CN114818166A - Vibration and noise reduction optimization design method for switched reluctance motor - Google Patents
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Abstract
The invention discloses a vibration and noise reduction optimization design method for a switched reluctance motor. The traditional switched reluctance motor design method is single in optimization target, and mostly takes mechanical efficiency as a main optimization target, but in many application scenes, the torque pulsation and vibration behavior of the switched reluctance motor are also key evaluation indexes of the performance of the switched reluctance motor. Stator vibration caused by radial forces of switched reluctance motors is a major source of noise in switched reluctance motors. Especially when the excitation frequency is close to the eigenfrequency of the machine, the vibration amplitude of the switched reluctance machine will increase significantly (i.e. resonate), and therefore the eigenfrequency of the machine should be far from the excitation frequency at the nominal rotational speed. The maximum radial force in the dynamic operation process of the motor is an important index for evaluating the mechanical vibration performance, so that a suitable design optimization method is found in the design optimization stage of the switched reluctance motor, the vibration characteristics of the motor are taken into consideration, and the design method for reducing vibration and noise of the switched reluctance motor is realized, and has important significance.
Description
Technical Field
The invention relates to a vibration reduction and noise reduction optimization design method for a switched reluctance motor, and belongs to the field of motor design.
Background
The switched reluctance motor has very wide application prospect in the standby generator of the power grid due to the characteristics of high robustness, low-cost structure, strong environment adaptability and the like. The traditional switched reluctance motor design method is single in optimization target, and mostly takes efficiency as a main optimization target, but in many application scenes, the torque ripple and the vibration behavior of the switched reluctance motor are also key evaluation indexes of the performance of the switched reluctance motor.
In the mechanical design optimization stage of the switched reluctance motor, the establishment of a detailed three-dimensional structure dynamic model results in large calculation amount and long time consumption, and a single optimization target cannot take the vibration characteristics of the switched reluctance motor into consideration. In high speed applications, to achieve higher efficiency, switched reluctance motors typically operate in single pulse mode, and radial force induced stator vibration is a major source of noise for switched reluctance motors. Especially when the excitation frequency is close to the eigenfrequency of the machine, the vibration amplitude of the switched reluctance machine will increase significantly (i.e. resonate), and therefore the eigenfrequency of the machine should be far from the excitation frequency at the nominal rotational speed. The maximum radial force in the dynamic operation process of the motor is an important index for evaluating the mechanical vibration performance, so that in the design optimization stage of the switched reluctance motor, a suitable design optimization method is found to be of great significance in considering the vibration characteristic of the motor.
Disclosure of Invention
Aiming at the problems that the traditional switched reluctance motor design method consumes long time in calculation and fails to give consideration to the multi-aspect performance of the motor. The invention provides a vibration reduction and noise reduction optimization design method for a switched reluctance motor, which is characterized by firstly establishing a nonparametric model of the switched reluctance motor through Gaussian process regression analysis in order to reduce calculation workload and improve modeling precision, calculating a first-order sensitivity index and a global sensitivity index on the basis of the model to carry out sensitivity analysis on design parameters and determine main optimization parameters. And further taking efficiency improvement and torque ripple and vibration reduction as optimization targets, carrying out multi-objective optimization by a mode search method to obtain a pareto optimal solution set, and selecting an optimal compromise solution from the pareto optimal solution set by applying a compromise decision method. And finally, adjusting design parameters according to the resonance frequency analysis to obtain a design scheme with the optimal comprehensive benefit. The method deeply optimizes the efficiency of the motor, inhibits the torque pulsation of the motor, and reduces the resonance of the motor within the full rotating speed range by adjusting the stator parameters. The technical scheme is as follows:
the method comprises the following steps: and (5) initially selecting motor optimization design parameters and ranges. The geometric design parameters include rotor shaft radius (r) sh ) Outer radius of rotor (r) r ) Stator outer radius (r) s ) Rotor pole arc angle (b) r ) Stator pole arc angle (b) s ) Thickness of rotor yoke (h) ry ) Stator yoke thickness (h) sy ) Width of rotor magnetic pole (w) rp ) Stator pole width (w) sp ) Air gap length (g) and stack length (L) of silicon steel sheets stk ) (ii) a Wherein the parameter r s 、r r And L stk Is a key factor of the power density of the motor, and the variation of +/-5% of the initial value is regarded as an optimization range.
