Permanent magnet motor cogging torque analysis method considering iron core saturation

Abstract

The invention discloses a permanent magnet motor cogging torque analysis method considering iron core saturation. Different from an existing analysis method which does not consider iron core saturation, after the iron core saturation is considered, air gap magnetic conductance varies, a saturation coefficient is introduced, and a modulation unit is converted into stator slot and saturation coefficient combined modulation from stator slot independent modulation, so that harmonic components of air gap flux density are changed. The number of harmonic pole pairs and the rotating speed after the air gap flux density is changed are determined through Fourier decomposition, the traveling wave pair generating the cogging torque is found out according to the cogging torque generation condition of the same number of pole pairs and different rotating speeds, and effective supplement is made for an existing cogging torque analysis method.

Description

Technical Field

[0001] The invention belongs to the technical field of motor body design, and in particular relates to a method for analyzing the cogging torque of a permanent magnet motor. Background Art

[0002] Permanent magnet motors are widely used in aerospace, electric vehicles, household appliances and other fields due to their high power density, high power factor and high efficiency. However, in permanent magnet motors, the cogging torque generated by the interaction between the permanent magnets and the stator slots will produce additional torque pulsation, affecting the motor control accuracy. Therefore, how to reduce the cogging torque has always been one of the hot topics in the field of permanent magnet motors.

[0003] The analysis methods of cogging torque mainly include finite element method and analytical method. The finite element method has fast calculation speed and high accuracy, but it cannot reveal the generation mechanism of cogging torque. The analytical method can explain the cause of cogging torque through theoretical deduction, which has certain guiding significance for reducing cogging torque. At present, scholars usually use energy method to analyze cogging torque.

[0004] In recent years, with the emergence of magnetic field modulation motors, a new motor theory corresponding to it, the magnetic field modulation theory, has attracted widespread attention from scholars. At first, the magnetic field modulation theory was only applied to a few special motors such as magnetic gear motors, vernier motors, reverse flux motors, and magnetic field modulation dual-rotor motors. Later, scholars gradually discovered that many magnetic problems in traditional motors can be explained by the principle of magnetic field modulation. As a result, a new motor research theory based on the principle of magnetic field modulation has been developed, providing new ideas for the design and analysis of traditional motors.

[0005] In 2020, Liu Jiaqi and others from Harbin Institute of Technology proposed a new permanent magnet motor cogging torque analysis method based on magnetic field modulation in the paper "Research on Cogging Torque Based on Magnetic Field Modulation Principle" published in the Journal of Electrotechnical Engineering, and explained the generation mechanism of cogging torque. However, the premise of the method proposed in the article is that core saturation is not considered. Maxwell simulation shows that the cogging torque of permanent magnet motors has obvious changes when considering core saturation or not. Therefore, the analysis method of cogging torque still has defects.

[0006] For example, in a 1-pole permanent magnet motor, the permanent magnets are magnetized in parallel, and the permanent magnet air gap magnetic field has only the fundamental wave. According to the conditions for the generation of traditional detent torque, even if the modulation effect of the stator teeth is considered, the motor will not generate two sets of traveling waves with equal pole pairs and different mechanical speeds, and will not generate detent torque. However, through simulation and experiments, the motor has a certain value of detent torque. The traditional detent torque theory cannot explain this phenomenon, and thus cannot parse and analyze the detent torque. Summary of the invention

[0007] In order to solve the problems mentioned in the above background technology, the purpose of the present invention is to provide an analytical method for the cogging torque of a permanent magnet motor taking into account the core saturation, introduce the saturation coefficient, and remodel the variable air gap magnetic permeability taking into account the core saturation, so as to completely determine the effective traveling wave pairs of the air gap magnetic flux of the permanent magnet motor, and then accurately calculate the traveling wave pairs that generate the cogging torque (based on the condition that the cogging torque will be generated under the same number of pole pairs and different rotation speeds, find the corresponding harmonic order and obtain the reason for the generation of the cogging torque).

[0008] The purpose of the present invention can be achieved through the following technical solutions:

[0009] An analytical method for the cogging torque of a permanent magnet motor considering core saturation is divided into five main steps: parallel magnetization of permanent magnets, introduction of a saturation coefficient to obtain a variable air gap permeance, obtaining a changed air gap flux density, Fourier decomposition of the air gap flux density, and obtaining harmonics that generate the cogging torque.

