Page 55 - Electric Drives and Electromechanical Systems
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48 Electric Drives and Electromechanical Systems
Table 2.2 Rolling resistance coefficients and static friction coefficient for
a number of combinations of wheel and surface.
Coefficient of rolling Static coefficient of
Wheel surface combination resistance, C rr friction, m
Steel on steel 0.0005 0.5
Hard rubber on concrete 0.01e0.02 0.6e0.8
BMX bicycle tires on road surface 0.0055 0.9
The grade resistance is determined by the slope and mass of the vehicle,
G r ¼ mg sin a (2.22)
The final term, F a , is the force required to accelerate the vehicle,
F a ¼ m € x (2.23)
Summing Eqs (2.21)e(2.23) gives the force that is required to drive the vehicle up a
slope, while accelerating, this can be converted to the required wheel torque, T d , if there
are n d driven wheels, each with a radius, r, then,
E t
T d ¼ r (2.24)
n d
The final step in the process is to determine if the vehicle can transmit the torque to
the ground without slipping, this depends on the static friction coefficient, m, as dis-
cussed in Section 2.5, and the load on each of the wheels. If it is assumed that the weight
of the vehicle is evenly distributed over all wheels, n tot , which can equal or exceed n d , the
maximum possible tractive effort must be greater that the tractive effort required at the
time,
mgmr sin a
T max ¼ > T d (2.25)
e
n tot
Once the wheel torque requirement has been determined, it will be possible to specify
the components of the associated power train and motor. It should be noted that the
sizing process is iterative, as following the selection of motors, gearboxes and batteries
has been undertaken, the torque requirements need to be verified.
nnn
Example 2.2
A small four wheeled mobile robot, with a mass of 5 kg, is required to climb a slope of 8 degrees
2
while accelerating at 0.05 ms . If the slope has a coefficient of rolling friction of 0.02 and a
static friction coefficient of 0.6, can the slope be overcome if only two wheels are driven. The
wheels have a radius of 0.1 m.
The total tractive effort is firstly calculated:
R r ¼ mgC rr cos a ¼ 0:97 N
