 2

= RAD~, (1)

yr21 "b Xr21 = ( Y c - drl) 2 q" ( / r l -

XC) 2

= RAD~b where RADtl and RADa indicate the turning radii of the left front and rear tires. The above equations are nonlinear simultaneous equations. The X - Y coordinates, Yc and Xc, were calculated by the Newton-Raphson method using a computer. The average side slip angles and the average slips of the four driven tires in 7th gear were calculated by the average X - Y coordinates of the turning center. Excepting the calculation of the turning center in 7th gear, the slip and the side slip angle of each tire were calculated by the same method used in the previous paper [1]. SOIL PROPERTIES OF THE RICE FIELD TESTED Soil properties of the rice field are shown in Table 1. Figure 5 shows the result of a plate penetration test. The hand-operated self-recording type soil penetrometer TN-4 was used. Two plates whose length and width are 8 x 7 cm and 6 x 7 cm were tested

268

H.

Itoh et al.

Table 1. Soil properties of the rice field Silty clay loam (Sand 19.6%, Silt 50.1%, Clay 30.3%) 31,68% 25,75% 42.05% 16.30 2.62 23.26° 24.4 kPa

Soil type Moisture content (db) Plasticity limit Liquid limit Plasticity index Specific gravity Internal friction angle Cohesion

{Size t)l the Plate i~, 7(cm) )~ 8(cmn 70

60

5O

40

30

~,

2o

0

2

4

6

8

10

12

14

Sinkage (cm) Fig. 5. Result of plate penetration test. in the preliminary penetration test. As the result of it, the larger plate showed better results for an estimation of the pressure-sinkage relationship. Figure 6 shows the relationship between the shear stress and the deformation of the soil which was obtained by a direct shear apparatus which has a cell of 5 cm diameter. The soil cohesion and the internal friction angle of soil were calculated from the result of the measurement.

TEST RESULTS Figure 7 shows the definition of the signs of measured values. A left steering angle of a tire was defined, as a negative angle. A lateral force acting from the right side of a wheel plane to the left side was positive and a side slip angle deviating rightward from a wheel plane was defined as negative. In this study, only the forces on the right front and rear tires were measured. In the results shown hereafter, where the steering wheel angle is negative, the data relate to the outside tires of the tractor in a turn, and when the steering wheel angle is positive, the results relate to the inside tires. Tire n o r m a l load on the tires

Figure 8 shows the average normal loads on the right front and rear tires in 4WS and 2WS.

Measurement of forces acting on 4 W D - 4 W S tractor tires 120

: -- ~ ............... ~.............. . . . . . . . ~,--.r¢~ t ' : - 4 - ~ - ~ L ~ m [] [] ~ ~ ~ ,,x i r-] [ ] ~ Y X ~ ~ • • • •

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269

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(-) Lateral force

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Fig. 7. Definition of signs of steering angle, side slip angle and lateral force of tire.

In the case of 4WS The outside front tire load (for negative steering wheel angle) increased with the increase of the absolute value of the steering wheel angle and the forward speed. The inside front tire load (for positive steering wheel angle) decreased as the steering wheel angle increased. The outside rear tire load in 4WS in 3rd and 5th gears decreased with the increase of the absolute value of the steering wheel angle, whereas the load did not change so much in 7th gear. The inside rear tire load (for positive

270

H, Itoh et al. 1700

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Steering Wheel Angle (°)

Fig. 8, Average normal loads on the measured tires in the rice field. (In the above legend 3, 5 and 7 indicate the 9osition of the transmission shift lever and F and R indicate "front" and "rear".)

steering wheel angle) in 4WS in 3rd and 5th gears increased as the steering wheel angle increased. On the other hand, the load decreased in 7th gear. The tire load on the outside rear tire was less than that of the inside rear tire up to 5th gear, but this tendency reversed in 7th gear.

