A brush model for detailed commutation analysis of universal motors

A brush model for commutation analysis of small commutator motors is presented. Equivalent circuits of the brush are established for the cases of one coil shorted and two coils shorted by one brush, and a strategy to obtain their elements is proposed. This uses a fast and dedicated finite-difference program to calculate the effective brush resistance between all pairs of terminals. The treatment of the boundary conditions is critical in this process. The resulting terminal resistances are regarded as combinations of a set of internal resistances and this nonlinear relationship is inverted to obtain the internal resistors using a modified Newton-Raphson´s method. Results are presented showing the influence of anisotropy and geometry, and a simplified example of commutation analysis using the model established is given.