CN110569574A - Method for improving rotor out-of-plane vibration stability by sinusoidal magnetic pole of permanent magnet motor - Google Patents
Method for improving rotor out-of-plane vibration stability by sinusoidal magnetic pole of permanent magnet motor Download PDFInfo
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Abstract
The invention discloses a method for improving the out-of-plane vibration stability of a rotor by a sinusoidal magnetic pole of a permanent magnet motor, which comprises the following steps: respectively establishing a dynamic model of a sinusoidal magnetic pole and a uniform magnetic pole in 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 calculating the characteristic equation of the out-of-plane vibration in a classified manner; and calculating a characteristic value according to a characteristic equation to obtain an unstable region. The invention provides a method for improving the stability of a common uniform magnetic pole, so that the designed permanent magnet motor can better meet the engineering requirements.
Description
Technical Field
The invention relates to the field of vibration suppression, in particular to a technology for improving stability of out-of-plane vibration of a permanent magnet motor rotor.
background
In various engineering fields, for example: 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 vibration and noise of the motor mainly originate from electromagnetic vibration, and at present, the stability of the motor is mainly improved by optimizing the opening width, optimizing the pole arc coefficient and the like, but the methods have the situations of examples and special cases, so that a technology which is generally applicable and is used for improving the stability is particularly needed.
Document (y.b. yang, x.h. wang, c.q. zhu.reducing coupling Torque by adapting equal diameter Permanent magnet. ieee reference on Industrial Electronics & applications, ieee, 2009) reduces Cogging Torque by introducing equal diameter magnetic poles and is validated by finite elements. However, the method proposed by the authors is only directed to a single example and does not reveal the general rule.
in the literature (n.r. tavana, a.shoula.pole-shape optimization of permanent-magnet linear synchronous motor for reduction of ripple. energy conversion & Management,2011,52(1):349-354.), circular arc-shaped magnetic poles are designed so as to reduce the influence of ripple, and then the correctness of the research is verified through a finite element method. However, the arc-shaped magnetic pole designed by the document has a complex structure and is difficult to machine.
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 method for improving the stability of the out-of-plane vibration of a rotor by a sinusoidal magnetic pole of a permanent magnet motor, and solves the defect that the out-of-plane vibration of the rotor is unstable, so that the designed rotor can better meet the engineering requirements, and the details are described as follows:
The purpose of the invention is realized by the following technical scheme:
A method for improving out-of-plane vibration stability of a rotor by a sinusoidal magnetic pole of a permanent magnet motor comprises the following steps:
(1) Respectively establishing a dynamic model of a sinusoidal magnetic pole and a uniform magnetic pole in 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 calculating the characteristic equation of the out-of-plane vibration in a classified manner;
(3) And calculating a characteristic value according to a characteristic equation to obtain an unstable region.
Further, the dynamic model specifically includes:
Wherein Ω is the rotation speed, ktFor the centrifugal stiffness operator, krpand krsRespectively representing the dynamic and static support stiffness operators, kpRepresenting a magnetic stiffness operator; the sinusoidal magnetic pole and the uniform magnetic pole are different in magnetic rigidity 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 the characteristic equations of the out-of-plane vibration are calculated in a classified mode, wherein the characteristic equations are as follows:
When 2N/NmWhen int, the characteristic equation is
When 2N/NmNot equal to int, the characteristic equation is
Wherein N is the number of vibration waves, NmIs the number of magnetic poles, int is an integer, w is out-of-plane vibration displacement, M is a mass matrix, G is a gyro matrix, KcAnd Kuthe stiffness matrices are unaffected and affected by the combinatorial relationship, respectively.
Further, calculating a characteristic value according to a characteristic equation to obtain an unstable region; the effect of the sine magnetic pole on improving the stability can be judged according to the unstable region image.
