Vibration calculation method of embedded spoke type permanent magnet motor for flywheel energy storage

Abstract

The invention relates to a vibration calculation method of an embedded spoke type permanent magnet motor for flywheel energy storage, which comprises the following steps of: respectively establishing equivalent magnetic network models for stator, air gap and rotor areas of the embedded spoke type permanent magnet motor according to the distribution characteristics of magnetic lines in the embedded spoke type permanent magnet motor; based on a Maxwell stress tensor method, calculating the time domain electromagnetic force density and the centralized electromagnetic force of the stator tooth surface of the spoke-embedded permanent magnet motor through the air gap magnetic flux density calculated by the equivalent magnetic network model; solving a vibration transfer function set of the embedded spoke type permanent magnet motor containing the electromagnetic force modulation effect through an analytical method; and finally, calculating the vibration response of the embedded spoke type permanent magnet motor through the combination of the vibration transfer function set and the centralized electromagnetic force in the frequency domain. According to the method, rapid calculation of the vibration response of the embedded spoke type permanent magnet motor is realized.

Description

Technical Field

[0001] The invention belongs to the field of electromagnetic mechanical structure response calculation of an embedded spoke type permanent magnet motor, and in particular relates to a vibration calculation method of an embedded spoke type permanent magnet motor for flywheel energy storage. Background Art

[0002] Flywheel energy storage technology is a technology that uses an electric motor to drive a flywheel to accelerate rotation and store energy, and converts kinetic energy into electrical energy through a generator when needed. When the flywheel rotates at high speed, it can store a large amount of energy. With the advancement of materials science, especially the application of high-strength composite materials, the energy density of flywheel energy storage systems has been significantly improved.

[0003] Flywheel energy storage technology is widely used in uninterruptible power supply (UPS), power grid frequency regulation, electric vehicle fast charging stations and other fields. Its main advantages include high efficiency, long life, fast response capability, and environmental friendliness. Due to the lack of chemical reaction, flywheel energy storage devices have high charging and discharging efficiency and are relatively simple to maintain. They can achieve tens of thousands of charge and discharge cycles with almost no change in performance.

[0004] In order to maximize the efficiency and extend the service life of the flywheel energy storage system, the motor inside the system must run at a very high speed, usually up to tens of thousands to hundreds of thousands of revolutions per minute. This requires the motor to have extremely high running stability. Any slight imbalance or vibration may lead to increased mechanical wear, reduce system efficiency, and even cause safety problems. Therefore, it is very necessary to accurately evaluate the electromagnetic vibration performance of the motor and take measures to optimize it.

[0005] At present, the traditional method for evaluating the electromagnetic vibration performance of motors is mainly to use commercial finite element analysis (FEA) software for simulation calculations. Although this method can provide relatively accurate results, it has some obvious disadvantages. First, the simulation process is time-consuming, especially when performing multi-condition or multi-parameter optimization, which requires a lot of computing resources and time. Secondly, complex model settings and solution conditions may increase the uncertainty of the results, which prolongs the design optimization cycle. In addition, for motors with complex structures, traditional finite element methods may not be able to fully simulate some dynamic effects in actual operation, thus affecting the accuracy of the evaluation. Summary of the invention

[0006] The present invention aims to provide a vibration calculation method for an embedded spoke permanent magnet motor for flywheel energy storage, so as to solve the technical problem of how to quickly and accurately evaluate and optimize the electromagnetic vibration performance of the motor.

[0007] To achieve the above purpose, the specific technical solution of a vibration calculation method of an embedded spoke permanent magnet motor for flywheel energy storage of the present invention is as follows:

[0008] A vibration calculation method for an embedded spoke permanent magnet motor for flywheel energy storage comprises the following steps:

[0009] S1. Model the equivalent magnetic network of the stator region of the embedded spoke permanent magnet motor;

[0010] S2, perform equivalent magnetic network modeling on the air gap region of the embedded spoke permanent magnet motor;

[0011] S3, perform equivalent magnetic network modeling on the inner rotor area of ​​the embedded spoke permanent magnet motor;

[0012] S4, connecting the equivalent magnetic network models of the stator region, the air gap region and the rotor region in the embedded spoke permanent magnet motor to establish an equivalent magnetic network model matrix equation;

[0013] S5. Solve the matrix equation of the equivalent magnetic network model to calculate the electromagnetic force density distribution of the motor in the time domain and space during the entire calculation cycle, and calculate the concentrated electromagnetic force acting on each tooth surface of the stator according to the concentrated force calculation model;

[0014] S6. Calculate the vibration transfer function of the concentrated force on each tooth surface to a point on the outer surface of the stator to obtain a complete vibration transfer function;

[0015] S7. The concentrated electromagnetic force and the vibration transfer function calculated according to the equivalent magnetic network model are jointly superimposed to calculate the vibration acceleration of a point on the stator surface when electromagnetic forces of different orders act on each stator tooth surface, thereby completing the calculation of the motor vibration.

