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We present a new approach for generating fast simulation models of electromagnetic (EM) devices that contain moving components and magnetic materials with nonlinear properties. Our approach is based on generating low-dimensional simulation models that approximate the original spatially discretized models of electromagnetic field and their variations under conditions of component movement and material nonlinearity. The movement of the modeled device components is simulated by coupling the reduced-order EM field models weakly to the mechanical equations. We have successfully used our approach to generate a fast simulation model of a simple electromagnetic device with a moving component and nonlinear material properties.