Built-in self-starting permanent magnet synchronous motor magnetic field analytical algorithm based on equivalent magnetic circuit and analytical method

Abstract

The invention discloses a built-in self-starting permanent magnet synchronous motor magnetic field analytical algorithm based on an equivalent magnetic circuit and an analytical method, and relates to the field of motor design. A self-starting permanent magnet synchronous motor has a starting cage and rotor surface slotting, so that magnetic field distribution is complex, a magnetic field analysis model is difficult to establish in a polar coordinate system, and meanwhile, rotor surface slotting causes air-gap magnetic field distortion, so that a traditional path calculation method is insufficient in precision and low in calculation precision. Although the numerical simulation result is accurate, the consumed time is long and the efficiency is low in the optimization design process of the motor; therefore, the invention provides a new thought for magnetic field analysis research of the self-starting permanent magnet synchronous motor, an equivalent magnetic circuit method is adopted to model a rotor structure, an analysis method is adopted to model an air gap domain and a stator structure, coupling is realized through a magnetic field continuity relation of a rotor and an air gap interface, and a conformal transformation method is combined to obtain the self-starting permanent magnet synchronous motor. A magnetic field analysis calculation model considering rotor slotting is established, efficient and accurate calculation of the magnetic field of the self-starting permanent magnet synchronous motor is achieved, and the design, research and development period of the motor can be greatly shortened; according to the research thought, the flux density, harmonic analysis and cogging torque of the air gap domain can be obtained, the accuracy of the magnetic field analytical model is verified through comparison with a finite element method, and an analytical method is provided for subsequent electromagnetic design and structure optimization.

Description

Technical Field:

[0001] The present invention relates to the field of motor design, and particularly to a built-in self-starting permanent magnet synchronous motor with a complex rotor structure, and a magnetic field analysis algorithm for a built-in self-starting permanent magnet synchronous motor based on an equivalent magnetic circuit and an analytical method. Background Art:

[0002] Explosion-proof self-starting permanent magnet synchronous motors are widely used in high-risk industrial fields such as petrochemical and coal mining to provide stable and reliable power. Compared with ordinary permanent magnet motors, this type of motor does not require an additional starting device, has a high starting torque, and can withstand complex operating conditions such as frequent starting and stopping. However, its rotor integrates a starting cage and a permanent magnet structure, resulting in a complex magnetic field distribution; the compact explosion-proof structure design inevitably exacerbates the difficulty of heat dissipation, thereby threatening the operating stability of the motor. This not only places higher requirements on the motor performance, but also increases the difficulty and cycle of the optimization design.

[0003] Due to the complex magnetic field distribution caused by the rotor starting cage and the rotor surface slots in the self-starting permanent magnet synchronous motor, it is difficult to establish a magnetic field analysis model in the polar coordinate system, resulting in insufficient accuracy of the current traditional circuit calculation method. Although the finite element method can achieve accurate calculation for it, in the design optimization process, due to the large number of rotor structure parameters, frequent parameter adjustments make the finite element calculation efficiency low, and it is difficult to intuitively reflect the influence of the structural parameter adjustment on the air-gap magnetic field. Summary of the Invention:

[0004] In view of the above-mentioned defects in the prior art, the present invention proposes a magnetic field analysis algorithm for a built-in self-starting permanent magnet synchronous motor based on an equivalent magnetic circuit and an analytical method to improve the accuracy and rapidity of the electromagnetic calculation and design of the motor.

[0005] The technical solution adopted by the present invention is as follows: A magnetic field analysis algorithm for a built-in self-starting permanent magnet synchronous motor based on an equivalent magnetic circuit and an analytical method, including solving area division and establishment of an equivalent magnetic circuit model in the rotor domain, establishment of an analytical model in the air-gap and stator regions, coupling and solution of the equivalent magnetic circuit and the analytical model, establishment of a magnetic field analysis model considering rotor slots, and comparison and verification between the analytical value range and the numerical simulation results.

[0006] For the solving area division and establishment of the equivalent magnetic circuit model in the rotor domain, the model is divided into four solution domains: the rotor domain, the air-gap domain, the stator slot opening domain, and the stator slot domain according to the solving method. Taking the rotor center as the origin of the polar coordinate system, considering the periodicity of the motor operation, a two-dimensional polar coordinate system is established. Subsequently, according to the magnetic force trace line direction in the rotor domain, the equivalent magnetic circuit method is used to construct a model for the rotor domain containing a starting cage structure, and the scalar magnetic potential at the interface between the rotor and the air-gap and the magnetic flux entering the air-gap are solved.

