CN111695254B - Permanent magnet synchronous motor multi-objective optimization method based on double-response curved surface method and Taguchi method - Google Patents
Permanent magnet synchronous motor multi-objective optimization method based on double-response curved surface method and Taguchi method Download PDFInfo
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Abstract
A permanent magnet synchronous motor multi-objective optimization method based on a double-response curved surface method and a Taguchi method belongs to the field of permanent magnet synchronous motor optimization algorithms. The method solves the problems that the existing multi-objective optimization algorithm has large optimization calculation amount and mutual influence among parameters, and cannot accurately and efficiently realize multi-objective optimization. The invention utilizes the response surface equation and the specific gravity of the Taguchi method to combine and calculate, greatly reduces the difficulty of weight fusion, saves a great amount of time, fully utilizes the self-contained function of software to provide convenience for multi-objective optimization, and provides a new thought and method for multi-objective optimization of the permanent magnet synchronous motor in the future. The algorithm is flexible and can be suitable for various multi-objective optimization occasions. The invention is suitable for the optimized use of the permanent magnet synchronous motor.
Description
Technical Field
The invention belongs to the field of permanent magnet synchronous motor optimization algorithms.
Background
The permanent magnet synchronous motor has the advantages of high power factor, small heating, no transmission gear abrasion, small noise, high reliability and high efficiency, and can bear large overload current, and is widely applied to various fields. Such as numerical control machine tools, elevator systems, new energy automobiles, etc.
Because the cogging torque and the reluctance torque of the built-in permanent magnet synchronous motor have larger torque pulsation, mechanical vibration and noise can be generated, and the running stability and the service life of the motor are seriously affected. However, as the built-in permanent magnet synchronous motor is easy to obtain higher average torque due to the asymmetric reactance of the alternating-direct axis, the improvement of the average torque is realized by multi-objective optimization of the permanent magnet motor nowadays, but in the multi-objective optimization process, the searching times are increased exponentially along with the increase of the optimization targets, so that the algorithm cannot effectively detect huge searching space in limited time; the traditional motor optimization method is used for optimizing a single target by means of finite element simulation software, so that the problems that the optimization calculation amount is large, the mutual influence among parameters is easy to ignore exist, and meanwhile, multi-target optimization cannot be accurately and efficiently realized.
Disclosure of Invention
The invention provides a permanent magnet synchronous motor multi-target optimization method based on a double-response curved surface method and a Taguchi method, which aims to solve the problems that the existing multi-target optimization algorithm has large optimization calculation amount and mutual influence among parameters and cannot accurately and efficiently realize multi-target optimization.
The invention discloses a permanent magnet synchronous motor multi-objective optimization method based on a double-response curved surface method and a Taguchi method, which comprises the following specific steps:
step one, determining an optimization target of a permanent magnet synchronous motor, and selecting three parameters related to the optimization target from rotor optimization parameters of the permanent magnet synchronous motor as optimization variables;
step two, determining the optimal range of the optimization variable in the step one;
thirdly, constructing a response surface model by using the optimized variable, judging the rationality of the response surface model by using an analysis of variance verification equation, and if the response surface model is unreasonable; executing the fourth step, when the response surface model is reasonable, acquiring a response surface equation, and executing the fifth step;
step four, three parameters are selected from rotor optimization parameters of the permanent magnet synchronous motor again to serve as optimization variables; returning to the execution step II; the three parameters in the step are not identical to the three parameters in the step one;
fifthly, carrying out an orthogonal test method by using a Taguchi method, and calculating an influence proportion value of an optimization variable on a response value; executing the step six;
step six, fusing the response surface equation and the specific gravity value in the step five through a weight fusion algorithm to obtain a final optimization correction equation;
and step seven, obtaining a linear function relation between the optimization variable and the optimization target by utilizing the property that the difference between the final optimization correction equation and the estimated objective function is close to zero, and obtaining an optimal function value of the optimization target of the permanent magnet synchronous motor by utilizing the optimal value range of the optimization variable determined in the step two as a constraint condition.