In the case of 2WS The test results as to the front tire load in 2WS are similar to that in 4WS except that the outside front tire load decreased suddenly under - 4 0 0 ° of the steering wheel angle in 7th gear. Furthermore the inside front tire load in 7th gear was extremely large at the steering wheel angle of under 350 ° , and suddenly decreased at the steering wheel angles of 400 ° and 450 ° . The outside rear tire load (for negative steering wheel angle) showed the same tendency as that in 4WS. The inside rear tire load (for positive steering wheel angle) in 2WS in 3rd gear changed little, and the tire load decreased as the steering wheel angle increased in 5th and 7th gears. The inside rear tire load was greater than that of the outside rear tire in 3rd gear and this tendency reversed in 7th gear. There was no significant difference between the inside rear tire load and the outside one in 5th gear.

Ratio of normal load on the tire Figure 9 shows ratios of the right front and rear tire load. The ratio is defined as the measured normal load on the tire on the paved road divided by that in the rice •

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Steering Wheel Angle (°)

-400

-200

0

200

400

Steering Wheel Angle (°)

Fig. 9. Ratio of normal load on the tires on the paved road to that in rice field.

7

Measurement of forces acting on 4WD-4WS tractor tires

271

field for the same experimental condition, such as the steering wheel angle and the forward speed of the 4 W D - 4 W S and the 4 W D - 2 W S tractors. As for the front tire load, almost all of the outside front tire loads in the rice field are larger than those on the paved road. This tendency was reversed in the case of the inside front tire. Excepting some large ratios in 2WS, the loads on the front tire on both types of ground became similar. The ratios of the load on the rear tire also came near to 1.0. However, the rear tire ratio has the opposite tendency to the results of the front tire ratio.

Rolling resistance The tested tractor was pulled by another tractor in a straight line under the condition that the clutch disk was disconnected and the drawbar pull was measured. It was assumed that the drawbar pull represented the total rolling resistance of the tested tractor and the rolling resistance of each tire was proportional to its normal load. The measured drawbar pull of 1535.7 N was assumed to be the rolling resistance of the tested tractor. The average rolling resistances of the measured tires are shown in Fig. 10. The tendency of variation of the rolling resistance in relation to the steering wheel angle is to become reverse to that of the tire normal load.

Ratio of rolling resistance Figure 11 shows the ratio of the rolling resistance. The ratio is calculated in the same manner as that of the normal load. As described above, the rolling resistance was derived from the tire normal load. The results of the ratio thus have similar variation to that of the ratio of the tire load. Because the tractor tires have to run on the soft soil in the rice field, the rolling resistance became larger than that on the paved road.

Lateral force and side slip angle Figures 12 and 13 show the average values of the lateral forces and the side slip angles of the right front and rear tires both in 4WS and 2WS. The results of the side slip angle in 7th gear were calculated from the location of the turning center derived from the turning radii of the tires. o

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Fig. 10. The average rolling resistance of the measured tires in the rice field.

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Fig. 11. Ratio of rolling resistance on the tires on the paved road to that in rice field.

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Fig. 12. Average tire lateral force in the rice field.

In the case of 4WS The average lateral force on the outside front tire (for negative steering wheel angle in Fig. 12) became positive and did not show a noticeable change with the increase of the absolute value of steering wheel angle. The lateral force on the inside front tire (for positive steering wheel angle) became negative and decreased with the increase of the steering wheel angle. The average side slip angle of the outside front tire (for negative steering wheel angle in Fig. 13) became negative and decreased with the decrease of the steering wheel angle. The side slip angle of the inside front tire showed the reverse tendency to that of the outside front tire. Figure 14 shows the effects of the side slip angle in 5th gear in 4WS on the instantaneous coefficients of lateral force on the right front and rear tires in left and right turns. The lateral force divided by the normal load on the tire was named the coefficient of lateral force. The side slip angle of the outside front tire (the result of the front right: FR tire in a left turn) decreased, but the instantaneous coefficient did not change so much when the steering wheel angle decreased. As for the coefficient and the side slip angle of the inside front tire (the result of FR tire in a right turn), the plotted data scattered, but the same tendency seen in the average results was observed. From the above results it was found that the moving directions of the outside and inside front tires deviated to the outside of the left and right turns. Then, the lateral forces on the front tires acted to the inside of the turns (Fig. 7).

