A Low Vibration and Noise Design Method for a Permanent Magnet Flat Wire Drive Motor Based on Harmonics

Abstract

The present invention discloses a low vibration and noise design method for a permanent magnet flat wire drive motor based on harmonics. Considering that the permanent magnet flat wire drive motor is small in size and there is a risk of deformation and fracture of the motor rotor at high speeds, the constraint conditions of each variable of the motor are determined based on the strength parameters of the motor materials, so that the optimized motor has sufficient structural stability. The harmonics that are the sources of the radial electromagnetic force that dominates the motor vibration and noise, the torque and torque ripple of the motor are set as the optimization objectives. The harmonics that are the sources of each radial force in the optimization set are used to optimize the entire harmonic set, reducing the amount of calculation and directly and effectively providing a basis for reducing the vibration and noise of the permanent magnet flat wire drive motor from the root. According to the established constraint conditions and optimization objectives, a multi-objective genetic algorithm is used for iterative solution to determine the final variable parameters of the motor. The optimized permanent magnet flat wire drive motor has the characteristics of low vibration and noise and sufficient structural stability while ensuring the output performance.

Description

Technical Field

[0001] The present invention belongs to the field of permanent magnet flat wire drive motor design, and specifically relates to a design method of a permanent magnet flat wire drive motor with low vibration and low noise characteristics. Background Art

[0002] In recent years, new energy vehicles have become one of the important development directions in the automotive field due to their advantages such as high efficiency, energy conservation, and environmental protection. However, since the drive motors used in new energy vehicles replace traditional internal combustion engines, their vibration and noise have become more obvious, directly affecting the vehicle's overall noise, vibration, and comfort (NVH) performance. Therefore, the high comfort requirements of new energy vehicles impose more stringent performance requirements on their drive motors. To improve the motor performance, researchers have proposed various improvement measures. Among them, the permanent magnet flat wire drive motor is a popular choice in recent years. The permanent magnet flat wire drive motor with a flat wire winding has improved in terms of electromagnetic performance, volume, and cost compared to the traditional permanent magnet round wire winding drive motor. The great potential of the permanent magnet flat wire motor has gradually made it the development trend of new energy vehicle drive motors. However, the permanent magnet flat wire drive motor itself also has some disadvantages. For example, the high standard requirements for processing technology, the vibration and noise caused by the use of flat wires, and the problem of optimized design all restrict the development of the permanent magnet flat wire drive motor.

[0003] When the permanent magnet flat wire motor is running, there are interactions between the stator-rotor resultant magnetomotive force and the air-gap permeance in its air gap. It will not only generate tangential electromagnetic force, thus generating tangential electromagnetic torque, but also generate radial electromagnetic force. The radial electromagnetic force is the main cause of motor vibration and noise. And for the permanent magnet flat wire drive motor, as the designed speed of the motor gets higher and higher, higher vibration and noise will inevitably be generated, posing higher requirements for the structural stability of the motor. Therefore, how to suppress the vibration and noise of the permanent magnet flat wire drive motor and improve the quality level of the motor body design is an urgent problem to be solved in the motor industry.

[0004] The vibration and noise reduction technology of permanent magnet motors has always been a recognized problem. Previous researchers have conducted extensive and in-depth research on this issue and proposed many effective optimization design methods, such as: [1] skewed poles (see Mohammad S. Islam, Sayeed Mir, and Tomy Sebastian, Reducing the torque ripple problem of mass-produced DC brushless motors. IEEE, Journal of Industrial Applications, 2004, 40(3): 813-820); [2] skewed slots (see Tang Renyuan, Modern Permanent Magnet Motor Theory and Design, Beijing: Machinery Industry Press, 1997); [3] tooth crown slotting (see Chen Xia, Zou Jibin, et al., Effectively Suppressing the Tooth Torque of Permanent Magnet Motors by Using Tooth Crown Slotting, Micro-Electromechanical, 2006, 34(11): 9-10, 42). The shortcomings of these optimization design methods are that they do not consider the structural stability of the motor at high speeds, and fail to propose an effective method for determining the radial electromagnetic force that dominates the motor's vibration noise. The optimization methods are not comprehensive. It can be seen that the current motor optimization design method is difficult to fully meet the requirements of low vibration and high reliability of permanent magnet flat wire drive motors. Therefore, how to obtain a low-vibration and high-reliability permanent magnet flat wire drive motor while ensuring basic electromagnetic performance is still one of the urgent problems to be solved in the field of automotive drive motors. Summary of the invention

[0005] The purpose of the present invention is to solve the above problems existing in the existing permanent magnet flat wire drive motor optimization design method, and propose a low vibration and noise design method for permanent magnet flat wire drive motor based on harmonics, which can directly and efficiently achieve low vibration and low noise characteristics while ensuring the output performance of the motor.

[0006] To achieve the above object, the technical solution adopted by the present invention comprises the following steps:

[0007] Step (1): determining the design variables to be optimized for the permanent magnet flat wire drive motor;

[0008] Step (2): Analyze the radial electromagnetic force of the motor to obtain the harmonic order μp±να±kz of the radial electromagnetic force generated by the permanent magnetic field and the armature magnetic field, where μ and ν are the harmonic orders of the magnetomotive force of the permanent magnetic field and the armature magnetic field, k is the harmonic order of the magnetomotive force of the stator slot permeance, p and α are the number of motor pole pairs and the number of units, and z is the number of motor slots;

[0009] Step (3): Calculate the amplitude of the ζ-th order radial electromagnetic force harmonic The force that meets the requirements is determined as the dominant vibration radial electromagnetic force, and the harmonics of the dominant vibration radial electromagnetic force constitute the set G f , ω is the current angular frequency, n is the motor speed, ∑R r is the sum of the amplitudes of the radial electromagnetic force harmonics;

[0010] Step (4): Calculate the values of μ and ν that satisfy the equation ζ = |μp ± να|, then the permanent magnet magnetomotive force F corresponding to μ and ν PM_μ and the armature magnetomotive force F ARM_v are the source magnetomotive forces of the radial electromagnetic force, and the set G f is obtained for the source magnetomotive force harmonics of each radial electromagnetic force in it. All the source magnetomotive force harmonics form the set S G ;

[0011] Step (5): Take the source magnetomotive force harmonic set S G , the torque T of the motor and the torque ripple Tr as the final optimization objectives, and the objective function is [Min(S G ), Max(T), Min(Tr)], and the constraint condition is that the design variables vary within their respective precise selection ranges.

