Mathematical Modeling of Semicircular Linear Motor Based on Vector Potential With Landen's Transformation

A semicircular linear motor that realizes a motion along circumference of the circle has been developed. To settle the optimal design of this motor by mathematical analysis, the theoretical equation of motor performance has to be clarified. In this paper, the mathematical modeling of semicircular linear motor is carried out from the viewpoint of Lorentz force and magnetic flux density derived by vector potential. By comparing calculated, analyzed, and measured magnetic flux density and thrust force, the validity of derived mathematical model is confirmed. In addition, the cause of difference among three results is also discussed.