[0010] 1. The permanent magnets are magnetized in parallel, and the magnetomotive force is perfectly sinusoidal. There is no need to perform Fourier decomposition on the magnetomotive force, and the magnetomotive force only has the fundamental wave.

[0011] Mathematical model of magnetomotive force: F(θ,t)=Acosp r (ω r t-θ)

[0012] A is the magnetomotive force amplitude, p r is the number of rotor pole pairs, ω r is the rotor mechanical angular frequency, and θ is the magnetomotive force phase angle.

[0013] 2. Mathematical model after Fourier decomposition of air gap permeability without considering core saturation:

[0014]

[0015] P j is the permeability amplitude, N s is the number of stator slots and θ is the rotor angle.

[0016] Considering the variation of air gap permeability after core saturation, the saturation coefficient after Fourier decomposition is introduced:

[0017]

[0018] a0 is the saturation coefficient constant term, P r is the number of rotor pole pairs, ω r is the rotor mechanical angular frequency, a n is the amplitude of each saturation coefficient harmonic, n is the number of saturation coefficient harmonic, and t is time.

[0019] The final air gap permeability is the original permeability multiplied by the saturation coefficient:

[0020]

[0021] 3. The air gap magnetic flux density B is equal to the product of the permanent magnet magnetomotive force F and the air gap magnetic permeability P:

[0022]

[0023] 4. Perform Fourier decomposition on the air gap magnetic flux:

[0024]

[0025] 5. According to the expression derived in step 4, different harmonic pole pairs and rotation speeds can be obtained. They are pole pairs|p r -jN s |, rotation speed Pole pair number p r +jN s , rotation speed Pole pair number|(2n+1)p r -jN s |, rotation speed Pole pair number (2n+1)p r +jN s , rotation speed Pole pairs|(2n-1)p r -jN s |, rotation speed Pole pair number (2n-1)p r +jN s , rotation speed Six different harmonics.

[0026] The obtained harmonics are shown in Tables 1, 2, and 3 below.

[0027] Table 1 Harmonics generated by stator slot modulation only

[0028]

[0029]

[0030] Table 2 Harmonics generated by saturation coefficient modulation only

[0031] Harmonic order Speed 1 (1 is adjusted to 1 by the saturation factor 2) <![CDATA[ω r t]]> 3 (1 is adjusted to 3 by the saturation factor 2) <![CDATA[ω r t]]> 5 (1 is adjusted to 5 by the saturation factor 4) <![CDATA[ω r t]]> 7 (1 is adjusted to 7 by the saturation factor 6) <![CDATA[ω r t]]>

[0032] Table 3 Harmonics generated by simultaneous modulation of stator slots and saturation coefficient

[0033]

[0034] According to the condition that only harmonics with the same pole pair number and different speeds can produce cogging torque, if the saturation effect is not considered, the motor does not have cogging torque, as shown in Table 1. It also cannot accurately describe the size of the cogging torque and provide a basis for the compensation of the control system, and the motor speed fluctuates greatly.

[0035] According to Table 2 and Table 3 established by the present invention, it is found that the 1st, 3rd, 5th, and 7th harmonics all have different rotation speeds, so they all generate cogging torque. The reason why the motor generates cogging torque is found, and the harmonic order that generates cogging torque is clarified. The amplitude and phase of these harmonics are obtained according to the specific motor parameters. The amplitude and phase of these harmonics are brought into the cogging torque expression, and the value of the cogging torque can be accurately calculated. Provide a basis for the compensation of the control system and reduce the fluctuation of the motor speed.

[0036] At the same time, we also get the reason why the motor will not produce cogging torque according to the traditional positioning torque theory but the actual prototype has cogging torque.