Further, the rotor optimization parameters of the permanent magnet synchronous motor in the step one include: the inner and outer diameters of the rotor, silicon steel sheet materials and the type of magnetic poles on the rotor; for the permanent magnet of the built-in motor, the pole arc coefficient, the thickness of the permanent magnet, the width of a magnetic isolation bridge, the thickness of magnetic steel and the material of the permanent magnet can be used.
Further, the method for constructing the response surface model by using the optimized variables in the third step comprises the steps of constructing by using Minitap software, MATLAB software or Design-Expert software.
Further, in the fifth step, the specific method for obtaining the influence specific gravity value of the optimization variable on the response value by using the Taguchi to perform the orthogonal test method is as follows:
fifthly, sampling each optimized variable, wherein each optimized variable obtains N groups of sampling data, and calculating the average value of the N groups of sampling data of each optimized variable under an orthogonal test; wherein n is a positive integer greater than or equal to 4;
step five, calculating the average value of performance indexes of the three optimized variables under different permanent magnet thickness horizontal values;
step five, calculating the variance of each optimized variable under different permanent magnet thickness level values;
and fifthly, calculating the influence proportion of each optimization parameter on the optimization target.
Further, in the fifth step, the specific method for calculating the average value of n groups of sampling data of each optimization variable under the orthogonal test is as follows:
using the formula:
the average value of n groups of sampling data under the orthogonal test is calculated and obtained, wherein,for the average value of the performance index of an optimization variable, i represents the i-th group of sampling data of the optimization variable, T i Represents the average value of the performance index of the i-th group of sampling data.
Further, the specific method for calculating the average value of the performance indexes under the different permanent magnet thickness level values of the three optimization variables in the fifth step is as follows:
the formula is adopted:
calculating to obtain the average value of the performance index of the thickness level value of the permanent magnet with optimized variable, wherein M T The torque of the optimization factor under the thickness level of the permanent magnet is represented, and T (1), T (2), T (3) and T (4) are the torques in the 1 st, 2 nd, 3 rd and 4 th orthogonal experiments under one thickness level of the permanent magnet respectively.
Further, the specific method for calculating the variance of each optimization variable under different permanent magnet thickness level values in the fifth step is as follows:
when the variance of the torque is found, S in the formula s Representing an optimization target variance; by usingThe optimization objective of the ith test at the jth permanent magnet thickness level is represented, and m (S) is the average value of the motor optimization objective.
Further, the specific method for calculating the influence specific gravity of each optimization parameter on the optimization target in the fifth step is as follows:
z represents the specific gravity of the variance of each optimization objective to the sum of the variances of all optimization objectives.
Further, the weight fusion algorithm in the step six adopts the formula:
converting the multi-objective optimization into a process of solving the optimal value of the independent variable by the known optimal variable, and converting the final optimization result into a constraint relation between optimization target value functions; wherein A represents an optimization objective function, g u The method comprises the steps of estimating corresponding first derivatives in Taylor expansion of an objective function, wherein the estimated objective function is represented by an equation obtained by a response surface method, and P is the number of optimized variables; u represents the u-th optimization variable, I u Is a set of values of the optimized variable, gamma is the influence degree of the optimized variable on each performance of the permanent magnet, and w * For the optimal specific gravity, the optimal specific gravity was calculated using the Taguchi method orthogonal test.
Further, the estimating objective function in the seventh step is:
wherein A (Θ) is an estimateAn objective function; x is x i The samples representing the optimization variables, the estimation error μ () is the error estimation sum function caused by the permanent magnet leakage;due to x i The value is changed to make y i A changing measurement function, y i Representing an estimated target value that is updated continuously with the optimization process; k is y i The number of updates, k, represents the permanent magnet thickness level value, f when k is 1 ki Is along with y i The degree of influence on the specific gravity of the parameter when the thickness level of the permanent magnet is 1 is added, ψ (f ki )＝y i +(1/2γ) 2 。
The invention utilizes the response surface equation and the specific gravity of the Taguchi method to combine and calculate, greatly reduces the difficulty of weight fusion, saves a great amount of time, fully utilizes the self-contained function of software to provide convenience for multi-objective optimization, and provides a new thought and method for multi-objective optimization of the permanent magnet synchronous motor in the future. The algorithm is flexible and can be suitable for various multi-objective optimization occasions. The optimization algorithm is applied to the optimization design of the built-in permanent magnet synchronous motor. The method ensures the higher approximation precision of the response surface method and ensures the efficiency of the Taguchi method in the optimization later period.
