Modeling of a Rotary Actuator Using Elliptical Coordinates and Differential Flux Tubes

Analytical models are useful in the design of electromagnetic devices. In this article, a model is developed for a rotary actuator whose stator curvature is elliptically shaped to have a reluctance torque that restores the rotor to the maximum torque per ampere position. The total torque is decomposed into the coil torque and a reluctance torque. The rotor is a permanent magnet represented by equivalent Amperian currents. The stator geometry is simplified to an ellipse having surface current densities at the interpolar regions that are equivalent to the stator currents. Then, the field solution within the ellipse is obtained using Laplace’s equation in elliptical coordinates so that the coil torque can be obtained by the Lorentz force. The reluctance torque is derived by the energy method and an approach referred to here as differential flux tubes, which is similar to the use of conventional flux tubes in magnetic equivalent circuits. A rotating reference frame on the rotor is also adopted to simplify the mathematics. The finite element method (FEM) is also used in the field analysis and development of the proposed model. Finally, the actuator is prototyped, and experimental results are employed to evaluate the results obtained from the analytical model and FEM.