CN114491915A - Bearing dynamic performance analysis method considering rotor and spring support influence - Google Patents

Bearing dynamic performance analysis method considering rotor and spring support influence Download PDF

Info

Publication number
CN114491915A
CN114491915A CN202111223596.8A CN202111223596A CN114491915A CN 114491915 A CN114491915 A CN 114491915A CN 202111223596 A CN202111223596 A CN 202111223596A CN 114491915 A CN114491915 A CN 114491915A
Authority
CN
China
Prior art keywords
rotor
bearing
retainer
displacement
rolling body
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
CN202111223596.8A
Other languages
Chinese (zh)
Other versions
CN114491915B (en
Inventor
唐瑞
余丹
高利霞
赵强
晏军
高平
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.)
AECC Sichuan Gas Turbine Research Institute
Original Assignee
AECC Sichuan Gas Turbine Research Institute
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 AECC Sichuan Gas Turbine Research Institute filed Critical AECC Sichuan Gas Turbine Research Institute
Priority to CN202111223596.8A priority Critical patent/CN114491915B/en
Publication of CN114491915A publication Critical patent/CN114491915A/en
Application granted granted Critical
Publication of CN114491915B publication Critical patent/CN114491915B/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
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M13/00—Testing of machine parts
    • G01M13/04—Bearings
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G06F17/13—Differential equations
    • 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
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/04—Constraint-based CAD
    • 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

  • Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Computational Mathematics (AREA)
  • Pure & Applied Mathematics (AREA)
  • Geometry (AREA)
  • Mathematical Physics (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • General Engineering & Computer Science (AREA)
  • Computer Hardware Design (AREA)
  • Evolutionary Computation (AREA)
  • Data Mining & Analysis (AREA)
  • Operations Research (AREA)
  • Algebra (AREA)
  • Databases & Information Systems (AREA)
  • Software Systems (AREA)
  • Rolling Contact Bearings (AREA)

Abstract

The invention provides a bearing dynamic performance analysis method considering the influence of a rotor and a spring support, which comprises the following steps: calculating the acting force of the rolling body and the ferrule by combining the force balance relationship of the bearing-rotor-elastic support system; calculating acting forces of the rolling body, the retainer and the lubricating oil by combining oil supply conditions; solving a motion differential equation of the rolling body and the retainer to obtain the motion of the rolling body and the retainer; solving the motion states of the rolling body and the retainer after correction by a motion differential equation of the supporting substructure, and calculating the performance parameters of the bearing at the moment and the constraint counter force of the supporting substructure; solving a rotor motion differential equation to obtain rotor displacement and speed response; and substituting the displacement of the rotor node where the bearing is located into a bearing mechanical model, and repeating the process to obtain the time domain response of the bearing-rotor-elastic support system in a preset time period. The method comprehensively considers the coupling relation of the lubrication effect, the vibration of the retainer, the inertia of the rotor and the deformation of the elastic support, and provides a theoretical method for introducing the influence of the elastic support and the rotor during the performance simulation of the bearing.