[0016] As a further improvement of the present invention, in S1, according to the magnetic line distribution and electromagnetic topological characteristics of the stator area in the embedded spoke permanent magnet motor, the stator yoke area is equivalently modeled using a circumferential magnetic permeance, and the number of magnetic permeances is twice the number of stator teeth; the stator teeth are equivalently modeled using two radial magnetic permeances, and the equivalent magnetomotive force source generated by the winding in the slot is between the two magnetic permeances; the stator tooth pole shoes and stator slot area are equivalently modeled using multiple rectangular cross magnetic permeance grids; the stator slot is modeled using a radial magnetic permeance to reflect the influence of leakage flux in the slot.

[0017] As a further improvement of the present invention, in S2, the air gap area between the stator and rotor components in the embedded spoke permanent magnet motor is in a regular circular shape, and a rectangular cross grid is used to arrange two layers of magnetic permeability grids in the air gap area to achieve complete division, and the number of circumferential air gap areas corresponds to the number of circumferential magnetic permeability units in the stator tooth area.

[0018] As a further improvement of the present invention, in S3, according to the magnetic field line distribution and electromagnetic topological characteristics of the rotor area inside the embedded spoke permanent magnet motor, the surface area of ​​the rotor core is divided into multiple grid units of the same width along the circumferential direction, and the core area in each unit is modeled using a rectangular cross magnetic guide grid, and the air area is modeled using a single radial magnetic guide and connected to the rectangular cross magnetic guide grid of the core area below; the rectangular permanent magnet in the rotor is modeled in sections, and each section has a radial magnetic guide and an equivalent magnetic potential source; the core area below the permanent magnet is modeled using multiple arc-shaped magnetic guides.

[0019] As a further improvement of the present invention, in S4, the magnetic permeances located at the tooth pole shoes and stator slots in the stator region of the embedded spoke permanent magnet motor are connected correspondingly to the magnetic permeances of the uppermost layer of the air gap region, and the magnetic permeances of the lowermost layer of the air gap region are connected to the magnetic permeances of the mixed region at the uppermost layer of the rotor region. According to the number of magnetic permeances and the values ​​of each magnetic permeance, the magnetic permeance matrix, node magnetic potential matrix and magnetic flux matrix of the equivalent magnetic network model of the embedded spoke permanent magnet motor are established and merged into one matrix equation; when performing transient solution, the rotation of the motor is simulated by changing the node connection relationship between the magnetic permeance of the air gap region and the magnetic permeance of the stator core surface region to solve the internal magnetic field of the motor under transient state.

[0020] As a further improvement of the present invention, in S5, the matrix equation of the constructed equivalent magnetic network model of the embedded spoke permanent magnet motor is solved, and the magnetic permeability of the magnetic permeance in the core saturation area is iteratively updated during the transient solution. The magnetic density on the magnetic permeance between two nodes is calculated by solving the node magnetic potential value of the equivalent magnetic network in the air gap area, and then the electromagnetic force density in the time domain and space of the motor in the entire calculation cycle is calculated by the Maxwell stress tensor method, and the force transfer model is used to calculate the concentrated electromagnetic force acting on each tooth surface of the stator.

[0021] As a further improvement of the present invention, in S6, based on the dynamic equations of the equivalent circular ring model and the material property parameters and dimensions of the motor stator, an analytical method is used to calculate the transfer function of the vibration generated at a certain point on the outer surface of the stator under the action of the concentrated force on each stator tooth surface and the magnitude of each modal frequency of the stator, and a complete vibration transfer function is obtained based on the superposition principle.