[0012] Furthermore, screen the source magnetomotive force harmonics of each radial electromagnetic force in the harmonic set G f that dominates the vibration radial electromagnetic force. If it satisfies the permanent magnet magnetomotive force or satisfies the armature magnetomotive force then F PM_μλ , F ARM_vλ are the main source magnetomotive force harmonics of each radial electromagnetic force in the set G f and form the set S G ; λ ∈ [1, ε], where ε is the number of solutions that satisfy the equation ζ = |μp ± να|, F μλ and F vλ ∈ {[F PM_μ1 , F ARM_v1 , [F PM_μ2 , F ARM_v2 , …, [F PM_με , F ARM_vε}, ∑(F PM_μ + F ARM_v ) is the sum of the amplitudes of each magnetomotive force harmonic in {[F PM_μ1 , F ARM_v1 , [F PM_μ2 , F ARM_v2 , …, [F PM_με , F ARM_vε}, and F PM_μλ , F ARM_vλ , ∑F PM_μ and ∑F ARM_v are all calculated by finite element software.

[0013] The beneficial effects of the present invention adopting the above technical solutions are:

[0014] 1. In view of the characteristics of the permanent magnet flat linear drive motor of the present invention, which is small in volume and difficult to process, making it difficult to ensure the structural stability of the motor at high speeds, the ultimate strength of the motor material is first determined, and the precise range of design variables is determined. Before optimization, the precise range of variables to be optimized is determined according to the ultimate yield strength of the material to ensure the reliability of the motor design. Within this range, the mechanical strength of the rotor is ensured, and sufficient structural stability of the optimized motor is ensured, avoiding the problem that the structural stability of the motor does not meet the mechanical strength of the material after optimization by traditional optimization methods.

[0015] 2. The present invention is an optimization design method that combines the electromagnetic, vibration, and structural multi-physical characteristics of the motor. Moreover, the present invention adopts an optimization means based on harmonics, further improving the feasibility and efficiency of the optimization design scheme; through analytical derivation, the harmonic orders and sources of the radial electromagnetic forces of the motor are solved, and according to the law of the influence of the radial electromagnetic force on the vibration degree, an index for effectively determining the radial electromagnetic force harmonics that dominate the motor vibration is defined, which can effectively screen out the radial electromagnetic forces that dominate the motor vibration. It directly and effectively provides a basis for reducing the vibration and noise of the permanent magnet flat wire drive motor, avoiding the disadvantages of repeated trial and error and low efficiency in traditional vibration reduction methods, and providing a general method for the permanent magnet flat wire drive motor to achieve low vibration and noise characteristics.

[0016] 3. The present invention takes the magnetomotive force harmonics of the sources of the radial electromagnetic forces in the set of radial electromagnetic forces that dominate the motor vibration as the optimization objective, optimizes the harmonic set by optimizing the source harmonics of each radial force in the set, reduces the calculation amount, saves the optimization time, improves the overall design optimization efficiency and quality of the motor, and directly and efficiently realizes the low vibration characteristic while ensuring the output performance.

[0017] 4. The present invention combines the electromagnetic characteristics, vibration characteristics, and structural characteristics of the motor, introduces a multi-objective genetic algorithm, while achieving low vibration and high reliability of the motor, considers the torque output ability of the motor, and ensures the output performance of the motor. It is a multi-objective optimization design method that combines the multi-physical characteristics of the motor, avoiding the problem of incomplete consideration in the traditional optimization design method of the permanent magnet flat wire drive motor.

[0018] 5. The present invention selects the second-generation non-dominated genetic algorithm, avoiding problems such as low solution efficiency and mutual restriction of optimization objectives in traditional optimization methods. Moreover, compared with the traditional non-dominated sorting genetic algorithm, it reduces the complexity of the non-dominated sorting genetic algorithm, has the advantages of fast running speed and good convergence of the solution set, and improves the optimization efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] The following further detailed description of the present invention is made in accordance with the drawings and specific embodiments;

[0020] Figure 1It is a flowchart of a low vibration and noise design method for a permanent magnet flat wire drive motor based on harmonics of the present invention;

[0021] Figure 2 It is a schematic structural diagram taking a permanent magnet flat wire drive motor as an example in the embodiment;

[0022] Figure 3 Is Figure 2 An enlarged schematic diagram of the local structure and geometric dimension marking of the rotor in ;

[0023] Figure 4 Is Figure 2 The radial electromagnetic force harmonic distribution diagram of the motor in ;

[0024] Figure 5 Is Figure 2 The permanent magnet magnetomotive force harmonic distribution diagram of the motor in ;

[0025] Figure 6 It is the non-dominated solution set obtained after adopting the multi-objective optimization genetic algorithm;

[0026] Figure 7 It is a schematic diagram of the permanent magnet magnetomotive force amplitude, torque and torque ripple of the dominant low-order radial force of the motor in the embodiment;

[0027] In the figure: 1. Stator; 2. Permanent magnet; 3. Rotor; 4. Rotating shaft; 5. Mounting screw hole; 6. Magnetic barrier. Detailed implementation manners

[0028] See Figure 1 , for a design method of a permanent magnet flat wire motor based on harmonics proposed by the present invention, first, considering the characteristics that the permanent magnet flat wire drive motor has a small volume and there is a risk of deformation and fracture of the motor rotor at high speeds, according to the basic structure of the motor, select the design variables to be optimized for the motor, and determine its constraint conditions according to the strength parameters of the motor materials, so that the optimized motor has sufficient structural stability; set the source harmonics of the radial electromagnetic force that dominates the motor vibration and noise, the torque and torque ripple of the motor as the optimization objectives; according to the established constraint conditions and optimization objectives, use the multi-objective genetic algorithm for iterative solution to determine the final variable parameters of the motor; finally, based on the optimized permanent magnet flat wire drive motor, in addition to ensuring the basic electromagnetic performance, it has the characteristics of low vibration and noise and sufficient structural stability, providing a method for the permanent magnet flat wire drive motor to achieve low vibration and noise characteristics. Specifically:

[0029] First, determine the design variables to be optimized for the permanent magnet flat wire drive motor and the initial ranges of the corresponding design variables.

