CN114818166B - 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 design method of the switch reluctance motor has single optimization target and mostly uses mechanical efficiency as a main optimization target, but in various application scenes, the torque pulsation and vibration behaviors of the switch reluctance motor are also key evaluation indexes of the performance of the switch reluctance motor. Stator vibration caused by radial forces of a switched reluctance motor is a major source of noise in a switched reluctance motor. In particular, when the excitation frequency approaches the eigenfrequency of the motor, the vibration amplitude of the switched reluctance motor will increase significantly (i.e. resonate), so that the eigenfrequency of the motor should be far from the excitation frequency at the rated rotational speed. The maximum radial force in the dynamic running 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 proper design optimization method is found, the vibration characteristics of the motor are taken into consideration, and the vibration reduction and noise reduction design method of the switched reluctance motor is realized, so that the method has important significance.
Description
Technical Field
The invention relates to a vibration and noise reduction optimization design method for a switched reluctance motor, and belongs to the field of motor design.
Background
The switch reluctance motor has very wide application prospect in the power grid standby generator due to the characteristics of high robustness, low cost structure, strong environment adaptability and the like. The traditional design method of the switch reluctance motor is single in optimization target and mostly takes efficiency as a main optimization target, but in various application scenes, the torque pulsation and vibration behaviors of the switch reluctance motor are also key evaluation indexes of the performance of the switch reluctance motor.
In the mechanical design optimization stage of the switch reluctance motor, a detailed three-dimensional structure dynamics model is established, so that the calculation amount is large, the time consumption is long, and the vibration characteristics of the switch reluctance motor cannot be considered by a single optimization target. In a high-speed application scenario, to achieve higher efficiency, the switched reluctance motor is usually operated in a single pulse mode, and stator vibration caused by radial force is a main source of noise of the switched reluctance motor. In particular, when the excitation frequency approaches the eigenfrequency of the motor, the vibration amplitude of the switched reluctance motor will increase significantly (i.e. resonate), so that the eigenfrequency of the motor should be far from the excitation frequency at the rated rotational speed. The maximum radial force in the dynamic running 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, the search of a proper design optimization method takes the vibration characteristic of the motor into consideration, and the method has important significance.
Disclosure of Invention
Aiming at the problems of long calculation time consumption and incapacitation of considering the performance of the motor in multiple aspects existing in the traditional design method of the switch reluctance motor. The invention provides a vibration and noise reduction optimization design method of a switched reluctance motor, which aims at reducing the calculation workload and improving the modeling precision, firstly establishes a non-parametric model of the switched reluctance motor through Gaussian process regression analysis, calculates a first-order sensitivity index and a global sensitivity index on the basis of the non-parametric model to carry out sensitivity analysis on design parameters and determine main optimization parameters. And further taking the improvement of efficiency, the reduction of torque pulsation and vibration as optimization targets, carrying out multi-target optimization through a mode search method to solve the pareto optimal solution set, and selecting an optimal compromise solution from the pareto set by using a compromise decision method. Finally, the design parameters are adjusted according to the resonance frequency analysis to obtain the design scheme with the best comprehensive benefit. The method deeply optimizes the motor efficiency, suppresses motor torque pulsation, and reduces motor resonance in the full rotation speed range by adjusting stator parameters. The technical proposal is as follows:
step one: and optimizing design parameters and range of the primary motor. The geometric design parameters mainly include rotor shaft radius (r sh ) Rotor outer radius (r) r ) Outer radius of stator (r) s ) Polar arc angle of rotor (b) r ) Polar arc angle of stator (b) s ) Rotor yoke thickness (h ry ) Stator yoke thickness (h) sy ) Rotor pole width (w) rp ) Stator pole width (w) sp ) Air gap length (g) and stacking length (L) of silicon steel sheets stk ) The method comprises the steps of carrying out a first treatment on the surface of the Wherein the parameter r s 、r r And L stk Is a key factor of the motor power density, and the change of + -5% of the initial value is regarded as an optimization range.
Step two: and establishing a non-parametric model of the switched reluctance motor through Gaussian process regression analysis. The regression analysis of Gaussian process is carried out on the multivariate normal distribution equation as follows
Where X represents the training input and y represents the training output, both obtained by finite element simulation. X is X * Representing the test input, obtained by Latin hypercube sampling, y * Representing a test output; sigma (sigma) n Is the signal noise variance of y. I is the identity matrix. K. K (K) * 、K * T K is as follows ** Is covariance matrix;
further, the posterior pre-test value calculation formula is as follows
Further, the post-average calculation formula is as follows
The post average value can be regarded as a solution of Gaussian process regression analysis, so that a non-parametric model of the switched reluctance motor is obtained.