[0022] As a further improvement of the present invention, in S7, the electromagnetic concentrated force calculated by the equivalent magnetic network model is subjected to two-dimensional Fourier decomposition to obtain the electromagnetic force amplitude and phase of each order of the concentrated force on each tooth surface and the corresponding frequency, which are multiplied with the vibration transfer function obtained by analysis to obtain the vibration acceleration on the stator tooth surface, thereby completing the calculation of the motor vibration.

[0023] As a further improvement of the present invention, the embedded spoke permanent magnet motor is a three-phase embedded spoke permanent magnet motor with 6 slots and 4 poles, including a stator, a rotor, an air gap, an external support and a rotating shaft; the stator includes a stator yoke, stator teeth, stator slots, stator tooth pole shoes, stator slots, and windings in the slots; the rotor includes a rotor core and permanent magnets; four permanent magnets are inserted into the rotor core in a spoke shape, and the surface of the rotor core is an irregular curve to suppress back electromotive force harmonics and torque pulsation, and the stator and rotor of the motor are fastened together by bolts through the skeletons at the front and rear ends.

[0024] Beneficial effects:

[0025] The present invention proposes a vibration calculation method for an embedded spoke permanent magnet motor for flywheel energy storage, which provides an efficient solution to the problems existing in the prior art, such as long calculation time and insufficient simulation accuracy.

[0026] The present invention adopts the equivalent magnetic network model method to replace the traditional finite element analysis method, which greatly reduces the calculation time and required computing resources. The equivalent magnetic network model can quickly solve the electromagnetic force density distribution of the motor by simplifying the modeling of each key area inside the motor, thereby improving the overall calculation efficiency.

[0027] By carrying out detailed equivalent magnetic network modeling for the stator, air gap and rotor regions respectively, and taking into account the electromagnetic topological characteristics and magnetic line distribution of each region, the present invention can accurately calculate the electromagnetic force density distribution of the motor and its influence on the stator vibration while maintaining high accuracy.

[0028] Compared with traditional finite element simulation, the method of the present invention is simpler in the model establishment process. By establishing an equivalent magnetic network model, the difficulty of processing complex geometric shapes is reduced, making the model easier to establish and adjust.

[0029] By accurately calculating the vibration characteristics of the motor, the present invention can help designers better understand the behavior of the motor in actual operation, thereby guiding the design optimization of the motor, reducing the vibration and noise during motor operation, and improving the overall performance of the motor.

[0030] The method provided by the present invention can not only calculate the electromagnetic force distribution, but also further calculate the vibration acceleration of the stator surface through the vibration transfer function, providing important basic data for subsequent motor structure strength analysis, noise control and other aspects.

[0031] In summary, the vibration calculation method of the embedded spoke permanent magnet motor for flywheel energy storage proposed in the present invention can not only effectively improve the calculation efficiency, but also ensure the accuracy of the calculation results, which is of great significance for the design optimization and performance improvement of the motor. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 It is a two-dimensional electromagnetic topological diagram of the embedded spoke permanent magnet motor of the present invention;

[0033] Figure 2 It is a magnetic force line distribution diagram of the embedded spoke type permanent magnet motor of the present invention;

[0034] Figure 3 It is a schematic diagram of an equivalent magnetic network model of the stator region of the embedded spoke type permanent magnet motor of the present invention;

[0035] Figure 4 It is a schematic diagram of an equivalent magnetic network model of a rotor region of an embedded spoke permanent magnet motor of the present invention;

[0036] Figure 5 It is a schematic diagram of an equivalent magnetic network model of an air gap area and an irregularly modified area on the rotor surface of an embedded spoke type permanent magnet motor of the present invention;

[0037] Figure 6 It is a comparison diagram of the air gap radial magnetic flux density results calculated by the present invention and the finite element method;

[0038] Figure 7 It is a comparison diagram of the air gap tangential magnetic flux density results calculated by the present invention and the finite element method;

[0039] Figure 8 It is a comparison diagram of the radial electromagnetic force density results calculated by the present invention and the finite element method;

[0040] Fig. 9 It is a comparison diagram of the radial electromagnetic force density harmonic distribution results calculated by the present invention and the finite element method;

[0041] Fig.10 It is the force transmission model from distributed force to concentrated force adopted by the present invention;

[0042] Fig.11 The distribution of concentrated force application points and vibration measurement points in the model for calculating the transfer function of the present invention;

[0043] Fig.12 is a time domain waveform diagram of the concentrated force on each stator tooth surface obtained by the present invention;

