Analysis of dynamic behaviour of rotor-bearing system

2013 ◽  
Vol 228 (12) ◽  
pp. 2141-2161 ◽  
Author(s):  
Janko D Jovanović ◽  
Radoslav N Tomović
Keyword(s):  
Mathematical Model ◽  
Dynamic Behaviour ◽  
Direct Determination ◽  
Rolling Bearing ◽  
Plane Motion ◽  
Radial Clearance ◽  
Largest Lyapunov Exponent ◽  
Non Linear ◽  
Rotor Bearing ◽  
Bearing System

This paper deals with a non-linear mathematical model for simulation and analysis of a dynamic behaviour of a rotor-bearing system. The model is used for the simulation of plane motion of a centre of rotor’s cross-section which makes the model convenient for the analysis of vibrations generated in a rolling bearing as well as for the analysis of accuracy of the revolution of rotor supported on a rolling bearing. The model takes into account the following quantities: internal radial clearance, external radial load and unbalanced load. Differential equations of a motion are derived using Lagrange’s equations. The contacts between the balls and the rings are considered to be non-linear with a stiffness derived by the Hertzian theory of an elastic contact. The proposed model enables direct determination of local contact deformations which significantly reduces needed computations and CPU time. The results obtained by the model are used to reconstruct phase-space trajectories and Poincaré maps and to calculate the largest Lyapunov exponent in order to establish the stability of rotor-bearing system motion. A computer program is developed based on the mathematical model for the simulation and analysis of a dynamic behaviour of a rotor-bearing system.

Vibration Signature Analysis of a Rotor Bearing System Using Response Surface Method

2009 ◽  
Author(s):  
P. K. Kankar ◽  
Satish C. Sharma ◽  
S. P. Harsha
Keyword(s):  
Response Surface ◽  
Response Surface Method ◽  
High Speed ◽  
Vibration Response ◽  
Radial Clearance ◽  
System Response ◽  
Surface Waviness ◽  
Surface Method ◽  
Rotor Bearing ◽  
Bearing System

The vibration response of a rotor bearing system is extremely important in industries and is challenged by their highly non-linear and complex properties. This paper focuses on performance prediction using response surface method (RSM), which is essential to the design of high performance rotor bearing system. Response surface method is utilized to analysis the effects of design and operating parameters on the vibration response of a rotor-bearing system. A test rig of high speed rotor supported on rolling bearings is used. Vibration response of the healthy ball bearing and ball bearings with various faults are obtained and analyzed. Distributed defects are considered as surface waviness of the bearing components. Effects of internal radial clearance and surface waviness of the bearing components and their interaction are analyzed using design of experiment (DOE) and RSM.

Nonlinear vibration characteristics of the rotor bearing system with bolted flange joints

2019 ◽  
Vol 233 (4) ◽  
pp. 910-930
Author(s):  
Yifu Zhou ◽  
Zhong Luo ◽  
Zifang Bian ◽  
Fei Wang
Keyword(s):  
Nonlinear Vibration ◽  
Time Domain ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Rolling Bearing ◽  
Vibration Characteristics ◽  
Rotor System ◽  
Rotor Bearing ◽  
Bolted Flange ◽  
Bearing System

As sophisticated mechanical equipment, the rotor system of aero-engine is assembled by various parts; bolted flange joints are one of the essential ways of joints. Aiming at the analysis of the nonlinear vibration characteristics of the rotor-bearing system with bolted flange joints, in this paper, a finite element modeling method for a rotor-bearing system with bolted flange joints is proposed, and an incremental harmonic balance method combined with arc length continuation is proposed to solve the dynamic solution of the rotor system. In order to solve the rotor system with rolling bearing nonlinearity, the alternating frequency/time-domain process of the rolling bearing element is deduced. Compared with the conventional harmonic balance method and the time-domain method, this method has the characteristics of fast convergence and high computational efficiency; solving the rotor system with nonlinear bearing force; overcome the shortcoming that the frequency–response curve of the system is too sharp to continue solving. By using this method, the influence of bearing clearance and stiffness on vibration characteristics of the rotor system with bolted flange joints is studied. The evolution law of the state of the rotor system with bolt flange is investigated through numerical simulation and experimental data. The results indicated that the modeling and solving method proposed in this paper could accurately solve the rotor-bearing system with bolted flange joints and analyze its vibration characteristics.