Step three: carrying out modeling error quantification on the normalized root mean square error, and repeating the Gaussian regression analysis of the second step if the error range is not met; the normalized root mean square error is the actual value y for N samples and the corresponding pre-determinedMeasurement value y * A measure of normalized difference between, 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;
wherein S is i Represents a first-order sensitivity index, S Ti Represents a global sensitivity index, X i Is the ith input design parameter; x is X ～i Is to divide X i All design parameters except; y represents the set motor performance parameters; e (E) Xi (Y|X ～i ) X represents ～i Taking the expectation of Y under the condition, var (Y) represents the variance of Y.
Step five: determining main optimization parameters and optimization targets according to the result of the step four, and performing multi-target optimization by using a mode search algorithm on the basis of Gaussian process regression analysis modeling; firstly, setting related parameters such as initial point number, grid size and maximum iteration number of a mode search algorithm, and generating initial data through Latin hypercube sampling. Secondly, creating grid points based on the generated initial data and the grid size; then, all grid points are polled in one mode, the current point is replaced if the polling is successful, the grid size is doubled, the current point is kept and the grid size is reduced by half if the polling is failed; and when all modes are successfully polled, ending the mode searching 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, taking the pareto set obtained in the fifth step as decision matrixes of J solutions and n objective functions, and defining an optimal value f according to the decision matrixes i * And the worst value f i - The method comprises the steps of carrying out a first treatment on the surface of the Group benefit value S i The calculation formula is as follows:
wherein omega is i Representing the weights of the objective functions.
Further, individual regrettability R j Can be calculated by the following formula.
Wherein v is the maximum population policy weight;
further, the compromise value Q of the decision scheme j The formula can be obtained as:
Q i index value Q representing compromise value of decision scheme i Smaller schemes are more preferred. The values of the solutions are arranged in descending order according to the value of S, R, Q. The optimal solution a' needs to simultaneously satisfy the following formula 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. The calculation formula of the average radius is as follows:
wherein r is avg Is the average radius, r s Is the outer diameter of the stator, h sy Is the stator yoke thickness.
Secondly, calculating correction parameters considering stator poles and windings, wherein the calculation formula is as follows:
the eigenfrequency calculation formula of the motor at mode 0 is:
wherein r is avg Is the average radius, delta mass Is a correction term considering stator pole and winding quality, E is Young's modulus of the stator material;
further, the calculation formula of the eigenfrequency of the motor when the vibration mode is greater than 2 is:
where n represents a vibration mode.
Step eight: and adjusting stator design parameters in combination with vibration analysis. Firstly, based on the calculation result of the seven eigenfrequencies, calculating the critical speed of the switched reluctance motor as follows:
wherein k is 3, 6, 9 and … at mode 0; 1, 2, 4, 5, … under mode 4. f is the harmonic frequency of radial force at critical rotation speed, N r The number of poles of the rotor;
further, the expression for adjusting the thickness of the stator yoke based on the critical speed is:
wherein f h Is the harmonic frequency average of the radial force at the critical rotational speed. f (f) e Is the eigenfrequency of the switched reluctance motor in mode 4.
The beneficial effects of the invention are that
The invention provides a vibration and noise reduction optimization design method of a switched reluctance motor, which aims at reducing the calculation workload and improving the modeling precision, firstly establishes a non-parametric model of the switched reluctance motor through Gaussian process regression analysis, calculates a first-order sensitivity index and a global sensitivity index on the basis of the non-parametric model to carry out sensitivity analysis on design parameters and determine main optimization parameters. And further taking the improvement of efficiency, the reduction of torque pulsation and vibration as optimization targets, carrying out multi-target optimization through a mode search method to solve the pareto optimal solution set, and selecting an optimal compromise solution from the pareto set by using a compromise decision method. Finally, the design parameters are adjusted according to the resonance frequency analysis to obtain the design scheme with the best comprehensive benefit. The effectiveness of the method was verified experimentally. The method provides a global sensitivity analysis method, and key design parameters affecting the performance of the motor are obtained; the vibration damping and noise reducing optimization design method for the switched reluctance motor has the advantages that the torque pulsation and mechanical vibration are reduced while the motor efficiency is improved.