[0037] By adopting the above technical solution conceived by the present invention, the beneficial effects that can be achieved are as follows:

[0038] Considering the saturation of the core, the saturation coefficient is introduced, and the effective traveling wave pair of the air gap magnetic flux density of the permanent magnet motor is completely obtained. The traditional theory does not consider the saturation of the core, the permanent magnet is magnetized in parallel, and the permanent magnet motor will not generate cogging torque. However, after considering the saturation of the core, the cogging torque generated by the permanent magnet motor is significantly increased. The saturation of the core will have an important impact on the cogging torque of the permanent magnet motor. Therefore, the present invention considers the saturation of the core, introduces the saturation coefficient, and introduces the variable air gap magnetic permeability formula to obtain the harmonics that generate the cogging torque, which is a supplement and improvement to the existing magnetic field modulation theory to analyze the cause of the cogging torque of the permanent magnet motor. For a series of motors that the traditional cogging torque theory believes that the cogging torque is 0, the reason why the motor generates the cogging torque is found, and the harmonic order of the cogging torque is clarified, and the value of the cogging torque is accurately calculated, which provides a basis for the compensation of the control system and reduces the motor speed fluctuation. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 A magnetomotive force mathematical model established for parallel magnetization of the permanent magnet of the present invention;

[0040] Figure 2 A mathematical model established for the present invention that does not consider the air gap permeability of the core saturation;

[0041] Figure 3 The present invention considers the saturation of the core and establishes a mathematical model for the saturation coefficient;

[0042] Figure 4 The 6-slot 1-pole permanent magnet synchronous motor topology used as an example in the present invention;

[0043] Figure 5 This is the cogging torque waveform of a permanent magnet motor with 6 slots and 1 pole pair without considering core saturation;

[0044] Figure 6 This is the FFT decomposition diagram of the radial air gap flux density of a permanent magnet motor with 6 slots and 1 pole pair without considering core saturation;

[0045] Figure 7 This is the cogging torque waveform of a permanent magnet motor with 6 slots and 1 pole pair considering core saturation;

[0046] Figure 8 This is the FFT decomposition diagram of the radial air gap flux density of a permanent magnet motor with 6 slots and 1 pole pair considering core saturation;

[0047] Fig. 9 The present invention provides a schematic diagram of the cogging torque of a permanent magnet motor considering core saturation for analysis. DETAILED DESCRIPTION

[0048] like Figure 4 The figure shows a fractional-slot permanent magnet motor with 6 stator teeth and 1 pair of poles.

[0049] A method for analyzing the cogging torque of a permanent magnet motor considering core saturation is divided into five main steps: parallel magnetization of permanent magnets, introduction of a saturation coefficient to obtain a variable air gap permeability, obtaining a changed air gap flux density, Fourier decomposition of the air gap flux density, and obtaining harmonics that generate the cogging torque.

[0050] 1. The permanent magnets are magnetized in parallel, and the magnetomotive force is perfectly sinusoidal, such as Figure 1 As shown, there is no need to perform Fourier decomposition on the magnetomotive force. The magnetomotive force only has the fundamental wave, and the permanent magnet has one pair of poles. The mathematical model of the magnetomotive force is: F(θ, t) = Acosp r (ω r t-θ).

[0051] 2. Ignoring the air gap permeability of the core saturation, Figure 2 As shown, N s is 6. The mathematical model after Fourier decomposition:

[0052]

[0053] Considering that after the core is saturated, the air gap permeability changes, the saturation coefficient is introduced, such as Figure 3 As shown. The saturation coefficient after Fourier decomposition is:

[0054]

[0055] The final air gap permeability is the original permeability multiplied by the saturation coefficient:

[0056]

[0057] 3. The air gap magnetic flux density B is equal to the product of the permanent magnet magnetomotive force F and the air gap magnetic permeability P:

[0058]

[0059] 4. Perform Fourier decomposition on the air gap magnetic flux:

[0060]

[0061] 5. Get different harmonic pole pairs and rotation speeds. s =6, p r =1 and substitute, respectively, the number of pole pairs |1-j6|, the rotation speed Pole pair number 1+j6, rotation speed Pole pair number |(2n+1)-j6|, rotation speed Pole pair number (2n+1)+j6, rotation speed Pole pair number |(2n-1)-j6|, rotation speed Pole pair number (2n-1)+j6, rotation speed Six different harmonics.

[0062] The obtained harmonics are shown in Tables 1, 2, and 3 below.