Step two: and (4) carrying out Gaussian process regression analysis to establish a nonparametric model of the switched reluctance motor. The multivariate normal distribution equation of the Gaussian process regression analysis is as follows
Where X represents the training input and y represents the training output, both obtained by finite element simulation. X * Representing the test input, obtained by Latin hypercube sampling, y * Representing a test output; sigma n Is the signal-to-noise variance of y. I is the identity matrix. K. K * 、K * T And K ** Is a covariance matrix;
further, the post-check value is calculated by the formula
Further, the post-average value calculation formula is as follows
And the latter average value can be regarded as a solution of the regression analysis of the Gaussian process, so that a nonparametric model of the switched reluctance motor is obtained.
Step three: modeling error quantization is carried out on the normalized root mean square error, and if the error range is not met, Gaussian regression analysis in the second step is repeated; the normalized root mean square error is the actual value y and the corresponding predicted value y for the N samples * A measure of normalized difference between, which is defined as:
step four: solving a first-order sensitivity index and a global sensitivity index; on the basis of establishing the motor model in the second step, the first-order sensitivity index can be solved as follows
Further, the global sensitivity index can also be obtained by the following formula;
in the formula, S i Denotes the first order sensitivity index, S Ti Representing a global sensitivity index, X i Is the ith input design parameter; x ～i Is except for X i All design parameters except; y meterDisplaying the set motor performance parameters; e Xi (Y|X ～i ) Represents X ～i Assuming an expectation of Y, Var (Y) represents the variance of Y.
Step five: determining main optimization parameters and optimization targets according to the results of the step four, and performing multi-target optimization by using a pattern search algorithm on the basis of the regression analysis modeling of the Gaussian process; firstly, setting related parameters such as initial points, grid size and maximum iteration times of a pattern search algorithm, and generating initial data through Latin hypercube sampling. Secondly, creating grid points based on the generated initial data and grid sizes; then polling all grid points in a mode, replacing the current point and expanding the grid size by two times if the polling is successful, and keeping the current point and reducing the grid size by half if the polling is failed; and when all the modes are successfully polled, ending the mode search algorithm and updating the pareto optimal solution set.
Step six: searching for an optimal compromise solution of the design parameters of the switched reluctance motor by using a compromise decision method; firstly, the pareto set obtained in the fifth step is taken as a decision matrix of J solutions and n objective functions, and an optimal value f is defined according to the decision matrix i * And the worst value f i - (ii) a Group benefit value S i The calculation formula is as follows:
in the formula, omega i Representing the weight of the objective function.
Further, the respective regressions R j Can be calculated from the following formula.
Wherein v is the maximum population policy weight;
further, the compromise value Q of the decision scheme j It can be found that the formula is:
Q i compromise, index Q, representing a decision scheme i Smaller size is preferred. The values of the sequences are sorted in descending order according to the value of S, R, Q. The optimal solution a' should satisfy the following formula at the same time, and is also the optimal solution of S, R;
where a "is the second best (smallest) solution in the ranked list of Q.
Step seven: and calculating the eigenfrequency of the switched reluctance motor. First, the average radius is calculated as:
in the formula, r avg Is the average radius, r s Is the outer diameter of the stator, h sy Is the stator yoke thickness.
Secondly, calculating and considering correction parameters of the stator poles and the windings, wherein the calculation formula is as follows:
the eigenfrequency calculation for the motor at mode 0 is:
in the formula, r avg Is the mean radius, Δ mass The correction term of stator magnetic pole and winding quality is considered, and E is the Young modulus of the stator material;
further, when the vibration mode is greater than 2, the eigenfrequency of the motor is calculated as:
in the formula, n represents a vibration mode.
Step eight: and adjusting the design parameters of the stator by combining vibration analysis. Firstly, based on the calculation result of the seventh eigenfrequency, the critical speed of the switched reluctance motor is calculated as follows:
where k is 3, 6, 9 … at mode 0; at mode 4, 1, 2, 4, 5 …. f is the harmonic frequency of the radial force at the critical speed, N r The number of rotor poles;
further, the expression for adjusting the thickness of the stator yoke based on the critical speed is:
in the formula (f) h Is the harmonic frequency average of the radial force at the critical rotational speed. f. of e The eigenfrequency of the switched reluctance motor in mode 4.
