Research on Cogging Torque of Surface-type Permanent Magnet Motor with Rotor Static Eccentricity

The cogging effect consists of a tangential component of the force between the permanent magnet and the stator tooth. When the rotor rotates, it is in the Permanent Magnet Arc Fund Project: Research Fund Project for Returned Overseas Students of the Ministry of Education (2003.406).

The magnetic conductance between the stator teeth and the permanent magnets is almost constant, and therefore the magnetic field around the stator teeth is also substantially constant, and within a small area formed by one or two stator teeth corresponding to both sides of the permanent magnets. However, the magnetic susceptibility change is very large, which causes the magnetic field energy storage to change, resulting in cogging torque. After each tooth pitch of the rotor is rotated, the sum of the pulsating torques generated on both sides constitute the cogging torque.

The cogging torque will reduce system control accuracy, especially at low speeds, it will also bring vibration and noise. As a problem unique to permanent magnet motors, the cogging torque is one of the important contents of permanent magnetic motor research. The calculation method and elimination method are studied and some results are obtained. The calculation method of the cogging torque is given in this paper. The influence of several parameters of the motor on the cogging torque is studied.

However, the premise of the above study is that the stator and rotor are coincident with each other, that is, the air gap is uniform. However, in the actual production, due to the limitation of the processing technology, it is impossible for the stator and rotor to completely coincide with each other, and there are different degrees of uneven air gaps. In the motor, there are two types of eccentricity: static eccentricity and dynamic eccentricity. Static eccentricity is caused by factors such as the ellipse of the stator core, improper installation position of the stator or rotor, and the like, which is characterized in that the position of the minimum air gap does not change. The reasons for dynamic eccentricity are: rotor shaft bending, bearing wear, mechanical resonance at the limit rotational speed, etc. Its characteristic is that the center of the rotor is not the center of rotation, and the position of the minimum air gap changes with the rotation of the rotor. When the air gap is uniform, the magnetomotive force of the permanent magnet acting in the corresponding position in the air gap is the same, and the air gap permeance varies in a period of one tooth pitch. When the air gap is not uniform, the permanent magnet acts on the magnetomotive force of the air gap in the corresponding position. Different, air-gap permeation cycle is the circumference of the entire air gap, it will inevitably affect the size of air gap flux density, and then affect the cogging torque size and distribution. There is no relevant research yet.

In order to study the effect of static eccentricity on the cogging torque, an analytical expression of the cogging torque that can be used to qualitatively analyze the influence of eccentricity is obtained based on the energy method and the Fourier transform. The effect of static air gap eccentricity on the cogging torque is studied. , and verified using the finite element method. Studies have shown that eccentricity only has a great influence on the size and distribution of the cogging torque of those motors whose pole number and slot number combination satisfy a specific relationship, but it has little effect on the motor whose pole number and slot number combination does not satisfy this specific relationship.

2 The effect of air gap eccentricity on the air gap flux density distribution.

In a permanent magnet motor, since the magnetic paths of adjacent magnetic poles are connected in series, compared with the case where the air gap is uniform, when the air gap is not uniform, the difference in air gap length in the two magnetic circuits will inevitably cause a change in the magnetic density of the air gap. Schematic diagram of surface type permanent magnet motor with eccentric rotor.

It is assumed that both the inner surface of the housing and the outer surface of the rotor core are equipotential surfaces, and the presence of the tooth groove is ignored. In this paper, the distribution of the air-gap flux density around the eccentricity of a 6-pole motor before and after eccentricity is calculated by the finite element method. As shown, the air gap length is 0.6mm when the eccentricity is not deviated, and the minimum air gap is 0.lmm after the eccentricity. Changed. In the following text, 5::2 is considered, so the distribution waveform is given as shown. It can be seen that the eccentricity has a certain influence on the size and distribution of the square of the equivalent remanence.

3 Analytical analysis of the cogging torque when the rotor eccentricity 3.1 General The cogging torque is the torque generated by the interaction between the permanent magnet and the grooved armature core in the permanent magnet motor. It can be defined as a displacement. The angle between the centerline of a given tooth and the centerline of a given permanent magnet.

Assuming that the magnetic permeability of the iron core is infinite, the stored energy in the motor is approximately the energy in the air gap of the motor and the permanent magnet, that is, assuming that the magnetic permeability of the permanent magnet is the same as that of the air, in the permanent magnet motor, in any relative position”, The distribution of air gap magnetic flux along the armature surface can be expressed as the air gap flux density distribution. The rotor g changes with eccentricity and changes with g. Considering that there is a cloth in the permanent magnet motor, the permanent magnet equivalent remanence can be approximated. Density B (distribution.

