A New Dynamic Model of Ball-Bearing Rotor Systems Based on Rigid Body Element

2016 ◽  
Vol 138 (7) ◽  
Author(s):  
Hongrui Cao ◽  
Yamin Li ◽  
Xuefeng Chen
Keyword(s):  
Rigid Body ◽  
Dynamic Model ◽  
Ball Bearing ◽  
Rotor System ◽  
Radial Clearance ◽  
Fe Model ◽  
Ball Bearings ◽  
Rolling Ball ◽  
Rotor Systems ◽  
Body Element

Ball-bearing rotor systems are key components of rotating machinery. In this work, a new dynamic modeling method for ball-bearing rotor systems is proposed based on rigid body element (RBE). First, the concept of RBE is given, and then the rotor is divided into several discrete RBEs. Every two adjacent RBEs are connected by imaginary springs, whose stiffness is calculated according to properties of the RBEs. Second, all the parts of rolling ball bearings (i.e., outer ring, inner ring, ball, and cage) are considered as RBEs, and Gupta's model is employed to model bearings which include radial clearance, waviness, pedestal effect, etc. Finally, the rotor and all the rolling ball bearings are coupled to develop a dynamic model of the ball-bearing rotor system. The vibration responses of the ball-bearing rotor system can be calculated by solving dynamic equations of each RBE. The proposed method is verified with both simulation and experiment. The RBE model of the rotor is compared with its finite element (FE) model first, and numerical simulation shows the validity of the RBE model. Then, experiments are conducted on a rotor test rig which is supported with two rolling ball bearings as well. Good agreements between measurement and simulation show the ability of the model to predict the dynamic behavior of ball-bearing rotor systems.

Modeling of Flexible Coupling to Connect Misaligned Flexible Rotors Supported on Ball Bearings

2014 ◽  
Author(s):  
T. C. Gupta ◽  
K. Gupta
Keyword(s):  
Dynamic Response ◽  
Stiffness Matrix ◽  
Ball Bearing ◽  
Radial Clearance ◽  
Fe Model ◽  
Ball Bearings ◽  
Flexible Coupling ◽  
Flexible Rotors ◽  
Deep Groove ◽  
Coupling Stiffness

Parallel or/and angular misalignment between rotors connected by flexible coupling causes deformation of coupling elements and rotor shafts both. The forces and moments from flexible coupling act on driver and driven rotors simultaneously and depend upon dynamic response of coupled rotor system. The authors’ aim in the present work is to propose a methodology to incorporate the coupling stiffness matrix and coupling loads into the finite element model of flexibly coupled flexible rotors supported on deep groove ball bearings. The coefficients of coupling stiffness matrix and coupling loads are nonlinear and depend upon the amount of parallel and angular misalignments. To segregate the effect of nonlinear stiffness of coupling on the dynamic response of the system, the stiffness of ball bearing is initially considered to be linear. Thereafter, ball bearing nonlinearities arising from radial clearance, Hertzian deformation of balls and races, and varying compliance effect are included into the FE model of the system. Considering different types of misalignments in succession and combination, the dynamic response is characterized by the presence of 1N, 2N and other super or sub harmonics. The misalignment in one plane is found to affect the dynamic response in both the orthogonal planes. Comparing to the stiffness of flexible coupling, the stiffness of ball bearing is of higher order and therefore, nonlinear coupling forces and moments have dominant influence on the dynamic response of the system.

Study on the Dynamic Response of an Unbalanced Rotor System Supported by Ball Bearings

2019 ◽  
Author(s):  
Bin Fang ◽  
Jinhua Zhang ◽  
Ke Yan ◽  
Jun Hong
Keyword(s):  
Dynamic Model ◽  
Ball Bearing ◽  
Great Influence ◽  
Rotor System ◽  
Dynamic Responses ◽  
Ball Bearings ◽  
Motion Patterns ◽  
Symmetric Rotor ◽  
Asymmetric Rotor ◽  
Restoring Forces

