Electromagnetic Vibration Analysis of Common Rotor Structures of Permanent Magnet Synchronous Motors

introduction

Scholars from some developed countries abroad first began to explore the electromagnetic vibration of permanent magnet motors. In the 1940s, some scholars studied the electromagnetic vibration and noise of motors, found out the influencing factors of the two, and mastered certain laws. Later, with the widespread application of motors, the problem of motor vibration has become more and more prominent in various fields such as industry and life. Therefore, the research value of motor vibration has become increasingly greater, and scholars from various countries have carried out research on motor vibration.

1 Common rotor structures of permanent magnet synchronous motors

This paper will analyze the mechanical vibration of the motor structure caused by electromagnetic force for several common rotor structures, including surface-mounted, tangential, V-type and straight-line rotor structures. Figure 1 shows the cross-sectional view of four motors. The four motors have the same stator inner diameter, stator outer diameter, rotor inner diameter and rotor outer diameter. The specific parameters are shown in Table 1. In this paper, a two-dimensional electromagnetic field analysis is first performed on the motors of several structures to obtain the distribution of the magnetic field and electromagnetic force inside the motors, and a two-dimensional FFT analysis is performed to compare the electromagnetic force distribution characteristics of motors with different rotor structures. On this basis, the electromagnetic force obtained by the analysis is applied to the transient structural analysis model, and the vibration conditions of the four motors are analyzed and compared through finite element simulation.

2 Analysis of electromagnetic force of motor stator

In this paper, two-dimensional time-stepping finite element method is used to calculate the electromagnetic field of four motors with different rotor structures, and the distribution of electromagnetic force of the four motors on the inner surface of the stator is obtained. The electromagnetic force is calculated using Maxwell stress method.

According to Maxwell's formula, for a steady-state or slowly varying magnetic field, the electromagnetic stress acting on any unit surface area in a vacuum (or air) medium is:

The simplified radial electromagnetic force density is expressed as:

Where br is the radial magnetic flux density; bt is the tangential magnetic flux density; μo is the air magnetic permeability.

Generally, since the radial component of the magnetic flux density is much larger than the tangential component, the tangential magnetic flux density is ignored in the calculation.

This paper mainly conducts comparative study on no-load electromagnetic vibration, and the permanent magnet synchronous motors with different rotor structures are studied separately below.

2.1 Analysis of spatial harmonics of radial electromagnetic force of motor

Based on the air gap flux and the radial flux at a certain point in the air gap obtained in the simulation, the radial electromagnetic force can be calculated according to formula (2). In the vibration problem of the motor, the radial electromagnetic force on the inner surface of the stator teeth is studied. Therefore, when calculating the radial electromagnetic force, the air gap flux close to the stator layer is used. In this way, the calculated radial electromagnetic force is closer to the actual force condition of the stator.

The waveform of the radial electromagnetic force density on the inner surface of the stator when no-load is obtained by simulation as a function of spatial position is shown in Figure 2. Since the radial magnetic flux density at the junction of two magnetic poles of the radial motor is zero, the radial electromagnetic force density on the surface of the stator teeth of the motor with surface-mounted, straight-line, and V-shaped rotor structures will always be zero at some spatial positions. The radial electromagnetic force density on the surface of the stator teeth of the motor with a tangential rotor structure is zero only at a small part of the position. In the surface-mounted structure, the air gap magnetic flux density is the largest, and the magnetic field waveform is greatly affected by the slot, so the magnetic flux density fluctuates at the slot. It can be seen from formula (2) that the electromagnetic force density is the square of the magnetic flux density, so the electromagnetic force density on the stator teeth is more sensitive to the tooth slot and has a larger fluctuation peak. Although this force will cause deformation of the stator core, it will not cause the motor to vibrate and generate noise; the fundamental wave (force wave modulus is 4) of the surface-mounted structure has the largest amplitude, followed by the straight-line structure, and the fundamental wave electromagnetic force amplitudes of these two structures are more than twice that of the tangential and V-type structures.

2.2 Analysis of time harmonics of radial electromagnetic force of motor

The waveform of the radial electromagnetic force density at the middle point of the stator tooth at no load varies with time is shown in Figure 3. The electromagnetic force density of the surface-mounted motor has a small fluctuation, because the permanent magnet is non-magnetic and is similar to air, so it belongs to a hidden pole motor and the magnetic flux density does not fluctuate; however, the tangential, straight, and V-type motors all have permanent magnets placed in the rotor, so the magnetic flux density fluctuates, and the electromagnetic force density will fluctuate, but because the magnetic flux density of the V-type structure is smaller, the fluctuation of the electromagnetic force density is smaller.

3. Stator electromagnetic vibration analysis

According to the theory of classical mechanics, the dynamic equilibrium equation of an object is:

Where [M] is the mass matrix, [C] is the damping matrix, [K] is the stiffness matrix, (x) is the displacement vector, (x') is the velocity vector, (x") is the acceleration vector, and (F(1)) is the force vector.

This paper calculates the electromagnetic force through the electromagnetic field, and then loads it into the transient structural field. The three-dimensional transient structural finite element method is used to simulate the motor stator vibration caused by the electromagnetic force. The transient simulation comprehensively considers the various parameters of the above formula to model, and can obtain the vibration displacement, velocity and acceleration of each point on the stator of the motor during the entire operation process. It can also display the deformation cloud map and stress cloud map of the stator. Figure 4 is the coupling diagram of the electromagnetic field and the transient structural field, and Figure 5 is the electromagnetic force density vector diagram loaded into the transient field.

Figure 4 Electromagnetic field and transient structural field coupling diagram

Figure 5 Electromagnetic force density vector diagram in transient field

From the displacement time curve in Figure 6, it can be seen that the surface-mounted motor has the largest stator vibration and deformation, followed by the straight-type motor. The deformation of the surface-mounted and straight-type rotor structures is much larger than that of the tangential and V-type rotor structures. The V-type rotor structure motor has the smallest stator vibration and deformation.

Figure 6 Stator vibration displacement time curve

Since the DC component of the electromagnetic force of the surface-mounted rotor structure is the largest, while the DC component of the electromagnetic force of the V-type rotor structure is the smallest, the motor deformation of the surface-mounted rotor structure is the largest, while the motor deformation of the V-type rotor structure is the smallest. It is generally believed that the vibration amplitude is proportional to the inverse of the fourth power of the force wave modulus. The smaller the electromagnetic force wave modulus of the motor, the greater the mechanical deformation and vibration will be for the same mechanical structure. In the previous radial electromagnetic force analysis, the fundamental wave (force wave modulus is 4) of the surface-mounted structure has the largest amplitude, followed by the straight type, and the fundamental electromagnetic force amplitude of these two structures is more than twice that of the tangential and V-type. Therefore, the vibration of the motor of the surface-mounted rotor structure and the straight rotor structure is much greater than that of the other two. Although the fundamental wave of the electromagnetic force of the V-type rotor structure is larger than that of the tangential rotor structure, the amplitude of the 2nd, 3rd, and 4th harmonics of its electromagnetic force is much smaller than that of the tangential rotor structure, so the vibration of the motor of the V-type rotor structure is smaller than that of the tangential rotor structure.

4 Conclusion

By analyzing the electromagnetic force on the inner surface of the stator of permanent magnet motors with four common rotor structures, it can be concluded that: for the same stator, the deformation and vibration of the permanent magnet motor with a surface-mounted rotor structure are the largest, and the deformation and vibration of the permanent magnet motor with a V-type rotor structure are the smallest.