CN112270065A - Dynamic stability prediction method for eccentric rotation annular periodic structure - Google Patents

Dynamic stability prediction method for eccentric rotation annular periodic structure Download PDF

Info

Publication number
CN112270065A
CN112270065A CN202010870254.4A CN202010870254A CN112270065A CN 112270065 A CN112270065 A CN 112270065A CN 202010870254 A CN202010870254 A CN 202010870254A CN 112270065 A CN112270065 A CN 112270065A
Authority
CN
China
Prior art keywords
periodic structure
dynamic stability
eccentric
annular
internal force
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN202010870254.4A
Other languages
Chinese (zh)
Other versions
CN112270065B (en
Inventor
王世宇
李海洋
王姚志豪
夏春花
刘晨
王久霞
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Tianjin University
Original Assignee
Tianjin University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Tianjin University filed Critical Tianjin University
Priority to CN202010870254.4A priority Critical patent/CN112270065B/en
Publication of CN112270065A publication Critical patent/CN112270065A/en
Application granted granted Critical
Publication of CN112270065B publication Critical patent/CN112270065B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Geometry (AREA)
  • General Physics & Mathematics (AREA)
  • Evolutionary Computation (AREA)
  • General Engineering & Computer Science (AREA)
  • Computer Hardware Design (AREA)
  • Computational Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Pure & Applied Mathematics (AREA)
  • Gyroscopes (AREA)

Abstract

The invention discloses a method for predicting dynamic stability of an eccentric rotating annular periodic structure. And the characteristic values are solved by adopting a classical vibration theory, and the modal characteristics and the instability of the annular periodic structure under different parameter combinations are analyzed. The invention well solves the problems of insufficient consideration of actual working conditions, complex simulation process and inaccurate prediction of analysis results of the existing vibration analysis technology of the annular periodic structure, and provides reference and reference for parameter design and vibration control of the structure in engineering practice.