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 foregoing and/or additional aspects and advantages of the invention will become apparent and may be better understood from the following description of embodiments taken in conjunction with the accompanying drawings in which:
fig. 1 is a diagram of the main design parameters of a switched reluctance motor.
FIG. 2 is a flow chart of a method for optimizing the design of multiple physical fields of a switched reluctance motor
Fig. 3 is a calculation result of the regression analysis efficiency of the gaussian process.
Fig. 4 is a calculation of torque ripple from a gaussian process regression analysis.
Fig. 5 is a calculation of maximum radial force from a gaussian process regression analysis.
Fig. 6 is a set of mechanical properties pareto produced by the pattern search algorithm.
FIG. 7 is a compromise decision method for finding the optimal compromise calculation result of the design parameters of the switched reluctance motor.
Fig. 8 is a spectral analysis result of an initial practical solution of the switched reluctance motor.
Fig. 9 shows the result of spectral analysis of the switched reluctance motor after adjusting the stator structural parameters using vibration analysis.
Detailed Description
The following detailed description of embodiments of the invention is exemplary and intended to be illustrative of the invention and not to be construed as limiting the invention.
The example motor is designed as a three-phase 12/8 pole switched reluctance motor rated at 15000 rpm.
Step one: and optimizing design parameters and range of the primary motor. The geometric design parameters mainly include rotor shaft radius (r sh ) Rotor outer radius (r) r ) Outer radius of stator (r) s ) Polar arc angle of rotor (b) r ) Polar arc angle of stator (b) s ) Rotor yoke thickness (h ry ) Stator yoke thickness (h) sy ) Rotor pole width (w) rp ) Stator pole width (w) sp ) Air gap length (g) and stacking length (L) of silicon steel sheets stk ) The method comprises the steps of carrying out a first treatment on the surface of the The main design parameters of the switched reluctance motor are shown in fig. 1. Wherein the parameter r s 、r r And L stk Is a key factor of the motor power density, and the change of + -5% of the initial value is regarded as an optimization range. For high speed motor design, to ensure high aligned to unaligned position inductance ratio and switched reluctance motor self-starting capability, rotor to stator pole-to-arc ratio k arc ＝b r /b s Remain within the following ranges: k is more than or equal to 1.0 arc Less than or equal to 1.2. To reduce high-speed applicationYoke thickness to pole width ratio k for iron loss and vibration minimization s ＝h sy /w sp And k r ＝h ry /w rp The values of (2) should be within the following ranges: k is more than or equal to 0.6 s ,k r ≤1.4。
Step two: and establishing a non-parametric model of the switched reluctance motor through Gaussian process regression analysis. The flow chart of the multi-physical field optimization design method of the switch reluctance motor of the high-speed standby generator is shown in fig. 2, a Gaussian process regression analysis multi-element normal distribution equation is shown in a formula (1), a post pre-verification value calculation formula is shown in a formula (2), a post-average value is shown in a formula (3), and the post-average value can be regarded as a solution of the Gaussian process regression analysis;
wherein X represents training input and y represents training output, and the training input and the training output are obtained through finite element simulation; x is X * Representing test input, obtained from Latin hypercube samples, y * Representing a test output; sigma (sigma) n Is the signal noise variance of y; i is an identity matrix; K. k (K) * 、K * T K is as follows ** As the covariance matrix, the covariance matrix is solved by a Gaussian kernel function as shown in formula (4), where K * ＝K(X,X * )。K ** Is y * Covariance matrix, K ** ＝K(X * ,X * )；
In sigma f And l is Gaussian kernelDigital parameters, signal noise variance sigma of joint y n Three parameters are estimated by maximizing edge log likelihood as shown in equation (5); the three parameters can be solved by adopting the maximum value of the conjugate gradient technique edge log likelihood log p (y|X).
Step three: carrying out modeling error quantification on the normalized root mean square error, and repeating the Gaussian regression analysis of the second step if the error range is not met; the normalized root mean square error is the actual value y and the corresponding predicted value y for N samples * A measure of the normalized difference between them 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, the first-order sensitivity index and the global sensitivity index can be further solved, and the expressions are shown in formulas (7) and (8);
wherein S is i Represents a first-order sensitivity index, S Ti Represents a global sensitivity index, X i Is the ith input design parameter; x is X ～i Is to divide X i All design parameters except; y represents the set motor performance parameters; e (E) Xi (Y|X ～i ) X represents ～i Taking the expectation of Y under the condition, var (Y) represents the variance of Y. The calculation result of the regression analysis efficiency of the Gaussian process is shown in FIG. 3; regression analysis of torque ripple by gaussian processThe calculation result of (2) is shown in fig. 4. The calculation result of the maximum radial force of the regression analysis of the Gaussian process is shown in FIG. 5; the calculation result shows that: r is (r) r 、β s 、k arc 、k r 、k s θ off Has high sensitivity to the mechanical performance of the motor, and g and r s L and stk the sensitivity to the mechanical properties of the motor is not high.
