Evaluation design method and system considering stator auxiliary slot opening of built-in permanent magnet synchronous motor

Abstract

The invention provides a design method and system for a built-in permanent magnet synchronous motor considering stator auxiliary slot opening, and relates to the technical field of built-in permanent magnet synchronous motors. The method comprises the steps that a motor model is constructed through finite element simulation, the slot depth and the slot width of an auxiliary slot are scanned under the non-excitation constant-speed 1-degree / s condition, and a motor model is constructed; the groove depth and the groove width are increased to 3.5 mm according to the step length of 0.1 mm to obtain cogging torque data; an orthogonal polynomial fitting method is adopted to carry out independent fitting on the relation among the slot width, the slot depth and the cogging torque, and global optimal parameters are determined through weighted coupling processing (the weight of the slot width is 0.64, and the weight of the slot depth is 0.36); and the inhibition effect of the auxiliary slot on the torque ripple and the total harmonic distortion (THD) of the back electromotive force is verified by taking the non-slotted motor as a contrast. Experiments show that when the slot width is 2.74 mm and the slot depth is 1.2 mm, the cogging torque peak value is reduced by 96.79%, the average torque is reduced by 3.42%, the torque ripple is reduced from 22.42% to 11.78%, and the total harmonic distortion (THD) of the back electromotive force is reduced from 8.7% to 3.1%.

Description

Technical Field

[0001] The present application relates to the technical field of built-in permanent magnet synchronous motors, and in particular to a design method and system for a built-in permanent magnet synchronous motor that takes into account the provision of auxiliary slots in the stator. Background Art

[0002] In the field of built-in permanent magnet synchronous motors, research on straight or skewed stator slots is relatively mature. Straight or skewed slots are usually designed in the stator to suppress motor vibration and noise. Straight slots are simple to manufacture but have limited harmonic suppression effects. Although skewed slots can improve electromagnetic performance, they complicate the winding process. However, the design of auxiliary slots in the stator is lacking in the industry. In particular, there is no parameter design optimization method for the auxiliary slot structure. Therefore, it is of great practical significance to develop a method that can accurately evaluate the design of stator auxiliary slots and determine the optimal slot parameters. Summary of the Invention

[0003] In order to solve the above technical problems, the present application provides an evaluation and design method for a built-in permanent magnet synchronous motor considering the opening of stator auxiliary slots, which can determine the optimal stator auxiliary slot parameter design and optimize the motor performance; at the same time, it is verified based on multiple factors such as cogging torque, no-load back electromotive force and torque pulsation to support and verify the feasibility of the design method of this application.

[0004] The technical solutions provided in this application are as follows: An evaluation and design method for an interior permanent magnet synchronous motor considering stator auxiliary slots includes the following steps: Import the prepared motor model diagram into the finite element software, build a finite element simulation model of the permanent magnet synchronous motor, preset the simulation model parameters of the motor, and set the grids for the stator, rotor, and air gap; Using a stator without auxiliary slots as a comparison object, under no excitation and constant rotation speed of 1° / s, the slot depth and slot width of the stator auxiliary slots were scanned in steps of 0.1mm to a preset range. Multiple sets of sampling data were obtained, and cogging torque waveforms were generated, as well as cogging torque data. The obtained slot width and slot depth corresponding to the cogging torque are fitted with data, and the optimal slot width and slot depth parameter values ​​are obtained by the orthogonal method.

[0005] Furthermore, the simulation model parameters of the preset motor include: pole arc coefficient, stator core and rotor core materials, permanent magnet material; setting the stator / rotor grid to 4mm and the air gap to 0.1mm; the slot depth and slot width of the stator auxiliary slot are increased from 0.1mm to 3.5mm respectively; 3.5mm is the preset range value of the scanning setting in this embodiment.

[0006] Furthermore, the cogging torque data is analyzed by the following formula: 1); In formula 1), z is the number of stator slots, is the axial length of the stator core, is the relative position angle between the stator and the rotor, R1 is the inner radius of the stator, R2 is the outer radius of the armature, G n is the Fourier decomposition coefficient of the square of the relative air gap permeance, B rnz / 2p is the Fourier decomposition coefficient of the square of the air gap magnetic flux generated by the permanent magnet, n is the number of cogging torques.

[0007] Furthermore, the formula 1) is calculated according to the following formula: 2); Where: W is the energy stored in the motor magnetic field, is the relative position angle between the stator and rotor, T cog is the permanent magnet motor cogging torque; 3); Where: W airgap is the air gap magnetic field energy, W PM is the magnetic field energy of the permanent magnet, μ 0 is the relative magnetic permeability, B ( θ , α） is the distribution function of the air gap magnetic flux density, V is the integral area of ​​the permanent magnet and the air gap; 4); Where: B r ( θ) is the remanence of the permanent magnet, h m ( θ) is the distribution of the permanent magnet's magnetizing length along the circumferential direction, δ ( θ ,α) is the effective air gap length; 5); To [h m ( θ ) / h m ( θ )+ δ( θ , α)] 2 and B r 2 ( θ) Expand the expression after Fourier transform: 6); 7); Where: G0 is a constant; B r0 =α P (B r ) 2 ; B rn =(2 / nπ)(B r ) 2 sin(nα p π); B r is the remanent magnetism of the permanent magnet at 0 degrees; α p is the pole arc coefficient of the permanent magnet pole; Substituting Equations 6) and 7) into Equation 5) and then combining Equation 2) yields the formula for the cogging torque in Equation 1).

[0008] Furthermore, the cogging torque is periodic, and the periodicity of the cogging torque is expressed as: 8); The harmonic order expression formula of the cogging torque is: 9); Where: N p is the number of cycles of the cogging torque; is the harmonic order of the cogging torque; GCD ( z , 2p ) indicates the number of slots z and number of poles 2p The greatest common divisor of LCM ( z , 2p） is the number of stator slots z and number of poles 2p The least common multiple of .