Description

Bearing dynamic performance analysis method considering rotor and spring support influence
Technical Field
The disclosure relates to the technical field of mechanical dynamics, in particular to a bearing dynamic performance analysis method considering influence of a rotor and a spring support.
Background
The rolling bearing is widely applied to various rotating machines such as an aircraft engine, a gas turbine, a rocket engine and the like, the elastic bearing is used for being matched with the rolling bearing to jointly support the rotor system to work, the critical rotating speed area of the rotor system is adjusted, the damping and deformation of the elastic bearing can absorb the vibration of a part of rotors, the impact effect on each element in the bearing is further reduced, a large number of designs and test processes are found, the working performance of the rolling bearing can be influenced by the design parameters of the rotors and the elastic support, and the failure rate of the bearing can be increased by the unreasonable design of the elastic support and the rotor system.
In order to improve the cooperative working performance of the rolling bearing, the rotor and the spring support and improve the working reliability of the rolling bearing, the influence of the spring support and the rotor needs to be considered during the design and analysis of the rolling bearing, and a theoretical method for introducing mechanical action factors of the spring support and the rotor during the dynamic performance analysis of the bearing is researched. Currently, bearing-rotor-spring-supported models established based on the prior art are divided into two categories: one type of the model simplifies a system bearing or rotor model, and the model cannot truly reflect the coupling rule of the internal slip effect of the bearing, the motion of the retainer, the deformation of the rotor and the motion inertia. The other model preliminarily establishes a model and an algorithm for coupling analysis of bearing complete dynamics and a rotor and a bearing seat, but in order to achieve calculation stability, the algorithm needs to introduce artificially increased damping to a support, and a calculation result has uncertainty.
Therefore, in order to accurately and comprehensively analyze the influence of the spring support and the rotor on the working performance of the rolling bearing, a dynamic performance modeling, analyzing and solving algorithm of the rolling bearing capable of considering the influence of the rotor and the spring support is established on the basis of considering the mutual influence of the bearing element, lubricating oil, rotor vibration and spring support deformation according to the characteristics of the rolling bearing and the coupling working mode of the bearing-rotor-spring support.
Disclosure of Invention
In view of this, the embodiment of the present disclosure provides a bearing dynamic performance analysis method considering the influence of a rotor and a spring support, and the method is a dynamic performance modeling and solving method capable of comprehensively considering the spatial three-dimensional motion of a rolling element and a retainer of a rolling bearing, the coupling influence of a lubricating oil effect and rotor vibration and spring support deformation, and lays a theoretical foundation for joint simulation and matching design of the rolling bearing and the spring support and the rotor.
In order to achieve the above purpose, the invention provides the following technical scheme:
a bearing dynamic performance analysis method considering the influence of a rotor and a spring support comprises the following steps:
s1, establishing a bearing-elastic support-rotor system force balance equation by combining the force balance relationship of the bearing, the rotor and the elastic support, and solving the equation to obtain the acting force of the rolling body and the ferrule;
s2, calculating the proportion of the oil-gas mixture, the resistance of lubricating oil on the rolling element and the thickness of a friction pair oil film in the bearing according to the oil supply condition of the bearing, calculating the acting force of the rolling element, the retainer and the lubricating oil according to the acting force of the rolling element and the ferrule obtained in S1, and calculating the acting force of the rolling element and the retainer according to the acting force of the rolling element, the retainer and the lubricating oil to obtain the acting moment of the rolling element and the retainer;
s3, establishing a motion differential equation of the rolling body and the retainer, substituting the acting force of the rolling body, the retainer, the lubricating oil and the acting torque of the rolling body and the retainer into the motion differential equation, and solving the motion differential equation of the rolling body and the retainer to obtain the motion state of the rolling body and the retainer at the next moment;
s4, establishing a motion differential equation of the supporting substructure by taking the motion states of the rolling body and the retainer obtained in S3 as initial values, solving the motion states of the rolling body and the retainer after correction by adopting an implicit integration method of a rigid differential equation, and calculating dynamic performance parameters of the bearing at the moment and the constraint reaction force of the supporting structure to the rotor;
s5, establishing a rotor motion differential equation, substituting the acting force and the acting torque of the supporting substructure on the rotor into the rotor motion differential equation, solving the rotor motion differential equation by adopting an explicit integral method of structural dynamics, and obtaining the rotor displacement and speed response of the rotor at the next moment;
and S6, substituting the displacement of the rotor node where the bearing is located into a bearing mechanical model, repeating the steps S2-S5 until the time reaches a preset moment, obtaining the acting force, time domain displacement, speed and acceleration response of each element of the bearing-rotor system in a preset integration time period, and completing the performance analysis of the bearing.
Further, the S1 includes:
s101, when the calculation time i is equal to 0, calculating an initial time speed of the bearing rolling element and the cage according to the ring control theory, when the calculation time i is greater than 0, calculating a centrifugal force and a friction force of the bearing rolling element according to the revolution speed of the rolling element obtained in step S4, and establishing a force balance equation of the bearing-spring support-rotor system according to the interaction relationship among the elements in the bearing ring, the rolling element, the spring support, and the rotor system, specifically formula 1:
Figure BDA0003313480920000041
s102, calculating an instantaneous radial load FBj (j is more than or equal to 1 and less than or equal to n) of the rotor load distributed to the jth bearing through a force balance relation between a fulcrum and an external load, wherein the solving method is as follows:
Figure BDA0003313480920000042
calculating the instantaneous load on each bearingFBj, calculating the bearing displacement of the jth bearing at the moment by combining a bearing pseudo-static model
Figure BDA0003313480920000043
Displacement of spring support
Figure BDA0003313480920000044
And rotor displacement
Figure BDA0003313480920000045
S103, setting the system displacement at the ith moment
Figure BDA0003313480920000046
Establishing a function formula 3:
Figure BDA0003313480920000047
let the k iteration variable at the ith moment of the function be
Figure BDA0003313480920000048
For bearing displacement vector
Figure BDA0003313480920000049
Vector of rotor displacement
Figure BDA00033134809200000410
Displacement vector of bullet
Figure BDA00033134809200000411
Respectively assigned a small increment
Figure BDA00033134809200000412
Then substituted into the function formula to respectively obtain the corresponding function values,
Figure BDA00033134809200000413
Figure BDA00033134809200000414
Will be provided with
Figure BDA00033134809200000415
Group integration matrix theta, set intermediate variable Xm＝[x1,x2,…,xn]TTo obtain the bearing displacement of the jth bearing at the moment
Figure BDA0003313480920000051
Displacement of spring support
Figure BDA0003313480920000052
And rotor displacement
Figure BDA0003313480920000053
As an initial iteration value, X is calculated based on an iteration formulamThe specific calculation process is as follows:
Figure BDA0003313480920000054
