An Analytical Calculation Method for Vibration and Noise of an Outer Rotor Axial Flux Hub Motor

Through the modal superposition method and air gap magnetic field model, the vibration and noise of the axial flux motor are calculated, which solves the problem of not considering the acoustic radiation efficiency in the existing technology, and realizes high-precision vibration and noise analysis, supporting the motor optimization design.

CN113868929BActive Publication Date: 2025-06-24ANHUI UNIV
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Patent Information

Application Number
CN202111295874.0
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2021-11-03
Publication Date
2025-06-24
Estimated Expiration
2041-11-03

AI Technical Summary

Technical Problem

In the prior art, the vibration noise analytical model of axial flux motor does not take into account the influence of acoustic radiation efficiency, so the accuracy is poor.

Method used

The modal superposition method is used to establish an air gap magnetic field model and calculate the electromagnetic force, calculate the modal parameters and vibration mode of the end cap, obtain the overall sound power level of the flux motor, and verify the analysis and calculation results through simulation and experiments.

Benefits of technology

High-precision analysis and calculation of vibration and noise of the axial flux hub motor of the external rotor is realized, which can quickly predict electromagnetic vibration and noise within the entire speed range, providing a theoretical basis for the optimization design of the axial flux motor.

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Abstract

The present invention discloses a method for analytically calculating the vibration and noise of an outer-rotor axial-flux hub motor, belonging to the technical field of motor vibration and noise calculation, and comprising the following steps: S1: Establish an air-gap magnetic field model and calculate the electromagnetic force; S2: Calculate the modal parameters and vibration modes of the end cover; S3: Calculate the vibration response of the end cover; S4: Obtain the overall sound power level of the flux motor; S5: Verify the results. Based on the modal superposition method, the present invention can calculate the vibration response of any point on the end cover surface and quickly predict the electromagnetic vibration and noise in the entire speed range, providing a theoretical basis for the optimal design of the axial-flux motor vibration and noise, and is worthy of being popularized and used.
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Description

Technical Field

[0001] The present invention relates to the technical field of motor vibration and noise calculation, and particularly to an analytical calculation method for the vibration and noise of an outer-rotor axial-flux hub motor. Background Art

[0002] Electromagnetic noise, mechanical noise, and aerodynamic noise are the main sources of motor noise. At present, researchers have only conducted extensive research on the vibration and noise of traditional radial motors. Compared with radial motors, axial-flux motors have a series of advantages such as high power density, high efficiency, and compact structure. However, as a new type of motor, the vibration and noise of axial-flux motors have not received effective attention. Especially for low-speed outer-rotor axial-flux hub motors, electromagnetic noise dominates.

[0003] Two effective ways to calculate the vibration and noise of motors are the numerical method and the analytical method. Currently, researchers have proposed many numerical prediction models. For example, Belgian scholar dos Santos et al. established a multi-physics field model for switched reluctance motors to predict vibration and noise, which takes into account the control model of the motor. An important drawback of the numerical method is that it consumes a large amount of computing resources. In addition, since vehicle motors often operate under variable-speed conditions, it is necessary to predict the vibration and noise under their acceleration conditions. Using a numerical model is obviously unrealistic.

[0004] Extensive research has been conducted on the analytical modeling of the vibration and noise of radial motors. For example, the Chinese patent application with publication number CN109214125A proposed an analytical calculation method for electromagnetic noise for radial motors. However, due to the obvious differences in the structures of radial motors and axial-flux motors, the modal vibration modes and the calculation methods of the sound radiation efficiency of the two are different. Therefore, the analytical model of radial motors is no longer applicable to axial-flux motors. In order to quickly predict the vibration and noise of axial-flux motors, it is necessary to establish an analytical model for the vibration and noise of axial-flux motors. W. Wang et al. calculated the vibration and noise of axial-flux motors using a lumped parameter model in their paper, and did not consider the influence of the sound radiation efficiency, so the accuracy is poor. Therefore, an analytical calculation method for the vibration and noise of an outer-rotor axial-flux hub motor is proposed. Summary of the Invention

