Carbon fiber sheath rotor three-dimensional stress analysis simplified model and multi-objective optimization method

Abstract

The invention discloses a carbon fiber sheath rotor three-dimensional stress analysis simplified model and a multi-objective optimization method, and belongs to the field of motors. The method comprises the following steps: step 1, establishing a carbon fiber sheath rotor three-dimensional stress analysis simplified model considering axial stress of a permanent magnet motor rotating shaft and a permanent magnet; and 2, fusing the analysis simplified model into an improved multi-objective particle swarm optimization algorithm, and carrying out multi-objective optimization design on the rotor strength. According to the analysis simplified model provided by the invention, the axial stress of the rotating shaft and the permanent magnet is considered, and the radial stress and the tangential stress are considered only on the thin carbon fiber sheath, so that the analysis result is more in line with the actual situation, and the analysis model is simplified to the greatest extent. Besides, analysis of a simplified model and an improved multi-objective particle swarm optimization algorithm are combined to realize the optimization method for the rotor strength, and the proposed rotor strength optimization method ensures the accuracy and reliability of an optimization scheme and also realizes the simplicity and high efficiency of the optimization process.

Description

Technical Field

[0001] The invention belongs to the field of motors, and relates to a rotor strength analytical analysis and multi-objective optimization method of a carbon fiber material sheath in a surface-mounted permanent magnet synchronous motor. Background Art

[0002] The rotor of a high-speed surface-mounted permanent magnet motor usually requires a sleeve to protect the permanent magnet from tensile stress. Since carbon fiber materials have significantly better performance than alloy materials in high-speed applications, they are more suitable for rotor sleeves of high-speed surface-mounted permanent magnet motors. In the analysis and optimization of the rotor strength of high-speed surface-mounted permanent magnet motors, the current research only considers the radial and tangential stresses of various parts of the rotor for the rotor strength analysis of anisotropic material sleeves, which will make the rotor stress analysis results difficult to conform to the actual situation (because the axial stress is ignored). And due to the complex material properties of anisotropic materials and the relatively thin wall thickness when used as rotor sleeves, considering axial stress will make the analysis process too complicated and the accuracy improvement effect is not obvious. In addition, due to the high strength of carbon fiber sleeves, a large safety margin is usually reserved for its stress when strength design is performed in engineering. Therefore, the stress of permanent magnets is the main research object of rotor strength problems. If the axial stress of the shaft and permanent magnets is considered simultaneously in the analytical model of such rotor strength, it can not only significantly improve the accuracy of permanent magnet stress analysis, but also will not make the analytical model too complicated. Furthermore, this analytical model is combined with the improved multi-objective particle swarm optimization algorithm to achieve the multi-objective optimization design of rotor strength. Summary of the invention

[0003] The purpose of the present invention is to solve the problem that the existing analytical results of the rotor strength of the anisotropic material sleeve are difficult to conform to the actual situation, and the optimization process of the current optimization method for the strength of such rotors is relatively complicated and time-consuming. A simplified three-dimensional stress analytical model of a carbon fiber sleeve rotor considering the axial stress of the shaft and permanent magnet is proposed, and an improved multi-objective particle swarm optimization algorithm is integrated into the simplified analytical model to perform multi-objective optimization design of the rotor strength.

[0004] The method proposed in the present invention takes the newly established analytical simplified model as the main body to ensure that the analytical results of the rotor strength are more in line with the actual situation. Furthermore, the rotor strength is optimized by combining the improved multi-objective particle swarm optimization algorithm. This method not only effectively simplifies the process of such rotor strength optimization, but also achieves the high efficiency of the optimization process.

[0005] To achieve the above object, the technical solution adopted by the present invention is:

[0006] A simplified three-dimensional stress analysis model and a multi-objective optimization method for a carbon fiber sheath rotor, the method comprising the following steps:

[0007] Step 1: Establish a simplified three-dimensional stress analysis model of the carbon fiber sheath rotor considering the axial stress of the permanent magnet motor shaft and permanent magnet;

[0008] Step 2: Integrate the analytical simplified model established in step 1 into the improved multi-objective particle swarm optimization algorithm to perform multi-objective optimization design on the rotor strength.

