Interaction Between Ring-Shaped Permanent Magnets With Symbolic Gradients: Application to Magnetic Bearing System Optimization

This paper presents a semi-analytical calculation of the interaction between magnetic bodies with ring shapes. It leads to fast and accurate evaluation of forces and torques but also to the symbolic expression of their gradients. Our method can be used to compute partial derivatives to address optimization needs. It has been implemented into an available software environment in order to be automatically available for end users. Efficient optimization can be done to size magnetic bearing systems.