Drawings
FIG. 1 is a graph of a model of a response surface between an average output torque and a tri-variable obtained by the invention;
FIG. 2 is a graph of a model of a response surface between torque ripple coefficients and tri-variables obtained by the present invention;
FIG. 3 is a graph of a model of a response surface between efficiency and tri-variables obtained by the present invention;
FIG. 4 is a graph comparing torque performance before and after optimization;
FIG. 5 is a graph of waveform contrast of radial air gap magnetic density before and after optimizing load;
FIG. 6 is a graph comparing harmonic analysis of radial air gap flux density before and after optimization.
Detailed Description
A first embodiment of the present invention is described with reference to fig. 1 to 3, in which the method for optimizing multiple targets of a permanent magnet synchronous motor based on a dual-response curved surface method and Taguchi (Tian Koufa) includes the following specific steps:
step one, determining an optimization target of a permanent magnet synchronous motor, and selecting three parameters related to the optimization target from rotor optimization parameters of the permanent magnet synchronous motor as optimization variables;
step two, determining the optimal value range of the optimization variable in the step one;
thirdly, constructing a response surface model by using the optimized variable, judging the rationality of the response surface model by using an analysis of variance verification equation, and if the response surface model is unreasonable; executing the fourth step, when the response surface model is reasonable, acquiring a response surface equation, and executing the fifth step;
step four, three parameters are selected from rotor optimization parameters of the permanent magnet synchronous motor again to serve as optimization variables; returning to the execution step II; the three parameters in the step are not identical to the three parameters in the step one;
fifthly, performing an orthogonal test method by using a Taguchi method, and calculating an influence proportion value of an optimization variable on a response value; executing the step six;
step six, fusing the response surface equation and the specific gravity value in the step five through a weight fusion algorithm to obtain a final optimization correction equation;
and step seven, obtaining a linear function relation between the optimization variable and the optimization target by utilizing the property that the difference between the final optimization correction equation and the estimated objective function is close to zero, and obtaining an optimal function value of the optimization target of the permanent magnet synchronous motor by utilizing the optimal value range of the optimization variable determined in the step two as a constraint condition.
In this embodiment, the optimal range of the optimization variables of the first step is determined by using Ansoft Maxwell software.
In the invention, when the estimated value of the objective function is closer to the expected objective function value, the corresponding loss error function is smaller. However, when the difference between the two is close to zero, the optimal effect is considered, and the final optimization objective function is solved by utilizing the characteristic by updating the estimation objective function to be close to the final optimization objective function. When the estimated objective function is updated to meet min (A-A (theta)), the proportion of the front coefficient of the parameter quantity of the response surface equation to the total coefficient sum can be respectively brought into an optimized objective equation to obtain 6 unknown equation, and the problem can be converted into a simple linear programming problem by adding constraint conditions.
Further, in this embodiment, the rotor optimization parameters of the permanent magnet synchronous motor in the step one include: the inner and outer diameters of the rotor, silicon steel sheet materials and the type of magnetic poles on the rotor; for the permanent magnet of the built-in motor, the pole arc coefficient, the thickness of the permanent magnet, the width of a magnetic isolation bridge, the thickness of magnetic steel and the material of the permanent magnet can be used.
Further, in this embodiment, the method for constructing the response surface model by using the optimization variables in the third step includes constructing by using minitpap software, MATLAB software or Design-Expert software.
