Nonlinear Dynamics of Flexible Rotors Supported on Journal Bearings—Part I: Analytical Bearing Model

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Mohammad Miraskari ◽  
Farzad Hemmati ◽  
Mohamed S. Gadala
Keyword(s):  
Journal Bearing ◽  
Nonlinear Coefficient ◽  
Journal Bearings ◽  
Flexible Rotor ◽  
Dynamic Coefficients ◽  
Flexible Rotors ◽  
Rotor Bearing ◽  
Bearing Force ◽  
Derivatives Of ◽  
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.

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

2017 ◽  
Vol 140 (2) ◽  
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.

Nonlinear Vibration Analysis of a Flexible Rotor Supported by a Journal Bearing Considering Journal Angular Motion

2019 ◽  
Author(s):  
Nuntaphong Koondilogpiboon ◽  
Tsuyoshi Inoue
Keyword(s):  
Nonlinear Vibration ◽  
Ball Bearing ◽  
Journal Bearing ◽  
Angular Motion ◽  
Experimental Result ◽  
Flexible Rotor ◽  
Large Disk ◽  
Rotor Bearing ◽  
Bearing Force ◽  
Bearing System

Abstract The effect of bearing length to diameter (L/D) ratio and large disk position on nonlinear vibration (limit cycle and bifurcation type) of a flexible rotor-bearing system is investigated. The rotor consists of a shaft modeled by 1-D finite elements (FE), two small disks and a large disk. It is supported by a self-aligning ball bearing and an axial-groove journal bearing with L/D ratio of 0.4 and 0.6. Two large disk positions: 340 and 575 mm measured from the ball bearing are investigated. The journal angular motion, which is essential for the highly flexible rotor but typically not considered in the previous nonlinear vibration literature; is considered in nonlinear bearing force calculation. The degrees of freedom (DOF) of the rotor-bearing system are reduced to those of the node that the nonlinear journal bearing force and moment act on by real mode component mode synthesis (CMS) that retains only the 1st forward and backward modes. Shooting method and Floquet multiplier analysis are applied to the reduced rotor-bearing system to obtain limit cycles and their stability of each bearing L/D ratio and large disk position case. Numerical results indicate that supercritical Hopf bifurcation only occurs in the case of L/D = 0.4 and large disk position 575 mm, otherwise subcritical occurs. However, if the typical bearing model that does not consider journal angular motion is used, the bifurcation type for the case of L/D = 0.6 with large disk position 575 mm will change to supercritical. Lastly, the experiments with the same L/D ratio and large disk position investigated in the calculation are performed as a validation. The experimental result of each case shows the same bifurcation type as the calculation result using the bearing model that considers the journal angular motion.

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

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.

Journal Bearing Rotor Speed Effect on Dynamics Coefficients and Film Pressure

2013 ◽  
Vol 274 ◽  
pp. 320-323
Author(s):  
Nai Wen Hu ◽  
Guang Bin Yu ◽  
Xue Mei Wu ◽  
Chang Sheng Hu ◽  
Zhi Gang Qu ◽  
...  
Keyword(s):  
Thermal Instability ◽  
Journal Bearing ◽  
Pressure Effect ◽  
Rotor Speed ◽  
Film Pressure ◽  
Dynamic Coefficients ◽  
Rotor Bearing ◽  
Speed Effect ◽  
Analytical Expressions ◽  
Bearing System

The dynamic coefficients and film pressure effect in rotor-bearing systems may lead to an unstable station. The mechanism of the dynamic coefficients and film pressure induced thermal instability in the rotor-bearing system has been studied. The journal bearing model is adopted for the derivation of analytical expressions. The results show that the rotor speed has some effect on bearing dynamic coefficients and film pressure.

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

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Nuntaphong Koondilogpiboon ◽  
Tsuyoshi Inoue
Keyword(s):  
Nonlinear Vibration ◽  
Journal Bearing ◽  
Rolling Element Bearing ◽  
Flexible Rotor ◽  
Large Disk ◽  
Subcritical Bifurcation ◽  
Whirling Motion ◽  
Vibration Prediction ◽  
Rotor Bearing ◽  
Bearing System

Abstract 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 rolling element bearing (REB) and an axial groove journal bearing (JB) of length-to-diameter ratio (L/D) = 0.6. Three positions of the large disk: 410, 560, and 650 mm measured from the REB, are investigated. Numerical integration of the rotor-bearing system which is modally reduced to the first forward (FWD) 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 (IB) 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. Finally, the experiments at the same three large disk positions are performed. Subcritical bifurcation with the contact between the journal and the IB side of the bearing is observed in all large disk positions, which conforms with the calculation result of model A. Hence, model A is essential in nonlinear vibration analysis of a highly flexible rotor system.

