Three-dimensional angle eccentric permanent magnet synchronous motor electromagnetic force wave calculation method based on magnetic conductance correction

Abstract

The invention discloses a three-dimensional angle eccentric permanent magnet synchronous motor electromagnetic force wave calculation method based on magnetic conductance correction, and the method comprises the following steps: obtaining the parameter information of a motor in a normal state, calculating the air gap flux density of the permanent magnet synchronous motor under a load through the parameter information of the motor, and obtaining the radial flux density and the tangential flux density; a magnetic conductance correction coefficient under static eccentricity is introduced, and radial flux density and tangential air gap flux density after eccentricity are obtained through calculation; calculating radial force waves and tangential force waves acting on the surfaces of the stator and the rotor during eccentricity according to the flux density after eccentricity; and introducing a magnetic conductance correction coefficient under inclined eccentricity to obtain a three-dimensional electromagnetic force wave which changes along with a space axial position under angular eccentricity of the inner rotor of the permanent magnet synchronous motor. According to the method, by introducing the axial eccentricity correction coefficient, the electromagnetic force wave of the permanent magnet synchronous motor in the angular eccentricity state of the inner rotor is represented as a function about the axial coordinate, and the technical problem that a traditional two-dimensional eccentricity model cannot process axial angular eccentricity is effectively solved.

Description

Technical Field

[0001] This invention belongs to the field of magnetic field analysis technology for permanent magnet synchronous motors, specifically relating to a method for calculating electromagnetic force waves of a three-dimensional angularly eccentric permanent magnet synchronous motor based on magnetic permeability correction. Background Technology

[0002] In recent years, permanent magnet synchronous motors (PMSMs) have been widely used in high-performance fields such as new energy vehicles due to their advantages such as high power density, high efficiency, large torque-to-inertia ratio, and wide speed range.

[0003] However, due to manufacturing and assembly errors, wear, or load deformation, motors often exhibit axial static angular eccentricity, dynamic angular eccentricity, and their coupling effects. Angular eccentricity causes changes in the distribution of the air gap magnetic field, leading to electromagnetic vibration and noise problems. This is because angular eccentricity disrupts the originally relatively uniform distribution of the air gap magnetic field, altering the electromagnetic force waves (especially radial force waves) generated by the harmonic interaction of the air gap magnetic field, severely affecting the motor's performance and stability. Therefore, timely and accurate calculation of the electromagnetic force of a permanent magnet synchronous motor under angular eccentricity is crucial for studying the vibration characteristics of the motor under tilt eccentricity and diagnosing the form of rotor eccentricity. Summary of the Invention

[0004] To overcome the shortcomings of existing technologies, this invention provides a method for calculating electromagnetic force waves of a three-dimensional angularly eccentric permanent magnet synchronous motor based on magnetic permeability correction. By introducing an axial eccentricity correction coefficient, the electromagnetic force waves of the permanent magnet synchronous motor under internal rotor angular eccentricity are characterized as a function of the axial coordinate, effectively solving the technical problem that traditional two-dimensional eccentricity models cannot handle axial angular eccentricity. Furthermore, this method greatly reduces the complexity of electromagnetic force wave mathematical calculations, significantly simplifying the entire calculation process compared to finite element simulation.

[0005] The aforementioned method for calculating electromagnetic force waves of a three-dimensional angularly eccentric permanent magnet synchronous motor based on magnetic permeability correction includes the following steps:

[0006] S1: Obtain parameter information of the motor under normal conditions, and use the motor parameter information to calculate the air gap magnetic flux density of the permanent magnet synchronous motor under load, and obtain the radial magnetic flux density B. r With tangential magnetic flux density B t ;

[0007] S2: Introducing the magnetic permeability correction coefficient under static eccentricity, the radial magnetic flux density B after eccentricity is calculated. rs With tangential air gap magnetic flux density B ts ;

[0008] S3: Calculate the radial force wave P acting on the stator and rotor surfaces during eccentricity based on the magnetic flux density after eccentricity. rs With tangential force wave P ts ;

[0009] S4: By introducing the magnetic permeability correction coefficient under tilted eccentricity, the three-dimensional electromagnetic force wave of the permanent magnet synchronous motor under the angular eccentricity of the inner rotor varies with the spatial axial position.

