# Modeling and Simulation Analysis of Permanent Magnet Brushless Motor

1 Brushless motor modeling 12 The positive direction of each variable and the origin of the coordinates are the principles of the highlighted model. In the analysis process, the following basic assumptions are made: three-phase windings are completely symmetric and can be treated as concentrated windings, the number of pole pairs p =1 motor magnetic field is isotropic, can not consider the magnetic field saturation; temporarily does not consider the armature reaction to the air gap magnetic field influence.

The control of the brushless motor is closely related to the position of the motor and the state variables. For the convenience of analysis, the direction of the specified state variables is as follows: a phase current flows from the a end of the winding ax to the positive winding (bc analogy) b winding ax The position of the a terminal conductor is the origin of the air gap circumferential coordinate (9p=0); the initial position of the rotor is set when the N pole axis of the rotor magnetic field coincides with the origin of the air gap circumferential coordinate (9=0); the clockwise rotation of the motor is positive Turn it.

Under this specified condition, the motor windings are deployed along the air gap circumference, and the direction of each state variable and the rotor position are as shown.

As shown, the coordinate position of a point on the circumference of the air gap is denoted by 9 and the angular displacement of the rotor relative to the original position is denoted by 9, the magnetic induction intensity Br(9p,0)=Bm/ produced by the rotor at the air gap circumference 9 (0p-9), Bm is the amplitude of the magnetic density; / (9-0) is the distribution function of the rotor flux density, the function / form is determined by the structure of the motor, and it is numerically relative to the position of the stator (9p- 9) related. At the same time, due to the symmetry of the motor structure, it is obvious/an even function. A motor with a pole logarithm P = 1 and a rotor magnetic field sinusoidally distributed has, for example, /(0p-0)=cos(0p-0). Let 0p=0Â°, 120Â°240Â° and according to the function/parity, obtain the magnetic induction intensity generated by the rotor at a, b, c on the air gap circumference: 9: Dr. Tao Guishu, male | Graduate student e Wuhan i School of Electrical and Electronic Engineering, Huazhong University of Science and Technology (430Â°74) - http:// Thus, the electromagnetic forces acting on the conductors at ab, c are: the effective length of the body. The conductor-induced electromotive force at ab, c is: degree. When the motor uses a full-range winding, the current direction of the other conductor flowing through the same winding changes polarity at the same time as the magnetic field. Therefore, the total electromagnetic torque received by the winding of a winding is: Ta=a winding-induced winding. The total back electromotive force is: Therefore, according to the magnetic field distribution of the rotor and the armature current, and the effective number of turns of the winding, the electromagnetic torque and back electromotive force can be obtained.

The magnetic field distribution of the rotor and the number of turns of the winding have been determined when designing the motor, and the current of the armature can be obtained by solving the circuit equation of the motor.

1.3 Circuit equation of the motor a Circuit equation without commutation state. According to the trigger logic of a large-scale permanent-magnet brushless motor, in the non-commutated state, current flows through both windings of the motor at the same time, and there is no current in the neutral line. Non-commutated states can be described by the following equations: resistance and mutual inductance; Uk and U/ are the voltages of the motor phase windings; U is the voltage of the neutral line; ek and e/ are the opposing forces of the motor's phase windings.

b. Circuit equations for commutation states. In the commutation state of the motor, only one winding state changes, so it can be described by the following equation: According to the trigger logic, automatic switching. For brushless motors with other commutation modes, corresponding equivalent circuits can be used to implement the corresponding motor models.

1.4 Motor's equation of motion.

2 Circuit Model and Simulation Analysis of Brushless Motor Based on the above analysis, the circuit model of the permanent magnet brushless motor is composed of the following five parts, as shown... Magnetic flux density distribution function, and the air gap magnetic flux density is calculated according to the position of the motor. b. Back-EMF calculation section, according to the position and speed of the motor, calculate the back EMF. c. The circuit calculation section calculates the current of each phase winding according to the equivalent circuit. d. Torque calculation link, calculate electromagnetic torque based on current and magnetic density. e. The equation of motion, which calculates the speed and position of the motor based on the electromagnetic torque.

Circuit model based on permanent magnet brushless motor. The simulation results also show that this method has high computational efficiency and greatly reduces the complexity of the simulation. This model is derived from a brushless motor with a neutral conductor. It is also suitable for brushless motors that do not require a neutral conductor. It can also be used directly as a constituent element of a multi-phase brushless motor, and therefore has greater applicability. There is a certain significance for the modeling of multiphase, multipole brushless motors.

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