[0009] Furthermore, in step 1, the process of establishing the analytical simplified model is:

[0010] Step 1: For a thin-walled carbon fiber sheath with a wall thickness of 4 mm or less, analyze the relationship between the diameter, tangential strain and displacement of the circular arc unit of the carbon fiber sheath; specifically:

[0011] Take a microcircular arc with an angle of dθ and a radial length of dr on the carbon fiber sheath, and analyze the relationship between its diameter, tangential strain and displacement:

[0012] According to the structural dynamics theory, formula (1) is obtained:

[0013]

[0014] Where: ε r , ε θ Respectively represent radial and tangential strains, r is the radius of the inner arc surface of the micro-element arc, the radial displacement of the inner arc surface of the micro-element arc is u, and the radial displacement of the outer arc surface of the micro-element arc is u+du. Then, the definition of stress and strain gives formula (2):

[0015]

[0016] Where: μ θr ,μ rθ are the tangential and radial Poisson's ratios respectively; E θ ,E r are the tangential and radial elastic moduli respectively; β θ ,β r are the tangential and radial thermal expansion coefficients respectively; ΔT is the temperature change value;

[0017] Step 1 and 2: For a thin-walled carbon fiber sheath with a wall thickness of 4 mm or less, analyze the relationship between the radial and tangential stresses of the circular arc unit of the carbon fiber sheath; specifically:

[0018] Take a micro-circular arc with an angle of dθ and a radial length of dr on the carbon fiber sheath, analyze its radial and tangential stresses, and obtain formula (3):

[0019]

[0020] From the infinitesimal radial force balance, we can get formula (4):

[0021]

[0022] Where: ρ is the material density, ω is the rotor speed;

[0023] Simplifying formula (4) yields formula (5):

[0024]

[0025] Substitute equation (3) into equation (5) and arrange it according to the symmetry of the flexibility matrix to obtain equation (6):

[0026]

[0027] For thin-walled carbon fiber sheaths, without considering the temperature as a function of radial position, the differential equation (6) is solved to obtain equation (7):

[0028]

[0029] Where: U is the radial displacement of the carbon fiber sheath, C 1 ,C 2 is the unknown parameter, a, k are known coefficients;

[0030] Then the radial and tangential strains are obtained as follows:

[0031]

[0032] Substituting the above formula (8) into formula (3), we can get the radial and tangential stress expressions of the thin-walled carbon fiber sheath;

[0033] Step 13: For the two main rotor structures of the shaft and the permanent magnet, consider their axial stress and assume that they have no axial deformation, then:

[0034]

[0035] Where: E is the elastic modulus of the material, μ is the Poisson's ratio of the material, σ r , σ θ , σ Z They are radial stress, tangential stress, and axial stress, respectively. In the following text, the subscripts 1, 2, and 3 are used to distinguish the stresses when only the interference, centrifugal force, and thermal stress are considered. At the same time, the superscript ' is used to distinguish the stress expressions of the shaft, permanent magnet, and carbon fiber sheath. The superscript ' is the stress expression of the carbon fiber sheath;

[0038] From formula (9), we can further deduce:

[0039]

[0040] The same formula (7) gives formula (11):

[0041]

[0042] Where: C 3、5 , C 4、6 are the unknown coefficients in the expressions of radial displacement of permanent magnet and shaft respectively;

[0043] Step 14: Calculate using the stress separation method under three conditions: static, rotating, and heated;

[0044] First, the static stress when only the interference is considered; the stress in each direction of the shaft and the permanent magnet is:

[0045]

[0046] The isotropic stress of the carbon fiber sheath is:

[0047]

[0048] According to the binding method used for the contact between the permanent magnet and the rotating shaft, and the interference method used for the contact between the permanent magnet and the sleeve, the following static boundary conditions are obtained:

[0049]

[0050] Where: r h is the outer wall radius of the carbon fiber sheath, r p is the outer wall radius of the permanent magnet, r z is the outer wall radius of the shaft, δ is the selected interference; u h 、u z are the displacements of the carbon fiber sheath and the shaft at different radii; σ rh , σ rp , σ rz By σ r The subscripts h, p, and z of radial stress represent the radial stress of the carbon fiber sheath, permanent magnet, and shaft, respectively;

[0051] By combining the six boundary conditions in the above equation and introducing six known parameters h 1 -h 6 , that is, the six unknowns C in the expression of the displacement of the permanent magnet, the shaft and the carbon fiber sheath under static conditions are obtained 1j -C 6j , and then obtain the static stress values ​​of the permanent magnet, the shaft and the carbon fiber sheath;

[0052] When only the rotating centrifugal force is considered, the isotropic stresses of the shaft and the permanent magnet are:

[0053]

[0054] The isotropic stress of the carbon fiber sheath is:

[0055]

[0056] Then, the anisotropic stresses of the permanent magnet, the shaft, and the carbon fiber sheath are solved by the following boundary conditions:

[0057]

[0058] At this time, three known parameters A, B, and C are introduced; similarly, six unknown parameters C are obtained when only centrifugal force is considered. 1l -C 6l , and then the centrifugal stress values ​​of the permanent magnet, the shaft and the carbon fiber sheath and the interference loss caused by the centrifugal force are obtained:

[0059] Δu 1 =u h1 (r p )-u p1 (r p ) (18)

[0060] When only thermal conditions are considered, ΔT is simplified to a constant; then the isotropic thermal stress of the shaft and the permanent magnet is:

