Closed-form Computation of Electromagnetic Fields in Induction Motors

A closed-form solution of the electromagnetic field equations for a three-phase squirrel-cage induction motor is presented. The analysis starts from the application of the Galilean transformation to Maxwell equations for moving media at constant speed. The induction motor is modelled as five concentric cylindrical layers representing the different construction components of the motor. By solving the Helmholtz and Laplace equations for conducting and non-conducting layers, we obtain a coupled set of Bessel and Euler equations that are solved analytically. The obtained formulas allow for the efficient calculation of important information for the designer regarding the electromagnetic fields, losses, force and torque. Parametric analyses are shown for illustration of the benefits of the closed form solution. The analytical expressions are validated against finite element simulations. Analytical expressions to compute the parameters of the equivalent circuit from the dimensions of the motor are also provided.