according to the obtained XmFurther calculating
Figure BDA0003313480920000055
Figure BDA0003313480920000056
Setting the upper limit of the error acceptable for system convergence to be EsetWhen it is satisfied
Figure BDA0003313480920000057
And is
Figure BDA0003313480920000058
Obtained from formula 5
Figure BDA0003313480920000059
Is the bearing displacement at the ith moment
Figure BDA00033134809200000510
Displacement of spring support
Figure BDA00033134809200000511
And rotor displacement
Figure BDA00033134809200000512
Further, the S2 includes:
s201, according to the obtained
Figure BDA00033134809200000513
Combining the theory of tribology to calculate the oil film thickness and friction force of the contact area of the rolling body and the ferrule
Figure BDA00033134809200000514
Acting force vector of retainer and rolling body
Figure BDA00033134809200000515
Cage and guide ferrule interaction force vector
Figure BDA00033134809200000516
S202, according to the displacement vector of the bearing element at the ith moment
Figure BDA00033134809200000517
According to obtaining
Figure BDA00033134809200000518
And calculating the action moment of the bearing rolling body according to the relative position relationship among the retainer, the ferrule and the rolling body, wherein the calculation process is as shown in formula 6:
Figure BDA0003313480920000061
and then calculating the action moment of the bearing retainer as shown in the formula 7:
Figure BDA0003313480920000062
further, the S3 includes:
calculating the acting force vector of the lubricating oil on the rolling body and the retainer according to the motion speed and the oil supply condition of the rolling body and the retainer at the ith moment
Figure BDA0003313480920000063
Establishing differential equations of motion between the rolling elements and the cage of the bearing, e.g.
Formula 8:
Figure BDA0003313480920000064
and (3) solving the formula (8) by adopting a numerical integration method to obtain the displacement, the speed and the acceleration of the rolling body and the retainer at the (i + 1) th moment.
Further, the S4 specifically includes:
the corresponding movements of the rotor, the support substructure 1 and the support substructure 2 are indicated by the generalized coordinates qr, q1 and q2, respectively, let CIAnd CIIExpressing a constraint link corresponding relation, and writing a constraint equation between the supporting substructure and the rotor system flexible structure body into a formula 9:
Figure BDA0003313480920000071
based on the constraint equation, a Lagrange multiplier lambda and a constraint relation are introduced, and a bearing-elastic support-rotor system dynamic differential equation is established as formula 10:
Figure BDA0003313480920000072
partitioning the support subsystem and the rotor system in the formula 10 to obtain a dynamic differential equation of the support subsystem as a formula 11:
Figure BDA0003313480920000073
and (4) taking the position vectors and the speed vectors of the rolling body and the retainer obtained in the step (S3) as initial values, numerically integrating the support substructure at the time t by adopting an implicit integration method of a rigid differential equation according to a motion differential equation 10 and an equation 11, solving the corrected displacement, speed and acceleration of the rolling body and the retainer, and calculating the constraint reaction forces of the support substructure at the time t + delta t/2 and the time t + delta t to the rotor according to the corrected displacement, speed and acceleration of the rolling body.
Further, the S5 specifically includes:
according to the constraint relation between the rotor and the supporting substructure, a rotor motion differential equation is established as formula 12:
Figure BDA0003313480920000074
and substituting the constraint reaction force of the supporting substructure on the rotor into a rotor differential equation 10, and performing numerical integration solution on the rotor structure by using an explicit integral method of structural dynamics to calculate the rotor displacement, speed and acceleration response of the rotor at the next moment.
The bearing dynamic performance analysis method considering the influence of the rotor and the elastic support has the following specific beneficial effects:
1) the method provides a general theoretical framework and algorithm for modeling and calculation of a bearing-rotor-elastic support system, is easy to realize in a flow manner, and is compiled into a modular calculation program;
2) the method can process the condition that the difference between the rotor rigidity, the elastic support rigidity and the bearing rigidity is large, improve the calculation stability of the joint simulation of the bearing-rotor-elastic supporting system and reduce the probability of divergence in calculation;
3) the method can comprehensively consider the influence of the rotor and the elastic support on the dynamic performance (such as slipping, heat generation and motion stability of the retainer) of the bearing when the rolling bearing is designed and analyzed, and lays a theoretical foundation for the integrated design of the rolling bearing, other support structures and a rotor system.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present disclosure, the drawings needed to be used in the embodiments will be briefly described below, and it is apparent that the drawings in the following description are only some embodiments of the present disclosure, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flow chart of the present invention for bearing dynamic performance analysis considering spring support and rotor effects;
FIG. 2 is a schematic diagram of the overall structure of the bearing-spring support-rotor system of the present invention;
FIG. 3 is a schematic view of the partial support structure A of FIG. 2;
FIG. 4 is a schematic view of the mechanical coupling relationship of the rotor-bearing-spring support system of the present invention;
FIG. 5 is a schematic diagram of the bearing-spring support-rotor system dynamics solving process of the present invention;
FIG. 6 is a graph of the movement locus of each node of the rotor calculated based on the method of the present invention;
FIG. 7 is a diagram of the autorotation speeds of the 1 st, 2 nd and 3 rd rolling elements of the angular contact ball bearing calculated based on the method of the invention;
FIG. 8 is a force diagram of the angular contact ball bearing of the 1 st, 2 nd, 3 rd rolling elements and the cage calculated based on the method of the invention;
FIG. 9 is a graph of the angular contact ball bearing retainer centroid whirl trajectory calculated based on the method of the present invention;
FIG. 10 shows the revolution speed of the 1 st rolling element and the retainer of the angular contact ball bearing calculated based on the method of the present invention;
wherein: 1-elastic support; 2-a rotor; 3-a bearing; 4-bearing I; 5-bearing II; 6-elastic support I; 7, elastic support II; 8-turntable I; 9-turntable II; 1-1: a disc element; 2-2: a beam unit; 3-3: supporting the substructure.
Detailed Description
The embodiments of the present disclosure are described in detail below with reference to the accompanying drawings.
The embodiments of the present disclosure are described below with specific examples, and other advantages and effects of the present disclosure will be readily apparent to those skilled in the art from the disclosure in the specification. It is to be understood that the described embodiments are merely illustrative of some, and not restrictive, of the embodiments of the disclosure. The disclosure may be embodied or carried out in various other specific embodiments, and various modifications and changes may be made in the details within the description without departing from the spirit of the disclosure. It is to be noted that the features in the following embodiments and examples may be combined with each other without conflict. All other embodiments, which can be derived by a person skilled in the art from the embodiments disclosed herein without making any creative effort, shall fall within the protection scope of the present disclosure.
It is noted that various aspects of the embodiments are described below within the scope of the appended claims. It should be apparent that the aspects described herein may be embodied in a wide variety of forms and that any specific structure and/or function described herein is merely illustrative. Based on the disclosure, one skilled in the art should appreciate that one aspect described herein may be implemented independently of any other aspects and that two or more of these aspects may be combined in various ways. For example, an apparatus may be implemented and/or a method practiced using any number of the aspects set forth herein. Additionally, such an apparatus may be implemented and/or such a method may be practiced using other structure and/or functionality in addition to one or more of the aspects set forth herein.