[0005] The technical problem to be solved by the present invention is: how to solve the problem that the analytical model of the vibration and noise of axial-flux motors in the prior art does not consider the influence of the sound radiation efficiency, resulting in poor accuracy, and provides an analytical calculation method for the vibration and noise of an outer-rotor axial-flux hub motor. This method is based on the modal superposition method, can calculate the vibration at any position of the motor structure, and obtain the sound radiation of the entire motor by calculating the sound radiation efficiency of each mode.

[0006] The present invention solves the above technical problems through the following technical solutions, which include the following steps:

[0007] S1: Establish an air-gap magnetic field model and calculate the electromagnetic force

[0008] Establish an air-gap magnetic field model for the outer-rotor axial-flux motor, consider the influence of edge effects through a radial dependence function, and calculate the electromagnetic force acting on the surface of the permanent magnet;

[0009] S2: Calculate the modal parameters and vibration modes of the end cover

[0010] Calculate the modal parameters and vibration modes of the end cover according to the plate and shell theory;

[0011] S3: Calculate the vibration response of the end cover

[0012] Calculate the vibration response of the end cover according to the modal superposition method;

[0013] S4: Obtain the overall sound power level of the flux motor

[0014] Calculate the sound radiation efficiency of each order mode of the end cover, and then obtain the overall sound power level of the axial-flux motor;

[0015] S5: Result verification

[0016] Verify the analytical calculation results through simulation and experiments.

[0017] Furthermore, the step S1 includes the following sub-steps:

[0018] S11: Model the axial-flux motor along the circumferential direction of the permanent magnet, where the Z direction and the θ direction represent the axial and circumferential directions of the axial-flux motor respectively; assume that the rotor is fixed and the stator system rotates in the opposite direction at the same angular velocity, then the expressions of the permanent magnet magnetic field, armature reaction magnetic field, and relative air-gap permeance are:

[0019]

[0020]

[0021]

[0022] Among them, B z_mag represents the axial magnetic field of the permanent magnet without slotting, B z_arm represents the armature reaction magnetic field without slotting, λ a represents the relative air-gap permeance, n represents the spatial order of the permanent magnet and takes an odd number, h represents the current order, N t = GCD(2p, Q s ), s ν represents the rotation direction of the ν-th order armature reaction magnetic field; B mn and Bav represent the amplitudes of the permanent magnet magnetic field and the armature reaction magnetic field respectively, and λ aμ represents the amplitude of the relative air-gap permeance, p represents the number of pole pairs of the permanent magnet, and w r represents the angular velocity of the motor rotation, t represents time, and θ represents the spatial angle.

[0023] S12: Introduce a radial correction function to consider the influence of the edge effect, and the expression is:

[0024]

[0025] wherein, R1 and R2 represent the inner diameter and the outer diameter of the permanent magnet respectively, r represents the solution radius, and β is used to correct the decreasing speed of the magnetic flux density at the inner and outer diameters of the permanent magnet;

[0026] S13: The axial air-gap magnetic flux density considering the edge effect and the slotting is expressed as:

[0027] B z (θ, t, r) = (B z_mag + B z_arm )λ a G(r);

[0028] According to the Maxwell tensor method, ignoring the influence of the tangential magnetic flux density, the axial electromagnetic force is expressed as:

[0029]

[0030] wherein, μ0 represents the vacuum permeability;

[0031] S14: Calculate the electromagnetic force wave of the outer-rotor axial-flux hub motor by using the above formulas.

