A precision micro generator key design parameter optimization method based on double response surfaces

Abstract

The application provides a precision micro special motor key design parameter optimization method based on double response surfaces, and has the advantages that a performance response surface and a reliability response surface are constructed by using the double response surface method, the optimal parameter combination under the performance and reliability constraint conditions can be obtained, the influence of parameters on the performance and reliability of the precision micro special motor is displayed through an image, and the precision micro special motor design work is facilitated.

Description

Technical Field

[0001] This invention belongs to the field of simulation design of key parameters of precision micromotors, and particularly relates to a method for optimizing key design parameters of precision micromotors based on dual response surfaces. Background Technology

[0002] Precision micromotors refer to motors with a diameter less than 160mm and a rated power less than 750W, or motors with special requirements for application, performance, and environmental conditions. Precision micromotors are indispensable key products in national defense equipment, characterized by high speed, high precision, low vibration and noise, and high reliability. The key design parameters of precision micromotors are crucial to their performance and reliability. Traditional precision micromotors involve a cyclical process of "design + production + testing + modification + redesign," resulting in a relatively long design and production cycle and high design and manufacturing costs. The purpose of this patent is to obtain the relationship between key design parameters and output characteristics and reliability through digital simulation modeling. By completing a "modeling + simulation + production" cycle, design requirements can be met, aiming to achieve optimal results in a single production run, avoiding repeated work and reducing the design and production cycle and costs. Summary of the Invention

[0003] To address the aforementioned issues, this invention provides a method for optimizing key design parameters of precision micromotors based on dual response surfaces, which can simultaneously obtain the optimal parameter combination under performance and reliability constraints.

[0004] A method for optimizing key design parameters of precision micromotors based on dual response surfaces includes the following steps:

[0005] The digital simulation model of the micro motor was tested under no-load and rated operating conditions. Based on the test results, the digital simulation model of the micro motor was corrected so that the output characteristics of the digital simulation model of the micro motor are consistent with those of the actual micro motor.

[0006] By performing sensitivity analysis on the modified digital simulation model of the micro-motor, the two model parameters that have the greatest impact on the output characteristics of the modified digital simulation model of the micro-motor were identified as key parameters.

[0007] By selecting different values ​​for the two key parameters, and then using different combinations of values, simulation experiments were conducted on the modified digital simulation model of the micro-motor to obtain the performance response and reliability corresponding to different combinations of values. Among them, the reliability is related to the speed.

[0008] By fitting data to each combination of values ​​and the corresponding performance response using the least squares method, a bivariate quadratic performance response surface is obtained.

[0009] By fitting data to each combination of values ​​and the corresponding reliability using the least squares method, a bivariate quadratic reliability response surface is obtained.

[0010] Given a range of rotational speeds, select the values ​​of two key parameters from the performance response surface and the reliability response surface that maximize reliability and result in a performance response greater than the set value.

[0011] Furthermore, the digital simulation model of the micro-motor includes a speed controller, a driver, and a motor. The method for constructing the digital simulation model of the micro-motor is as follows:

[0012] The shape, size, material properties, electrical parameters, environmental conditions, and operating conditions of the micro motor are set in the simulation software to obtain a digital simulation model of the micro motor.

[0013] Furthermore, the digital simulation model of the micro-motor was further modified based on the test results as follows:

[0014] The digital simulation model of the micro motor is tested under no-load and rated operating conditions. The duty cycle of the motor drive circuit, the voltage between two phases of the three-phase motor, and the speed output to the load are obtained as test results. It is then determined whether the test results are the same as the test results of the actual micro motor. If not, the electrical parameters of the digital simulation model of the micro motor are adjusted and the test is repeated until the result is yes. If yes, the correction ends and the final digital simulation model of the micro motor is obtained.