It should be further noted that the drawings provided in the following embodiments are only schematic illustrations of the basic concepts of the present disclosure, and the drawings only show the components related to the present disclosure rather than the numbers, shapes and dimensions of the components in actual implementation, and the types, the numbers and the proportions of the components in actual implementation may be arbitrarily changed, and the layout of the components may be more complicated.
In addition, in the following description, specific details are provided to facilitate a thorough understanding of the examples. However, it will be understood by those skilled in the art that the aspects may be practiced without these specific details.
The embodiment of the disclosure provides a bearing performance analysis method considering the influence of a rotor and a spring support. The embodiments of the present disclosure will be described in further detail below with reference to the accompanying drawings. Refer to FIGS. 1-10.
Fig. 1 shows a flow chart of the method of this embodiment, which mainly includes the following steps:
1) acquiring structural parameters, material parameters and bearing oil supply conditions of a bearing, an elastic support and a rotor system, wherein the structural parameters comprise specific sizes of a rolling bearing, a rotor and the elastic support, the material parameters comprise elastic modulus, Poisson's ratio and density of each element of the rolling bearing, the rotor and the elastic support material, the Hertz contact rigidity between the rolling body and a ferrule and between the rolling body and a retainer is calculated according to the material parameters, the bearing oil supply conditions comprise a bearing oil supply mode, flow and lubricating oil temperature, the lubricating oil viscosity and density are calculated according to the Hertz contact rigidity, and data are provided for subsequent analysis of the thickness of an oil film contacting the rolling body and the ferrule and the acting force of the lubricating oil on the retainer and the rolling body;
2) matrix M for calculating inertia of rolling bodybAnd a centrifugal force matrix MballAnd a cage inertia matrix McEstablishing a rotor finite element model and an elastic support finite element model according to an elastic deformation theory, and calculating a rotor stiffness matrix KrRotor mass matrix MrSpring support stiffness matrix KsqAccording to the working conditions of the load and the rotating speed of the rotor and the combination of the force balance relation of the bearing-rotor-elastic support system, a force balance equation of the bearing-rotor-elastic support system is established, and the displacement vector of the bearing at the ith moment is calculated
Figure BDA0003313480920000111
And rotor displacement vector
Figure BDA0003313480920000112
Displacement vector of spring support
Figure BDA0003313480920000113
Further calculating to obtain the interaction force between the rolling body and the ferrule;
3-1) according to the bearing oil supply flow QflowBearing ring rotation speed omegaringBearing pitch diameter DmThe fuel-air ratio is calculated according to the following formula (1)
Figure BDA0003313480920000114
Calculating the effective density rho of the lubricating oil according to the obtained oil-gas ratio chieffAnd effective viscosity
Figure BDA0003313480920000115
The effective density calculation process is formula (2):
ρeff＝ρoilχ+(1-χ)ρair (2)
the effective viscosity calculation process is formula (3):
Figure BDA00033134809200001210
3-2) substituting the calculation result into a Hamrock-Dowson film thickness formula to obtain the thickness of the contact oil film of the rolling body and the ferrule, and combining the thicknesses
Figure BDA0003313480920000121
Combining the theory of tribology to calculate the friction force vector of the rolling body
Figure BDA0003313480920000122
Acting force vector of retainer and rolling body
Figure BDA0003313480920000123
Cage and guide ferrule interaction force vector
Figure BDA0003313480920000124
4) Establishing differential equation of the rolling body and the retainer, and substituting each acting force obtained by the above stepsEntering a motion differential equation of the rolling body and the retainer, and calculating the revolution speed vector of the rolling body at the (i + 1) th moment by adopting a numerical integration method
Figure BDA0003313480920000125
Self rotation velocity vector
Figure BDA0003313480920000126
And cage motion velocity vector
Figure BDA0003313480920000127
And the (i + 1) th moment rolling element space position vector
Figure BDA0003313480920000128
And cage spatial position vector
Figure BDA0003313480920000129
Accordingly, the motion states of the rolling body and the retainer at the next moment are obtained;
5) establishing a motion differential equation of the supporting substructure, taking the motion states of the rolling body and the retainer obtained in S3 as initial values, solving the motion differential equation of the supporting substructure by adopting an implicit integration method of a rigid differential equation to obtain the motion states of the rolling body and the retainer after correction, and calculating various dynamic performance parameters of the bearing at the moment and the constraint counter force of the supporting structure to the rotor according to the motion differential equation;
6) establishing a rotor motion differential equation, acquiring the excitation force of a corresponding node of a bearing mounting position according to the constraint counter force of the bearing substructure on the rotor obtained in the step S5, substituting the excitation force into the rotor motion differential equation, and calculating the displacement of the rotor at the (i + 1) th moment by numerical integration in combination with an explicit integration method of structure dynamics
Figure BDA0003313480920000131
Speed response
Figure BDA0003313480920000132
And acceleration response
Figure BDA0003313480920000133
7) According to the i +1 th moment displacement of the rotor
Figure BDA0003313480920000134
Speed response
Figure BDA0003313480920000135
And acceleration response
Figure BDA0003313480920000136
Obtaining the displacement of a rotor node where the bearing is positioned, turning to the step 2), substituting the displacement into the bearing, the rotor and the support mechanical model, and repeating the process until the time reaches the preset time tsThe response of the acting force and the time domain displacement, the speed and the acceleration of each element of the bearing-rotor system in the preset integral time period can be obtained;
further, in step 2), when the calculation time i is 0, the initial time velocity of the bearing rolling element and the cage is calculated according to the ring control theory, and when the calculation time i is 0>0, according to the revolution speed vector of the rolling body obtained in the step 4)
Figure BDA0003313480920000137
Calculating the centrifugal force vector of the bearing rolling body
Figure BDA0003313480920000138
And the vector of friction force
Figure BDA0003313480920000139
Establishing a force balance equation of the bearing-elastic support-rotor system according to the interaction relation among the elements in the bearing ring, the rolling body, the elastic support and the rotor system, wherein the equation is specifically shown as a formula (4):
Figure BDA00033134809200001310
in the formula (4), FeIs the centrifugal force vector to which the rotor is subjected, FoFor non-centring force vector to which the rotor is subjected,FhIs a constant load vector experienced by the rotor. GhIs the rotor gravity vector.
Calculating the instantaneous radial load FBj (j is more than or equal to 1 and less than or equal to n) distributed to the jth bearing by the rotor load through the force balance relation between the fulcrum and the external load, and solving the following formula (5) specifically:
Figure BDA0003313480920000141
in the formula, Cij is the axial distance (i is more than or equal to 1 and j is more than or equal to n) from the ith bearing to the jth bearing, and Mj is the equivalent moment generated by the centrifugal force, the constant load, the unbalanced force and the unbalanced force borne by the rotor at the moment at the jth bearing.