[0044] Fig.13 is a frequency domain distribution diagram of concentrated force on a single stator tooth surface obtained by the present invention;

[0045] Fig.14 It is a comparison diagram of the vibration acceleration results obtained by the present invention and finite element and experimental tests;

[0046] Explanation of the markings in the figure: 1. stator yoke; 2. stator teeth; 3. stator slots; 4. stator tooth pole shoes; 5. stator slot openings; 6. windings in slots; 7. air gap; 8. rotor core; 9. permanent magnet; 10. air gap area; 11. rotor surface area; 12. air area; 13. vibration measurement point. DETAILED DESCRIPTION

[0047] In order to better understand the purpose, structure and function of the present invention, the vibration calculation method of the embedded spoke permanent magnet motor for flywheel energy storage of the present invention is further described in detail below with reference to the accompanying drawings.

[0048] Implementation example:

[0049] like Figure 1 As shown, the embedded spoke permanent magnet motor in this embodiment is a three-phase embedded spoke permanent magnet motor with 6 slots and 4 poles, which includes a stator, a rotor, an air gap 7, an external support and a rotating shaft; wherein the stator component includes a stator yoke 1, stator 2 teeth, stator slots 3, stator tooth pole shoes 4, stator slots 5, and slot windings 6; the rotor component includes a rotor core 8 and a permanent magnet 9. Four permanent magnets 9 are inserted into the rotor core in the shape of spokes, with an angle of 90 degrees between them, and the surface of the rotor core 8 is an irregular curve to suppress back electromotive force harmonics and torque pulsation. The stator and rotor of the motor are fastened and connected by bolts through the skeletons at the front and rear ends.

[0050] A vibration calculation method for an embedded spoke permanent magnet motor for flywheel energy storage is as follows:

[0051] Step 1: According to the magnetic field line distribution and electromagnetic topological characteristics of the stator region in the embedded spoke permanent magnet motor, different magnetic permeability equivalent units and equivalent magnetic potential units are used to model the equivalent magnetic network of the stator core and air slot region.

[0052] Figure 3 FIG. 1 is a schematic diagram of an equivalent magnetic network model of a motor stator region used in an embodiment of the present invention. w is the equivalent magnetomotive force source generated by the winding in the slot, P yoke is the magnetic permeance on the stator yoke area, P tooth is the magnetic permeance on the stator teeth, P slot is the magnetic permeability in the stator slot, P r and P t are the radial and tangential permeances of the rectangular cross permeance unit, H cell and W cell is the height and width of the rectangular cross-magnetic permeability unit. Among them, the equivalent magnetomotive force source generated by the winding in the slot can be expressed as:

[0053] F n =N c I w sin(2πfe t+θ w ) (1)

[0054] In the formula, w=1, 2, 3 represent the A phase, B phase and C phase winding respectively, N c is the number of winding turns, I w is the current amplitude of the w-phase winding, f e and θ w are the frequency and phase of the current respectively, and t represents time.

[0055] The stator yoke 1 consists of two tangential magnetic permeabilities P yoke After decomposition, it can be expressed as:

[0056]

[0057] Where μ0 and μ r are vacuum magnetic permeability and relative magnetic permeability, L stack is the effective axial length of the motor, θ yoke is the angle between the center lines of two adjacent stator teeth, R o and R i are the outer and inner diameters of the stator yoke respectively.

[0058] Stator tooth 2 consists of two radially arranged magnetic permeance P tooth Modeling can be expressed as:

[0059]

[0060] Where W t and H s are the width and height of the stator teeth respectively.

[0061] The stator slot 3 consists of a radially arranged magnetic permeability P slot Modeling can be expressed as:

[0062]

[0063] Where W s is the average width of the stator slot area.

[0064] The model is divided and modeled by a series of rectangular magnetic permeability units, in which the radial and tangential magnetic permeabilities G t and G r Can be expressed as:

[0065]

[0066] The stator tooth pole shoe 4 and the stator slot 5 are modeled by a series of rectangular cross permeability units. The radial and tangential permeabilities P r and P tCan be expressed as:

[0067]

[0068] Step 2: mesh the air gap area between the stator and rotor components of the embedded spoke permanent magnet motor using multiple layers of rectangular cross flux units to complete the equivalent magnetic network modeling of the area.