[0032] Furthermore, the step S2 includes the following sub-steps:

[0033] S21: Equivalent the end cover by using an annular thin plate model, and the vibration equation of the thin plate in polar coordinates satisfies:

[0034]

[0035] wherein, ρ represents the density of the end cover, h represents the thickness of the end cover, w represents the axial displacement response of the end cover, is the bending stiffness of the plate, ν is the Poisson's ratio, E is the Young's modulus, and t is time;

[0036] S22: The vibration mode solution is calculated as:

[0037] W mn (r, θ) = [A mn J m (α mn r) + B mn Im (α mn r)+C mn Y m (α mn r)+D mn K m (α mn r)]cos(mθ+φ);

[0038] Among them, J m , Y m and I m , K m respectively represent the first and second kind of Bessel functions and the first and second kind of modified Bessel functions; A mn , B mn , C mn and D mn are four undetermined coefficients; represents the frequency constant, ω mn represents the natural frequency, W mn (r,θ) represents the modal vibration mode.

[0039] Furthermore, the step S3 includes the following sub-steps:

[0040] S31: Considering damping, the structural vibration equation of the plate when the electromagnetic force acts is expressed as:

[0041]

[0042] Then substituting the thin plate vibration equation in step S21 into the above formula, we get:

[0043]

[0044] Multiplying both sides by the pq-order vibration mode function and integrating along the radial and circumferential directions, we can obtain:

[0045]

[0046] Among them, η mn represents the modal participation factor, and m, n, p, and q respectively represent the axial and radial spatial orders of the mode;

[0047] Due to the orthogonality of the vibration mode function, the above formula is transformed into:

[0048]

[0049] Among them,

[0050] The electromagnetic force wave at any radius is expressed as:

[0051]

[0052] Its amplitude and phase can be obtained through two-dimensional Fourier decomposition;

[0053] S32: Calculate the modal participation factor as:

[0054]

[0055] Phase:

[0056]

[0057] where ω m represents the frequency of the electromagnetic force, ω mn represents the natural frequency of the end cover, and ξ mn is the damping ratio;

[0058] S33: Based on the modal superposition method, obtain the vibration response of the overall end cover:

[0059]

[0060] Furthermore, in the step S4, calculate the sound radiation efficiency of each order mode of the end cover, and then obtain the overall sound power level of the axial flux motor. The analytical formula used is:

[0061]

[0062] where represents the wave number, ρ0 is the air density, c0 is the speed of sound in air, S is the noise radiation surface area, is the mean square vibration velocity;

[0063] Sound power:

[0064] Sound power level:

[0065] where ∏ ref = 10 -12 W represents the reference sound power.

[0066] Furthermore, the step S5 includes the following sub-steps:

[0067] S51: Calculate the electromagnetic force acting on the surface of the permanent magnet through JMAG software, load it on the structural model by means of node force transfer, and finally calculate in LMS virtual lab according to the modal superposition method and the boundary element method respectively;

[0068] S52: Test the electromagnetic noise of the axial flux motor in an anechoic chamber to verify the effectiveness of the analytical model.

[0069] The present invention has the following advantages compared with the prior art: The analytical calculation method for the vibration and noise of the outer rotor axial flux hub motor can calculate the vibration response of any point on the end cover surface based on the modal superposition method, and can quickly predict the electromagnetic vibration and noise in the entire speed range, providing a theoretical basis for the optimal design of the axial flux motor vibration and noise, and is worthy of being popularized and used. Description of the Drawings

[0070] Figure 1 is a schematic structural diagram of the axial flux motor in the embodiment of the present invention;

[0071] Figure 2 is a flowchart of the analytical calculation method for the vibration and noise of the outer rotor axial flux hub motor provided in the embodiment of the present invention;

[0072] Figure 3 is a schematic diagram of the sound radiation efficiency of each order mode obtained by calculation of the motor in the embodiment of the present invention;

[0073] Figure 4 is a schematic diagram of the multi-physics field model used in the numerical simulation in the embodiment of the present invention;

[0074] Figure 5 is a schematic diagram of the comparison between the analytical calculation and the numerical calculation results of the electromagnetic vibration of the motor under no-load conditions in the embodiment of the present invention;

[0075] Figure 6 is a schematic diagram of the comparison between the analytical calculation and the numerical calculation results of the electromagnetic noise of the motor under no-load conditions in the embodiment of the present invention;

[0076] Figure 7 is a schematic diagram of the comparison between the analytical calculation and the numerical calculation results of the electromagnetic vibration of the motor under load conditions in the embodiment of the present invention;

[0077] Figure 8 is a schematic diagram of the comparison between the analytical calculation and the numerical calculation results of the electromagnetic noise of the motor under load conditions in the embodiment of the present invention.