After the instantaneous load FBj on each bearing is obtained through the method, the bearing displacement of the jth bearing at the moment is calculated by combining a bearing pseudo-static model
Figure BDA0003313480920000142
Displacement of spring support
Figure BDA0003313480920000143
And rotor displacement
Figure BDA0003313480920000144
In order to solve the bearing-elastic support-rotor force balance equation (4), the system displacement at the ith moment is set
Figure BDA0003313480920000145
The function is established as equation (6):
Figure BDA0003313480920000146
suppose that the function has a k iteration variable at the ith time of
Figure BDA0003313480920000147
For bearing displacement vector
Figure BDA0003313480920000148
Displacement vector of each node of rotor
Figure BDA0003313480920000149
Displacement vector of bullet
Figure BDA00033134809200001410
Respectively assigned a small increment
Figure BDA00033134809200001411
Then substituting into the above function formula to obtain corresponding function values respectively
Figure BDA00033134809200001412
P(Si S,Si B,Si R)ΔB、P(Si S,Si B,Si R)ΔRWill be
Figure BDA00033134809200001521
Figure BDA0003313480920000152
Group integration matrix theta, set intermediate variables
Figure BDA0003313480920000153
So as to obtain the bearing displacement of the jth bearing at the moment
Figure BDA0003313480920000154
Spring-supported nodal displacement
Figure BDA0003313480920000155
And rotor displacement
Figure BDA0003313480920000156
As an initial iteration value, X is calculated based on the following formulamThe specific calculation process is as the following formula (7);
Figure BDA0003313480920000157
according to the obtained XmFurther calculate
Figure BDA0003313480920000158
Figure BDA0003313480920000159
Setting the upper limit of the error acceptable for system convergence to be EsetWhen it is satisfied
Figure BDA00033134809200001510
And is
Figure BDA00033134809200001511
Obtained from the formula (8)
Figure BDA00033134809200001512
Is just the ith moment displacement of the bearing
Figure BDA00033134809200001513
Displacement of projectile at ith moment
Figure BDA00033134809200001514
And displacement of the rotor at the ith moment
Figure BDA00033134809200001515
Further, in step 3), according to the obtained
Figure BDA00033134809200001516
Combining the theory of tribology to calculate the oil film thickness and friction force of the contact area of the rolling body and the ferrule
Figure BDA00033134809200001517
Acting force vector of retainer and rolling body
Figure BDA00033134809200001518
Cage and guide ferrule interaction force vector
Figure BDA00033134809200001519
According to the displacement vector of the bearing element at the ith moment
Figure BDA00033134809200001520
Sequentially calculating the vector O from the center of the rolling body to the contact point of the rolling body and the ferrulebOtVector O from center of rolling body to contact point of rolling body with cagebOctVector O from the center of the cage to the contact point of the rolling element with the cagecOctVector O from the center of the cage to the minimum clearance between the cage guide face and the ferrule guide facecOtgAnd a transformation matrix T from the inertial frame to the azimuthal frame of the rolling elementsiaAnd calculating the acting moment on the bearing rolling body according to the formula (9):
Figure BDA0003313480920000161
the moment of action to which the bearing cage is subjected is calculated accordingly, as in equation (10)
Figure BDA0003313480920000162
Further, in step 4), a lubricant acting force vector F received during the revolution motion of the rolling elements is calculated based on the moving speed of the rolling elements and the cage at the ith time and the oil supply conditioni ball_dActing force vector F of lubricating oil received by rolling element during self-rotationi ball_rdActing force vector F of lubricating oil received during revolution of retaineri cdActing force vector F of lubricating oil received by the cage during its rotationi crdEstablishing a differential equation of motion of the bearing rolling elements and the retainer as followsFormula (11):
Figure BDA0003313480920000163
in the formula (2), the reaction mixture is,
Figure BDA0003313480920000164
and
Figure BDA0003313480920000165
for revolution and autorotation acceleration vectors of rolling elements at the ith time, Vi ball_pAnd Vi ball_rThe revolution and rotation speed vectors of the rolling bodies at the ith moment,
Figure BDA0003313480920000166
and
Figure BDA0003313480920000167
for the holder translation and autorotation acceleration vectors at the ith moment, Vi c_pAnd Vi c_rFor the holder translation and rotation speed vectors at the ith moment, Cball_pAnd Cball_rFor rolling-body translational damping matrix and rotational damping matrix, CcpAnd CcrThe holder translates and rotates the damping matrix.
Solving the formula (2) by adopting a numerical integration method to obtain the revolution acceleration vector of the rolling element at the (i + 1) th moment
Figure BDA0003313480920000171
And the self-rotation acceleration vector
Figure BDA0003313480920000172
Holder translational acceleration
Figure BDA0003313480920000173
And acceleration of autorotation
Figure BDA0003313480920000174
Revolution velocity vector of rolling element
Figure BDA0003313480920000175
And the rotation velocity vector
Figure BDA0003313480920000176
Translational speed of retainer
Figure BDA0003313480920000177
And the speed of rotation
Figure BDA0003313480920000178
And a rolling element revolution speed vector W at the i +1 th timebSelf-rotation velocity vector WrAnd the cage motion velocity vector VcSpace position vector U of rolling elementBAnd cage spatial position vector Uc。
Further, in step 5), the spring-bearing-rotor system shown in fig. 4 is divided into two parts, namely a rotor system and a support structure, wherein the rotor part is regarded as a flexible structural body, the mass distribution of the flexible structural body is represented by a matrix Mr, the spring and the bearing are regarded as support subsystems, and the mass of the two support subsystems is represented by matrixes M1 and M2 respectively. The corresponding motion of the three masses Mr, M1 and M2 is represented by generalized coordinates qr, q1 and q2, respectively. Let kb、ksqThe equivalent bearing stiffness and the elastic support stiffness of the bearing are respectively. m isnr、mwrThe mass of the bearing inner ring and the outer ring is shown. CIAnd CIIAnd (3) expressing a constraint link corresponding relation, and writing a constraint equation between the supporting substructure and the flexible structure body of the rotor system into an equation (12):
Figure BDA0003313480920000179
according to the constraint equation, introducing a Lagrange multiplier lambda and a constraint relation, and finishing a bearing-elastic branch-rotor system dynamic differential equation corresponding to the bearing-elastic branch-rotor system shown in the figure 4 into an equation (13):
Figure BDA0003313480920000181
wherein Q isv1And Qv2To support coupled inertial forces on the subsystem; f. ofvrIs the nodal internal force on the rotor structure; f. ofv1And fv2Acting force for each element in the supporting substructure; qe1Is a generalized external force.
Partitioning the support subsystem and the rotor system in the formula (13) to obtain a dynamic differential equation of the support subsystem as a formula (14):
Figure BDA0003313480920000182
the latter two rows of the analytical formula are known to belong to the system constraint equations for support structure displacement and rotor acceleration, which represent: the acceleration of the rotor at each moment and the displacement of the supporting substructure have a quantitative relation, and by utilizing the relation, the subsequent fractional solution of the transient response of the rotor system and the transient response of the supporting structure can be conveniently carried out.