Abstract This paper proposed a new four-degree-of-freedom dynamic model of the bearing-rotor system based on ball bearing without Raceway Control Hypothesis, and both the inertia forces of balls and the tilting motions of rotor are fully considering in the calculation of restoring forces and moments of ball bearings. Then the dynamic model are solved by the fourth-step Runge-Kutta method, and the dynamic responses of rotor system including the displacement, velocity and center orbits are obtained, and the influences of rotating speeds, eccentricity and symmetry of rotor are studied and analyzed. The results show that both the varying compliance of ball bearing and rotor eccentric force have a great influence on the dynamic responses and motion patterns of bearing-rotor system, and the titling motion of bearing-rotor should be considered in the analysis of asymmetric rotor or the symmetric rotor under some specific conditions.

A General Method for the Dynamic Modeling of Ball Bearing–Rotor Systems

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
Yamin Li ◽  
Hongrui Cao ◽  
Linkai Niu ◽  
Xiaoliang Jin
Keyword(s):  
Rigid Body ◽  
Dynamic Modeling ◽  
Ball Bearing ◽  
Elastic Vibration ◽  
Rigid Body Motion ◽  
Rotor System ◽  
Body Motion ◽  
Rotor Systems ◽  
Proposed Model ◽  
Vibration Responses

A general dynamic modeling method of ball bearing–rotor systems is proposed. Gupta's bearing model is applied to predict the rigid body motion of the system considering the three-dimensional motions of each part (i.e., outer ring, inner ring, ball, and rotor), lubrication tractions, and bearing clearances. The finite element method is used to model the elastic deformation of the rotor. The dynamic model of the whole ball bearing–rotor system is proposed by integrating the rigid body motion and the elastic vibration of the rotor. An experiment is conducted on a test rig of rotor supported by two angular contact ball bearings. The simulation results are compared with the measured vibration responses to validate the proposed model. Good agreements show the accuracy of the proposed model and its ability to predict the dynamic behavior of ball bearing–rotor systems. Based on the proposed model, vibration responses of a two bearing–rotor system under different bearing clearances were simulated and their characteristics were discussed. The proposed model may provide guidance for structural optimization, fault diagnosis, dynamic balancing, and other applications.

Nonlinear Dynamic Analysis of an Asymmetric Ball Bearing Rotor System

2019 ◽  
Author(s):  
Doğancan Bahan ◽  
Ender Ciğeroğlu
Keyword(s):  
Ball Bearing ◽  
Nonlinear Dynamic Analysis ◽  
Harmonic Balance Method ◽  
Beam Theory ◽  
Hertzian Contact ◽  
Radial Clearance ◽  
Ball Bearings ◽  
Algebraic Equations ◽  
Rotor Systems ◽  
Nonlinear Algebraic Equations

Abstract Performance of ball bearing–rotor systems are highly dependent on and often limited by characteristics of ball bearings. Several studies are available in the literature, investigating varying compliance and subharmonic resonances of ball bearings. Most of the studies are carried out with rigid rotors to focus on modelling of the bearings. There exist few studies which take flexibility of rotors into account. Furthermore, even if the rotor flexibility is modelled, most of the time symmetrical rotors are considered. However, rotors are rarely symmetric in realistic applications due to different locations of bearings and different weights of rotor components (compressors, turbines etc.). In this study, an asymmetric, balanced, flexible rotor supported by ball bearings considering Hertzian contact and radial clearance is investigated. Rotor shaft is modelled with Nelson finite rotor elements using Timoshenko beam theory and disks are considered as rigid masses. Harmonic Balance Method (HBM) is used to obtain nonlinear algebraic equations in the frequency domain and Alternating Frequency Time (AFT) method is utilized to find Fourier coefficients of nonlinear bearing forces. In order to decrease the number of nonlinear equations to be solved, Receptance Method (RM) is applied. Resulting set of nonlinear algebraic equations is solved by using Newton’s method with arclength continuation. Several case studies are performed and effects of asymmetry on nonlinear periodic vibration response of rotors are studied.

scholarly journals Study on the Dynamic Problems of Double-Disk Rotor System Supported by Deep Groove Ball Bearing