[0010] Further, in step S1, the air gap magnetic flux density is obtained by multiplying the magnetomotive force by the air gap permeability. The magnetomotive force includes the stator fundamental magnetomotive force, the stator harmonic magnetomotive force, and the rotor harmonic magnetomotive force, which are calculated in detail below:

[0011] S11. Calculate the stator fundamental magnetomotive force:

[0012]

[0013] In the formula, F p θ represents the fundamental amplitude, p represents the number of pole pairs, θ represents the spatial angular coordinate, and ω1 represents the electric angular frequency. Indicates the initial phase angle of the fundamental wave;

[0014] S12. Calculate the stator harmonic magnetomotive force:

[0015]

[0016] In the formula, v represents the harmonic order, which is determined by the stator winding distribution and the number of slots, and F v This represents the amplitude of the vth harmonic magnetomotive force. This represents the initial phase angle of the vth harmonic;

[0017] S13. Calculate the rotor harmonic magnetomotive force:

[0018]

[0019] In the formula, μ represents the harmonic order of the rotor permanent magnet magnetic field, which is related to the shape of the permanent magnet and the magnetization method, and F μ ω represents the amplitude of the μ-th harmonic magnetomotive force. μ Represents the rotational angular frequency of the μth harmonic. This represents the initial phase angle of the μth harmonic;

[0020] S14. Calculate the air gap permeability, and expand the air gap permeability into a Fourier series:

[0021] Λ(θ)=Λ0+Λ1cos(Z1θ),

[0022] In the formula, Λ(θ) represents the air gap permeability distribution function with respect to angle, Λ0 represents the constant component of air gap permeability, Λ1 represents the amplitude of the first harmonic of air gap permeability, and Z1 represents the number of stator slots.

[0023] Multiplying the total magnetomotive force by the air gap permeability, we obtain the expression for the air gap magnetic flux density:

[0024]

[0025] Wherein, the radial magnetic flux density is:

[0026] Tangential magnetic flux density is:

[0027] In the formula, B r B represents the radial air gap magnetic flux density. t The tangential air gap magnetic flux density is represented by μ0, the free permeability is represented by g, and the nominal air gap length is represented by f. r The radial air gap magnetic flux density is represented by , k represents the magnetic permeability harmonic order number, and Z represents the number of stator slots.

[0028] Furthermore, in step S2, a static eccentricity permeability correction coefficient is introduced, and the eccentricity-corrected air gap magnetic flux density is obtained by multiplying the static eccentricity permeability correction coefficient with the air gap magnetic flux density:

[0029]

[0030] Among them, the radial magnetic flux density after eccentricity is: B rs (θ,t)=B r (θ,t)ε δs (θ),

[0031] The tangential air gap magnetic flux density is: B ts (θ,t)=B t (θ,t)ε δs (θ),

[0032] In the formula, ε δs ε′ represents the static eccentricity correction factor, and ε′ represents the static eccentricity.

[0033] Furthermore, the calculation steps for step S3 are as follows:

[0034] S31. The electromagnetic force wave acting on the stator and rotor surfaces under static eccentricity is obtained from the air gap magnetic flux density calculation under static eccentricity:

[0035] The radial force wave is:

[0036] The tangential force wave is:

[0037] S32. Introduce a permeability correction coefficient under dynamic eccentricity. The air gap magnetic flux density after eccentricity is obtained by multiplying the permeability correction coefficient under dynamic eccentricity with the air gap magnetic flux density:

[0038]

[0039] Among them, the radial magnetic flux density after eccentricity is: B rd (θ,t)=B r (θ,t)ε δd(θ,t),

[0040] The tangential air gap magnetic flux density is: B td (θ,t)=B t (θ,t)ε δd (θ,t),

[0041] In the formula, ε δd ε represents the dynamic eccentricity permeability correction factor. d ′ represents the dynamic eccentricity, ω d Indicates the dynamic eccentric rotation angular frequency;

