Radial split two-degree-of-freedom permanent magnet motor and layered optimization method thereof

Abstract

The application discloses a radial separation type two-degree-of-freedom permanent magnet motor and a layered optimization method thereof, and belongs to the technical field of motors. A motor structure and an optimization design method corresponding to the motor structure are provided. The motor structure adopts a topology of'single mover, double stator and radial separation', is simple in structure, high in mechanical strength and easy to process and assemble. The magnetic circuit of the rotary unit and the linear unit is radially separated in space, the magnetic circuit coupling between the rotary unit and the linear unit is inhibited, and the two units can be designed and controlled relatively independently. In the design optimization of the motor, the double-layer optimization framework is used to effectively reduce the calculation complexity of the problem, and the Gram matrix principal eigenvector method is used to combine and weight to overcome the deviation of the single weighting method, so that the optimization result is more in line with the engineering practice. By using the above method, the calculation amount of multivariable three-dimensional optimization can be reduced under the condition of considering the electromagnetic performance of the rotary unit and the linear unit.

Description

Technical Field

[0001] This invention relates to the field of motor technology, and in particular to a radially separated two-degree-of-freedom permanent magnet motor and its hierarchical optimization method. Background Technology

[0002] With the development of renewable energy, the joint development and utilization of offshore wind power and wave energy has attracted attention due to its resource complementarity and platform sharing advantages. In existing technologies, wind and wave combined power generation systems mostly adopt a discrete layout, that is, vertical axis wind turbines and wave energy capture devices (such as floats) are installed on the same floating platform, each equipped with an independent generator set. This scheme has low system integration and large size and weight.

[0003] To address this problem, researchers have proposed a two-degree-of-freedom rotating linear permanent magnet generator, attempting to simultaneously achieve rotational (wind energy capture) and linear (wave energy capture) motion within a single electromagnetic structure. Existing rotating linear permanent magnet generator technology suffers from the following main drawbacks: Topological defects: Existing shared winding or stacked winding structures suffer from severe magnetic circuit coupling problems, making it difficult to decouple the back electromotive force and optimize them. While some separate winding structures (such as those using hybrid permanent magnet arrays or Halbach arrays) alleviate coupling, the mover structure is complex, making manufacturing and assembly difficult.

[0004] Insufficient optimization methods: The rotating linear permanent magnet generator has a complex three-dimensional structure, resulting in high computational costs for optimization. Existing optimization methods either fail to adequately consider the three-dimensional magnetic circuit coupling between two units or employ simple linear weighting methods in multi-objective optimization, ignoring conflicts between objectives with different physical dimensions. Furthermore, a single weighting method struggles to balance the empirical preferences of engineering designers with the objective laws governing the data itself. Summary of the Invention

[0005] The purpose of this invention is to provide a radially separated two-degree-of-freedom permanent magnet motor and its hierarchical optimization method. The motor structure achieves radial separation by employing a single mover combined with two stators, resulting in high mechanical strength and ease of processing and assembly. Simultaneously, it achieves spatial radial separation of the magnetic circuits of the rotating and linear units, suppressing magnetic circuit coupling between them and allowing for relatively independent design and control of the two units. For motor design parameter optimization, a two-layer framework is used: the mover optimization is the first layer, and the rotating and linear stators are optimized separately in the second layer. This reduces the computational complexity of high-dimensional, multi-objective three-dimensional optimization problems. The Gram matrix principal eigenvector method is used for weighting to overcome the bias of single weighting methods, making the optimization results more consistent with engineering practice. In the second layer optimization, the rotating stator uses a combination of orthogonal experiment and grey relational analysis, while the linear stator uses a non-dominated sorting genetic algorithm II to obtain the Pareto solution set before selecting the optimal solution through grey relational analysis. This method is suitable for expensive simulation optimization scenarios with small samples and multiple indicators, improving computational efficiency.

[0006] To achieve the above objectives, the present invention provides a radially separated two-degree-of-freedom permanent magnet motor. The permanent magnet motor includes a linear motion stator, a rotary motion stator, and a mover arranged radially coaxially. The rotary motion stator and the linear motion stator are respectively disposed on both radial sides of the mover. The mover includes axially magnetized annular permanent magnets and a mover core arranged alternately along the axial direction, with adjacent annular permanent magnets having opposite magnetization directions. Each mover core has a plurality of protruding mover salient pole teeth on its radial side facing the rotary motion stator. The rotary motion stator and the mover salient pole teeth form a rotary motion unit, and the side surface of the mover core facing the linear motion stator and the linear motion stator form a linear motion unit.

[0007] Preferably, the rotating stator includes a rotating stator core and a rotating winding, and the rotating stator and the mover form a rotating motor structure; The linear motion stator includes a linear motion stator core and a linear motion winding, and the linear motion stator and the mover form a linear motor structure.

[0008] Preferably, when the permanent magnet motor is used as a generator, relative rotational motion occurs between the mover and the rotating stator, causing periodic changes in the magnetic flux linkage in the rotating winding and generating an induced electromotive force; relative linear motion occurs between the mover and the linear stator, causing periodic changes in the magnetic flux linkage in the linear winding and generating an induced electromotive force; when relative rotational motion and relative linear motion occur simultaneously, both the rotating winding and the linear winding generate induced electromotive forces simultaneously. When the permanent magnet motor is used as an electric motor, three-phase alternating current is supplied to the rotating motion winding to generate electromagnetic torque, driving the mover and the rotating motion stator to achieve relative rotation; three-phase alternating current is supplied to the linear motion winding to generate axial electromagnetic thrust, driving the mover and the linear motion stator to achieve relative linear motion; when three-phase alternating current is supplied to both the rotating motion winding and the linear motion winding, electromagnetic torque and axial electromagnetic thrust are generated simultaneously, driving the mover to perform helical motion relative to the rotating motion stator and the linear motion stator.