[0030] For a permanent magnet flat wire drive motor with a basic structure, the design variables to be optimized are m1, m2,... m i(where \(i\) is the number of design variables to be optimized for the motor). For example, the design variables can be the length and width of the permanent magnet, the size of the magnetic isolation bridge between adjacent permanent magnets, the magnetic barrier, the magnetic assistance size, etc. in the permanent magnet flat wire drive motor. At the initial stage of motor design, based on the designed power requirements and design experience, the initial ranges corresponding to each design variable are \([a_1, b_1]\), \([a_2, b_2]\), … \([a_{i}, b_{i}]\) respectively. i , \(b\) i , and the initial range of the design variable \(m\) i is \([a\) i , \(b\) i , where \(a\) i and \(b\) i are the minimum and maximum values of the initial range of the design variable respectively.

[0031] The silicon steel sheet material used in the permanent magnet flat wire drive motor is a known selected model, and the ultimate yield strength of the silicon steel sheet used can be found in existing literature and materials, which is \(G\) with the unit of MPa. Taking the ultimate yield strength \(G\) of the silicon steel sheet as a constraint, the precise selection ranges of each design variable \(m_1, m_2, \ldots m_i\) are determined accordingly. i

[0032] The rated speed of the permanent magnet flat wire drive motor is \(n\) revolutions per minute. At high speeds, it is generally more than five times the rated speed. Since there are risks of deformation and fracture of the motor rotor at high speeds, in order to ensure the structural stability of the motor, it is necessary to further obtain the precise selection ranges of the design variables. In the Static Structural module of Ansys Workbench finite element software, set the motor speed to \(Xn\) revolutions per minute, where \(X\) is an integer greater than or equal to 5, and the design variables are \(m_1, m_2, \ldots m_i\). i The corresponding stress at high speeds is \(\sigma[m_1, m_2, \ldots m_i]\). i

[0033] The initial values given for the design variables \(m_1, m_2, \ldots m_i\) are the averages of the initial ranges of these design variables, that is, the initial values are \((a_1 + b_1) / 2\), \((a_2 + b_2) / 2\), … \((a_{i}+b_{i}) / 2\). For a single design variable \(m_j\), it varies within the initial range \([a_j, b_j]\), and the other design variables except this single design variable \(m_j\) are set to their initial values. Through finite element software simulation, the stress \(\sigma[(a_1 + b_1) / 2, (a_2 + b_2) / 2, \ldots m_j]\) at high speeds corresponding to this single design variable \(m_j\) and \(m_j\) can be obtained. i i \(+b\) i \(_{i})\) / 2. For a single design variable \(m\) i , it varies within the initial range \([a\) i , \(b\) i , and the other design variables except this single design variable \(m\) i are set to their initial values. Through finite element software simulation, the stress \(\sigma[(a_1 + b_1) / 2, (a_2 + b_2) / 2, \ldots m]\) at high speeds corresponding to this single design variable \(m\) and \(m\) i can be obtained. i and \(m\) iThe variation relationship.

[0034] Taking the ultimate yield strength G of the silicon steel sheet used in the permanent magnet flat wire drive motor as a constraint condition to judge the single design variable m i The corresponding stress σ[(a1 + b1) / 2, (a2 + b2) / 2, … m i and the ultimate yield strength G of the silicon steel sheet are compared. When σ[(a1 + b1) / 2, (a2 + b2) / 2, … m i ≤ G, that is, the corresponding stress is less than or equal to the ultimate yield strength G, the requirement of structural stability is met. Then within the initial range [a i , b i of the single design variable m, select the maximum range that meets the constraint condition σ[(a1 + b1) / 2, (a2 + b2) / 2, … m i ≤ G, which is the precise selection range [c i , d i of the design variable m. i , d i .

[0035] Similarly, the initial ranges [a1, b1], [a2, b2], … [a i-1 , b i-1 can be narrowed down, and the corresponding precise selection ranges of the design variables can be obtained as [c1, d1], [c2, d2], … [c i-1 , d i-1 . Within the precise selection ranges [c1, d1], [c2, d2], … [c i , d i , it not only ensures the structural stability of the motor, but also reduces the variable range while ensuring the high reliability of the optimized motor, saving time for the subsequent optimization design of the motor.

[0036] Next, optimize the vibration performance of the motor. The radial electromagnetic force is the main cause of the motor vibration. Through the analytical derivation of the radial electromagnetic force, the magnetomotive force harmonics that constitute the dominant vibration radial electromagnetic force harmonics are obtained for subsequent optimization. In the process of deriving the radial electromagnetic force, it is not necessary to quantitatively calculate the specific amplitude of the radial electromagnetic force harmonics, but only to qualitatively determine the order and source of the radial electromagnetic force harmonics.

[0037] According to the Maxwell stress tensor method, the radial electromagnetic force P r (θ, t) is:

[0038]

[0039] In the above formula, b r (θ, t) is the radial air-gap magnetic density, b L2(θ, t) is b r the square of (θ, t), b t (θ, t) is the tangential air-gap magnetic flux density, b t 2 (θ, t) is the square of, due to the tangential air-gap magnetic flux density b t (θ, t) has a small amplitude, so this variable is not considered in this optimization. θ is the mechanical angle, t is the operating time of the motor, and the vacuum permeability is μ0 = 4π×10 -7 .