Description

Dynamic stability prediction method for eccentric rotation annular periodic structure
Technical Field
The invention relates to the field of vibration of a ring-shaped periodic structure, in particular to a dynamic stability prediction method of an eccentric rotating ring-shaped periodic structure.
Background
Various rotating parts are widely applied in engineering practice to realize functions of transmission, driving, energy conversion and the like, such as gear transmission, rolling bearings, rotating motors and the like. The annular periodic structure used in the component is generally formed by a plurality of symmetrical units with the same configuration and geometric parameters through a circumferential array, such as a gear ring, an inner ring, an outer ring, a stator and a rotor. The rotational symmetry design is beneficial to realizing load balance and improving the structural stability. However, in engineering practice, such structures usually exhibit eccentric rotation due to the special requirements of the application to the form of movement, or manufacturing and installation errors which are difficult to avoid. Under high speed conditions, eccentric rotation will generate significant centrifugal force, which in turn induces vibration and noise, affecting the efficiency of operation. Therefore, it is particularly important to research the modal characteristics and dynamic stability of the rotating annular periodic structure under the influence of eccentric motion.
Three-dimensional bending vibration of eccentric micro-rotating shafts was studied in the literature (HASEMI M, ASGHARI M. analytical stuck with micro-rotating skin with the objective tuning the strain of the same [ J ]. Meccania, 2016, 51(6): 1435-.
The document (LIU T, ZHANG W, MAO J. nonlinear cutting vibration of eccentric rotating composite coated circular cylindrical shell, rolling speed and external vibration [ J ] Mechanical Systems and Signal Processing,2019,127(15):463 and 498.) adopts a multi-scale method to study the nonlinear vibration of the eccentric rotating composite laminated cylindrical shell and discloses the influence rule of geometrical parameters such as eccentricity on the dynamic behavior.
It should be noted that in the prior art, there is also relatively little research on the dynamics of cyclic periodic structures under eccentric motion. In addition, the prior art adopts a numerical method to predict the dynamic stability, the calculation efficiency of the method is low, and the general rule cannot be revealed.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and provide a dynamic stability prediction method with strong applicability, which is specially used for counting an annular periodic structure of eccentric motion. So as to improve the current situation that the existing research only focuses on the fixed shaft rotation and ignores the eccentric motion. Under actual conditions, most of the annular periodic structures are limited by the requirements of motion forms and manufacturing and installation errors, ideal fixed-axis rotation is difficult to realize, and eccentric motion occurs. Aiming at the current situation, the invention takes the influence caused by eccentric motion into account, and utilizes a complete model to carry out kinetic analysis to obtain a general guiding theory with wider application range and higher practical value.
The purpose of the invention is realized by the following technical scheme:
a dynamic stability prediction method for an eccentric rotating annular periodic structure comprises the following steps:
(1) on the basis of using the additional mass to simplify the periodic distribution characteristics, calculating the internal force distribution of the annular structure during eccentric rotation by adopting a infinitesimal method and a superposition principle;
(2) establishing a dynamic model of the eccentric motion annular periodic structure under an inertial coordinate system by using a Hamilton principle;
(3) according to a classical vibration theory, obtaining an eccentric rotating annular periodic structure characteristic equation; and (4) predicting the modal characteristic and the dynamic stability law of the annular periodic structure under different parameter combinations by solving the characteristic value.
Further, the internal force distribution includes radial and tangential internal force distributions, which are respectively:
Figure BDA0002650862670000021
further, the dynamic model of the annular periodic structure under eccentric rotation is specifically as follows:
Figure BDA0002650862670000022
in the formula
Figure BDA0002650862670000023
Figure BDA0002650862670000024
Figure BDA0002650862670000025
Figure BDA0002650862670000026
Figure BDA0002650862670000027
Figure BDA0002650862670000028
Figure BDA0002650862670000031
Figure BDA0002650862670000032
Figure BDA0002650862670000033
A6＝1+Nm*，
Figure BDA0002650862670000034
In the formula, M1、G1、K1、D1And F is a mass operator, a gyro operator, a stiffness operator, an additional stiffness operator and an excitation operator generated by the reaction force, q is1Is a displacement vector;
Figure BDA0002650862670000035
A0，A1，A2，A3， A4，A5，A6，fθthe specific expressions are respectively designated, and no practical significance is realized; u and v are tangential and radial displacements, R, R respectivelyΔD, b, h, E and rho represent the neutral circle radius, eccentricity, axial thickness, radial thickness, Young's modulus and density of the ring, respectively; i (I ═ bh)3/12) the section moment of inertia of the stator; n is the number of the additional mass blocks; omegavAnd ΩavDimensionless rotational angular velocity and revolution angular velocity are respectively.
Further, a Galerkin method is used to obtain a characteristic equation, which is as follows:
Figure BDA0002650862670000036
in the formula, M2、G2、K2Respectively a mass matrix, a gyro matrix, a rigidity matrix, q2Is a feature vector.
Compared with the prior art, the technical scheme of the invention has the following beneficial effects:
