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The torque
versus position curve shown in Figure 2.1 does not take
into account the torque the motor must exert to overcome
friction! Note that frictional forces may be divided
into two large categories, static or sliding friction,
which requires a constant torque to overcome, regardless
of velocity, and dynamic friction or viscous drag, which
offers a resistance that varies with velocity. Here, we
are concerned with the impact of static friction.
Suppose the torque needed to overcome the static
friction on the driven system is 1/2 the peak torque of
the motor, as illustrated in Figure 2.4.
Figure 2.4 
The dotted
lines in Figure 2.4 show the torque needed to overcome
friction; only that part of the torque curve outside the
dotted lines is available to move the rotor. The curve
showing the available torque as a function of shaft
angle is the difference between these curves, as shown
in Figure 2.5:
Figure 2.5 
Note that
the consequences of static friction are twofold. First,
the total torque available to move the load is reduced,
and second, there is a dead zone about each of
the equilibria of the ideal motor. If the motor rotor is
positioned anywhere within the dead zone for the current
equilibrium position, the frictional torque will exceed
the torque applied by the motor windings, and the rotor
will not move. Assuming an ideal sinusoidal torque
versus position curve in the absence of friction, the
angular width of these dead zones will be:
d = 2 ( S / ( /2)
) arcsin( f / h ) = ( S / (/4)
) arcsin( f / h )
where:
d -- width of
dead zone, in radians
S -- step angle, in radians
f -- torque needed to overcome static
friction
h -- holding torque
The
important thing to note about the dead zone is that it
limits the ultimate positioning accuracy! For the
example, where the static friction is 1/2 the peak
torque, a 90° per step motor will have dead-zones 60°
wide! That means that successive steps may be as large
as 150° and as small as 30°, depending on where in the
dead zone the rotor stops after each step!
The presence
of a dead zone has a significant impact on the utility
of microstepping! If the dead zone is x° wide, then
microstepping with a step size smaller than x° may not
move the rotor at all. Thus, for systems intended to use
high resolution micro stepping, it is very important to
minimize static friction. |
