Field Identification of Dynamic Coefficients of Journal Bearings on Flexible Rotor-Bearing System

To determine the bifurcation types in a rotor-bearing system, it is required to find higher order derivatives of the bearing forces with respect to journal velocity and position. As closed-form expressions for journal bearing force are not generally available, Hopf bifurcation studies of rotor-bearing systems have been limited to simple geometries and cavitation models. To solve this problem, an alternative nonlinear coefficient-based method for representing the bearing force is presented in this study. A flexible rotor-bearing system is presented for which bearing force is modeled with linear and nonlinear dynamic coefficients. The proposed nonlinear coefficient-based model was found to be successful in predicting the bifurcation types of the system as well as predicting the system dynamics and trajectories at spin speeds below and above the threshold speed of instability.

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Nonlinear Dynamics of Flexible Rotors Supported on Journal Bearings—Part II: Numerical Bearing Model

Journal of Tribology ◽

10.1115/1.4037731 ◽

2017 ◽

Vol 140 (2) ◽

Cited By ~ 1

Author(s):

Mohammad Miraskari ◽

Farzad Hemmati ◽

Mohamed S. Gadala

Keyword(s):

Nonlinear Stability ◽

Nonlinear Dynamic ◽

Shooting Method ◽

Monodromy Matrix ◽

Nonlinear Coefficient ◽

Journal Bearings ◽

Flexible Rotor ◽

Dynamic Coefficients ◽

Rotor Bearing ◽

Bearing System

The nonlinear stability of a flexible rotor-bearing system supported on finite length journal bearings is addressed. A perturbation method of the Reynolds lubrication equation is presented to calculate the bearing nonlinear dynamic coefficients, a treatment that is suitable to any bearing geometry. A mathematical model, nonlinear coefficient-based model, is proposed for the flexible rotor-bearing system for which the journal forces are represented through linear and nonlinear dynamic coefficients. The proposed model is then used for nonlinear stability analysis in the system. A shooting method is implemented to find the periodic solutions due to Hopf bifurcations. Monodromy matrix associated to the periodic solution is found at any operating point as a by-product of the shooting method. The eigenvalue analysis of the Monodromy matrix is then carried out to assess the bifurcation types and directions due to Hopf bifurcation in the system for speeds beyond the threshold speed of instability. Results show that models with finite coefficients have remarkably better agreement with experiments in identifying the boundary between bifurcation regions. Unbalance trajectories of the nonlinear system are shown to be capable of capturing sub- and super-harmonics which are absent in the linear model trajectories.

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Numerical Analysis of Nonlinear Behaviors of a Flexible Rotor Dynamic System with Turbulent Journal Bearings Support

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.142.7 ◽

2011 ◽

Vol 142 ◽

pp. 7-11

Author(s):

Yan Jun Lu ◽

Yong Fang Zhang ◽

Xiao Yong Ma ◽

Xu Liu

Keyword(s):

Period Doubling ◽

Journal Bearings ◽

Flexible Rotor ◽

Chaotic Motions ◽

System A ◽

Runge Kutta Method ◽

Lubricant Flow ◽

Rotor Bearing ◽

The Rich ◽

Bearing System

For description of rotor-bearing system, a symmetrical flexible rotor supported by two turbulent journal bearings is modeled. The analysis of the rotor-bearing system is implemented under the assumptions of turbulent lubricant flow and a long bearing approximation. The bifurcation and chaos behaviors of the system are investigated for various rotational speeds. The motion equations are solved by the self-adaptive Runge-Kutta method. The numerical results show that the bifurcation of nonlinear responses of the system varies with the rotational speed of the rotor. It is found that the rich and complex dynamic behaviors of the system include period-1, period-doubling, quasi-periodic and chaotic motions etc.

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Dynamic Characteristics of Rotor-Bearing System with a Labyrinth Seal

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.739.169 ◽

2017 ◽

Vol 739 ◽

pp. 169-181

Author(s):

Shiuh Hwa Shyu ◽

Yu Wei Chen

Keyword(s):

Dynamic Characteristics ◽

Labyrinth Seal ◽

Perturbation Approach ◽

Flexible Rotor ◽

The Finite Element Method ◽

Governing Equations ◽

Dynamic Coefficients ◽

Rigid Disks ◽

Rotor Bearing ◽

Bearing System

In this paper, the dynamic characteristics of rotor-bearing system with a labyrinth seal are investigated. The dynamic coefficients of labyrinth seal and the whirl speeds of rotor-bearing system are analyzed. The simplified rotor-bearing model consists of a rigid disk and a flexible shaft. The rotor-bearing system supported by two ball bearings, which are modeled as the spring-damper systems. A labyrinth seal supports one of the rigid disks. The perturbation approach has been applied to the governing equations of the bulk-flow model to calculate the dynamic coefficients of labyrinth seal. The Finite Element Method (FEM) is utilized to model the flexible-rotor system. The numerical results show the labyrinth seal effect on the dynamic characteristics of rotor-bearing system, which depend on a great variety of parameters such as geometry of the labyrinth seal.

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Nonlinear Vibration Prediction of a Highly Flexible Rotor Supported by an Axial Groove Journal Bearing Considering Journal Angular Whirling Motion

Volume 7B: Structures and Dynamics ◽

10.1115/gt2019-90951 ◽

2019 ◽

Author(s):

Nuntaphong Koondilogpiboon ◽

Tsuyoshi Inoue

Keyword(s):

Nonlinear Vibration ◽

Ball Bearing ◽

Journal Bearing ◽

Flexible Rotor ◽

Large Disk ◽

Subcritical Bifurcation ◽

Whirling Motion ◽

Vibration Prediction ◽

Rotor Bearing ◽

Bearing System

Abstract In this study, the difference in dynamic behavior of the rotor-bearing system supported by the bearing model that considers both lateral and angular whirling motions of the journal (model A), and the model that considers only lateral whirling motion (model B) is investigated. The rotor model consists of a slender shaft, a large disk and two small disks supported by a self-aligning ball bearing and an axial groove journal bearing of L/D = 0.6. Three positions of the large disk: 410, 560, and 650 mm measured from the ball bearing, are investigated. Numerical integration of the rotor-bearing system which is modally reduced to the 1st forward mode is performed at above the onset speed of instability until either a steady state journal orbit or contact between the journal and the bearing occurs to identify the bifurcation type. Numerical results using model A indicate subcritical bifurcation with the contact between the journal and the inboard side of the bearing in all three large disk positions, whereas those of model B indicate subcritical bifurcation when the large disk position is at 410 mm, and supercritical bifurcation is observed in the other two cases. Lastly, the experiments at the same three large disk positions are performed. Subcritical bifurcation with the contact between the journal and the inboard side of the bearing is observed in all large disk positions, which conforms with the calculation result of model A. As a result, model A is essential in nonlinear vibration analysis of a highly flexible rotor system.

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