2. Mathematical Modelling of Electromagnetic Forces Due to Finite Width Effects of a Single-Sided Linear Induction Motor

The chapter focuses on the mathematical modeling of electromagnetic forces in a Single-Sided Linear Induction Motor (SLIM) with finite width effects. It begins by considering the practical dimensions of the stator and rotor, which differ from the idealized infinite width assumption. The analysis involves calculating the field due to the stator winding, considering both axial and peripheral components of linear current density. The induced currents in the rotor sheet are also modeled, taking into account the finite width of the rotor. The vector potential due to both stator and rotor currents is derived, and the flux density components are calculated. The chapter then proceeds to calculate the propulsion, levitation, and lateral forces on the rotor, using established relations. The results are validated through comparisons with experimental data, showing good agreement. The chapter concludes by highlighting the inherent lateral instability of the rotor, which increases with rotor offset. The detailed mathematical formulations and numerical methods used in this chapter provide valuable insights into the behavior of SLIMs under practical conditions.