[0040] The radial air-gap magnetic flux density b r (θ, t) is:

[0041] b r (θ,t) = [f PM (θ,t) + f ARM (θ,t)] × Λ s (θ) (2)

[0042]

[0043]

[0044]

[0045] where f PM (θ,t), f ARM (θ,t) are the magnetomotive force of the permanent magnet and the armature magnetomotive force respectively. μ and ν are the magnetomotive force harmonic orders of the permanent magnet magnetic field and the armature magnetic field respectively. F μ and F ν are the amplitudes of the μ-th permanent magnet magnetic field magnetomotive force harmonic and the ν-th armature magnetic field magnetomotive force harmonic respectively. p and α are the number of pole pairs and the number of motor units of the motor respectively. ω is the current angular frequency. S ν denotes the rotation direction of the v-th harmonic of the armature magnetic field (where 1 represents forward rotation and -1 represents reverse rotation). z is the number of stator slots of the motor. Λ s (θ) is the air-gap permeance considering the stator slotting effect. k is the magnetomotive force harmonic order of the stator slot permeance. Λ0 is the average permeance value. Λ k is the permeance amplitude of the k-th harmonic (k = 1, 2, 3...). According to the radial air-gap magnetic flux density, the permanent magnet magnetomotive force, the armature magnetomotive force, and the air-gap permeance considering the stator slotting effect, the expansion formula of the radial electromagnetic force P r (θ,t) is obtained. That is, substituting formulas (2), (3), (4), and (5) into formula (1), the expansion formula of the radial electromagnetic force P r (θ,t) is:

[0046]

[0047] To distinguish partial items, such as F μ After multiplying the squares and expanding, in the formula, μ is μ1 and μ2 (μ1 = μ2) or (μ1 ≠ μ2), and the same applies to ν1 and ν2, k1 and k2. ν is ν1 and ν2, and k is k1 and k2. Through the expansion and analysis of the above formula, it can be deduced that the radial electromagnetic force is generated by the interaction of the permanent magnet magnetic field, the armature magnetic field, and the stator slotting, and its order is μp ± να ± kz. Since the stator slotting parameters have been set as the design variables to be optimized in the subsequent variable selection, the influence of the stator slotting is not considered in the analysis of the source of the radial electromagnetic force, and the focus is mainly on the radial electromagnetic force generated by the interaction of the permanent magnet magnetic field and the armature magnetic field, and its harmonic order is:

[0048] μp ± να (7)

[0049] where μ = 2a + 1, (a = 0, 1, 2…); ν = 3b + 1, (b = 0, ±1, ±2…). From this, the harmonic order of the radial electromagnetic force generated by the interaction of the permanent magnet magnetic field and the armature magnetic field can be calculated. p and α are the number of pole pairs and the number of motor units of the motor respectively. The number of motor units α satisfies the following rule:

[0050] α = GCD(z, p) (8)

[0051] GCD(z, p) is the greatest common divisor of the number of motor slots z and the number of pole pairs p. Combining formula (7) and formula (8), the harmonic order and source of each radial electromagnetic force of the motor can be calculated. Generally speaking, the vibration amplitude of the motor stator core is inversely proportional to the harmonic order of the radial electromagnetic force and directly proportional to the amplitude. Therefore, to optimize the electromagnetic vibration and noise of the motor, it is necessary to identify and screen out the radial electromagnetic force harmonics with low order and large amplitude, that is, the dominant radial electromagnetic force harmonics that cause the motor vibration and then radiate noise outward. However, it is very difficult to quantitatively screen out the radial electromagnetic force harmonics that dominate the vibration only based on the fact that the amplitude is inversely proportional to the harmonic order of the radial electromagnetic force and directly proportional to the amplitude. Therefore, the present invention determines the radial electromagnetic force harmonics that dominate the motor vibration noise according to the relationship between the amplitude of the radial electromagnetic force harmonics and the total amplitude of the radial electromagnetic force harmonics:

[0052]

[0053] In the formula, ω is the current angular frequency; n is the motor speed; p is the number of pole pairs of the motor; α is the number of motor units; R ζ is the amplitude of the ζ-th order radial electromagnetic force harmonic, ζ belongs to μp ± να, ∑R r represents the total amplitude of the radial electromagnetic force harmonics; among them, R ζ and ∑R r can both be calculated by finite element software, and n, p, α, and ω are all specific motor parameters. In formula (9), As a coefficient of ∑R r Substitute the parameters n, p, α, and ω into Equation (9). If the inequality in (9) holds, then determine R ζ as the dominant vibration radial electromagnetic force; otherwise, it is a non-dominant vibration radial electromagnetic force. According to this method, substitute each radial electromagnetic force harmonic one by one, and select the radial electromagnetic force harmonics that satisfy Equation (9) to form a set G f , then each radial electromagnetic force harmonic in set G f is a dominant harmonic of the motor vibration.

[0054] Analyze all the source magnetomotive force harmonics of the radial electromagnetic force harmonics in set G f : From μp ± να in Equation (7), it can be seen that the order of the radial electromagnetic force formed by the permanent magnet magnetic field and the armature magnetic field is |μp ± να|; μ represents the μth-order permanent magnet magnetomotive force harmonic, and ν represents the νth-order armature magnetomotive force harmonic. To obtain all the source magnetomotive force harmonics of the ζth-order radial electromagnetic force R f , let ζ = |μp ± να|, and find all the values of μ and ν that satisfy this equation. The corresponding permanent magnet magnetomotive force F ζ and armature magnetomotive force F PM_μ are the source magnetomotive forces of this radial electromagnetic force. If the solutions that satisfy ζ = |μp ± να| are: {[μ1, ν1], [μ2, ν2], …, [με, νε]} (ε is the number of solutions that satisfy the equation ζ = |μp ± να|), it means that the source magnetomotive force harmonics of the ζth-order radial electromagnetic force are {[F ARM_v , F PM_μ1 , [F ARM_v1 , F PM_μ2 , …, [F ARM_v2 , F PM_με}. According to this method, the source magnetomotive force harmonics of each radial electromagnetic force in G ARM_vε can be obtained: {[F f , F PM_μ1 , [F ARM_v1 , F PM_μ2 , …, [F ARM_v2 , F PM_με} (ε is the number of groups of source magnetomotive force harmonics of each radial electromagnetic force in set G ARM_vε ). f If directly for the source magnetomotive force harmonics {[F

