Robust design method for surface-mounted permanent magnet synchronous motor considering manufacturing tolerance

Abstract

The application discloses a robust design method of surface-mounted permanent magnet synchronous motor considering manufacturing tolerance, and the method is as follows: step 1, a parameterized model and a data set of the surface-mounted permanent magnet synchronous motor are established; step 2, a multi-output proxy model based on integrated learning is constructed; step 3, a manufacturing tolerance model is constructed; step 4, a robust genetic algorithm considering manufacturing tolerance is executed; and step 5, evolution optimization and verification are performed. Through construction of a high-precision mapping model of structure parameters-performance indexes, and embedding tolerance analysis based on Monte Carlo sampling in the individual evaluation link of the genetic algorithm, the performance robustness optimization of the motor design scheme in the manufacturing error environment is realized. Compared with the method of optimization only under the nominal size, the application can significantly reduce the performance discreteness of batch products, improve the tolerance to manufacturing deviation and the qualified rate while maintaining the motor efficiency and output torque level, and is suitable for structural design and parameter optimization of various permanent magnet motors.

Description

Technical Field

[0001] This invention belongs to the field of motor design and intelligent optimization technology, and relates to a robust optimization method for manufacturing tolerance of permanent magnet motors, specifically a robust optimization method for manufacturing tolerance of surface-mounted permanent magnet synchronous motors based on a machine learning surrogate model. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) are widely used in CNC machine tools, servo systems, electric vehicles, and intelligent manufacturing equipment due to their high efficiency, high power density, and fast control response. For these motors, structural parameters such as stator and rotor geometry, magnet dimensions and pole arc coefficient, and air gap length have a highly nonlinear coupling relationship with electromagnetic performance characteristics such as output torque, torque ripple, and total harmonic distortion. In engineering practice, analytical equivalent models or finite element simulations are typically used to calculate and compare several candidate structural schemes, and iterative modifications are made based on experience to obtain a combination of structural parameters that meets the required specifications.

[0003] With the improvement of computing power, some research and engineering practices have begun to introduce multi-objective optimization algorithms (such as genetic algorithms, particle swarm optimization, NSGA-II, etc.) to automatically optimize the structural parameters of permanent magnet motors based on finite element simulation. These methods can achieve good efficiency and output torque levels under nominal dimensions and ideal assembly conditions. However, in the traditional design process, structural optimization is generally only performed under nominal geometric and material parameters. Manufacturing tolerances such as dimensional deviations, rotor eccentricity, and magnetic property dispersion of magnets are usually indirectly considered through empirical safety margins, increasing air gaps, or relaxing performance indicators. This can easily lead to two types of problems: First, ignoring the statistical impact of manufacturing tolerances on performance results in large dispersion of indicators such as torque fluctuation and total harmonic distortion in batch products, and some prototypes may exceed limits, increasing rework and screening costs. Second, the practice of uniformly increasing the safety factor is too conservative, making the nominal design point far from the upper limit of performance potential, affecting the power density and efficiency of the motor.

[0004] In recent years, machine learning has been increasingly applied in motor design. By training surrogate models based on finite element simulation data, a rapid mapping from structural parameters to performance indicators can be achieved, significantly reducing simulation overhead during the optimization process. However, existing machine learning-based optimization methods for permanent magnet motors typically still use nominal dimensions as input and only perform tolerance analysis or Monte Carlo simulations on a small number of candidate solutions after optimization to verify the robustness of the design. These methods do not explicitly introduce manufacturing tolerance models during the optimization process, nor do they use robustness indicators such as the mean, variance, or quantiles of performance as optimization objectives or constraints. They are difficult to actively exclude structural solutions sensitive to manufacturing errors during the search process, often requiring extensive post-hoc simulation verification to select designs with better stability, resulting in long design cycles and low computational resource utilization efficiency.

[0005] In summary, existing technologies lack an optimization method that can uniformly consider the impact of manufacturing tolerances during the structural parameter optimization stage of permanent magnet motors and efficiently evaluate robust performance using machine learning surrogate models. This makes it impossible to effectively reduce the performance dispersion and risk of exceeding limits of batch prototypes under actual manufacturing conditions while ensuring nominal performance such as output torque. Therefore, it is necessary to provide a machine learning-based robust optimization method for manufacturing tolerances of permanent magnet motors to achieve robust, multi-indicator comprehensive optimization of structural parameters with limited simulation costs. Summary of the Invention

[0006] This invention provides a robust design method for surface-mounted permanent magnet synchronous motors that takes into account manufacturing tolerances. This method can effectively solve the problems of long calculation time and difficulty in taking into account manufacturing tolerances in existing motor optimization methods.