[0007] Furthermore, the scalar magnetic potential at the interface between the rotor and the air gap and the magnetic flux entering the air gap are respectively:

[0008]

[0009] In the formula, is the scalar magnetic potential at the corresponding position at the interface between the rotor and the air gap, and Φ q1 , Φ q2 are the magnetic fluxes entering the corresponding positions of the air gap, and the specific positions are as shown in Figure 2 ; R b2 / R b1 = α b ; The magnetic flux passing through the magnetic bridge 1 is: Φ b1 = B s w1L; The magnetic flux passing through the magnetic bridge 2 is: Φ b2 = B s w2L; The leakage magnetic flux of the permanent magnet slot is: Φ c = B s1 w c L; The magnetomotive force of the permanent magnet is: F M = H c ·l h ; The magnetic resistance of the permanent magnet: R M = l h / μ0μ r l w L;

[0010] In the formula, H c is the magnetic induction intensity of the permanent magnet; l h is the path length of the magnetic voltage drop; L is the axial length; μ0 is the magnetic permeability of air; μ r is the relative magnetic permeability of the ferromagnetic material;

[0011] After the scalar magnetic potential waveform on the rotor surface is equivalently processed, its Fourier series form expression is:

[0012]

[0013] In the formula, θ t = νt + θ0, θ0 is the initial position of the rotor, θ t is the position of the rotor at time t, ν is the rotational speed, ω = 1, 2, 3... is the harmonic coefficient, the maximum value is taken as W, p is the number of pole pairs, is the Fourier series coefficient of the scalar magnetic potential related to the rotor position. When ω / p is even, is zero, otherwise, The expression is:

[0014]

[0015] In the formula, θ p1, θ p2 and θ b1 , θ b2 The values of Figure 2 are as shown, and the expression of Γ ω is:

[0016]

[0017] The coupling and solution of the equivalent magnetic circuit and the analytical model can simplify the solution of the electromagnetic field in the motor by means of the vector magnetic potential A. The general solution of the partial differential equation of the vector magnetic potential A in the stator slot domain, stator slot opening domain and air gap domain is obtained by the method of separating variables and the interface boundary conditions;

[0018] Furthermore, the equivalent principle means that the air gap magnetic field distribution of the motor remains unchanged before and after equivalence, has regular radial and tangential boundaries after equivalence, the slot opening width and its depth remain unchanged before and after equivalence, the slot body width after equivalence is equal to the average width of the slot body before equivalence, and the depth of the slot remains unchanged. The equivalent diagram of the stator slot area is as Figure 3 shown;

[0019] Furthermore, the vector magnetic potential equations and position ranges of the stator slot domain are respectively:

[0020]

[0021] Furthermore, to obtain the general solution of the partial differential equation, the method of separating variables is used to transform the vector magnetic potential equation into solving the Laplace equation, that is, the multi-variable partial differential equation is split into one or more ordinary differential equations of single variables, and then the general solutions of each split ordinary differential equation are solved, and then the general solutions of each equation are linearly combined, and finally the general solution in the form of a series of the partial differential equation is obtained; the general solution of the Laplace equation is:

[0022]

[0023] where A 0t , B 0t , A 1m and B 1m are undetermined coefficients, τ m = mπ / β, m is the harmonic order of the slot domain, and the maximum value is taken as M.

[0024] Furthermore, there is no current density and magnetization intensity in the stator slot opening domain, and its vector magnetic potential satisfies the Laplace equation. The vector magnetic potential equation and position range of this solution domain are:

[0025]

[0026] The expression of the vector magnetic potential in the stator slot opening domain is:

[0027]

[0028] Wherein, A a2n and B a2n are the undetermined coefficients of the Fourier series of the magnetic field in the stator slot opening region, η n = nπ / β1, where n is the harmonic order of the slot opening sub-region, and the maximum value is taken as N; wherein, r, R2, R3, β1, θ a take values as Figure 3 shown;

[0029] Furthermore, the air gap is similar to the stator slot opening region, and its vector magnetic potential equation and position range are:

[0030]

[0031] Based on the same principle, the general solution of the vector magnetic potential equation in the air gap region can be obtained as:

[0032]