1. the method comprises the steps of firstly calculating the internal force distribution of the annular periodic structure by adopting a infinitesimal method and a superposition principle, obtaining an analytic dynamic model under an inertial coordinate system by adopting a Hamilton principle and a Galerkin method, solving characteristic values by adopting a classical vibration theory, predicting the inherent frequency and dynamic stability rules under different parameter combinations, and providing thought reference and method reference for vibration control of the structure.
2. The invention analyzes the centrifugal force of the annular structure under the eccentric motion based on the kinematics law. And analyzing the single stress situation by a infinitesimal method, and calculating the internal force distribution of the annular structure under the action of uniformly distributed centrifugal force by a superposition method.
3. According to the method, under an inertial coordinate system, a steady kinetic equation of the system under the condition of different parameter combinations is deduced by means of special properties of trigonometric function summation according to a Hamilton principle and a Galerkin method. Solving the characteristic value by means of a classical vibration theory, and analyzing the modal characteristic and the dynamic stability law of the annular periodic structure under different parameter combinations;
4. the invention has the characteristics of high efficiency, accuracy and universality. According to the technology, the relation between parameters such as eccentricity, period distribution characteristics and rotating speed and modal characteristics and dynamic stability can be revealed, the vibration condition under the actual working condition is estimated in the design stage, and the boundary of an unstable domain is determined, so that poor parameter combination is avoided, the dynamic design of the annular periodic structure is guided, and the stability and the reliability of the operation of equipment are improved.
Drawings
FIG. 1 is a schematic diagram of an eccentric rotating ring periodic structure provided by the present invention;
FIGS. 2a and 2b are F obtained according to the method provided by the present inventionef1，Fef2Infinitesimal stress under action;
3a to 3d are the natural frequency variation with rotation speed at low wavenumber obtained by the method provided by the invention;
FIGS. 4a and 4b are schematic diagrams illustrating the variation of the imaginary part of the eigenvalue with the rotation speed at high wavenumber according to the method provided by the present invention;
5a to 5h show the variation law of the imaginary parts of the characteristic values of different mass ratios with the rotation speed obtained by the method provided by the invention;
6a to 6d are the change rule of the real parts of the eigenvalues of different mass ratios with the rotating speed obtained by the method provided by the invention;
FIGS. 7a to 7d are graphs showing the variation of unstable regions with rotation speed under different eccentricities obtained by the method of the present invention;
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.
Aiming at the annular periodic structure widely applied in the engineering field, the invention researches the influence of the periodic distribution characteristics and the eccentricity on the natural frequency and the dynamic stability under the premise of considering the eccentric motion. The internal force distribution of the structure is calculated by adopting a infinitesimal method and a superposition principle, and a dynamic model is established under an inertial system according to a Hamilton principle. And the characteristic values are solved by adopting a classical vibration theory, and modal characteristics and instability under different parameter combinations are analyzed. The result shows that when the period distribution characteristic and the wave number meet a certain relation, the natural frequency of the system is split; for varying eccentricity and periodic distribution characteristics, the system exhibits divergent or flutter instability at different rotational speeds. The research is helpful for analyzing the dynamic stability of the structure in engineering practice and provides thought reference and method reference for vibration control of the structure. The specific implementation steps are as follows:
(S1) the mathematical model of the eccentric rotating ring periodic structure shown in FIG. 1 is composed of a thin ring and N (N is more than or equal to 1) uniformly distributed additional mass blocks m0 (j)And (4) forming. Wherein the additional mass is considered as a mass point to simplify the periodic distribution feature. The structure rotates around its geometric centroid o at an angular velocity Ω while following a rigid trajectory at an angular velocity ΩaRevolving around the eccentric o'. And the o-r theta z is a follow-up coordinate system, the o '-r theta z is an inertia coordinate system, and the initial time connecting line o' o is superposed with the polar axis. p is any point on the neutral circle, u and v are the tangential and radial displacements of this point, R, RΔD, b, h, E and ρ represent the neutral radius, eccentricity, axial thickness, radial thickness, young's modulus and density, respectively, of the ring.
In the inertial coordinate system, the angular coordinate of the first mass block is assumed to be theta1When equal to 0, the jth mass block is located at theta j2 pi (j-1) N, and the distribution law of the additional mass can be expressed as
Figure BDA0002650862670000051
Where δ (θ) is the dirac function.
According to a simple kinematic relationship, the rotation and revolution of the ring satisfy the following relationship
Figure BDA0002650862670000052
In the motion state, the position p generates a rotation centrifugal force and a revolution centrifugal force which are respectively
Figure BDA0002650862670000053
F is to ber' decomposition in radial and tangential directions of the ring, the projection of the centrifugal force in the radial and tangential directions can be obtained
Figure BDA0002650862670000054
The centrifugal force applied to p can be expressed as
Figure BDA0002650862670000055
Further, the track has a support reaction force against the ring of
Figure BDA0002650862670000056