The invention has the advantages of
The invention provides a vibration reduction and noise reduction optimization design method for a switched reluctance motor, which is characterized by firstly establishing a nonparametric model of the switched reluctance motor through Gaussian process regression analysis in order to reduce calculation workload and improve modeling precision, calculating a first-order sensitivity index and a global sensitivity index on the basis of the model to carry out sensitivity analysis on design parameters and determine main optimization parameters. And further taking efficiency improvement and torque ripple and vibration reduction as optimization targets, carrying out multi-objective optimization solution by a mode search method to obtain a pareto optimal solution set, and selecting an optimal compromise solution from the pareto optimal solution set by applying a compromise decision method. Finally, design parameters are analyzed and adjusted according to the resonance frequency so as to obtain a design scheme with the best comprehensive benefit. The effectiveness of the method is verified through experiments. The method provides a global sensitivity analysis method, and key design parameters influencing the performance of the motor are obtained; the optimized design method for vibration reduction and noise reduction of the switched reluctance motor is provided, so that the motor efficiency is improved, and meanwhile, the torque pulsation and the mechanical vibration are reduced.
Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
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The above and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
fig. 1 shows the main design parameters of a switched reluctance motor.
FIG. 2 is a flow chart of a multi-physical field optimization design method for a switched reluctance motor
FIG. 3 is a calculation result of the regression analysis efficiency of the Gaussian process.
Fig. 4 is a calculation result of the gaussian process regression analysis of the torque ripple.
FIG. 5 is a calculation of the maximum radial force of the Gaussian process regression analysis.
FIG. 6 is a set of mechanical properties pareto generated by the pattern search algorithm.
Fig. 7 finds the optimal compromise calculation result of the design parameters of the switched reluctance motor by using a compromise decision method.
FIG. 8 shows the spectrum analysis result of the initial practical scheme of the switched reluctance motor.
Fig. 9 shows a result of a spectrum analysis of the switched reluctance motor after adjusting structural parameters of the stator by vibration analysis.
Detailed Description
The following detailed description of embodiments of the invention is intended to be illustrative, and not to be construed as limiting the invention.
Example the designed motor is a three-phase 12/8 pole switched reluctance motor with a rated speed of 15000 rpm.
The method comprises the following steps: and initially selecting motor optimization design parameters and ranges. GeometryThe design parameters include rotor shaft radius (r) sh ) Outer radius of rotor (r) r ) Stator outer radius (r) s ) Rotor pole arc angle (b) r ) Stator pole arc angle (b) s ) Thickness of rotor yoke (h) ry ) Stator yoke thickness (h) sy ) Width of rotor magnetic pole (w) rp ) Stator pole width (w) sp ) Air gap length (g) and stack length (L) of silicon steel sheets stk ) (ii) a The main design parameters of a switched reluctance machine are shown in fig. 1. Wherein the parameter r s 、r r And L stk Is a key factor of the power density of the motor, and the variation of +/-5% of the initial value is regarded as an optimization range. For high speed motor designs, to ensure high aligned to misaligned position inductance ratios and switched reluctance motor self-starting capability, the rotor to stator pole arc ratio k arc ＝b r /b s The following ranges were maintained: k is more than or equal to 1.0 arc Less than or equal to 1.2. To reduce core loss and minimize vibration considerations for high speed applications, the yoke thickness to pole aspect ratio k s ＝h sy /w sp And k r ＝h ry /w rp The value of (b) should be in the following range: k is more than or equal to 0.6 s ,k r ≤1.4。
Step two: and (4) carrying out Gaussian process regression analysis to establish a nonparametric model of the switched reluctance motor. The flow chart of the switched reluctance motor multi-physical field optimization design method of the high-speed standby generator is shown in fig. 2, a Gaussian process regression analysis multivariate normal distribution equation is shown in a formula (1), a posterior pre-test value calculation formula is shown in a formula (2), a posterior average value is shown in a formula (3), and the posterior average value can be regarded as a solution of the Gaussian process regression analysis;
in the formula, X represents training input, y represents training output, and both are obtained through finite element simulation; x * Representing test input, obtained by Latin hypercube sampling, y * Representing a test output; sigma n A signal-to-noise variance of y; i is an identity matrix; K. k * 、K * T And K ** Is a covariance matrix which is solved by a Gaussian kernel function as shown in formula (4), where K is * ＝K(X,X * )。K ** Is y * Covariance matrix of, K ** ＝K(X * ,X * )；
In the formula, σ f And l is a parameter of the Gaussian kernel function, in combination with the signal-to-noise variance σ of y n Estimating the three parameters by maximizing the edge log-likelihood as shown in formula (5); three parameters can be solved by adopting the maximum value of the edge log likelihood log p (y | X) of the conjugate gradient method.