[0033] Wherein, A 30 , B 30 , A 3ω , B 3ω , C 3ω and D 3ω are the undetermined coefficients of the Fourier series of the magnetic field in the air gap region, and ω is the harmonic order of the air gap region;

[0034] The establishment of the magnetic field analysis model considering rotor slotting mainly involves the continuity of the scalar magnetic potential at the junction of the rotor and the air gap and the continuity of the air gap magnetic flux at the junction of the rotor and the air gap;

[0035] The comparison and verification between the analysis value range and the numerical simulation results. After obtaining the undetermined coefficients of the Fourier series of each harmonic order of the vector magnetic potential in each sub-region, the radial component B r3 and the tangential component B t3 of the air gap magnetic density of the self-starting permanent magnet synchronous motor are:

[0036]

[0037] Furthermore, based on the conformal transformation algorithm, the complex air gap specific permeance λ is introduced. Assume that the air gap magnetic densities before and after slotting are B slotloss and B slot (both are complex numbers), and the conjugate of the ratio of the two is λ. The air gap specific permeance function λ obtained through conformal transformation is:

[0038]

[0039] Furthermore, assume that B slotloss = B slr + jB slt , B slot = Bsr +jB st where B slr and B slt are the radial and tangential magnetic flux density components before slotting respectively, and B sr and B st are the radial and tangential magnetic flux density components after slotting. According to the definition of the air-gap specific permeance function, we can obtain:

[0040] B sr = Re(B slotloss λ * ) = B slr λ a + B slt λ b

[0041] B st = Im(B slotloss λ * ) = B slt λ a - B slr λ b

[0042] Furthermore, the Maxwell tensor method is adopted to analytically calculate the cogging torque of the self-starting permanent magnet synchronous motor. The specific calculation formula is as follows:

[0043]

[0044] The object of the present invention is to: aiming at the problems that the magnetic field distribution of the self-starting permanent magnet synchronous motor is complex due to the rotor starting cage and the rotor surface slotting, it is difficult to establish a magnetic field analytical model in the polar coordinate system, the accuracy of the traditional circuit calculation method is insufficient, and the finite element method is accurate but inefficient in optimization, a magnetic field analytical algorithm for an interior permanent magnet self-starting synchronous motor based on the equivalent magnetic circuit and the analytical method is proposed to improve the accuracy and rapidity of the electromagnetic calculation and design of the motor;

[0045] The beneficial effects of the present invention are as follows: a magnetic field analytical algorithm for an interior permanent magnet self-starting synchronous motor based on the equivalent magnetic circuit and the analytical method is proposed, which can accurately analyze the electromagnetic parameters of the four solution domains of the rotor domain, the air-gap domain, the stator slot opening domain and the stator slot domain, as well as the coupling calculation of the interfaces between the rotor domain and the air-gap domain, and between the stator domain and the air-gap domain, greatly shortening the calculation period of the motor design and optimization, and the accuracy meets the engineering actual requirements; Description of the drawings:

[0046] Figure 1 A flowchart of the implementation of a magnetic field analytical algorithm for an interior permanent magnet self-starting synchronous motor based on the equivalent magnetic circuit and the analytical method;

[0047] Figure 2 Rotor magnetic force lines and their equivalent magnetic circuit diagram;

[0048] Figure 3 Equivalent process diagram for the stator slot area;

[0049] Figure 4 Boundary condition diagrams for each solution domain;

[0050] Figure 5 Air gap flux density and its harmonic decomposition diagram considering rotor slotting in an example scenario;

[0051] Figure 6 Comparison of cogging torque waveforms between analytical and numerical simulation in an example scenario; Specific implementation method:

[0052] In order to make the purpose, technical solutions and advantages of the present invention more clear, the following will combine specific examples to clearly and completely describe the technology in the present invention and the method of the present invention, but it should be understood that these descriptions are exemplary and do not limit the scope of the present invention.