[0009] A hierarchical optimization method for a radially separated two-degree-of-freedom permanent magnet motor includes the following steps: Step S1: Using the parametric finite element modeling method, a three-dimensional finite element initial model of the radially separated two-degree-of-freedom permanent magnet motor is established; based on the motor's magnetic circuit structure, dimensional relationships, and the electromagnetic functions undertaken by each component, the motor's geometric parameters are divided into mover parameters, rotational stator parameters, and linear stator parameters; using a combination of single-factor parameter scanning and finite element sensitivity analysis, parameters with a significant impact on performance indicators are selected as candidate motor geometric parameters; based on the assembly relationships between motor components, preset external dimensions, air gap dimensions, material mechanical strength, manufacturing requirements, and electromagnetic performance requirements, the value range and constraints of each candidate motor geometric parameter are determined. Step S2: For the design optimization of the permanent magnet motor mover, form M experimental schemes, select N performance indicators, select several mover parameters as optimization variables from the candidate motor geometric parameters, and optimize the mover to obtain the optimal mover parameters; Step S3: Based on the optimal mover parameters, select from N performance indicators. Using performance indicators as optimization targets, several rotating stator parameters corresponding to the candidate motor geometric parameters are selected as optimization variables to optimize the rotating stator and obtain the optimal rotating stator parameters. Step S4: Based on the optimal mover parameters, select from N performance indicators. Using performance indicators as optimization targets, several linear motion stator parameters are selected from the candidate motor geometric parameters as optimization variables to optimize the linear motion stator and obtain the optimal linear stator parameters. Step S5: Combine the optimal mover parameter combination determined in Step S2, the optimal rotary stator parameter combination determined in Step S3, and the optimal linear stator parameter combination determined in Step S4; synthesize the three optimal parameter combinations into a final parameter vector according to the parameter order of the mover, rotary stator, and linear stator; update the parameterized finite element model of the motor based on the final parameter vector; and obtain the final structural dimensions of the permanent magnet motor after structural constraint checks and finite element performance verification.

[0010] Preferably, in step S2, the specific process of mover optimization is as follows: S21: Select several motion parameters, obtain several performance indicators by means of finite element analysis under rotational and linear no-load conditions, and calculate the subjective weight and objective weight of each performance indicator. S22: Obtain the combined weights of subjective and objective weights using the Gram matrix principal eigenvector method. ; S23: Set the reference sequence Based on the combined weight The optimal mover parameters were determined based on the grey relational analysis method.

[0011] Preferably, the specific process of step S21 is as follows: Step S211: Select several motion parameters according to the user's needs, and use the motion parameters to construct an orthogonal experimental table to form M experimental schemes; Step S212: For each experimental scheme, a three-dimensional finite element no-load analysis is performed under both rotational and linear motion conditions. Based on the user's needs, N performance indicators are selected from several performance indicators as optimization targets. Step S213: Based on the selected N performance indicators, calculate the subjective and objective weights of each performance indicator: Use the analytic hierarchy process (AHP) to obtain the subjective weights, and construct a judgment matrix using the performance indicators as the criterion layer and the 1-9 scaling method. : In the above formula, Indicators of performance relative to performance metrics The importance of Represents the total number of performance metrics, with subjective weights. This is obtained by solving the characteristic equation: In the above formula, Represents the judgment matrix The largest eigenvalue is used to ensure the consistency of the judgment logic in the judgment matrix, and the consistency ratio is calculated. : ; In the above formula, Indicators of consistency As a random consistency index, when the judgment matrix satisfies the consistency ratio At that time, the subjective weight value of each performance indicator is obtained using the corresponding judgment matrix. Combining to form subjective weights ; The objective weight of each indicator is calculated using the entropy weight method (EWM). Based on the indicator attributes of the selected performance indicators, range normalization is performed using either benefit-based or cost-based methods to eliminate dimensions and map them to the [0,1] interval. For benefit-based indicators, a larger value is better. The standardized formula for the corresponding benefit-based indicator is as follows: in Describe the value of the nth performance index of the mth experimental scheme; This represents the normalized value; smaller cost indicators are better, and the standardized formula for the corresponding cost indicator is: The proportions of different experimental schemes corresponding to the orthogonal experimental table of mover parameters under various performance indices were calculated, and the standardized values ​​were normalized column-wise to form a proportion matrix. The data in the m rows and n columns of the weight matrix for: Using the weight matrix Calculate the information entropy for different performance metrics. For the nth performance metric, what is the information entropy? The formula is: when When it is 0, it is stipulated that The smaller the information entropy, the greater the amount of information provided by the performance indicators. Then, the information entropy is used to calculate the difference coefficient. The formula reflecting the degree of variation in performance indicators is as follows: Using the coefficient of difference Calculate the objective weights, normalize the difference coefficients to obtain the entropy weights of each performance index, and obtain the objective weight value of the nth performance index. as follows: The objective weight values ​​for each performance indicator are obtained through the above calculations. The objective weights are obtained by combining them. .

[0012] Preferably, in step S22, the Gram matrix principal eigenvector method is used to combine subjective weights. and objective weight To form combined weights, first establish the Gram matrix. The formula is as follows: In the above formula, Subjective weighting, For objective weights, the corresponding superscripts Indicate the transpose, then solve for the Gram matrix. The unit principal eigenvector corresponding to the largest eigenvalue : in yes The largest eigenvalue, for The corresponding unit principal eigenvector, normalized and The weights corresponding to subjective weights and objective weights and as follows: In the above formula, The combination coefficients representing subjective weights The combination coefficients represent the objective weights, and the final combination weights are calculated. as follows: The above formula yields the combined weights of the Gram matrix principal eigenvector method.