[0063] Table 1 Harmonics generated by stator slot modulation only

[0064]

[0065] Table 2 Harmonics generated by saturation coefficient modulation only

[0066] Harmonic order Speed 1 (1 is adjusted to 1 by the saturation factor 2) <![CDATA[ω r t]]> 3 (1 is adjusted to 3 by the saturation factor 2) <![CDATA[ω r t]]> 5 (1 is adjusted to 5 by the saturation factor 4) <![CDATA[ω r t]]> 7 (1 is adjusted to 7 by the saturation factor 6) <![CDATA[ω r t]]>

[0067] Table 3 Harmonics generated by simultaneous modulation of stator slots and saturation coefficient

[0068]

[0069] According to the condition that two harmonics with the same pole pair number and different speeds will produce cogging torque, there is no harmonic that meets the condition in Table 1, and no cogging torque will be generated, such as Figure 5 As shown, the cogging torque is very small and can be ignored.

[0070] However, considering the saturation effect proposed by the present invention, the analysis of the saturation coefficient is introduced. In Table 3, taking the fifth harmonic as an example, two fifth harmonics appear, and their rotation speeds are not equal, generating cogging torque. Harmonics in Table 3 that meet the condition that "two harmonics with the same pole pair number and different rotation speeds will generate cogging torque" will all generate cogging torque.

[0071] contrast Figure 6 and Figure 8 The FFT analysis of the air gap flux density of the permanent magnet motor (obtained by finite element software) shows that, taking the fifth harmonic as an example, after considering the saturation effect, Figure 8 The amplitude of the fifth harmonic increases, and the fifth harmonics at different speeds appear, which verifies the correctness of the present invention.

[0072] In summary, the present invention has found the reason why the motor generates cogging torque, and has clarified the harmonic order that generates cogging torque. The amplitude and phase of these harmonics are calculated based on the specific motor parameters, and the amplitude and phase of these harmonics are brought into the cogging torque expression to accurately calculate the value of the cogging torque. The peak value of the cogging torque is fitted to 0.8Nm according to the analysis method of the present invention, which is in line with the actual situation. It provides a basis for the compensation of the control system and reduces the fluctuation of the motor speed.

Claims

1. An analytical method for the cogging torque of a permanent magnet motor considering core saturation, characterized in that: The steps include: The mathematical model of the air gap permeance without considering the core saturation is multiplied by the saturation coefficient to obtain the air gap permeance P(θ, t) considering the core saturation. The saturation coefficient is: Among them, a0 is the saturation coefficient constant term, P r is the number of rotor pole pairs, ω r is the rotor mechanical angular frequency, θ is the magnetomotive force phase angle, a n is the amplitude of each saturation coefficient harmonic, n is the number of saturation coefficient harmonic, and t is time; Multiply P(θ, t) by the permanent magnet magnetomotive force F(θ, t) to obtain the air gap flux density B(θ, t): Perform Fourier decomposition on the air gap magnetic flux B(θ, t) to obtain different harmonic pole pairs and rotation speeds; According to the condition that the same number of pole pairs but different speeds will produce cogging torque, the harmonic order that produces cogging torque is found, and the amplitude and phase of these harmonics are obtained according to the specific motor parameters. The amplitude and phase of these harmonics are substituted into the cogging torque expression to calculate the value of the cogging torque, thereby providing a basis for the torque compensation of the permanent magnet motor control system and reducing the speed fluctuation of the permanent magnet motor.

2. The analytical method for the cogging torque of a permanent magnet motor considering core saturation according to claim 1, characterized in that: The permanent magnets are magnetized in parallel, and the magnetomotive force is perfectly sinusoidal. There is no need to perform Fourier decomposition on the magnetomotive force, and the magnetomotive force only has the fundamental wave.

3. The analytical method for the cogging torque of a permanent magnet motor considering core saturation according to claim 1, characterized in that: The air gap magnetic flux B(θ, t) is decomposed by Fourier to obtain: Where A is the magnetomotive force amplitude, P j is the permeability amplitude, N s is the number of stator slots.

4. The analytical method for the cogging torque of a permanent magnet motor considering core saturation according to claim 3, characterized in that: By Fourier decomposition of the air gap magnetic flux B(θ,t), different air gap magnetic flux harmonic pole pairs and rotation speeds are obtained, which are pole pairs|p r -jN s |, rotation speed Pole pair number p r +jN s , rotation speed Pole pair number|(2n+1)p r -jN s |, rotation speed Pole pair number (2n+1)p r +jN s , rotation speed Pole pairs|(2n-1)p r -jN s |, rotation speed Pole pair number (2n-1)p r +jN s , rotation speed Six different harmonics.

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