Step three: modeling error quantization is carried out on the normalized root mean square error, and if the error range is not met, Gaussian regression analysis in the second step is repeated; the normalized root mean square error is the actual value y and the corresponding predicted value y for the N samples * A measure of normalized difference therebetween, which is defined as shown in equation (6).
Step four: solving a first-order sensitivity index and a global sensitivity index; on the basis of establishing the motor model in the second step, a first-order sensitivity index and a global sensitivity index can be further solved, and expressions of the first-order sensitivity index and the global sensitivity index are shown as formulas (7) and (8);
in the formula, S i Denotes the first order sensitivity index, S Ti Representing a global sensitivity index, X i Is the ith input design parameter; x ～i Is except for X i All design parameters except; y represents a set motor performance parameter; e Xi (Y|X ～i ) Represents X ～i Assuming an expectation of Y, Var (Y) represents the variance of Y. The calculation results of the regression analysis efficiency of the gaussian process are shown in fig. 3; the results of the gaussian process regression analysis for torque ripple are shown in fig. 4. The calculation result of the maximum radial force of the gaussian process regression analysis is shown in fig. 5; the calculation result shows that: r is a radical of hydrogen r 、β s 、k arc 、k r 、k s And theta off Has high sensitivity to the mechanical performance of the motor, and g and r s And L stk It is not very sensitive to the mechanical behaviour of the machine.
Step five: determining main optimization parameters and optimization targets according to the results of the step four, and performing multi-target optimization by using a pattern search algorithm on the basis of the regression analysis modeling of the Gaussian process; firstly, setting relevant parameters of a pattern search algorithm, X L ≤x≤X U Wherein: x ═ r r ,β s ,k arc ,k r ,k s ,θ off )，X L Is the lower limit of X, X U Is the upper limit value of x; the optimization objective function is shown as formula (9);
initial data was generated by latin hypercube sampling. Secondly, creating grid points based on the generated initial data and grid sizes; initial data, grid size and number of iterations were set to 300, 0.001 and 50, respectively; then polling all grid points in a mode, replacing the current point and expanding the grid size by two times if the polling is successful, and keeping the current point and reducing the grid size by half if the polling is failed; when all the modes are successfully polled, ending the mode search algorithm and updating the pareto boundary condition; the pattern search algorithm produces a pareto set of mechanical properties as shown in fig. 6.
Step six: and searching for the optimal compromise solution of the design parameters of the switched reluctance motor by using a compromise decision method. Firstly, the pareto set obtained in the fifth step is taken as a decision matrix of J solutions and n objective functions, and an optimal value f is defined according to the decision matrix i * And the worst value f i - (ii) a Then, S is calculated according to the expressions (10), (11) and (12) j 、R j 、Q j The values sorted in descending order according to the value of S, R, Q; the optimal solution a' needs to satisfy equation (13) at the same time, and is also the optimal solution of S, R;
in the formula, S i Denotes the value of the population benefit, R i Indicating individual regret, Q i Compromise, index Q, representing a decision scheme i Smaller the more optimal the solution, omega i Is the weight of the objective function; v is the maximum group policy weight, a "is the second in the ranked list of QAn optimal (minimum) solution; the result of the calculation of the optimal compromise solution of the design parameters of the switched reluctance motor by using the compromise decision method is shown in fig. 7.
