CN110569575A - method for predicting out-of-plane vibration stability of permanent magnet motor rotor - Google Patents
method for predicting out-of-plane vibration stability of permanent magnet motor rotor Download PDFInfo
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Abstract
the invention discloses a method for predicting out-of-plane vibration stability of a permanent magnet motor rotor, which comprises the following steps of: establishing a dynamic model under a follow-up coordinate system; judging the combination relation between the vibration wave number and the number of the permanent magnets by means of the operational property of the trigonometric function, and then calculating the characteristic value of the out-of-plane vibration in a classified manner; obtaining an unstable region transition curve according to the characteristic value of out-of-plane vibration, and proposing the design requirement of the spoke plate; and predicting an instability rule according to the characteristic value. The invention overcomes the defect of the prior elastic vibration analysis technology on the out-of-plane vibration stability analysis, thereby leading the calculation result to better meet the engineering requirement.
Description
Technical Field
the invention relates to the field of elastic vibration calculation, in particular to a technology for predicting out-of-plane vibration stability of a permanent magnet motor rotor.
Background
The rotor structure of the permanent magnet motor is a typical annular periodic structure and is widely applied to various engineering fields, such as: fans and water pumps in industry and agriculture, high-precision servo systems, hard disk drive spindle motors and the like. In actual operation, vibration and noise are often generated, and the stability of operation is affected. The existing vibration suppression method is mostly analyzed from the aspects of vibration source, machining precision and the like, and a group of solutions are obtained through numerical simulation, so that an analysis technology which considers complex actual working conditions and is efficient and accurate is particularly needed to be provided.
the literature (W.Wei, W.Hang, R.K. Hamid. study on the characteristics of electromagnetic noise of axial fluorine permanent magnet synchronous vibration. Abstract and Applied Analysis,2014,1-8) studies the electromagnetic noise of permanent magnet motors due to rotational loads and finds the vibration source. However, the article does not address the stability problem of the system.
the literature (M.Aydin, Z.Q.Zhu, T.A.Lipo, D.Howe.minimization of magnetizing in axial-flux permanent-magnet magnets: design constraints.IEEE Transactions on magnetics,2007,43: 3614-3622) studies the influence of cogging torque on vibration and proposes some lines of ways to reduce cogging torque. However, this document focuses only on the effect of the mechanical structure on the vibrations, and neglects to explore the nature of the vibrations.
in addition, the prior art also generally adopts a numerical method to predict the dynamic stability, and the method has low calculation efficiency and can not reveal the universal rule.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, provides a prediction method for the out-of-plane vibration stability of a permanent magnet motor rotor, and solves the problem that the existing elastic vibration analysis technology is only limited to in-plane vibration, so that the calculation result can better meet the engineering requirement.
the purpose of the invention is realized by the following technical scheme:
A prediction method for out-of-plane vibration stability of a permanent magnet motor rotor comprises the following steps:
(1) Establishing a dynamic model under a follow-up coordinate system;
(2) judging the combination relation between the vibration wave number and the number of the permanent magnets by means of the operational property of the trigonometric function, and then calculating the characteristic value of the out-of-plane vibration in a classified manner;
(3) Obtaining an unstable region transition curve according to the characteristic value of out-of-plane vibration, and proposing the design requirement of the spoke plate;
(4) and predicting an instability rule according to the characteristic value.
further, the dynamic model specifically includes:
wherein, t is a time,Is the position angle, w is the out-of-plane vibration displacement, Ω is the rotation speed, ktFor the centrifugal stiffness operator, krpAnd krsrespectively representing the dynamic and static support stiffness operators, kpRepresenting the magnetic stiffness operator.
Further, the combination relation between the vibration wave number and the number of the permanent magnets is judged by means of the operational property of the trigonometric function, and then the characteristic values of the out-of-plane vibration are calculated in a classified mode, wherein the characteristic equations are respectively as follows:
when 2N/NmWhen int, the characteristic equation is
when 2N/NmNot equal to int, the characteristic equation is
in the formula, NmIs the number of magnetic poles, int is an integer, M is a mass matrix, G is a gyro matrix, KcAnd KuThe stiffness matrices are unaffected and affected by the combinatorial relationship, respectively.
further, the step (3) specifically comprises the following steps:
divergent unstable transition curve:
flutter unstable transition curve:
Thus, the necessary condition for unstable flutter to exist is obtained:
n4+krs-kp＜0
however, the static stability conditions were:
n4+krs-kp＞0
The influence of flutter instability is eliminated by adjusting the thickness of the spoke plate and the like by utilizing the contradiction; in the formula, n is the vibration wave number, and gamma is the included angle of the magnetic poles.