Compared with the prior art, the technical scheme of the invention has the following beneficial effects:
1. according to the invention, firstly, a sinusoidal magnetic pole dynamic equation and a uniform magnetic pole dynamic equation are respectively 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 relationship. Then calculating a characteristic value according to a characteristic equation to obtain an unstable region;
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, can reveal the relationship between parameters and modal characteristics and dynamic stability according to the technology, and provides a technology for improving the out-of-plane vibration stability of the rotor by changing the shape of a magnetic pole, thereby guiding the dynamic design of a rotational symmetry machine and improving the operation stability and reliability.
Drawings
Fig. 1 is a schematic view of a sinusoidal magnetic pole rotor of a permanent magnet motor according to the present invention;
FIG. 2a is the distribution of unstable regions of sinusoidal magnetic poles under different rotation speeds and remanence when the vibration wave number is 2;
FIG. 2b is the distribution of unstable regions of sinusoidal magnetic poles under different rotation speeds and remanence when the vibration wave number is 3;
FIG. 3a is the distribution of unstable regions of uniform magnetic poles at different rotation speeds and remanence when the vibration wave number is 2;
FIG. 3b is the distribution of unstable regions of the uniform magnetic poles at different rotational speeds and remanence when the vibration wave number is 3;
FIG. 4a is the distribution of unstable regions of sinusoidal magnetic poles under different rotation speeds and magnetizing thicknesses when the vibration wave number is 2;
FIG. 4b is the distribution of unstable regions of sinusoidal magnetic poles under different rotation speeds and magnetizing thicknesses when the vibration wave number is 3;
FIG. 5a is the distribution of unstable regions of uniform magnetic poles at different rotation speeds and magnetizing thicknesses when the vibration wave number is 2;
FIG. 5b is the distribution of unstable regions of the uniform magnetic poles at different rotation speeds and magnetizing thicknesses when the vibration wave number is 3;
FIG. 6a is the distribution of unstable regions under different rotation speeds of sinusoidal magnetic poles and included angles of the magnetic poles when the number of vibration waves is 2;
FIG. 6b is the distribution of unstable regions under different rotation speeds of sinusoidal magnetic poles and included angles of the magnetic poles when the number of vibration waves is 3;
FIG. 7a is the distribution of unstable regions of uniform magnetic poles at different rotation speeds and included angles when the number of vibration waves is 2;
FIG. 7b is the distribution of unstable regions of the uniform magnetic poles at different rotation speeds and included angles when the number of vibration waves is 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 improving the out-of-plane vibration stability of a rotor by sinusoidal magnetic poles of a permanent magnet motor.
The embodiment of the invention can be suitable for designing the magnetic pole of the permanent magnet motor.
The technical scheme of the embodiment of the invention is as follows: a technology for improving the stability of the out-of-plane vibration of a rotor by using a sine-shaped magnetic pole of a permanent magnet motor compares the stability of the out-of-plane vibration of the sine-shaped magnetic pole and a uniform magnetic pole.
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, spoke respectivelythe inner and outer diameters of the plate are RaAnd 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. The sinusoidal magnetic pole and the uniform magnetic pole are different in magnetic rigidity operator.
For a magnetic pole of the sinusoidal type,
for the magnetic poles of the uniform type,
in the formula, hm0And d0Respectively the maximum magnetizing thickness of the sinusoidal magnetic pole and the maximum distance between the stator and the rotor, Brand hmRemanence and magnetizing thickness, mu, of permanent magnet0for vacuum permeability, δ is the length of the air gap between the stator and rotor.
