scholarly journals A Model To Estimate Synchronous Vibration Amplitude For Detection of Unbalance in Rotor-Bearing System

2021 ◽  
Vol 26 (2) ◽  
pp. 161-169
Author(s):  
I.M. Jamadar
Keyword(s):  
Mathematical Model ◽  
Vibration Amplitude ◽  
Numerical Technique ◽  
Operating Conditions ◽  
Box Behnken Design ◽  
Unbalanced Rotor ◽  
Mass Eccentricity ◽  
Rotor Bearing ◽  
Different Levels ◽  
Bearing System

A numerical technique for detection of unbalance magnitude of a rotor-bearing system is proposed and verified by experimental analysis. Dimensional analysis is used for development of mathematical model of an unbalanced rotor-bearing system following rigid rotor approach. A developed mathematical model is solved by factorial regression analysis method using the experimental data obtained by a Box-Behnken design. The proposed approach integrates the rotor parameters, disc parameters, bearing parameters and operating conditions with the synchronous vibration amplitude. Confirmation experiments are conducted using Taguchi design methodology with unbalance mass, rotor speed, mass eccentricity and radial load as parameters with different levels assigned to them.

Periodicity and Stability in Transverse Motion of a Nonlinear Rotor-Bearing System Using Generalized Harmonic Balance Method

2016 ◽  
Vol 139 (2) ◽  
Author(s):  
Zhiwei Liu ◽  
Yuefang Wang
Keyword(s):  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Iteration Scheme ◽  
Balance Method ◽  
Transverse Motion ◽  
Harmonic Load ◽  
Mass Eccentricity ◽  
Rotor Bearing ◽  
Generalized Harmonic Balance Method ◽  
Bearing System

Many rotor assemblies of industrial turbomachines are supported by oil-lubricated bearings. It is well known that the operation safety of these machines is highly dependent on rotors whose stability is closely related to the whirling motion of lubricant oil. In this paper, the problem of transverse motion of rotor systems considering bearing nonlinearity is revisited. A symmetric, rigid Jeffcott rotor is modeled considering unbalanced mass and short bearing forces. A semi-analytical, seminumerical approach is presented based on the generalized harmonic balance method (GHBM) and the Newton–Raphson iteration scheme. The external load of the system is decomposed into a Fourier series with multiple harmonic loads. The amplitude and phase with respect to each harmonic load are solved iteratively. The stability of the motion response is analyzed through identification of eigenvalues at the fixed point mapped from the linearized system using harmonic amplitudes. The solutions of the present approach are compared to those from time-domain numerical integrations using the Runge–Kutta method, and they are found to be in good agreement for stable periodic motions. It is revealed through bifurcation analysis that evolution of the motion in the nonlinear rotor-bearing system is complicated. The Hopf bifurcation (HB) of synchronous vibration initiates oil whirl with varying mass eccentricity. The onset of oil whip is identified when the saddle-node bifurcation of subsynchronous vibration takes place at the critical value of parameter.

Experimental dynamic analysis of rod-fastening rotor bearing system with a transverse crack

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Nanshan Wang ◽  
Heng Liu ◽  
Qidan Wang ◽  
Shemiao Qi ◽  
Yi Liu
Keyword(s):  
Peer Review ◽  
Dynamic Characteristics ◽  
Vibration Amplitude ◽  
Critical Speed ◽  
Transverse Crack ◽  
Content Type ◽  
Rotor Bearing ◽  
Speed Up ◽  
Rod Fastening Rotor ◽  
Bearing System

Purpose This study aims to obtain the dynamic behaviours of cracked rod-fastening rotor bearing system (RFBS), and experimental investigation was carried out to examine the dynamic characteristics of this kind of assembled rotor bearing system with a transverse crack passing through the critical speed. Design/methodology/approach An experimental test rig of cracked RFBS was established for examining the vibration behaviours between intact and cracked system. The crack on the surface of a fastening rod was simulated by wire-electrode cutting processing method. The comprehensive analysis method of vibration was used to obtain the dynamic characteristics such as vibration amplitude, acceleration and whirling orbits before and after the critical speed as well as the instantaneous response in the process of speed up. Findings Some experimental vibration datum is obtained for cracked RFBS. The appearance of a crack will introduce the initial bending and make the vibration amplitude, acceleration and instant response in the process of speed up increase greatly as well as the change of whirling orbits. Originality/value The actual vibration characteristics for this complex assembled rotor system with a transverse crack are given passing through the critical speed. It can provide some useful help for monitoring the vibration behaviours of this kind of assembled rotor system as well as the detection of the crack fault. Peer review The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-07-2020-0260/

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.