Measurement of forces acting on 4WD-4WS tractor tires

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Steering Wheel Angle (°)

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Steering Wheel Angle (°) (7th gear)

20

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Steering Wheel Angle (°) Fig. 13. Average tire side slip angle in the rice field in 3rd, 5th and 7th gears. The average lateral forces on the inside and outside rear tires decreased as the absolute value of steering wheel angle increased and became negative at a large absolute value of steering wheel angle (Fig. 12). The average side slip angle of the outside rear tire became slightly negative and changed little with the steering wheel angle. The side slip angle of the inside rear tire became positive and increased with the increase of the steering wheel angle (Fig. 13). Relationships among the instantaneous coefficient of the lateral force, the side slip angle of the inside rear tire (the result of R R tire in a right turn in Fig. 14) and the steering wheel angle were the same as those observed in the average results. As for the inside rear tire, the positive increase of the side slip angle made the lateral force on the tire decreasing and negative.

In the case of 2WS The average lateral forces on the outside and inside front tires became negative, except for the results at the steering wheel angle of - 2 5 0 ° , and decreased with the increase of the absolute value of the steering wheel angle (Fig. 12). The results of the measured average side slip angle of the tires in 2WS were similar to that in 4WS (Fig. 13). Figure 15 shows the effect of the side slip angle in 5th gear in 2WS on the instantaneous coefficients of the lateral force on the right front and rear tires in left and right turns. The results of the front tires (results of FR tire in left and right turns) indicated the same tendency as the results of the average lateral force and the side

274

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al.

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Side Slip Angle of FR Tire (°) (LEFTTURN)

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Fig. 14. Effect of tire side slip angle in 5th gear in 4WS on the instantaneous coefficients of lateral force on the measured tires in left and right turns. (In the above notation, FR represents "front right" and RR expresses "rear right", 250F in the legend means "front tire at the steering wheel angle of +250 °", and so on.)

slip angle. The increase of the side slip angles of the inside front tire brought the decrease and the negative values to the lateral force. The average lateral forces on the inside and outside rear tires became positive and did not show a clear tendency with the steering wheel angle (Fig. 12). It can be seen from Fig. 15, that the instantaneous coefficient of the lateral force on the inside rear tire decreased with the increase of the side slip angle and the steering wheel angle. It was then revealed that the lateral force on the inside rear tire decreases with an increase of the side slip angle. From above results as to the lateral force on the measured tires of both the 4WS and the 2WS tractors, it is clear that all the lateral forces on the tires do not act to the inside of the turns in the rice field as well as on a paved road.

Ratio of the lateral force Figure 16 shows the ratio of lateral force. Ratio of lateral force is defined as lateral force on a paved road divided by that in the rice field. In 4WS, the absolute value of the lateral force in the rice field became smaller than that on the paved road. In 2WS, the large ratio that is seen in 4WS was not observed except the ratio of lateral force of the outside front tire.

Measurement of forces acting on 4WD-4WS tractor tires

275

(RIGHT

TURN)

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Side Slip Angle of FR Tire (°)

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Side Slip Angle of RR Tire (°)

Side Slip Angle of RR Tire (°)

Fig. 15. Effect of tire side slip angle in 5th gear in 2WS on the instantaneous coefficients of lateral force on the measured tires in left and right turns.

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Steering Wheel Angle (°)

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200

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Steering Wheel Angle (°)

Fig. 16. Ratio of lateral force on the tires on the paved road to that in rice field.

Thrust and slip T h e axle t o r q u e d i v i d e d by a tire radius w a s s u p p o s e d to be t h e thrust. F i g u r e s 17 a n d 18 s h o w t h e a v e r a g e thrusts a n d slips o f t h e right front a n d rear tires. T h e a v e r a g e slip in 7th g e a r w a s c a l c u l a t e d f r o m t h e l o c a t i o n o f the t u r n i n g c e n t e r o f the tractor d e r i v e d f r o m the t u r n i n g radii o f t h e f o u r d r i v e n tires.

276

H. I t o h et al. 200

750I

150

.........i + .........tl • 4WS~SFI'"i•"i.........i • If i •,w~ ira! =

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Fig. 17. A v e r a g e thrust o f the tires in the rice field.

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Steering Wheel Angle (°) Fig. 18. A v e r a g e tire slip in the rice field in 3rd, 5th and 7th gears.