[0015] Furthermore, sensitivity analysis was performed on the modified digital simulation model of the micro-motor to obtain two key parameters. The specific method for this was as follows:

[0016] Sensitivity acquisition is performed on each model parameter of the micro-motor digital simulation model as the current parameter to obtain the sensitivity of each model parameter to the output characteristics. The sensitivity acquisition operation is as follows:

[0017] Different values ​​are selected for the current parameter, and the nominal values ​​are selected for the other model parameters to obtain different combinations of model parameters; the output characteristics of the micro-motor digital simulation model under different combinations of model parameters are obtained, and the sensitivity of the current parameter to the output characteristics is obtained from the output characteristics corresponding to each combination of model parameters. Among them, the larger the absolute value of the sensitivity, the greater the influence of the current parameter on the output characteristics.

[0018] The two model parameters with the largest absolute values ​​of sensitivity to output characteristics are selected as key parameters.

[0019] Furthermore, the two model parameters that have the greatest impact on the output characteristics of the corrected digital simulation model of the micro-motor are the back electromotive force constant ke and the internal resistance r.

[0020] Furthermore, the reliability calculation method for different combinations of values ​​is as follows:

[0021] Multiple Monte Carlo simulation experiments were conducted on the modified micro-motor digital simulation model using different combinations of values ​​to obtain the mean speed n0 and the speed variance σ0 corresponding to each combination of values.

[0022] Based on the mean speed n0 and the variance of speed σ0 corresponding to each value combination, the reliability distribution function f(n) for each value combination is obtained as follows:

[0023]

[0024] Where n represents the rotational speed;

[0025] Calculate the reliability R for each value combination based on the reliability distribution function f(n) for each value combination:

[0026]

[0027] Where, n max n represents the maximum permissible rotational speed. min This indicates the minimum permissible rotational speed.

[0028] Beneficial effects:

[0029] 1. This invention provides a method for optimizing key design parameters of precision micromotors based on dual response surfaces. The advantage is that the dual response surface method is used to construct performance response surfaces and reliability response surfaces, which can simultaneously obtain the optimal parameter combination under performance and reliability constraints. The influence of parameters on the performance and reliability of precision micromotors is displayed through intuitive images, which facilitates the design of precision micromotors.

[0030] 2. This invention provides a method for optimizing key design parameters of precision micromotors based on dual response surfaces. The performance response surface model can vividly and directly describe the relationship between output performance and key parameters, while the reliability response surface model can vividly and directly describe the relationship between output reliability and key parameters. In other words, the dual response surface method of this invention can simultaneously handle multi-objective function problems. Compared with the single response surface method, it considers more factors, is more in line with the actual situation, reduces design iterations, lowers the cost of trial and error, and is beneficial to the refined design of precision micromotors.

[0031] 3. This invention provides a method for optimizing key design parameters of precision micromotors based on dual response surfaces. By using modeling and simulation experiments, the nonlinear relationship between the objective function and key design parameters can be easily handled, reducing the difficulty of optimization calculations. Attached Figure Description

[0032] Figure 1 A flowchart illustrating a method for optimizing key design parameters of a precision micromotor based on a dual response surface, provided by this invention;

[0033] Figure 2 The results are from sensitivity simulation analysis.

[0034] Figure 3 For performance response surface;

[0035] Figure 4 This is the reliability response surface. Detailed Implementation

[0036] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings.

[0037] This invention belongs to the field of simulation science and technology in information and systems science, and also to the field of aircraft instruments and equipment in aerospace science and technology. Specifically, it involves digital modeling of precision motors, determination of key design parameters, construction of performance response surfaces, construction of reliability response surfaces, and optimization of key design parameters.

[0038] Specifically, such as Figure 1 As shown, a method for optimizing key design parameters of a precision micromotor based on dual response surfaces includes the following steps:

[0039] Step 1: Test the digital simulation model of the micro motor under no-load and rated operating conditions. Based on the test results, correct the digital simulation model of the micro motor to make the output characteristics of the micro motor consistent with those of the actual micro motor.

[0040] It should be noted that the digital simulation model of the micro motor includes a speed controller, a driver, and a motor. The method for constructing the digital simulation model of the micro motor is as follows: set the shape, size, material properties, electrical parameters, environmental conditions, and operating conditions of the micro motor in the simulation software to obtain the digital simulation model of the micro motor.