Further, in the present embodiment, the specific method for obtaining the influence specific gravity value of the optimization variable on the response value by using the Taguchi method to perform the orthogonal test in the fifth step is as follows:
fifthly, sampling each optimized variable, wherein each optimized variable obtains N groups of sampling data, and calculating the average value of the N groups of sampling data of each optimized variable under an orthogonal test; wherein n is a positive integer greater than or equal to 4;
step five, calculating the average value of performance indexes of the three optimized variables under different permanent magnet thickness horizontal values;
step five, calculating the variance of each optimized variable under different permanent magnet thickness level values;
and fifthly, calculating the influence proportion of each optimization parameter on the optimization target.
Further, in the embodiment, the specific method for calculating the average value of n groups of sampling data of each optimization variable in the fifth step under the orthogonal test is as follows:
using the formula:
the average value of n groups of sampling data under the orthogonal test is calculated and obtained, wherein,for the average value of the performance index of an optimization variable, i represents the i-th group of sampling data of the optimization variable, T i Represents the average value of the performance index of the i-th group of sampling data.
Further, in the embodiment, the specific method for calculating the average value of the performance indexes under the different permanent magnet thickness level values of the three optimization variables in the fifth step is as follows:
the formula is adopted:
calculating to obtain the average value of the performance index of the thickness level value of the permanent magnet with optimized variable, wherein M T The torque of the optimization factor under the thickness level of the permanent magnet is represented, and T (1), T (2), T (3) and T (4) are the torques in the 1 st, 2 nd, 3 rd and 4 th orthogonal experiments under one thickness level of the permanent magnet respectively.
Further, in the present embodiment, the specific method for calculating the variance of each optimization variable under different permanent magnet thickness level values in the fifth step is as follows:
when the variance of the torque is found, S in the formula s Representing an optimization target variance; by usingThe optimization objective of the ith test at the jth permanent magnet thickness level is represented, and m (S) is the average value of the motor optimization objective.
Further, in the present embodiment, the specific method for calculating the specific gravity of each optimization parameter on the optimization target in the fifth step is as follows:
z represents the specific gravity of the variance of each optimization objective to the sum of the variances of all optimization objectives.
Further, in this embodiment, the weight fusion algorithm described in the step six adopts the formula:
converting the multi-objective optimization into a process of solving the optimal value of the independent variable by the known optimal variable, and converting the final optimization result into a constraint relation between optimization target value functions; wherein A represents an optimization objective function, g u The method comprises the steps of estimating corresponding first derivatives in Taylor expansion of an objective function, wherein the estimated objective function is represented by an equation obtained by a response surface method, and P is the number of optimized variables; u represents the u-th optimization variable, I u Is a set of values of the optimized variable, gamma is the influence degree of the optimized variable on each performance of the permanent magnet, and w * For the optimal specific gravity, the optimal specific gravity was calculated using the Taguchi method orthogonal test.
Further, in the present embodiment, the estimation objective function described in the step seven is:
wherein a (Θ) is an estimated objective function; x is x i The samples representing the optimization variables, the estimation error μ () is the error estimation sum function caused by the permanent magnet leakage;due to x i The value is changed to make y i A changing measurement function, y i Representing an estimated target value that is updated continuously with the optimization process; k is y i The number of updates, k, represents the permanent magnet thickness level value, f when k is 1 ki Is along with y i The degree of influence on the specific gravity of the parameter when the thickness level of the permanent magnet is 1 is added, ψ (f ki )＝y i +(1/2γ) 2 。
Specific examples: taking a 3kW built-in permanent magnet synchronous motor as an example, taking the thickness of a permanent magnet, the width of a magnetism isolating bridge and the polar arc coefficient as variables, and taking the torque fluctuation coefficient and the average output torque and efficiency as optimization targets, carrying out an optimization design test, wherein the main size parameters and the main technical requirements of the motor are shown in a table 1.
Table 1 dimensional parameters and main technical requirements of permanent magnet synchronous motor
Because the invention aims to improve the average output torque and reduce the torque fluctuation, the experiment only considers the condition of the motor when the motor runs under the load working condition, and analyzes the efficiency and the torque performance of the motor.