[0055] obtained in the above steps for each radial electromagnetic force in G f : [F PM_μ1 , F ARM_v1 , [F PM_μ2 , F ARM_v2 , …, [F PM_με , F ARM_vε} If optimized, the computational load will be huge. To improve the optimization efficiency and save optimization time, it is necessary to screen the magnetomotive force harmonics that are the sources of the radial electromagnetic forces in the above G f to select all the main source harmonics of the radial electromagnetic forces in the set G f . Therefore, the present invention screens according to the magnetomotive force harmonics that are the sources of the radial electromagnetic forces and the sum of the amplitudes of the magnetomotive force harmonics:

[0056]

[0057]

[0058] where λ ∈ [1, ε]; F μλ and F vλ ∈ {[F PM_μ1 , F ARM_v1 , [F PM_μ2 , F ARM_v2 , …, [F PM_με , F ARM_vε}; ∑(F PM_μ +F ARM_v ) represents the sum of the amplitudes of the magnetomotive force harmonics in {[F PM_μ1 , F ARM_v1 , [F PM_μ2 , F ARM_v2 , …, [F PM_με , F ARM_vε}, where F PM_μλ , F ARM_vλ , ∑F PM_μ and ∑F ARM_v can all be obtained by finite element software. According to the finite element calculation results, substitute F PM_μλ and F ARM_vλ into formulas (10) and (11). If the inequality in formula (10) or formula (11) is satisfied, then determine the F PM_μλ , F ARM_vλ in the corresponding formula as the main source magnetomotive force harmonics of the radial electromagnetic forces in the set G f , otherwise they are non-main source magnetomotive force harmonics. According to this method, substitute the amplitudes of the magnetomotive force harmonics in {[F PM_μ1 , F ARM_v1 , [F PM_μ2 , F ARM_v2 , …, [F PM_με , F ARM_vε} into (10) and (11) one by one, and screen out all the magnetomotive force harmonics that satisfy the inequalities in (10) and (11) to form the set S G , then the set S G is the main source magnetomotive force harmonics of the radial electromagnetic forces that dominate the motor vibration. Let SG For subsequent optimization as one of the optimization objectives.

[0059] The present invention realizes the low vibration and noise characteristics for the permanent magnet flat wire drive motor. Through the two proposed screening means, two rounds of screening are carried out on the factors affecting the motor vibration and noise. First, the radial electromagnetic forces that meet the conditions are screened to construct the set G f ; then the main source harmonics S of each radial electromagnetic force in G f are screened out G , and finally S G is determined as the optimization objective. Through two rounds of screening, a large number of irrelevant variables are eliminated, greatly reducing the calculation amount, saving the optimization time, and providing a general method for the permanent magnet flat wire drive motor to achieve low vibration and noise characteristics.

[0060] In order to ensure the electromagnetic performance of the motor while having the characteristics of low vibration and high structural stability, the torque T and torque ripple Tr of the motor are set as the optimization objectives. Among them, the torque T reflects the torque output ability of the motor. The higher the torque, the stronger the torque output and load-bearing capacity of the motor; while the torque ripple reflects the running stability of the motor. The smaller the torque ripple, the smaller the torque fluctuation during the operation of the motor, and the more stable the torque output of the motor.

[0061] The magnetomotive force harmonic set S G , the torque T and torque ripple Tr of the motor are set as the final variable optimization objectives. These objectives vary with i design variables within the accurately selected ranges [c1, d1], [c2, d2], … [c i , d i , ensuring that the parameters of the optimized motor meet the requirements of structural stability. Combining the electromagnetic characteristics, vibration characteristics and structural characteristics of the motor, an optimization model is constructed, and the optimal size of the motor is determined through the multi-objective genetic algorithm.

[0062] In the problem of multi-objective optimization, it is difficult to simultaneously achieve the optimal for multiple optimization objectives, and even the unique optimal solution does not exist. Therefore, multi-objective optimization needs to balance each objective. Common traditional optimization methods such as the parameter scanning method, weighted synthesis method, constraint method, etc. will encounter difficulties in solving when dealing with multiple parameters and multiple objectives, and cannot well balance the problem of mutual constraints between multiple optimization objectives. The second-generation non-dominated genetic algorithm (NSGA-II) is one of the currently popular multi-objective optimization genetic algorithms, which avoids problems such as low solution efficiency and mutual constraints of optimization objectives in traditional optimization methods. Compared with the traditional non-dominated sorting genetic algorithm, it reduces the complexity of the non-dominated sorting genetic algorithm, has the advantages of fast running speed and good convergence of the solution set, and improves the optimization efficiency. Therefore, the present invention uses the second-generation non-dominated genetic algorithm of the non-dominated sorting genetic algorithm to solve the optimization model.

[0063] Combined with the electromagnetic performance of the motor, the source magnetomotive force harmonic set S G , the torque T of the motor, and the torque ripple Tr are set as the scanning targets. The i design variables vary within the precise ranges [c1, d1], [c2, d2], … [c i , d i . The initial population H[h1, h2, … h e generated by simulation, where h1[S G , T, Tr], h2[S G , T, Tr], … h e [S G , T, Tr] are the individuals in the population, and e is the population size. According to the design requirements, the smaller the amplitude of the magnetomotive force harmonic set S G , the better the vibration performance of the motor, the larger the torque T, and the smaller the torque ripple Tr. Based on this, a multi-physical characteristic optimization model involving the electromagnetic performance, vibration performance, and structural stability of the motor is constructed. The genetic algorithm is used to select, inherit, and mutate in the initial population H[h1, h2, … h e , and finally the non-dominated solution set C that meets the above optimization model is obtained. In the non-dominated solution set C, the solution that appears most frequently in the non-dominated solution set is selected and combined with the actual design requirements of the motor to determine the optimized design variables of the motor, thereby obtaining the final optimized structure of the motor.