In the case of 4WS A s for the thrust of the front tires, no n o t i c e a b l e t e n d e n c y was o b s e r v e d . T h e thrusts b e c a m e positive e x c e p t for the case in 7th gear at a 450 ° steering w h e e l angle. V a l u e s of the nine or 10 instantaneous slips of the tires at o n e turning w e r e included in a w i d e range. T h e variation of the circumferential s p e e d of the fifth w h e e l w a s greater than that of the outside front tire. So, the fluctuation of the rotation of the fifth w h e e l caused the slip to scatter in a large range. F r o m this result it was thought that the average slip, rather than the i n s t a n t a n e o u s slip, w o u l d better express

Measurement of forces acting on 4WD-4WS tractor tires

277

the actual slip. Therefore, the thrust of the tires was analysed with the average slip thereafter. The slip of the outside front tire was not so large and did not change as much with the levels of the steering wheel angle (Fig. 18). The normal load on the tire increased as the absolute value of steering wheel angle increased. Then, the thrust of the outside front tire increased with the increase of the absolute value of steering wheel angle (Fig. 8). The slip of the inside front tire became negative and decreased with the increase of the steering wheel angle in 3rd and 5th gears and became positive in 7th gear. The minimum average slip of the inside front tire was about - 1 5 % . A thrust in the slight skid may become positive. The decrease of the slip in 3rd and 5th gears made the thrust of the inside front tire decrease with the increase of the steering wheel angle. In 7th gear, the slip of the inside front tire was positive and increased with the steering wheel angle but the normal load on the tire decreased with the increase of the steering wheel angle (Fig. 8). Therefore, the thrust of the inside front tire decreased in 7th gear. The thrusts of the outside and inside rear tires (for negative and positive steering wheel angle in Fig. 17) in 4WS became positive and increased with the increase of the absolute value of steering wheel angle. The thrusts were similar among the three gears. The slips of the outside and inside rear tires shown in Fig. 18 became positive except in 7th gear, and increased with the increase of the absolute value of steering wheel angle. The increase of the slips of the rear tires made the thrusts increase.

In the case of 2WS

The thrusts of the outside and inside front tires in 2WS decreased with the increase of the absolute value of the steering wheel angle. The thrusts of the tires became negative for absolute values of the steering wheel angle of over 400 °. The slip of the outside front tire (for negative steering wheel angle in Fig. 18) in 2WS became small in 3rd and 5th gears and did not change with the steering wheel angle. The slip in 7th gear became negative and decreased with the increase of the absolute value of the steering wheel angle. Therefore, the thrust of the outside front tire decreased with the decrease of the slip in 7th gear, but the thrust of the outside front tire did not have a clear relationship with the slip in 3rd and 5th gears. The average slip of the inside front tire in 2WS became negative in 3rd and 5th gears and decreased as the steering wheel angle increased. The slip became positive and increased with the increase of the steering wheel angle in 7th gear. The decrease of the slip and the normal load of the inside front tire made the thrust decrease with the increase of the steering wheel angle. The thrust of the outside and inside rear tires in 2WS shown in Fig. 17 became positive and increased as the absolute value of steering wheel angle increased. The slip of the outside rear tire in 2WS became slightly positive in 3rd and 5th gears and became negative in 7th gear except at the steering wheel angle of -450 °. The increase of the slip made the thrust of the outside rear tire increase with the increase of the absolute value of steering wheel angle in 3rd and 5th gears. The thrust in 7th gear also increased in spite of the decrease of the slip. The slip of the inside rear tire became positive and increased with the increase of the steering wheel angle in all gears. The increase of the slip made the thrust of the inside rear tire increase with the steering wheel angle.

278

H. I t o h et al.

Consideration The thrusts of the rear tires became positive and increased with the increase of the absolute value of steering wheel angle in both 4WS and 2WS. The thrusts of the front tires became negative for larger steering wheel angles in 2WS. The tight corner braking phenomena were observed at the large steering wheel angles in 2WS. It was made clear that the tractive performance of the 4WS tractor is better than that of the 2WS tractor in the steady-state turn in the rice field.