In order to determine the distribution of internal force caused by the centrifugal force of rotation and revolution, the single radial force F applied to the ring is firstly studied respectivelyef1With tangential force Fef2Distribution of internal forces when acting. Using the infinitesimal method, the force analysis is performed by intercepting the micro-segment d theta at p, as shown in fig. 2a and 2b, where Fsf、FtfAnd MbmRespectively showing the shearing force, the axial force and the bending moment applied to the micro-segment.
According to theoretical mechanics, Fef2Can be equivalently F 'applied at the geometric centroid'ef2With torques T uniformly distributed in the circumferential directiontm2. Under the two stress conditions shown in fig. 2a and fig. 2b, the ring neutral lines are distributed with uniform virtual forces
Figure BDA0002650862670000057
And
Figure BDA0002650862670000058
in balance with external force, have
Figure BDA0002650862670000059
The virtual forces in FIGS. 2a and 2b are projected in normal and tangential directions, while taking the moment for the center p of the micro-segment, in both cases
Figure BDA0002650862670000061
Figure BDA0002650862670000062
Considering the relation between tangential force and bending moment and radial deformation
Figure BDA0002650862670000063
Wherein mu is Poisson's ratio. At the same time, the boundary condition of the deformation of the ring under stress under two conditions is considered
Figure BDA0002650862670000064
Figure BDA0002650862670000065
According to the equations (8), (10) and (11), the high-order trace is omitted, and the radial force F can be solved by an operator methodef1Distribution of internal forces of the ring under action
Figure BDA0002650862670000066
Similarly, according to equations (9), (10) and (12), the tangential force F can be obtainedef2Distribution of internal forces of the ring under action
Figure BDA0002650862670000071
Distribution of tangential internal forces resulting from the radial and tangential forces available from equations (13) and (14), respectively
Figure BDA0002650862670000072
In summary, the tangential internal force of the ring can be expressed as
Fθ＝Fθv+Fθu+Fsv (16)
In the formula Fθv、FθuAnd FsvRespectively representing the distribution of tangential internal forces due to radial and tangential components of the centrifugal force and orbital bearing forces, and having
Figure BDA0002650862670000073
(S2) according to fig. 1, a position vector at any point p on the neutral circle of the torus can be represented as
Figure BDA0002650862670000074
Absolute velocity v of point p in inertial frameaCan be expressed as
va＝ve+vr (19)
In the formula, veVelocity (relative velocity) v of point p with respect to the following coordinate systemrIs the velocity (tie-in velocity) of the follow-up coordinate system relative to the inertial coordinate system, and is known
Figure BDA0002650862670000075
The kinetic energy of the ring can be expressed as
Figure BDA0002650862670000076
The potential energy of the ring includes strain energy caused by elastic vibration and strain energy caused by centrifugal force, taking into account the characteristics of the eccentric motion. In the in-plane strain state, the tangential strain at point p is
εθ＝εθ0+(r-R)εθ1 (21)
In the formula
Figure BDA0002650862670000081
The strain energy of the ring can be expressed as
Figure BDA0002650862670000082
Wherein A and I are the area of the section of the ring (A ═ bh) and the main moment of inertia (I ═ bh) respectively3/12)。
(S3) according to Hamilton' S principle, the kinetic equation can be derived:
Figure BDA0002650862670000083
in the formula
Figure BDA0002650862670000084
Figure BDA0002650862670000085
Figure BDA0002650862670000086
Figure BDA0002650862670000087
Figure BDA0002650862670000088
Figure BDA0002650862670000089
Figure BDA00026508626700000810
A0＝Ωav+Ωv，
Figure BDA0002650862670000091
A2＝ΩavΩv，
Figure BDA0002650862670000092
A6＝1+Nm*，
Figure BDA0002650862670000093
In the formula, M1、G1、K1、D1And F is a mass operator, a gyro operator, a stiffness operator,Additional stiffness and excitation operators for the generation of support forces, q1Is a displacement vector;
Figure BDA0002650862670000094
A1，A2，A3，A4， A5，A6，fθthe specific expressions are respectively designated, and no practical significance is realized; u and v are the tangential and radial displacements of the point, R, R respectivelyΔD, b, h, E and ρ represent the neutral radius, eccentricity, axial thickness, radial thickness, young's modulus and density, respectively, of the ring. I (I ═ bh)3And/12) the section moment of inertia of the stator. And N is the number of the additional mass blocks. OmegavAnd ΩavRespectively, a dimensionless rotation angular velocity and a revolution angular velocity.
(S4) in order to solve the free vibration response, Galerkin dispersion is applied to construct tangential and radial vibration displacement
Figure BDA0002650862670000095
Where i is an imaginary unit, "-" represents a complex conjugate operation, and U (t) and V (t) are unknown functions of the minimum residual force constructed in discrete operations, both complex functions of time, and thus can be defined
Figure BDA0002650862670000096
In the formula, xu(t)、yu(t)、xv(t) and yv(t) are all real functions of time. Defining inner product operations
Figure BDA0002650862670000097
Where x and y are both complex functions.
Then with einθInner product is made and real and imaginary parts are separated and arranged to obtain
Figure BDA0002650862670000098
In the formula
Figure BDA0002650862670000099
Figure BDA0002650862670000101
Figure BDA0002650862670000102
Figure BDA0002650862670000103
Figure BDA0002650862670000104
Figure BDA0002650862670000105
Figure BDA0002650862670000106
Figure BDA0002650862670000107
Figure BDA0002650862670000108
Figure BDA0002650862670000109
Figure BDA00026508626700001010
Figure BDA00026508626700001011
Figure BDA00026508626700001012
In the formula, M2、G2、K2Respectively a mass matrix, a gyro matrix, a rigidity matrix, q2Is a feature vector.
Figure BDA00026508626700001013
Figure BDA00026508626700001014
B0，B′0，B1，B′1，B2，B′2The expressions are respectively referred to, and have no practical significance.
According to the Euler formula and the arithmetic series summation characteristics of trigonometric functions, the method comprises
Figure BDA0002650862670000111
To further simplify the kinetic equations, the effect of the parameter combinations on the summation terms was analyzed herein, with the results as set forth in table 1.