[0064] According to the design requirements, the corresponding objective function and constraint conditions are given as follows:

[0065]

[0066] Among them, Min(S G ) represents the minimum value of the magnetomotive force harmonic S G ; Max(T) and Min(Tr) represent the maximum torque and the minimum torque ripple of the motor, respectively. The constraint condition is that the design variables vary within their respective precise selection ranges, that is, the design variables m1, m2, … m i vary within the precise selection ranges [c1, d1], [c2, d2], … [c i , d i . Through iterative solution of the multi-objective genetic algorithm, the optimized variable parameters of the motor are determined, thereby obtaining the final optimized structure of the motor.

[0067] A design method of a permanent magnet flat wire motor based on harmonics proposed by the present invention. First, considering that the permanent magnet flat wire drive motor is small in size and there is a risk of deformation and fracture of the motor rotor at high speeds, the constraint conditions of each variable of the motor are determined based on the strength parameters of the motor materials, so that the optimized motor has sufficient structural stability; further, the harmonics that are the source of the radial electromagnetic force that dominates the motor vibration and noise, the torque and torque ripple of the motor are set as the optimization objectives; furthermore, according to the constraint conditions and optimization objectives established in the above steps, a multi-objective genetic algorithm is used for iterative solution to determine the final variable parameters of the motor. Finally, the permanent magnet flat wire drive motor optimized based on the above steps has the characteristics of low vibration and noise and sufficient structural stability in addition to ensuring the basic electromagnetic performance, providing a general method for the permanent magnet flat wire drive motor to achieve low vibration and noise characteristics.

[0068] The following provides an embodiment of the present invention:

[0069] To clearly illustrate the optimization design method of the present invention and facilitate the understanding of those skilled in the art, the present invention takes a conventional permanent magnet flat wire drive motor as an example to detail the low vibration and noise design method of the permanent magnet flat wire drive motor based on harmonics. The structure of this motor is as Figure 2 shown. This motor includes an outer stator 1, an inner rotor 3 and permanent magnets 2. The inner rotor 3 is coaxially sleeved outside the rotating shaft 4. Arc-shaped permanent magnets 2 are evenly attached to the outer surface of the inner rotor 3. Magnetic barriers 6 are provided on both the outer stator 1 and the inner rotor 3. The outer stator 1 and the inner rotor 3 adopt a combination of 9 slots / 6 poles. Three-phase windings and mounting screw holes 5 are wound on the outer stator 1. For Figure 2 The optimization design process of the shown permanent magnet flat wire drive motor includes the following steps:

[0070] Step 1: Determine the design variables to be optimized for this permanent magnet flat wire drive motor. As Figure 3As shown in the figure, after determining the initial structure of the motor, a circle is drawn with the inner edge of the permanent magnet 2 as the arc, the center of the circle is O1, and L1 is the length of the inner edge of the permanent magnet; a circle is drawn with the outer edge of the permanent magnet 2 as the arc, the center of the circle is O2, and L2 is the length of the outer edge of the permanent magnet 2; D1 is the distance between the center O1 of the inner circle of the permanent magnet and the center O2 of the outer circle of the permanent magnet; the thickness of the permanent magnet 2 in the radial section is D2; the above four parameters L1, L2, D1, D2 are used as the design variables to be optimized. According to previous design experience and reference documents, their initial ranges are L1 ∈ [8.2 mm, 10.4 mm], L2 ∈ [11.6 mm, 13.0 mm], D1 ∈ [0 mm, 6 mm], D2 ∈ [2 mm, 4 mm]. The unit of the above four variables is millimeter (mm). The materials used for the motor stator and rotor are silicon steel sheets, and their model is DW470. By querying existing materials, the ultimate yield strength G of the silicon steel sheet of this material is obtained as 235 MPa. This value is used as one of the constraint conditions for subsequent optimization design.

[0071] Step 2: Take the ultimate yield strength G of the silicon steel sheet of the motor stator and rotor obtained by query as one of the constraint conditions, and determine the precise selection range of each design variable. The rated speed of this motor is designed to be 3500 r / min. In the high-speed operation state, it generally needs to reach more than five times the base speed of the motor. Therefore, in this embodiment, 17500 r / min is selected as the high speed. In the Ansys Workbench finite element software, the motor speed is set to 17500 r / min for simulation, and the stress is set as σ[L1, L2, D1, D2]. The initial values set for the design variables L1, L2, D1, D2 correspond one by one to the average values of the initial setting ranges, which are 9.3, 13.0, 4, 3.5 respectively, and the unit is millimeter (mm). For the selected design variable L1, it varies within the initial range [8.2 mm, 10.4 mm], and the other design variables except L1 are set to the initial values, that is, L2, D1, D2 are 13.0, 4, 3.5 respectively, and the unit is millimeter (mm). Through software simulation, the variation relationship between the stress σ[L1, 13.0 mm, 4 mm, 3.5 mm] of the design variable L1 and L1 is obtained. Taking the ultimate yield strength G = 235 MPa of the material as the constraint, compare the stress σ[L1, 13.0 mm, 4 mm, 3.5 mm] with G. When the stress σ[L1, 13.0 mm, 4 mm, 3.5 mm] ≤ G, that is, when the stress σ[L1, 13.0 mm, 4 mm, 3.5 mm] ≤ 235 Mpa, it is considered that the mechanical strength design requirements are met. The maximum range that satisfies the constraint condition G of the material ultimate yield strength within the initial range [8.2 mm, 10.4 mm] is [9.0 mm, 10.2 mm], which is the precise range of the design variable L1.

[0072] Similarly, for the design variable L2, it varies within the initial range [11.6 mm, 13.0 mm], and other design variables except L2 are set to their initial values. That is, the given initial values of L1, D1, and D2 are 8.2, 4, and 3.5 respectively, with the unit of millimeters (mm). In this way, the variation relationship between the stress σ[8.2 mm, L2 mm, 4 mm, 3.5 mm] of the design variable L2 and L2 can be obtained. By comparing the stress σ[8.2 mm, L1, 4 mm, 3.5 mm] with the ultimate yield strength G of the material, the maximum range of the design variable L2 is obtained as [11.9 mm, 13.0 mm].