[0069] Figure 5 The figure shows a schematic diagram of the equivalent magnetic network model of the motor air gap area and the irregular modified area on the rotor surface used in the present invention. The air gap area between the stator and the rotor components in the embedded spoke permanent magnet motor is a regular ring shape. A rectangular cross grid is used to arrange two layers of magnetic permeability grids in this area to achieve complete segmentation. The calculation formula is the same as that of equations (7) and (8), except that the relative magnetic permeability is 1. In addition, the number of circumferential magnetic permeability units needs to be consistent with the number of circumferential magnetic permeability units in the stator tooth area in order to establish a one-to-one connection relationship.

[0070] Step 3: According to the magnetic field line distribution and electromagnetic topological characteristics of the rotor area in the embedded spoke permanent magnet motor, a hybrid modeling method of rectangular cross magnetic permeability units and series single magnetic permeabilities is adopted for the non-uniform area on the surface of the rotor core, a segmented modeling method is adopted for the spoke permanent magnets in the rotor area, and a multi-segment arc magnetic permeability modeling method is adopted for the core area under the permanent magnet, and the equivalent magnetic network models of each part are connected according to the spatial position relationship;

[0071] Figure 4 The figure shows the schematic diagram of the equivalent magnetic network model of the motor rotor area used in the present invention. It can be seen that the area is mainly divided into four parts for modeling and calculation. The first part is the irregularly modified area of ​​the outermost layer of the rotor core, and its modeling schematic diagram is shown in FIG. Figure 5 As shown in . The non-uniform shape area on the surface of the rotor core contains the core and air. The area is divided into multiple grid units of the same width along the circumferential direction. The core area in each unit is modeled using a rectangular cross magnetic permeance grid. If it contains an air area, a single radial magnetic permeance is used to model it and connected to the rectangular cross magnetic permeance grid of the core area below. The magnetic permeance P ca It can be expressed as:

[0072]

[0073] Where W1 and H1 are the width and height of the rectangular unit area. The second part is a crescent-shaped area on the permanent magnet, which also uses a series of radial magnetic permeability P perpendicular to the permanent magnet. core Modeling can be expressed as:

[0074]

[0075] Among them, W cc and H cc is the width and height of the rectangular unit. The third part is the permanent magnet area. The rectangular permanent magnet adopts a segmented modeling method. Each segment has a radial magnetic permeability PPM and an equivalent magnetic potential source FPM, which can be expressed as:

[0076]

[0077] Among them, B rm is the remanent magnetic density of the permanent magnet material, h PM and w PM is the height and width of the permanent magnet, N PM is the number of segmented modeling of the permanent magnet. The fourth part is the area below the permanent magnet. The core area below the permanent magnet is modeled using multiple arc-shaped magnetic permeability Pcells, which can be expressed as:

[0078]

[0079] In the formula, R co and R ci are the outer and inner diameters of the arc area, θ cell is the arc length of the arc area. After completing the division and calculation of the magnetic permeance, the magnetic permeances are connected in sequence from top to bottom according to the spatial corresponding position relationship of each magnetic permeance.

[0080] Step 4, the equivalent magnetic network models of the stator, air gap and rotor regions of the embedded spoke permanent magnet motor are compared and connected according to the actual summary topological position relationship, and the equivalent magnetic network model matrix equation of the motor is established. The rotation of the motor is simulated by changing the node connection relationship between the magnetic permeance of the air gap region and the magnetic permeance of the stator core surface region, so as to solve the internal magnetic field of the motor under transient state;

[0081] The permeance and equivalent magnetic potential sources established in the above steps 1-4 are connected in sequence according to the spatial arrangement to form a complete equivalent magnetic network model of the motor. Based on the circuit principle, the matrix equations of the permeance matrix P, the equivalent magnetic potential matrix F and the magnetic flux matrix Φ are established as follows:

[0082]

[0083] Where n represents the number of nodes in the equivalent magnetic network. When performing transient solutions, the magnetic permeability connection relationship between the air gap and the stator tooth pole shoe area in the magnetic permeability matrix P needs to be changed to meet the magnetic field solution under rotation. Since the magnetic permeability of the core area material of the motor is nonlinear, the magnetic permeability of the core area needs to be updated and iterated during the solution. First, the magnetic flux density B(i,j) of the magnetic permeability between two nodes in the core area is calculated as:

[0084]

[0085] Where F(i) and F(j) are the node magnetomotive force of i and j respectively, S(i,j) is the cross-sectional area of ​​the permeance between i and j, and P(i,j) is the permeance between i and j. When the magnetic flux density iteration of the permeance satisfies the following formula, it can be considered to meet the calculation requirements:

[0086] max|B (k) (i,j)-B (k+1) (i,j)|<ζ (15)

[0087] Where ξ is the error, which is 1×10-3.

