Page 103 - Electric Drives and Electromechanical Systems

96 Electric Drives and Electromechanical Systems

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Example 3.4
Determine the minimum diameter of a 1 m long steel shaft required to transmit 3000 Nm,
without exceed the shear stress of 50 MNm 1 or a twist of 0.1 rad m 1 The shear modulus for
steel is given as 80 GNm 2
Using Eqs (3.32) and (3.34) it is possible to calculate the minimum radius for both the
stress and twist conditions,
s ffiffiffiffiffiffiffiffiffiffiffiffi
2T
s max I o 3
r stress ¼ ¼ ¼ 33:7mm
T ps max
r ffiffiffiffiffiffiffiffiffiffi
4 2 TL
r twist ¼ ¼ 22:1mm
Gqp
To satisfy both constraints the shaft should not have a radius of less than 33.7 mm.
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In most systems the effects of transient behaviour can be neglected for selecting the
components of the mechanical drive train, because, in practice, the electrical time
constants are normally smaller than the mechanical time constant. However, it is worth
examining the effects of torque pulsations on a shaft within a system. These can be
generated either by the load (such as a compressor) or by the drive’s power electronics.
While these problems are not commonly found, they must be considered if a large inertia
load has to be driven by a relatively long shaft.
The effect can be understood by considering Fig. 3.17, as the torque is transmitted to
the load, the shaft will twist and carry the load. The twist at the motor end, q m , will be
greater than the twist at the load end, q l , because of the flexibility of the shaft; the

FIG. 3.17 The effect of coupling a motor to a high-inertia load via a flexible shaft.