Many experiments of relations between tractive force, tractive horse power, tractive efficiency and slippage of tractor rigid wheels are reported. But few of these relations are explained theoretically.
Some qualitative explanations are tried on these relations, supposing tractive forces of a tractor depend on slippage of driving wheels.
(1) Tangential component
vt and horizontal component
vh of peripheral velocity
v0 at any point of a wheel may be written as follows (Fig. 1),
v
t=v
0-vcosρ
v
h=v
0cosρ-v
Average values of
vt and
vh along contact part of the wheel with soil,
vt and
vh, are calculated. Then it is assumed that brake force
Nt at the driving wheel is proportional to
vtn and tractive force
Nh is proportional to
vhn.
N
t=kv
0n(bS+a)
n……(3)
N
h=kv
0n(S-a)
n……(4)
a=(α-sinα)/α, b=sinα/α
where
S is slippage of the wheel. From these equations many relations are deduced as follows. (2) Equation (4) indicates that tractive force increases as slippage increases, as shown in many experiments of literature 4), 5), 6).(Fig 2-
a)
(3) The relation between tractive horse power
H and slippage is,
H=k/75v
0n+1(S-a)
n(1-S)……(5)
From equation (8), the maximum value of tractive horse power
H about slippage will exist, as shown experimentally in literature 7), 8). (Fig 2-
b)
(4) The tractive horse power is expressed in other form concerning tractive force;
H=v
0/75N
h{1-a-1/v
0(N
h/k)
1/n}……(7)
A tendency of relation between
H and
Nh is shown as Fig. 2-
C, and an experiment in literature 9) may be explained by equation (7).
(5) Brake horse power is from equation (3),
L=k/75v
0n+1(bS+a)
nTherefore tractive efficiency is;
η=H/L=(S-a/bS+a)
n(1-S)……(8)
Efficiency η is 0 at
S=1 and η may be the highest near S=0. Thus η decreases as
S increases, as shown in literature 10). (Fig. 2-
d)
(6) Tractive efficiency η is noted in other form concerning tractive force
Nh,
η=N
h/N
t{1-a-1/v
0(N
h/k)
1/n}……(9)
From this equation there is the maximum value of η, as shown in literature 9), 11). (Fig. 2-
e)
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