Aiming at the characteristics of the decoupling equation of the system, the bearing-elastic support-rotor system is subjected to characteristic division and model division so as to solve the system equation by adopting a method of fractional solution and step-by-step iteration, and the specific process is shown in the following figure 5. FIG. 5 shows the solution method for different parts of the system and the system coupling solution method in one time step. According to the flow chart, firstly, a combined formula (14) is combined, the position vector and the speed vector of the rolling body and the retainer obtained in the step 4) are used as initial values, the implicit integration method of a rigid differential equation is adopted to carry out numerical integration on the support substructure at the moment t, the corrected displacement, speed and acceleration of the rolling body and the retainer are solved, the dynamic performance parameters such as the contact stress, the contact angle, the rolling ratio, the PV value and the speed whirling deviation ratio of the retainer at the moment are calculated according to the corrected displacement, speed and acceleration of the rolling body and the retainer, and the constraint reaction Q of the support substructure at the moment t + delta t/2 and the constraint reaction Q of the support substructure at the moment t + delta t to the support substructure at the moment tκ+ΔQκ/2 and Qκ+ΔQκWherein Q isκIs the restraining reaction at time t, Δ QκTo constrain the amount of change in the counter force over a time increment step.
In the step 6), the equation (12) is analyzed, and a rotor system dynamic differential equation can be separately formulated as the following equation (15):
Figure BDA0003313480920000191
in the formula (I), the compound is shown in the specification,
Figure BDA0003313480920000192
and
Figure BDA0003313480920000193
and the constraint counter force is generated for the system structure, is used as a bridge for connecting the support substructure and the rotor substructure, and belongs to a link for expressing the mechanical coupling relationship among different subsystems and data transmission among the subsystems.
And (3) respectively transmitting the constraint counter force obtained by solving the supporting structure to two time sub-steps in a time increment step of the rotor system, and on the basis, carrying out numerical solution on the rotor structure by using an explicit integral method of the structure dynamics by using a combined formula (15) to obtain the displacement response, the speed response and the acceleration response of the rotor at the next moment so as to finish the system dynamics response solution in a time step.
According to a preferred embodiment:
taking the dynamic performance analysis of a certain type of bearing-elastic support-rotor system as an example, the method for analyzing the dynamic performance of the bearing considering the rotor and the elastic support in the embodiment of the disclosure is described in detail, and meanwhile, the effectiveness of the method in the embodiment of the disclosure is explained. The structural parameters are listed in tables 1-5. In fig. 2-3, a schematic assembly diagram of the bearing-rotor-elastic support system is shown, wherein one end of the rotor is provided with an angular contact ball bearing, the other end of the rotor is provided with a cylindrical roller bearing, and the angular contact ball bearing and the outer ring of the cylindrical roller bearing are both arranged on the elastic support.
TABLE 1 angular contact ball bearing and its main parameters
(symbol) Description of the invention Value of Unit of
Dw Diameter of rolling element 19.05 mm
di Inner diameter of bearing 100 mm
do Bearing outside diameter 180 mm
Z Number of rolling elements 18
a0 Initial contact Angle 25 °
B Bearing width 28 mm
Dc Outer diameter of cage 148.8 mm
dc Inner diameter of retainer 129 mm
Dp Cage pocket diameter 0.826 mm
L Width of cage guide surface 27.3 mm
Cg Cage guide gap 1.46 mm
f1 Outer ring groove curvature coefficient 0.52
f2 Coefficient of curvature of inner ring groove 0.54
Kr Spring supported radial stiffness used with ball bearing 9.8e6 N/m
Ka Spring fulcrum axial stiffness used with ball bearing 1.7e9 N/m
den Density of bearing material 7750 Kg/m^3
E Modulus of elasticity of bearing material 200 GPa
μ Poisson ratio of bearing material 0.3 GPa
TABLE 2 cylindrical roller bearing of a certain type and its main parameters of spring support
(symbol) Description of the invention Value of Unit of
Dw Diameter of rolling element 10 mm
di Inner diameter of bearing 100 mm
do Bearing outside diameter 140 mm
Z Number of rolling elements 26
ddi Diameter of groove bottom of bearing inner ring 110 mm
ddo Diameter of groove bottom of bearing outer ring 130 mm
Dm Pitch circle diameter 120 mm
L Length of roller 10 mm
Pd Bearing play 0 mm
B Bearing width 20 mm
dc Inner diameter of retainer 116.8 mm
Dc Outer diameter of cage 129 mm
Cg Cage guide gap 0.9 mm
B Width of cage 18 mm
DDp Circumferential clearance of cage pocket 0.1 mm
Dpp Cage pocket axial clearance 0.1 mm
Kr Spring-supported radial stiffness for use with roller bearings 9.8e6 N/m
Ka Spring support axial stiffness for use with roller bearings 1.7e9 N/m
den Density of bearing material 7750 Kg/m^3
E Modulus of elasticity of bearing material 200 GPa
μ Poisson ratio of bearing material 0.3 GPa
TABLE 3 Main parameters of bearing oil supply
(symbol) Description of the invention Value of Unit of
Vis Viscosity of lubricating oil 0.055 Pa·s
den Density of lubricating oil 970 Kg/m^3
Qflow Flow rate of lubricating oil 5 L/min
t Inlet oil temperature 20 ℃
TABLE 4 rotor principal parameters
(symbol) Description of the invention Value of Unit of
Dr1 Outer diameter of rotor 100 mm
Dr2 Inner diameter of rotor 0 mm
Lr Rotor length 900 mm
N Number of finite element elements divided by rotor 9
Mre Unbalance of rotor 1e-7 Kg·m
Jl Ball bearing position distance from left end of rotor 0 mm
Jr The distance between the position of the roller bearing and the left end of the rotor 500 mm
TABLE 5 Condition parameters
(symbol) Description of the invention Value of Unit of
Nm Rotor speed 6000 rpm
Fx Node x-direction axial load 10000 N
Fy Node y-direction radial load 3000 N
Fz Node z-direction radial load 33 N
NodeF Position of applied load according to distance of left end of rotor 300 mm
NodeFe The distance of the unbalance amount according to the left end of the rotor 100 mm
According to the steps of the invention, the coupling response of the bearing, the rotor and the elastic support within 0-0.32 s can be calculated, fig. 6 shows a motion locus diagram of each node of the rotor, fig. 7 shows a self-rotation speed diagram of the 1 st, 2 nd and 3 rd rolling elements of the angular contact ball bearing, fig. 8 shows an action force diagram of the 1 st, 2 nd and 3 th rolling elements of the angular contact ball bearing and the retainer, fig. 9 shows a centroid whirl locus diagram of the angular contact ball bearing retainer, and fig. 10 shows a revolution speed diagram of the 1 st rolling element of the angular contact ball bearing and the retainer.
Therefore, the embodiment of the disclosure aims to provide a dynamic performance modeling and solving method capable of comprehensively considering the spatial three-dimensional motion of a rolling element and a retainer of a rolling bearing, the lubricating oil effect, the rotor vibration and the deformation coupling influence of a spring support, and lays the theoretical foundation of the joint simulation and matching design of the rolling bearing, the spring support and the rotor.
In summary, the present invention belongs to the field of mechanical dynamics, and particularly provides a dynamic performance analysis method for a rolling bearing considering a rotor and a spring support, which includes the following steps: 1) collecting system attribute parameters; 2) calculating the acting force of the rolling body and the ferrule by combining the force balance relationship of the bearing-rotor-elastic support system; 3) calculating acting forces of the rolling body, the retainer and lubricating oil according to the acting forces of the rolling body and the ferrule and the oil supply condition; 4) solving a motion differential equation of the rolling body and the retainer to obtain the motion of the rolling body and the retainer; 5) solving a rotor motion differential equation to obtain rotor displacement and speed response; 6) and substituting the displacement of the rotor node where the bearing is located into a bearing mechanical model, and repeating the process to calculate the time domain response of the bearing-rotor-elastic support system in the preset integral time period. The method can comprehensively consider the coupling relation among the lubricating effect, the vibration of the retainer, the inertia of the rotor and the deformation of the elastic support, and provides a theoretical method for introducing the influence of the elastic support and the rotor during the bearing performance simulation.
The above description is only for the specific embodiments of the present disclosure, but the scope of the present disclosure is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present disclosure should be covered within the scope of the present disclosure. Therefore, the protection scope of the present disclosure shall be subject to the protection scope of the claims.