[0013] Preferably, step S23 specifically includes the following: First, Z-score standardization is performed on each performance metric. To eliminate differences in units and orders of magnitude, the overall standard deviation is used for standardization. In the above formula, Let be the mean of the nth performance index. Let the population standard deviation of the nth performance index across M experimental schemes be defined. After standardization, the performance indexes are categorized into benefit-type and cost-type performance indexes. The optimal performance index is defined as the one where the benefit-type index reaches its maximum value and the cost-type index reaches its minimum value. A reference sequence is then formed based on the optimal values ​​of all performance indices. Reference sequence The nth reference value as follows: Grey relational analysis was used to calculate the impact of each experimental scheme on the reference sequence. The grey relational degree is used to calculate the correlation coefficient between each performance index and the reference value in the reference sequence of the corresponding index. : In the above formula, The resolution coefficient is combined with the combined weights. Calculate the weighted grey relational degree, and the relational degree of the m-th experimental scheme. as follows: The different experimental schemes corresponding to the orthogonal experimental table for the mover parameters are... The experimental schemes with the largest values ​​are sorted from largest to smallest, and the experimental schemes with the highest correlation are selected as the optimal mover parameters.

[0014] Preferably, in step S3, the optimization process for the rotating stator is as follows: For the rotating stator, the outer radius of the rotating stator is fixed, and several rotating stator parameters are selected as optimization variables; corresponding to the parameters selected in S2... Among the performance metrics Using the rotational motion stator parameters as the optimization objective and serving as the performance index for step S3, an orthogonal experimental table is constructed, resulting in several experimental schemes. These schemes are then analyzed using the finite element method, and the corresponding subjective weights from S2 for S3 are selected. The weighted values ​​of each performance indicator are normalized to obtain S3. Subjective weighting values ​​for each performance metric : Based on subjective weight values Accordingly, obtain the subjective weights of the optimization objectives. The objective weights of the optimization objective are obtained using the entropy weight method (EWM). The combined weights obtained based on the Gram matrix principal eigenvector method are: Then, the grey relational degree of all experimental schemes for the rotating stator is calculated based on grey relational analysis. The scheme with the largest grey relational degree value is the optimal scheme, and the optimal design parameter combination of the rotating stator is obtained.

[0015] Preferably, in step S4, the optimization process of the linear motion stator is as follows: For the linear motion part, the outer radius of the linear motion stator is fixed, and several linear motion stator parameters are selected as optimization variables. The N performance indicators from step S2 are selected... The performance indicators are selected as optimization objectives, and used as performance indicators in step S4. The constraint on the number of selected indicators is as follows: The stator parameters for linear motion are optimized based on a non-dominated sorting genetic algorithm II. The value range of each optimization variable is as follows: in, For the first k Optimization variables for a linear motion stator for The minimum value that can be obtained. for After obtaining the maximum achievable value and the multi-objective optimization results, the Pareto optimal solution set is obtained. Then, the corresponding weight in S4 from the combined weights of step S2 is selected. The weight values ​​of each performance indicator are obtained by normalization. The combined weight value of each performance indicator The formula is as follows: Then, for each solution in the Pareto solution set, its grey relational degree is calculated, and the solution with the highest relational degree is the optimal combination of design parameters for the linear motion stator.

[0016] Therefore, the present invention employs the above-described radially separated two-degree-of-freedom permanent magnet motor and its hierarchical optimization method, which has the following advantages: (1) In this invention, a radially separated double stator and single mover structure is used: the rotating stator is located on one side of the mover and the linear stator is located on the other side, and magnetic circuit decoupling is achieved through radial spatial separation; (2) A ring-shaped permanent magnet mover with alternating axial magnetization: The mover has a simple structure, is easy to manufacture, and participates in both rotational and linear electromagnetic energy conversion; (3) A two-layer framework is used for the optimization of motor design parameters. The optimization of the mover is the first layer, and the rotational stator and linear stator are optimized in the second layer respectively. This reduces the computational complexity of high-dimensional, multi-objective three-dimensional optimization problems. The Gram matrix principal eigenvector method is used to overcome the bias of the single weighting method, making the optimization results more in line with engineering practice. In the second layer, the rotational stator adopts the method of combining orthogonal experiment and grey relational analysis. The linear stator adopts the non-dominated sorting genetic algorithm II to obtain the Pareto solution set and then selects the best by grey relational analysis. This is suitable for expensive simulation optimization scenarios with small samples and multiple indicators, and improves the computational efficiency.

[0017] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0018] Figure 1 This is an overall structural diagram of the permanent magnet motor in the radially separated two-degree-of-freedom permanent magnet motor and its hierarchical optimization method of the present invention. Figure 2 This is a cross-sectional view of the permanent magnet motor in the radially separated two-degree-of-freedom permanent magnet motor and its hierarchical optimization method of the present invention. Figure 3 This is a schematic diagram of the mover core in the permanent magnet motor of the radially separated two-degree-of-freedom permanent magnet motor and its hierarchical optimization method of the present invention. Figure 4 This is a schematic diagram of the permanent magnet in the permanent magnet motor of the radially separated two-degree-of-freedom permanent magnet motor and its hierarchical optimization method of the present invention; Figure 5 This is a schematic diagram showing the positions of the optimization variables of the rotating stator and mover in the permanent magnet motor of the radially separated two-degree-of-freedom permanent magnet motor and its hierarchical optimization method of the present invention. Figure 6 This is a schematic diagram showing the positions of the optimization variables of the linear motion stator and mover in the permanent magnet motor of the radially separated two-degree-of-freedom permanent magnet motor and its hierarchical optimization method of the present invention. Figure 7 This invention provides a two-dimensional optimization model of the linear motion stator in a radially separated two-degree-of-freedom permanent magnet motor and its hierarchical optimization method. Figure 8 This is a flowchart of the hierarchical optimization method in the radially separated two-degree-of-freedom permanent magnet motor and its hierarchical optimization method of the present invention; Reference numerals: 100, mover; 110, mover core; 111, mover salient pole tooth; 120, toroidal permanent magnet; 200, rotating stator; 210, rotating stator core; 220, rotating winding; 300, linear stator; 310, linear stator core; 320, linear winding. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Specific model specifications need to be selected and determined according to the actual specifications of the device, etc. The specific selection calculation method adopts existing technology in the art, and therefore will not be described in detail.