[0053] Step 1: First, according to the physical structure of the self-starting permanent magnet synchronous motor, it is divided into four solution domains: rotor domain, air gap domain, stator slot opening domain and stator slot domain. The rotor center is used as the polar coordinate origin. Considering the periodicity of the motor operation, a two-dimensional polar coordinate system is established. Then, according to the magnetic force trajectory of the rotor domain, the equivalent magnetic circuit method is used to model the rotor domain containing the starting cage structure, and the scalar magnetic potential at the interface between the rotor and the air gap and the magnetic flux entering the air gap are solved. The rotor magnetic lines and their equivalent magnetic circuit diagrams are shown in the figure below. Figure 2 As shown;

[0054] Step 2: Use analytical methods to model the air gap domain and stator structure. Based on the rationalized structural equivalence, the vector magnetic potential A is used to simplify the electromagnetic solution in the motor. The general solution of the partial differential equation of the vector magnetic potential A in the stator slot domain, stator slot domain and air gap domain is obtained through the separation of variables method and interface boundary conditions. The equivalent process of the stator slot region is as follows: Figure 3 As shown;

[0055] Furthermore, the equivalent stator slot area is based on the condition that the air gap magnetic field distribution of the motor before and after the equivalent is unchanged, and has regular radial and tangential boundaries after the equivalent, which solves the problem that the stator slot and opening area boundaries are irregular in shape under polar coordinates and are difficult to analyze by formula;

[0056] Furthermore, the interface boundary condition is to determine the Fourier series coefficients corresponding to each harmonic, and specifically adopts the magnetic field continuity condition at the interface of adjacent solution domains, that is, the vector magnetic potential is continuous and the tangential magnetic induction intensity is equal, to obtain an equation containing the Fourier series coefficients, and the equations are combined and solved to obtain the Fourier series coefficients of each solution domain. The boundary conditions of each solution domain are as follows: Figure 4 As shown;

[0057] Furthermore, the magnetic field continuity conditions are that the tangential magnetic flux density at the interface between the stator slot domain and the stator slot opening domain is equal, the vector magnetic potential at the interface between the stator slot domain and the slot opening domain is equal, the vector magnetic potential at the interface between the stator slot opening domain and the air-gap domain is equal, and the tangential magnetic flux density at the interface between the stator slot opening domain and the air-gap domain is equal.

[0058] Step 3: Represent the magnetic potential distribution of the entire interface in the form of Fourier series. Based on the scalar magnetic potential continuity at the interface between the rotor and the air-gap and the air-gap magnetic flux continuity at the interface between the rotor and the air-gap, construct a constraint matrix equation according to the boundary conditions of different solution domains to achieve the magnetic field continuity of the stator domain, the air-gap domain, and the rotor domain, that is, the coupling and solution of the equivalent magnetic circuit and the analytical model;

[0059] Step 4: For the starting cage and slotted structure in the rotor domain, introduce the air-gap complex specific permeance using the conformal transformation method, establish an analytical model of the magnetic field considering rotor slotting; and calculate the air-gap magnetic flux density using the analytical model, and then calculate the cogging torque in combination with the Maxwell tensor method;

[0060] Step 5: Verify the accuracy and applicability of the proposed algorithm and process. Introduce the air-gap complex specific permeance using the conformal transformation method, map the unknown field domain with complex boundary conditions to the known field domain with simple boundaries, realize the equivalent transformation from the slotted air-gap to the non-slotted air-gap, establish an analytical model of the magnetic field considering rotor slotting, calculate the air-gap magnetic flux density using the analytical model, and then calculate the cogging torque in combination with the Maxwell tensor method. Finally, compare the analytical calculation results with the numerical simulation results to verify the accuracy of the proposed analytical model. At the same time, it also provides ideas for the magnetic field calculation and modeling of the same type of motors.

[0061] To verify the accuracy of the engineering application of the present invention, an example of a mine explosion-proof type built-in self-starting permanent magnet synchronous motor is used to prove this. Electromagnetic calculations are carried out based on the above analytical algorithm and Ansys software respectively, and the accuracy of the analytical algorithm is verified by comparing the analytical results with the numerical simulation results.

[0062] The air-gap magnetic flux density considering rotor slotting and its harmonic decomposition under the example scenario are as Figure 5 shown. After the motor runs stably, the tangential and radial air-gap magnetic flux density components considering rotor slotting within one period are obtained. Further calculate the root mean square errors of the radial and tangential magnetic flux densities, and the results are 0.0429 and 0.1583 respectively; and the harmonic distortion rates of the radial air-gap magnetic flux density are 26.2% and 27.2% respectively. By comparing the results, the accuracy of the analytical method can be known;

[0063] The comparison of the cogging torque waveforms between the analytical and numerical simulations under the example scenario is as Figure 6As shown, the waveform trend obtained by the analytical method is basically consistent with the finite element calculation results. The peak value of the cogging torque obtained by the analytical calculation is 2.6 N·m, and that by the finite element method is 2.7 N·m, further indicating the accuracy of the analytical model, and both meet the motor design requirements, further demonstrating the effectiveness of the present invention. Transplanting the results of the present invention to the same type of self-starting permanent magnet synchronous motor can also achieve the same effect, and no example will be given here for demonstration.