Numerical Simulation of a Bending-Torsion Coupling Gear Transmission System

2013 ◽  
Vol 448-453 ◽  
pp. 3403-3407
Author(s):  
Chao Feng Li ◽  
Shi Hua Zhou ◽  
Jie Liu
Keyword(s):  
Rotation Frequency ◽  
Variable Stiffness ◽  
Rolling Bearing ◽  
Rotational Frequency ◽  
Helical Gear ◽  
Angular Contact Ball Bearing ◽  
Rotating Speed ◽  
Response Characteristics ◽  
Rotor Bearing ◽  
Bearing System

Based on the establishment of angular contact ball bearing mechanical model, a nonlinear coupled lateral, torsional and axial dynamic model of helical gear-rotor-bearing system is established, and the dynamic differential equations of the coupled lateral-torsional-axial nonlinear vibration are deduced for imbalance rotors. The investigations are systematically carried out by oscillograms and spectrograms with rotating speed, taking into account eccentricity and nonlinear supporting by rolling bearing. The results show that the rotation frequency of the driven shaft appears in the driving shaft. In addition, the rotation frequencies and meshing frequency appear obviously in torsional direction. It can be seen that the lateral, torsional and axial response characteristics of driving and driven shafts obvious differences are due to the effects of the gear assembly characteristic, gear geometry parameters and the angular contact ball bearings characteristics. As a result, not only appear the rotational frequency and stiffness frequency, but also yield the bearing variable stiffness frequency and conbined frequency in lateral directions. However, the theory of the helical gear-rotor-bearing system still needs further research.

Non-linear dynamic behaviour of rotor—bearing system trained by bevel gears

2008 ◽  
Vol 222 (4) ◽  
pp. 617-627 ◽  
Author(s):  
M Li
Keyword(s):  
Equilibrium Points ◽  
Rotor System ◽  
Design Stage ◽  
Oil Film ◽  
Bevel Gears ◽  
Linear Dynamic ◽  
Non Linear ◽  
Rotor Bearing ◽  
Stability And Bifurcations ◽  
Bearing System

The vibrations of parallel geared rotor—bearing system have been intensively discussed; however, little attention has been paid to the dynamic analysis of angled bevel-geared system supported on journals. In the present work, the non-linear dynamics of a bevel-geared rotor system on oil film bearings is studied. First, the dynamic model is developed under some assumptions, such as rigid rotors, short-bearings, small teeth errors, and so forth. Then, the non-linear dynamic behaviours of both the balanced and unbalanced rotor system are analysed, respectively, in which the equilibrium points, limit cycles, their stability, and bifurcations are paid more attention. Numerical results show that in the bevel-geared rotor system under the action of non-linear oil film forces there exists a series of complex non-linear dynamic phenomena of rotor orbits, such as Hopf bifurcation, torus-doubling bifurcation, and jump phenomenon. All these features can help us to understand the dynamic characteristics of bevel-geared rotor—bearing system at design stage and during running period. Finally, some concerned problems during the investigation are also present.

Study of Transfer Matrix of Rolling Bearing Including Squeeze Film Damper

2012 ◽  
Vol 490-495 ◽  
pp. 618-622
Author(s):  
Hua Tao Tang ◽  
Xin Yue Wu
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Rolling Bearing ◽  
Squeeze Film ◽  
Body System ◽  
Squeeze Film Damper ◽  
Rotor Bearing ◽  
Multi Body ◽  
Bearing System

The transfer matrix of rolling bearing including squeeze film damper (SFD) is studied, and the rotor – bearing system is modeled by transfer matrix method of multi-body system. It is proved by an example that the method, which provides a new idea to solve the problem of complex rotor – bearing system, is feasible and effective.

