Modeling magnetic torque and force for controlled manipulation of soft-magnetic bodies

We calculate the torque and force generated by an arbitrary magnetic field on an axially symmetric soft-magnetic body. We consider the magnetization of the body as a function of the applied field, using a continuous model that unifies two disparate magnetic models. The continuous torque and force follow. The model is verified experimentally, and captures the often neglected region between weak and saturating fields, where interesting behavior is observed. We provide the field direction to maximize torque for a given field magnitude. We also find an absolute maximum torque, for a given body geometry and material, which can be generated with relatively weak applied fields. This paper is aimed at those interested in systems-level analysis, simulation, and real-time control of soft-magnetic bodies.