Ratio of the thrust Figure 19 shows the ratio of the thrust of the tires. In the case of 4WS, the thrust of the rear tire in the rice field was greater than that on the paved road and as for the thrust of the front tire on both types of ground, no large difference was observed. The absolute value of thrust of the front tire in 2WS on the paved road was greater than that in the rice field and its sign became negative. The ratio of rear tire thrusts in 2WS resulted in the same tendency as that in 4WS. The front tires produced a braking force when the steering wheel angle was large in the case of the 2WS and this phenomenon was obvious on the paved road. As for the 4WS tractor, the above phenomenon hardly occurred on both types of ground. Therefore, even in the rice field, the tight corner braking phenomenon occurred in 2WS and it was obvious that the 4WS system can prevent the thrust of the front tires from becoming negative.

Turning radius of the center of gravity of the tractor Turning radii in 7th gear were calculated by the location of the turning center derived from the turning radii of the tires. The results in other gears were calculated from the steering angles of the fifth front and rear wheels. Figure 20 shows the average turning radii of the center of gravity of the tractor in 4WS and 2WS. The turning radii in 4WS were smaller than those in 2WS except the case for the steering wheel angle of - 2 5 0 ° in 3rd and 5th gears. The oversteer phenomenon was observed in left turns in 4WS. As described in the previous report [1], the center of gravity is located at the right side of the longitudinal center line of the tested tractors because of the effect of the force transducers which were fixed to only right front and rear tires. This is the reason why the turning radius in the left turn was larger than that in the right turn.

1.2

20 10

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2ws/3

~ ~

2WS ~

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1

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-40

-

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........... i-:,-=....~......... i.......... inni ....... ~,

........ i ...... t ..... ! ...........................

.......

1. ....

-0,2 -400

-200

0

200

400

Steering Wheel Angle (°)

-400

-200

0

200

400

Steering Wheel Angle (°)

Fig. 19. Ratio of thrust of the tires on the paved road to that in the rice field.

Measurement of forces acting on 4WD-4WS tractor tires 5

I

i

lui

....... i............ .............. 1

4.5

i

i

I

i

•

,ws,3

i l •

~

279

! ........... i ........................

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i,,i

i

4

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i~I

il

o ~ws~3 ~--~--i- ...........~........... ~' 2wsls l~......i......... ~ ......... i ........... []

2wsn i

°~ ~

2.5

E ~

.

~ 1.5 1

[".I

-500

-300

i - 1O0

. 0

1O0

i 300

500

Steering Wheel Angle (°) Fig. 20. Average turning radius of the center of gravity of the tested tractor in the rice field.

Consideration As to the normal loads on the front and rear tires, the variation with the steering wheel angle in 4WS was almost similar to that in 2WS in spite of the smaller turning radius of the center of gravity than that in 2WS. The absolute values of lateral forces on the front tires in 4WS were smaller than those in 2WS. The absolute values of lateral forces on the inside rear tire in 7th gear in 4WS were greater than those in 2WS (Fig. 12). This may have been caused by an inadequacy of the steering angle arrangement of the rear tires because the absolute values of the side slip angle of the inside rear tire in 7th gear in 4WS were greater than those in 2WS as shown in Fig. 13. The forces and the slips of the outside tire were measured in left turns, whereas those of the inside tire were measured in right turns in relation to the right side tires. So, according to the average results of the side slip angle, the moving directions of the rear tires deviated to the outside of the turns (Figs 7 and 13). Therefore, it might have shown a better result to give larger steering angles than the initial setting angles to the rear tires. The tight corner braking phenomenon was observed at a large steering wheel angle in 2WS. As for the turning radius of the tractor center of gravity, almost all of the turning radii of the 4WS tractor were smaller than those of the 2WS tractor. The turning radius of the 4WS tractor was reduced to about 80% of that of the 2WS tractor in the rice field and 75% on the paved road on the average as shown in Fig. 21. It was found in the figure that the percentage of turning radius of the 4WS tractor decreased with increasing the absolute value of the steering wheel angle on the paved road and the rice field. The percentage decreased as the forward speed increased in a left turn in the rice field. Finally it was evident that the four wheel steering system could supply a higher tractive performance and higher turnability with smaller turning radius than the two wheel steering system in the steady-state turn in the rice field.

THE SUM TOTAL OF THE FORCES ACTING ON ALL THE TIRES The measured thrusts, rolling resistances and lateral forces acting on all the tires were added in the longitudinal and lateral directions in left turns in the X - Y vehicle

280

H. Itoh

et al. (paved road)

( r i c e field) c~c

140

95

6 1

'

!