[0009] Furthermore, the cogging torque corresponding to the acquired slot width and slot depth is fitted with data, and the optimal slot width and slot depth parameter values ​​are obtained by orthogonal method; specifically including: Perform polynomial fitting of the slot width and the corresponding cogging torque data in MATLAB software; Perform polynomial fitting of the groove depth and the corresponding cogging torque data in MATLAB software; After fitting the groove width and groove depth in MATLAB software, the data is subjected to weighted coupling processing.

[0010] Furthermore, the evaluation and design method of the built-in permanent magnet synchronous motor of the present application considering the stator auxiliary slots also includes: using a straight slot motor with a stator without auxiliary slots as a comparison object to verify the performance of the motor with auxiliary slots in the stator, and the verified motor performance includes the motor output torque pulsation and the total harmonic distortion rate of the motor back electromotive force.

[0011] Furthermore, a three-phase current excitation is added to the simulation software, and a no-load back-EMF periodic function waveform is generated based on multiple sets of sampled data obtained by scanning. The fundamental and harmonic components are extracted through Fourier transform processing, and the total harmonic distortion rate of the back-EMF is calculated. Add three-phase current excitation in the simulation software. The three-phase current excitation is set according to the following formula: 10); The extracted fundamental and harmonic components are expressed as harmonic amplitudes. The formula for expressing harmonic amplitudes is: 11); Where: Z represents the harmonic amplitude, the real part a and the imaginary part b represent the coefficients of the cosine and sine components respectively; The calculation formula of the total harmonic distortion rate of back electromotive force is: 12); Among them, THD is the total harmonic distortion rate of back electromotive force; U1 is the effective value of fundamental voltage; U3, U 5、 U 7... U n etc. are the effective values ​​of each harmonic voltage.

[0012] It should be noted that those skilled in the art know that the effective value of the harmonic voltage can be calculated using the formula of the harmonic amplitude.

[0013] Furthermore, an output torque waveform is generated based on the multiple sets of sampled data obtained by scanning, and the output torque pulsation is calculated; the calculation formula of the output torque pulsation is: 13); Where: Tr is the output torque ripple, Tomax and Tomin represent the highest peak and lowest peak values ​​in the output torque waveform, respectively, and Ton is the average output torque.

[0014] Specifically including: generating multiple sets of sampled data output torque T through simulation out , set the highest peak and the lowest peak in the waveform as T omax With T omin , subtract the two components and divide them by the average output torque Ton to obtain the output torque pulsation Tr.

[0015] The present application also provides a design system for an interior permanent magnet synchronous motor taking into account stator auxiliary slots, comprising: a motor model construction module, a cogging torque simulation module, and an orthogonal polynomial fitting module; The motor model building module is used to build a finite element simulation model of the permanent magnet synchronous motor, preset the simulation model parameters of the motor, and set grids for the stator, rotor, and air gap; The cogging torque simulation module is used to scan the slot depth and slot width of the stator auxiliary slots in a preset range with a step size of 0.1 mm under no excitation and constant rotation speed of 1° / s, obtain multiple sets of sampled data, generate a cogging torque waveform, and obtain cogging torque data; The orthogonal polynomial fitting module is used to perform data fitting on the cogging torque corresponding to the acquired slot width and slot depth, and obtain the optimal slot width and slot depth parameter values ​​through the orthogonal method.

[0016] Furthermore, the design system for an interior permanent magnet synchronous motor considering stator auxiliary slots in the present application also includes a motor performance testing module, which is used to verify the output torque ripple performance and back electromotive force total harmonic distortion rate performance of the motor using a straight slot motor without stator auxiliary slots as a comparison object; the motor performance verification module includes: The excitation condition setting module is used to set the three-phase current as the excitation in the simulation; the three-phase current is set as the excitation according to formula 10): 10); The no-load back-electromotive force analysis module is used to perform FFT processing on the no-load back-electromotive force periodic function waveform generated by multiple sets of sampled data obtained by scanning, and calculate the total harmonic distortion rate of the back-electromotive force; The calculation formula of the total harmonic distortion rate of back electromotive force is: 12); Among them, THD is the total harmonic distortion rate of back electromotive force; U1 is the effective value of fundamental voltage; U3, U 5、 U 7... U n etc. are the effective values ​​of each harmonic voltage; The torque pulsation calculation module is used to scan multiple sets of sampled data to generate an output torque waveform and calculate the output torque pulsation. The calculation formula for the output torque pulsation is: 13); Where: Tr is the output torque ripple, Tomax and Tomin represent the highest peak and lowest peak values ​​in the output torque waveform, respectively, and Ton is the average output torque.

[0017] Beneficial effects: The optimization design method of this application constructs a motor model through finite element simulation. The auxiliary slot depth and width are scanned at a constant speed (1° / s) without excitation. The slot depth and slot width are scanned in increments of 0.1mm to 3.5mm, respectively, with a step size of 0.1mm to obtain the corresponding cogging torque data. An orthogonal polynomial fitting method is used to independently fit the relationship between slot width, slot depth, and cogging torque. A weighted coupling process (slot width weight 0.64, slot depth weight 0.36) is used to determine the optimal parameters (slot width and slot depth) of the stator auxiliary slot. Under these optimal parameters, the quantified effect of the motor performance is verified: Cogging torque suppression: Under the optimal parameters (groove width 2.74 mm, groove depth 1.2 mm) in the embodiment, the peak cogging torque is reduced from 1383.11 mN·m to 44.298 mN·m (a decrease of 96.79%). Harmonic optimization: The amplitudes of the 3rd / 9th / 13th / 15th harmonics of the air gap magnetic flux density decreased by more than 40%, and the total harmonic distortion (THD) of the back electromotive force decreased from 8.7% to 3.1%; Improved torque stability: Output torque ripple is reduced from 22.42% to 11.78%, while average torque is reduced by only 3.42% (from 13.567N·m to 13.103N·m). BRIEF DESCRIPTION OF THE DRAWINGS

