A method to obtain the linear dynamic coefficients for journal bearing in vertical rotors

2019 ◽  
Vol 72 (1) ◽  
pp. 38-45 ◽  
Author(s):  
Changmin Chen ◽  
Jianping Jing ◽  
Jiqing Cong
Keyword(s):  
Coordinate System ◽  
Linear Models ◽  
Journal Bearing ◽  
Leading Edge ◽  
Content Type ◽  
Linear Dynamic ◽  
Dynamic Coefficients ◽  
Vertical Rotor ◽  
Rotor Bearing ◽  
Stiffness And Damping

Purpose The infinitesimal perturbation (IP) method is commonly used in calculating stiffness and damping of journal bearing in horizon rotor systems. The boundary condition (BC) for the perturbed pressure is assumed being zero at leading edge of film, although it is usually not zero because of nonzero pressure gradient. This assumption is sufficiently accurate for most purpose in horizon rotors. However, for journal bearing in vertical rotor-bearing systems, the BC with the assumption in IP method will bring in significant errors in calculating linear dynamic coefficients. This paper aims to propose a method to obtain the dynamic coefficients of journal bearing in vertical rotors. Design/methodology/approach The stiffness and damping are approached based on IP method and the modified BC of perturbed pressure. As it is difficult to predict perturbed pressure at leading edge at a fixed coordinate system using IP method, a dynamic coordinate system is introduced in this method, of which the origin on circumferential direction is defined as the leading edge of film. Findings The effectiveness and accuracy of proposed IP method in dynamic coordinate (IPMDC) system are verified by comparing the obtained results with analytical solutions. The comparison shows that the results from IPMDC present a good agreement with the analytic solutions. Originality/value The proposed method can be applied in obtaining linear dynamic coefficients of journal bearing in vertical rotors with high precisions. Instead of the usual nonlinear analysis of vertical rotors, this method provides a feasibility of predicting the instability threshold of vertical rotor-bearing systems via linear models.

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.

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.

Numerical and experimental study on dynamic characteristics of tilting-pad journal bearings considering pivot stiffness in a vertical rotor system

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Fan Zhang ◽  
Peng Yin ◽  
Yuyang Liu ◽  
Jianmei Wang
Keyword(s):  
Dynamic Characteristics ◽  
Journal Bearings ◽  
Rotor System ◽  
Obvious Effect ◽  
Content Type ◽  
Vertical Rotor ◽  
Tilting Pad ◽  
Rotor Bearing ◽  
The Stability ◽  
Tilting Pad Journal Bearings

Purpose The purpose of this paper is to study the influence of pivot stiffness on the dynamic characteristics of tilting-pad journal bearings (TPJBs) and the stability of the bearing-rotor system. Design/methodology/approach A theoretical numerical model is established, and the influences of pivot stiffness on TPJBs and a bearing-rotor system are analyzed. Then, two kinds of pivot structures with different stiffness are designed and the vibration characteristics are tested on the vertical rotor bearing test bench. Findings The pivot stiffness has an obvious effect on the dynamic characteristics of the TPJBs and the stability of the bearing-rotor system. As a result of appropriate pivot stiffness, the critical speed and the vibration amplification factor can be reduced, the logarithmic decay rate and the stability of the rotor system can be effectively increased. While the journal whirl orbit is smoother and the rubbing is obviously reduced when the bearings have flexible pivots. Originality/value The influence of pivot stiffness on TPJBs and a vertical rotor-bearing system is studied by theoretical and experimental methods.

scholarly journals Alternation of the dynamic coefficients of short journal bearings due to wear

2015 ◽  
Vol 6 (5) ◽  
pp. 649-664
Author(s):  
Michael G. Papanikolaou ◽  
Michael G. Farmakopoulos ◽  
Chris A. Papadopoulos
Keyword(s):  
Dynamic Stiffness ◽  
Journal Bearings ◽  
Fe Analysis ◽  
Operating Conditions ◽  
Wear Depth ◽  
Content Type ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Low Viscosity ◽  
Stiffness And Damping

Purpose – Wear in journal bearings occurs when the operating conditions (high load, high temperature, low angular velocity or low viscosity), downgrade the ability of the bearing to carry load. The wear depth increases because the rotor comes in contact with the bearing surface. Wear in journal bearings affects their characteristics because of its influence on the thickness of the fluid film. This influence can be detected in the dynamic behavior of the rotor and especially in the dynamic stiffness and damping coefficients. The paper aims to discuss these issues. Design/methodology/approach – In this paper, the effect of wear on the rotor dynamic stiffness and damping coefficients (K and C) of a short journal bearing is investigated. K and C in this work are estimated by using two methods a semi-analytical method and finite element (FE) analysis implemented in the ANSYS software. Findings – The main goal of this research is to make the identification of wear in journal bearings feasible by observing the alternation of their dynamic coefficients. Both of the methods implemented are proven to be useful, while FE analysis can provide more accurate results. Originality/value – This paper is original and has not been published elsewhere.

scholarly journals A Nonlinear Model for Prediction of Dynamic Coefficients in a Hydrodynamic Journal Bearing

2004 ◽  
Vol 10 (6) ◽  
pp. 507-513 ◽  
Author(s):  
Jerzy T. Sawicki ◽  
T. V. V. L. N. Rao
Keyword(s):  
Equilibrium Position ◽  
Nonlinear Dynamic ◽  
Static Pressure ◽  
Journal Bearing ◽  
Dynamic Pressure ◽  
Higher Order ◽  
Pressure Gradients ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Stiffness And Damping