[0042] S33. The electromagnetic force wave acting on the stator and rotor surfaces during dynamic eccentricity is obtained from the air gap magnetic flux density calculation:

[0043] The radial force wave is:

[0044] The tangential force wave is:

[0045] Further, step S4 calculates the static eccentricity and dynamic eccentricity, where,

[0046] Quiet bias:

[0047] Motion bias:

[0048] In the formula, z represents the axial position coordinate, ε′(z) s The static eccentricity, ε′(z), represents the axial variation. d The dynamic eccentricity represents the change in axial direction.

[0049] Compared with the prior art, the present invention has the following advantages:

[0050] The method of this invention can take into account the rotor axial angular eccentricity of the internal rotor permanent magnet synchronous motor, overcoming the problem that the traditional two-dimensional analytical model ignores the rotor shaft angular eccentricity in three-dimensional space. At the same time, compared with three-dimensional finite element simulation, this method has higher computational efficiency while ensuring a certain level of accuracy. It can be used to guide motor vibration reduction and design optimization. It is of great significance for timely and accurate detection and resolution of shaft eccentricity problems of permanent magnet synchronous motors, ensuring stable motor operation, extending motor service life, and reducing operating costs. Attached Figure Description

[0051] Figure 1 This is a flowchart of the method of the present invention;

[0052] Figure 2 This is a comparison diagram of the spatial distribution of eccentric radial magnetic flux density (calculation and simulation) of the present invention (eccentricity 0.25mm);

[0053] Figure 3This is a comparison diagram of the spatial distribution (calculation and simulation) of the eccentric tangential magnetic flux density of the present invention (eccentricity 0.25mm);

[0054] Figure 4 This is a comparison diagram of the spatial distribution of radial force waves with and without eccentricity in this invention (eccentricity 0.25mm);

[0055] Figure 5 This is a comparison diagram of the spatial distribution of eccentric and non-eccentric tangential force waves in this invention (eccentricity 0.25mm);

[0056] Figure 6 This is a diagram showing the spatial distribution of radial force waves in this invention (eccentricity 0.25mm on the left and 0mm on the right) as a function of axial position. Detailed Implementation

[0057] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0058] like Figure 1 As shown, the method for calculating electromagnetic force waves of a three-dimensional angularly eccentric permanent magnet synchronous motor based on magnetic permeability correction includes the following steps:

[0059] (i) Obtain parameter information of the motor under normal conditions, and use the motor parameter information to calculate the air gap magnetic flux density of the permanent magnet synchronous motor under load, and obtain the radial magnetic flux density B. r With tangential magnetic flux density B t .

[0060] Table 1 below shows the parameter information of the motor under normal conditions. The air gap magnetic flux density of the permanent magnet synchronous motor under load is calculated using the motor parameter information. The air gap magnetic flux density is obtained by multiplying the magnetomotive force by the air gap permeability.

[0061] The calculation example in this application is a surface-mounted internal rotor permanent magnet synchronous motor: b(θ,t)=f(θ,t)*Λ(θ,t).

[0062] Table 1

[0063] Parameter name numerical values Stator tooth count Ns 6 <![CDATA[Stator outer diameter S od / mm]]> 55 <![CDATA[Inner diameter of stator S id / mm]]> 26.8 <![CDATA[Stator tooth width S tw / mm]]> 4 <![CDATA[Stator tooth slot depth S sd / mm]]> 10 <![CDATA[Stator tooth surface thickness S tft / mm]]> 2.5 <![CDATA[Stator tooth surface width S tfw / mm]]> 12.5 Axial length of stator and rotor l / mm 60 <![CDATA[Rotor outer diameter R od / mm]]> 26 <![CDATA[Inner diameter R of the rotor id / mm]]> 12 <![CDATA[Radial length b of the permanent magnet m / mm]]> 12 <![CDATA[Tangential length h of the permanent magnet m / mm]]> 4 <![CDATA[Axial length l of the permanent magnet m / mm]]> 60 Extreme logarithm Pn 2 Number of coil turns N 6

[0064] Magnetomotive force includes stator fundamental magnetomotive force, stator harmonic magnetomotive force, and rotor harmonic magnetomotive force. The specific calculation process is as follows:

[0065] (1) Calculate the fundamental magnetomotive force of the stator:

[0066]

[0067] In the formula, F pθ represents the fundamental amplitude, p represents the number of pole pairs, θ represents the spatial angular coordinate, and ω1 represents the electric angular frequency. This represents the initial phase angle of the fundamental wave.