[0018] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments recorded in this application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0019] Figure 1 This is a flow chart of a design method for an interior permanent magnet synchronous motor considering stator auxiliary slots in this application; Figure 2 Schematic diagram of the axial cross-sectional structure of the stator in an interior permanent magnet synchronous motor (a is a structure without auxiliary slots (straight stator slots), b is a structure with auxiliary slots, c is a quarter of a, and d is a quarter of b). Figure 3 is the polynomial fitting relationship diagram between the cogging torque and the auxiliary slot width; Figure 4 for Figure 3 Polynomial fitting relationship diagram of local sampling points of the auxiliary slot width; Figure 5 is the polynomial fitting relationship diagram between cogging torque and auxiliary groove depth; Figure 6 for Figure 5 Polynomial fitting relationship diagram of local sampling points of the auxiliary groove depth; Figure 7 The relationship diagram of the coupling between the cogging torque and the auxiliary slot width and depth (3D); Figure 8 is the relationship diagram of the coupling treatment between the cogging torque and the auxiliary slot width and depth (two-dimensional); Figure 9 This is a comparison of the cogging torque waveforms before and after auxiliary slots are opened in the stator of an interior permanent magnet synchronous motor; Figure 10 This is a comparison of the air gap flux density before and after the stator auxiliary slots are opened in the interior permanent magnet synchronous motor; Figure 11 This is a comparison diagram of the Fourier decomposition of the air gap flux density before and after the auxiliary slots are opened in the stator of an interior permanent magnet synchronous motor; Figure 12 This is a comparison of the no-load back electromotive force waveforms before and after the auxiliary slots are opened in the stator of the interior permanent magnet synchronous motor; Figure 13 This is a comparison diagram of the Fourier decomposition of the no-load back electromotive force before and after the auxiliary slots are opened in the stator of the interior permanent magnet synchronous motor; Figure 14 This is a comparison diagram of the output torque waveform before and after the auxiliary slots are opened in the stator of the interior permanent magnet synchronous motor; DETAILED DESCRIPTION

[0020] In order to help those skilled in the art better understand the technical solutions in this application, the technical solutions in the embodiments of this application will be clearly and completely described below. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without making any creative efforts shall fall within the scope of protection of this application.

[0021] It should be noted that when an element is referred to as being “fixed on” or “set on” another element, it can be directly on the other element or indirectly set on the other element; when an element is referred to as being “connected to” another element, it can be directly connected to the other element or indirectly connected to the other element.

[0022] It should be understood that the terms "length", "width", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", etc., indicating the orientation or position relationship, are based on the orientation or position relationship shown in the accompanying drawings, and are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the design method or elements of the internal permanent magnet synchronous motor considering the auxiliary slots in the stator must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on this application.

[0023] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be understood to indicate or imply relative importance or implicitly specify the number of technical features indicated. Thus, a feature specified as "first" or "second" may explicitly or implicitly include one or more of such features. Throughout the description of this application, "plurality" or "several" means two or more, unless otherwise specifically defined.

[0024] It should be noted that the structures, proportions, sizes, etc. illustrated in the drawings of this specification are only used to match the contents disclosed in the specification for people familiar with this technology to understand and read, and are not used to limit the conditions under which this application can be implemented. Therefore, they have no substantive technical significance. Any structural modification, change in proportional relationship or adjustment of size should still fall within the scope of the technical content disclosed in this application without affecting the efficacy and purpose that can be achieved by this application.

[0025] The embodiments of the present application are written in a progressive manner.

[0026] See also Figures 1 to 14 A method for evaluating and designing an interior permanent magnet synchronous motor considering stator auxiliary slots is provided, comprising the following steps: Import the prepared motor model diagram into the finite element software, build a finite element simulation model of the permanent magnet synchronous motor, preset the simulation model parameters of the motor, and set the grids for the stator, rotor, and air gap; Using a stator without auxiliary slots as a comparison object, under no excitation and constant rotation speed of 1° / s, the slot depth and slot width of the stator auxiliary slots were scanned in steps of 0.1mm to a preset range. Multiple sets of sampling data were obtained, and cogging torque waveforms were generated, as well as cogging torque data. The obtained slot width and slot depth corresponding to the cogging torque are fitted with data, and the optimal slot width and slot depth parameter values ​​are obtained by the orthogonal method.

[0027] The preset motor simulation model parameters include: pole arc coefficient, stator core and rotor core materials, permanent magnet materials; setting the stator / rotor grid to 4mm and the air gap to 0.1mm; and increasing the depth and width of the stator auxiliary slots by 0.1mm to 3.5mm. As a feasible method, the motor simulation model parameters are set according to Table 1: Table 1

[0028] The motor model can be created using CAD software. The motor designed in this method is a 4-pole, 24-slot interior permanent magnet synchronous motor. The motor speed is set to a constant 1° / s, and the current in the stator winding is zero. The cogging torque of the motor is observed using the auxiliary slot width and depth as variables, with the pole arc coefficient set to 0.775. Both the stator and rotor cores are made of 20WTG-1500 material, and the permanent magnet steel is Sm2Co17-32H (2:17 samarium-cobalt alloy), a rare earth metal with excellent magnetic properties. The model is then imported into finite element simulation software to create a simulation model. A mesh is then set for the stator, rotor, and air gap. The mesh size for the stator and rotor is 4 mm, and the air gap is 0.1 mm.

[0029] Furthermore, the cogging torque data is analyzed by the following formula: 1); In formula 1), z is the number of stator slots, is the axial length of the stator core, is the relative position angle between the stator and the rotor, R1 is the inner radius of the stator, R2 is the outer radius of the armature, G n is the Fourier decomposition coefficient of the square of the relative air gap permeance, B rnz / 2p is the Fourier decomposition coefficient of the square of the air gap magnetic flux generated by the permanent magnet, n is the number of cogging torques.

[0030] Furthermore, the formula 1) is calculated according to the following formula: 2); Where: W is the energy stored in the motor magnetic field, is the relative position angle between the stator and rotor, T cog is the permanent magnet motor cogging torque; It should be noted that the cogging torque in a permanent magnet motor is caused by the interaction between the permanent magnets and the motor core slot structure. When the armature winding is not energized, it is the negative derivative of the magnetic field energy with respect to the position angle; that is, the expression in equation 2) above.