Table 1 values of the summation terms under different parameter combinations
Figure BDA0002650862670000112
Equation (27), a dynamic differential equation of the eccentric rotating ring periodic structure, can be obtained by combining the results in Table 1 with the parameters in Table 2And solving the characteristic value lambda by using a classical vibration force theory so as to predict the dynamic stability of the structure. If not specifically mentioned below, the eccentricity k is 4/3, and the mass ratio m is taken*＝0.1。
TABLE 2 basic parameters of the cyclic periodic Structure
Figure BDA0002650862670000113
Fig. 3a to 3d illustrate the variation of the natural frequency of the ring-shaped periodic structure with the revolution speed in the case of low wave number, respectively representing the imaginary part of the first and second order eigenvalues and the corresponding real part of the eigenvalue, as in fig. 3 a. The solid line and the dotted line are respectively the forward wave mode and the backward wave mode. It can be seen that at a wavenumber of 0, the system has instability problems and is associated with only first order vibrations. According to the classical vibration theory, if the real part of the eigenvalue is greater than zero, the system will appear unstable, and when the corresponding imaginary part is zero, divergence instability will appear. In contrast, when the wave number is 1, the system has better stability, the forward traveling wave of the imaginary part of the first-order eigenvalue coincides with the backward traveling wave mode, and modal transition occurs between the forward traveling wave and the second-order eigenvalue, as shown in the partial enlarged views (i) and (ii). It is noted that for the case of 2N/N being an integer, the cyclic periodic structure undergoes natural frequency splitting at rest and is more pronounced with an increase in the number of additional masses.
For the case of high wavenumbers, fig. 4a and 4b depict the effect of the rotation speed, the wavenumber and the additional mass number on the natural frequency. Obviously, there is a positive correlation between the stability of the system and the wavenumber at different additional mass numbers. Similarly, frequency splitting that occurs at rest only occurs where 2N/N is an integer. Moreover, as the additional mass number increases, its degree of fragmentation becomes more pronounced.
Fig. 5a to 6d illustrate the effect of revolution speed and additional mass on the dynamics of the ring structure, taking the combination of parameters { N is 2, N is 4} as an example, for the typical case of natural frequency splitting in the case of high wavenumber. Fig. 5a shows the result of removing the additional mass, all with a different additional mass. It can be seen that there is little instability of the system when the additional mass is removed and the ring has good stability at medium and high rotational speeds. Compared with the prior art, the additional mass causes the system to be unstable in dispersion at low rotating speed, and along with the continuous increase of the additional mass, the backward traveling wave mode of the first-order characteristic value is overlapped with the forward traveling wave mode of the first-order and second-order characteristic values in sequence, a plurality of wave crests appear in the real part of the characteristic value in the process of increasing the revolving speed of the circular revolution, and multiple times of flutter instability appear in sequence under the influence of the softening effect.
In consideration of the influence of eccentricity on eccentric motion, fig. 7a to 7d illustrate the variation law of the unstable region of the annular periodic structure with the eccentricity and the revolution speed under different mass ratios. Combining the above-described natural frequency characteristics, it can be seen that the domain of fig. 7a is a divergence unstable domain at a low rotation speed, and the domains of c and c are flutter unstable domains at medium and high rotation speeds, respectively. It is not difficult to find that the stable region of the circular ring under the low eccentricity continuously shrinks along with the increase of the additional mass, the region II gradually disappears, the region I and the region III are in contact with each other, and the stability of the system is obviously reduced. It is worth noting that when the eccentricity ratio is continuously increased (k is more than 2, the center of the revolution moves to the outside of the ring), the rigidizing effect caused by the revolution obviously influences the softening effect of the rotation, and the system reappears the stabilization phenomenon at low rotation speed and gradually spreads to a wider rotation speed range.
In general, under different rotating speeds, the annular periodic structure has dispersion and flutter instability, the former generally appears in a low rotating speed parameter domain, and the latter often appears in a medium and high rotating speed parameter domain with high mass ratio. The phenomenon has a specific dependence on eccentricity and period distribution characteristic parameters, and a significant difference exists between the low wave number and the high wave number. By increasing the eccentricity, the stress-hardening effect caused by the revolution can significantly suppress the instability, thereby improving the system stability. This instability suppression method is easy to operate at low mass ratios, but relatively severe conditions are achieved at high mass ratios.
In summary, the invention provides a method for predicting dynamic stability of an eccentric rotating annular periodic structure. The method fully considers the influence caused by eccentric motion, obtains the characteristic value of the system through the analytic method, improves the accuracy, the calculation efficiency and the universality, and better meets the actual requirements of engineering.
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 specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art, having the benefit of this disclosure, may effect numerous modifications thereto and changes may be made without departing from the scope of the invention as defined by the claims and their equivalents.

