Model for Electromagnetic Actuator With Significant Fringing Using Minimal Fitting Parameters

In a number of electromagnetic actuators, the stator and translator are structured to create highly nonlinear fringing flux to generate force that varies linearly with displacement. Reliable prediction of such force requires an accurate model for the fringing flux. Assuming that saturation is neglected and the fringings are elliptical, a reluctance model for fringing flux is derived that depends on displacement, material properties, and one tuning parameter describing the shape of the ellipse. Fringing-related reluctances are assembled with the reluctances of the regions with linear flux to predict magnetic field, energy, and force. Upon tuning, the force predicted by the model is within 10% of the simulated and measured forces.