[0031] Compared with air and permanent magnets, the change in magnetic field energy stored in the motor core is negligible, so the energy stored in the motor can be expressed as: 3); Where: W airgap is the air gap magnetic field energy, W PM is the magnetic field energy of the permanent magnet, μ0 is the relative magnetic permeability, B ( θ , α） is the distribution function of the air gap magnetic flux density, V is the integral area of ​​the permanent magnet and the air gap; 4); Where: B r ( θ) is the remanence of the permanent magnet, h m ( θ) is the distribution of the permanent magnet's magnetizing length along the circumferential direction, δ ( θ ,α) is the effective air gap length; 5); To [h m ( θ ) / h m ( θ )+ δ( θ , α)] 2 and B r 2 ( θ) Expand the expression after Fourier transform: 6); 7); Where: G0 is a constant; B r0 =α P (B r ) 2 ; B rn =(2 / nπ)(B r ) 2 sin(nα p π); B r is the remanent magnetism of the permanent magnet at 0 degrees; α p is the pole arc coefficient of the permanent magnet pole; Substituting Equations 6) and 7) into Equation 5) and then combining Equation 2) yields the formula for the cogging torque in Equation 1).

[0032] The cogging torque is periodic, and the formula for expressing the period number of the cogging torque is: 8); The harmonic order expression formula of the cogging torque is: 9); Where: N p is the number of cycles of the cogging torque; is the harmonic order of the cogging torque; GCD( z , 2p ) indicates the number of slots z and number of poles 2p The greatest common divisor of LCM ( z , 2p） is the number of stator slots z and number of poles 2p The least common multiple of .

[0033] Furthermore, the cogging torque corresponding to the acquired slot width and slot depth is fitted with data, and the optimal slot width and slot depth parameter values ​​are obtained by orthogonal method; specifically including: Perform polynomial fitting of the slot width and the corresponding cogging torque data in MATLAB software; Perform polynomial fitting of the groove depth and the corresponding cogging torque data in MATLAB software; After fitting the groove width and groove depth in MATLAB software, the data is subjected to weighted coupling processing.

[0034] This embodiment uses orthogonal polynomial fitting in MATLAB software, which can be used to fit complex data to obtain the best fitting results. The basic idea of ​​orthogonal polynomial fitting is to fit a set of data to a polynomial function so that the residual of the fitting function is minimized. Orthogonal polynomial fitting basically includes: determining the order of the fitting function based on obtaining a given data set; then, constructing an orthogonal polynomial function based on the given data set so that the residual of the fitting function is minimized; then, based on the constructed orthogonal polynomial function, calculating the coefficients of the fitting function; finally, based on the calculated coefficients, finding the value of the fitting function.

[0035] The auxiliary slot is a rectangular slot. While keeping other slot parameters unchanged, the cogging torque is analyzed as a function of slot depth and width. The slot depth is 1.2 mm, and the slot width increases from the minimum value of 0, which is sufficient for the crown, to 3.5 mm in increments of 0.1 mm. Finite element simulation software is used to obtain sample data, which is then analyzed using MATLAB software. In this embodiment, 36 sets of sample data are obtained. The sample data of slot width and cogging torque obtained by MATLAB software are shown in Table 2: Polynomial fitting of the slot width and the corresponding cogging torque data was performed in MATLAB software. The sampling data of slot width and cogging torque obtained by MATLAB software are shown in Table 2: Table 2

[0036] A specific application of polynomial fitting of slot width and corresponding cogging torque data in MATLAB software is as follows: clear all; % Read table data filename = 'A.xlsx';% table file name data = readtable(filename);% Read the data table x = data{, 1};% The first column is x y = data{, 2};% The second column is y % Set the interpolation range xq = linspace(0, 3.5, 1000); % Generate 1000 points % Use cubic spline interpolation calculation y_spline = spline(x, y, xq); % Calculate spline interpolation % Find the minimum value of spline interpolation [min_y_spline, min_index_spline] = min(y_spline); % Find the minimum y value and its index min_x_spline = xq(min_index_spline); % corresponding x value % Define the optimization objective function objective = @(p) sum((polyval(p, xq) - y_spline).^2); % Define the objective function % Initialize the parameters of the sixth-order polynomial initial_p = zeros(1, 5); % Initialize the coefficients of the sixth-order polynomial to 0 (7 coefficients) % Optimize options = optimset('Display', 'off'); % Turn off output display optimized_p = fminunc(objective, initial_p, options); % Optimize to obtain polynomial coefficients % Calculate the optimized sixth-order polynomial value y_poly_optimized = polyval(optimized_p, xq); % Find the minimum value of the optimized polynomial [min_y_poly, min_index_poly] = min(y_poly_optimized); % Find the minimum value min_x_poly = xq(min_index_poly); % corresponding x value % Drawing figure; % Set the graphic size (e.g. width 12 inches, height 9 inches) set(gcf, 'Position', [100, 100, 1200, 900]);% Set the graphics window size (1200px wide, 900px high) % Set the renderer to paintrs, providing higher quality (suitable for vector graphics) set(gcf, 'Renderer', 'painters'); hold on; % Original data points h1 = plot(x, y, 'ro', 'MarkerFaceColor', 'r', 'MarkerSize', 8);% Return handle h1 hold on;% Keep the current graph so that subsequent graphs can be drawn on the same graph % Draw a cubic spline interpolation curve h2 = plot(xq, y_spline, 'b--', 'LineWidth', 1);% Return handle h2 % Draw the optimized sixth-order polynomial curve h3 = plot(xq, y_poly_optimized, 'g-', 'LineWidth', 2);% Return handle h3 % Set the legend and manually specify the label legend([h1, h2, h3], {'Test point', 'Cubic spline interpolation', 'Quartic polynomial curve'}, 'FontSize',26);% Manually specify legend labels and font size % Graphics Settings xlabel('Auxiliary groove depth b (mm)', 'FontSize', 28, 'Fontweight','bold'); % Set the X-axis label font size ylabel('Tcog (mN·m)', 'FontSize', 28, 'Fontweight', 'bold'); % Set the Y-axis label font size ax = gca; % Get the current axis handle ax.XAxis.FontSize = 28; % Set the X-axis scale font size ax.YAxis.FontSize = 28; % Set the Y-axis scale font size grid on; hold off; % Set the Y-axis scale with a step size of 100 ytick_vals = 0:200:1400; % from 0 to 1400, with a step size of 100 yticks(ytick_vals); % Output results disp('Relationship between cogging torque and auxiliary slot width:'); disp(['Min y (polynomial): ', num2str(min_y_poly), ' at x: ', num2str(min_x_poly)]); disp('Cubic Spline Interpolation:'); disp(['Min y: ', num2str(m)]) The change trend was calculated by the Matlab polynomial curve fitting function. The relationship curve between the auxiliary slot width a and the cogging torque is close to the sixth-order polynomial relationship. It was found that when the auxiliary slot width a is less than 2.7 mm, the cogging torque gradually decreases with the increase of the slot width. When the auxiliary slot width a is greater than 2.9 mm, the cogging torque gradually decreases with the increase of the slot width. The cogging torque suppression effect is best when the slot width is between 2.7 mm and 2.9 mm. Figure 3 In order to more accurately find the auxiliary groove width a that best suppresses the cogging torque, 11 sets of auxiliary groove widths were designed with every 0.02 mm between 2.7 mm and 2.9 mm for comparison. When the groove width was 2.74 mm, the cogging torque suppression effect was optimal, which was 44.298 mN·m. Figure 4As shown in the figure, the cogging torque is reduced by 96.79% compared to the unslotted state (1383.11 mN·m). The value of 0 mm represents the unslotted state.