Study on Bifurcation of Rigid Rotor Roller Bearings System Considering Nonlinear Dynamic Behavior

2010 ◽  
Vol 34-35 ◽  
pp. 467-471
Author(s):  
Li Cui ◽  
Jian Rong Zheng
Keyword(s):  
Dynamic Behavior ◽  
Nonlinear Dynamic ◽  
Roller Bearing ◽  
Radial Clearance ◽  
Rigid Rotor ◽  
Rotating Speed ◽  
Rotor Bearing ◽  
Nonlinear Dynamic Behavior ◽  
Bifurcation And Stability ◽  
Bearing System

Rigid rotor roller bearing system displays complicated nonlinear dynamic behavior due to nonlinear Hertzian force of bearing. Nonlinear bearing forces of roller bearing and dynamic equations of rotor bearing system are established. The bifurcation and stability of the periodic motion of the system in radial clearance-rotating speed and ellipticity-rotating speed parametric domains are studied by use of continuation-shooting algorithm for periodic solutions of nonlinear non-autonomous dynamics system. Results show that the parameters of rotor bearing system should be designed carefully in order to obtain period-1 motion.

Study On the Bistable Vibration Behaviour of a Rod Fastened Rotor-Bearing System

2021 ◽  
Author(s):  
Jiaqi Li ◽  
YANG Zhongyu ◽  
REN Qingzhao ◽  
MO Guyun ◽  
ZHONG Wenyuan ◽  
...  
Keyword(s):  
Test Bench ◽  
Dynamic Behaviour ◽  
Lagrange Equation ◽  
Phase Spectrum ◽  
Contact Interface ◽  
Transient Responses ◽  
Rotor Bearing ◽  
Acceleration And Deceleration ◽  
Bearing System ◽  
Eccentric Distance

Abstract Based on the Lagrange equation, the motion equation of a rod fastened rotor-bearing system considering the damping of the contact interface is established. The numerical method is employed for numerical analysis. The bifurcation diagram, time series, frequency waveform, phase spectrum and Poincare map are used to illustrate the nonlinear dynamic behaviour. The transient responses during acceleration and deceleration are calculated to reveal the dynamic behaviour of the system. The numerical results hold that since the oil film is nonlinear, the system presents obvious bistable behaviour and a jumping phenomenon. In addition, a test bench of the rod fastened rotor-bearing system is built. The bistable behaviour and jumping phenomenon are experimentally proven, and the effect of the eccentric distance of the rotor on the bistable behaviour is experimentally explored. The results of this paper can be used for the basic design and fault diagnosis of rod fastened rotors.

The bifurcation and chaos of a gear pair system based on a strongly non-linear rotor—bearing system

2010 ◽  
Vol 224 (9) ◽  
pp. 1891-1904 ◽  
Author(s):  
C-W Chang-Jian
Keyword(s):  
Operating Conditions ◽  
Speed Ratio ◽  
Gear Pair ◽  
Chaotic Motions ◽  
Systematic Analysis ◽  
Gear Mesh ◽  
Non Linear ◽  
Rotor Bearing ◽  
Linear Effects ◽  
Bearing System

A systematic analysis of the dynamic behaviours of a gear pair system based on a rotor—bearing system under strongly non-linear effects (i.e. non-linear suspension effect, non-linear oil-film force, non-linear rub-impact force, and non-linear gear mesh force) is presented in this study. The dynamic orbits of the system are observed using bifurcation diagrams plotted using the dimensionless unbalance coefficient, the dimensionless damping coefficient, and the dimensionless rotational speed ratio as control parameters. The onset of chaotic motion is specified from the phase diagrams, power spectra, Poincaré maps, Lyapunov exponents, and fractal dimension of the system. There exists various forms of periodic, quasi-periodic, and chaotic motions at different bifurcation parameters. The simulation results also found that highly non-periodic motions do exist in gear—rotor—bearing systems under those non-linear effects. The results presented in this study provide a better understanding of the operating conditions under which undesirable dynamic motion takes place in a gear—bearing system; they would therefore serve as a useful source of reference for engineers in designing and controlling such systems.

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