[0007] The objective of this invention is achieved through the following technical solution:

[0008] A robust design method for surface-mounted permanent magnet synchronous motors considering manufacturing tolerances includes the following steps:

[0009] Step 1: Establish the parametric model and dataset for the surface-mounted permanent magnet synchronous motor:

[0010] Step 1-1: Design the variable vector ,in For the first One design variable, , For variable dimensions;

[0011] Steps 1-2, Performance Index Vector , respectively corresponding to output torque Cogging torque Torque fluctuation Total Harmonic Distortion ;

[0012] Steps 1-3: Select experimental design methods within the design space. A set of sample points were used to calculate the corresponding performance indicators using finite element analysis software, thus constructing the original dataset. ;

[0013] Step 2: Construct a multi-output agent model based on ensemble learning:

[0014] Step 2-1: Using the dataset constructed in Step 1 Train an agent model ;

[0015] Step 2-2, the proxy model is... Decision Tree Composition, for any input structure parameters The predicted output of the proxy model The average of all decision tree predictions:

[0016]

[0017] Steps 2-3: After training is complete, use the test set to verify the determination coefficient R² and mean absolute error MAE of the surrogate model to ensure that the model accuracy meets the requirements of engineering optimization.

[0018] Step 3: Construct a manufacturing tolerance model:

[0019] Step 3-1, targeting Assuming that the manufacturing errors of each variable are independent, and based on the statistical laws of mass production, each design variable is set. Manufacturing error It follows a normal distribution with a mean of 0, that is... ,in, For the first The relative standard deviation of each design variable;

[0020] Step 3-2: For any given nominal design scheme , For the first The formula for calculating the actual manufacturing value of a nominal design scheme with one design variable is defined as follows:

[0021]

[0022] in: This represents the actual structural parameter vector that includes manufacturing errors; Represents element-wise multiplication of vectors; It is a vector consisting entirely of 1s; The relative error vector is generated randomly.

[0023] Step 4: Execute a robust genetic algorithm for manufacturing tolerance awareness:

[0024] Global optimization is performed using a genetic algorithm. In each generation of the algorithm, for each individual in the population, the following embedded robust evaluation process is executed:

[0025] Step 4-1, Monte Carlo sampling:

[0026] Based on the manufacturing tolerance model in step 3, for the current individual conduct A set of virtual prototypes containing manufacturing errors is generated through random sampling. :

[0027]

[0028] in: For the first A virtual prototype that includes manufacturing errors. ;

[0029] Step 4-2, Batch Fast Prediction:

[0030] Call the proxy model trained in step 2 For sets Batch prediction is performed on all samples to obtain the corresponding set of performance metrics:

[0031]

[0032] in: For the first One performance indicator;

[0033] Step 4-3, Calculation of robust statistical indicators:

[0034] For the prediction results Perform statistical analysis and calculate the mean of key performance indicators. and standard deviation :

[0035]

[0036] At the same time, calculate the product pass rate. Let the torque ripple threshold be... The THD threshold is The number of qualified samples The pass rate is the number of samples that meet the criteria:

[0037]

[0038] Step 4-4: Construct the robust fitness function:

[0039] Construct the following comprehensive objective function:

[0040]

[0041] in: For fitness value, This indicates a pursuit of maximizing average output torque; For robustness penalty items, These are weighting coefficients used to suppress performance fluctuations; Let be the pass rate penalty function, when Apply a high penalty value when the target is not met. :

[0042]

[0043] Step 5: Evolutionary Optimization and Verification:

[0044] Step 5-1, based on the calculation in step 4 The next generation population is generated using selection operators, simulated binary crossover (SBX), real-weighted crossover, polynomial mutation, or Gaussian mutation operators.

[0045] Step 5-2: Repeat steps 4 and 5-1 until the maximum number of iterations is met, and output the optimal robust design scheme. The system performs high-fidelity verification on a large sample and outputs the final performance distribution probability density.

[0046] Compared with the prior art, the present invention has the following advantages:

[0047] This invention achieves robust performance optimization of motor designs under manufacturing error environments by constructing a high-precision mapping model between structural parameters and performance indicators, and embedding tolerance analysis based on Monte Carlo sampling into the individual evaluation stage of the genetic algorithm. Compared with methods that only optimize under nominal dimensions, this invention can significantly reduce the performance dispersion of batch products while maintaining motor efficiency and output torque levels, and improve the tolerance and yield rate to manufacturing deviations. It is applicable to the structural design and parameter optimization of various permanent magnet motors. Attached Figure Description

[0048] Figure 1 A flowchart of a robust design method for surface-mounted permanent magnet synchronous motors that takes into account manufacturing tolerances;

[0049] Figure 2 The total harmonic distortion (THD) distribution diagram is shown.

