# Modeling and Simulation Analysis of Permanent Magnet Brushless Motor

1 Modeling of brushless motor 12 The positive direction of each variable and the origin of the coordinate are the principle of the prominent model. In the process of analysis, the following basic assumptions are made: the three-phase winding is completely symmetrical, and can be processed by concentrated winding, the pole pair p =1 motor magnetic field isotropic, can not consider magnetic field saturation; temporarily do not consider the impact of armature reaction on air gap magnetic field.
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 variable is as follows: the phase a current flows from the a terminal of the winding ax to the winding as a positive current (bc phase analogy) b winding ax The position of the a-end conductor is the origin of the air-gap circumference coordinate (9p=0); when the N-pole axis of the rotor magnetic field coincides with the origin of the air-gap circumference coordinate, the initial position of the rotor is set (9=0); the motor rotates clockwise to positive Turn to the direction.
Under the specified conditions, the motor windings are deployed along the circumference of the air gap, 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 indicated by 9, and the angular displacement of the rotor with respect to the original position is indicated by 9, and the magnetic induction Br (9p, 0) = Bm/ generated by the rotor at the circumference 9 of the air gap. (0p-9), Bm is the amplitude of the magnetic density; /(9-10) is the distribution function of the rotor magnetic density, and the form of the function/ is determined by the structure of the motor, and the value is only relative to the fixed rotor (9pâ€• 9) Relevant. At the same time, due to the symmetry of the motor structure, it is obvious / is an even function. Taking the motor with the pole pair P=1 and the sinusoidal distribution of the rotor magnetic field as an example, /(0pâ€•0)=cos(0pâ€•0). Let 0p=0Â°, 120Â°240Â° and according to the parity of the function, we can find the magnetic induction intensity generated by the rotor on the circumference of a, b, c on the air gap: 9: Dr. Tao Guishunan | Graduate student e Wuhan i. School of Electrical and Electronic Engineering, Huazhong University of Science and Technology (430Â°74)-http:// Thus, the electromagnetic force of each conductor at ab, c is: the effective length of the body. The electromotive force induced by the conductor at the end of ab, c is: degrees. When the motor adopts the full-winding winding, the current direction of the other conductor flowing through the same winding changes the polarity simultaneously with the direction of the magnetic field. Therefore, the total electromagnetic torque received by the winding coil is: Ta=winding-coil-induced The total back electromotive force is: Therefore, the electromagnetic torque and the back electromotive force can be obtained according to the rotor magnetic field distribution and the armature current, and the effective number of turns of the winding.
The rotor magnetic field distribution 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 of non-commutation state. According to the trigger logic of a large permanent magnet brushless motor, in the non-commutated state, the current flows through the two windings of the motor at the same time, and there is no current in the neutral line. The non-commutation state can be described by the following equations: resistance and phase 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 anti-electric cloud forces of the motor phase windings.
b. Circuit equation for commutation state. The motor is in the commutation state, and only one winding has a change in state, so it can be described by the following equation: automatic switching according to the trigger logic. For other brushless motors of the commutation method, the corresponding motor model can be realized by using the equivalent circuit corresponding thereto.
1.4 Motor's equation of motion.
2 Circuit model and simulation analysis of brushless motor According to the above analysis, the circuit model of permanent magnet brushless motor is composed of the following five parts, as shown... magnetic density distribution function, calculating the magnetic density of the air gap according to the position of the motor. b. Back EMF calculation link, calculate the back EMF according to the position and speed of the motor. c. Circuit calculation link, calculate 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. Equation of motion, calculating the speed and position of the motor based on the electromagnetic torque.
The circuit model of a permanent magnet brushless motor is based. The simulation results also show that the method has high computational efficiency and greatly reduces the complexity of the simulation. This model is derived from a brushless motor with a neutral line. It is also suitable for brushless motors that do not require a neutral line. It can also be used directly as a component of a multi-phase brushless motor, so it has greater applicability. Modeling multi-phase and multi-pole brushless motors has certain significance.

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