Claims (6)

1. A bearing dynamic performance analysis method considering the influence of a rotor and a spring support is characterized in that: the method comprises the following steps:
s1, establishing a bearing-elastic support-rotor system force balance equation by combining the force balance relationship of the bearing, the rotor and the elastic support, and solving the equation to obtain the acting force of the rolling body and the ferrule;
s2, calculating the proportion of the oil-gas mixture, the resistance of lubricating oil on the rolling element and the thickness of a friction pair oil film in the bearing according to the oil supply condition of the bearing, calculating the acting force of the rolling element, the retainer and the lubricating oil according to the acting force of the rolling element and the ferrule obtained in S1, and calculating the acting force of the rolling element and the retainer according to the acting force of the rolling element, the retainer and the lubricating oil to obtain the acting moment of the rolling element and the retainer;
s3, establishing a motion differential equation of the rolling body and the retainer, substituting the acting force of the rolling body, the retainer, the lubricating oil and the acting torque of the rolling body and the retainer into the motion differential equation, and solving the motion differential equation of the rolling body and the retainer to obtain the motion state of the rolling body and the retainer at the next moment;
s4, establishing a motion differential equation of the supporting substructure by taking the motion states of the rolling body and the retainer obtained in S3 as initial values, solving the motion states of the rolling body and the retainer after correction by adopting an implicit integration method of a rigid differential equation, and calculating dynamic performance parameters of the bearing at the moment and the constraint reaction force of the supporting structure to the rotor;
s5, establishing a rotor motion differential equation, substituting the acting force and the acting torque of the supporting substructure on the rotor into the rotor motion differential equation, solving the rotor motion differential equation by adopting an explicit integral method of structural dynamics, and obtaining the rotor displacement and speed response of the rotor at the next moment;
and S6, substituting the displacement of the rotor node where the bearing is located into a bearing mechanical model, repeating the steps S2-S5 until the time reaches a preset moment, obtaining the acting force, time domain displacement, speed and acceleration response of each element of the bearing-rotor system in a preset integration time period, and completing the performance analysis of the bearing.
2. The method of claim 1 for analyzing dynamic performance of a bearing considering the influence of a rotor and a spring support, wherein: the S1 includes:
s101, when the calculation time i is equal to 0, calculating an initial time speed of the bearing rolling element and the cage according to the ring control theory, when the calculation time i is greater than 0, calculating a centrifugal force and a friction force of the bearing rolling element according to the revolution speed of the rolling element obtained in step S4, and establishing a force balance equation of the bearing-spring support-rotor system according to the interaction relationship among the elements in the bearing ring, the rolling element, the spring support, and the rotor system, specifically formula 1:
Figure FDA0003313480910000021
s102, calculating the instantaneous radial load FBj (j is more than or equal to 1 and less than or equal to n) of the rotor load distributed to the jth bearing through the force balance relation between the pivot and the external load, wherein the solving method is as follows:
Figure FDA0003313480910000022
calculating to obtain the instantaneous load FBj on each bearing, and then combining a bearing pseudo-static model to calculate the bearing displacement of the jth bearing at the moment
Figure FDA0003313480910000023
Displacement of spring support
Figure FDA0003313480910000024
And rotor displacement
Figure FDA0003313480910000025
S103, setting the system displacement at the ith moment
Figure FDA0003313480910000026
Establishing a function equation 3
Figure 1
Let the k iteration variable at the ith moment of the function be
Figure FDA0003313480910000032
For bearing displacement vector
Figure FDA0003313480910000033
Displacement vector of rotor
Figure FDA0003313480910000034
Displacement vector of bullet
Figure FDA0003313480910000035
Respectively assigned with a small increment
Figure FDA0003313480910000036
Then substituted into the function formula to respectively obtain corresponding function values
Figure FDA0003313480910000037
Figure FDA0003313480910000038
Will be provided with
Figure FDA0003313480910000039
Group integration matrix theta, set intermediate variable Xm＝[x1,x2,…,xn]TTo obtain the bearing displacement of the jth bearing at the moment
Figure FDA00033134809100000310
Displacement of spring support
Figure FDA00033134809100000311
And rotor displacement
Figure FDA00033134809100000312
As an initial iteration value, X is calculated based on an iteration formulamThe specific calculation process is as follows:
Figure FDA00033134809100000313
according to the obtained XmFurther, furtherComputing
Figure FDA00033134809100000314
Figure FDA00033134809100000315
Setting the upper limit of the error acceptable for system convergence to be EsetWhen it is satisfied
Figure FDA00033134809100000316
And is
Figure FDA00033134809100000317
Obtained from formula 5
Figure FDA00033134809100000318
Is the bearing displacement at the ith moment
Figure FDA00033134809100000319
Displacement of spring support
Figure FDA00033134809100000320
And rotor displacement
Figure FDA00033134809100000321
3. The method of claim 2 for analyzing dynamic performance of a bearing considering the influence of a rotor and a spring support, wherein: the S2 includes:
s201, according to the obtained
Figure FDA0003313480910000041
Combining the theory of tribology to calculate the oil film thickness and friction force of the contact area of the rolling body and the ferrule
Figure FDA0003313480910000042
Acting force vector of retainer and rolling body
Figure FDA0003313480910000043
Cage and guide ferrule interaction force vector
Figure FDA0003313480910000044
S202, according to the displacement vector of the bearing element at the ith moment
Figure FDA0003313480910000045
According to obtaining
Figure FDA0003313480910000046
And calculating the action moment of the bearing rolling body according to the relative position relationship among the retainer, the ferrule and the rolling body, wherein the calculation process is as shown in formula 6:
Figure FDA0003313480910000047
and then calculating the action moment of the bearing retainer as shown in the formula 7:
Figure FDA0003313480910000048
4. the method of claim 3 for analyzing dynamic performance of a bearing considering the influence of a rotor and a spring support, wherein: the S3 includes:
calculating the acting force vector of the lubricating oil on the rolling body and the retainer according to the motion speed and the oil supply condition of the rolling body and the retainer at the ith moment
Figure FDA0003313480910000049
Establishing a motion differential equation of the bearing rolling body and the retainer, wherein the equation is as follows:
Figure FDA00033134809100000410
and (3) solving the formula (8) by adopting a numerical integration method to obtain the displacement, the speed and the acceleration of the rolling body and the retainer at the (i + 1) th moment.
5. The method of claim 4 for analyzing dynamic performance of a bearing considering the influence of a rotor and a spring support, wherein: the S4 specifically includes:
the corresponding movements of the rotor, the support substructure 1 and the support substructure 2 are indicated by the generalized coordinates qr, q1 and q2, respectively, let CIAnd CIIExpressing a constraint link corresponding relation, and writing a constraint equation between the supporting substructure and the rotor system flexible structure body into a formula 9:
Figure FDA0003313480910000051
based on the constraint equation, a Lagrange multiplier lambda and a constraint relation are introduced, and a bearing-elastic support-rotor system dynamic differential equation is established as formula 10:
Figure FDA0003313480910000052
partitioning the support subsystem and the rotor system in the formula 10 to obtain a dynamic differential equation of the support subsystem as a formula 11:
Figure FDA0003313480910000053
and (4) taking the position vectors and the speed vectors of the rolling body and the retainer obtained in the step (S3) as initial values, numerically integrating the support substructure at the time t by adopting an implicit integration method of a rigid differential equation according to a motion differential equation 10 and an equation 11, solving the corrected displacement, speed and acceleration of the rolling body and the retainer, and calculating the constraint reaction forces of the support substructure at the time t + delta t/2 and the time t + delta t to the rotor according to the corrected displacement, speed and acceleration of the rolling body.
6. The method of claim 5 for analyzing dynamic performance of a bearing considering the influence of a rotor and a spring support, wherein: the S5 specifically includes:
according to the constraint relation between the rotor and the supporting substructure, a rotor motion differential equation is established as formula 12:
Figure FDA0003313480910000061
and substituting the constraint reaction force of the supporting substructure on the rotor into a rotor differential equation 10, and performing numerical integration solution on the rotor structure by using an explicit integral method of structural dynamics to calculate the rotor displacement, speed and acceleration response of the rotor at the next moment.
CN202111223596.8A 2021-10-20 2021-10-20 Bearing performance analysis method considering rotor and spring bearing influence Active CN114491915B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202111223596.8A CN114491915B (en) 2021-10-20 2021-10-20 Bearing performance analysis method considering rotor and spring bearing influence