[0050] Figure 3 This is a graph showing the torque fluctuation distribution (probability density).

[0051] Figure 4 A comparison chart of overall performance yield rates;

[0052] Figure 5 A comparison diagram of the convergence process of the genetic algorithm optimization. Detailed Implementation

[0053] The technical solution of the present invention will be further described below with reference to the accompanying drawings, but it is not limited thereto. Any modifications or equivalent substitutions to the technical solution of the present invention that do not depart from the spirit and scope of the technical solution of the present invention should be covered within the protection scope of the present invention.

[0054] This invention provides a robust design method for surface-mounted permanent magnet synchronous motors considering manufacturing tolerances. First, a parametric electromagnetic finite element model of the permanent magnet motor is established. Experimental design and batch simulations are performed on structural parameters such as stator inner diameter, rotor outer diameter, air gap length, magnet dimensions, and pole arc coefficient to obtain multi-indicator data including output torque, torque ripple, and total harmonic distortion, constructing a training sample set. Second, using structural parameters and key manufacturing error parameters as inputs and various performance indicators as outputs, a machine learning surrogate model capable of rapidly predicting motor performance is trained. Then, a manufacturing tolerance probability model is established based on processing statistics. Multiple random sampling evaluations are performed on candidate structures on the surrogate model, calculating robustness indicators such as performance mean, standard deviation, and quantiles. These robustness indicators are then incorporated into the objective function and constraints. An intelligent optimization algorithm searches for the optimal structural parameters that meet performance requirements and are insensitive to manufacturing errors. Figure 1 As shown, the specific steps are as follows:

[0055] Step 1: Establish the parametric model and dataset for the surface-mounted permanent magnet synchronous motor:

[0056] Step 1-1: Design the variable vector ,in For the first One design variable, , For variable dimensions (in this embodiment) ), including stator outer diameter ( ), stator inner diameter ( ), air gap length ( ), permanent magnet width ( ), rotor inner diameter ( ), center thickness of permanent magnet ( ), Permanent magnet edge thickness ( ) and tooth groove width ( ).

[0057] Steps 1-2, Performance Index Vector , respectively corresponding to the output torque ( ), cogging torque ( Torque fluctuation () ) and total harmonic distortion ( ).

[0058] Steps 1-3: Select samples using experimental design methods (such as Latin hypercube sampling) within the design space. The original dataset is constructed by using a set of sample points and calculating the corresponding performance indicators using finite element analysis (FEA) software. .

[0059] Step 2: Construct a multi-output agent model based on ensemble learning:

[0060] Step 2-1: Using the dataset constructed in Step 1 Train a nonlinear mapping function (surrogate model). This method is used to replace time-consuming finite element calculations. The random forest regression algorithm is preferably used in this invention.

[0061] Step 2-2, the proxy model is... Decision Tree Composition, for any input structure parameters The predicted output of the proxy model The average of all decision tree predictions:

[0062]

[0063] Steps 2-3: After training is complete, use the test set to verify the determination coefficient R² and mean absolute error MAE of the surrogate model to ensure that the model accuracy meets the requirements of engineering optimization.

[0064] Step 3: Construct a manufacturing tolerance model:

[0065] To simulate the unavoidable processing and assembly errors in actual motor production, a stochastic tolerance mathematical model is established for subsequent robustness evaluation. The specific process is as follows:

[0066] Step 3-1, regarding the determination in Step 1 Key structural design variable vectors (For example, stator outer diameter, permanent magnet thickness, air gap length, etc.), assuming that the manufacturing errors of each variable are independent. Based on the statistical laws of mass production, each design variable is set. Manufacturing error It follows a normal distribution with a mean of 0, that is... .in, For the first The relative standard deviation of each design variable reflects the precision level of the manufacturing process (for example, for precision machining, a value of 10 ... That is, a relative tolerance of 1%.

[0067] Step 3-2: For any given nominal design scheme , For the first The nominal design scheme of each design variable, and its actual manufacturing value. It is no longer a fixed value, but a random vector. Its actual value is calculated using the formula:

[0068]

[0069] in: This represents the actual structural parameter vector that includes manufacturing errors; This represents the ideal (nominal) structure parameter vector currently searched by the optimization algorithm; Represents element-wise multiplication of vectors; It is a vector consisting entirely of 1s; This is a randomly generated relative error vector.

