Page 576 - Mechanical Engineers' Handbook (Volume 2)

5 Stepper Motors 567

Figure 17 Bipolar-wound stepper motor.

5.3 Mathematical Model of a Permanent-Magnet Stepper Motor
The mathematical model of a stepper is generally much more complex than a conventional
dc motor since the voltages applied to the various phases change in a discontinuous fashion.
These discontinuities in the applied voltages result directly in corresponding discontinuities
in the phase currents. This effect is further complicated by the spatial variation of the mag-
netic reluctance. Reference 20 gives detailed mathematical models for permanent-magnet
and variable-reluctance stepper motors. Computer codes (in FORTRAN IV) are available in
Ref. 20 for these stepper motors.
The mathematical models of stepper motors are inherently nonlinear due to disconti-
nuities in input voltages and due to the transcendental spatial variation of the self and mutual
inductances. Hence these models do not lend themselves to a frequency-domain analysis.

5.4 Numerical Example
Table 6 gives the specifications of a Crouzet model no. 82 940.0 stepper motor. The motor
2
is to be used to drive a rotary viscometer that has a rotary inertia of 3.88 10 3 in. oz s /
2
rad (2.74 10 5 N m s /rad), a constant frictional torque of 1.3 in. oz (9.18 10 3
N m). and a viscous damping coefficient of 0.96 in. oz s/rad (6.8 10 3 N m s/rad).
The motor is required to accelerate the viscometer from 5.2 to 13.1 rad/s in a maximum
of 0.1 s.
The maximum torque developed by the motor may be estimated as follows:
d
T (J J ) m B T (33)
m m L L m ƒ
dt
where B rotary damping coefficient of viscometer cup
L
J polar moment of inertia of viscometer cup
L
J polar moment of inertia of motor
m