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An important
consideration in designing high-speed stepping motor
controllers is the effect of the inductance of the motor
windings. As with the torque versus angular position
information, this is frequently poorly documented in
motor data sheets, and indeed, for variable reluctance
stepping motors, it is not a constant! The inductance of
the motor winding determines the rise and fall time of
the current through the windings. While we might hope
for a square-wave plot of current versus time, the
inductance forces an exponential, as illustrated in
Figure 2.10:
Figure 2.10 
The details
of the current-versus-time function through each winding
depend as much on the drive circuitry as they do on the
motor itself! It is quite common for the time constants
of these exponentials to differ. The rise time is
determined by the drive voltage and drive circuitry,
while the fall time depends on the circuitry used to
dissipate the stored energy in the motor winding.
At low
stepping rates, the rise and fall times of the current
through the motor windings has little effect on the
motor's performance, but at higher speeds, the effect of
the inductance of the motor windings is to reduce the
available torque, as shown in Figure 2.11:
Figure 2.11 
The motor's
maximum speed is defined as the speed at which
the available torque falls to zero. Measuring maximum
speed can be difficult when there are resonance
problems, because these cause the torque to drop to zero
prematurely. The cutoff speed is the speed above
which the torque begins to fall. When the motor is
operating below its cutoff speed, the rise and fall
times of the current through the motor windings occupy
an insignificant fraction of each step, while at the
cutoff speed, the step duration is comparable to the sum
of the rise and fall times. Note that a sharp cutoff is
rare, and therefore, statements of a motor's cutoff
speed are, of necessity, approximate.
The details
of the torque versus speed relationship depend on the
details of the rise and fall times in the motor
windings, and these depend on the motor control system
as well as the motor. Therefore, the cutoff speed and
maximum speed for any particular motor depend, in part,
on the control system! The torque versus speed curves
published in motor data sheets occasionally come with
documentation of the motor controller used to obtain
that curve, but this is far from universal practice!
Similarly,
the resonant speed depends on the moment of inertia of
the entire rotating system, not just the motor rotor,
and the extent to which the torque drops at resonance
depends on the presence of mechanical damping and on the
nature of the control system. Some published torque
versus speed curves show very clear resonances without
documenting the moment of inertia of the hardware that
may have been attached to the motor shaft in order to
make torque measurements.
The torque
versus speed curve shown in Figure 2.11 is typical of
the simplest of control systems. More complex control
systems sometimes introduce electronic resonances that
act to increase the available torque above the motor's
low-speed torque. A common result of this is a peak in
the available torque near the cutoff speed. |
