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Abstract <p>This article presents an analytical model of a squirrel-cage induction motor based on solving the 3D Laplace partial differential equation using the separation of variables method for nested hollow cylinders of finite length, where the boundary conditions correspond to those of the magnetic field generated by stator- and rotor-winding currents and induced magnetizations in the ferromagnetic regions of both cores. For electromagnetic analysis, the active components of the induction motor are divided into structurally homogeneous hollow cylinders (tori) based on geometry and material properties: stator- and rotor-core yokes, air gap, and stator and rotor teeth. The constants for the separation of variables method are determined by solving a system of linear algebraic equations, the coefficient matrix of which has dimensions of 8 × 8 in the analyzed case. The matrix elements consist of modified Bessel functions (Infeld and MacDonald functions). The magnetic-flux density distribution in the motor’s air gap is analyzed, which includes slot harmonics and nonuniform induction along the length of both stator and rotor cores. The electromagnetic torque of the motor is calculated.</p>

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Improved Academic Translation Three-Dimensional Analytical Model of a Squirrel-Cage Induction Motor

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • A. A. Afanasyev,
  • V. S. Genin,
  • N. V. Russova,
  • G. M. Tutaev

摘要

Abstract

This article presents an analytical model of a squirrel-cage induction motor based on solving the 3D Laplace partial differential equation using the separation of variables method for nested hollow cylinders of finite length, where the boundary conditions correspond to those of the magnetic field generated by stator- and rotor-winding currents and induced magnetizations in the ferromagnetic regions of both cores. For electromagnetic analysis, the active components of the induction motor are divided into structurally homogeneous hollow cylinders (tori) based on geometry and material properties: stator- and rotor-core yokes, air gap, and stator and rotor teeth. The constants for the separation of variables method are determined by solving a system of linear algebraic equations, the coefficient matrix of which has dimensions of 8 × 8 in the analyzed case. The matrix elements consist of modified Bessel functions (Infeld and MacDonald functions). The magnetic-flux density distribution in the motor’s air gap is analyzed, which includes slot harmonics and nonuniform induction along the length of both stator and rotor cores. The electromagnetic torque of the motor is calculated.