[0070] Step 4: Execute a robust genetic algorithm for manufacturing tolerance awareness:

[0071] Global optimization is performed using a genetic algorithm (GA). In each generation of the algorithm, for each individual in the population (representing a nominal set of design parameters)... Perform the following embedded robustness evaluation process:

[0072] Step 4-1, Monte Carlo sampling:

[0073] Based on the manufacturing tolerance model in step 3, for the current individual conduct random sampling (e.g.) Generate a set of virtual prototypes that include manufacturing errors. :

[0074]

[0075] in: For the first A virtual prototype that includes manufacturing errors. ;

[0076] Step 4-2, Batch Fast Prediction:

[0077] Call the proxy model trained in step 2 For sets Batch prediction is performed on all samples to obtain the corresponding set of performance metrics:

[0078]

[0079] in: For the first One performance indicator;

[0080] Step 4-3, Calculation of robust statistical indicators:

[0081] For the prediction results Perform statistical analysis and calculate key performance indicators (such as output torque). mean and standard deviation :

[0082]

[0083] At the same time, calculate the product pass rate. Let the torque ripple threshold be... The THD threshold is The number of qualified samples The pass rate is the number of samples that meet the criteria:

[0084]

[0085] Step 4-4: Construct the robust fitness function:

[0086] To maximize average performance while minimizing performance fluctuations and ensuring a high pass rate, the following comprehensive objective function is constructed (taking the minimization problem as an example):

[0087]

[0088] in: For fitness value, This indicates a pursuit of maximizing average output torque; For robustness penalty items, These are weighting coefficients used to suppress performance fluctuations; Let be the pass rate penalty function, when Apply a high penalty value when the result falls below a preset target (e.g., 95%). :

[0089]

[0090] Step 5: Evolutionary Optimization and Verification:

[0091] Step 5-1: Fitness value calculated in Step 4 The next generation population is generated using selection operators, simulated binary crossover (SBX), real-weighted crossover, polynomial mutation, or Gaussian mutation operators.

[0092] Step 5-2: Repeat steps 4 and 5-1 until the maximum number of iterations is met. Output the optimal robust design scheme. and perform large-scale sampling (e.g.) High-fidelity verification is performed to output the final performance distribution probability density.

[0093] To verify the effectiveness of this invention, a comparative experiment was conducted, comparing the proposed solution (robust optimization) with a prior art solution (ordinary optimization) that did not consider manufacturing tolerances. The experimental results are as follows: Figures 2 to 5 As shown, the specific analysis is as follows:

[0094] like Figure 2 and Figure 3As shown, the present invention has significant advantages in suppressing performance fluctuations caused by manufacturing tolerances:

[0095] Depend on Figure 2 It is known that the torque fluctuation of existing technical solutions exhibits a typical bimodal distribution, indicating that their design point is located in a parameter-sensitive region. Even small manufacturing errors (such as deviations in magnet dimensions) can cause drastic jumps in motor performance between two discrete states, resulting in extremely poor consistency. In contrast, the torque fluctuation probability density curve of this invention exhibits an extremely narrow single-peak shape ("sharp peak"), indicating that even with manufacturing errors, the torque fluctuation values ​​of mass-produced motors are highly concentrated around the optimal value (approximately 0.010), demonstrating extremely strong robustness.

[0096] Depend on Figure 3 It can be seen that the THD distribution of the present invention is extremely convergent, with a density peak of over 40 and no obvious tail; while the THD distribution of the prior art is relatively flat and has a long tail effect, indicating that its anti-interference ability is weak and it is easy to produce unqualified products with excessive harmonics.

[0097] like Figure 4 As shown, when strict comprehensive performance evaluation standards are introduced, the yield rates of the two technical solutions differ significantly: Existing technology (ordinary optimization): Although it may perform reasonably well in a single indicator (torque fluctuation), because the erosion of average torque by tolerance is not considered during the optimization process, approximately 13.5% of products become scrap due to insufficient output torque or excessive fluctuation in actual manufacturing, resulting in an overall yield rate of only 86.5%. This invention (robust optimization): By considering the mean, standard deviation, and pass rate in the objective function, this invention successfully achieves low fluctuation while ensuring high torque (meeting power requirements). Experimental data shows that the overall yield rate of this invention is as high as 99.8%, almost eliminating production scrap caused by manufacturing errors and significantly reducing manufacturing costs.

[0098] Thanks to the high-precision random forest proxy model constructed in step S2 of this invention, time-consuming finite element simulation is replaced. Figure 5 As can be seen, although the algorithm of this invention requires a large number of Monte Carlo samplings in each generation to evaluate robustness, its fitness evolution curve can still quickly reach a convergence state around the 10th generation. This means that this invention can complete complex robust optimization tasks in a very short computation time, significantly shortening the research and development cycle.

