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 optimal field direction for a given field magnitude. We find a maximum possible torque, which can be generated with relatively weak applied fields. This paper facilitates systems-level analysis, simulation, and real-time control of soft-magnetic bodies.