[0078] Figure 1 In the figure: 1. End cover; 2. Stator; 3. Rotating shaft; 4. Housing; 5. Permanent magnet. Detailed Embodiment

[0079] The following is a detailed description of the embodiments of the present invention. The embodiments are implemented on the premise of the technical solution of the present invention, and detailed implementation manners and specific operation processes are given. However, the protection scope of the present invention is not limited to the following embodiments.

[0080] For a certain type of 30-pole 27-slot (30p27s) outer rotor axial flux hub motor with a rated speed of 600 rpm, its structure is as Figure 1As shown, the implementation test of the present invention was carried out;

[0081] As Figure 2 shown, this embodiment provides a technical solution: a method for analyzing and calculating the vibration and noise of an outer-rotor axial-flux hub motor, including the following steps:

[0082] Step 1): Establish an air-gap magnetic field model of the outer-rotor axial-flux motor (i.e., the axial motor in Figure 2 ), consider the influence of edge effects through a radial dependence function, and calculate the electromagnetic force acting on the surface of the permanent magnet.

[0083] 11) Model the axial-flux motor along the circumferential direction of the permanent magnet, where the Z-direction and the θ-direction represent the axial and circumferential directions of the axial-flux motor respectively. Assuming the rotor is fixed and the stator system rotates in the opposite direction at the same angular velocity, the expressions for the permanent magnet magnetic field, armature reaction magnetic field, and relative air-gap permeance are:

[0084]

[0085]

[0086]

[0087] Among them, B z_mag represents the axial magnetic field of the permanent magnet when there is no slotting, B z_arm represents the armature reaction magnetic field when there is no slotting, λ a represents the relative air-gap permeance, n represents the spatial order of the permanent magnet and takes an odd number, h represents the current order, N t =GCD(2p,Q s ), s ν represents the rotation direction of the ν-th order armature reaction magnetic field, B mn and B av respectively represent the amplitudes of the permanent magnet magnetic field and the armature reaction magnetic field, λ aμ represents the amplitude of the relative air-gap permeance, p represents the number of pole pairs of the permanent magnet, w r represents the angular velocity of the motor rotation, t represents time, and θ represents the spatial angle.

[0088] 12) Introduce a radial correction function to consider the influence of edge effects, and the expression is:

[0089]

[0090] Among them, R1 and R2 respectively represent the inner diameter and outer diameter of the permanent magnet, r represents the solution radius, β is used to correct the decrease rate of the magnetic flux density at the inner and outer diameters of the permanent magnet, and its value can be obtained through parametric finite element analysis.

[0091] 13) The axial air-gap magnetic density considering the edge effect and slotting can be expressed as:

[0092] B z (θ,t,r) = (B z_mag +B z_arm )λ a G(r) (5);

[0093] According to the Maxwell tensor method, ignoring the influence of the tangential magnetic density, the axial electromagnetic force is expressed as:

[0094]

[0095] Among them, μ0 represents the vacuum permeability;

[0096] 14) According to Equation (6), the electromagnetic force wave of the outer-rotor axial-flux hub motor can be calculated.