Claims

1. A robust design method for surface-mount permanent magnet synchronous motors considering manufacturing tolerances, characterized in that... The method includes the following steps: Step 1: Establish the parametric model and dataset of the surface-mounted permanent magnet synchronous motor; Step 2: Construct a multi-output agent model based on ensemble learning: Step 2-1: Using the dataset constructed in Step 1 Train an agent model ; Step 2-2, the proxy model is... Decision Tree Composition, for any input structure parameters The predicted output of the proxy model The average of all decision tree predictions: Steps 2-3: After training is complete, use the test set to verify the determination coefficient R² and mean absolute error MAE of the surrogate model to ensure that the model accuracy meets the requirements of engineering optimization. Step 3: Construct a manufacturing tolerance model: Step 3-1: For the design variable vector ,in For the first One design variable, , Assuming that the manufacturing errors of each variable are independent, and based on the statistical laws of mass production, each design variable is defined. Manufacturing error It follows a normal distribution with a mean of 0, that is... ,in, For the first The relative standard deviation of each design variable; Step 3-2: For any given nominal design scheme , For the first The formula for calculating the actual manufacturing value of a nominal design scheme with one design variable is defined as follows: in: This represents the actual structural parameter vector that includes manufacturing errors; Represents element-wise multiplication of vectors; It is a vector consisting entirely of 1s; The relative error vector is generated randomly. Step 4: Execute a robust genetic algorithm for manufacturing tolerance awareness: Global optimization is performed using a genetic algorithm. In each generation of the algorithm, for each individual in the population, the following embedded robust evaluation process is executed: Step 4-1, Monte Carlo sampling: Based on the manufacturing tolerance model in step 3, for the current individual conduct A set of virtual prototypes containing manufacturing errors is generated through random sampling. : in: For the first A virtual prototype that includes manufacturing errors. ; Step 4-2, Batch Fast Prediction: Call the proxy model trained in step 2 For sets Batch prediction is performed on all samples to obtain the corresponding set of performance metrics: in: For the first One performance indicator; Step 4-3, Calculation of robust statistical indicators: For the prediction results Perform statistical analysis and calculate the mean of key performance indicators. and standard deviation Simultaneously, calculate the product qualification rate. ; Step 4-4: Construct the robust fitness function: Construct the following comprehensive objective function: in: For fitness value, This indicates a pursuit of maximizing average output torque; For robustness penalty items, These are weighting coefficients used to suppress performance fluctuations; The pass rate penalty function; Step 5: Evolutionary Optimization and Verification Step 5-1, based on the calculation in step 4 This generates the next generation of the population; Step 5-2: Repeat steps 4 and 5-1 until the maximum number of iterations is met, and output the optimal robust design scheme. The system performs high-fidelity verification on a large sample and outputs the final performance distribution probability density.

2. The robust design method for surface-mounted permanent magnet synchronous motors considering manufacturing tolerances according to claim 1, characterized in that... The specific steps of step 1-1 are as follows: Step 1-1: Design the variable vector ,in For the first One design variable, , For variable dimensions; Steps 1-2, Performance Index Vector , respectively corresponding to output torque Cogging torque Torque fluctuation Total Harmonic Distortion ; Steps 1-3: Select experimental design methods within the design space. A set of sample points were used to calculate the corresponding performance indicators using finite element analysis software, thus constructing the original dataset. .

3. The robust design method for surface-mounted permanent magnet synchronous motors considering manufacturing tolerances according to claim 2, characterized in that... In step 1-1, the design variables include the stator outer diameter. , stator inner diameter Air gap length Permanent magnet width Rotor inner diameter Permanent magnet center thickness Permanent magnet edge thickness and tooth groove width .

4. The robust design method for surface-mounted permanent magnet synchronous motors considering manufacturing tolerances according to claim 1, characterized in that... In step 4-3, the mean and standard deviation The calculation formula is: 。 5. The robust design method for surface-mounted permanent magnet synchronous motors considering manufacturing tolerances according to claim 1, characterized in that... In step 4-3, The calculation formula is: in: This represents the number of qualified samples.

6. The robust design method for surface-mounted permanent magnet synchronous motors considering manufacturing tolerances according to claim 1, characterized in that... In step 4-4, The following conditions must be met: 。 7. The robust design method for surface-mounted permanent magnet synchronous motors considering manufacturing tolerances according to claim 1, characterized in that... In step 5-1, the next generation population is generated using selection operators, simulated binary crossover, real number weighted crossover, polynomial mutation, or Gaussian mutation operators.

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