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202111223596.8A CN114491915B (en) 2021-10-20 2021-10-20 Bearing performance analysis method considering rotor and spring bearing influence

Publications (2)

Publication Number Publication Date
CN114491915A true CN114491915A (en) 2022-05-13
CN114491915B CN114491915B (en) 2023-06-30

Family

ID=81493098

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202111223596.8A Active CN114491915B (en) 2021-10-20 2021-10-20 Bearing performance analysis method considering rotor and spring bearing influence

Country Status (1)

Country Link
CN (1) CN114491915B (en)

Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20040243332A1 (en) * 2003-05-27 2004-12-02 University Of Washington Method for predicting vibrational characteristics of rotating structures
CN103821567A (en) * 2014-01-23 2014-05-28 西北工业大学 Structural dynamic design method for high-pressure rotor of aircraft engine
CN103912315A (en) * 2014-04-14 2014-07-09 西北工业大学 Structural dynamics design method of rotor of aerial engine
CN105738057A (en) * 2016-02-24 2016-07-06 中国航空动力机械研究所 Mouse cage elastic supporting device vibration strain and amplitude calibration system and method
CN105928707A (en) * 2016-04-27 2016-09-07 西安交通大学 Roller bearing-rotor system dynamic coupling modeling method
CN110132556A (en) * 2019-04-30 2019-08-16 中国航发湖南动力机械研究所 Modularization turbine test part and its test method
CN112364463A (en) * 2020-11-27 2021-02-12 中国航发四川燃气涡轮研究院 Squirrel-cage elastic support rigidity and stress analysis method

Patent Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20040243332A1 (en) * 2003-05-27 2004-12-02 University Of Washington Method for predicting vibrational characteristics of rotating structures
CN103821567A (en) * 2014-01-23 2014-05-28 西北工业大学 Structural dynamic design method for high-pressure rotor of aircraft engine
CN103912315A (en) * 2014-04-14 2014-07-09 西北工业大学 Structural dynamics design method of rotor of aerial engine
CN105738057A (en) * 2016-02-24 2016-07-06 中国航空动力机械研究所 Mouse cage elastic supporting device vibration strain and amplitude calibration system and method
CN105928707A (en) * 2016-04-27 2016-09-07 西安交通大学 Roller bearing-rotor system dynamic coupling modeling method
CN110132556A (en) * 2019-04-30 2019-08-16 中国航发湖南动力机械研究所 Modularization turbine test part and its test method
CN112364463A (en) * 2020-11-27 2021-02-12 中国航发四川燃气涡轮研究院 Squirrel-cage elastic support rigidity and stress analysis method

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
ZHUOLIN YE等: "Analysis of Parallel Misalignment of Gear Coupling in Rotor System Using EEMD-median Filter Method", 《2021 IEEE 5TH ADVANCED INFORMATION TECHNOLOGY, ELECTRONIC AND AUTOMATION CONTROL CONFERENCE (IAEAC)》 *
夏玉磊等: "非稳态工况下弹支SFD圆柱滚子轴承动态特性分析", 《机械传动》 *

Also Published As

Publication number Publication date
CN114491915B (en) 2023-06-30

Similar Documents

Publication Publication Date Title
Cao et al. Mechanical model development of rolling bearing-rotor systems: A review
CN110617953B (en) New energy automobile high-speed motor bearing-rotor system dynamic characteristic analysis method
CN104239654B (en) A kind of bearing method for simplifying in Finite Element Simulation Analysis
Ghalamchi et al. Simple and versatile dynamic model of spherical roller bearing
Xu et al. Modeling and analysis of planar multibody systems containing deep groove ball bearing with clearance
CN105928707B (en) A kind of Rotor System with Rolling Bearings Dynamic Coupling modeling method
CN109027017A (en) A kind of Space Rolling Bearing state of wear appraisal procedure
CN109550979B (en) Method for determining axial thermal displacement of bearing ring of high-speed spindle unit
CN107153734B (en) Computing system and method for positioning nonlinear stiffness of angular contact ball bearing under pre-tightening
CN107989818B (en) A kind of W2B type water pump shaft connecting bearings and its durability analysis method
CN113496091A (en) Method for simulating contact dynamic characteristics of high-speed heavy-load ball bearing of liquid rocket engine
CN111813159B (en) Indication method for controlling moment gyro output moment
WO2020019377A1 (en) Dynamic design method for high-speed duplex rolling bearing electric spindle rotor system
CN110399628B (en) Constant-pressure pre-tightening angular contact bearing rigidity value correction method considering vibration influence
CN112329173A (en) Parameter optimization method for rotor-bearing bending-torsion coupling system
Cheng et al. Research on mechanical characteristics of fault-free bearings based on centrifugal force and gyroscopic moment
CN108228991B (en) Method for solving numerical value of high-speed angular contact ball bearing
CN114491915A (en) Bearing dynamic performance analysis method considering rotor and spring support influence
CN110532732B (en) Method for determining rubbing relationship between blade and casing
CN115470584B (en) Dynamic modeling method applied to planetary gear and rolling bearing coupling system
CN116907776A (en) Vibration characteristic analysis method for high-speed electric spindle complete machine
Jin et al. Reliability coupling mechanism analyses of T-rotation-type CMA with frame deformation in CNC machine tools
CN116579104A (en) Method and system for acquiring internal dynamic load of intermediate bearing with inner ring and outer ring rotating simultaneously
Sun et al. Modeling of rotation accuracy of multi-support rotating machinery considering geometric errors and part deformation
Yao et al. Multibody contact dynamics on mechanisms with deep groove ball bearing joints

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