A Method of Calculation of Critical Stepping Rate in Stepping Motor

Abstract

This paper presents a simple method to calculate the critical stepping rate of a variable reluctance stepping motor, of which the rotor is made up of mild steel cores. The stepping rate is a very important design parameter of a motor of this type.
In this analysis, a critical stepping rate is determined by equating the average torque generated in the coils in one stationary cycle to the external load torque. Here the Fourier series expansion of the normalized current and voltage in a phase is employed to calculate the average normalized torque. As a result, an algebraic equation for coefficients in Fourier expansion of a normalized phase current is derived. The average normalized torque is iteratively calculated for various switching electrical angles so that it is maximized, since it depends on the switching electrical angle with respect to the equilibrium angular position and the rotor normalized velocity.
It can be said, in comparison with the exact numerical solutions of the system equations of a stepping motor with 2 phase or 1-2 phase excitation, that at most the second or third term of Fourier series expansion will be needed to approximate the motor dynamics used to determine the critical stepping rate.