[0097] Step 2): Calculate the modal parameters and vibration modes of the end cover according to the plate and shell theory, including:

[0098] 21) The end cover is equivalent using the circular thin plate model, and the vibration equation of the thin plate in polar coordinates satisfies:

[0099]

[0100] Among them, ρ represents the density of the end cover, h represents the thickness of the end cover, w represents the axial displacement response of the end cover, is the bending stiffness of the plate, ν is the Poisson's ratio, E is the Young's modulus, and t is the time;

[0101] The vibration mode solution is:

[0102] W mn (r,θ) = [A mn J m (α mn r)+B mn I m (α mn r)+C mn Y m (α mn r)+D mn K m (α mn r)]cos(mθ + φ) (8);

[0103] Among them, J m 、Y m and I m 、K m represent the first and second kind Bessel functions and the first and second kind modified Bessel functions respectively. A mn 、B mn 、C mnand D mn The four undetermined coefficients depend on the boundary conditions at the inner and outer boundaries; Denotes the frequency constant, ω mn Denotes the natural frequency, W mn (r, θ) represents the modal vibration mode.

[0104] 22) Large vibrations and noises will occur only when the spatial order of the electromagnetic force is equal to the modal order and the frequency is close to the modal frequency; for the 30-pole 27-slot axial-flux motor in this embodiment, the spatial order of its electromagnetic force is an integer multiple of 3.

[0105] First, perform modal calculations on the axial-flux motor in the finite element. For modes of the 6th order and higher, due to their high frequencies, their influence on vibration and noise is small and is not considered in this embodiment. And for the 0th(a) order mode, its boundary condition is close to the state of being fixed inside and free outside, while the 0th(b) and 3rd order modes are close to being fixed inside and simply supported outside. Solve their modal vibration modes according to these two boundary conditions.

[0106] For the 0th(a) order mode, the boundary conditions:

[0107]

[0108] Where a and b are the outer diameter and inner diameter of the end cover respectively, M r Is the bending moment of the annular plate around the r direction, V r Is the Kelvin-Kirchhoff resultant force;

[0109] For the 0th(b) and 3rd order modes, the boundary conditions:

[0110]

[0111] Where,

[0112]

[0113] In the formula, a and b represent the inner and outer diameters of the end cover respectively, w represents the axial displacement response of the end cover, Is the gradient operator;

[0114] Substitute (9)-(11) into (8) to solve for the frequency constant α mn And A mn 、B mn 、C mn and D mn The four undetermined coefficients.

[0115] Then the natural frequency:

[0116]

[0117] For the mode with axial modulus \(m = 0\), its mode shape function is:

[0118] W mn (r,θ) = [A mn J m (α mn r)+B mn I m (α mn r)+C mn Y m (α mn r)+D mn K m (α mn r)] (13);

[0119] For the mode with \(m≠0\), there are phase angles \(\varphi≠0\) and two mode shapes. Since the end cover has an axisymmetric structure, the two mode shapes have exactly the same modal frequency, and the mode shape function is:

[0120]

[0121] Step 3): Calculate the vibration response of the end cover according to the modal superposition method, including:

[0122] 31) Considering damping, the structural vibration equation of the plate under the action of electromagnetic force can be expressed as:

[0123]

[0124] Substituting the aforementioned thin plate vibration equation, we can get:

[0125]

[0126] Multiply both sides by the \(pq\)-order mode shape function obtained in Equation (14) and integrate along the radial and circumferential directions to get:

[0127]

[0128] Due to the orthogonality of the mode shape function, the above equation can be reduced to:

[0129]

[0130] where, The electromagnetic force wave at any radius can be expressed as:

[0131]

[0132] Its amplitude and phase can be obtained through two-dimensional Fourier decomposition.

[0133] When \(m = 0\),

[0134]

[0135] Similarly, when m = 3,

[0136]

[0137]

[0138] 32) The modal participation factor is calculated from Equation (18) as:

[0139]

[0140] Phase:

[0141]

[0142] where ω m represents the frequency of the electromagnetic force, ω mn represents the natural frequency of the end cover, and ξ mn is the damping ratio. 33) Based on the modal superposition method, the overall vibration response of the end cover is obtained:

[0143]

[0144] where m and n respectively represent the axial and radial modal orders, η mn (t) represents the modal participation factor, and w is the axial displacement of the end cover.