The specific implementation steps are as follows:
step 1: determining the thickness of a permanent magnet, the width of a magnetic isolation bridge and the polar arc coefficient as three optimization variables, the torque fluctuation coefficient and the average output torque and efficiency as optimization targets;
step 2: parameterized analysis is carried out on the motor model by utilizing Ansoft Maxwell, and optimized variables and parameterized scanning results are obtained as shown in the following table 2;
table 2 optimization variables and parameterized scan results
Step 3: three factor levels of 1, 2 and 3 are selected as variables, and specific values of optimization parameters under the three factor levels are shown in the following table 3; according to design-expert self-provided function design 14 groups of tests and unreasonable test factor combinations, as shown in the following table 4, a response surface model and an equation are established, and the rationality of the equation is verified according to analysis of variance;
table 3 specific values of optimization parameters at three factor level
TABLE 4 results of orthogonal experiments
In the table, the thickness of the permanent magnet is Thicknes, the width of the Bridge magnetism isolating Bridge is equal to a polar arc coefficient;
the response surface equation is:
equation 1:
Tav＝-1214.2+157.6D+802.8B+373.6C-88.2AB-521.0BC+427.9C 2
TF＝288.6-57.0D+8.5B-388.6C+48.8DB+0.5×DC+347.2BC-3.0D 2 -138.4B 2 -181.5C 2
η＝-470.8+11.6D+584.6B+8.8C+11.0AB+3.0DC+64.5BC-3.2D 2 -190.6B 2 -100.5C 2
equation 2:
Tav＝40.1-0.6D-0.7B+4.2C-2.2DB-2.1BC+2.7C 2
TF＝13.9+0.8D+0.2B-1.8C+1.2DB+0.02DC+1.4BC-0.7D 2 -0.4B 2 -1.2C 2
η＝89.6+0.8D-2.6e×10 -3 B-0.4C+0.3DB+0.1DC+0.3BC-0.8D 2 -0.5B 2 -0.6C 2
(1) response value: tav: output average torque (Unit N.m)
TF: torque ripple factor
η: efficiency (%)
(2) Independent variable: d: permanent magnet thickness (Unit mm)
B: magnetic bridge width (Unit mm)
C: polar arc coefficient
Each quantity in the formula 1 is an actual value; the coding values under the two permanent magnet thickness level factors are shown in the formula 2; t (T) max For maximum torque of the motor, T min Is the minimum torque of the motor.
The response surface models obtained through the steps are shown in fig. 2, 3 and 4, wherein the reliability test of the results is shown in fig. 4, and the response surface models have accuracy and reliability as shown in fig. 4.
Step 4: the Taguchi method is used for designing 14 groups of orthogonal tests, and the influence proportion of each variable on the optimization target is calculated through finite element simulation or the result of the test combination, wherein the formula is as follows:
(1) all the result means are calculated: ( The mean is the mean of each optimization objective calculated under 14 sets of orthogonal experiments. Wherein T is used to represent the output torque, for example, the average of the average output torque under 14 sets of orthogonal tests is given by the following formula, and the torque ripple coefficient and the average of the efficiency under 14 sets of orthogonal tests can be obtained respectively )
The calculation results are shown in table 5 below:
table 5 optimization target average
(2) Calculating the average value of the performance indexes under the level values of all parameters:
the calculation results are shown in table 6 below:
TABLE 6 mean values of performance indicators at various parameter levels
(3) Variance calculation for each parameter:
when the variance of the torque is found, S in the formula s Representing an optimization target variance; by usingThe optimization objective of the ith test at the jth permanent magnet thickness level is represented, and m (S) is the average value of the motor optimization objective.
(4) Influence specific gravity of each optimization parameter on the optimization objective:
wherein: as shown in the specific gravity of the influence of the optimization parameters on the optimization target in table 7;
TABLE 7 optimization parameters influencing specific gravity of optimization objective
Step 5: the specific gravity calculated by the response surface equation and the Taguchi method is combined by a weight fusion algorithm, and the process is as follows:
setting variable parameters and objective functions as a number set, and integrating a number model as follows:
wherein x is i Samples representing optimization variables; k is y i The number of updates, k, represents a horizontal value, f when k is 1 k Is along with y i Adding the degree of influence on the specific gravity of the parameter at a level,due to x i The value is changed to make y i A changing measurement function, y i Representing an estimated target value that is updated continuously with the optimization process.