'

!

"

'

!

'

!

'

I

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!

'

!

'

!

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~ .~

90

120

_

....... . L . a . . . : ................. [ v : r " :, [ ] i I I-

/k

~

...........

~

~o

40

:

~

3rdgear].i 5th gear 7thgearl::

J:

.................... i ........ i ~ .

.........

:

:

......... J .......... L.........

......

-400

L/

-200

i i 200

~j

~:

75

~7o

Percentage

of turning

:

t

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:

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7th gear J"~"........ i--N---! ........

......... i ......... i ........ i......... i .......... i ........ +......... i.

~ .......

......... ~......... i ........ ~......... i ....... 4.......... i ......... + ......... .......... :5-

~,

6o 55

400

radii of the 4WS

..... ~ " - - i .......... i ~ -o~

...... i......... i ......... !...... ........................... i.......... i ...... !........ . iO

i , i . i ,

-400

Steering Wheel Angle (°) Fig. 21.

.

8O

~......... i .................... i ......... i .......... i ......... ~.......... i ........

...................

t,?i

© ~. []

-200

.

•0

. i . i . i . 200

400

Steering Wheel Angle (°) tractor

to those

of the 2WS

tractor.

fixed system whose origin was located at the center of gravity of the tested tractor as shown in Fig. 22. In this sum total of forces, the lateral force, S and the tractive force, F, which consists of the thrust and the rolling resistance, were considered. The sum of forces in the X - Y directions were given by equations (2) and (3). The sum of the X directional forces:

S U M x = Ell cos 71 + Sfl sin ]/1 + FR COS ]/2 + Fr2 C O S

O~2 +

+

Sf2 sin Y2 + Frl cos oq

+ Srl sin 0q

Sr2 sin a2.

(2)

The sum of the Y directional forces:

S U M v = - Ffl sin ]/1 + Sfl cos 71 - FR sin Y2 + ST2 cos 72 - Frl sin oq + St1 cos at - Fr2 sin 0:2 + Sr2 c o s

o~2.

(3)

The left steering angle of a tire was assumed to be negative and as to the sign of forces, forward tractive force and leftward lateral force were set to positive. The forces acting on only the right front and rear tires were measured in this experiment. It was assumed that the left and right turns were done under the same condition and the measured forces obtained in right turns could be regarded as those of the left front and rear tires in left turns, Therefore the measured forces and the steering angles of the right front and rear tires in right turns were substituted into the above equations in relation to the forces and steering angles of the left front and rear tires. In the substitution, the sign of the lateral force and the steering angle obtained in right turns were reversed to adapt to the left turns. Figure 23 shows the resultant force of the total X and Y directional forces and their directions obtained by the experiment on the paved road and the rice field. The direction of the resultant force was indicated by the angle from the X axis. The angle deviated leftward from the X axis was defined as positive. The resultant force increased with the absolute value of the steering wheel angle in both the steering systems on the paved road and the rice field. The direction of the resultant force was rearward and rightward (to the outside of the left turn) in 3rd and 5th gears in both 4WS and 2WS in the rice field. In 7th gear the resultant force

Measurement of forces acting on 4WD-4WS tractor tires

281

X

dr

_1_

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turned to rearward and leftward in the rice field in 4WS. There were some results whose direction turned to the forward direction in 7th gear in 2WS. On the paved road the resultant force turned to forward and rightward in 3rd and 5th gears in 4WS, whereas the resultant force in 3rd and 5th gears in 2WS turned to rearward and rightward. In 7th gear in both steering systems the direction of the resultant force was forward and leftward. It was found as to the X direction that in the rice field the braking force acted both on the tested tractors except the case in 7th gear in 2WS due to the zero steering angle of the rear tires, whereas the forward force acted on the paved road in 4WS. The 2WS tractor received the braking force in 3rd and 5th gears on the paved road. The braking force in 4WS in the rice field was smaller than that in 2WS and the forward force in 4WS on the paved road was greater than that in 2WS in all gears. For the Y direction, the resultant force turned to the outside of a left turn in 3rd and 5th gears in both steering systems on both the paved road and the rice field. On the other hand the direction was the inside of a left turn in 7th gear in 4WS. The rightward movement of the tractor seemed to cause the leftward force (which was the inside force of the left turn) to generate. Therefore in order to move the tractor to the inside of a turn in 7th gear the lateral force should be small (Fig. 12). This would

282

H. Itoh

et al.