This paper investigates the variation of nonlinear stiffness and damping coefficients in a journal orbit with respect to equilibrium position. The journal orbit is obtained by the combined solution of equations of motion and Reynolds equation. In the linearized dynamic analysis, dynamic pressure is written as a perturbation of static pressure and pressure gradients at equilibrium position. However, in order to obtain nonlinear dynamic coefficients about equilibrium position, the dynamic pressure gradients in the orbit are also written as the first order perturbation of static pressure gradients and higher order pressure gradients for displacement and velocity perturbations. The dynamic coefficients are functions of bearing displacement and velocity perturbations. The higher order pressure gradients at equilibrium position are evaluated at various eccentricity ratios and L/D ratios of 0.5 and 1.0. The variation of nonlinear dynamic coefficients is analyzed for three Sommerfeld numbers of a two-axial groove journal bearing under the action of an external synchronous load along and perpendicular to the radial journal load. Results indicate that the oil film nonlinearities affect the journal motion at lower eccentricity ratios (higher Sommerfeld numbers) with wide variation in stiffness and damping coefficients.

The Influence of Pad Flexibility on the Dynamic Coefficients of a Tilting Pad Journal Bearing

1987 ◽  
Vol 109 (1) ◽  
pp. 65-70 ◽  
Author(s):  
Jorgen W. Lund ◽  
Lars Bo Pedersen
Keyword(s):  
Approximate Method ◽  
Small Amplitude ◽  
Journal Bearing ◽  
Damping Properties ◽  
Dynamic Coefficients ◽  
Tilting Pad ◽  
Hydrodynamic Solution ◽  
Stiffness And Damping ◽  
Tilting Pad Journal Bearing ◽  
Good Agreement

An approximate method is developed to include the flexibility of the pad in the calculation of the stiffness and damping properties of a tilting pad journal bearing. It is a small-amplitude perturbation solution in which the pad deformation is accounted for solely by the change in clearance. A comparison of results with those obtained from a more complete elasto-hydrodynamic solution shows good agreement.

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.

Estimation of Rotor-Bearing Parameters by a Global Optimization Method

2006 ◽  
Author(s):  
E. A. Khorshid ◽  
A. H. Falah
Keyword(s):  
Journal Bearing ◽  
Optimization Methods ◽  
Optimization Method ◽  
Air Gap ◽  
Outer Diameter ◽  
Rotor Bearing ◽  
Vibration Responses ◽  
Optimized Model ◽  
Stiffness And Damping ◽  
Good Agreement

Modeling, experiments and system identification of the linear dynamics of a flexible multi-bearing rotor with two concentrated disks are presented in this paper. Both rotor unbalanced vibration responses through critical speeds were experimentally obtained through accurate control of journal bearing static load. Vibration simulations of this laboratory rotor-bearing system were performed as a linear system. The simulation and the experimental results have large differences for both rotors. These differences occur because of (1)The errors in estimating the journal bearing damping and stiffness coefficients, and, (2)The neglect of the effect of the small radial air gap (20 Mils) at the two disks' outer diameter which provides some additional bearing-like radial stiffness and damping effects. An estimate of these coefficients for both the journal bearing and the rotor-radial air gap is obtained using optimization methods. Good agreement was found between the experimental and the optimized model.

Paper 15: Determination and Application of the Dynamic Properties of a Turbo-Rotor Bearing Oil Film

1969 ◽  
Vol 184 (12) ◽  
pp. 111-119
Author(s):  
J. S. Woodcock ◽  
R. Holmes
Keyword(s):  
Journal Bearing ◽  
Dynamic Properties ◽  
Damping Properties ◽  
Experimental Assessment ◽  
Oil Film ◽  
Rotor Bearing ◽  
Stiffness And Damping ◽  
Oil Films

This paper presents a theoretical and experimental assessment of the eight coefficients which describe the stiffness and damping properties of journal bearing oil films, together with their subsequent use in predicting the performance of a real rotor. The performance is checked experimentally.

Vibration and critical characteristics of the tilting pads journal bearing-rotor system

2019 ◽  
Vol 71 (2) ◽  
pp. 295-300 ◽  
Author(s):  
Zhiming Zhao ◽  
Feng Ji ◽  
Yongsheng Guan ◽  
Xiaoyang Yuan
Keyword(s):  
Theoretical Calculation ◽  
System Design ◽  
Critical Speed ◽  
Journal Bearing ◽  
Large Diameter ◽  
Vibration Monitoring ◽  
Content Type ◽  
Vibration Data ◽  
Rotor Bearing ◽  
Bearing System

Purpose High power rotating machinery requires large diameter bearings that can perform under extreme conditions. Vibrations and critical speeds of rotor supported by tilting pad journal bearing (TPJBs) exceeding their design limits may cause unit failure. This paper aims to investigate the experimental technique for large diameter bearings. Design/methodology/approach To obtain the experimental support for rotor-bearing system design, an experiment focusing on vibration monitoring is given. The sensors arrangement, monitoring system and critical speed identification method are provided. Findings By using test bench in factory unit, a large amount of vibrations data of different working situations is obtained. In addition, a method named non-excitation identification for critical speed is proposed. The critical speed of rotor identified through vibration data is given. The theoretical calculation results are also presented. Originality/value The basis for rotor-bearing system design can be obtained through comparisons between the experimental results and the theoretical calculation data.

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