A (Θ) is an estimated objective function; μ is the estimation error, here the error estimation sum function caused by the permanent magnet leakage;
w represents a weight value, which is calculated by a Taguchi method; y is i Is a value which is assumed empirically, because the influence proportion of the optimization parameters on the optimization target is changed by continuously adding a new optimization target f in the optimization process, a formula four pairs of predicted values y are adopted i Updating, and updating the objective function according to a formula V:
wherein t represents the number of added optimization targets f;indicating that y was not updated before the new optimization objective f was not added i A predicted value; psi (f) t ) Updated values of ψ (f) after adding new optimization objectives; when t=1, f t (x i ) Denoted as adding an optimization objective f, f (x i ) Is a new value of (1); />Representing y which has been updated after adding the new optimization objective f i Predicted value, f (x) i ) Is an optimization objective function that is updated continuously with the addition of optimization variables.
And performing second-order Taylor expansion on the obtained product to obtain a formula six:
where λ is a constant obtained by taylor expansion of the fifth equation. u represents the u-th optimization variable, I u Is a set of optimized variable values.
w u ＝f(x i ),i∈I u
Wherein P is the number of optimization variables; g i And h i Respectively a first derivative and a second derivative corresponding to the Taylor formula; let w be u When w is equal, a target optimal solution is obtained, wherein w is as follows * Influence specific gravity of each optimization variable obtained for Taguchi (Tian Koufa) on the optimization target;
converting the multi-objective optimization into a process of solving the optimal value of the independent variable by the known optimal variable, and converting the final optimization result into a constraint relation between optimization target value functions; wherein A represents an optimization objective function, g u The method comprises the steps of estimating corresponding first derivatives in Taylor expansion of an objective function, wherein the estimated objective function is represented by an equation obtained by a response surface method, and P is the number of optimized variables; u represents the u-th optimization variable, I u Is a set of values of the optimized variable, gamma is the influence degree of the optimized variable on each performance of the permanent magnet, and w * For the optimal specific gravity, the optimal specific gravity was calculated using the Taguchi method orthogonal test.
Step 6: the closer the objective function estimate is to the expected objective function value, the smaller the corresponding loss error function. However, when the difference between the two is close to zero, the optimal effect is considered, and the final optimization objective function is solved by utilizing the characteristic by updating the estimation objective function to be close to the final optimization objective function. When min (A-A (Θ)) is satisfied, the ratio of the front coefficient of the parametric quantity of the response surface equation to the total coefficient sum can be respectively brought into an optimization objective equation, so that constraint conditions obtained in the process of adding 6 unknown equation (the unknown equation is respectively three optimization variables and three optimization objectives) into parameterized scanning can be obtained, and the problem can be converted into a simple linear programming problem. Finally, the optimal solution of the three variables and the three responses of the permanent magnet synchronous motor is obtained as shown in the following table 8;
table 8 optimization parameters and optimization objective optimal solutions
Inputting an optimal parameter combination of a motor, and performing torque performance simulation, wherein the torque performance indexes of the motor before and after optimization are compared with those shown in figure 5; for the built-in permanent magnet synchronous motor of 3kW, when the permanent magnet thickness is 5.2mm, the magnetism isolating bridge width is 1.8mm, and the pole arc coefficient is 0.8, the output average torque is 50.81N.m, the torque fluctuation coefficient is 7.89%, the efficiency is 89.53%, and the cogging torque is 1.1227 N.m. Compared with the original motor, the torque average value is increased from 39.39N.m to 50.81N.m, the torque fluctuation coefficient is reduced from original 12.5% to 7.89%, and the efficiency is improved by 3%. And in the error range, the finite element verification result accords with the calculation result, and the reliability and the accuracy of the optimal design scheme are illustrated.