And further, predicting an out-of-plane vibration instability rule according to the divergence instability transition curve and the characteristic value.
compared with the prior art, the technical scheme of the invention has the following beneficial effects:
1. according to the invention, a kinetic equation is established by means of a follow-up coordinate system, and then characteristic equations under different combinations of wave numbers and magnetic pole numbers are obtained according to a trigonometric function relation. Then obtaining an unstable region transition curve according to the characteristic value, proposing a design requirement of a spoke plate, and predicting an unstable rule of the system through a basic vibration theory;
2. The method adopts an analytical method to give a characteristic value of the out-of-plane vibration of the rotor, and judges the dynamic stability of the system according to the characteristic value;
3. Compared with the prior art, the method has the characteristics of high efficiency, accuracy and universality, and can reveal the relationship between parameters and modal characteristics and dynamic stability according to the technology, so that the vibration condition can be estimated in the design stage, particularly the unstable region of each order of vibration is determined, the dynamic design of the rotational symmetry machine is guided, and the operation stability and reliability are improved.
drawings
FIG. 1 is a schematic view of a permanent magnet motor rotor provided in accordance with the present invention;
FIG. 2a is a graph showing the distribution of unstable regions at different gap lengths and spin speeds for a wavenumber of 2;
FIG. 2b is the distribution of unstable regions at different gap lengths and spin speeds for a wavenumber of 3;
FIG. 3a is a three-dimensional instability diagram illustrating a rule of selection for a web design;
FIG. 3b is a front view of a web design selection rule;
FIG. 3c is a side view of a web design selection rule;
FIG. 3d is a top view of a web design selection rule;
FIG. 4a shows the distribution of unstable regions at different remanence and rotation speeds;
FIG. 4b is the distribution of unstable regions under different magnetizing thicknesses and rotation speeds;
FIG. 5a shows the real part of eigenvalue at different parameter combinations for a wavenumber of 2;
FIG. 5b is the real part of eigenvalue at different parameter combinations for a wave number of 3;
FIG. 6a shows the imaginary components of the eigenvalues at different parameter combinations for a wavenumber of 2;
FIG. 6b shows the imaginary components of the eigenvalues at different parameter combinations for a wavenumber of 3.
wherein B isr1＝1.46,Br2＝1,hm1＝0.6×10-3,hm2＝2×10-3；
Detailed Description
The invention is described in further detail below with reference to the figures and specific examples. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The embodiment of the invention provides a technology for predicting the out-of-plane vibration stability of a permanent magnet motor rotor.
The embodiment of the invention can be applied to the fields with wide application to permanent magnet motors and the like, such as fans and water pumps in industry and agriculture, auxiliary equipment in automobile electrical and electronic technology and the like.
the technical scheme of the embodiment of the invention is as follows: a technology for predicting out-of-plane vibration stability of a permanent magnet motor rotor simultaneously considers dynamic stability generated by axial (w) elastic vibration of the motor rotor.
The motor rotor structure consists of an equivalent outer ring, an equivalent spoke plate support and discrete and uniform permanent magnets; the structure is subject to self-rotation; the elastic vibration analysis technology is characterized in that: the dynamic stability analysis prediction of the annular periodic structure is realized by adopting a follow-up coordinate system, and the method specifically comprises the following steps:
(A1) Figure 1 shows the rotation of a permanent magnet motor rotor around a spatial axis and a coordinate system,Is a follow-up coordinate system. The radius, width and thickness of the neutral circle of the outer ring are R, b and h respectively, and the inner diameter and outer diameter of the spoke plate are R respectivelyaand Rbthe Young's modulus is E. Evenly distributing N on the outer ringmAn i (i ═ 1, 2.) represents the i-th magnetic pole, and its position is described by an H (·) function, i.e., a step function, thenAndRespectively the lower edge and the upper edge of the ith magnetic pole, and the lower edge of the first magnetic pole is positioned on the pole axis, and the included angle of the magnetic poles is gamma, so thatAnd
establishing a dynamic model of the annular periodic structure according to the Hamilton principle by means of a follow-up coordinate system:
Wherein, t is a time,Is the position angle, w is the out-of-plane vibration displacement, omega is the rotation speed, ktFor the centrifugal stiffness operator, krpAnd krsRespectively representing the dynamic and static support stiffness operators, kpRepresenting the magnetic stiffness operator.