By first order Galerkin discretization
wherein W (t) represents an out-of-plane complex vibration function, "-" represents a conjugate, n represents a vibration wave number, i represents an imaginary unit, a partial differential equation is converted into an ordinary differential equation,
S1+S2+S3+S4＝0 (5)
for a sinusoidal magnetic pole, in the formula,
for a uniform type of magnetic pole, in the formula,
a general formula (4) isperforming inner product operation, defining inner product operation,
(A2) further, the combination relation between the vibration wave number and the number of the permanent magnets is judged according to the operational property of the trigonometric function, and then the characteristic value of the out-of-plane vibration is calculated in a classified mode, wherein the trigonometric function property comprises the following steps:
In the formula, int represents an integer. When 2N/Nmwhen int, the characteristic equation is
When 2N/NmNot equal to int, the characteristic equation is
wherein w is an axial vibration displacement matrix and M is a unit massQuantity matrix, G is a sub diagonal gyro matrix, KcAnd KuThe stiffness matrices are unaffected and affected by the combinatorial relationship, respectively. For the case of a matrix of gyros,
G12＝-G21＝2nΩ (20)
In the stiffness matrix KcIn (1),
For a sinusoidal magnetic pole, in the formula,
For a uniform type of magnetic pole, in the formula,
In the stiffness matrix KuIn the case of a sinusoidal magnetic pole, in the formula,
for a uniform type of magnetic pole, in the formula,
(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 equations (18) and (19)
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. For further analytical analysis, the eigenvalues are written in real and imaginary form,
λ＝λRe+iλIm (27)
In the formula, λReAnd λImFor the real part and the imaginary part of the eigenvalue, equation (27) is substituted into equation (26), so that the real part and the imaginary part of the eigenvalue of the external vibration under different combinations can be obtained.
(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. The influence of the sine magnetic pole on the stability improvement can be judged by comparing the unstable region conditions of the sine magnetic pole and the uniform magnetic pole.
Aiming at the characteristics of the vibration equation, the embodiment of the invention provides a technology for improving the out-of-plane vibration stability of a rotor by a sinusoidal magnetic pole of a permanent magnet motor, the technology can obtain a characteristic value in an analytic form and predict the dynamic stability according to the characteristic value, so that the technology for improving the stability is provided, and the specific process is as follows:
(B1) respectively establishing a dynamic model of a sinusoidal magnetic pole and a uniform magnetic pole in 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 calculating the characteristic equation of the out-of-plane vibration in a classified manner;
(B3) And calculating a characteristic value according to a characteristic equation to obtain an unstable region.
The technology for improving the out-of-plane vibration stability of the rotor by considering the sinusoidal magnetic pole of the permanent magnet motor comprises the following specific steps:
(C1) respectively establishing a dynamic model of a sinusoidal magnetic pole and a uniform magnetic pole in a follow-up coordinate system;
(C2) 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 calculating the characteristic equation of the out-of-plane vibration in a classified manner;
Assuming that the characteristic equations of the dynamic equation in the step (C1) are respectively formula (18) and formula (19) under different combinations of wave numbers and magnetic pole numbers, the instability rule of vibration is further revealed according to the virtual and real parts of the characteristic values by solving the characteristic values, thereby providing a technology for improving stability.
(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) And (C2) according to the characteristic value of the out-of-plane vibration obtained in the step (C2), when the vibration wave number is 2, the distribution of unstable regions of the sinusoidal magnetic poles under different rotation speeds and remanence is shown in fig. 2 a.
(C5) and (C2) when the out-of-plane vibration eigenvalue obtained in the step (C2) is a vibration wave number of 3, the distribution of unstable regions of the sinusoidal magnetic poles under different rotation speeds and remanence is shown in fig. 2 b.
(C6) according to the characteristic value of the out-of-plane vibration obtained in the step (C2), when the vibration wave number is 2, the distribution of the unstable region of the uniform magnetic pole under different rotation speeds and remanence is shown in fig. 3 a.
(C7) When the out-of-plane vibration eigenvalue obtained in step (C2) is the vibration wave number of 3, the distribution of unstable regions of the uniform magnetic pole under different rotation speeds and remanence is shown in fig. 3 b.
(C8) And (C2) when the out-of-plane vibration eigenvalue obtained in the step (C2) is a vibration wave number of 2, the distribution of unstable regions of the sinusoidal magnetic poles under different rotation speeds and magnetizing thicknesses is shown in fig. 4 a.
