Twice-Running-Speed Resonances of a Paper Machine Tube Roll Supported by Spherical Roller Bearings: Analysis and Comparison With Experiments

2014 ◽  
Author(s):  
Janne Heikkinen ◽  
Behnam Ghalamchi ◽  
Jussi Sopanen ◽  
Aki Mikkola
Keyword(s):  
Finite Element ◽  
Hertzian Contact ◽  
Fast Fourier Transformation ◽  
Paper Machine ◽  
Test Rig ◽  
Running Speed ◽  
Roller Bearings ◽  
Measurement Results ◽  
Rotor Bearing ◽  
Bearing System

Imperfections in a rotor-bearing system may cause undesirable subcritical resonances occurring when the rotating speed of the rotor is a fraction of the natural frequency of the system. These resonances arise partly from rotor imperfections and partly from bearing imperfections. This study demonstrates that the subcritical twice-running-speed vibrations originating from bearing waviness may be investigated by combining a simplified rotor model with a detailed bearing model, using a finite element method. The rotor-bearing system under investigation is a roller test rig consisting of the tube roll of a paper machine supported by spherical roller bearings. The bearing waviness from the second to the fourth orders is emulated as accurately as possible in the finite element model. This is achieved by measuring the waviness of the real bearings and then incorporating the measurement results into a simulation model. The tube roll of the test rig is modeled as a symmetric tube, neglecting the effects of the uneven mass and stiffness distribution of the roll. The contact between the rotor and the bearings is described using nonlinear Hertzian contact theory. The subcritical responses of the system are studied by means of time integration, and the results are converted into the frequency domain using fast Fourier transformation. The results of the analysis are compared with the measurement results for the subcritical responses of the roll. The agreement between the simulation and experimental results of the studied system can be observed even though rotor imperfections are not considered.

Subcritical Twice-Running-Speed Vibrations of a Non-Ideal Rotor-Bearing-System: Simulation and Experiments

2012 ◽  
Author(s):  
Janne E. Heikkinen ◽  
Jussi T. Sopanen ◽  
Aki M. Mikkola
Keyword(s):  
Simulation Model ◽  
Paper Machine ◽  
Flexible Rotor ◽  
Running Speed ◽  
Measurement Results ◽  
Rotor Bearing ◽  
Existing Structure ◽  
Speed Response ◽  
Bearing System

Subcritical twice-running-speed resonances of a paper machine tube roll are studied in this paper. Resonances arise partly from the non-idealities of the rotor and partly from the non-idealities of the bearings. Resonances are affecting the quality of end product and therefore have to be studied precisely. The complex rotor-bearing system is modeled by using a flexible multibody simulation approach. Non-idealities of the rotor-bearing system are measured from the existing structure under investigation and the parameters of the real structure are emulated as accurately as possible in the simulation model. The simulation model is verified using the results from experimental modal analysis and the measurement results for the subcritical twice-running-speed response of the roll. The inertia modeling of the flexible rotor is also studied. It is found that inertia coupling between the rigid body rotation and body deformation must be included into analysis in order to achieve accurate results.

Natural frequency analysis of a functionally graded rotor-bearing system with a slant crack subjected to thermal gradients

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Arnab Bose ◽  
Prabhakar Sathujoda ◽  
Giacomo Canale
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Power Law ◽  
Beam Theory ◽  
Functionally Graded ◽  
Thermal Gradients ◽  
Element Analysis ◽  
Rotor Bearing ◽  
Natural Frequency Analysis ◽  
Bearing System

Abstract The present work aims to analyze the natural and whirl frequencies of a slant-cracked functionally graded rotor-bearing system using finite element analysis for the flexural vibrations. The functionally graded shaft is modelled using two nodded beam elements formulated using the Timoshenko beam theory. The flexibility matrix of a slant-cracked functionally graded shaft element has been derived using fracture mechanics concepts, which is further used to develop the stiffness matrix of a cracked element. Material properties are temperature and position-dependent and graded in a radial direction following power-law gradation. A Python code has been developed to carry out the complete finite element analysis to determine the Eigenvalues and Eigenvectors of a slant-cracked rotor subjected to different thermal gradients. The analysis investigates and further reveals significant effect of the power-law index and thermal gradients on the local flexibility coefficients of slant-cracked element and whirl natural frequencies of the cracked functionally graded rotor system.

