Analysis of Longitudinal End Effects in a Single Sided Linear Induction Motor Using Stream Function Approach
Analysis of longitudinal end effects in a Single Sided Linear Induction Motor using Stream Function approach
Abstract-This paper presents the analysis of longitudinal end effects in a single sided linear induction motor leading to the calculation of fields and currents in the rotor sheet and propulsion and levitation forces. Such problem can be tackled by vector potential or stream function approach. The present paper adopts the second approach. A second order partial differential equation has been formulated for calculation of stream function or current density in the rotor sheet. As the end effects have not been considered in the direction of width of the rotor sheet, the said formulation merges to a second order PDE in one dimension i.e. the length of the rotor. For solution of such problem suitable boundary conditions have been imposed based on the fact that current cannot escape the rotor sheet. Based on the numerical calculations for current and flux density in the rotor sheet, the important performance figures such as Propulsion and levitation force have been calculated. These performance figures have been expressed as normalized quantities and plotted against magnetic Reynolds number. Such plots become helpful for a designer to design a realistic Transportation system using magnetic levitation, taking finite length and finite width effect of the rotor sheet in consideration.
Index Terms—SLIM, vector potential, stream function, infinitely long rotor, Reynolds number.
Introduction
T he analysis presented in [3] takes into account the finite width effects of the rotor in a SLIM while [4] deals with the effects of both finite length and finite width of the rotor. In this literature, the longitudinal end effects of the rotor are exclusively considered to give a better understanding of the effects due to discontinuity of the rotor in the longitudinal direction without being bothered about the discontinuity of the rotor in the transverse direction. In
Abstract-This paper presents the analysis of longitudinal end effects in a single sided linear induction motor leading to the calculation of fields and currents in the rotor sheet and propulsion and levitation forces. Such problem can be tackled by vector potential or stream function approach. The present paper adopts the second approach. A second order partial differential equation has been formulated for calculation of stream function or current density in the rotor sheet. As the end effects have not been considered in the direction of width of the rotor sheet, the said formulation merges to a second order PDE in one dimension i.e. the length of the rotor. For solution of such problem suitable boundary conditions have been imposed based on the fact that current cannot escape the rotor sheet. Based on the numerical calculations for current and flux density in the rotor sheet, the important performance figures such as Propulsion and levitation force have been calculated. These performance figures have been expressed as normalized quantities and plotted against magnetic Reynolds number. Such plots become helpful for a designer to design a realistic Transportation system using magnetic levitation, taking finite length and finite width effect of the rotor sheet in consideration.
Index Terms—SLIM, vector potential, stream function, infinitely long rotor, Reynolds number.
Introduction
T he analysis presented in [3] takes into account the finite width effects of the rotor in a SLIM while [4] deals with the effects of both finite length and finite width of the rotor. In this literature, the longitudinal end effects of the rotor are exclusively considered to give a better understanding of the effects due to discontinuity of the rotor in the longitudinal direction without being bothered about the discontinuity of the rotor in the transverse direction. In