[0061]

[0062] At this time, the permanent magnet, shaft and carbon fiber sheath have the following boundary conditions:

[0063]

[0064] After introducing two known parameters X, Y and two functions M(r), N(r), we can solve for six unknowns C 1r -C 6r , and the radial and tangential stresses of the carbon fiber sheath 1 are obtained:

[0065]

[0066] The interference loss at this time is:

[0067] Δu 2 =u h2 (r p )-u p2 (r p ) (twenty two)

[0068] Therefore, the final interference fit is:

[0069] δ g =δ-Δu 1 -Δu 2 (twenty three)

[0070] Where: Δu1 , Δu 2 are the interference loss of the rotor under the two conditions represented by equations (18) and (22) respectively;

[0071] The isotropic stress of the rotor under working condition is the superposition of static stress, thermal stress and centrifugal force values, and the static stress value is the stress calculated from the actual interference value under working condition:

[0072]

[0073] Finally, the equivalent stress of the permanent magnet, the shaft and the carbon fiber sheath is obtained by formula (25):

[0074]

[0075] Furthermore, in step 1, the known coefficients and parameters are set as follows:

[0076]

[0077]

[0078] Furthermore, step 2 is specifically as follows:

[0079] Step 21: Improve the multi-objective particle swarm optimization algorithm;

[0080] Step 2-1: Introduce nonlinear inertia weight and particle mutation rate;

[0081] By using the combination of Sigmoid function and linear function, the nonlinear change of inertia weight is realized as formula (34) and the nonlinear change of particle mutation rate is realized as formula (35);

[0082]

[0083] Where: sigmoidPart is the nonlinear function part; linearPart is the linear function part; gen is the current iteration number; genmax is the maximum iteration number; w is the inertia weight; mut sl is the particle mutation rate;

[0084] Step 212: Obtain the optimal solution set through multiple iterations;

[0085] According to the setting of constraints, optimization objective function, optimization parameters and their value ranges, the optimization algorithm calculates the objective function values ​​of all particles within the set value range based on the analytical model, and screens all particles that have completed the objective function value calculation according to the set conditions. After multiple iterations, the optimal particle swarm individuals within the set range are finally obtained as the optimal solution set of this optimization problem.

[0086] The beneficial effects of the present invention relative to the prior art are:

[0087] 1. The axial stress of the shaft and permanent magnet is considered in the simplified analytical model, making the analytical results more consistent with the actual situation, significantly improving the strength analysis accuracy of such rotors, and being able to more accurately analyze whether the operating status of the permanent magnet is safe.

[0088] 2. For anisotropic materials with complex material properties, especially considering their relatively thin wall thickness when used as rotor sleeves, the proposed simplified analytical model focuses on analyzing the radial and tangential stresses of the rotor sleeve, which reduces the complexity of the model to the greatest extent without affecting the accuracy of the analytical results.

[0089] 3. Improvements are made to the multi-objective particle swarm optimization algorithm, mainly including adaptive inertia weight and adaptive mutation rate, so that it has stronger global search capabilities and effectively avoids the inherent disadvantage of premature convergence of this optimization algorithm.

[0090] 4. The proposed analytical simplified model is combined with the improved multi-objective particle swarm optimization algorithm to realize an optimization method for the strength of this type of rotor. The proposed rotor strength optimization method not only ensures the accuracy and reliability of the optimization scheme, but also realizes the simplicity and efficiency of the optimization process, which is suitable for the rapid optimization of the strength of this type of rotor. BRIEF DESCRIPTION OF THE DRAWINGS

[0091] Figure 1 is the rotor cross-section diagram; where r h is the outer wall radius of the sheath, r p is the outer wall radius of the permanent magnet, r z is the radius of the outer wall of the shaft.

[0092] Figure 2 is the stress cloud diagram of the rotor in the hot rotation state, where: Figure 2 (a) is the radial stress cloud diagram of the rotor in hot spinning state; Figure 2 (b) is the tangential stress cloud diagram of the rotor in the hot rotation state; Figure 2 (c) is the axial stress cloud diagram of the rotor in hot spinning state; Figure 2 (d) is the equivalent stress cloud diagram of the rotor in the hot rotation state.

[0093] Figure 3 This is the stress comparison diagram of the hot rotation state, where: Figure 3 (a) is a comparison diagram of radial stress in hot rotation state; Figure 3 (b) is the comparison diagram of tangential stress in hot rotation state; Figure 3 (c) is a comparison diagram of axial stress in hot rotation state; Figure 3 (d) is the comparison diagram of equivalent stress in thermal rotation state.

[0094] Figure 4This is the inertia weight change curve.

[0095] Figure 5 This is the variation rate curve.

[0096] Figure 6 It is a Pareto front diagram.

[0097] Figure 7 This is a comparison chart of the optimization solutions.