As can be seen from the accompanying drawings 5 and 6, the invention improves the fundamental wave and simultaneously has weakening effects on 3 rd harmonic wave, 5 th harmonic wave and 11 th harmonic wave, and the harmonic wave of the radial air gap flux density is the main source of vibration and noise, so the invention can effectively weaken the vibration and noise of the built-in permanent magnet synchronous motor. The practical value of the combination of the response surface method and Taguchi for multi-objective optimization design is also shown, and a new scheme is provided for the optimization design and research of the permanent magnet synchronous motor in the future.
From the aspect of an optimization algorithm, the method greatly reduces the difficulty of weight fusion by combining a response surface equation and Taguchi specific gravity calculation, saves a large amount of time, fully utilizes the self-contained function of software, provides convenience for multi-objective optimization, and provides a new thought and method for multi-objective optimization of the permanent magnet synchronous motor in the future. The algorithm is verified to be flexible, and can be suitable for various multi-objective optimization occasions. The scheme provides an optimization algorithm combining the two modes in a mathematical mode and is applied to the optimization design of the built-in permanent magnet synchronous motor. The method ensures the higher approximation precision of the response surface method and ensures the efficiency of the Taguchi method in the optimization later period.
The present invention is described herein with reference to particular embodiments, but it is to be understood that these embodiments are merely illustrative of the principles and applications of the present invention. It is therefore to be understood that numerous modifications may be made to the illustrative embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that the different dependent claims and the features described herein may be combined in ways other than as described in the original claims. It is also to be understood that features described in connection with separate embodiments may be used in other described embodiments.
Claims (10)
1. A permanent magnet synchronous motor multi-objective optimization method based on a double-response curved surface method and a Taguchi method is characterized by comprising the following specific steps:
step one, determining an optimization target of a permanent magnet synchronous motor, and selecting three parameters related to the optimization target from rotor optimization parameters of the permanent magnet synchronous motor as optimization variables;
step two, determining the optimal value range of the optimization variable in the step one;
thirdly, constructing a response surface model by using the optimized variable, judging the rationality of the response surface model by using an analysis of variance verification equation, and if the response surface model is unreasonable; executing the fourth step, when the response surface model is reasonable, acquiring a response surface equation, and executing the fifth step;
step four, three parameters are selected from rotor optimization parameters of the permanent magnet synchronous motor again to serve as optimization variables; returning to the execution step II; the three parameters in the step are not identical to the three parameters in the step one;
fifthly, performing an orthogonal test method by using a Taguchi method, and calculating an influence proportion value of an optimization variable on a response value; executing the step six;
step six, fusing the response surface equation and the specific gravity value in the step five through a weight fusion algorithm to obtain a final optimization correction equation;
and step seven, obtaining a linear function relation between the optimization variable and the optimization target by utilizing the property that the difference between the final optimization correction equation and the estimated objective function is close to zero, and obtaining an optimal function value of the optimization target of the permanent magnet synchronous motor by utilizing the optimal value range of the optimization variable determined in the step two as a constraint condition.
2. The multi-objective optimization method for a permanent magnet synchronous motor based on a double-response curved surface method and a Taguchi method according to claim 1, wherein the rotor optimization parameters of the permanent magnet synchronous motor in the step one include: the inner and outer diameters of the rotor, silicon steel sheet materials and the type of magnetic poles on the rotor; the permanent magnet parameters of the built-in motor comprise pole arc coefficient, permanent magnet thickness, permanent magnet width, magnetism isolating bridge width, magnetic steel thickness and permanent magnet materials.
3. The method for optimizing the multiple targets of the permanent magnet synchronous motor based on the double-response surface method and the Taguchi method according to claim 2, wherein the method for constructing the response surface model by using the optimized variables in the step three comprises the steps of constructing by using minitpap software, MATLAB software or Design-Expert software.