[0037] While keeping other auxiliary slot parameters unchanged, the cogging torque was analyzed as a function of slot depth and width. The slot width was 2.74 mm, and the slot depth increased from the minimum value of 0, which is accommodated by the tooth crown, to 3.5 mm in increments of 0.1 mm. Finite element simulation software was used to scan and obtain sampling data, which was then analyzed using MATLAB software. In this embodiment, 36 sets of sampling data were obtained. The sampling data of slot depth and cogging torque obtained by MATLAB software are shown in Table 3: Table 3

[0038] A specific application of polynomial fitting of groove depth and corresponding cogging torque data in MATLAB software is as follows: clear all; % Read table data filename = 'jyl.xlsx';% table file name data = readtable(filename);% Read the data table x = data{, 1};% The first column is x y = data{, 2};% The second column is y % Set the interpolation range xq = linspace(0, 3.5, 1000); % Generate 1000 points % Use cubic spline interpolation calculation y_spline = spline(x, y, xq); % Calculate spline interpolation % Find the minimum value of spline interpolation [min_y_spline, min_index_spline] = min(y_spline); % Find the minimum y value and its index min_x_spline = xq(min_index_spline); % corresponding x value % Define the optimization objective function objective = @(p) sum((polyval(p, xq) - y_spline).^2); % Define the objective function % Initialize the parameters of the quartic polynomial initial_p = zeros(1, 5); % Initialize the coefficients of the quartic polynomial to 0 (5 coefficients) % Optimize options = optimset('Display', 'off'); % Turn off output display optimized_p = fminunc(objective, initial_p, options); % Optimize to obtain polynomial coefficients % Calculate the optimized quartic polynomial value y_poly_optimized = polyval(optimized_p, xq); % Find the minimum value of the optimized polynomial [min_y_poly, min_index_poly] = min(y_poly_optimized); % Find the minimum value min_x_poly = xq(min_index_poly); % corresponding x value % Drawing figure; % Set the graphic size (e.g. width 12 inches, height 9 inches) set(gcf, 'Position', [100, 100, 1200, 900]);% Set the graphics window size (1200px wide, 900px high) % Set the renderer to paintrs, providing higher quality (suitable for vector graphics) set(gcf, 'Renderer', 'painters'); hold on; % Draw the original data points h1 = plot(x, y, 'ro', 'MarkerFaceColor', 'r', 'MarkerSize', 8);% Return handle h1 hold on;% Keep the current graph so that subsequent graphs can be drawn on the same graph % Draw a cubic spline interpolation curve h2 = plot(xq, y_spline, 'b--', 'LineWidth', 1);% Return handle h2 % Draw the optimized quartic polynomial curve h3 = plot(xq, y_poly_optimized, 'g-', 'LineWidth', 2);% Return handle h3 % Set the legend and manually specify the label legend([h1, h2, h3], {'Test point', 'Cubic spline interpolation', 'Sixth-degree polynomial curve'}, 'FontSize', 26);% Manually specify legend labels and font size % Graphics Settings xlabel('Auxiliary groove width a (mm)', 'FontSize', 28, 'Fontweight','bold'); % Set the X-axis label font size ylabel('Tcog (mN·m)', 'FontSize', 28, 'Fontweight', 'bold'); % Set the Y-axis label font size ax = gca; % Get the current axis handle ax.XAxis.FontSize = 28; % Set the X-axis scale font size ax.YAxis.FontSize = 28; % Set the Y-axis scale font size grid on; hold off; % Set the Y-axis scale with a step size of 100 ytick_vals = 0:200:1400; % from 0 to 1400, with a step size of 100 yticks(ytick_vals); % Output results disp('Relationship between cogging torque and auxiliary groove depth:'); disp(['Min y (polynomial): ', num2str(min_y_poly), ' at x: ', num2str(min_x_poly)]); disp('Cubic Spline Interpolation:'); disp(['Min y: ', num]) The change trend and auxiliary groove depth are calculated by Matlab polynomial curve fitting function. b The relationship curve between the cogging torque and the fourth-order polynomial is close to the relationship between the auxiliary groove depth and the cogging torque. b When the depth is less than 1.1 mm, the cogging torque decreases gradually with the increase of the groove depth. b When the depth is greater than 1.3mm and less than 3.5mm, the cogging torque is in a slightly pulsating state as the groove depth increases. b The cogging torque suppression effect is best when the distance is between 1.1mm and 1.3mm. Figure 5 In order to more accurately find the best auxiliary groove depth to suppress the cogging torque b , 11 sets of auxiliary groove depths were designed with every 0.02mm between 1.1mm and 1.3mm for comparison, and the cogging torque variation with the groove depth as a variable was obtained as follows Figure 6 As shown in the figure; when the groove depth is 1.2 mm, the cogging torque suppression effect is optimal, which is 44.298 mN·m. Compared with the cogging torque of 1383.11 mN·m when the groove is not opened, the cogging torque is reduced by 96.79%.