Step five: determining main optimization parameters and optimization targets according to the result of the step four, and performing multi-target optimization by using a mode search algorithm on the basis of Gaussian process regression analysis modeling; firstly, setting related parameters of a mode searching algorithm, X L ≤x≤X U Wherein: x= (r r ,β s ,k arc ,k r ,k s ,θ off )，X L X is lower limit value of X U An upper limit value of x; the optimization objective function is shown as a formula (9);
initial data is generated by Latin hypercube sampling. Secondly, creating grid points based on the generated initial data and the grid size; the initial data, the mesh size and the number of iterations are set to 300, 0.001 and 50, respectively; then, all grid points are polled in one mode, the current point is replaced if the polling is successful, the grid size is doubled, the current point is kept and the grid size is reduced by half if the polling is failed; when all modes are successfully polled, ending the mode searching algorithm and updating the pareto boundary conditions; the set of mechanical properties pareto produced by the pattern search algorithm is shown in fig. 6.
Step six: and searching the optimal compromise of the design parameters of the switched reluctance motor by using a compromise decision method. Firstly, taking the pareto set obtained in the fifth step as decision matrixes of J solutions and n objective functions, and defining an optimal value f according to the decision matrixes i * And the worst value f i - The method comprises the steps of carrying out a first treatment on the surface of the S is then calculated according to equations (10), (11) and (12), respectively j 、R j 、Q j According to the value of S, R, QThe values of the solutions are arranged in descending order of values; the optimal solution a' needs to simultaneously satisfy the formula (13) and is also the optimal solution of S, R;
wherein S is i Represents the group benefit value, R i Representing individual regrets, Q i Index value Q representing compromise value of decision scheme i Smaller schemes are more optimal, ω i The weights of the objective functions; v is the maximum group policy weight, a "is the second best (smallest) solution in the ranked list of Q; the best compromise calculation result of searching 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 an average radius as shown in a formula (14), and secondly, calculating correction parameters considering stator poles and windings as shown in a formula (15); the eigenfrequency of the motor in mode 0 is shown as formula (16), and when the vibration mode is greater than 2, the eigenfrequency of the motor is shown as formula (17);
wherein r is avg Is the average radius, r s Is the outer diameter of the stator, h sy Is the thickness of the stator yoke, delta mass Is a correction term that considers stator pole and winding quality, and E is the young's modulus of the stator material.
Step eight: adjusting stator design parameters in combination with vibration analysis; firstly, calculating the critical speed of the switched reluctance motor as shown in a formula (18) based on the calculation result of the seven eigenfrequencies; then, the thickness of the stator yoke is adjusted based on the critical speed as shown in (19)
Wherein k is 3, 6, 9 and … at mode 0; 1, 2, 4, 5, … under mode 4; f (f) h Is the harmonic frequency average of the radial force at the critical rotational speed. f (f) e The eigenfrequency of the switched reluctance motor in mode 4;
for a three-phase motor, reducing the excitation frequency at mode 4 can improve the torque ripple and maximum radial force of the motor; 10000rpm-15000rpm is the speed operation range of the power generation application of the switched reluctance motor, and is based on the average value f of the excited first harmonic frequency at the rated rotation speed of 15000rpm and the excited second harmonic frequency at 10000rpm h And eigenfrequency f at mode 4 e The motor design parameters are adjusted accordingly:the results of the vibration spectrum analysis of the switch reluctance motor design before and after the stator design parameters are adjusted by vibration analysis are shown in fig. 8 and 9.
Although embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and not to be construed as limiting the invention, and that variations, modifications, alternatives, and variations may be made in the above embodiments by those skilled in the art without departing from the spirit and principles of the invention.