[0020] Example like Figures 1-4 As shown, the present invention provides a radially separated two-degree-of-freedom permanent magnet motor. The permanent magnet motor includes a linear motion stator 300, a rotary motion stator 200, and a mover 100 arranged radially and coaxially. The rotary motion stator 200 and the linear motion stator 300 are respectively arranged on both radial sides of the mover 100. In actual engineering design, the rotary motion stator 200 can be arranged on the inner or outer side, and the linear motion stator 300 is arranged on the other side corresponding to the rotary motion stator 200. The mover 100 includes axially alternating axially magnetized annular permanent magnets 120 and mover cores 110. Adjacent annular permanent magnets 120 are magnetized in opposite directions. Each mover core 110 has several protruding mover salient pole teeth 111 on its radial side facing the rotating stator 200. The rotating stator 200 and the mover salient pole teeth 111 form a rotating motion unit. The side surface of the mover core 110 facing the linear stator 300 forms a linear motion unit with the linear stator 300. The rotary motion stator 200 includes a rotary motion stator core 210 and a rotary motion winding 220. The rotary motion stator 200 and the mover 100 together form a rotary motor structure. The linear motion stator 300 includes a linear motion stator core 310 and a linear motion winding 320. The linear motion stator 300 and the mover 100 together form a linear motor structure.

[0021] In practical applications, permanent magnet motors can operate in generator mode or motor mode, as detailed below: When the permanent magnet motor is used as a generator, relative rotational motion occurs between the mover 100 and the rotating stator 200, causing periodic changes in the magnetic flux in the rotating winding 220 and generating an induced electromotive force to capture energy; relative linear motion occurs between the mover 100 and the linear stator 300, causing periodic changes in the magnetic flux in the linear winding 320 and generating an induced electromotive force to capture energy; when relative rotational motion and relative linear motion occur simultaneously between the mover 100 and the two stators, an electromotive force is simultaneously induced in both the rotating winding 220 and the linear winding 320 to capture the energy of both motions.

[0022] When the permanent magnet motor is used as an electric motor, three-phase alternating current is supplied to the rotating motion winding 220 to generate electromagnetic torque, driving the mover 100 to rotate relative to the rotating motion stator 200; three-phase alternating current is supplied to the linear motion winding 320 to generate axial electromagnetic thrust, driving the mover 100 to move relative to the linear motion stator 300; when three-phase alternating current is supplied to both the rotating motion winding 220 and the linear motion winding 320, electromagnetic torque and axial electromagnetic thrust are generated simultaneously, driving the mover 100 to move relative to the linear motion stator 300 or the rotating motion stator 200 in a relative helical motion.

[0023] like Figure 8 As shown, a hierarchical optimization method for a radially separated two-degree-of-freedom permanent magnet motor includes the following steps: Step S1: Specifically, a parametric finite element modeling method is used to establish a three-dimensional finite element initial model of the permanent magnet motor, and the geometric parameters that can change the motor's structural dimensions are set as adjustable parameters. Candidate geometric parameters include mover geometric parameters, rotary stator geometric parameters, and linear stator geometric parameters.

[0024] In this embodiment, the candidate geometric parameters of the mover include the axial polar arc coefficient. Circumferential polar arc coefficient and salient pole tooth height Candidate geometric parameters for rotating stators include slot depth. Groove height Groove width Stator yoke thickness Tooth width Candidate geometric parameters for linear motion stators include linear motion tooth width. Linear motion groove depth The width of the teeth on the left end of the linear motion. The height difference between the left end teeth and the ordinary teeth in linear motion The width of the right end teeth in linear motion Height difference between the right end teeth and ordinary teeth in linear motion Single-factor parameter scanning was performed on each motor geometric parameter. While keeping other motor geometric parameters constant, one motor geometric parameter was changed within a preset range, and three-dimensional finite element analysis was used to obtain the cogging torque, root mean square value of rotating back EMF, total harmonic distortion of rotating back EMF, positioning force, root mean square value of linear back EMF, and total harmonic distortion of linear back EMF. Based on the rate of change of performance indicators caused by different changes in motor geometric parameters, the sensitivity of each motor geometric parameter was determined, and motor geometric parameters with sensitivity higher than a preset threshold were selected as candidate motor geometric parameters.

[0025] The range of values ​​for the geometric parameters of each candidate motor is determined based on the initial model dimensions, component assembly relationships, and manufacturing requirements. Parameter combinations that could lead to structural interference, local dimensions smaller than the minimum machining dimensions, magnetic circuit oversaturation, or the inability of the finite element model to solve correctly are eliminated through finite element trial calculations. Thus, the geometric parameters of the z-th candidate motor are determined. lower limit and upper limit To satisfy Meanwhile, the geometric parameters of each candidate motor should also meet the following constraints: there is no structural interference between the stator and the mover; the air gap for rotational motion and the air gap for linear motion are greater than the preset minimum air gap; the stator tooth width and the stator yoke thickness are greater than the preset minimum mechanical dimensions; and the axial polar arc coefficient and the circumferential polar arc coefficient are both greater than 0 and not greater than 1.