Formula (4) can be expressed as passing and Fourier expansion, and the expression of the cogging torque can be obtained by obtaining the magnetic co-energy in the motor.

The Fourier expansion of 2 (can be expressed as the distribution of the effective air gap length in the circumferential direction, and I is the magnetization direction length of the magnetic pole center position.

This is the result of Fourier decomposition of the six-pole motor before and after eccentricity. For clarity, only 0-25 times are given.

For the case of no eccentricity, equation (7) has 0 and 2 times, where it is a positive integer and p is the number of pole pairs.

For the decentralized case, all harmonics exist, and their amplitudes are related to the degree of eccentricity. Among them, there are mainly 2 knowledge times and 2 knowledge times. Among them, the amplitude of eccentricity is smaller than that of no eccentricity.

3.3 The Fourier expansion of the rotor when the rotor eccentricity is no longer uniform, as shown, the minimum air gap is frO, the location of the first pole edge. The air gap length at any position satisfies the distance. Defining the degree of eccentricity as 2 does not take into account the influence of relative position, and the position of 6*=0 is set on the centerline of a certain tooth. The Fourier expansion is obtained to consider the relative position between the permanent magnet and the tooth, and the Fourier expansion of /(center+hair(4)))2 is a case where there is no misalignment, there are only mz times, where m is a positive integer and z is the number of slots. For the case of eccentricity, there are various harmonics, but except for the 1st order and the mz order, the harmonic amplitudes of other orders are negligible.

Armature outer diameter and stator yoke inner diameter.

4 Influence of eccentricity on the cogging torque The expression of the cogging torque at the time of eccentricity is also applicable to the case where the eccentricity is not applied. Both have the same form except that the coefficients of the expression are different.

In the Fourier decomposition of eccentricity, 2 divisions and 2 knowledge 1 coefficients are the main components, and other coefficients can be ignored. The cogging torque can only be generated when the number of times that cogging torque is used by Equation (13) is equal to, ie, the number of cogging torques is equal. For the first order coefficient in Fourier decomposition of 2, Gi is negligible. The heart and G do not produce cogging torque. Therefore, the number of cogging torques that can generate G is mz times, and the number of times B is the second time and the first two times are ±1 time, that is, when n=mz=2kp is satisfied, or when it is satisfied, the eccentricity ratio is slightly reduced when it is not decentered. Therefore, the former has a slightly smaller cogging torque than the latter.

When "=mz=2 cut ±1" is satisfied, the eccentricity is much larger than when the eccentricity is not eccentric, so the former is much larger than the latter's cogging torque.

In addition, the sum (3) decreases with the increase of n, so the magnitude of the cogging torque is mainly determined by satisfying the "=mz=2 minimum or the corresponding" and G. The correctness of the above conclusions was verified. The method of calculating the cogging torque by the finite element method is to calculate the magnetic field distribution according to the relative position of different stators and rotors, and then calculate the alveolus using the Maxwelltensor method according to the distribution of air-gap magnetic field. / Indium Indium Torque Considering the presence of fractional slots per pole, the entire motor section is used as the solution area, which is the magnetic field distribution at a certain moment.

Magnetic Field Distribution In this paper, the cogging torque of a 6-pole, 30-slot permanent magnet motor at different eccentricities is calculated using the above method. The results are shown. For this motor, since 1X30=6X5, that is, satisfies mz=2, eccentricity has little effect on the cogging torque. This can be verified from. It can be seen that the eccentric cogging torque amplitude is slightly reduced.

The situation where the relative position of the stator (pitch) to the cogging torque is small is the cogging torque of a 6-pole, 31-slot permanent magnet motor before and after eccentricity. Since (z-1)/2/=5 at this time, satisfies mz=2/tp±l, the cogging torque when the motor is eccentric is much larger than when it is not eccentric, which can be verified from that of the rotor. Eccentricity is 0.83. 0.2 t eccentric eccentricity The relative position of the rotor (pitch) has a great influence on the cogging torque. 5 Conclusion Based on the energy method and Fourier transform, the paper analyzes the slot of permanent magnet motor with surface eccentricity. Analytical method of torque analysis, and studied the effect of static air gap eccentricity on cogging torque. The analysis shows that eccentricity only has a great influence on the size and distribution of the cogging torque of the motor in which the number of poles and the number of slots satisfy a specific relationship, and the effect of the combination of the number of poles and the number of slots does not satisfy the specific relationship.

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