Comparison between analytical and numerical methods of calculating tooth ripple losses in salient pole synchronous machines

Over the last two decades, analytical methods for solving problems involving eddy currents have been largely replaced by numerical ones such as finite elements or finite differences. This process has been particularly necessary in situations where magnetic saturation is present. In the present paper, the application of analytical and numerical methods to an electromagnetic problem requiring an accurate representation of saturation is examined. The problem considered is that of tooth-ripple losses in salient-pole synchronous machines for the situation where the pole pitch is much greater than the armature slot pitch so that the applied DC field can be taken as uniform. To calculate these losses, several analytical methods have been developed over a period of many years. Two such methods, one devised by Oberretl [1] and a modified version of the considerably older one-dimensional approach of Gibbs [2], are compared with results obtained from the finite-element and finite-difference methods. Using a time-stepping finite-difference calculation, the influence of moving boundaries and the imposed DC held are taken into account for the first time in this tooth-ripple calculation. A saturation factor is defined that allows the designer to calculate the tooth-ripple losses of solid salient-pole synchronous machines for a aide range of machine size taking magnetic saturation into account. To verify the theory, the results are compared with measurements on a small model. These measurements were done using a torque meter placed between the model and a DC drive motor and were cross-checked by the Poynting vector method [3]. Rules and limits are given for the use of the analytical methods.