Claims (4)

1. A dynamic stability prediction method of an eccentric rotating annular periodic structure is characterized by comprising the following steps:
(1) on the basis of using the additional mass to simplify the periodic distribution characteristics, calculating the internal force distribution of the annular structure during eccentric rotation by adopting a infinitesimal method and a superposition principle;
(2) establishing a dynamic model of the eccentric motion annular periodic structure under an inertial coordinate system by using a Hamilton principle;
(3) according to a classical vibration theory, obtaining a characteristic equation of the eccentric rotating annular periodic structure; and predicting the modal characteristic and the dynamic stability law of the annular periodic structure under different parameter combinations by solving the characteristic value.
2. The method for predicting the dynamic stability of the eccentric rotating ring-shaped periodic structure according to claim 1, wherein the internal force distribution comprises a radial internal force distribution and a tangential internal force distribution, and the radial internal force distribution and the tangential internal force distribution are respectively as follows:
Figure FDA0002650862660000011
3. the method for predicting the dynamic stability of the eccentric rotating annular periodic structure according to claim 1, wherein the dynamic model of the annular periodic structure under the eccentric rotation is specifically as follows:
Figure FDA0002650862660000012
in the formula
Figure FDA0002650862660000013
Figure FDA0002650862660000014
Figure FDA0002650862660000015
Figure FDA0002650862660000016
Figure FDA0002650862660000017
Figure FDA0002650862660000018
Figure FDA0002650862660000021
Figure FDA0002650862660000022
Figure FDA0002650862660000023
In the formula, M1、G1、K1、D1And F is a mass operator, a gyro operator, a stiffness operator, an additional stiffness operator and an excitation operator generated by the reaction force, q is1Is a displacement vector;
Figure FDA0002650862660000024
A0，A1，A2，A3，A4，A5，A6，fθthe specific expressions are respectively designated, and no practical significance is realized; u and v are tangential and radial displacements, R, R respectivelyΔD, b, h, E and rho represent the neutral circle radius, eccentricity, axial thickness, radial thickness, Young's modulus and density of the ring, respectively; i (I ═ bh)3/12) the section moment of inertia of the stator; n is the number of the additional mass blocks; omegavAnd ΩavDimensionless rotational angular velocity and revolution angular velocity are respectively.
4. The method for predicting the dynamic stability of the eccentric rotating ring periodic structure according to claim 1, wherein the Galerkin method is used to obtain the characteristic equation as follows:
Figure FDA0002650862660000025
in the formula, M2、G2、K2Respectively a mass matrix, a gyro matrix, a rigidity matrix, q2Is a feature vector.
CN202010870254.4A 2020-08-26 2020-08-26 Dynamic stability prediction method for eccentric rotary annular periodic structure Active CN112270065B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202010870254.4A CN112270065B (en) 2020-08-26 2020-08-26 Dynamic stability prediction method for eccentric rotary annular periodic structure