Nonlinear Dynamic Analysis of a Flexible Rod Fastening Rotor Bearing System

2010 ◽  
Author(s):  
Heng Liu ◽  
Chen Li ◽  
Weimin Wang ◽  
Xiaobin Qi ◽  
Minqing Jing
Keyword(s):  
Periodic Motion ◽  
Great Influence ◽  
Periodic Motions ◽  
Stability And Bifurcation ◽  
Mass Eccentricity ◽  
Rotor Bearing ◽  
Rod Fastening Rotor ◽  
The Stability ◽  
Tie Rods ◽  
Bearing System

This paper is concerned the stability and bifurcation of a flexible rod-fastening rotor bearing system (FRRBS). Here the shaft is considered as an integral or continuous structure and be modeled by using Timoshenko beam-shaft element which can take the effects of axial load into consideration. And using Hamilton’s principle, model tie rods distributed along the circumference as a constant stiffness matrix and an add-moment which caused by unbalanced pre-tightening forces. Then the model is reduced by a component mode synthesis method, which can conveniently account for nonlinear oil film forces of the bearing. This study focuses on the influence of nonlinearities on the stability and bifurcation of T periodic motion of the FRRBS subjected to the influence of mass eccentricity. The periodic motions and their stability margin are obtained by shooting method and path-following technique. The local stability and bifurcation behaviors of periodic motions are obtained by Floquet theory. The results indicate that mass eccentricity and unbalanced pre-tightening forces of tie rods have great influence on nonlinear stability and bifurcation of the T periodic motion of system, cause the spillover of system nonlinear dynamics and degradation of stability and bifurcation of T periodic motion.

scholarly journals Nonlinear Dynamic Analysis of Rotor-Bearing System with Cubic Nonlinearity

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Guofang Nan ◽  
Yujie Zhu ◽  
Yang Zhang ◽  
Wei Guo
Keyword(s):  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Analysis ◽  
Hertzian Contact ◽  
Stable Operation ◽  
Nonlinear Stiffness ◽  
Cubic Nonlinearity ◽  
Dynamic Behaviors ◽  
Mass Eccentricity ◽  
Rotor Bearing ◽  
Bearing System

Nonlinear dynamic characteristics of a rotor-bearing system with cubic nonlinearity are investigated. The comprehensive effects of the unbalanced excitation, the internal clearance, the nonlinear Hertzian contact force, the varying compliance vibration, and the nonlinear stiffness of support material are considered. The expression with the linear and the cubic nonlinear terms is adopted to characterize the synthetical nonlinearity of the rotor-bearing system. The effects of nonlinear stiffness, rotating speed, and mass eccentricity on the dynamic behaviors of the system are studied using the rotor trajectory diagrams, bifurcation diagrams, and Poincaré map. The complicated dynamic behaviors and types of routes to chaos are found, including the periodic doubling bifurcation, sudden transition, and quasiperiodic from periodic motion to chaos. The research results show that the system has complex nonlinear dynamic behaviors such as multiple period, paroxysmal bifurcation, inverse bifurcation, jumping phenomena, and chaos; the nonlinear characteristics of the system are significantly enhanced with the increase of the nonlinear stiffness, and the material with lower nonlinear stiffness is more conducive to the stable operation of the system. The research will contribute to a comprehensive understanding of the nonlinear dynamics of the rotor-bearing system.

Effective Evaluation of Rotordynamic Performance Within Rotor-Bearing System Design Bounds

2021 ◽  
Author(s):  
Zhusan Luo ◽  
Carl L. Schwarz
Keyword(s):  
System Design ◽  
Operating Conditions ◽  
Performance Parameters ◽  
Critical Speeds ◽  
Effective Evaluation ◽  
Analytical Results ◽  
Design Variables ◽  
Rotor Bearing ◽  
Current Design ◽  
Bearing System

Abstract This paper presents a study on the effective evaluation of rotordynamic performance for multiple analysis cases within rotor-bearing system design bounds. The variations in rotordynamic design variables and operating conditions are usually considered in a rotordynamic analysis. This can provide useful information about the current design, potential for modification, and the capability of off-design operation. Typical design bounds of a tilting pad journal bearing are discussed to show the complexity of multiple design cases and a demand for a method to postprocess the analytical results. Rotordynamic performance is conventionally assessed by examining undamped critical speed maps, damped modes, stability, and unbalance responses. Evaluating rotordynamic performance for multiple cases is a tedious task for both rotordynamicists and reviewers. A new approach is studied to effectively extract, present and evaluate analytical results. A theoretical study shows the analytical results can be synthesized to determine key performance parameters. It is proposed that the amplification factors at critical speeds can be converted to equivalent logarithmic decrements. Based on the two studies, a new rotordynamic performance diagram is created to present damped modes, critical speeds and relevant acceptance criteria. With this informative diagram, one can quickly and effectively evaluate the acceptability and robustness of multiple design cases. This diagram can also convey the trends of key performance parameters, comparisons between cases, and the sensitivities of key performance parameters to design variables more clearly and concisely. This synthesizing approach and the rotordynamic performance diagram may be useful in modifying an existing design, determining a proper off-design operation range, and investigating rotordynamic issues.