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Yang Liu ◽  
Jiyuan Han ◽  
Siyao Zhao ◽  
Qingyu Meng ◽  
Tuo Shi ◽  
...  
Keyword(s):  
Ball Bearing ◽  
Structural Characteristics ◽  
Great Influence ◽  
Vibration Characteristics ◽  
Rotor System ◽  
Ball Bearings ◽  
Bearing Clearance ◽  
Deep Groove ◽  
Deep Groove Ball Bearing ◽  
System Nodes

Aiming at the analysis of the dynamic characteristics of the rotor system supported by deep groove ball bearings, the dynamic model of the double-disk rotor system supported by deep groove ball bearings was established. In this paper, the nonlinear finite element method is used combined with the structural characteristics of deep groove ball bearings. Based on the nonlinear Hertz contact theory, the mechanical model of deep groove ball bearings is obtained. The excitation response results of the rotor system nodes are solved by using the Newmark-β numerical solution method combined with the Newton–Raphson iterative method. The vibration characteristics of the rotor system supported by deep groove ball bearings are studied deeply. In addition, the effect of varying compliance vibration (VC vibration) caused by the change in bearing support stiffness on the dynamics of the system is considered. The time domain and frequency domain characteristics of the rotor system at different speeds, as well as the influence of bearing clearance and bearing inner ring’s acceleration on the dynamics of the rotor system are analyzed. The research shows that the VC vibration of the bearing has a great influence on the motion of the rotor system when the rotational speed is low. Moreover, reasonable control of bearing clearance can reduce the mutual impact between the bearing rolling element and the inner or outer rings of the bearing and reduce the influence of unstable bearing motion on the vibration characteristics of the rotor system. The results can provide theoretical basis for the subsequent study of the nonlinear vibration characteristics of the deep groove ball bearing rotor system.

A Simulation Study on the Effects of Race Surface Waviness on Cage Dynamics in High-Speed Ball Bearings

2019 ◽  
Vol 141 (5) ◽  
Author(s):  
Linkai Niu
Keyword(s):  
Wear Rate ◽  
Dynamic Model ◽  
High Speed ◽  
Wave Amplitude ◽  
Ball Bearing ◽  
Ball Bearings ◽  
Cage Effect ◽  
Surface Waviness ◽  
Slip Ratio ◽  
Wear Rates

The effects of the race surface waviness on the cage dynamics, including cage slip ratios, cage instabilities, and time-averaged cage wear rates, in high-speed ball bearings are investigated. A dynamic model of high-speed ball bearings considering the cage effect and the race surface waviness is proposed. Based on the proposed dynamic model, the effects of the maximum wave amplitude (MWA) and the wave order (WO) of race surface waviness on cage slip ratio, cage instability, and time-averaged cage wear rate are investigated. The results show that the race surface waviness has a great effect on the cage dynamics. The waviness would increase the random impacts between balls and cage pockets and thus cause more instable motion of the cage. Although the ball skidding and the cage slip ratio decrease with the increase of MWA, the cage instability and the cage wear rate become severe when MWA increases. In addition, the effect of WO on cage dynamics is nonlinear. The current investigation could provide a theoretical tool for an in-depth understanding of the dynamics in a high-speed ball bearing.

A 4-DOF dynamic model for ball bearing with multiple defects on raceways

2020 ◽  
pp. 146441932097287
Author(s):  
Xianghong Gao ◽  
Changfeng Yan ◽  
Yaofeng Liu ◽  
Pengfei Yan ◽  
Junbao Yang ◽  
...  
Keyword(s):  
Dynamic Model ◽  
Characteristic Frequency ◽  
Ball Bearing ◽  
Elastohydrodynamic Lubrication ◽  
Radial Clearance ◽  
Multiple Defects ◽  
Single Defect ◽  
Localized Defects ◽  
Fourier Function ◽  
Fault Characteristic