[0064] The above examples describe the principles and technical routes of the present invention for patent, rather than limiting the present invention. What is described in the above examples and the specification is only to illustrate the logic and ideas of the present patent. Without departing from the spirit, ideas and scope of the invention patent, various changes and improvements will occur to the present invention patent, and these changes and improvements will fall within the scope of the invention patent claimed.

Claims

1. An analytical algorithm for the magnetic field of an interior permanent magnet synchronous motor with self-starting based on equivalent magnetic circuit and analytical method, characterized in that: The specific implementation steps of the magnetic field analysis algorithm of the built-in self-starting permanent magnet synchronous motor are: Step 1: First, according to the physical structure of the self-starting permanent magnet synchronous motor, it is divided into four solution domains: rotor domain, air gap domain, stator slot opening domain and stator slot domain. The rotor center is used as the polar coordinate origin. Considering the periodicity of the motor operation, a two-dimensional polar coordinate system is established. Then, according to the magnetic force trajectory of the rotor domain, the equivalent magnetic circuit method is used to construct a model of the rotor domain containing the starting cage structure, and the scalar magnetic potential at the interface between the rotor and the air gap and the magnetic flux entering the air gap are solved; Step 2: Use analytical methods to model the air gap domain and stator structure. Based on the rationalized structural equivalence, use vector magnetic potential A to simplify the solution of electromagnetics in the motor. Use the separation of variables method and interface boundary conditions to obtain the general solution of the partial differential equations of vector magnetic potential A in the stator slot domain, stator notch domain and air gap domain. Step 3: Express the magnetic potential distribution of the entire interface in the form of Fourier series. According to the continuity of the scalar magnetic potential at the interface between the rotor and the air gap and the continuity of the air gap flux at the interface between the rotor and the air gap, the constraint matrix equation is constructed according to the boundary conditions of different solution domains to achieve the continuity of the magnetic field in the stator domain, air gap domain and rotor domain, that is, the coupling and solution of the equivalent magnetic circuit and the analytical model; Step 4: For the starting cage and slotted structure in the rotor domain, the air gap complex ratio permeance is introduced using the conformal transformation method, and a magnetic field analytical model considering the rotor slots is established; the air gap flux density is calculated using the analytical model, and the cogging torque is calculated in combination with the Maxwell tensor method; Step 5: Verify the accuracy and applicability of the proposed algorithm and process, use the conformal transformation method to introduce the complex ratio permeability of the air gap, map the unknown field with complex boundary conditions to the known field with simple boundaries, and realize the equivalent transformation from slotted air gap to slotless air gap. Establish an analytical model of the magnetic field considering the rotor slots, and use the analytical model to calculate the air gap magnetic flux density, and then use the Maxwell tensor method to calculate the cogging torque. Finally, compare the analytical calculation results with the numerical simulation results to verify the accuracy of the proposed analytical model.

2. According to step 2 as described in claim 1, it is characterized in that: The equivalent stator slot area is based on the condition that the air gap magnetic field distribution of the motor before and after the equivalence remains unchanged. After the equivalence, it has regular radial and tangential boundaries, which solves the problem that the stator slot and opening area boundaries are irregular in shape under polar coordinates and are difficult to analyze by formula.

3. According to step 2 described in claim 1, it is characterized in that: The interface boundary condition is used to determine the undetermined coefficients of the Fourier series corresponding to each harmonic. Specifically, the magnetic field continuity condition at the interface of adjacent solution domains is adopted, that is, the vector magnetic potential continuity and the tangential magnetic induction intensity are equal, to obtain an equation containing the undetermined coefficients of the Fourier series. The equations are combined and solved to obtain the undetermined coefficients of the Fourier series in each solution domain.

4. According to step 2 described in claim 1, it is characterized in that: The magnetic field continuity condition is that the tangential magnetic flux density at the interface between the stator slot domain and the stator slot domain is equal, the vector magnetic potential at the interface between the stator slot domain and the slot opening domain is equal, the vector magnetic potential at the interface between the stator slot domain and the air gap domain is equal, and the tangential magnetic flux density at the interface between the stator slot domain and the air gap domain is equal.

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