Step seven: calculating the eigenfrequency of the switched reluctance motor; firstly, calculating the average radius as shown in the formula (14), and secondly, calculating and considering correction parameters of the stator poles and the windings as shown in the formula (15); the eigenfrequency of the motor in mode 0 is shown in formula (16), and the eigenfrequency of the motor in vibration mode greater than 2 is shown in formula (17);
in the formula, r avg Is the average radius, r s Is the outer diameter of the stator, h sy Is stator yoke thickness, Δ mass Is a correction term that takes into account the stator pole and winding quality, and E is the young's modulus of the stator material.
Step eight: adjusting stator design parameters by combining vibration analysis; firstly, calculating the critical speed of the switched reluctance motor according to the calculation result of the seventh eigenfrequency in the step (18); then, the thickness of the stator yoke is adjusted based on the critical speed as shown in formula (19)
Where k is 3, 6, 9 … at mode 0; 1, 2, 4, 5 … at mode 4; f. of h Is the harmonic frequency average of the radial force at the critical rotational speed. f. of e Is the eigenfrequency of the switched reluctance motor in mode 4;
for a three-phase motor, reducing the excitation frequency in mode 4 can improve the torque ripple and the maximum radial force of the motor; 10000rpm-15000rpm is the speed operation range of the switch reluctance motor of this example, according to the average value f of the excited first harmonic frequency at the rated speed of 15000rpm and the excited second harmonic frequency at 10000rpm h And eigenfrequency f in mode 4 e Correspondingly, the design parameters of the motor are adjusted as follows:
the results of the analysis of the designed vibration spectrum of the switched reluctance motor before and after the design parameters of the stator are adjusted by using vibration analysis are shown in fig. 8 and 9.
Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made in the above embodiments by those of ordinary skill in the art without departing from the principle and spirit of the present invention.
Claims (7)
1. A switched reluctance motor vibration reduction and noise reduction optimization design method is characterized by comprising the following steps: in the design stage of the switched reluctance motor, main design parameters influencing the performance of the motor are obtained by using sensitivity analysis, the optimal compromise solution of the design parameters of the switched reluctance motor is searched by a mode search algorithm and a compromise decision method algorithm, and the design parameters of the motor stator are adjusted according to vibration characteristics. This method not only has efficiency as the primary optimization objective, but also takes into account torque ripple and maximum radial force. The method comprises the following implementation steps:
the method comprises the following steps: primarily selecting motor optimization design parameters and ranges; geometric design parameters ofIncluding the rotor shaft radius (r) sh ) Outer radius of rotor (r) r ) Stator outer radius (r) s ) Rotor pole arc angle (b) r ) Stator pole arc angle (b) s ) Thickness of rotor yoke (h) ry ) Stator yoke thickness (h) sy ) Width of rotor magnetic pole (w) rp ) Stator pole width (w) sp ) Air gap length (g) and stack length (L) of silicon steel sheets stk ) Wherein the parameter r s 、r r And L stk The variation of the initial value +/-5% is regarded as an optimization range;
step two: a non-parameter model of the switched reluctance motor is established through Gaussian process regression analysis; obtaining a posterior pre-test value by using a Gaussian process regression analysis multivariate normal distribution equation, further calculating a posterior average value, and regarding the posterior average value as a solution of the Gaussian process regression analysis, thereby obtaining a non-parametric model of the switched reluctance motor;
step three: modeling error quantization is carried out on the normalized root mean square error, and if the error range is not met, Gaussian regression analysis in the second step is repeated;
step four: solving a first-order sensitivity index and a global sensitivity index; on the basis of establishing the switched reluctance motor model in the second step, a first-order sensitivity index and a global sensitivity index of design parameters to the motor performance can be solved;
step five: determining main optimization parameters and optimization targets according to the results of the step four, and performing multi-target optimization by using a pattern search algorithm on the basis of the regression analysis modeling of the Gaussian process; firstly, setting related parameters such as initial points, grid size and maximum iteration times of a pattern search algorithm, and generating initial data through Latin hypercube sampling; secondly, creating grid points based on the generated initial data and grid sizes; then polling all grid points in a mode, replacing the current point and expanding the grid size by two times if the polling is successful, and keeping the current point and reducing the grid size by half if the polling is failed; when all the modes are successfully polled, ending the mode search algorithm, and updating the pareto optimal solution set;
