Development of a Mathematical Model of a Brushless Direct Current Motor Based on the Finit Element Method to Optimize Motor's Geometry

Brushless direct current motors are a class of electric machines that is dynamically developing. One of the directions of this development is related to the optimization of the geometry of the magnetic system, which provides high mass-energy performance. The existing mathematical models for optimization calculations based on the method of equivalent substitution schemes do not meet the requirements for the accuracy of determining the basic parameters. This reduces the quality of optimal design and slows down the development of electric drives. The purpose of the study: to develop a mathematical model that, on the one hand, would be simple, on the other hand, would have sufficient accuracy in determining the main energy parameters. Methods: the finite element method was chosen to build a mathematical model, but the number of elements into which the transverse geometry is divided is limited in advance. The model is parameterized and allows you to calculate any geometry. This approach allows you to create a simple and accurate model for optimization. Results: the technique is implemented in software code in the algorithmic Python language. The mathematical model includes 53 algebraic equations. The program takes into account the use of various electrical materials for electrical steel, high-coercive permanent magnets, copper armature windings. The mathematical model takes into account the lateral scattering fluxes of a permanent magnet, grooved scattering and scattering along the crowns of the teeth. Practical significance: the creation of a mathematical model with a limited number of elements is a new approach in electrical engineering. It allows you to make optimization calculations more accurate, thereby improving the mass-energy characteristics. This approach can be recommended for optimizing thermal conditions and aerodynamic calculations of electric machines. The proposed methodology will improve the design quality of brushless direct current motors and electric machines of other classes.