A new predictor-corrector approach for the numerical integration of coupled electromechanical equations

In this paper, a new approach for the numerical solution of coupled electromechanical problems is presented. The structure of the considered problem consists of the low-frequency integral formulation of the Maxwell equations coupled with Newton-Euler rigid-body dynamic equations. Two different integration schemes based on the predictor-corrector approach are presented and discussed. In the first method, the electrical equation is integrated with an implicit single-step time marching algorithm, while the mechanical dynamics is studied by a predictor-corrector scheme. The predictor uses the forward Euler method, while the corrector is based on the trapezoidal rule. The second method is based on the use of two interleaved predictor-corrector schemes: one for the electrical equations and the other for the mechanical ones. Both the presented methods have been validated by comparison with experimental data (when available) and with results obtained by other numerical formulations; in problems characterized by low speeds, both schemes produce accurate results, with similar computation times. When high speeds are involved, the first scheme needs shorter time steps (i.e., longer computation times) in order to achieve the same accuracy of the second one. A brief discussion on extending the algorithm for simulating deformable bodies is also presented. An example of application to a two-degree-of-freedom levitating device based on permanent magnets is finally reported.