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202010870254.4A CN112270065B (en) 2020-08-26 2020-08-26 Dynamic stability prediction method for eccentric rotary annular periodic structure

Publications (2)

Publication Number Publication Date
CN112270065A true CN112270065A (en) 2021-01-26
CN112270065B CN112270065B (en) 2023-09-08

Family

ID=74349627

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202010870254.4A Active CN112270065B (en) 2020-08-26 2020-08-26 Dynamic stability prediction method for eccentric rotary annular periodic structure

Country Status (1)

Country Link
CN (1) CN112270065B (en)

Citations (10)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20090064771A1 (en) * 2007-09-06 2009-03-12 Andrew James Dick Method of operating an atomic force microscope in tapping mode with a reduced impact force
US20160054329A1 (en) * 2013-04-08 2016-02-25 Northeastern University Novel sensor system utilizing piezoelectric microcantilever coupled with resonating circuit
CN106528959A (en) * 2016-10-19 2017-03-22 天津大学 Simplified analysis method for inherent frequency and stability of rotational symmetric structure
CN106547957A (en) * 2016-10-19 2017-03-29 天津大学 A kind of rotating annular periodic structure ginseng swashs elastic vibration analysis method
CN109683481A (en) * 2019-01-09 2019-04-26 东华大学 A kind of shaftless intaglio press horizontal register control method
CN109800512A (en) * 2019-01-23 2019-05-24 东北大学 Rotating cylindrical shell-variable cross-section disk-pretwist blade system dynamic modeling method
CN110569560A (en) * 2019-08-16 2019-12-13 天津大学 Method for superposing stresses of mirror topology tangential loaded circular ring
CN110580383A (en) * 2019-08-16 2019-12-17 天津大学 method for stacking stress of grouped topological radial loaded circular ring
US20200055184A1 (en) * 2018-08-16 2020-02-20 Hehua Ju Axis-Invariant based Multi-axis robot kinematics modeling method
US20200055192A1 (en) * 2018-08-16 2020-02-20 Hehua Ju Axis-Invariant based Multi-axis robot inverse kinematics modeling and solving method