[0026] Step S2: For the optimization of the mover design of the permanent magnet motor, M experimental schemes are formed, N performance indicators are selected, and the specific process of obtaining the optimal mover parameters is as follows: S21: Select several motion parameters, and obtain several performance indicators through finite element analysis under rotational and linear no-load conditions, and calculate subjective and objective weights. The specific process is as follows: S211: Select the mover parameters according to the user's needs. In this embodiment, the selected mover parameters include the axial polar arc coefficient. Circumferential polar arc coefficient and salient pole tooth height Using the motion parameters, an orthogonal experimental array is constructed to form M experimental schemes; in this embodiment, each of the three motion parameters takes 6 levels, and an L36 orthogonal array is constructed accordingly to form 36 experimental schemes. Step S212: For each experimental scheme, a three-dimensional finite element no-load analysis is performed under both rotational and linear motion conditions. Based on the user's needs, N performance indicators are selected from several performance indicators. In this embodiment, a total of six performance indicators are extracted, including cogging torque. , Root mean square value of rotating back electromotive force Total harmonic distortion of rotating back electromotive force Positioning force Root mean square value of linear back electromotive force and total harmonic distortion of linear back electromotive force ; Step S213: Based on the six selected performance indicators, calculate the subjective and objective weights of each performance indicator: Use the analytic hierarchy process (AHP) to obtain the subjective weights, and construct a judgment matrix using the performance indicators as the criterion layer and the 1-9 scaling method. : In the above formula, Indicators of performance relative to performance metrics The importance of Represents the total number of performance metrics, with subjective weights. This is obtained by solving the characteristic equation: In the above formula, Represents the judgment matrix The largest eigenvalue is used to ensure the consistency of the judgment logic in the judgment matrix, and the consistency ratio is calculated. : ; In the above formula, Indicators of consistency As a random consistency index, when the judgment matrix satisfies the consistency ratio In this embodiment, the maximum eigenvalue is calculated based on the data and performance indicators of the judgment matrix. The consistency test results are shown in Table 1 below: Table 1 Judgment Matrix

[0027] Based on the above, the subjective weight values ​​of each performance indicator are obtained using the corresponding judgment matrix. Combining to form subjective weights Subjective weight Specifically: ; The objective weight of each indicator is calculated using the entropy weight method (EWM). First, data standardization is performed. Based on the selected performance indicators' attributes, either benefit-based or cost-based range normalization is applied to eliminate dimensions and map to the [0,1] interval. For benefit-based indicators, a larger value is better. For the corresponding performance indicators, the root mean square value of the rotating back electromotive force is... and the root mean square value of the linear back electromotive force Set it as a benefit-type indicator; the larger the better. The standardized formula for the corresponding benefit-type indicator is: in Describe the value of the nth performance index of the mth experimental scheme; This represents the normalized value; the smaller the cost-related indicator, the better, including the cogging torque. Total harmonic distortion of rotating back electromotive force Positioning force and total harmonic distortion of linear back electromotive force Set as a cost-type indicator, the standardized formula for the corresponding cost-type indicator is: The proportions of different experimental schemes corresponding to the orthogonal experimental table of mover parameters under various performance indices were calculated, and the standardized values ​​were normalized column-wise to form a proportion matrix. The data in the m rows and n columns of the weight matrix for: Using the weight matrix Calculate the information entropy for different performance metrics. For the nth performance metric, what is the information entropy? The formula is: when When it is 0, it is stipulated that The smaller the information entropy, the greater the amount of information provided by the performance indicators. Then, the information entropy is used to calculate the difference coefficient. The formula reflecting the degree of variation in performance indicators is as follows: Using the coefficient of difference Calculate the objective weights, normalize the difference coefficients to obtain the entropy weights of each performance index, and obtain the objective weight value of the nth performance index. as follows: The objective weight values ​​for each performance indicator are obtained through the above calculations. The objective weights are obtained by combining them. The corresponding cogging torque is obtained. , Root mean square value of rotating back electromotive force Total harmonic distortion of rotating back electromotive force Positioning force Root mean square value of linear back electromotive force and total harmonic distortion of linear back electromotive force The EWM objective weights, specifically: ; S22: Obtain the combined weights of subjective and objective weights using the Gram matrix principal eigenvector method. ; Subjective weights are combined using the Gram matrix principal eigenvector method. and objective weight To form combined weights, first establish the Gram matrix. The formula is as follows: in, Subjective weighting, For objective weights, the corresponding superscripts Indicate the transpose, then solve for the Gram matrix. The unit principal eigenvector corresponding to the largest eigenvalue : in yes The largest eigenvalue, for The corresponding unit principal eigenvector, normalized and The combination coefficients corresponding to subjective weights and objective weights and as follows: In the above formula, The combination coefficients representing subjective weights The combination coefficients represent the objective weights, and the final combination weights are calculated. as follows: The above formula calculates the combined weights of the principal eigenvector method of the Gram matrix. .

[0028] S23: Set the reference sequence Based on the combined weight Determining the optimal dynamic parameters based on grey relational analysis First, Z-score standardization is performed on each performance metric. To eliminate differences in units and orders of magnitude, the overall standard deviation is used for standardization. In the above formula, Let be the mean of the nth performance index. Let the population standard deviation of the nth performance index across M experimental schemes be defined. After standardization, the performance indexes are categorized into benefit-type and cost-type performance indexes. The optimal performance index is defined as the one where the benefit-type index reaches its maximum value and the cost-type index reaches its minimum value. A reference sequence is then formed based on the optimal values ​​of all performance indices. Reference sequence The nth reference value as follows: Grey relational analysis was used to calculate the impact of each experimental scheme on the reference sequence. The grey relational degree is used to calculate the correlation coefficient between each performance index and the reference value in the reference sequence of the corresponding index. : In the above formula, The resolution coefficient is set to 0.5, combined with the combined weights. Calculate the weighted grey relational degree, and the relational degree of the m-th experimental scheme. as follows: The different experimental schemes corresponding to the orthogonal experimental table for the mover parameters are... The experimental schemes are sorted from largest to smallest, and the one with the largest value is the one with the highest correlation. The experimental scheme with the highest correlation is taken as the optimal mover parameter. In this embodiment, the calculation results of the correlation of the corresponding schemes are shown in Table 2 below: Table 2: Results of the Motor Parameter Optimization Scheme