[0145] Step 4): Calculate the sound radiation efficiency of each order of the end cover, and then obtain the overall sound power level of the axial flux motor. The analytical formula used is:

[0146]

[0147] where represents the wave number.

[0148] Substitute Equations (13)-(14) into (26) to calculate the sound radiation efficiency of each order, as shown in Figure 3 shown.

[0149] Sound power:

[0150] Sound power level:

[0151] where Π ref = 10 -12 W represents the reference sound power.

[0152] In Step 5), it specifically includes the following steps:

[0153] Verify the results of the analytical calculation through simulation. First, calculate the electromagnetic force acting on the surface of the permanent magnet by JMAG software, load it on the structural model by means of node force transfer, and finally calculate in LMS virtual lab according to the modal superposition method and the boundary element method respectively. The calculation process is as Figure 4 shown, Figure 5 and Figure 6 are the comparisons of the analytical calculation and the numerical calculation results under no-load and load conditions. It can be seen that the two are in good agreement in the whole frequency band, and the analytical calculation results can reflect the main peaks and trends of electromagnetic vibration and noise.

[0154] Test the electromagnetic noise of the axial flux motor in the semi-anechoic chamber, as Figure 7 shown. Verify the effectiveness of the analytical model of the present invention through the comparison of the electromagnetic noise calculated analytically in Figure 8 and the test.

[0155] In summary, the analytical calculation method of the vibration and noise of the outer-rotor axial flux hub motor in the above embodiments, based on the modal superposition method, can calculate the vibration response of any point on the end cover surface, and quickly predict the electromagnetic vibration and noise in the whole speed range, providing a theoretical basis for the optimal design of the axial flux motor vibration and noise, and is worthy of being popularized and used.

[0156] Although the embodiments of the present invention have been shown and described above, it can be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those of ordinary skill in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. An analytical calculation method for the vibration and noise of an outer-rotor axial-flux hub motor, characterized in that, It includes the following steps: S1: Establish an air-gap magnetic field model and calculate the electromagnetic force Establish an air-gap magnetic field model of an outer-rotor axial-flux motor, consider the influence of edge effect through a radial dependence function, and calculate the electromagnetic force acting on the surface of the permanent magnet; The step S1 includes the following sub-steps: S11: Model the axial-flux motor along the circumferential direction of the permanent magnet, where the Z direction and the θ direction represent the axial and circumferential directions of the axial-flux motor respectively; assuming the rotor is fixed and the stator system rotates in the opposite direction at the same angular velocity, the expressions of the permanent magnet magnetic field, armature reaction magnetic field, and relative air-gap permeance are: Among them, B z_mag represents the axial magnetic field of the permanent magnet without slots, B z_arm represents the armature reaction magnetic field without slots, λ a represents the relative air-gap permeance, n represents the spatial order of the permanent magnet and takes an odd number, h represents the current order, N t = GCD(2p, Q s ), s ν represents the rotation direction of the ν-th order armature reaction magnetic field, B mn and B av respectively represent the amplitudes of the permanent magnet magnetic field and the armature reaction magnetic field, λ aμ represents the amplitude of the relative air-gap permeance, p represents the number of pole pairs of the permanent magnet, w r represents the angular velocity of the motor rotation, t represents time, and θ represents the spatial angle; S12: Introduce a radial correction function to consider the influence of edge effect, and the expression is: where, R1 and R2 represent the inner diameter and outer diameter of the permanent magnet respectively, r represents the solution radius, and β is used to correct the decreasing speed of the magnetic flux density at the inner and outer diameters of the permanent magnet; S13: The axial air-gap magnetic flux density considering edge effect and slotting is expressed as: B z (θ,t,r) = (B z_mag + B z_arm )λ a G(r); According to the Maxwell tensor method, ignoring the influence of tangential magnetic flux density, the axial electromagnetic force is expressed as: where, μ0 represents the vacuum permeability; S14: Calculate the electromagnetic force wave of the outer-rotor axial-flux hub motor using the axial electromagnetic force expression; S2: Calculate the modal parameters and vibration modes of the end cover Calculate the modal parameters and vibration modes of the end cover according to the plate and shell theory; S3: Calculate the vibration response of the end cover Calculate the vibration response of the end cover according to the modal superposition method; S4: Obtain the overall sound power level of the flux motor Calculate the sound radiation efficiency of each order mode of the end cover, and then obtain the overall sound power level of the axial-flux motor; S5: Result verification Verify the analytical calculation results through simulation and experiment.