Hertzian Contact Stress Modeling in Railway Bearings for Assorted Load Conditions and Geometries

2014 ◽  
Author(s):  
Michael A. Mason ◽  
Charles P. Cartin ◽  
Parham Shahidi ◽  
Mark W. Fetty ◽  
Brent M. Wilson
Keyword(s):  
Finite Element ◽  
Contact Stress ◽  
Rolling Contact ◽  
Hertzian Contact ◽  
Modeling Tools ◽  
Heat Treat ◽  
Roller Bearings ◽  
Tapered Roller ◽  
Tapered Roller Bearings ◽  
Load Conditions

Increasing freight car loads demand higher performance tapered roller bearings. As the stress state on railway bearing applications continues to increase, further advancement in the modeling tools and methods used for subsurface contact stress evaluations are needed. Heat treat specifications and contact geometries for railway bearings were originally developed for ideal load conditions. However, in railroad applications, tapered roller bearings are exposed to a vast range of load conditions that are seldom perfect. Moreover, when comparing global rail markets, there are often differences in bearing loads, railcar wear conditions, maintenance practices, and reliability versus utilization expectations. Advanced modeling techniques need to be developed by bearing designers in order to meet the specific needs of each individual rail market. Prior research has shown that subsurface stresses, resulting from rolling contact, are the primary factor in the development of fatigue cracks in railway bearings. In addition, finite element modeling software has previously been used to analyze Hertzian contact stresses under rolling contact. Recent advancements in the technology and computational power of finite element methods can be used to numerically analyze more detailed simulations of complex geometries and biased load conditions in railway bearings. These improvements in the tapered roller bearing modeling methodology are necessary to determine the material, heat treat specifications, and geometry required to meet the demands of specific railway bearing applications. Furthermore, the specific risks associated with some common railway bearing design and modeling assumptions will be evaluated. An exploratory list of these assumptions include: line versus point contact, load deflection factor, zero contact angle, rigid body assumptions, linear material behavior, neglect for overload, and uniform loading on the bearing. Emphasis will be placed on potential improvements in the theoretical and finite element prediction of surface and subsurface stresses in railway bearings under rolling contact with a review of prior research on the subject.

Nonlinear Vibration Signature Analysis of a High Speed Rotor Bearing System Due to Race Imperfection

2011 ◽  
Vol 7 (1) ◽  
Author(s):  
P. K. Kankar ◽  
Satish C. Sharma ◽  
S. P. Harsha
Keyword(s):  
High Speed ◽  
Nonlinear Differential Equations ◽  
Mathematical Formulation ◽  
Nonlinear Damping ◽  
Dynamic Responses ◽  
Fast Fourier Transformation ◽  
Surface Waviness ◽  
Contact Points ◽  
Rotor Bearing ◽  
Bearing System

In this paper the nonlinear dynamic responses of a rigid rotor supported by ball bearings due to surface waviness of bearing races are analyzed. A mathematical formulation has been derived with consideration of the nonlinear springs and nonlinear damping at the contact points of rolling elements and races, whose stiffnesses are obtained by using Hertzian elastic contact deformation theory. The numerical integration technique Newmark-β with the Newton–Raphson method is used to solve the nonlinear differential equations, iteratively. The effect of bearing running surface waviness on the nonlinear vibrations of rotor bearing system is investigated. The results are mainly presented in time and frequency domains are shown in time-displacement, fast Fourier transformation, and Poincaré maps. The results predict discrete spectrum with specific frequency components for each order of waviness at the inner and outer races, also the excited frequency and waviness order relationships have been set up to prognosis the race defect on these bearing components. Numerical results obtained from the simulation are validated with respect to those of prior researchers.

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.

Analysis and Experimental Study on Stability of Nonlinear Rotor-Bearing System

2011 ◽  
Vol 236-238 ◽  
pp. 2626-2629
Author(s):  
Wei Dong Gu ◽  
Yong Liang Wang ◽  
Bo Fang ◽  
Zhan Sheng Liu ◽  
Wen Hu Huang
Keyword(s):  
Finite Element Method ◽  
Experimental Study ◽  
Test Rig ◽  
Model Simulations ◽  
Oil Whip ◽  
Film Instability ◽  
Oil Whirl ◽  
Rotor Bearing ◽  
Practical Model ◽  
Bearing System

The paper established the model of the practical Model test rig rotor-bearing system using finite element method, and discusses the phenomena of oil whirl and oil whip occurred in fluid lubricated bearing. The characteristics of stability of the nonlinear rotor-bearing system were numerically studied under different unbalance and different parameter of bearings, the model simulations are compared with measurements at the test rig, which can provide the theoretical reference for forecasting malfunction of oil film instability.