[0068] (2) Calculate the stator harmonic magnetomotive force:

[0069]

[0070] In the formula, v represents the harmonic order, which is determined by the stator winding distribution and the number of slots, and F v This represents the amplitude of the vth harmonic magnetomotive force. This represents the initial phase angle of the vth harmonic.

[0071] (3) Calculate the rotor harmonic magnetomotive force:

[0072]

[0073] In the formula, μ represents the harmonic order of the rotor permanent magnet magnetic field, which is related to the shape of the permanent magnet and the magnetization method, and F μ ω represents the amplitude of the μ-th harmonic magnetomotive force. μ Represents the rotational angular frequency of the μth harmonic. This represents the initial phase angle of the μth harmonic.

[0074] (4) Calculate the air gap permeability, mainly due to the influence of stator slotting. The air gap permeability is expanded into a Fourier series:

[0075] Λ(θ)=Λ0+Λ1cos(Z1θ),

[0076] In the formula, Λ(θ) represents the air gap permeability distribution function with respect to angle, Λ0 represents the constant component of air gap permeability, Λ1 represents the amplitude of the first harmonic of air gap permeability, and Z1 represents the number of stator slots.

[0077] Multiplying the total magnetomotive force by the air gap permeability, we obtain the expression for the air gap magnetic flux density:

[0078]

[0079] Wherein, the radial magnetic flux density is:

[0080] Tangential magnetic flux density is:

[0081] In the formula, B r B represents the radial air gap magnetic flux density. t The tangential air gap magnetic flux density is represented by μ0, the free permeability is represented by g, and the nominal air gap length is represented by f. r The radial air gap magnetic flux density is represented by , k represents the magnetic permeability harmonic order number, and Z represents the number of stator slots.

[0082] (ii) Introducing the magnetic permeability correction coefficient under static eccentricity, the radial magnetic flux density B after eccentricity is calculated. rs With tangential air gap magnetic flux density B ts .

[0083] The air gap magnetic flux density after eccentricity is obtained by multiplying the permeability correction coefficient under static eccentricity with the air gap magnetic flux density:

[0084]

[0085] Among them, the radial magnetic flux density after eccentricity is: B rs (θ,t)=B r (θ,t)ε δs (θ),

[0086] The tangential air gap magnetic flux density is: B ts (θ,t)=B t (θ,t)ε δs (θ),

[0087] In the formula, ε δs ε′ represents the static eccentricity correction factor, and ε′ represents the static eccentricity.

[0088] (III) Calculation of the radial force wave P acting on the stator and rotor surfaces during eccentricity from the magnetic flux density after eccentricity rs With tangential force wave P ts .

[0089] (1) The electromagnetic force wave acting on the stator and rotor surfaces under static eccentricity is obtained by calculating the air gap magnetic flux density under static eccentricity:

[0090] The radial force wave is:

[0091] The tangential force wave is:

[0092] (2) Introduce a permeability correction coefficient under dynamic eccentricity, and obtain the air gap magnetic flux density after eccentricity by multiplying the permeability correction coefficient under dynamic eccentricity with the air gap magnetic flux density:

[0093]

[0094] Among them, the radial magnetic flux density after eccentricity is: B rd (θ,t)=B r (θ,t)ε δd (θ,t),

[0095] The tangential air gap magnetic flux density is: B td (θ,t)=B t (θ,t)ε δd (θ,t),

[0096] In the formula, ε δdε represents the dynamic eccentricity permeability correction factor. d ′ represents the dynamic eccentricity, ω d This represents the dynamic eccentric rotational angular frequency.