[0029] Based on Table 2 above, Scheme 5 is selected as the optimal mover parameter; Step S3: Based on the optimal mover parameters, select from N performance indicators. Using one performance index as the optimization target, and correspondingly selecting several rotating stator parameters as optimization variables, the rotating stator is optimized to obtain the optimal rotating stator parameters; For a specific rotating stator, the outer radius of the rotating stator is fixed, and several rotating stator parameters are selected as optimization variables. In this embodiment, the outer radius of the rotating stator is fixed at 48mm. Fixing the outer radius during the calculation process reduces the optimization complexity. Figure 5 As shown, five rotational stator parameters are selected as optimization variables, including slot depth. Groove height Groove width Stator yoke thickness Tooth width ; In the corresponding selection step S2 Among the performance metrics The optimization objective is set as the performance indicator for step S3. In this embodiment, the cogging torque is specifically selected. , Root mean square value of rotating back electromotive force Total harmonic distortion of rotating back electromotive force Using three performance indicators as optimization targets, an orthogonal experimental table is constructed using the rotational motion stator parameters, resulting in several experimental schemes. In this embodiment, each rotational motion stator parameter has five different levels, generating L... 25 An orthogonal array was used to generate 25 experimental schemes. The experimental schemes were analyzed using the finite element method, and the subjective weights in step S2 corresponding to those in step S3 were selected. In this embodiment, three performance indicators are selected as optimization targets: cogging torque, root mean square value of rotating back electromotive force, and total harmonic distortion of rotating back electromotive force; the weight values ​​of these performance indicators are then normalized to obtain the values ​​in step S3. Subjective weighting values ​​for each performance metric : Based on subjective weight values Accordingly, obtain the subjective weights of the optimization objectives. Corresponding to the cogging torque obtained in this embodiment , Root mean square value of rotating back electromotive force Total harmonic distortion of rotating back electromotive force The subjective weight is as follows: ; Then, the cogging torque is obtained using the entropy weight method (EWM). , Root mean square value of rotating back electromotive force Total harmonic distortion of rotating back electromotive force The objective weight is : ; The combined weights obtained based on the Gram matrix principal eigenvector method are: for: =[0.3157,0.4225,0.2618]; Next, the grey relational degree of all experimental schemes for the rotating stator was calculated using grey relational analysis. The scheme with the largest grey relational degree value was the optimal scheme. Based on 25 experimental schemes, Table 3 is as follows: Table 3. Analysis Results of Rotating Stator

[0030] The grey relational analysis method was used to calculate the grey relational degree of 25 experimental schemes for the rotating stator. The scheme with the largest grey relational degree value is the optimal scheme. The results are shown in Table 3. Among the 25 stator schemes of AMRLG, scheme 5 is the best, with the best overall performance. The parameters of the optimal rotating stator corresponding to the optimal rotating stator configuration are: =14mm, =3.6 mm, =8 mm, =3.8 mm, and =12mm, which corresponds to the optimal design parameter combination for the rotating stator.

[0031] Step S4: Optimize the linear motion stator based on the optimal mover parameters. The optimization process is as follows: Figure 7 As shown, for the linear motion part, in this embodiment, the outer radius of the linear motion stator is fixed at 110mm. Fixing the outer radius reduces the optimization complexity. Several linear motion stator parameters are selected as optimization variables. In this embodiment, as shown... Figure 6 As shown, six linear motion stator parameters are selected as optimization variables, including the linear motion tooth width. Linear motion groove depth The width of the teeth on the left end of the linear motion. The height difference between the left end teeth and the ordinary teeth in linear motion The width of the right end teeth in linear motion Height difference between the right end teeth and ordinary teeth in linear motion Select the performance indicators in step S2. The optimization objective is to select a quantity that serves as the performance indicator for step S4, and this quantity is a constraint. In this embodiment, positioning force is used. Root mean square value of linear back electromotive force and total harmonic distortion of linear back electromotive force To optimize the objective, the stator parameters for linear motion are optimized using a non-dominated sorting genetic algorithm II. A total of 40 generations are performed, with 36 individuals per generation. In this embodiment, the value range for each optimization variable is as follows: After obtaining the multi-objective optimization results, the Pareto optimal solution set is obtained. Then, the corresponding weights from step S2 in step S4 are selected. The weight values ​​of each performance indicator are normalized to obtain step S4. The combined weight value of each performance indicator : For each solution in the Pareto solution set, the same method as in step S213 is used to calculate its grey relational degree. The solution with the highest relational degree is the optimal combination of design parameters for the linear motion stator.

[0032] Step S5: Obtain the optimal mover parameter combination determined in Step S2, the optimal rotary stator parameter combination determined in Step S3, and the optimal linear stator parameter combination determined in Step S4; combine the three optimal parameters in the order of mover, rotary stator, and linear stator to form the final parameter vector; update the parameterized finite element model of the motor based on the final parameter vector; after structural constraint checking and finite element performance verification, obtain the final structural dimensions of the permanent magnet motor. Therefore, this invention employs a radially separated two-degree-of-freedom permanent magnet motor and its hierarchical optimization method. It utilizes a single mover combined with two stators to achieve a radially separated motor structure, resulting in high mechanical strength and ease of processing and assembly. Simultaneously, it achieves spatial radial separation of the magnetic circuits of the rotating and linear units, suppressing magnetic circuit coupling between them and enabling relatively independent design and control of the two units. For motor design parameter optimization, a two-layer framework is used. The optimization of the mover serves as the foundation for the first layer, while the rotating and linear stators are optimized separately in the second layer. This reduces the computational complexity of high-dimensional, multi-objective three-dimensional optimization problems. The Gram matrix principal eigenvector method is used for weighting to overcome the bias of single weighting methods, making the optimization results more consistent with engineering practice. In the second layer, the rotating stator employs a combination of orthogonal experiment and grey relational analysis, while the linear stator uses a non-dominated sorting genetic algorithm II to obtain Pareto solutions before selecting the optimal solution through grey relational analysis. This approach is suitable for expensive simulation optimization scenarios with small samples and multiple indicators, improving computational efficiency.

