Page 220 - Electric Drives and Electromechanical Systems

216 Electric Drives and Electromechanical Systems

The permanent magnets of the hybrid motor will produce a continuous detent
torque, ensuring that the motor retains its position without the necessity of
energising the drive. This is particularly useful for fail-safe applications, for
example, following a power failure.
The rotor’s mass in variable reluctance stepper motors is less than its mass in
hybrid motors; this ensures that the speed of response to a change in the demand
is maximised. As will be discussed later, the inertia determines the mechanical
resonance of the drive system the lower is the inertia, the higher is the allowable
frequency of operation.
While a linear motion can be obtained by the combination of a ball screw with any
type of stepper motor, giving a low-cost linear actuator, the liners stepper motor
has a number of performance advantages. However, it should be noted that as with
any linear motor, vertical operation can prove problematic.

8.2 Static-position accuracy

The majority of stepper-motor applications require accurate positioning of a mechanical
load, for example within a small industrial robot. An externally applied load torque will
give rise to positional errors when the motor is stationary, since the motor must develop
sufficient torque to balance the load torque, otherwise it will be displaced from its
equilibrium position. This error is noncumulative, and it is independent of the number
of steps which have been previously executed. As the system’s allowable error will
determine which motor is selected for a particular application, the relationship between
the motor, the drive and the load must be understood.
Fig. 8.5 shows the relationship between the generated torque and the rotor position
when a single phase is excited. At the point where the rotor and the stator teeth of the
excited phase are in total alignment, no torque will be produced. As the rotor is moved
away, a restoring torque results. The static-torque-rotor position characteristics repeats
with a wavelength of one-rotor-tooth pitch; thus, if the rotor is moved by greater than 1/
4 tooth pitch, the rotor will not return to the initial position, but it will move to the next
stable position. The shape of the curve is a function of the mechanical and the magnetic
design of the motor, but it can be approximated to a sinusoidal curve with the peak value
determined by the excitation current. If an external load is applied to the motor, the rotor
must adopt an equilibrium position where the generated torque is equal to the external
load torque. If the load exceeds the peak torque, the position cannot be held. The posi-
tional error introduced by an external load can be approximated by,
1
sin ð T L =T pk Þ
q e ¼ (8.4)
R t
where R t is the number of rotor teeth. The value of q e can be reduced by either increasing
the peak torque, T pk , by an increased winding current, or by selecting a different motor
with a larger number of rotor teeth.