[0098] Figure 1 The names and reference numerals of the components are as follows:

[0099] 1-sheath; 2-permanent magnet; 3-rotating shaft. DETAILED DESCRIPTION

[0100] This embodiment describes a simplified three-dimensional stress analysis model and a multi-objective optimization method for a carbon fiber sheath rotor, the method comprising the following steps:

[0101] Step 1: Establish a simplified three-dimensional stress analysis model of the carbon fiber sheath rotor considering the axial stress of the permanent magnet motor shaft 3 and the permanent magnet 2 (the carbon fiber sheath 1 mainly focuses on analyzing its radial and tangential stresses, and the shaft 3 and the permanent magnet 2 mainly focus on analyzing the axial stress, thereby realizing a comprehensive analysis of the radial, tangential and axial stresses of the carbon fiber sheath rotor); the establishment process is as follows:

[0102] Step 1: For a thin-walled carbon fiber sheath 1 with a wall thickness of 4 mm or less, the relationship between the diameter, tangential strain and displacement of the circular arc unit of the carbon fiber sheath 1 is analyzed; specifically:

[0103] Take a micro-circular arc with an angle of dθ and a radial length of dr on the carbon fiber sheath 1, and analyze the relationship between its diameter, tangential strain and displacement:

[0104] According to the structural dynamics theory, formula (1) is obtained:

[0105]

[0106] Where: ε r , ε θ Respectively represent radial and tangential strains, r is the radius of the inner arc surface of the micro-element arc, the radial displacement of the inner arc surface of the micro-element arc is u, and the radial displacement of the outer arc surface of the micro-element arc is u+du. Then, the definition of stress and strain gives formula (2):

[0107]

[0108] Where: μ θr ,μ rθ are the tangential and radial Poisson's ratios respectively; E θ ,E rare the tangential and radial elastic moduli respectively; β θ ,β r are the tangential and radial thermal expansion coefficients respectively; ΔT is the temperature change value;

[0109] Step 1 and 2: For a thin-walled carbon fiber sheath 1 with a wall thickness of 4 mm or less, the relationship between the diameter and tangential stress of the circular arc unit of the carbon fiber sheath 1 is analyzed; specifically:

[0110] Take a micro-circular arc with an angle of dθ and a radial length of dr on the carbon fiber sheath 1, analyze its diameter and tangential stress (for the thin-walled carbon fiber sheath 1, only the diameter and tangential stress are concerned), and obtain formula (3):

[0111]

[0112] From the infinitesimal radial force balance, we can get formula (4):

[0113]

[0114] Where: ρ is the material density, ω is the rotor speed;

[0115] Simplifying formula (4) yields formula (5):

[0116]

[0117] Substitute equation (3) into equation (5) and arrange it according to the symmetry of the flexibility matrix to obtain equation (6):

[0118]

[0119] For the thin-walled carbon fiber sheath 1, without considering the temperature as a function of the radial position, the differential equation (6) is solved to obtain equation (7):

[0120]

[0121] Where: U is the radial displacement of the carbon fiber sheath, C 1 ,C 2 is the unknown parameter, a, k are known coefficients;

[0122] Then the radial and tangential strains are obtained as follows:

[0123]

[0124] Substituting the above formula (8) into formula (3), we can get the radial and tangential stress expressions of the thin-walled carbon fiber sheath 1;

[0125] Step 13: For the two rotor main structures of the shaft 3 and the permanent magnet 2, consider their axial stress and assume that they have no axial deformation, then:

[0126]

[0127] Where: E is the elastic modulus of the material, μ is the Poisson's ratio of the material, σ r , σ θ , σ Z They are radial stress, tangential stress, and axial stress, respectively. In the following text, the subscripts 1, 2, and 3 are used to distinguish the stresses when only the interference, centrifugal force, and thermal stress are considered. At the same time, the superscript ' is used to distinguish the stress expressions of the shaft 3, the permanent magnet 2, and the carbon fiber sheath 1. The superscript ' is the stress expression of the carbon fiber sheath 1;

[0128] From formula (9), we can further deduce:

[0129]

[0130] The same formula (7) gives formula (11):

[0131]

[0132] Where: C 3、5 , C 4、6 are the undetermined coefficients in the radial displacement expressions of the permanent magnet 2 and the rotating shaft 3 respectively;

[0133] Step 14: Calculate using the stress separation method under three conditions: static, rotating, and heated;

[0134] First, the static stress when only the interference is considered; the stress in each direction of the rotating shaft 3 and the permanent magnet 2 is:

[0135]

[0136] The isotropic stress of the carbon fiber (anisotropic material) sheath 1 is:

[0137]

[0138] According to the binding method used for the contact between the permanent magnet 2 and the rotating shaft 3, and the interference method used for the contact between the permanent magnet 2 and the sleeve 1, the following static boundary conditions are obtained:

[0139]

[0140] Where: r h is the outer wall radius of the carbon fiber sheath 1, r p is the outer wall radius of permanent magnet 2, r z is the outer wall radius of the shaft 3, δ is the selected interference; u h 、u z are the displacements of the carbon fiber sheath 1 and the shaft 3 at different radii; σ rh , σrp , σ rz By σ r The subscripts h, p, and z of radial stress represent the radial stress of the carbon fiber sheath 1, the permanent magnet 2, and the rotating shaft 3, respectively;

[0141] By combining the six boundary conditions in the above equation, and introducing six known parameters h 1 -h 6 , that is, the six unknowns C in the expression of the displacement of the permanent magnet 2, the rotating shaft 3 and the carbon fiber sheath 1 under static conditions are obtained 1j -C 6j , and then obtain the static stress values ​​of the permanent magnet 2, the rotating shaft 3 and the carbon fiber sheath 1;

[0142] When only the rotating centrifugal force is considered, the isotropic stresses of the rotating shaft 3 and the permanent magnet 2 are:

[0143]

[0144] The isotropic stress of the carbon fiber sheath 1 is:

[0145]

[0146] Then, the stresses in the permanent magnet 2, the rotating shaft 3 and the carbon fiber sheath 1 are solved by the following boundary conditions:

[0147]

[0148] At this time, three known parameters A, B, and C are introduced; similarly, six unknown parameters C are obtained when only centrifugal force is considered. 1l -C 6l , and then the centrifugal stress values ​​of the permanent magnet 2, the rotating shaft 3 and the carbon fiber sheath 1 and the interference loss caused by the centrifugal force are obtained:

[0149] Δu 1 =u h1 (r p )-u p1 (r p ) (18)

[0150] When only thermal conditions are considered, ΔT is simplified to a constant; then the isotropic thermal stress of the shaft 3 and the permanent magnet 2 is:

[0151]

[0152] At this time, the permanent magnet 2, the rotating shaft 3 and the carbon fiber sheath 1 have the following boundary conditions:

[0153]

[0154] After introducing two known parameters X, Y and two functions M(r), N(r), we can solve for six unknowns C 1r -C 6r , and the radial and tangential stresses of the carbon fiber sheath 1 are obtained:

[0155]

[0156] The interference loss at this time is:

[0157] Δu 2 =u h2 (r p )-u p2 (r p ) (twenty two)

[0158] Therefore, the final interference fit is:

[0159] δ g =δ-Δu 1 -Δu 2 (twenty three)

[0160] Where: Δu 1 , Δu 2 are the interference loss of the rotor under the two conditions represented by equations (18) and (22) respectively;

[0161] If the thermal interference loss is negative, it means that the interference between the permanent magnet 2 and the sleeve 1 increases due to the increase in temperature.

[0162] The isotropic stress of the rotor under working condition is the superposition of static stress, thermal stress and centrifugal force values, and the static stress value is the stress calculated from the actual interference value under working condition:

[0163]

[0164] Finally, the equivalent stress of the permanent magnet 2, the rotating shaft 3 and the carbon fiber sheath 1 is obtained by formula (25):

[0165]

[0166] The known coefficients and parameters are set as follows:

[0167]

[0168]

[0169] Step 2: Integrate the analytical simplified model established in step 1 into the improved multi-objective particle swarm optimization algorithm to perform multi-objective optimization design on the rotor strength (the improved multi-objective particle swarm optimization algorithm uses the same nonlinear change strategy to adjust the inertia weight and particle mutation rate, aiming to improve the global search capability of the algorithm and avoid premature convergence); the specific process is as follows:

[0170] Step 21: Improve the multi-objective particle swarm optimization algorithm;

[0171] Step 2-1: Introduce nonlinear inertia weight and particle mutation rate;

[0172] By adopting the combination of Sigmoid function and linear function, the nonlinear change of inertia weight is realized as formula (34) and the nonlinear change of particle mutation rate is realized as formula (35); this form can not only realize the nonlinear change of inertia weight and particle mutation rate through the nonlinear function part and control its change range, but also control the slope of the decrease or increase part of the curve through the linear function part, thereby better controlling the decrease or increase speed of inertia weight and particle mutation rate:

[0173]

[0174] Where: sigmoidPart is the nonlinear function part; linearPart is the linear function part; gen is the current iteration number; genmax is the maximum iteration number; w is the inertia weight; mut sl is the particle mutation rate;

[0175] Step 212: Obtain the optimal solution set through multiple iterations;

[0176] According to the setting of constraints, optimization objective function, optimization parameters and their value ranges, the optimization algorithm calculates the objective function values ​​of all particles within the set value range based on the analytical model, and screens all particles that have completed the objective function value calculation according to the set conditions (when the minimum objective function is used as the optimization goal, if the objective function value of a particle is the smallest but does not meet the constraints, a huge value such as 1e+6 is added to the objective function value through the conditional statement and then returned to the objective function value, so that its final objective function value is too large and is not considered). After multiple iterations (that is, the objective function values ​​of new points in the range are continuously calculated, so that particles with smaller objective function values ​​can replace the particles with insufficient objective function values ​​that were retained before), the optimal particle swarm individuals within the set range are finally obtained as the optimal solution set of this optimization problem.

