This paper describes an advanced method of modeling synchronous machines, in particular interior permanent magnet (IPM) motors. The dynamic motor model considers magnetic saturation and the dependence of electrical, magnetic and mechanical quantities on the rotation angle, and can be integrated into multidisciplinary system simulations. A set of magnetic finite element method (FEM) solutions is used to set up the model based on radial basis function (RBF) interpolation. The presented motor model can be used to simulate any time-stepping cases, such as studies of field weakening control, sensorless motor control algorithms or short circuit behavior. No magnetic FEM simulation is needed at runtime. We demonstrate the functionality of our method using the example of a BLDC motor simulation with voltage block commutation. The model derivated results are in good accordance with our measurements.