[0088] Step 5, during the entire solution cycle of the equivalent magnetic network model matrix simulation, record the node magnetic potential on the circumferential magnetic permeance in the air gap area at each moment, calculate its air gap magnetic density, and calculate the electromagnetic force density distribution in the time domain and space of the motor during the entire calculation cycle according to the Maxwell stress tensor method, and calculate the concentrated electromagnetic force acting on each tooth surface of the stator according to the concentrated force calculation model;

[0089] During the solution process of step 4, record the value of the magnetic flux density of the air gap permeance at each moment. Figure 6 and Figure 7 The following is a comparison of the radial and tangential magnetic flux density results of the air gap calculated by the present invention and the finite element method. The calculation results are basically consistent. The following formula is used to calculate the radial and tangential electromagnetic force density f in the air gap: n and f t :

[0090]

[0091] Among them B n and B t are the magnetic flux densities in the radial and tangential flux guides, respectively. Figure 8 Shown is a comparison diagram of radial electromagnetic force density results calculated by the present invention and the finite element method. Fig. 9 This is a comparison chart of the radial electromagnetic force density harmonic distribution results calculated by the present invention and the finite element method. The calculated results are relatively close. Fig.10 For the force transmission model from distributed force to concentrated force adopted by the present invention, the concentrated electromagnetic force on the z-th tooth surface can be expressed as:

[0092]

[0093] Where Q s is the number of stator teeth, θ s is the angle range of the stator tooth pole shoe, z represents the zth stator tooth, R si is the inner diameter of the stator.

[0094] Step 6, based on the structural dimension parameters of the stator of the embedded spoke permanent magnet motor, an analytical method is used to calculate the vibration transfer function of the concentrated force on each tooth surface to a point on the outer surface of the stator;

[0095] Fig.11 is the distribution of the concentrated force action points and vibration measurement points in the model for calculating the transfer function of the present invention, then the vibration response of the i-th point and the concentrated force F on the j-th tooth surface n,j The transfer function can be expressed as:

[0096]

[0097] Among them, R my is the average radius of the stator yoke, E is the Young's modulus of the stator core material, h y is the stator yoke thickness, ω fv is the angular velocity of the v-th order electromagnetic force, ω v is the frequency of the vth-order mode, is the damping coefficient of the vth-order mode, which can be expressed as:

[0098]

[0099] Step 7, the electromagnetic concentrated force and the vibration transfer function in the frequency domain calculated by the equivalent magnetic network model are superimposed to calculate the vibration acceleration of a point on the stator surface when electromagnetic forces of different orders act on each stator tooth surface;

[0100] The vibration acceleration at point i on the stator outer surface can be calculated by the following formula:

[0101]

[0102] Furthermore, the vibration acceleration of the entire stator surface can be expressed according to the superposition principle as follows:

[0103]

[0104] Fig.12 is the time domain waveform diagram of the concentrated force on each stator tooth surface obtained by the present invention, Fig.13 This is the frequency domain distribution diagram of the concentrated force on a single stator tooth surface solved by the present invention. Substituting the calculated concentrated electromagnetic force in the frequency domain into the transfer function, the vibration acceleration of the click can be calculated. In order to verify the proposed method, a 6-slot 4-pole embedded spoke permanent magnet motor was processed for vibration testing. Fig.14 This is a comparison chart of the vibration acceleration results obtained by the present invention and the finite element and experimental tests. By comparing the results of finite element simulation calculation and experimental test of the vibration response of the motor used in the present invention, it can be proved that the vibration calculation method of the embedded spoke permanent magnet motor proposed in the present invention is more accurate in calculation results.