[0177] The present invention includes a simplified three-dimensional stress analytical model of the shaft 3, permanent magnet 2 and anisotropic material sheath (carbon fiber sheath 1) of a three-layer surface-mounted permanent magnet motor, and an improved multi-objective particle swarm optimization algorithm, which are combined to achieve rapid optimization design of the strength of such rotors. Among them, the proposed simplified analytical model takes into account the axial stress of the shaft and permanent magnet, and only focuses on the radial and tangential stresses for the carbon fiber sheath with a thinner wall thickness, so that the analytical results are more in line with the actual situation while simplifying the analytical model to the greatest extent; the improved multi-objective particle swarm optimization algorithm used adopts the same nonlinear change strategy for the inertia weight and the particle mutation rate, so that it can have the same improvement effect and superposition, effectively improving the inherent shortcoming of premature convergence of the traditional form of this optimization algorithm; in the actual operation process, the thickness of the carbon fiber sheath, the tangential stress of the carbon fiber sheath, and the particle mutation rate are used to optimize the performance of the optimization algorithm. Force and radial stress of permanent magnets (in actual engineering, for permanent magnets, generally only the radial and tangential stresses are concerned, and no tensile stress occurs. However, the axial stress does exist, and according to the formula, there is interaction between the stresses in each direction. The change of one stress will cause the other two stresses to change. Here, the axial stress is considered to make its stress situation more realistic and make the analytical results of its radial and tangential stresses more accurate, so as to better analyze its radial and tangential stresses. At the same time, compared with the compressive stress of the tangential stress of the permanent magnet, the maximum value of the compressive stress of its radial stress is larger (this part can be obtained by Figure 3 As can be seen from the values ​​on the stress curve graph shown, the radial stress is selected as the minimization optimization target (where: tensile stress, that is, the value is positive, and compressive stress, that is, the value is negative). The optimization problem with minimization as the optimization target only takes about 15 seconds to obtain the optimal solution set of optimization parameters within the set range, proving that the proposed optimization method not only ensures the accuracy and reliability of the optimization scheme, but also achieves the high efficiency of the optimization process.

[0178] like Figure 1 As shown, the three-layer surface-mounted rotor of the permanent magnet synchronous motor is composed of a rotating shaft 3, a permanent magnet 2 and a carbon fiber sheath 1, wherein r h is the outer wall radius of the sheath, r p is the outer wall radius of the permanent magnet, r z is the radius of the outer wall of the shaft; in this embodiment, r h =45.5mm, r p =41.5mm, r z =29.5mm. The permanent magnet 2 is a samarium cobalt permanent magnet; and the sheath 1 is a carbon fiber sheath.

[0179] like Figure 2 and Figure 3As shown, the stress analysis of the rotor under working conditions was carried out by finite element and the proposed analytical simplified model, and then the rotor stress obtained by the two methods was compared. The results show that the error between the analytical simplified model and the finite element is small, and the overall error is basically stable below 5%. The stress distribution of the rotor in various states can be accurately analyzed. Compared with the two-dimensional stress analytical model of this type of rotor, the three-dimensional simplified analytical model proposed in the present invention is more in line with the actual situation, and has higher accuracy and reliability.

[0180] In order to solve the problem of efficient optimization of rotor strength, the proposed analytical simplified model is integrated into the improved multi-objective particle swarm optimization algorithm for parameter optimization. Figure 4 , Figure 5 The nonlinear inertia weight and mutation rate of the algorithm can improve the global search ability of the algorithm and avoid premature convergence. At the same time, it can effectively accelerate the convergence speed of the particle swarm and truly realize the fast and efficient optimization process, and finally obtain the following Figure 6 The Pareto frontier is the optimal solution set, and Figure 7 As shown in the figure, two optimization schemes focusing on different directions are selected for comparison with the original scheme, and the finite element results of several schemes are compared, which proves that the optimization method has significant optimization effect and is accurate and reliable. This method of combining the proposed simplified three-dimensional stress analysis model with the optimization algorithm to achieve the optimization of the rotor strength of the anisotropic material sleeve can fully solve the problem that the traditional finite element parameterized optimization method is time-consuming, and the problem that the approximate model method needs to construct a complex sample space. At the same time, it can also effectively avoid the parameter feasible domain solution process, which is significantly more complicated due to the consideration of the complex material properties of the anisotropic material and the axial stress when the analytical method is used to solve the optimal value of the parameters. This achieves a double improvement in the reliability and efficiency of this type of rotor strength optimization method.