2. The analytical calculation method for vibration and noise of an outer-rotor axial-flux hub motor according to claim 1, characterized in that: The step S2 includes the following sub-steps: S21: Equivalent the end cover using an annular thin plate model, and the vibration equation of the thin plate in polar coordinates satisfies: where ρ represents the density of the end cover, h represents the thickness of the end cover, and w represents the axial displacement response of the end cover. is the bending stiffness of the plate, ν is the Poisson's ratio, E is the Young's modulus, and t is the time. S22: The obtained vibration mode solution is: W mn (r,θ) = [A mn J m (α mn r) + B mn I m (α mn r) + C mn Y m (α mn r) + D mn K m (α mn r)] cos(mθ + φ); Among them, J m , Y m and I m , K m represent the first and second kind of Bessel functions and the first and second kind of modified Bessel functions respectively; A mn , B mn , C mn and D mn represent four undetermined coefficients; represents the frequency constant, ω mn represents the natural frequency, W mn (r,θ) represents the mode shape.

3. The analytical calculation method for vibration and noise of an outer rotor axial flux hub motor according to claim 2, wherein: The step S3 includes the following sub-steps: S31: Considering damping, the structural vibration equation of the plate when the electromagnetic force acts is expressed as: Substitute the thin plate vibration equation in step S21 into the above formula to get: Multiply both sides by the pq-order vibration mode function and integrate along the radial and circumferential directions to obtain: where η mn represents the modal participation factor, and m, n, p, and q respectively represent the axial and radial spatial orders of the mode; Due to the orthogonality of the vibration mode function, the above formula is transformed into: Among them, The electromagnetic force wave at any radius is expressed as: Its amplitude and phase can be obtained through two-dimensional Fourier decomposition; S32: Calculate the modal participation factor as: Phase: where, ω m represents the frequency of the electromagnetic force, ω mn represents the natural frequency of the end cover, and ξ mn is the damping ratio; S33: Based on the modal superposition method, obtain the overall vibration response of the end cover:

4. A method for analytically calculating the vibration and noise of an outer-rotor axial-flux hub motor according to claim 3, characterized in that: In the step S4, when calculating the sound radiation efficiency of each order mode of the end cover and then obtaining the overall sound power level of the axial-flux motor, the analytical formula used is: Among them, represents the wave number, ρ0 is the air density, c0 is the sound propagation speed in air, S is the noise radiation surface area, is the mean square vibration velocity; Sound power: Sound power level: Among them, Π ref = 10 -12 W, representing the reference sound power.

5. A method for analytically calculating the vibration and noise of an outer-rotor axial-flux hub motor according to claim 4, characterized in that: The step S5 includes the following sub-steps: S51: Calculate the electromagnetic force acting on the surface of the permanent magnet through JMAG software, load it on the structural model by the way of node force transfer, and finally calculate in LMS virtual lab according to the modal superposition method and the boundary element method respectively; S52: Test the electromagnetic noise of the axial-flux motor in an anechoic chamber to verify the effectiveness of the analytical model.

Citation Information

Patent Citations

  • A calculation method of electromagnetic vibration noise of electric machine

    CN109214125A