Study on Looseness and Impact - Rub Coupling Faults of a Vertical Dual-Disk Cantilever Rotor- Bearing System

2007 ◽  
Vol 353-358 ◽  
pp. 2479-2482
Author(s):  
Yan Jun Lu ◽  
Zhao Hui Ren ◽  
Hong Chen ◽  
Nai Hui Song ◽  
Bang Chun Wen
Keyword(s):  
Finite Element ◽  
Low Frequency ◽  
Element Model ◽  
Coupling Faults ◽  
Mechanics Model ◽  
Low Frequency Vibration ◽  
Rotor Bearing ◽  
Impact And Rubbing ◽  
The Impact ◽  
Bearing System

Because of wrong setting or long-term running of rotating machinery, the looseness may ouur in the bearing seats or bases. And also bring impact and rubbing of rotor-stator, That is the looseness and rub-impact coupling fault. In the paper,a mechanics model and a finite element model of a vertical dual-disk cantilever rotor- bearing system with coupling faults of looseness and rub-impact are set up. Based on the nonlinear finite element method and contact theory, the dynamical characteristices of the system under the influence of the looseness rigidity and impact-rub clearance is studied. The results show that the impact-rub of rotor-stator can reduce the low frequency vibration caused by looseness, and the impact-rub caused by looseness has obvious orientation. Also, the conclusion of diagnosing the looseness and rub-impact coupling faults is given in the end of the paper.

Effect of a transverse crack on the dynamic behaviours of a 3D rod-fastening rotor bearing system

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Nanshan Wang ◽  
Heng Liu ◽  
Yi Liu ◽  
Qidan Wang ◽  
Shemiao Qi ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Dynamic Model ◽  
Dynamic Characteristics ◽  
3D Finite Element ◽  
Content Type ◽  
Rotor Bearing ◽  
Rod Fastening Rotor ◽  
3D Finite Element Method ◽  
Bearing System

Purpose This paper aims to examine the dynamic behaviours of a three-dimensional (3D) rod-fastening rotor bearing system (RFBS) with a crack in a fastening rod. Design/methodology/approach Based on the 3D finite element method model and stress analysis of a cracked RFBS, a 3D dynamic model of the RFBS with a crack in a fastening rod is established with considering the initial bending and stress redistribution caused by the crack. A combined numerical simulation technology is used to investigate the dynamic behaviours of the system. Findings The distribution of contact stress between the two disks will be not uniform, and the initial bending of the system will occur due to the presence of a crack. This will lead to the change of system stiffness and the dynamic behaviours such as vibration amplitude, and motion orbits will change significantly. Research limitations/implications A 3D finite element method dynamic model is proposed for the study of dynamic characteristics of complex combined rotor bearing system with cracks. Practical implications It is helpful and significant to master the dynamic behaviours of cracked RFBS. It is helpful to detect the presence of a crack of the rotor bearing system. Social implications Some of the losses caused by crack failure may be reduced. Originality/value The proposed 3D method can provide a useful reference for the study of dynamic characteristics of complex combined rotor bearing system with cracks. Peer review The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-05-2020-0189

Rotordynamics analysis of a quill-shaft coupling-rotor-bearing system

2014 ◽  
Vol 229 (8) ◽  
pp. 1385-1398 ◽  
Author(s):  
S Feng ◽  
HP Geng ◽  
L Yu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Natural Frequency ◽  
Stiffness Matrix ◽  
Equation Of Motion ◽  
Numerical Results ◽  
The Finite Element Method ◽  
Rotor Bearing ◽  
Bearing System ◽  
Element Method

A quill-shaft coupling-rotor-bearing system is modeled and reported in this paper. The system consists of two rotors connected by a quill-shaft coupling in which each rotor is supported by two bearings. The stiffness matrix of the quill-shaft coupling is deduced and the equation of motion of the system is obtained by using the finite element method. Finally, the rotordynamics analysis of the system is conducted. The numerical results show that more frequency veering points occur for the quill-shaft coupling-rotor-bearing system compared with those of single rotor. In addition, the stiffness of the flexural element has significant effects on the first bending natural frequency of the quill shaft when the length of the quill shaft becomes shorter.

scholarly journals An Identification Method for the Unbalance Parameters of a Rotor-Bearing System

2016 ◽  
Vol 2016 ◽  
pp. 1-9
Author(s):  
Wengui Mao ◽  
Guiping Liu ◽  
Jianhua Li ◽  
Jie Liu
Keyword(s):  
Identification Problem ◽  
Convolution Integral ◽  
Test Rig ◽  
Identification Method ◽  
Rotor Bearing ◽  
Force Reconstruction ◽  
Deconvolution Problem ◽  
Unbalance Force ◽  
The Time Domain ◽  
Bearing System

This paper is to be submitting an identification method for the unbalance parameters of a rotor-bearing system. In the method, the unbalance parameters identification problem is formulated as the unbalance force reconstruction which belongs to solving deconvolution problem, in which the unbalance force is expressed in the time domain. The unbalance response is expressed by the convolution integral of Green’s function and the unbalance force. In order to avoid the unstable solution arising from the noisy responses and the deconvolution, a regularization method is adopted to stabilize the solution. Meanwhile, a searching of the sensitive measured point has also been carried out to confirm the robustness of the method. Numerical example and a test rig have been used to illustrate the proposed method.

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