step six: switched reluctance motor searching by compromise decision methodDesigning a parameter optimization compromise solution; firstly, the pareto set obtained in the fifth step is taken as a decision matrix of J solutions and n objective functions, and an optimal value f is defined according to the decision matrix i * And the worst value f i - (ii) a Respectively calculating group benefit values S j Respective regrettability R j Compromise Q of the summation decision scheme j (ii) a Index value Q i Smaller and better solutions; sorting the values in descending order according to the value of S, R, Q; the optimal solution a' should satisfy the following formula at the same time, and is also the optimal solution of S, R;
where a "is the second best (smallest) solution in the ranked list of Q;
step seven: calculating the eigenfrequency of the switched reluctance motor; first, the average radius r is calculated avg Second calculation takes into account the correction parameters Δ of the stator poles and the windings mass Thus at mode 0 and the eigenfrequency f of the machine 0 And f n Can be obtained by calculation;
step eight: adjusting stator design parameters by combining vibration analysis; firstly, calculating the critical speed n of the switched reluctance motor based on the calculation result of the six eigenfrequencies in the step c The expression for adjusting the thickness of the stator yoke based on the critical speed is:
in the formula (f) h The harmonic frequency average value of the radial force at the critical rotating speed; f. of e The eigenfrequency of the switched reluctance motor in mode 4.
2. The method for optimally designing vibration and noise reduction of the switched reluctance motor according to claim 1, wherein a first-order sensitivity index and a global sensitivity index are calculated and solved through Gaussian process regression analysis to obtain main design parameters influencing the performance of the motor.
3. The switched reluctance motor vibration reduction and noise reduction optimization design method according to claim 1, wherein a normalized root mean square error is calculated, and the magnitude of the error of the switched reluctance motor design parameter sensitivity analysis according to claim 1 is quantitatively analyzed.
4. The switched reluctance motor vibration reduction and noise reduction optimization design method according to claim 1, wherein a pattern search algorithm is used for multi-objective optimization.
5. The switched reluctance motor vibration reduction and noise reduction optimization design method according to claim 1, wherein a compromise decision method is used to find a compromise solution for optimization of the design parameters of the switched reluctance motor.
6. The switched reluctance motor vibration and noise reduction optimization design method according to claim 1, wherein the eigenfrequency of the switched reluctance motor is calculated.
7. The switched reluctance motor vibration damping and noise reduction optimization design method according to claim 1, wherein stator design parameters are adjusted in combination with vibration analysis.
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|---|---|---|---|---|
| CN106202836A (en) * | 2016-08-24 | 2016-12-07 | 江苏大学 | A kind of Optimization Design of piecemeal rotor switched reluctance motor |
| CN109245449A (en) * | 2018-11-12 | 2019-01-18 | 南京工程学院 | A kind of optimum design method of axial phase magnetic levitation switch magnetic resistance fly-wheel motor |
| CN113094911A (en) * | 2021-04-16 | 2021-07-09 | 江苏大学 | High power factor design method for magnetic field modulation permanent magnet fault-tolerant motor |
| WO2021237848A1 (en) * | 2020-05-27 | 2021-12-02 | 江苏大学 | Parametric equivalent magnetic network modeling method for multi-objective optimization of permanent magnet electric motor |
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2022
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| CN106202836A (en) * | 2016-08-24 | 2016-12-07 | 江苏大学 | A kind of Optimization Design of piecemeal rotor switched reluctance motor |
| CN109245449A (en) * | 2018-11-12 | 2019-01-18 | 南京工程学院 | A kind of optimum design method of axial phase magnetic levitation switch magnetic resistance fly-wheel motor |
| WO2021237848A1 (en) * | 2020-05-27 | 2021-12-02 | 江苏大学 | Parametric equivalent magnetic network modeling method for multi-objective optimization of permanent magnet electric motor |
| CN113094911A (en) * | 2021-04-16 | 2021-07-09 | 江苏大学 | High power factor design method for magnetic field modulation permanent magnet fault-tolerant motor |
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