Localized defects in ball bearing components would cause additional vibration and it is imperative to reveal the vibration mechanism. The relationship between fault characteristic frequency (fBPFI and fBPFO) and multiple defect parameters of ball bearing were given in this paper. Considering elastohydrodynamic lubrication (EHL), radial clearance, time-varying displacement and excitation force generated from multiple defects, a 4 degree-of-freedom (DOF) dynamic model for ball bearing with multiple defects on inner or outer raceway was established, and the model has been verified by experiments. Vibration signals of ball bearing with different defects parameters were simulated, the effects of the angle between two defects ( θIAD and θOAD), the number of defects ( NDI and NDO) and the location of defects on outer raceway on dynamic response were studied. Comparing simulated signals with experimental results, it is shown that more impulses of acceleration signals are generated by multiple defects than that by single defect, meanwhile time delay due to two defects on raceways could also be found, fault characteristic frequency and their harmonics frequencies appeared in the envelope spectrums. Harmonics frequencies of fBPFI are modulated mainly by 2 fs instead of fs in frequency domain for multiple defects on inner raceway. The amplitudes of fBPFO and fBPFI change as Fourier curve when θOAD and θIAD varied within a certain range, and a series of Fourier function are given to describe the mathematic relationship.

scholarly journals Effects of operation temperature on thermal expansion and main parameters of radial ball bearings

2015 ◽  
Vol 19 (5) ◽  
pp. 1835-1844 ◽  
Author(s):  
Radivoje Mitrovic ◽  
Ivana Atanasovska ◽  
Natasa Soldat ◽  
Dejan Momcilovic
Keyword(s):  
Finite Element ◽  
Thermal Expansion ◽  
Ball Bearing ◽  
Load Capacity ◽  
Radial Clearance ◽  
Contact Period ◽  
Ball Bearings ◽  
Finite Element Analyses ◽  
Main Bearing ◽  
Operation Temperature

The research of influence of operation temperature on the thermal expansion and main parameters of radial ball bearings is presented in this paper. The main bearing parameters are identified in accordance with the increasing requests concerning stability and load capacity. A series of Finite Element Analyses is performed for quasi-static analysis of all identified bearing parameters during contact period in referent temperature. Then, the dependence of bearing material characteristics on the operation temperature is discussed. Few series of Finite Element Analyses are performed for a particular radial ball bearing type, with characteristics in accordance with manufacturer specifications, for several operation temperatures. These two problems analyses include consideration of relation between the initial radial clearance, thermal expansion strains and contact deformations of the parts of the bearing assembly. The results for radial ball bearing parameters are monitored during a ball contact period for different temperatures and the appropriate discussion and conclusions are given. The conclusions about the contribution of developed procedure in defining the optimum operation temperature range are shown.

scholarly journals Multi-Dimensional Mathematical Wear Models of Vibration Generated by Rolling Ball Bearings Made of AISI 52100 Bearing Steel

Materials ◽  
2020 ◽  
Vol 13 (23) ◽  
pp. 5440
Author(s):  
Paweł Zmarzły
Keyword(s):  
Mathematical Models ◽  
Total Curvature ◽  
Bearing Steel ◽  
Radial Clearance ◽  
Ball Bearings ◽  
Wear Process ◽  
Rolling Ball ◽  
Aisi 52100 ◽  
Aisi 52100 Steel ◽  
The Impact

The paper features the development of multi-dimensional mathematical models used for evaluating the impact of selected factors on the vibration generated by 6304ZZ type rolling ball bearings from three manufacturers in the aspect of the wear process. The bearings were manufactured of AISI 52100 bearing steel. The analyzed factors included the inner and outer raceways’ roundness and waviness deviations, radial clearance and the total curvature ratio. The models were developed for vibration recorded in three frequency ranges: 50–300 Hz, 300–1800 Hz and 1800–10,000 Hz. The paper includes a specification of the principles of operation of innovative measuring systems intended for testing bearing vibration, raceway geometries and radial clearance. Furthermore, it features a specification of particular stages of the multi-dimensional mathematical models’ development and verification. Testing with the purpose of statistical evaluation of the analyzed factors is also presented. The test results and mathematical models indicate that the inner raceway’s waviness deviation had a dominant impact on the vibration examined in all frequencies. The roundness and waviness deviation of bearing raceways made of AISI 52100 steel propagates the bearing wear process.

Sign in / Sign up

Export Citation Format

Share Document