Analytic model for a nonlaminated cylindrical magnetic actuator including eddy currents

The eddy currents induced within a nonlaminated cylindrical magnetic actuator by a changing field have a fundamental influence on the actuator´s performance. Understanding of these dynamics is essential in designing high-performance actuators and developing control algorithms for them. This paper presents an analytical approach to modeling the relationship between applied magnetomotive force and mechanical force. The approach is based on dividing the actuator into elements according to the flux distribution inside the actuator and finding the frequency-dependent reluctance of the flux paths of each element. An analytic model and its half-order simplification are derived, both of which are explicitly dependent on actuator material and geometric properties. Performance predictions from both analytic models are compared with finite-element analysis, demonstrating the accuracy of the models.