[0073] Repeat the design in this way to obtain the respective precise ranges of the design variables D1 and D2 as [2.3 mm, 5.8 mm] and [2.7 mm, 3.8 mm] respectively. That is, by narrowing the initial selection range of the design variables, the respective precise selection ranges are obtained. Within the precise selection ranges, the stability of the motor structure is ensured, and the selection range is narrowed, saving time for subsequent optimization.

[0074] Step 3: Select the design objectives to be optimized for the motor. As Figure 4 shown, the amplitudes of the radial electromagnetic forces of each order of the motor are calculated through finite element software, and the amplitudes of the radial electromagnetic force harmonics are sorted out, as shown in Table 1:

[0075] Table 1. Radial Electromagnetic Force Harmonic Distribution of 9-Slot 6-Pole Permanent Magnet Flat Wire Drive Motor

[0076]

[0077] According to Table 1, substitute the amplitudes of the radial electromagnetic forces into formula (9), and filter out the radial electromagnetic force harmonics that satisfy formula (9) to form set G f . After calculation, R3, R6, and R9 are satisfied, that is, the 3rd, 6th, and 9th order radial electromagnetic forces satisfy formula (9). It is confirmed that the 3rd, 6th, and 9th order radial electromagnetic forces form set G f .

[0078] Furthermore, analyze the source of the radial electromagnetic forces in set G f . It can be deduced from formula (6) that the radial electromagnetic forces are generated by the interaction of the permanent magnet magnetic field, the armature magnetic field, and the stator slotting. Among them, the order expression of the radial electromagnetic force is (7): |μp ± να|, where: μ = 2a + 1, (a = 0, 1, 2...); ν = 3b + 1, (b = 0, ±1, ±2...), and μ and ν respectively represent the orders of the permanent magnet magnetomotive force and the armature magnetomotive force harmonics. The number of motor units α satisfies formula (8): α = GCD(z, p); taking this 9-slot 6-pole motor as an example, the number of pole pairs of the motor p = 3; the number of motor units α = 3. Since set G fIt contains 3rd-order, 6th-order, and 9th-order radial electromagnetic forces. Therefore, let |μp ± να| be equal to 3, 6, and 9 respectively, and solve for all values of μ and ν that satisfy this condition. The corresponding magnetomotive force harmonics F PM_μ and F ARM_v are the sources of the respective radial electromagnetic forces in set G f as shown in Table 2:

[0079] Table 2. Sources of Radial Electromagnetic Forces in a 9-Slot 6-Pole Permanent Magnet Flat Wire Drive Motor

[0080]

[0081]

[0082] As can be seen from Table 2, the sources of the respective radial electromagnetic forces in set G f To screen out the main source harmonics of the respective radial electromagnetic forces in set G f substitute the amplitudes of the respective magnetomotive force harmonics into equations (10) and (11). If the inequalities in (10) and (11) still hold, they are the main source harmonics of the respective radial electromagnetic forces in G f . The harmonic distributions of the permanent magnet magnetomotive force and the armature magnetomotive force calculated by the finite element software are respectively as shown in Figure 5 and Figure 6 . According to the finite element calculation results, the amplitudes F PM_μ of the respective permanent magnet magnetomotive force and armature magnetomotive force harmonics are obtained and shown in Tables 3 and 4: ARM_v as shown in Tables 3 and 4:

[0083] Table 3. Harmonic Distribution of Permanent Magnet Magnetomotive Force in a 9-Slot 6-Pole Permanent Magnet Flat Wire Drive Motor

[0084]

[0085] Table 4. Harmonic Distribution of Armature Magnetomotive Force in a 9-Slot 6-Pole Permanent Magnet Flat Wire Drive Motor

[0086]

[0087] Substitute the amplitudes F PM_μ of the respective magnetomotive force harmonics in Tables 3 and 4 and F ARM_v into equations (10) and (11). The magnetomotive force harmonics that satisfy equations (10) and (11) are the main source harmonics S f of the respective radial electromagnetic forces in set G G .

[0088] After calculation, only when μ = 9, that is, the 9th-order permanent magnet magnetomotive force harmonic F PM_9 satisfies the condition. Therefore, the 9th-order magnetomotive force harmonic is the main source of the respective harmonics in set G f , and determine the 9th-order magnetomotive force harmonic FPM_9 As the target of subsequent optimization, namely S G = F PM_9 , through two rounds of screening, a large number of irrelevant variables are eliminated, the amount of calculation is reduced, and the subsequent optimization time is saved.

[0089] Step 4: Determine the optimal size of the motor through the multi-objective genetic algorithm, and determine the magnetomotive force harmonics S G , the torque T of the motor and the torque ripple Tr are set as the final variable optimization objectives, and these objectives change with the variables. According to the design requirements, the smaller the magnetomotive force harmonics S G , the better the vibration performance of the motor, the larger the motor torque T, the smaller the torque ripple Tr, and it is required that the structural stability of the optimized motor meets the requirements of mechanical strength. Combining the electromagnetic characteristics, vibration characteristics and structural characteristics of the motor, an optimization model is constructed:

[0090] Objective function: [Min(S G ), Max(T), Min(Tr)]

[0091] Constraints:

[0092] Among them, Min(S G ) represents the minimum of the magnetomotive force harmonics S G . For the 9-slot 6-pole permanent magnet flat wire drive motor adopted, S G = F PM_9 , that is, it is required to minimize the 9th-order magnetomotive force harmonics; Max(T) and Min(Tr) represent the maximum torque and minimum torque ripple of the motor respectively. The four design variables L1, L2, D1, and D2 are constrained to vary within the precise ranges [9.0 mm, 10.2 mm], [11.9 mm, 13.0 mm], [2.3 mm, 5.8 mm], and [2.7 mm, 3.8 mm]. Through iterative solution of the multi-objective genetic algorithm, the variable parameters of the optimized motor are determined, thereby obtaining the final optimized structure of the motor.