[0181] The optimization method of the present invention solves the shortcomings of traditional optimization methods that are time-consuming, such as finite element parameterization and multiple iterations to seek the optimal solution. At the same time, it avoids the problem that when the analytical method is used in the entire optimization process, the feasible domain solution process of the optimization target is very complicated due to the consideration of the complex material properties of axial stress and anisotropic materials; and the problem that when optimizing by combining the approximate model with the optimization algorithm, it is necessary to construct a complex sample space and the model accuracy will decrease as the number of input variables increases. The optimization method of the present invention is based on the proposed analytical model and combines the improved multi-objective particle swarm optimization algorithm to optimize the rotor strength. On the premise of ensuring the accuracy and reliability of the optimization scheme, the method also realizes the high efficiency of the optimization process, and truly achieves the dual improvement of this type of motor rotor strength optimization method in terms of accuracy and reliability and rapidity and efficiency.

[0182] The working principle of the present invention is as follows: the present invention uses the proposed simplified three-dimensional stress analysis model as the main body in the improved multi-objective particle swarm optimization algorithm. According to the setting of constraints, optimization objective functions, optimization parameters and their value ranges, the optimization algorithm calculates the objective function values ​​of all particles within the set range based on the analytical model, and screens all particles that have completed the objective function value calculation according to the set conditions. After multiple iterations, the optimal particle swarm individuals within the set range are obtained as the optimal solution set of this optimization problem.

[0183] The above are only preferred specific implementation modes of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical solutions and inventive concepts of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A simplified three-dimensional stress analysis model and multi-objective optimization method for a carbon fiber sheathed rotor, characterized in that: The method comprises the following steps: Step 1: Establish a simplified three-dimensional stress analytical model of a carbon fiber sheath rotor that takes into account the axial stress of the permanent magnet motor shaft (3) and the permanent magnet (2); Step 2: Integrate the analytical simplified model established in step 1 into the improved multi-objective particle swarm optimization algorithm to perform multi-objective optimization design on the rotor strength.