[0105] In summary, the vibration calculation method of the embedded spoke permanent magnet motor of the present invention establishes equivalent magnetic network models for the stator, air gap and rotor regions of the embedded spoke permanent magnet motor according to the distribution characteristics of the magnetic lines of force inside the motor, calculates the time domain electromagnetic force density and concentrated electromagnetic force of the stator tooth surface of the embedded spoke permanent magnet motor based on the air gap flux density calculated by the equivalent magnetic network model using the Maxwell stress tensor method, and solves the vibration transfer function set of the embedded spoke permanent magnet motor including the electromagnetic force modulation effect by an analytical method, and calculates the vibration response of the embedded spoke permanent magnet motor by combining the vibration transfer function set with the concentrated electromagnetic force in the frequency domain. The provided scheme can provide a reference for the vibration calculation of this type of motor.

[0106] In the present invention, a rectangular cross permeance unit and a radial air permeance synthetic modeling method are used to perform refined equivalent magnetic network modeling on the irregular area on the surface of the motor rotor. Combined with a vibration transfer function construction model based on an analytical method, rapid calculation of the vibration response of the embedded spoke permanent magnet motor can be achieved; a rectangular cross permeance unit and a radial air permeance synthetic modeling method are used to divide the irregular modified area on the rotor surface into a plurality of grid units of equal width in the circumferential direction, and a rectangular cross permeance grid is used to model the core area in each unit. If an air area is included, a single radial permeance is used for modeling and connected to the rectangular cross permeance grid of the core area below, which can effectively reflect the influence of the irregular modified area on the rotor surface on the electromagnetic force of the motor and improve the calculation accuracy of the equivalent magnetic network model; based on the dynamic equation of the equivalent circular ring model and the material property parameters and size specifications of the motor stator, an analytical method is used to calculate the transfer function of the vibration generated at a certain point on the outer surface of the stator under the action of concentrated force on each stator tooth surface. Compared with the transfer function calculated by the finite element method, it has a higher calculation speed and maintains a certain accuracy. A strategy combining a hybrid equivalent magnetic network modeling method and an analytical-based vibration transfer function solution method is adopted to achieve rapid calculation of the vibration response of an embedded spoke permanent magnet motor.

[0107] It is to be understood that the present invention is described by some embodiments, and it is known to those skilled in the art that various changes or equivalent substitutions may be made to these features and embodiments without departing from the spirit and scope of the present invention. In addition, under the teachings of the present invention, these features and embodiments may be modified to adapt to specific circumstances and materials without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the scope of protection of the present invention.

Claims

1. A vibration calculation method for an embedded spoke permanent magnet motor for flywheel energy storage, characterized in that: The following steps are involved: S1. Model the equivalent magnetic network of the stator region of the embedded spoke permanent magnet motor; S2, perform equivalent magnetic network modeling on the air gap region of the embedded spoke permanent magnet motor; S3, perform equivalent magnetic network modeling on the inner rotor area of ​​the embedded spoke permanent magnet motor; S4, connecting the equivalent magnetic network models of the stator region, the air gap region and the rotor region in the embedded spoke permanent magnet motor to establish an equivalent magnetic network model matrix equation; S5. Solve the matrix equation of the equivalent magnetic network model to calculate the electromagnetic force density distribution of the motor in the time domain and space during the entire calculation cycle, and calculate the concentrated electromagnetic force acting on each tooth surface of the stator according to the concentrated force calculation model; S6. Calculate the vibration transfer function of the concentrated force on each tooth surface to a point on the outer surface of the stator to obtain a complete vibration transfer function; S7. The concentrated electromagnetic force and the vibration transfer function calculated according to the equivalent magnetic network model are jointly superimposed to calculate the vibration acceleration of a point on the stator surface when electromagnetic forces of different orders act on each stator tooth surface, thereby completing the calculation of the motor vibration.

2. The vibration calculation method of the embedded spoke permanent magnet motor for flywheel energy storage according to claim 1 is characterized in that: In S1, according to the magnetic line distribution and electromagnetic topological characteristics of the stator area in the embedded spoke permanent magnet motor, the stator yoke area is equivalently modeled using a circumferential magnetic permeance, and the number of magnetic permeances is twice the number of stator teeth; the stator teeth are equivalently modeled using two radial magnetic permeances, and the equivalent magnetomotive force source generated by the winding in the slot is between the two magnetic permeances; the stator tooth pole shoes and stator slot area are equivalently modeled using multiple rectangular cross magnetic permeance grids; the stator slot is modeled using a radial magnetic permeance to reflect the influence of leakage flux in the slot.

