The Schwarz-Christoffel Analytical Method Applied to Electric Machine Slot Shape Optimization

The Schwarz-Christoffel method is implemented in a Monte Carlo electric machine slot shape search algorithm attempting to maximize average torque under constrained flux density in a two-dimensional developed machine cross-section. A fixed slot current density is enforced, and the slot shape is varied over a twelve-variable search space. Rotor motion is simulated by changing the position of the machine air gap polygon's rotor vertices while maintaining both a simply-connected polygon and a 90deg shift between stator and rotor q-axis currents. Rotor force is calculated by integrating Maxwell's stress tensor along a closed path enclosing the rotor. A Monte Carlo search with 11,050 points is carried out and a minimum cost horizon curve is deduced from the data. A brief history and context for the Schwarz-Christoffel approach is given with a comparison to the finite element and boundary element methods.