[0041] Furthermore, the digital simulation model of the micro-motor was further modified based on the test results as follows:

[0042] The digital simulation model of the micro motor is tested under no-load and rated operating conditions. The duty cycle of the motor drive circuit, the voltage between two phases of the three-phase motor, and the speed output to the load are obtained as test results. It is then determined whether the test results are the same as the test results of the actual micro motor. If not, the electrical parameters of the digital simulation model of the micro motor are adjusted and the test is repeated until the result is yes. If yes, the correction ends and the final digital simulation model of the micro motor is obtained.

[0043] Step 2: By performing sensitivity analysis on the corrected digital simulation model of the micro-motor, the two model parameters that have the greatest impact on the output characteristics of the corrected digital simulation model of the micro-motor are identified as key parameters.

[0044] Furthermore, sensitivity analysis was performed on the modified digital simulation model of the micro-motor to obtain two key parameters. The specific method for this was as follows:

[0045] Sensitivity acquisition is performed on each model parameter of the micro-motor digital simulation model as the current parameter to obtain the sensitivity of each model parameter to the output characteristics. The sensitivity acquisition operation is as follows:

[0046] Different values ​​are selected for the current parameter, and the nominal values ​​are selected for the other model parameters to obtain different combinations of model parameters; the output characteristics of the micro-motor digital simulation model under different combinations of model parameters are obtained, and the sensitivity of the current parameter to the output characteristics is obtained from the output characteristics corresponding to each combination of model parameters. Among them, the larger the absolute value of the sensitivity, the greater the influence of the current parameter on the output characteristics.

[0047] The two model parameters with the largest absolute values ​​of sensitivity to output characteristics are selected as key parameters.

[0048] It should be noted that sensitivity can be magnituded or negative. A positive sensitivity indicates that the change in the output characteristics of the micromotor is consistent with the change in this parameter; a negative sensitivity indicates that the change in output characteristics is opposite to the change in this parameter. By analyzing and ranking the sensitivity, the two key design parameters with the greatest impact on performance can be identified. For example, the sensitivity simulation analysis results for a certain type of motor are as follows: Figure 2 The two factors that have the greatest impact on the output characteristics are the back electromotive force constant ke (V / rad / s) and the internal resistance r (Ω).

[0049] Step 3: Select different values ​​for the two key parameters, and then conduct simulation tests on the modified micro-motor digital simulation model using different combinations of values ​​to obtain the performance response and reliability corresponding to different combinations of values. Among them, reliability is related to speed.

[0050] For example, when it is necessary to obtain the performance response corresponding to different combinations of values, a two-factor, five-level orthogonal simulation experiment needs to be carried out. Specifically, ke and r are used as two key design parameters as experimental factors, and five different values ​​are taken for the experimental factors. The values ​​of ke (V / rad / s) are 0.023, 0.024, 0.025, 0.026, and 0.027, and the values ​​of internal resistance r (Ω) are 0.18, 0.185, 0.19, 0.195, and 0.20, respectively. Orthogonal simulation experiments are carried out, and one performance simulation experiment is carried out under each combination. A total of 25 performance simulation analyses are carried out to obtain 25 performance responses.

[0051] When it is necessary to obtain the reliability corresponding to different value combinations, Monte Carlo simulation analysis is required. Specifically, multiple Monte Carlo simulation tests are conducted on the modified micro-motor digital simulation model using different value combinations to obtain the mean speed n0 and speed variance σ0 corresponding to each value combination. Based on the mean speed n0 and speed variance σ0 corresponding to each value combination, the distribution function f(n) of the reliability corresponding to each value combination is obtained as follows:

[0052]

[0053] Where n represents the rotational speed;

[0054] Calculate the reliability R for each value combination based on the reliability distribution function f(n) for each value combination:

[0055]

[0056] Where, n max n represents the maximum permissible rotational speed. min This indicates the minimum permissible rotational speed.