Claims (7)
1. A vibration and noise reduction optimization design method for a switched reluctance motor is characterized by comprising the following steps of: in the design stage of the switch reluctance motor, main design parameters affecting the motor performance are obtained by utilizing sensitivity analysis, the optimal compromise solution of the design parameters of the switch reluctance motor is searched by a mode searching algorithm and a compromise decision method algorithm, and the design parameters of a motor stator are adjusted according to vibration characteristics; the method comprises the following implementation steps:
step one: optimizing design parameters and range of the primary motor; the geometric design parameters mainly include rotor shaft radius (r sh ) Rotor outer radius (r) r ) Outer radius of stator (r) s ) Polar arc angle of rotor (b) r ) Polar arc angle of stator (b) s ) Rotor yoke thickness (h ry ) Stator yoke thickness (h) sy ) Rotor pole width (w) rp ) Stator pole width (w) sp ) Air gap length (g) and stacking length (L) of silicon steel sheets stk ) Wherein the parameter r s 、r r And L stk Is a key factor of the power density of the motor, and takes the change of +/-5% of an initial value as an optimization range;
step two: establishing a non-parametric model of the switched reluctance motor through Gaussian process regression analysis; obtaining a posterior pre-verification value by regression analysis of a multi-element normal distribution equation through a Gaussian process, further calculating a posterior average value, and considering the posterior average value as a solution of the regression analysis of the Gaussian process, thereby obtaining a non-parametric model of the switched reluctance motor;
step three: carrying out modeling error quantification on the normalized root mean square error, and repeating the Gaussian regression analysis of the second step if the error range is not met;
step four: solving a first-order sensitivity index and a global sensitivity index; on the basis of establishing a switched reluctance motor model, a first-order sensitivity index and a global sensitivity index of design parameters to motor performance can be solved;
step five: determining main optimization parameters and optimization targets according to the result of the step four, and performing multi-target optimization by using a mode search algorithm on the basis of Gaussian process regression analysis modeling; firstly, setting related parameters such as initial point number, grid size, maximum iteration number and the like of a mode search algorithm, and generating initial data through Latin hypercube sampling; secondly, creating grid points based on the generated initial data and the grid size; then, all grid points are polled in one mode, the current point is replaced if the polling is successful, the grid size is doubled, the current point is kept and the grid size is reduced by half if the polling is failed; when all modes are successfully polled, ending the mode searching 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, taking the pareto set obtained in the fifth step as decision matrixes of J solutions and n objective functions, and defining an optimal value f according to the decision matrixes i * And the worst value f i - The method comprises the steps of carrying out a first treatment on the surface of the Respectively calculating group benefit value S j Individual regrettably R j Compromise value Q of counting and decision scheme j The method comprises the steps of carrying out a first treatment on the surface of the Index value Q i The smaller the scheme the better; the values of the solutions are arranged in descending order according to the value of S, R, Q; the optimal solution a' needs to simultaneously satisfy the following formula 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: computing intrinsic properties of a switched reluctance motorA frequency; first, the average radius r is calculated avg Secondly, calculating correction parameters delta considering stator poles and windings mass Then at mode 0 and the eigenfrequency f of the lower motor 0 And f n Can be calculated;
step eight: adjusting stator design parameters in combination with vibration analysis; firstly, calculating the critical speed n of the switched reluctance motor based on the calculation result of the step six eigenfrequency c The expression for adjusting the thickness of the stator yoke based on the critical speed is:
wherein f h Is the harmonic frequency average value of radial force at the critical rotation speed; f (f) e Is the eigenfrequency of the switched reluctance motor in mode 4.
2. The method for optimizing vibration and noise reduction of a switched reluctance motor according to claim 1, wherein the first-order sensitivity index and the global sensitivity index are calculated and solved by a gaussian process regression analysis to obtain main design parameters affecting motor performance.
3. The optimization design method for vibration and noise reduction of the switched reluctance motor according to claim 1, wherein normalized root mean square errors are calculated, and the sensitivity analysis error of the design parameters of the switched reluctance motor according to claim 1 is quantitatively analyzed.
4. The method for optimizing vibration and noise reduction of a switched reluctance motor according to claim 1, wherein the method is characterized in that a mode search algorithm is used for multi-objective optimization.
5. The method for optimizing vibration and noise reduction of a switched reluctance motor according to claim 1, wherein a compromise decision method is used to find an optimal compromise of the design parameters of the switched reluctance motor.
6. The optimized design method for vibration and noise reduction of the switched reluctance motor according to claim 1, wherein the eigenfrequency of the switched reluctance motor is calculated.
7. The optimized design method for vibration and noise reduction of a switched reluctance motor according to claim 1, wherein stator design parameters are adjusted in combination with vibration analysis.
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| 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 |
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