Patent Citations (10)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20090064771A1 (en) * 2007-09-06 2009-03-12 Andrew James Dick Method of operating an atomic force microscope in tapping mode with a reduced impact force
US20160054329A1 (en) * 2013-04-08 2016-02-25 Northeastern University Novel sensor system utilizing piezoelectric microcantilever coupled with resonating circuit
CN106528959A (en) * 2016-10-19 2017-03-22 天津大学 Simplified analysis method for inherent frequency and stability of rotational symmetric structure
CN106547957A (en) * 2016-10-19 2017-03-29 天津大学 A kind of rotating annular periodic structure ginseng swashs elastic vibration analysis method
US20200055184A1 (en) * 2018-08-16 2020-02-20 Hehua Ju Axis-Invariant based Multi-axis robot kinematics modeling method
US20200055192A1 (en) * 2018-08-16 2020-02-20 Hehua Ju Axis-Invariant based Multi-axis robot inverse kinematics modeling and solving method
CN109683481A (en) * 2019-01-09 2019-04-26 东华大学 A kind of shaftless intaglio press horizontal register control method
CN109800512A (en) * 2019-01-23 2019-05-24 东北大学 Rotating cylindrical shell-variable cross-section disk-pretwist blade system dynamic modeling method
CN110569560A (en) * 2019-08-16 2019-12-13 天津大学 Method for superposing stresses of mirror topology tangential loaded circular ring
CN110580383A (en) * 2019-08-16 2019-12-17 天津大学 method for stacking stress of grouped topological radial loaded circular ring

Non-Patent Citations (4)

* Cited by examiner, † Cited by third party
Title
A.A. MASLOV等: ""Dynamics of the Ring Micromechanical Gyroscope Taking into Account the Nonlinear Stiffness of the Suspension"", 《IEEE》 *
BINGQIANG LI等: ""Rotating blade-casing rubbing simulation considering casing flexibility"", 《INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES》 *
于桂杰: ""长效地应力机制下套管应力与抗挤强度理论研究"", 《中国博士学位论文全文数据库 工程科技II辑》 *
李凤云 等: ""弹性圆环在刚壁上的撞击回弹"", 《振动与冲击》 *

Also Published As

Publication number Publication date
CN112270065B (en) 2023-09-08

Similar Documents

Publication Publication Date Title
Tiwari et al. Dynamic response of an unbalanced rotor supported on ball bearings
TWI671612B (en) Control device and reducer system
Cooley et al. A review of planetary and epicyclic gear dynamics and vibrations research
CN110119532B (en) Elastic vibration calculation method of rotary annular periodic structure
Wang et al. Dynamic modeling and mesh phasing-based spectral analysis of quasi-static deformations of spinning planetary gears with a deformable ring
CN106528959B (en) A kind of reduced chemical reaction kinetics model of rotational symmetry structure intrinsic frequency and stability
Hua et al. Nonlinear dynamics of rub-impact on a rotor-rubber bearing system with the Stribeck friction model
Shi et al. Modal structure of centrifugal pendulum vibration absorber systems with multiple cyclically symmetric groups of absorbers
JP6565034B2 (en) Control device and reduction gear system
Lahriri et al. On the nonlinear dynamics of two types of backup bearings—theoretical and experimental aspects
Lam et al. Vibrations of thick rotating laminated composite cylindrical shells
Shi et al. Vibration modes and natural frequency veering in three-dimensional, cyclically symmetric centrifugal pendulum vibration absorber systems
Liu et al. Research nonlinear vibrations of a dual-rotor system with nonlinear restoring forces
CN112270065A (en) Dynamic stability prediction method for eccentric rotation annular periodic structure
CN112347591B (en) Internal force analysis and free vibration modeling method for eccentric rotating ring structure
CN114021326A (en) Method and system for analyzing vibration characteristics of helical bevel gear meshing system
Inoue et al. Chaotic vibration and internal resonance phenomena in rotor systems
CN113268908B (en) Response solving method and device of rotor system
Taplak et al. Passive balancing of a rotating mechanical system using genetic algorithm
Chen et al. Dynamic analysis of a double-helical geared rotor system with oil-film bearing
CN1103443C (en) Holographic dynamic balance method for asymmetric rotor
Shi et al. Study on nonlinear dynamics of the marine rotor-bearing system under yawing motion
Surovec et al. Lateral rotor vibration analysis model
CN111563323A (en) Transient POD method based on minimum error of bifurcation parameter
CN113378323A (en) Transient intrinsic orthogonal decomposition method applied to coupled fault rotor-bearing system

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant