Page 221 - Electric Drives and Electromechanical Systems

Chapter 8 Stepper motors 217

FIG. 8.5 The static-torque rotor-position characteristics of a stepper motor showing the static position error, q e
due to the applied load T L , the motor stiffness is given by the gradient, K.
Another measure of the motor’s static-position error is to use the concept of stiffness,
which is given by the gradient of the static-torque-position characteristic at the equilib-
rium position, K. The stiffness is given by the gradient of the torque-position characteristic
at the equilibrium point; so, for a given displacement, the load torque that the motor will
be able to support is given by
(8.5)
T ¼ K q e
In some motors the torque-position characteristic is shaped to result in a different
stiffness for different displacements; in this case, the stiffness which is closest to the
expected amplitude must be selected.

nnn
Example 8.1
Determine the static position error for a stepper motor with eight rotor teeth, rated at 1.2 Nm,
when a load of 0.6 Nm is applied.
The approximate positional error is defined by Eq. (8.4), hence
0:6
sin 1 T L sin 1
T pk 1:2 o
q e ¼ ¼ ¼ 3:8
R T 8
In practice this value is less than that experienced in an actual system, due to the approxi-
mations used.
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8.3 Torque-speed characteristics

In the application of a stepper motor to a motion-control system, the designer needs
knowledge of the motor’s torque-speed characteristics. This information is supplied by