[0097] (3) The electromagnetic force wave acting on the stator and rotor surfaces during dynamic eccentricity is obtained by calculating the air gap magnetic flux density during dynamic eccentricity:

[0098] The radial force wave is:

[0099] The tangential force wave is:

[0100] (iv) By introducing the magnetic permeability correction coefficient under tilted eccentricity, the three-dimensional electromagnetic force wave of the permanent magnet synchronous motor under the angular eccentricity of the inner rotor varies with the spatial axial position.

[0101] Quiet bias:

[0102] Motion bias:

[0103] In the formula, z represents the axial position coordinate, ε′(z) s The static eccentricity, ε′(z), represents the axial variation. d The dynamic eccentricity represents the change in axial direction.

[0104] The specific motor parameters for each embodiment are shown in Table 1. The results of each embodiment are as follows: Figures 2-6 .

[0105] like Figure 2 what Figure 3 The figure shows a comparison of the spatial distribution of radial and tangential air gap magnetic flux density under an eccentricity of 0.25 mm. The model calculation results (red line) and the three-dimensional finite element simulation results (blue line) exhibit consistent distribution characteristics in the spatial domain, with a maximum deviation of ≤2.5%. This comparison verifies that the analytical algorithm for air gap magnetic field based on the permeability correction coefficient (see steps S1-S2) has computational accuracy and meets the precision requirements for engineering analysis. Figure 4 what Figure 5 The figure shows a comparison of the spatial distribution of radial and tangential electromagnetic force waves under an eccentricity of 0.25 mm. As can be seen from the figure, the force wave in the eccentric state (red line) calculated using the patented model exhibits significant waveform distortion compared to the baseline condition without eccentricity (blue line), with an amplitude difference of 8.2%. Figure 4 Peak point). This result proves that the method of the present invention can effectively characterize the modulation effect of rotor angular eccentricity on electromagnetic force waves (corresponding to the force wave equation in step S3). Figure 6As shown, the patented model presents the electromagnetic force wave calculation output for three-dimensional asymmetric angular eccentricity (corresponding to the motor parameters in Table 1 of the embodiment). When the rotor's left eccentricity is 0.25mm and the right eccentricity is zero, the radial force wave spatial distribution exhibits gradient characteristics along the axial coordinate z (as shown by the gradient color scale), directly verifying the effectiveness of the axial magnetic permeability correction function ε. δs / d (θ,t,z)(Step S4) Analyze the effectiveness of the three-dimensional eccentric field.

[0106] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for calculating electromagnetic force waves of a three-dimensional angularly eccentric permanent magnet synchronous motor based on magnetic permeability correction, characterized in that, Includes the following steps: S1: Obtain parameter information of the motor under normal conditions, and use the motor parameter information to calculate the air gap magnetic flux density of the permanent magnet synchronous motor under load, and obtain the radial magnetic flux density B. r With tangential magnetic flux density B t ; S2: Introducing the magnetic permeability correction coefficient under static eccentricity, the radial magnetic flux density B after eccentricity is calculated. rs With tangential air gap magnetic flux density B ts ; S3: Calculate the radial force wave P acting on the stator and rotor surfaces during eccentricity based on the magnetic flux density after eccentricity. rs With tangential force wave P ts ; S4: By introducing the magnetic permeability correction coefficient under tilted eccentricity, the three-dimensional electromagnetic force wave of the permanent magnet synchronous motor under the angular eccentricity of the inner rotor varies with the spatial axial position.