(C9) And (C2) when the out-of-plane vibration eigenvalue obtained in the step (C2) is a vibration wave number of 3, the distribution of unstable regions of the sinusoidal magnetic poles under different rotation speeds and magnetizing thicknesses is shown in fig. 4 b.
(C10) When the wave number of the out-of-plane vibration is 2 according to the eigenvalue of the out-of-plane vibration determined in the step (C2), the distribution of the unstable region of the uniform magnetic pole under different rotation speeds and magnetizing thicknesses is shown in fig. 5 a.
(C11) When the out-of-plane vibration eigenvalue obtained in step (C2) is the vibration wave number of 3, the distribution of unstable regions of the uniform magnetic pole under different rotation speeds and magnetizing thicknesses is shown in fig. 5 b.
(C12) According to the characteristic value of the out-of-plane vibration obtained in the step (C2), when the vibration wave number is 2, the distribution of unstable regions of the sinusoidal magnetic poles under different rotation speeds and included angles of the magnetic poles is shown in fig. 6 a.
(C13) And (C2) when the out-of-plane vibration eigenvalue obtained in the step (C2) is a vibration wave number of 3, the distribution of unstable regions of the sinusoidal magnetic poles under different rotation speeds and included angles between the magnetic poles is shown in fig. 6 b.
(C14) When the out-of-plane vibration eigenvalue obtained in step (C2) is the vibration wave number of 2, the distribution of unstable regions of the uniform magnetic pole under different rotation speeds and included angles between the magnetic poles is shown in fig. 7 a.
(C15) When the out-of-plane vibration eigenvalue obtained in step (C2) is the vibration wave number of 3, the distribution of unstable regions of the uniform magnetic pole under different rotation speeds and included angles of the magnetic pole is shown in fig. 7 a.
in conclusion, the invention provides a technology for improving the out-of-plane vibration stability of a rotor by using a sinusoidal magnetic pole of a permanent magnet motor. 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 (4)
1. a method for improving out-of-plane vibration stability of a rotor by a sinusoidal magnetic pole of a permanent magnet motor is characterized by comprising the following steps:
(1) Respectively establishing a dynamic model of a sinusoidal magnetic pole and a uniform magnetic pole in 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 calculating the characteristic equation of the out-of-plane vibration in a classified manner;
(3) and calculating a characteristic value according to a characteristic equation to obtain an unstable region.
2. The method for improving the out-of-plane vibration stability of the rotor of the permanent magnet motor according to claim 1, wherein the dynamic model is specifically as follows:
Wherein Ω is the rotation speed, ktFor the centrifugal stiffness operator, krpAnd krsrespectively representing the dynamic and static support stiffness operators, kpRepresenting a magnetic stiffness operator; the sinusoidal magnetic pole and the uniform magnetic pole are different in magnetic rigidity operator.
3. the method for improving the out-of-plane vibration stability of the rotor by the aid of the sinusoidal magnetic poles of the permanent magnet motor according to claim 1 is characterized in that the combination relation between vibration wave numbers and the number of permanent magnets is judged by means of the operational properties of trigonometric functions, and out-of-plane vibration characteristic equations are calculated in a classified mode and are respectively as follows:
when 2N/Nmwhen int, the characteristic equation is
when 2N/NmNot equal to int, the characteristic equation is
Wherein N is the number of vibration waves, NmIs the number of magnetic poles, int is an integer, w is out-of-plane vibration displacement, M is a massquantity matrix, G gyro matrix, KcAnd Kuthe stiffness matrices are unaffected and affected by the combinatorial relationship, respectively.
4. the method for improving the out-of-plane vibration stability of the rotor of the permanent magnet motor according to the claim 3 is characterized in that an unstable region is obtained by calculating a characteristic value according to a characteristic equation; the effect of the sine magnetic pole on improving the stability can be judged according to the unstable region image.
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