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Fig. 23. Resultant force and its direction obtained by the experiment on the paved road and the rice field in left turns.

be realized by the modification of the steering angle of the rear tires for the 4WS tractor as described in the above section.

CONCLUSIONS In this paper the measuring method and the measured results of forces acting on the tires, slips, side slip angles of the tires and the turning radii of the center of gravity of the 4 W D - 4 W S and 4 W D - 2 W S tractors at the steady-state circular turns on the paved road and the rice field were shown. Furthermore the measured parameters were analysed in relation to the steering wheel angle and the forward speed. Finally the measured forces were added in the longitudinal and the lateral directions. From these analyses the following relationships were clarified. 1. The turning radius of the center of gravity of the 4WS tractor was reduced to 80% of that of the 2WS tractor in the rice field and 75% on the paved road on average. The reduction of the turning radius of the 4WS tractor became obvious on increasing the steering wheel angle. On the paved road there was not a remarkable effect of the forward speed on the turning radius, but the oversteer phenomenon was observed in the case of the 4WS tractor in the rice field. 2. The difference between the dynamic normal load on the outside tire and that on the inside tire in 2WS was less than that in 4WS on the paved road. It seemed that the smaller turning radius caused the imbalance of the normal load on the tires to

Measurement of forces acting on 4WD-4WS tractor tires

283

increase in 4WS. In the rice field however the m e a s u r e d normal loads on the tires in 4WS were similar to those in 2WS in spite of the smaller turning radii than those in 2WS. 3. As for the lateral forces on the tires, it was obvious that all the lateral forces on the tires did not act to the inside of the turn both on the paved road and the rice field. In some cases the lateral forces on the rear tires in 4WS were greater than those in 2WS. It seems that the effective modification of the steering angles of the rear tires would reduce the lateral forces both on the paved road and the rice field. 4. The tight corner braking p h e n o m e n o n was observed in the case of 2WS both on the paved road and in the rice field. The p h e n o m e n o n was especially marked on the paved road. Then, it was clear that the tractive performance of the 4WS tractor was better than that of the 2WS tractor during the steady-state turns especially on the paved road. 5. The resultant force of the forces acting on all the tires in the X - Y plane acted backward in the rice field and forward on the paved road in 4WS. The amount of backward force in 4WS was less than that in 2WS in the rice field and the forward force in 4WS was greater than-that in 2WS. Therefore, the four wheel steering system was found to reduce the braking force in t h e longitudinal direction during the steady-state turn. 6. The lateral component of the resultant force acted to the inside of the turn in 7th gear in both steering systems on the paved road and the rice field. The modification of the steering angle of the rear tires of the 4WS tractor would make the lateral component of the resultant force turn to the outside of a turn and this effect would force the tractor to move to the inside of the turn. 7. F r o m the experiment and its analysis, it became clear that the four wheel steering system could supply the high turnability even in the rice field, and the turnability of the 4WS tractor could be improved by the adequate modification of the steering angle of the rear tires. 8. Although the measurements of the swing angles and the circumferential speed of the fifth wheels were not perfect, the effects of the steering wheel angle, forward speed, slips and the side slip angles of the tires on the three dimensional forces of the tires could be analysed well by this experiment.

REFERENCES [1] H. Itoh, A. Oida and M. Yamazaki, Measurement of forces acting on 4WD-4WS tractor tires during steady-state circular turning on a paved road. J. Terramechanics 31 (5), 285-312 (1994). [2] A. Oida, H. Itoh and M. Yamazaki, Measurement of forces acting on 4WD-4WS farm tractor tires. Proc. llth Int. Conf. of lSTVS, Lake Tahoe, pp. 296-305 (1993). [3] A. Oida and H. Itoh, Study on turning behavior of a 4WS-4WS farm tractor. Proc. 2nd Asia-Pacific Conf. oflSTVS, Bangkok, pp. 397-411 (1988).