Abstract
Tractive performance of wheel type tractor operating directly uphill was investigated, basing ground-to-tire interaction:
1. Traction equation for front-(i=1) and rear-wheels (i=2) is expressed as:
Fi=(Ci+λi·ζmax, i)fi(si) (i=1, 2)…(1)
where, Fi is the traction component of soil reaction, Ci the adhesion, ζmax, i the maximum value of tractive coefficient at a driving wheel, and fi(si) the function of s and ground-to-tire coefficients. Then, supporting components of the soil reactions λi against the front or rearwheels when the tractor is operating uphill are expressed as λi(s), which is the function of s, ground-to-tire coefficients and slope of the field φ, eliminating Fi and D (tractive force) from Eq. (1) and three equations of motions of a tractor.
In this paper, Ci and ζmax, i are also called ground-to-tire coefficients.
2. Substituting Eq. (1), λ1(s), and λ2(s) into the force equation in the direction of motion, the tractive force of tractor DT [kg] is expressed as:
DT=∑2i=1(Ci+λi(s)·ζmax, i)·fi(si)-W(sinφ+x/g)…(2)
where, W is the weight of tractor and x the travelling acceleration. In case of rear-wheel-drive tractor, C1=0, f1(s1)=-μ1/ζmax, i.
3. Tractive coefficient of tracfor ζT is expressed as:
ζT=DT/W…(3)
4. Tractive horsepower of tractor HD is exprssed as:
HD=DTx/75=DT/75·Ai(1-si)·θi(i=1, 2)…(4)
where, Ai [m] is the rolling radius of a wheel and θi [rad/sec] the rotating speed of a wheel.
5. Power coefficient of tractor indicating output power of traction work ξT is expressed as:
ξT=ζT(1-s2)…(5)
6. Brake horsepower of tractor engine HE is expressed as:
HE=A2/75Ξ·Q·θ2…(6)
where,
Q=Q1+Q2
Q1=1-s2/1-s1{I1·θ1/A1+(C1+λ1(s)·ζmax, 1)f1(s1)+μ1·λ1(s)}
Q2 I2·θ2/A2+(C2+λ2(s)·ζmax, 2)f2(s2)+μ2·λ2(s)
Ξ is the transmission efficiency, Ii the mass moment of inertia about axle and μi the coefficient of rolling resistance. In case of rear-wheel drive tractor, Q1=0.
7. Tractive efficiency of tractor ηT is expressed as:
ηT=HD/HE=Ξ(1-s2)D/Q…(7)
Parameter ηT expresses power efficiency of traction work of tractor.
8. The relations between ηT and ζT, and ξT and ζ
