Chapter 8: variable - reluctance machines and stepping motors

Variable - Reluctance Machines

and Stepping Motors

This lecture note is based on the textbook # 1. Electric Machinery - A.E. Fitzgerald, Charles Kingsley, Jr., Stephen D. Umans- 6th edition- Mc Graw Hill series in Electrical Engineering. Power and Energy

• Variable-reluctance machines (VRMs) are perhaps the simplest of electrical machines. They consist of a stator with excitation windings and a magnetic rotor with saliency. Rotor conductors are not required because torque is produced by the tendency of the rotor to align with the stator- produced flux wave in such a fashion as to maximize the stator flux linkages that result from a given applied stator current. Torque production in these machines can be evaluated by using the techniques of Chapter 3 and the fact that the stator winding inductances are functions of the angular position of the rotor.
• Although the concept of the VRM has been around for a long time, only in the past few decades have these machines begun to see widespread use in engineering applications. This is due in large part to the fact that although they are simple in construction, they are somewhat complicated to control. The position of the rotor must be known in order to properly energize the phase windings to produce torque. It is the widespread availability and low cost of micro and power electronics that has made the VRM competitive with other motor technologies in a wide range of applications.
• By sequentially exciting the phases of a VRM, the rotor will rotate in a step- wise fashion, rotating through a specific angle per step. Stepper motors are designed to take advantage of this characteristic. Such motors often combine the use of a variable-reluctance geometry with permanent magnets to produce increased torque and precision position accuracy.

8.1 BASICS OF VRM ANALYSIS

• VRMs can be categorized into two types: singly- salient and doubly-salient. In both cases, their most noticeable features are that there are no windings or permanent magnets on their rotors and that their only source of excitation consists of stator windings.
• To produce torque, VRMs must be designed such that the stator-winding inductances vary with the position of the rotor.
• Figure 8.1a shows a cross-sectional view of a singly-salient VRM, which can be seen to consist of a nonsalient stator and a two-pole salient rotor, both constructed of high-permeability magnetic material. In the figure, a two-phase stator winding is shown although any number of phases is possible.
• Figure 8.2a shows the form of the variation of the stator inductances as a function of rotor angle θm for a singly-salient VRM of the form of Fig. 8.1 a. Notice that the inductance of each stator phase winding varies with rotor position such that the inductance is maximum when the rotor axis is aligned with the magnetic axis of that phase and minimum when the two axes are perpendicular. The mutual inductance between the phase windings is zero when the rotor is aligned with the magnetic axis of either phase but otherwise varies periodically with rotor position.
• Figure 8.lb shows the cross-sectional view of a two-phase doubly-salient VRM in which both the rotor and stator have salient poles. In this machine, the stator has four poles, each with a winding. However, the windings on opposite poles are of the same phase; they may be connected either in series or in parallel. Thus this machine is quite similar to that of Fig. 8.1a in that there is a two-phase stator winding and a two-pole salient rotor. Similarly, the phase inductance of this configuration varies from a maximum value when the rotor axis is aligned with the axis of that phase to a minimum when they are perpendicular.
• Unlike the singly-salient machine of Fig. 8.1 a, under the assumption of negligible iron reluctance the mutual inductances between the phases of the doubly-salient VRM of Fig. 8.1 b will be zero, with the exception of a small, essentially-constant component associated with leakage flux. In addition, the saliency of the stator enhances the difference between the maximum and minimum inductances, which in turn enhances the torque-producing characteristics of the doubly-salient machine. Figure 8.2b shows the form of the variation of the phase inductances for the doubly-salient VRM of Fig. 8.lb.
• The relationship between flux linkage and current for the singly-salient VRM is of the form