[0057] For example, if ke and r are taken as two key design parameters and five different values ​​are selected for the experimental factors, with ke (V / rad / s) being 0.023, 0.024, 0.025, 0.026, and 0.027 respectively, and the internal resistance r (Ω) being 0.18, 0.185, 0.19, 0.195, and 0.20 respectively, then 25 combinations of values ​​can be obtained. Each combination of values ​​is subjected to 100 Monte Carlo simulation analyses to obtain 25 reliability levels, resulting in a total of 2500 Monte Carlo simulation analyses.

[0058] Step 4: Use the least squares method to fit the data of each value combination and the corresponding performance response to obtain a bivariate quadratic performance response surface.

[0059] It should be noted that this invention uses simulation data to establish a binary quadratic performance response surface. The binary aspect refers to two selected key parameters, such as the back electromotive force coefficient ke and the resistance r. The values ​​of the back electromotive force constant, resistance, and rotational speed are extracted, and the data is fitted using the least squares method to obtain the following curve:

[0060] Z = A0 + A1*ke + A2*r + A3*ke 2 +A4*r 2 +A5*ke*r

[0061] Where 0.023≤ke≤0.027, 0.18≤r≤0.20, the performance response surface model can directly and vividly describe the relationship between output performance and key parameters. The constructed performance response surface is as follows: Figure 3 As shown.

[0062] Step 5: Use the least squares method to fit the data of each value combination and the corresponding reliability to obtain a bivariate quadratic reliability response surface;

[0063] It should be noted that the reliability response surface model can vividly and directly describe the relationship between output reliability and key parameters. The expression of the reliability response surface obtained by least squares fitting is displayed in MATLAB, as shown below. Figure 4 Therefore, it can be seen that the reliability is not directly proportional to the back electromotive force coefficient ke (V / rad / s) and resistance r of the precision micro motor. Instead, it exhibits an inverted U-shaped surface relationship, with the best reliability at the middle position. Similarly, the parameters corresponding to the middle position are the optimal performance parameters.

[0064] Step 6: Given a range of rotational speeds, select the values ​​of two key parameters from the performance response surface and the reliability response surface that maximize reliability and result in a performance response greater than the set value.

[0065] For example, based on performance requirements, such as a rotational speed z∈[1650,1700] and a higher reliability requirement, a performance and reliability optimization model can be established. The reliability model is based on the following formula:

[0066] max R

[0067] stZ∈[1650,1700]

[0068] ke∈[0.023,0.027]

[0069] r∈[0.18,0.2]

[0070] DVke,r

[0071] ke = 0.025363

[0072] r = 0.18

[0073] R = 0.99639

[0074] Using a nonlinear multi-parameter optimization function, the reliability in this case is found to be 0.99639, and the optimal parameter combination in this case is ke = 0.025363 and r = 0.18.

[0075] In summary, this invention first analyzes the shape, size, material properties, and electrical parameters of the motor to construct a digital model of a precision micro-motor; then, it tests and calibrates the model based on measured data; next, it obtains the key design parameters of the precision micro-motor through sensitivity analysis; then, it designs orthogonal simulation experiments for the key design parameters to construct a performance response surface model; then, it uses Monte Carlo simulation analysis to construct a reliability response surface model based on the threshold of the output characteristics; finally, it selects a suitable optimization algorithm to obtain the optimal combination of key design parameters.

[0076] Therefore, the advantages of this invention lie in its use of a dual response surface methodology to construct performance and reliability response surfaces, enabling the simultaneous acquisition of optimal parameter combinations under performance and reliability constraints. The impact of parameters on the performance and reliability of precision micromotors is displayed visually and intuitively, facilitating precision micromotor design. Furthermore, the modeling and simulation methods facilitate handling the nonlinear relationship between the objective function and key design parameters, reducing the difficulty of optimization calculations. The dual response surface methodology can simultaneously handle multi-objective function problems, considering more factors than the single response surface methodology, thus better reflecting reality, reducing design iterations, lowering trial-and-error costs, and promoting refined design of precision micromotors.

[0077] Of course, the present invention may have other various embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art can make various corresponding changes and modifications according to the present invention, but these corresponding changes and modifications should all fall within the protection scope of the appended claims.

