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If a rigidly
mounted stepping motor is rigidly coupled to a
frictionless load and then stepped at a frequency near
the resonant frequency, energy will be pumped into the
resonant system, and the result of this is that the
motor will literally lose control. There are three basic
ways to deal with this problem:
Controlling
resonance in the mechanism
Use of
elastomeric motor mounts or elastomeric couplings
between motor and load can drain energy out of the
resonant system, preventing energy from accumulating to
the extent that it allows the motor rotor to escape from
control.
Or, viscous
damping can be used. Here, the damping will not only
draw energy out of the resonant modes of the system, but
it will also subtract from the total torque available at
higher speeds. Magnetic eddy current damping is
equivalent to viscous damping for our purposes.
Figure 2.8
illustrates the use of elastomeric couplings and viscous
damping in two typical stepping motor applications, one
using a lead screw to drive a load, and the other using
a tendon drive:
Figure 2.8 
In Figure
2.8, elastomeric moter mounts are shown at a and
elastomeric couplings between the motor and load are
shown at b and c. The end bearing for the lead screw or
tendon, at d, offers an opportunity for viscous damping,
as do the ways on which the load slides, at e. Even the
friction found in sealed ballbearings or teflon on steel
ways can provide enough damping to prevent resonance
problems.
Controlling
resonance in the low-level drive circuitry
A resonating
motor rotor will induce an alternating current voltage
in the motor windings. If some motor winding is not
currently being driven, shorting this winding will
impose a drag on the motor rotor that is exactly
equivalent to using a magnetic eddy current damper.
If some
motor winding is currently being driven, the AC voltage
induced by the resonance will tend to modulate the
current through the winding. Clamping the motor current
with an external inductor will counteract the resonance.
Schemes based on this idea are incorporated into some of
the drive circuits illustrated in later sections of this
tutorial.
Controlling
resonance in the high-level control system
The high
level control system can avoid driving the motor at
known resonant frequencies, accelerating and
decelerating through these frequencies and never
attempting sustained rotation at these speeds.
Recall that
the resonant frequency of a motor in half-stepped mode
will vary by up to 20% from one half-step to the next.
As a result, half-stepping pumps energy into the
resonant system less efficiently than full stepping.
Furthermore, when operating near these resonant
frequencies, the motor control system may preferentially
use only the two-winding half steps when operating near
the single-winding resonant frequency, and only the
single-winding half steps when operating near the
two-winding resonant frequency. Figure 2.9 illustrates
this:
Figure 2.9 
The darkened
curve in Figure 2.9 shows the operating torque achieved
by a simple control scheme that delivers useful torque
over a wide range of speeds despite the fact that the
available torque drops to zero at each resonance in the
system. This solution is particularly effective if the
resonant frequencies are sharply defined and well
separated. This will be the case in minimally damped
systems operating well below the cutoff speed defined in
the next section. |