(A2) further, the combination relation between the vibration wave number and the number of the permanent magnets is judged by means of the operational property of the trigonometric function, and then the characteristic values of the out-of-plane vibration are calculated in a classified mode, wherein the characteristic equations are respectively as follows:
when 2N/Nmwhen int, the characteristic equation is
When 2N/NmNot equal to int, the characteristic equation is
In the formula, NmIs the number of magnetic poles, int is an integer, w is axial vibration displacement, M is a unit mass matrix, G is a sub diagonal gyro matrix, KcAnd KuThe stiffness matrices are unaffected and affected by the combinatorial relationship, respectively. In a gyro matrix
G12＝-G21＝2nΩ (4)
in the formula, n represents the number of vibration waves. For stiffness matrix
in the formula (I), the compound is shown in the specification,
In the formula (I), the compound is shown in the specification,
In the formula, Brand hmRemanence and magnetizing thickness, mu, of permanent magnet0The magnetic permeability of the vacuum is adopted, delta is the length of an air gap between a stator and a rotor,
With respect to the stiffness matrix, it is,
(A3) Solving the characteristic value of the out-of-plane vibration of the rotor of the permanent magnet motor, and setting the form of the characteristic solutions of the formulas (2) and (3)
in the formula, WReAnd WImThe vibration amplitude of the real part and the imaginary part is shown, lambda is a characteristic value, and beta is a phase. To further analyze, the eigenvalues are written as
λ＝λRe+iλIm (13)
In the formula, λReAnd λImAnd (3) substituting the formula (13) into the formula (12) to obtain the real part and the imaginary part of the external vibration characteristic value under different combinations, wherein i is an imaginary unit. From the result of equation (13), an unstable transition curve is obtained, where the divergent unstable transition curve is:
Flutter unstable transition curve:
wherein gamma is a magnetic pole included angle. From the basic vibration theory, if flutter instability exists, equation (15) must be less than 0. By analyzing the elements in the formula, the necessary condition for unstable existence of flutter is obtained:
n4+krs-kp＜0 (16)
However, for the motor, it is necessarily stable at a rotation speed of 0, i.e., at rest, so there is a stationary stable condition:
n4+krs-kp＞0 (17)
Since the expressions (16) and (17) are obviously contradictory, the influence of flutter instability is eliminated by adjusting the thickness of the web or the like by utilizing the contradiction.
(A4) And predicting the unstable vibration law according to the solved characteristic value of the out-of-plane vibration of the permanent magnet motor rotor.
Aiming at the characteristics of the vibration equation, the embodiment of the invention provides a technology for predicting the out-of-plane vibration stability of a permanent magnet motor rotor, which can obtain a characteristic value in an analytic form and predict the dynamic stability according to the characteristic value, and the specific process is as follows:
(B1) Establishing a dynamic model under a follow-up coordinate system;
(B2) Judging the combination relation between the vibration wave number and the number of the permanent magnets by means of the operational property of the trigonometric function, and then calculating the characteristic value of the out-of-plane vibration in a classified manner;
(B3) obtaining an unstable region transition curve according to the characteristic value of out-of-plane vibration, and proposing the design requirement of the spoke plate;
(B4) And predicting an instability rule according to the characteristic value.
the specific steps for the out-of-plane vibration stability prediction considering the permanent magnet motor rotor are as follows:
(C1) Establishing a dynamic equation of the system by means of a follow-up coordinate system;
(C2) Obtaining characteristic equations under different combinations of wave numbers and magnetic pole numbers according to the trigonometric function relationship;
assuming that the characteristic equations of the dynamic equation in the step (C1) are respectively formula (2) and formula (3) under different combinations of wave numbers and magnetic pole numbers, obtaining a transition curve formula (14) and a transition curve formula (15) of an unstable region by solving the characteristic values, and further revealing a vibration instability law according to the imaginary and real parts of the characteristic values.
(C3) Taking the parameters of the cyclic periodic structure in table 1 as an example, the characteristic value is calculated by a numerical method.
TABLE 1 basic parameters of the cyclic periodic Structure
(C4) When the wave number is 2, the characteristic value of the out-of-plane vibration obtained in step (C2) shows the distribution of unstable regions at different air gap lengths and spin speeds, and the specific result is shown in fig. 2 a.
(C5) when the wave number is 3, the characteristic value of the out-of-plane vibration obtained in step (C2) shows the distribution of unstable regions at different air gap lengths and spin speeds, and the specific result is shown in fig. 2 b.
(C6) according to the characteristic value of the out-of-plane vibration, the web design selection rule and the three-dimensional instability map, which are obtained in the step (C2), the specific result is shown in FIG. 3 a.
(C7) The web design selection rules, front view, and results from the out-of-plane vibration characteristic value determined in step (C2) are shown in FIG. 3 b.