[0039] A specific application of weighted coupling processing of data after fitting the groove width and groove depth in MATLAB software is as follows: clear all; % Define the range of a and b, increase the number of points a = linspace(0, 3.5, 200); % Increase to 200 points b = linspace(0, 3.5, 200); % Increase to 200 points [A, B] = meshgrid(a, b); % The first polynomial T1 = -13.008583* A.^6 + 116.648594* A.^5 -302.835934 * A.^4 +180.655659* A.^3 + 66.008177 * A.^2 - 334.995513 * A + 1383.11; % The second polynomial T2 = 72.898117 * B.^4 - 659.766830 * B.^3 + 2123.658513 * B.^2 -2785.567822 * B + 1383.11; % coupled into one surface T_combined = 0.64 * T1 + 0.36 * T2; % Find the minimum value and its index [min_value, min_index] = min(T_combined(:)); [row, col] = ind2sub(size(T_combined), min_index); % corresponding a and b values min_a = a(col); min_b = b(row); % Output the minimum value and its corresponding a and b fprintf('Minimum value: %.4f\n', min_value); fprintf('corresponding a value: %.4f\n', min_a); fprintf('Corresponding b value: %.4f\n', min_b); % Draw the coupling surface figure; % Set the graphic size (e.g. width 12 inches, height 9 inches) set(gcf, 'Position', [100, 100, 1200, 900]);% Set the graphics window size (1200px wide, 900px high) % Set the renderer to paintrs, providing higher quality (suitable for vector graphics) set(gcf, 'Renderer', 'painters'); surf(A, B, T_combined); xlabel('Slot width a(mm)', 'FontSize', 28 ); % Increase the font size ylabel('Slot depth b(mm)', 'FontSize', 28 ); % Increase the font size zlabel('Tcog(mN·m)', 'FontSize', 28); % Increase the font size grid on; % Set the Y-axis scale with a step size of 100 ztick_vals = 0:150:1500; % from 0 to 1400, with a step size of 100 zticks(ztick_vals); hold off; % Set the axis scale font size and thickness ax = gca; % Get the current axis handle ax.XAxis.FontSize = 28; % Set the X-axis scale font size ax.YAxis.FontSize = 28; % Set the Y-axis scale font size ax.ZAxis.FontSize = 28; % Enhance the plot colormap(jet); shading interp; light; lighting gouraud; view(30, 30); hold on; % Draw contour lines contour3(A, B, T_combined, 50, 'k'); % Add a solid red dot at the minimum position plot3(min_a, min_b, min_value, 'ro', 'MarkerSize', 10, 'MarkerFaceColor', 'r'); % solid red dot hold off; % Set the axis range xlim([0 3.5]); ylim([0 3.5]); zlim([min(T_combined(:)) max(T_combined(:))]); % Add color bar cbar = colorbar; % Get the color bar handle set(cbar, 'FontSize', 18); % Set the font size of the color bar numbers set(cbar, 'FontWeight', 'bold'); % Set the font weight of the color bar numbers Figure 7 and Figure 8 This is the relationship diagram between the output cogging torque and the auxiliary slot depth and width.

[0040] In this implementation, a continuous cogging torque curve is generated using cubic spline interpolation, with a sixth-order polynomial fitting the slot width-torque relationship and a fourth-order polynomial fitting the slot depth-torque relationship. The objective function is defined to minimize the fitting residual, and the polynomial coefficients are optimized and differentiated to determine the extreme points. Furthermore, it should be noted that the torque fluctuation amplitude caused by the slot width change is 1.78 times the slot depth, so the slot width weight is optimized to 0.64 and the slot depth weight to 0.36. The orthogonal method processing of this implementation is briefly summarized as follows: A sixth-order polynomial fit is made to the slot width-cogging torque data; A fourth-order polynomial fit is made to the slot depth-cogging torque data; The global minimum is obtained by coupling the fitting surfaces with weights 0.64 (groove width) and 0.36 (groove depth).

[0041] Furthermore, the evaluation and design method of the built-in permanent magnet synchronous motor of the present application considering the stator auxiliary slots also includes: using a straight slot motor with a stator without auxiliary slots as a comparison object to verify the performance of the motor with auxiliary slots in the stator, and verifying the motor performance including the motor output torque pulsation and the total harmonic distortion rate of the motor back electromotive force.

[0042] Three-phase current excitation is added to the simulation software. Based on the multiple sets of sampled data obtained by scanning, a periodic function waveform of the no-load back-electromotive force is generated. The fundamental and harmonic components are extracted through Fourier transform processing, and the total harmonic distortion rate of the back-electromotive force is calculated. Add three-phase current excitation in the simulation software. The three-phase current excitation is set according to the following formula: 10); The extracted fundamental and harmonic components are expressed as harmonic amplitudes. The formula for expressing harmonic amplitudes is: 11); Where: Z represents the harmonic amplitude, the real part a and the imaginary part b represent the coefficients of the cosine and sine components respectively; The calculation formula of the total harmonic distortion rate of back electromotive force is: 12); Among them, THD is the total harmonic distortion rate of back electromotive force; U1 is the effective value of fundamental voltage; U3, U 5、 U 7... U n etc. are the effective values ​​of each harmonic voltage.

[0043] It should be noted that those skilled in the art know that the effective value of the harmonic voltage can be calculated using the formula of the harmonic amplitude.

[0044] Furthermore, an output torque waveform is generated based on the multiple sets of sampled data obtained by scanning, and the output torque pulsation is calculated; the calculation formula of the output torque pulsation is: 13); Where: Tr is the output torque pulsation, Tomax and Tomin represent the highest peak and lowest peak in the output torque waveform respectively, and Ton is the average output torque. Specifically: the output torque T of multiple sets of sampling data is generated by simulation out , set the highest peak and the lowest peak in the waveform as T omax With T omin , subtract the two components and divide them by the average output torque Ton to obtain the output torque pulsation Tr.