Influence of Fluid Film Boundary Migration on Dynamic Coefficients of Journal Bearings and Behavior of Rotor System

2020 ◽  
Vol 142 (10) ◽  
Author(s):  
Changmin Chen ◽  
Jianping Jing ◽  
Jiqing Cong ◽  
Zezeng Dai ◽  
Jianhua Cheng
Keyword(s):  
Journal Bearing ◽  
Boundary Migration ◽  
Dynamical Behavior ◽  
Journal Bearings ◽  
Rotor System ◽  
Fluid Film ◽  
Dynamic Coefficients ◽  
Film Boundary ◽  
Rotor Bearing ◽  
Stiffness And Damping

Abstract The position of fluid film in journal bearing will change while the journal moving in bearing, which can be named fluid film boundary migration (FFBM). It is usually ignored in the calculation of linear dynamic coefficients. While, the errors brought by this neglection was not ever investigated in detail. In this paper, the influence of FFBM on bearing dynamic coefficients and rotor system dynamic behaviors are investigated. A new perturbation-based model is proposed to take the FFBM into account by modifying the boundary conditions of governing equations. It is then verified by the experimental results and analytical results from previous research. Furthermore, the effects of FFBM on stiffness and damping in two typical journal bearings are investigated. The result indicates that the FFBM has a significant influence on dynamic coefficients of full circular journal bearing but little impact on journal bearing with axial grooves. Moreover, it affects the stiffness and damping more significantly in the cases of large length-to-diameter ratios or small eccentricity ratios in full circle bearing. Finally, the dynamical behavior of a rotor-bearing system with considering the FFBM is also investigated. The result shows that the FFBM of oil film has remarkable influences on the instability threshold and imbalance responses of the rotor system, which should not be ignored. The conclusions obtained in this research are expected to be helpful for the design of full circular journal bearings or rotor-bearing systems.

The Excitability of Flexible Rotors in Short Sleeve Bearings

1975 ◽  
Vol 97 (1) ◽  
pp. 105-115 ◽  
Author(s):  
E. J. Hahn
Keyword(s):  
Flexible Rotor ◽  
External Disturbances ◽  
Stability Threshold ◽  
Flexible Rotors ◽  
Rotor Bearing ◽  
Operating Regions ◽  
The Stability ◽  
Linearized Model ◽  
Lubricant Viscosity ◽  
Bearing System

Assuming the short bearing approximation and constant lubricant properties, the root loci of the pertinent characteristic function were obtained for the linearized model of a simple symmetric flexible rotor bearing system. Using these loci, design maps consisting of lines of constant damping and vibration frequency pertaining to the dominant roots are presented as a function of the equilibrium eccentricity ratio and a frequency parameter for relevant degrees of flexibility. These maps display undesirable operating regions where external disturbances such as shock or unbalance loading are likely to excite undesirable vibrations, as well as regions of instability. The maps may conveniently be used to determine the effect of changing journal speed, lubricant viscosity and/or bearing clearance. Increased flexibility is seen to reduce the stability threshold in a predictable manner and to reduce damping at the pin-pin critical speed. The approach is applicable to more complex rotor bearing systems. It is felt that the use of such maps will enhance the understanding of rotor bearing system behavior, particularly at operating regions close to the stability threshold.

The effect of active control on stability characteristics of hydrodynamic journal bearings with an axial groove

2002 ◽  
Vol 216 (9) ◽  
pp. 939-946 ◽  
Author(s):  
B-H Rho ◽  
K-W Kim
Keyword(s):  
Active Control ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Linear Dynamic ◽  
Conventional Analysis ◽  
Theoretical Investigations ◽  
Rotor Bearing ◽  
Hydrodynamic Journal Bearing ◽  
The Stability ◽  
Bearing System

Results of theoretical investigations on stability characteristics of an actively controlled hydrodynamic journal bearing are presented. Proportional, derivative and integral controls are adopted for a hydrodynamic journal bearing with an axial groove. Furthermore, a cavitation algorithm, implementing the Jakobsson-Floberg-Olsson boundary condition, is adopted to predict cavitation regions in a fluid film more accurately than the conventional analysis, which uses the Reynolds condition. Using the bearing's linear dynamic coefficients, which are evaluated from the perturbation method, the stability characteristics of a rotor-bearing system are investigated using the Routh-Hurwitz criteria. It is shown that the instability threshold speed of a rotor-bearing system can be greatly increased and the unbalanced responses of the system can be markedly decreased by both proportional and derivative control of the bearing. Results show that active control of a hydrodynamic journal bearing can be adopted for stability improvement and reduction of the unbalanced whirl amplitude of a rotor-bearing system.

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

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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