(C8) based on the out-of-plane vibration characteristic value determined in step (C2), the web design selection rules, side view, and detailed results are shown in FIG. 3C.
(C9) Based on the out-of-plane vibration characteristic value determined in step (C2), the web design selection rule, top view, and the detailed results are shown in FIG. 3 d.
(C10) according to the characteristic value of the out-of-plane vibration obtained in the step (C2), the distribution of unstable regions under different remanence and rotation speeds is shown in fig. 4 a.
(C11) The distribution of the unstable region at different magnetizing thicknesses and rotation speeds according to the characteristic value of the out-of-plane vibration obtained in step (C2) is shown in fig. 4 b.
(C12) When the eigenvalue of the out-of-plane vibration calculated in step (C2) is the wave number of 2, the real parts of the eigenvalue under different parameter combinations, and the specific result is shown in fig. 5 a.
(C13) When the eigenvalue of the out-of-plane vibration calculated in step (C2) is wave number 3, the real parts of the eigenvalue under different parameter combinations, and the specific result is shown in fig. 5 b.
(C14) when the wave number is 2, the characteristic value of the out-of-plane vibration obtained in step (C2) is the imaginary part of the characteristic value under different parameter combinations, and the specific result is shown in fig. 6 a.
(C15) When the wave number is 3, the characteristic value of the out-of-plane vibration obtained in step (C2) is the imaginary part of the characteristic value under different parameter combinations, and the specific result is shown in fig. 6 b.
in conclusion, the invention provides a prediction technology for out-of-plane vibration stability of a permanent magnet motor rotor. The technology uses a follow-up coordinate system and adopts an analytic method to obtain the characteristic value of the system, so that the accuracy, the calculation efficiency and the universality are improved, and the actual requirements of the engineering are better met.
those skilled in the art will appreciate that the drawings are only schematic illustrations of preferred embodiments, and the above-described embodiments of the present invention are merely provided for description and do not represent the merits of the embodiments.
The present invention is not limited to the above-described embodiments. The foregoing description of the specific embodiments is intended to describe and illustrate the technical solutions of the present invention, and the above specific embodiments are merely illustrative and not restrictive. Those skilled in the art can make many changes and modifications to the invention without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (5)
1. A prediction method for out-of-plane vibration stability of a permanent magnet motor rotor is characterized by comprising the following steps:
(1) Establishing a dynamic model under a follow-up coordinate system;
(2) Judging the combination relation between the vibration wave number and the number of the permanent magnets by means of the operational property of the trigonometric function, and then calculating the characteristic value of the out-of-plane vibration in a classified manner;
(3) Obtaining an unstable region transition curve according to the characteristic value of out-of-plane vibration, and proposing the design requirement of the spoke plate;
(4) And predicting an instability rule according to the characteristic value.
2. The method for predicting the out-of-plane vibration stability of the rotor of the permanent magnet motor according to claim 1, wherein the dynamic model specifically comprises:
Wherein, t is a time,Is the position angle, w is the out-of-plane vibration displacement, Ω is the rotation speed, ktFor the centrifugal stiffness operator, krpand krsRespectively representing the dynamic and static support stiffness operators, kprepresenting the magnetic stiffness operator.
3. The method for predicting the out-of-plane vibration stability of the permanent magnet motor rotor according to claim 1, wherein the combination relationship between the vibration wave number and the number of the permanent magnets is judged according to the operational property of a trigonometric function, and then the characteristic values of the out-of-plane vibration are calculated in a classified manner, wherein the characteristic equations are respectively as follows:
When 2N/Nmwhen int, the characteristic equation is
when 2N/Nmnot equal to int, the characteristic equation is
In the formula, Nmis the number of magnetic poles, int is an integer, M is a mass matrix, G is a gyro matrix, KcAnd KuThe stiffness matrices are unaffected and affected by the combinatorial relationship, respectively.
4. the method for predicting the out-of-plane vibration stability of the rotor of the permanent magnet motor according to claim 1, wherein the step (3) specifically comprises the following steps:
divergent unstable transition curve:
flutter unstable transition curve:
Thus, the necessary condition for unstable flutter to exist is obtained:
n4+krs-kp＜0
However, the static stability conditions were:
n4+krs-kp＞0
The influence of flutter instability is eliminated by adjusting the thickness of the spoke plate and the like by utilizing the contradiction; in the formula, n is the vibration wave number, and gamma is the included angle of the magnetic poles.
5. The method for predicting the out-of-plane vibration stability of the rotor of the permanent magnet motor according to claim 4, wherein the out-of-plane vibration instability law is predicted according to a divergence instability transition curve and a characteristic value.
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