2. The simplified three-dimensional stress analysis model and multi-objective optimization method of the carbon fiber sheath rotor according to claim 1 is characterized in that: In step 1, the process of establishing the analytical simplified model is: Step 1: For a thin-walled carbon fiber sheath (1) with a wall thickness of 4 mm or less, the relationship between the diameter, tangential strain and displacement of the circular arc unit of the carbon fiber sheath (1) is analyzed; specifically: Take a micro-circular arc with an angle of dθ and a radial length of dr on the carbon fiber sheath (1) and analyze the relationship between its diameter, tangential strain and displacement: According to the structural dynamics theory, formula (1) is obtained: Where: ε r , ε θ Respectively represent radial and tangential strains, r is the radius of the inner arc surface of the micro-element arc, the radial displacement of the inner arc surface of the micro-element arc is u, and the radial displacement of the outer arc surface of the micro-element arc is u+du. Then, the definition of stress and strain gives formula (2): Where: μ θr ,μ rθ are the tangential and radial Poisson's ratios respectively; E θ ,E r are the tangential and radial elastic moduli respectively; β θ ,β r are the tangential and radial thermal expansion coefficients respectively; ΔT is the temperature change value; Step 1 and 2: For a thin-walled carbon fiber sheath (1) with a wall thickness of 4 mm or less, the relationship between the radial and tangential stresses of the circular arc unit of the carbon fiber sheath (1) is analyzed; specifically: Take a micro-circular arc with an angle of dθ and a radial length of dr on the carbon fiber sheath (1), analyze its radial and tangential stresses, and obtain formula (3): From the infinitesimal radial force balance, we can get formula (4): Where: ρ is the material density, ω is the rotor speed; Simplifying formula (4) yields formula (5): Substitute equation (3) into equation (5) and arrange it according to the symmetry of the flexibility matrix to obtain equation (6): For the thin-walled carbon fiber jacket (1), without considering the temperature as a function of the radial position, the differential equation (6) is solved to obtain equation (7): Where: U is the radial displacement of the carbon fiber sheath, C1, C2 are unknown parameters, a, k are known coefficients; Then the radial and tangential strains are obtained as follows: Substituting the above formula (8) into formula (3), we can get the radial and tangential stress expressions of the thin-walled carbon fiber sheath (1); Step 13: For the two rotor main structures, the shaft (3) and the permanent magnet (2), consider their axial stress and assume that they have no axial deformation, then: Where: E is the elastic modulus of the material, μ is the Poisson's ratio of the material, σ r σ θ σ Z They are radial stress, tangential stress, Axial stress, in the following text, the subscripts 1, 2, and 3 are used to distinguish the stress when only the interference, centrifugal force, and thermal stress are considered. At the same time, the superscript ' is used to distinguish the stress expressions of the shaft (3), the permanent magnet (2), and the carbon fiber sheath (1). The superscript ' is the stress expression of the carbon fiber sheath (1); From formula (9), we can further deduce: The same formula (7) gives formula (11): Where: C 3、5 , C 4、6 are the unknown coefficients in the radial displacement expressions of the permanent magnet (2) and the rotating shaft (3); Step 14: Calculate using the stress separation method under three conditions: static, rotating, and heated; First, the static stress when only the interference is considered; the stress in each direction of the rotating shaft (3) and the permanent magnet (2) is: The isotropic stress of the carbon fiber sheath (1) is: According to the contact between the permanent magnet (2) and the rotating shaft (3) using a binding method, and the contact between the permanent magnet (2) and the sleeve 1 using an interference method, the following static boundary conditions are obtained: Where: r h is the outer wall radius of the carbon fiber sheath (1), r p is the outer wall radius of the permanent magnet (2), r z is the outer wall radius of the shaft (3), δ is the selected interference; u h 、u z are the displacements of the carbon fiber sheath (1) and the shaft (3) at different radii; σ rh , σ rp , σ rz By σ r The subscripts h, p, and z of the radial stress respectively represent the radial stress of the carbon fiber sheath (1), the permanent magnet (2), and the rotating shaft (3); By combining the six boundary conditions in the above equation and introducing six known parameters h1-h6, we can obtain the six unknowns C in the displacement expressions of the permanent magnet (2), the rotating shaft (3) and the carbon fiber sheath (1) under static conditions. 1j -C 6j , and then obtain the static stress values ​​of the permanent magnet (2), the rotating shaft (3) and the carbon fiber sheath (1); When only the rotating centrifugal force is considered, the isotropic stresses of the rotating shaft (3) and the permanent magnet (2) are: The isotropic stress of the carbon fiber sheath (1) is: Then, the stresses in the permanent magnet (2), the rotating shaft (3) and the carbon fiber sheath (1) are solved by the following boundary conditions: At this time, three known parameters A, B, and C are introduced; similarly, six unknown parameters C are obtained when only centrifugal force is considered. 1l -C 6l , and then the centrifugal stress values ​​of the permanent magnet (2), the rotating shaft (3) and the carbon fiber sheath (1) and the interference loss caused by the centrifugal force are obtained: Δu1=u h1 (r p )-u p1 (r p ) (18) When only thermal conditions are considered, ΔT is simplified to a constant; then the isotropic thermal stress of the shaft (3) and the permanent magnet (2) is: At this time, the permanent magnet (2), the rotating shaft (3) and the carbon fiber sheath (1) have the following boundary conditions: After introducing two known parameters X, Y and two functions M(r), N(r), we can solve for six unknowns C 1r -C 6r , and the radial and tangential stresses of the carbon fiber sheath (1) are obtained at the same time: The interference loss at this time is: Δu2=u h2 (r p )-u p2 (r p ) (22) Therefore, the final interference fit is: d g =δ-Δu1-Δu2 (23) Where: Δu1 and Δu2 are the interference loss of the rotor under the two conditions represented by equations (18) and (22), respectively; The isotropic stress of the rotor under working condition is the superposition of static stress, thermal stress and centrifugal force values, and the static stress value is the stress calculated from the actual interference value under working condition: Finally, the equivalent stress of the permanent magnet (2), the rotating shaft (3) and the carbon fiber sheath (1) is obtained by formula (25):

3. The simplified three-dimensional stress analysis model and multi-objective optimization method of the carbon fiber sheath rotor according to claim 2 is characterized in that: In step 1, the known coefficients and parameters are set as follows:

4. The simplified three-dimensional stress analysis model and multi-objective optimization method of the carbon fiber sheath rotor according to claim 2 or 3 is characterized in that: Step 2 is as follows: Step 21: Improve the multi-objective particle swarm optimization algorithm; Step 2-1: Introduce nonlinear inertia weight and particle mutation rate; By using the combination of Sigmoid function and linear function, the nonlinear change of inertia weight is realized as formula (34) and the nonlinear change of particle mutation rate is realized as formula (35); Where: sigmoidPart is the nonlinear function part; linearPart is the linear function part; gen is the current iteration number; genmax is the maximum iteration number; w is the inertia weight; mut sl is the particle mutation rate; Step 212: Obtain the optimal solution set through multiple iterations; According to the setting of constraints, optimization objective function, optimization parameters and their value ranges, the optimization algorithm calculates the objective function values ​​of all particles within the set value range based on the analytical model, and screens all particles that have completed the objective function value calculation according to the set conditions. After multiple iterations, the optimal particle swarm individuals within the set range are finally obtained as the optimal solution set of this optimization problem.

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