[0033] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A radially separated two-degree-of-freedom permanent magnet motor, characterized in that: The permanent magnet motor includes a linear motion stator, a rotary motion stator, and a mover arranged radially and coaxially. The rotary motion stator and the linear motion stator are respectively disposed on both radial sides of the mover. The mover includes axially magnetized annular permanent magnets and a mover core arranged alternately along the axial direction, with adjacent annular permanent magnets having opposite magnetization directions. Each mover core has a plurality of protruding mover salient pole teeth on its radial side facing the rotary motion stator. The rotary motion stator and the mover salient pole teeth form a rotary motion unit, and the side surface of the mover core facing the linear motion stator and the linear motion stator form a linear motion unit.

2. The radially separated two-degree-of-freedom permanent magnet motor according to claim 1, characterized in that: The rotating stator includes a rotating stator core and rotating windings, and the rotating stator and the mover form a rotating motor structure; The linear motion stator includes a linear motion stator core and a linear motion winding, and the linear motion stator and the mover form a linear motor structure.

3. A radially separated two-degree-of-freedom permanent magnet motor according to claim 2, characterized in that: When a permanent magnet motor is used as a generator, relative rotational motion occurs between the mover and the rotating stator, causing periodic changes in the magnetic flux linkage in the rotating winding and generating an induced electromotive force; relative linear motion occurs between the mover and the linear stator, causing periodic changes in the magnetic flux linkage in the linear winding and generating an induced electromotive force; when relative rotational motion and relative linear motion occur simultaneously, both the rotating winding and the linear winding generate induced electromotive forces. When the permanent magnet motor is used as an electric motor, three-phase alternating current is supplied to the rotating motion winding to generate electromagnetic torque, driving the mover and the rotating motion stator to achieve relative rotation; three-phase alternating current is supplied to the linear motion winding to generate axial electromagnetic thrust, driving the mover and the linear motion stator to achieve relative linear motion; when three-phase alternating current is supplied to both the rotating motion winding and the linear motion winding, electromagnetic torque and axial electromagnetic thrust are generated simultaneously, driving the mover to perform helical motion relative to the rotating motion stator and the linear motion stator.

4. A hierarchical optimization method for a radially separated two-degree-of-freedom permanent magnet motor, applied to the radially separated two-degree-of-freedom permanent magnet motor according to any one of claims 1-3, characterized in that, Includes the following steps: Step S1: Using the parametric finite element modeling method, a three-dimensional finite element initial model of the radially separated two-degree-of-freedom permanent magnet motor is established; based on the motor's magnetic circuit structure, dimensional relationships, and the electromagnetic functions undertaken by each component, the motor's geometric parameters are divided into mover parameters, rotational stator parameters, and linear stator parameters; using a combination of single-factor parameter scanning and finite element sensitivity analysis, parameters with a significant impact on performance indicators are selected as candidate motor geometric parameters; based on the assembly relationships between motor components, preset external dimensions, air gap dimensions, material mechanical strength, manufacturing requirements, and electromagnetic performance requirements, the value range and constraints of each candidate motor geometric parameter are determined. Step S2: For the design optimization of the permanent magnet motor mover, form M experimental schemes, select N performance indicators, select several mover parameters as optimization variables from the candidate motor geometric parameters, and optimize the mover to obtain the optimal mover parameters; Step S3: Based on the optimal mover parameters, select from N performance indicators. Using performance indicators as optimization targets, several rotating stator parameters corresponding to the candidate motor geometric parameters are selected as optimization variables to optimize the rotating stator and obtain the optimal rotating stator parameters. Step S4: Based on the optimal mover parameters, select from N performance indicators. Using performance indicators as optimization targets, several linear motion stator parameters are selected from the candidate motor geometric parameters as optimization variables to optimize the linear motion stator and obtain the optimal linear stator parameters. Step S5: Combine the optimal mover parameter combination determined in Step S2, the optimal rotational stator parameter combination determined in Step S3, and the optimal linear stator parameter combination determined in Step S4 into a final parameter vector according to the parameter order of the mover, rotational stator, and linear stator. The parameterized finite element model of the motor is updated based on the final parameter vector. After structural constraint checks and finite element performance verification, the final structural dimensions of the permanent magnet motor are obtained.

5. The hierarchical optimization method for a radially separated two-degree-of-freedom permanent magnet motor according to claim 4, characterized in that: In step S2, the specific process of mover optimization is as follows: S21: Select several motion parameters, obtain several performance indicators by means of finite element analysis under rotational and linear no-load conditions, and calculate the subjective weight and objective weight of each performance indicator. S22: Obtain the combined weights of subjective and objective weights using the Gram matrix principal eigenvector method. ; S23: Set the reference sequence Based on the combined weight The optimal mover parameters were determined based on the grey relational analysis method.

