Magnetic circuit calculations for electric motors include calculating the magnetic potential difference of each segment of the magnetic circuit, calculating the no-load excitation magnetomotive force of various types of motors, and calculating no-load characteristics. Magnetic circuit calculations are the foundation of electromagnetic calculations for electric motors. Through them, not only can the basic operating characteristics and no-load characteristics of the motor be obtained, but also the core losses and other operating characteristics can be calculated. Furthermore, magnetic circuit calculations reveal the relationship between the magnetic circuit structure, materials, and geometry and motor performance, laying the foundation for the magnetic circuit design of electric motors.
01 Several Assumptions in Magnetic Circuit Calculation
Various forms of alternating electromagnetic fields actually exist inside the motor, and there is also relative motion between the stator and rotor. For simplification, the following assumptions are generally made in magnetic circuit calculations.
● The magnetic field of the rotating part of the motor is treated as a constant magnetic field, and it is assumed that the stator and rotor are relatively stationary. The calculation loop is taken through the relative position of the magnetic poles and the tooth center line (or the tooth center line).
● The effects of hysteresis and eddy current phenomena of ferromagnetic materials on the magnetic field distribution are ignored because the ferromagnetic materials located in the alternating magnetic field within the motor are usually composed of soft magnetic materials rolled into thin steel sheets. Therefore, the basic magnetization curve is used for calculation of the ferromagnetic part.
● The magnetic field actually existing in each part of the magnetic circuit within the motor is transformed into equivalent magnetic circuits. Equivalence means that after the field is transformed into a circuit, the magnetic potential difference between each segment of the magnetic circuit should be equal to the magnetic potential difference between corresponding points in the magnetic field. Typically, transforming a spatially non-uniformly distributed magnetic field into a magnetic circuit with uniform flux distribution along the cross-section and length is achieved through various correction coefficients. With the help of these correction coefficients, sufficiently accurate results can be conveniently obtained when calculating the magnetic circuits of various types of motors without involving field issues.
There is no fundamental difference in the magnetic circuit calculations for AC and DC motors. The core issue in magnetic circuit calculation is how to obtain the various correction coefficients after field-based circuitry in a convenient and sufficiently accurate manner.
The foundation of field-based circuitry lies in a thorough understanding of the magnetic field within the motor's magnetic circuit structure. The difficulty in studying the distribution of the magnetic field within a motor lies in the irregularity of the geometric shapes of the magnetic field boundaries in different parts, as well as the nonlinearity of the basic magnetization curve of ferromagnetic materials.
02 Common methods for studying the distribution of magnetic field inside an electric motor
● Analytical Magnetic Field Method. This method employs classical analytical methods such as the separation of variables method or conformal mapping to obtain mathematically rigorous solutions for magnetic fields. It is only suitable for analyzing fields with relatively simple geometry.
● Magnetic Circuit Analysis Method. This method involves defining artificial paths in the magnetic field diagram and then performing magnetic circuit calculations. For example, it might assume that only a radial magnetic field exists in the air gap, or that magnetic field lines consist of straight lines and arcs. This is the most commonly used analysis method in motor design. Another example is when calculating the magnetic potential difference of ferromagnetic parts. Approximate formulas are usually used to calculate the magnetic field strength of only one or a few cross-sections. However, this can introduce significant errors when the magnetic saturation increases or the cross-section changes greatly.
● Magnetic field mapping method. It can yield practically accurate results, but it requires time and certain skills. It is suitable for fields with complex geometries.
●Electrical modeling method. Based on the similarity of physical phenomena, electrical modeling methods such as electrolytic cells, electrical networks, or conductive paper are used to obtain the magnetic field distribution. Because it is very effective in dealing with magnetic fields of complex geometries, and is accurate and convenient enough, it is widely used in the study of air gap magnetic fields and leakage magnetic fields of motors.
● Numerical Solution. A discretized magnetic field model is established using the finite difference method or the finite element method, and the numerical solution of the magnetic field is obtained on a digital computer. Numerical solutions can consider very complex geometries, irregular distributions of field sources, and nonlinearities of ferromagnetic materials, and can obtain fairly accurate results. In recent years, numerical solutions combining the boundary element method and the finite element method have also emerged.
Disclaimer: This article is a reprint. If it involves copyright issues, please contact us promptly for deletion (QQ: 2737591964). We apologize for any inconvenience.