[0045] As a feasible approach, this application analyzes the motor performance before and after the auxiliary slots are opened by controlling variables and taking the straight slot motor without the auxiliary slots as the comparison object; specifically, See also Figure 9 The cogging torque waveform shown in the figure shows that when the auxiliary groove is not opened (straight groove) and when the auxiliary groove is opened, the cogging torque peak value drops from 1383.11mN·m to 44.298mN·m when the auxiliary groove width is 2.74mm and the auxiliary groove depth is 1.2mm, which is weakened by 96.79%, and the cogging torque suppression effect is the best.

[0046] This application will set up a built-in permanent magnet synchronous motor to run at a rated speed of 20000r / min, and compare and analyze the air gap magnetic density harmonics, no-load back electromotive force, and output torque before and after the auxiliary slot is opened. The performance of the motor after the auxiliary slot is opened; Figure 10 The air gap flux density waveform and air gap flux density harmonic comparison before and after the auxiliary slot is opened are shown. After the stator auxiliary slot is opened, the air gap flux density wave frequency increases. Figure 11 As shown in the figure, after the auxiliary slot is opened, the fundamental wave amplitude decreases, and the amplitudes of the 3rd, 9th, 13th and 15th harmonics all decrease significantly. Figure 12 and Figure 13 The back EMF waveform and harmonic comparison before and after the auxiliary slot is opened are shown. The back EMF tested in this application is the potential voltage, which is obtained by subtracting the B phase voltage from the A phase voltage. The no-load back EMF before and after the auxiliary slot is opened does not change much, the fundamental amplitude decreases, and the third harmonic amplitude decreases. The output torque is shown in Figure 14 As shown in the figure, the average output torque without slots is 13.567 N·m, and the average output torque with auxiliary slots is 13.103 N·m, which means the output torque is reduced by 3.42%; the torque ripple is reduced from 22.42% to 11.78%, and the output torque is slightly reduced, but the motor output is more stable.

[0047] The optimization design method of this application constructs a motor model through finite element simulation. The auxiliary slot depth and width are scanned (both increasing from 0.1mm to 3.5mm) at a constant speed (1° / s) without excitation, and cogging torque data is obtained with a step size of 0.1mm. The relationship between slot width, slot depth, and cogging torque is independently fitted using an orthogonal polynomial fitting method. The optimal parameters (slot width and slot depth) of the stator auxiliary slot are determined through weighted coupling processing (slot width weighting 0.64, slot depth weighting 0.36). Under these optimal parameters, the quantified motor performance is verified: Cogging torque suppression: Under the optimal parameters (groove width 2.74 mm, groove depth 1.2 mm) in the embodiment, the peak cogging torque is reduced from 1383.11 mN·m to 44.298 mN·m (a decrease of 96.79%). Harmonic optimization: The amplitudes of the 3rd / 9th / 13th / 15th harmonics of the air gap magnetic flux density decreased by more than 40%, and the total harmonic distortion (THD) of the back electromotive force decreased from 8.7% to 3.1%; Improved torque stability: Output torque ripple is reduced from 22.42% to 11.78%, while average torque is reduced by only 3.42% (from 13.567N·m to 13.103N·m).

[0048] The present application also provides a design system for an interior permanent magnet synchronous motor taking into account stator auxiliary slots, comprising: a motor model construction module, a cogging torque simulation module, an orthogonal polynomial fitting module, and a motor performance testing module; The motor model building module is used to build a finite element simulation model of the permanent magnet synchronous motor, preset the simulation model parameters of the motor, and set grids for the stator, rotor, and air gap; The cogging torque simulation module is used to scan the slot depth and slot width of the stator auxiliary slots in a preset range with a step size of 0.1 mm under no excitation and constant rotation speed of 1° / s, obtain multiple sets of sampled data, generate a cogging torque waveform, and obtain cogging torque data; The orthogonal polynomial fitting module is used to perform data fitting on the cogging torque corresponding to the acquired slot width and slot depth, and obtain the optimal slot width and slot depth parameter values ​​through the orthogonal method; The motor performance test module is used to verify the output torque ripple performance and back electromotive force total harmonic distortion rate performance of the motor using a straight slot motor with a stator without auxiliary slots as a comparison object; the motor performance verification module includes: The excitation condition setting module is used to set the three-phase current as the excitation in the simulation; the three-phase current is set as the excitation according to formula 10): 10); The no-load back-electromotive force analysis module is used to perform FFT processing on the no-load back-electromotive force periodic function waveform generated by multiple sets of sampled data obtained by scanning, and calculate the total harmonic distortion rate of the back-electromotive force; The calculation formula of the total harmonic distortion rate of back electromotive force is: 12); Among them, THD is the total harmonic distortion rate of back electromotive force; U1 is the effective value of fundamental voltage; U3, U 5、 U 7... U n etc. are the effective values ​​of each harmonic voltage; The torque pulsation calculation module is used to scan multiple sets of sampled data to generate an output torque waveform and calculate the output torque pulsation. The calculation formula for the output torque pulsation is: 13); Where: Tr is the output torque ripple, Tomax and Tomin represent the highest peak and lowest peak values ​​in the output torque waveform, respectively, and Ton is the average output torque.

[0049] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present application. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application is not limited to the embodiments shown herein, but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for evaluating and designing an interior permanent magnet synchronous motor considering stator auxiliary slots, characterized in that: The following steps are involved: Import the prepared motor model diagram into the finite element software, build a finite element simulation model of the permanent magnet synchronous motor, preset the simulation model parameters of the motor, and set the grids for the stator, rotor, and air gap; Using a stator without auxiliary slots as a comparison object, under no excitation and constant rotation speed of 1° / s, the slot depth and slot width of the stator auxiliary slots were scanned in steps of 0.1mm to a preset range. Multiple sets of sampling data were obtained, and cogging torque waveforms were generated, as well as cogging torque data. The obtained slot width and slot depth corresponding to the cogging torque are fitted with data, and the optimal slot width and slot depth parameter values ​​are obtained by the orthogonal method.