6. The hierarchical optimization method for a radially separated two-degree-of-freedom permanent magnet motor according to claim 5, characterized in that: The specific process of step S21 is as follows: Step S211: Select several motion parameters according to the user's needs, and use the motion parameters to construct an orthogonal experimental table to form M experimental schemes; Step S212: For each experimental scheme, a three-dimensional finite element no-load analysis is performed under both rotational and linear motion conditions. Based on the user's needs, N performance indicators are selected from several performance indicators as optimization targets. Step S213: Based on the selected N performance indicators, calculate the subjective and objective weights of each performance indicator: Use the analytic hierarchy process (AHP) to obtain the subjective weights, and construct a judgment matrix using the performance indicators as the criterion layer and the 1-9 scaling method. : In the above formula, Indicators of performance relative to performance metrics The importance of Represents the total number of performance metrics, with subjective weights. This is obtained by solving the characteristic equation: In the above formula, Represents the judgment matrix The largest eigenvalue is used to ensure the consistency of the judgment logic in the judgment matrix, and the consistency ratio is calculated. : ； In the above formula, Indicators of consistency As a random consistency index, when the judgment matrix satisfies the consistency ratio At that time, the subjective weight value of each performance indicator is obtained using the corresponding judgment matrix. Combining to form subjective weights ; The objective weight of each indicator is calculated using the entropy weight method (EWM). Based on the indicator attributes of the selected performance indicators, range normalization is performed using either benefit-based or cost-based methods to eliminate dimensions and map them to the [0,1] interval. For benefit-based indicators, a larger value is better. The standardized formula for the corresponding benefit-based indicator is as follows: in Describe the value of the nth performance index of the mth experimental scheme; This represents the normalized value; smaller cost indicators are better, and the standardized formula for the corresponding cost indicator is: The proportions of different experimental schemes corresponding to the orthogonal experimental table of mover parameters under various performance indices were calculated, and the standardized values ​​were normalized column-wise to form a proportion matrix. The data in the m rows and n columns of the weight matrix for: Using the weight matrix Calculate the information entropy for different performance metrics. For the nth performance metric, what is the information entropy? The formula is: when When it is 0, it is stipulated that The smaller the information entropy, the greater the amount of information provided by the performance indicators. Then, the information entropy is used to calculate the difference coefficient. The formula reflecting the degree of variation in performance indicators is as follows: Using the coefficient of difference Calculate the objective weights, normalize the difference coefficients to obtain the entropy weights of each performance index, and obtain the objective weight value of the nth performance index. as follows: The objective weight values ​​for each performance indicator are obtained through the above calculations. The objective weights are obtained by combining them. .

7. The hierarchical optimization method for a radially separated two-degree-of-freedom permanent magnet motor according to claim 5, characterized in that: In step S22, the subjective weights are combined using the Gram matrix principal eigenvector method. and objective weight To form combined weights, first establish the Gram matrix. The formula is as follows: In the above formula, Subjective weighting, For objective weights, the corresponding superscripts Indicate the transpose, then solve for the Gram matrix. The unit principal eigenvector corresponding to the largest eigenvalue : in yes The largest eigenvalue, for The corresponding unit principal eigenvector, normalized and The weights corresponding to subjective weights and objective weights and as follows: In the above formula, The combination coefficients representing subjective weights The combination coefficients represent the objective weights, and the final combination weights are calculated. as follows: The above formula yields the combined weights of the Gram matrix principal eigenvector method.

8. The hierarchical optimization method for a radially separated two-degree-of-freedom permanent magnet motor according to claim 5, characterized in that: In step S23, the specific details are as follows: First, Z-score standardization is performed on each performance metric. To eliminate differences in units and orders of magnitude, the overall standard deviation is used for standardization. In the above formula, Let be the mean of the nth performance index. Let the population standard deviation of the nth performance index across M experimental schemes be defined. After standardization, the performance indexes are categorized into benefit-type and cost-type performance indexes. The optimal performance index is defined as the one where the benefit-type index reaches its maximum value and the cost-type index reaches its minimum value. A reference sequence is then formed based on the optimal values ​​of all performance indices. Reference sequence The nth reference value as follows: Grey relational analysis was used to calculate the impact of each experimental scheme on the reference sequence. The grey relational degree is used to calculate the correlation coefficient between each performance index and the reference value in the reference sequence of the corresponding index. : In the above formula, The resolution coefficient is combined with the combined weights. Calculate the weighted grey relational degree, and the relational degree of the m-th experimental scheme. as follows: The different experimental schemes corresponding to the orthogonal experimental table for the mover parameters are... The experimental schemes with the largest values ​​are sorted from largest to smallest, and the experimental schemes with the highest correlation are selected as the optimal mover parameters.

9. The hierarchical optimization method for a radially separated two-degree-of-freedom permanent magnet motor according to claim 5, characterized in that: In step S3, the optimization process for the rotating stator is as follows: For the rotating stator, the outer radius of the rotating stator is fixed, and several rotating stator parameters are selected as optimization variables; corresponding to the parameters selected in S2... Among the performance metrics Using the rotational motion stator parameters as the optimization objective and serving as the performance index for step S3, an orthogonal experimental table is constructed, resulting in several experimental schemes. These schemes are then analyzed using the finite element method, and the corresponding subjective weights from S2 for S3 are selected. The weighted values ​​of each performance indicator are normalized to obtain S3. Subjective weighting values ​​for each performance metric : Based on subjective weight values Accordingly, obtain the subjective weights of the optimization objectives. The objective weights of the optimization objective are obtained using the entropy weight method (EWM). The combined weights obtained based on the Gram matrix principal eigenvector method are: Then, the grey relational degree of all experimental schemes for the rotating stator is calculated based on grey relational analysis. The scheme with the largest grey relational degree value is the optimal scheme, and the optimal design parameter combination of the rotating stator is obtained.

10. A hierarchical optimization method for a radially separated two-degree-of-freedom permanent magnet motor according to claim 5, characterized in that: In step S4, the optimization process of the linear motion stator is as follows: For the linear motion part, the outer radius of the linear motion stator is fixed, and several linear motion stator parameters are selected as optimization variables. Among the N performance indicators in step S2... The performance indicators are selected as optimization objectives, and used as performance indicators in step S4. The constraint on the number of selected indicators is as follows: The stator parameters for linear motion are optimized based on a non-dominated sorting genetic algorithm II. The value range of each optimization variable is as follows: in, For the first k Optimization variables for a linear motion stator for The minimum value that can be obtained. for After obtaining the maximum achievable value and the multi-objective optimization results, the Pareto optimal solution set is obtained. Then, the corresponding weight in S4 from the combined weights of step S2 is selected. The weight values ​​of each performance indicator are obtained by normalization. The combined weight value of each performance indicator The formula is as follows: Then, for each solution in the Pareto solution set, its grey relational degree is calculated, and the solution with the highest relational degree is the optimal combination of design parameters for the linear motion stator.

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