1. AGUS HARYANTO

2. TERMINOLOGY
Vertical load or weight on the wheel, W is the vertical force through the axle.
Travel (output) speed, V is the linear speed of driven wheel;
Travel speed < Rotational speed x Rolling radius
Rolling radius, r, is defined in terms of the ‘distance traveled per revolution’/2π under “zero conditions.”
Wheel-slip, i = (Vo – V)/Vo atau i = (mo – m)/mo
Input torque, T, is the (rotational) input effort on driven wheel which is converted to (linear) output effort (force or drawbar pull);
Drawbar pull < Input torque/Rolling radius

3. TERMINOLOGY
Rolling (motion) resistance, R is the force opposing motion of the wheel (in the horizontal direction) that arises from the non- recoverable energy expended in deforming the surface and wheel.
Tractive force, H is the horizontal reaction on a driven wheel by the soil in the contact area; it is equal and opposite to the horizontal force generated by the wheel on the soil.
Drawbar pull, P is the horizontal force at the axle generated by a driven wheel. From H = P + R  P = H – R
Towing force is the force to move a freely rolling wheel over the surface and is equal and opposite to the rolling resistance. P

4. Operational states of a wheel
Towed
Wheel is towed with zero opposing external torque; the unknown parameter is the R.
Self-propelled
Wheel is driven by external input torque to overcome R and to propel with no drawbar pull. The unknown is R.
Driven
Wheel is driven by external input torque and to develop a drawbar pull. The unknown is i. Extreme case: no move.
Braked
Wheel is towed against an opposing, external torque. The unknown is i. Extreme case: wheel skids.

8. THEORETICAL PREDICTION
Pz = [(Kc/b) + K] Zn
 log Pz = log [(Kc/b) + K] + n log Z
z is vertical soil deformation (sinkage)
Kc and Kφ are soil sinkage moduli
n is soil sinkage exponent
b is the width of the plate

9. SOIL APARATUS

11. WORK TO DEFORM SOIL

12. SOFT WHEEL ON SOFT SURFACE
Consider the work done in towing such a wheel a distance, l against the rolling resistance, R. In simple terms, if this is equal to the work done on forming the rut as for the plate, length l, width b pressed into the soil, then:

14. SOFT WHEEL ON SOFT SURFACE
Untuk n = 1

15. RIGID WHEEL ON SOFT SURFACE

17. TRACTIVE FORCE
Shear stress - deformation characteristic for soil S = Smax (1 – e-j/k) Smax = (c + σ tan φ) S = (c + σ tan φ) (1 – e-j/k) Where: c = soil cohesion φ = angle of internal friction σ = normal stress j = shear deformation k = shear deformation modulus

20. Analysis of track

21. Graphic H vs W

22. WORK EXAMPLES

23. Solution b

24. EXAMPLE 2
A rubber wheel carrying a load W of 5.4 kN has an effective ground contact area A of 0.09 m2 over which the pressure may be assumed to be uniform. The soil and rubber / soil strength characteristics are shown in Figure What is the maximum pull which can be generated by the wheel if:
the wheel has lugs which engage the soil?
the lugs are removed?

26. SOLUTION

27. Analysis of track with slip
H = Hmax (X)
Note:
For rubber tire, contact area
A = 0.78 b l.

28. DRAWBAR PULL, P = H - R
(i) tracks compared to 2WD on cultivated (loose) soil which shows the effect of area and length of contact patch and of weight
(ii) tracks on stubble (firm) compared to cultivated (loose) soil which shows the effect of soil strength and rigidity (deformation modulus)
(iii) 4WD compared to 2WD on cultivated (loose) soil which shows the effect of area and weight.

31. TUGAS (PR, individual)
Buatlah kurva gaya traksi (H) vs. selip (i) dan drawbar pull (P) vs. selip (i). Data berikut berlaku

33. DRAWBAR POWER Wheel-slip - drawbar power

34. EXAMPLE

35. optimum wheel-slip