Nonlinear dynamic characteristics of a three-dimensional rod-fastening rotor bearing system

2014 ◽  
Vol 229 (5) ◽  
pp. 882-894 ◽  
Author(s):  
Yi Liu ◽  
Heng Liu ◽  
Xin Wang ◽  
Minqing Jing
Keyword(s):  
Dynamic Characteristics ◽  
Nonlinear Dynamic ◽  
Three Dimensional ◽  
Dynamic Features ◽  
Stability Margins ◽  
Mass Eccentricity ◽  
Nonlinear Dynamic Characteristics ◽  
Rotor Bearing ◽  
Rod Fastening Rotor ◽  
Bearing System

The nonlinear dynamic characteristics of three-dimensional rod-fastening rotor bearing system are investigated in this paper. The rod-fastening rotor includes discontinuous shaft, rotating disks, circumferentially distributed rods, and macrointerfaces between disks. The first three parts are discretized by three dimensional elements, and the macrointerfaces are connected by some springs whose stiffness is determined by a proposed linear partition method. For comparison, the three-dimensional dynamic model of a corresponding complete rotor bearing system is also built. After the rod-fastening and complete rotor bearing system are reduced by a component mode synthesis, periodic motions and stability margins are calculated by using the shooting method and path-following technique, and the local stability of system is obtained by using the Floquet theory. Comparative results show the both systems have a resemblance in the bifurcation features when mass eccentricity and rotating speed are changed. The vibration response has the identical frequency components when typical bifurcations occur. The dynamic stress is obtained by regarding the displacements of all nodes as load. Moreover, the unbalanced and insufficient of the pre-tightening forces lead to obvious disadvantageous influence on the stability and vibration of the both systems. Generally, this paper considers the interfacial effect of the rod-fastening rotor bearing system and the relative nonlinear dynamic features are obtained.

A Numerical Approach to the Stability of Rotor-Bearing Systems

1982 ◽  
Vol 104 (2) ◽  
pp. 356-363 ◽  
Author(s):  
K. Athre ◽  
J. Kurian ◽  
K. N. Gupta ◽  
R. D. Garg
Keyword(s):  
Eigenvalue Problem ◽  
Characteristic Polynomial ◽  
Eigenvalue Problems ◽  
Numerical Technique ◽  
Numerical Approach ◽  
Generalized Eigenvalue ◽  
Generalized Eigenvalue Problems ◽  
Rotor Bearing ◽  
The Stability ◽  
Bearing System

The stability characteristics of a rotor-bearing system which indicate the threshold of instability are generally obtained by applying the Routh-Hurwitz criterion to the characteristic polynomial. Usually the characteristic polynomial is obtained analytically from the characteristic determinant. In the case of the generalized eigenvalue problems, this is practically impossible. To study the stability characteristics of a floating bush bearing, the characteristic polynomial is constructed from the generalized eigenvalue problem using a recently developed numerical technique. Results obtained through this computer package are compared with those already available in the literature.

Analysis of Rotor Bearing Systems With Uncertainties: A Fuzzy Approach

2009 ◽  
Author(s):  
Singiresu S. Rao ◽  
Yazhao Qiu
Keyword(s):  
Piecewise Linear ◽  
Piecewise Linear Function ◽  
Operating Conditions ◽  
Fourth Power ◽  
Fuzzy Approach ◽  
Restoring Force ◽  
Analysis And Design ◽  
Highly Sensitive ◽  
Rotor Bearing ◽  
Bearing System

The components of most structural and mechanical systems exhibit considerable variations or uncertainties in their properties and the performance characteristics of such systems are subject to uncertainties. In the case of a rotor bearing system, the nonlinear bearing restoring force is usually represented as a third or fourth power of displacement or as a piecewise linear function of displacement. The coefficients of these models are acquired from experiments and approximations, and will vary considerably during the operation of the bearing. Hence it is more reasonable to treat them as uncertain values. Other bearing parameters such as the inertial properties of concentrated disks, distributed mass and damping of the rotating assemblies are also uncertain due to manufacturing and assembly errors and imprecise operating conditions. It is known that the vibration response of a rotor is highly sensitive to small fluctuations or variations in the bearing parameters. Therefore, any realistic analysis and design of rotor-bearing systems must take the uncertainties into account. In this paper, a methodology is presented for the fuzzy analysis of nonlinear rotor-bearing systems along with numerical results to demonstrate the computational feasibility of the methodology.

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