4. The multi-objective optimization method for the permanent magnet synchronous motor based on the double-response curved surface method and the Taguchi method according to claim 1, wherein the specific method for obtaining the influence specific gravity value of the optimization variable on the response value by using the Taguchi to perform the orthogonal test method in the fifth step is as follows:
fifthly, sampling each optimized variable, wherein each optimized variable obtains N groups of sampling data, and calculating the average value of the N groups of sampling data of each optimized variable under an orthogonal test; wherein n is a positive integer greater than or equal to 4;
step five, calculating the average value of performance indexes of the three optimized variables under different permanent magnet thickness horizontal values;
step five, calculating the variance of each optimized variable under different permanent magnet thickness level values;
and fifthly, calculating the influence proportion of each optimization parameter on the optimization target.
5. The multi-objective optimization method for the permanent magnet synchronous motor based on the double-response curved surface method and the Taguchi method according to claim 4, wherein the specific method for calculating the average value of n groups of sampling data of each optimization variable in the fifth step under the orthogonal test is as follows:
using the formula:
the average value of n groups of sampling data under the orthogonal test is calculated and obtained, wherein,for the average value of the performance index of an optimization variable, i represents the i-th group of sampling data of the optimization variable, T i Represents the average value of the performance index of the i-th group of sampling data.
6. The multi-objective optimization method for the permanent magnet synchronous motor based on the double-response curved surface method and the Taguchi method according to claim 4, wherein the specific method for calculating the average value of the performance indexes under the different permanent magnet thickness level values of three optimization variables in the fifth step is as follows:
the formula is adopted:
calculating to obtain the average value of the performance index of the thickness level value of the permanent magnet with optimized variable, wherein M T The torque of the optimization factor under the thickness level of the permanent magnet is represented, and T (1), T (2), T (3) and T (4) are the torques in the 1 st, 2 nd, 3 rd and 4 th orthogonal experiments under one thickness level of the permanent magnet respectively.
7. The multi-objective optimization method for permanent magnet synchronous motor based on the double-response curved surface method and the Taguchi method according to claim 6, wherein the specific method for calculating the variance of each optimization variable under different permanent magnet thickness level values in the fifth step is as follows:
when solving for the variance of the torqueS in the formula s Representing an optimization target variance; by usingThe optimization objective of the ith test at the jth permanent magnet thickness level is represented, and m (S) is the average value of the motor optimization objective.
8. The multi-objective optimization method for the permanent magnet synchronous motor based on the double-response curved surface method and the Taguchi method according to claim 7, wherein the specific method for calculating the influence specific gravity of each optimization parameter on the optimization objective in the fifth step is as follows:
z represents the specific gravity of the variance of each optimization objective to the sum of the variances of all optimization objectives.
9. The multi-objective optimization method for the permanent magnet synchronous motor based on the double-response curved surface method and the Taguchi method according to claim 1, wherein the weight fusion algorithm in the step six adopts the formula:
converting the multi-objective optimization into a process of solving the optimal value of the independent variable by the known optimal variable, and converting the final optimization result into a constraint relation between optimization target value functions; wherein A represents an optimization objective function, g u The method comprises the steps of estimating corresponding first derivatives in Taylor expansion of an objective function, wherein the estimated objective function is represented by an equation obtained by a response surface method, and P is the number of optimized variables; u represents the u-th optimization variable, I u Is a set of values of the optimized variable, gamma is the influence degree of the optimized variable on each performance of the permanent magnet, and w * Is the optimal specific gravity.
10. The method for optimizing multiple targets of a permanent magnet synchronous motor based on a double-response surface method and a Taguchi method according to claim 5, wherein the estimated objective function in the step seven is:
wherein a (Θ) is an estimated objective function; x is x i The samples representing the optimization variables, the estimation error μ () is the error estimation sum function caused by the permanent magnet leakage;due to x i The value is changed to make y i A changing measurement function, y i Representing an estimated target value that is updated continuously with the optimization process; k is y i The number of updates, k, represents the permanent magnet thickness level value, f when k is 1 ki Is along with y i The degree of influence on the specific gravity of the parameter when the thickness level of the permanent magnet is 1 is added, ψ (f ki )＝y i +(1/2γ) 2 。/>
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