[0093] Combined with the actual design requirements, the final optimized design variable sizes of the motor are determined as: L1 is 9.7 mm, L2 is 12.2 mm, D1 is 3.7 mm, and D2 is 3.6 mm. At this time, the amplitude of the permanent magnet magnetomotive force that dominates the low-order radial force of the motor is 1.26 T, the torque is 4.05 Nm, and the torque ripple is 23.1%, as Figure 7 shown. The optimized motor has the advantages of low vibration and noise while ensuring torque performance.

[0094] The above is based on Figure 2The permanent magnet flat wire drive motor in [description] illustrates the optimization design method in the present invention. The method of the present invention has wide applicability and provides a general method for the permanent magnet flat wire drive motor to achieve low vibration and noise characteristics.

Claims

1. A low vibration and noise design method for a permanent magnet flat wire drive motor based on harmonics, characterized in that It includes the following steps: Step (1): Determine the design variables to be optimized for the permanent magnet flat wire drive motor; Step (2): Analyze the radial electromagnetic force of the motor, and obtain the harmonic orders μp±να of the radial electromagnetic force generated by the action of the permanent magnet magnetic field and the armature magnetic field, where μ and ν are the harmonic orders of the magnetomotive force of the permanent magnet magnetic field and the armature magnetic field respectively, and p and α are the number of pole pairs and the number of units of the motor respectively; Step (3): Determine the amplitude R of the ζ-th order radial electromagnetic force harmonic ζ Whether it satisfies Determine the radial electromagnetic force that meets the requirements as the dominant vibration radial electromagnetic force, and form a set G with the harmonics of the dominant vibration radial electromagnetic force f , ω is the current angular frequency, n is the motor speed, and ∑R r is the total amplitude of the radial electromagnetic force harmonics; Step (4): Calculate the values of μ and ν that satisfy the equation ζ = |μp ± να|, and then the permanent magnet magnetomotive force F corresponding to μ and ν PM_μ and the armature magnetomotive force F ARM_v are the source magnetomotive forces of the radial electromagnetic force, and obtain the set G f the source magnetomotive force harmonics of each radial electromagnetic force in it, and all the source magnetomotive force harmonics form the set S G ; For the harmonic set G of the dominant vibration radial electromagnetic force f Screen the source magnetomotive force harmonics of each radial electromagnetic force in . If it satisfies the permanent magnet magnetomotive force Or if it satisfies the armature magnetomotive force PM_μλ , F ARM_vλ Are the source magnetomotive force harmonics of each radial electromagnetic force in the set G f , constituting the set S G ; λ ∈ [1, ε], where ε is the number of solutions to the equation ζ = |μp ± να|, and ∑(F PM_μ + F ARM_v ) is the sum of the amplitudes of each magnetomotive force harmonic in {[F PM_μ1 , F ARM_v1 , [F PM_μ2 , F ARM_v2 ,..., [F PM_με , F ARM_vε}. F PM_μλ , F ARM_vλ , ∑F PM_μ And ∑F ARM_v Are all calculated by finite element software; Step (5): Take the source magnetomotive force harmonic set S G , the torque T of the motor, and the torque ripple Tr as the final optimization objectives, and the objective function is [Min(S G ), Max(T), Min(Tr)], and the constraint condition is that the design variables vary within their respective accurately selected ranges.

2. The low vibration and noise design method of a permanent magnet flat wire drive motor based on harmonics according to claim 1, characterized in that: The initial value given for the design variable is the average value of the initial range of the design variable. For a single design variable, the other design variables except this single design variable are set to the initial value. The relationship between the stress σ at high speed corresponding to this single design variable and the change of the design variable is obtained through finite element software simulation. Judge the magnitude of the stress σ corresponding to this single design variable and the ultimate yield strength G of the material used in the motor. Select the largest range that meets the constraint condition σ≤G within the initial range of the single design variable, which is the precise selection range of the design variable.

3. A low vibration and noise design method for a permanent magnet flat wire drive motor based on harmonics according to claim 1, characterized in that: The number of units α of the motor satisfies α = GCD(z, p), where GCD(z, p) is the greatest common divisor of the number of slots z and the number of pole pairs p of the motor.

4. A low vibration and noise design method for a permanent magnet flat wire drive motor based on harmonics according to claim 1, characterized in that: Set the source magnetomotive force harmonic set S G , torque T, and torque ripple Tr as the final variable optimization objectives, simulate and generate the initial population of the genetic algorithm, construct a multi-physical characteristic optimization model, use the genetic algorithm to select, inherit, and mutate in the initial population, and finally obtain a non-dominated solution set that meets the optimization model.

5. A low vibration and noise design method for a permanent magnet flat wire drive motor based on harmonics according to claim 4, characterized in that: at In the non-dominated solution set, select the solution that appears most frequently in the non-dominated solution set to determine the optimized design variables of the motor.

6. A low vibration and noise design method for a permanent magnet flat wire drive motor based on harmonics according to claim 2, characterized in that: Obtain the initial range corresponding to each design variable according to the designed power requirement and design experience.

7. A low vibration and noise design method for a permanent magnet flat wire drive motor based on harmonics according to claim 2, characterized in that: The above-mentioned high speed is more than five times the rated speed of the motor.

8. A low-vibration and low-noise design method for a permanent magnet flat wire drive motor based on harmonics according to claim 1, characterized in that: Radial electromagnetic force b r (θ, t) is the radial air-gap magnetic density, b t (θ, t) is the tangential air-gap magnetic density, θ is the mechanical angle, t is the running time of the motor, and the vacuum permeability is μ0 = 4π × 10 -7 .

9. A low vibration and noise design method for a permanent magnet flat wire drive motor based on harmonics according to claim 8, characterized in that: The radial electromagnetic force P is obtained based on the radial air-gap magnetic density, the magnetomotive force of the permanent magnet, the armature magnetomotive force, and the air-gap permeance considering the stator slotting effect. r (θ,t) expansion formula, and its harmonic orders are derived.

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