Claims

1. A method for optimizing key design parameters of precision micromotors based on dual response surfaces, characterized in that, Includes the following steps: The digital simulation model of the micro motor was tested under no-load and rated operating conditions. Based on the test results, the digital simulation model of the micro motor was corrected so that the output characteristics of the digital simulation model of the micro motor are consistent with those of the actual micro motor. By performing sensitivity analysis on the modified digital simulation model of the micro-motor, the two model parameters that have the greatest impact on the output characteristics of the modified digital simulation model of the micro-motor were identified as key parameters. By selecting different values ​​for the two key parameters, and then using different combinations of values, simulation experiments were conducted on the modified digital simulation model of the micro-motor to obtain the performance response and reliability corresponding to different combinations of values. Among them, the reliability is related to the speed. By fitting data to each combination of values ​​and the corresponding performance response using the least squares method, a bivariate quadratic performance response surface is obtained. By fitting data to each combination of values ​​and the corresponding reliability using the least squares method, a bivariate quadratic reliability response surface is obtained. Given a range of rotational speeds, select the values ​​of two key parameters that maximize reliability and result in a performance response greater than the set value from the performance response surface and the reliability response surface. The digital simulation model of the micro-motor includes a speed controller, a driver, and a motor. The method for constructing the digital simulation model of the micro-motor is as follows: The shape, size, material properties, electrical parameters, environmental conditions, and operating conditions of the micro motor are set in the simulation software to obtain a digital simulation model of the micro motor.

2. The method for optimizing key design parameters of a precision micromotor based on dual response surfaces as described in claim 1, characterized in that, The digital simulation model of the micro-motor was revised based on the test results as follows: The digital simulation model of the micro motor is tested under no-load and rated operating conditions. The duty cycle of the motor drive circuit, the voltage between two phases of the three-phase motor, and the speed output to the load are obtained as test results. It is determined whether the test results are the same as the test results of the actual micro motor in the past. If not, the electrical parameters of the digital simulation model of the micro motor are adjusted and the test is repeated until the judgment result is yes. If so, the correction ends, and the final digital simulation model of the micro-motor is obtained.

3. The method for optimizing key design parameters of a precision micromotor based on dual response surfaces as described in claim 1, characterized in that, The method for obtaining two key parameters by performing sensitivity analysis on the corrected digital simulation model of the micro-motor is as follows: Sensitivity acquisition is performed on each model parameter of the micro-motor digital simulation model as the current parameter to obtain the sensitivity of each model parameter to the output characteristics. The sensitivity acquisition operation is as follows: Different values ​​are selected for the current parameter, and the nominal values ​​are selected for the other model parameters to obtain different combinations of model parameters; the output characteristics of the micro-motor digital simulation model under different combinations of model parameters are obtained, and the sensitivity of the current parameter to the output characteristics is obtained from the output characteristics corresponding to each combination of model parameters. Among them, the larger the absolute value of the sensitivity, the greater the influence of the current parameter on the output characteristics. The two model parameters with the largest absolute values ​​of sensitivity to output characteristics are selected as key parameters.

4. The method for optimizing key design parameters of a precision micromotor based on a dual response surface, as described in any one of claims 1 to 3, is characterized in that... The two model parameters that have the greatest impact on the output characteristics of the corrected digital simulation model of the micromotor are the back electromotive force constant ke and the internal resistance r.

5. The method for optimizing key design parameters of a precision micromotor based on a dual response surface, as described in any one of claims 1 to 3, is characterized in that... The reliability calculation methods for different combinations of values ​​are as follows: Multiple Monte Carlo simulation experiments were conducted on the modified digital simulation model of the micromotor using different combinations of values ​​to obtain the average speed corresponding to each value combination. and speed variance ; Based on the average rotational speed corresponding to each value combination and speed variance Obtain the reliability distribution function for each value combination. as follows: in, Indicates rotational speed; Based on the reliability distribution function corresponding to each value combination Calculate the reliability R for each combination of values: in, This indicates the maximum permissible rotational speed. This indicates the minimum permissible rotational speed.

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