2. The method for calculating electromagnetic force waves of a three-dimensional angularly eccentric permanent magnet synchronous motor based on magnetic permeability correction according to claim 1, characterized in that, In step S1, the air gap magnetic flux density is obtained by multiplying the magnetomotive force by the air gap permeability. The magnetomotive force includes the stator fundamental magnetomotive force, the stator harmonic magnetomotive force, and the rotor harmonic magnetomotive force, which are calculated in detail below: S11. Calculate the stator fundamental magnetomotive force: In the formula, F p θ represents the fundamental amplitude, p represents the number of pole pairs, θ represents the spatial angular coordinate, and ω1 represents the electric angular frequency. Indicates the initial phase angle of the fundamental wave; S12. Calculate the stator harmonic magnetomotive force: In the formula, v represents the harmonic order, which is determined by the stator winding distribution and the number of slots, and F v This represents the amplitude of the vth harmonic magnetomotive force. This represents the initial phase angle of the vth harmonic; S13. Calculate the rotor harmonic magnetomotive force: In the formula, μ represents the harmonic order of the rotor permanent magnet magnetic field, which is related to the shape of the permanent magnet and the magnetization method, and F μ ω represents the amplitude of the μ-th harmonic magnetomotive force. μ Represents the rotational angular frequency of the μth harmonic. This represents the initial phase angle of the μth harmonic; S14. Calculate the air gap permeability, and expand the air gap permeability into a Fourier series: Λ(θ)=Λ0+Λ1cos(Z1θ), In the formula, Λ(θ) represents the air gap permeability distribution function with respect to angle, Λ0 represents the constant component of air gap permeability, Λ1 represents the amplitude of the first harmonic of air gap permeability, and Z1 represents the number of stator slots. Multiplying the total magnetomotive force by the air gap permeability, we obtain the expression for the air gap magnetic flux density: Wherein, the radial magnetic flux density is: Tangential magnetic flux density is: In the formula, B r B represents the radial air gap magnetic flux density. t The tangential air gap magnetic flux density is represented by μ0, the free permeability is represented by g, and the nominal air gap length is represented by f. r The radial air gap magnetic flux density is represented by , k represents the magnetic permeability harmonic order number, and Z represents the number of stator slots.

3. The method for calculating electromagnetic force waves of a three-dimensional angularly eccentric permanent magnet synchronous motor based on magnetic permeability correction according to claim 1, characterized in that, In step S2, a static eccentricity correction coefficient for magnetic permeability is introduced. The eccentricity-corrected air gap magnetic flux density is obtained by multiplying the static eccentricity correction coefficient for magnetic permeability by the air gap magnetic flux density. Among them, the radial magnetic flux density after eccentricity is: B rs (θ,t)=B r (θ,t)ε δs (θ), The tangential air gap magnetic flux density is: B ts (θ,t)=B t (θ,t)ε δs (θ), In the formula, ε δs ε′ represents the static eccentricity correction factor, and ε′ represents the static eccentricity.

4. The method for calculating electromagnetic force waves of a three-dimensional angularly eccentric permanent magnet synchronous motor based on magnetic permeability correction according to claim 1, characterized in that, The calculation steps for step S3 are as follows: S31. The electromagnetic force wave acting on the stator and rotor surfaces under static eccentricity is obtained from the air gap magnetic flux density calculation under static eccentricity: The radial force wave is: The tangential force wave is: S32. Introduce a permeability correction coefficient under dynamic eccentricity. The air gap magnetic flux density after eccentricity is obtained by multiplying the permeability correction coefficient under dynamic eccentricity with the air gap magnetic flux density: Among them, the radial magnetic flux density after eccentricity is: B rd (θ,t)=B r (θ,t)ε δd (θ,t), The tangential air gap magnetic flux density is: B td (θ,t)=B t (θ,t)ε δd (θ,t), In the formula, ε δd ε represents the dynamic eccentricity permeability correction factor. d ′ represents the dynamic eccentricity, ω d Indicates the dynamic eccentric rotation angular frequency; S33. The electromagnetic force wave acting on the stator and rotor surfaces during dynamic eccentricity is obtained from the air gap magnetic flux density calculation: The radial force wave is: The tangential force wave is:

5. The method for calculating electromagnetic force waves of a three-dimensional angularly eccentric permanent magnet synchronous motor based on magnetic permeability correction according to claim 1, characterized in that, Step S4 calculates the static and dynamic eccentricities, where, Quiet bias: Motion bias: In the formula, z represents the axial position coordinate, ε′(z) s The static eccentricity, ε′(z), represents the axial variation. d The dynamic eccentricity represents the change in axial direction.

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