2. The evaluation and design method for an interior permanent magnet synchronous motor considering stator auxiliary slots according to claim 1, characterized in that: The simulation model parameters of the preset motor include: pole arc coefficient, stator core and rotor core materials, permanent magnet materials; setting the stator / rotor grid to 4mm and the air gap to 0.1mm; and increasing the slot depth and slot width of the stator auxiliary slot by 0.1mm to 3.5mm respectively.

3. The evaluation and design method for an interior permanent magnet synchronous motor considering stator auxiliary slots according to claim 2, characterized in that: The cogging torque data is analyzed by the following formula: 1); In formula 1), z is the number of stator slots, is the axial length of the stator core, is the relative position angle between the stator and the rotor, R1 is the inner radius of the stator, R2 is the outer radius of the armature, G n is the Fourier decomposition coefficient of the square of the relative air gap permeance, B rnz / 2p is the Fourier decomposition coefficient of the square of the air gap magnetic flux generated by the permanent magnet, n is the number of cogging torques.

4. The evaluation and design method for an interior permanent magnet synchronous motor considering stator auxiliary slots according to claim 3, characterized in that: Formula 1) is calculated according to the following formula: 2); In formula 2): W is the energy stored in the motor magnetic field, is the relative position angle between the stator and rotor, T cog is the permanent magnet motor cogging torque; 3); Where: W airgap is the air gap magnetic field energy, W PM is the magnetic field energy of the permanent magnet, μ 0 is the relative magnetic permeability, B ( θ , α） is the distribution function of the air gap magnetic flux density, V is the integral area of ​​the permanent magnet and the air gap; 4); Where: B r ( θ) is the remanence of the permanent magnet, h m ( θ) is the distribution of the permanent magnet's magnetizing length along the circumferential direction, δ ( θ , α) is the effective air gap length; 5); To [h m ( θ ) / h m ( θ )+ δ( θ , α)] 2 and B r 2 ( θ) Expand the expression after Fourier transform: 6); 7); Where: G0 is a constant; B r0 =α P (B r ) 2 ; B rn =(2 / nπ)(B r ) 2 sin(nα p π); B r is the remanent magnetism of the permanent magnet at 0 degrees; α p is the pole arc coefficient of the permanent magnet pole; Substituting Equations 6) and 7) into Equation 5) and then combining Equation 2) yields the formula for the cogging torque in Equation 1).

5. The evaluation and design method for an interior permanent magnet synchronous motor considering stator auxiliary slots according to claim 4, characterized in that: The cogging torque is periodic, and the formula for expressing the period number of the cogging torque is: 8); The harmonic order expression formula of the cogging torque is: 9); Where: N p is the number of cycles of the cogging torque; is the harmonic order of the cogging torque; GCD ( z , 2p ) indicates the number of slots z and number of poles 2p The greatest common divisor of LCM ( z , 2p） is the number of stator slots z and number of poles 2p The least common multiple of .

6. The evaluation and design method for an interior permanent magnet synchronous motor considering stator auxiliary slots according to any one of claims 1 to 5, characterized in that: The method of fitting the obtained cogging torque corresponding to the slot width and slot depth and obtaining the optimal slot width and slot depth parameter values ​​by the orthogonal method specifically includes: Perform polynomial fitting of the slot width and the corresponding cogging torque data in MATLAB software; Perform polynomial fitting of the groove depth and the corresponding cogging torque data in MATLAB software; After fitting the groove width and groove depth in MATLAB software, the data is subjected to weighted coupling processing.

7. The evaluation and design method for an interior permanent magnet synchronous motor considering stator auxiliary slots according to claim 6, characterized in that: Also includes: Taking the straight slot motor with stator without auxiliary slots as the comparison object, the performance of the motor with auxiliary slots in the stator is verified. The verified motor performance includes the motor output torque ripple and the total harmonic distortion rate of the motor back electromotive force.

8. The evaluation and design method for an interior permanent magnet synchronous motor considering stator auxiliary slots according to claim 7, characterized in that: Three-phase current excitation is added to the simulation software. Based on the multiple sets of sampled data obtained by scanning, a periodic function waveform of the no-load back-electromotive force is generated. The fundamental and harmonic components are extracted through Fourier transform processing, and the total harmonic distortion rate of the back-electromotive force is calculated. Add three-phase current excitation in the simulation software. The three-phase current excitation is set according to the following formula: 10); The extracted fundamental and harmonic components are expressed as harmonic amplitudes. The formula for expressing harmonic amplitudes is: 11); Where: Z represents the harmonic amplitude, the real part a and the imaginary part b represent the coefficients of the cosine and sine components respectively; The calculation formula of the total harmonic distortion rate of back electromotive force is: 12); Among them, THD is the total harmonic distortion rate of back electromotive force; U1 is the effective value of fundamental voltage; U3, U 5、 U 7... U n etc. are the effective values ​​of each harmonic voltage.

9. The evaluation and design method for an interior permanent magnet synchronous motor considering stator auxiliary slots according to claim 7, characterized in that: The output torque waveform is generated based on the multiple sets of sampled data obtained by scanning, and the output torque pulsation is calculated. The calculation formula of the output torque pulsation is: 13); Where: Tr is the output torque ripple, Tomax and Tomin represent the highest peak and lowest peak values ​​in the output torque waveform, respectively, and Ton is the average output torque.

10. An evaluation and design system for an interior permanent magnet synchronous motor considering stator auxiliary slots, characterized in that: include: Motor model building module, cogging torque simulation module and orthogonal polynomial fitting module; The motor model building module is used to build a finite element simulation model of the permanent magnet synchronous motor, preset the simulation model parameters of the motor, and set grids for the stator, rotor, and air gap; The cogging torque simulation module is used to scan the slot depth and slot width of the stator auxiliary slots in a preset range with a step size of 0.1 mm under no excitation and constant rotation speed of 1° / s, obtain multiple sets of sampled data, generate a cogging torque waveform, and obtain cogging torque data; The orthogonal polynomial fitting module is used to perform data fitting on the cogging torque corresponding to the acquired slot width and slot depth, and obtain the optimal slot width and slot depth parameter values ​​through the orthogonal method.

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