3. The vibration calculation method of the embedded spoke permanent magnet motor for flywheel energy storage according to claim 1 is characterized in that: In S2, the air gap area between the stator and rotor components in the embedded spoke permanent magnet motor is in a regular circular shape. A rectangular cross grid is used to arrange two layers of magnetic permeability grids in the air gap area to achieve complete segmentation. The number of circumferential air gap areas corresponds to the number of circumferential magnetic permeability units in the stator tooth area.

4. The vibration calculation method of the embedded spoke permanent magnet motor for flywheel energy storage according to claim 1 is characterized in that: In S3, according to the magnetic field line distribution and electromagnetic topological characteristics of the rotor area in the embedded spoke permanent magnet motor, the surface area of ​​the rotor core is divided into multiple grid units of the same width along the circumferential direction. The core area in each unit is modeled with a rectangular cross flux grid, and the air area is modeled with a single radial flux and connected to the rectangular cross flux grid of the core area below. The rectangular permanent magnets in the rotor are modeled in sections, with each section having a radial flux and an equivalent magnetic potential source. The core area below the permanent magnets is modeled with multiple arc flux segments.

5. The vibration calculation method of the embedded spoke permanent magnet motor for flywheel energy storage according to claim 1 is characterized in that: In S4, the permeances at the tooth pole shoes and stator slots in the stator region of the embedded spoke permanent magnet motor are connected correspondingly to the permeances of the uppermost layer of the air gap region, and the permeances of the lowermost layer of the air gap region are connected to the permeances of the mixed region at the uppermost layer of the rotor region. According to the number of permeances and the values ​​of each permeance, the permeance matrix, node magnetic potential matrix and flux matrix of the equivalent magnetic network model of the embedded spoke permanent magnet motor are established and merged into one matrix equation. When performing transient solution, the rotation of the motor is simulated by changing the node connection relationship between the permeance of the air gap region and the permeance of the stator core surface region to solve the internal magnetic field of the motor under transient state.

6. The vibration calculation method of the embedded spoke permanent magnet motor for flywheel energy storage according to claim 1 is characterized in that: In S5, the matrix equation of the constructed equivalent magnetic network model of the embedded spoke permanent magnet motor is solved, and the magnetic permeability of the magnetic permeance in the core saturation area is iteratively updated during the transient solution. The magnetic flux density on the magnetic permeance between two nodes is calculated by solving the node magnetic potential value of the equivalent magnetic network in the air gap area, and then the electromagnetic force density in the time domain and space of the motor in the entire calculation cycle is calculated by the Maxwell stress tensor method, and the force transfer model is used to calculate the concentrated electromagnetic force acting on each tooth surface of the stator.

7. The vibration calculation method of the embedded spoke permanent magnet motor for flywheel energy storage according to claim 1 is characterized in that: In S6, based on the dynamic equations of the equivalent circular ring model and the material property parameters and dimensions of the motor stator, an analytical method is used to calculate the transfer function of the vibration generated at a certain point on the outer surface of the stator under the action of concentrated force on each stator tooth surface and the magnitude of each modal frequency of the stator, and the complete vibration transfer function is obtained based on the superposition principle.

8. The vibration calculation method of the embedded spoke permanent magnet motor for flywheel energy storage according to claim 1 is characterized in that: In S7, the electromagnetic concentrated force calculated by the equivalent magnetic network model is subjected to two-dimensional Fourier decomposition to obtain the electromagnetic force amplitude and phase of each order of the concentrated force on each tooth surface and the corresponding frequency, which are multiplied with the vibration transfer function obtained by analysis to obtain the vibration acceleration on the stator tooth surface, thus completing the calculation of the motor vibration.

9. The vibration calculation method of the embedded spoke permanent magnet motor for flywheel energy storage according to claim 1, characterized in that: The embedded spoke permanent magnet motor is a three-phase embedded spoke permanent magnet motor with 6 slots and 4 poles, including a stator, a rotor, an air gap, an external support and a rotating shaft; the stator includes a stator yoke, stator teeth, stator slots, stator tooth pole shoes, stator slots, and windings in the slots; the rotor includes a rotor core and permanent magnets; four permanent magnets are inserted into the rotor core in a spoke shape, and the surface of the rotor core is an irregular curve to suppress back electromotive force harmonics and torque pulsation. The stator and rotor of the motor are fastened and connected with bolts through the skeletons at the front and rear ends.

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