Identification of dynamic coefficients of the journal bearing considering velocity slip of cavitation zone in the rotating spindle unit

2018 ◽  
Vol 232 (10) ◽  
pp. 1304-1317
Author(s):  
Feng Cheng ◽  
Weixi Ji
Keyword(s):  
Journal Bearing ◽  
Dynamic Performance ◽  
Velocity Slip ◽  
Journal Bearings ◽  
Identification Accuracy ◽  
Identification Algorithm ◽  
Dynamic Coefficients ◽  
Displacement Error ◽  
Spindle Unit ◽  
Cavitation Erosion Resistance

A rotating spindle unit, supported by the journal bearings, is developed to improve the cavitation erosion resistance of the journal bearing as well as the spindle dynamic performance. The turbulent lubrication model considering velocity slip in cavitation zone is derived, and the static and dynamic parameters of the journal bearing are obtained. An identification algorithm is further derivated to identify simultaneously the 16 dynamic coefficients of the two journal bearings in the spindle unit. The available experimental results reveal that the journal bearing coefficients are well predicted and estimated by the present model, and the estimated bearing parameters by regularization solution are in good agreement with the assumed values, while it has opposite effect by directed solution for discrete ill-posed problems. It is concluded that the identification accuracy of bearing parameters is governed by the displacement error, and the percentage deviation of dynamic coefficients decreases with the decrease of the displacement error.

Theoretical Condition for the Cxy=Cyx Relation in Fluid Film Journal Bearings

1989 ◽  
Vol 111 (3) ◽  
pp. 426-429 ◽  
Author(s):  
T. Kato ◽  
Y. Hori
Keyword(s):  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Fluid Film ◽  
Finite Width ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Cross Terms ◽  
Linear Damping ◽  
Theoretical Condition

A computer program for calculating dynamic coefficients of journal bearings is necessary in designing fluid film journal bearings and an accuracy of the program is sometimes checked by the relation that the cross terms of linear damping coefficients of journal bearings are equal to each other, namely “Cxy = Cyx”. However, the condition for this relation has not been clear. This paper shows that the relation “Cxy = Cyx” holds in any type of finite width journal bearing when these are calculated under the following condition: (I) The governing Reynolds equation is linear in pressure or regarded as linear in numerical calculations; (II) Film thickness is given by h = c (1 + κcosθ); and (III) Boundary condition is homogeneous such as p=0 or dp/dn=0, where n denotes a normal to the boundary.

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.

On the linear stability analysis of finite-hydrodynamic porous journal bearings under coupled stress lubrication

2007 ◽  
Vol 221 (7) ◽  
pp. 831-840 ◽  
Author(s):  
S. K. Guha ◽  
A. K. Chattopadhyay
Keyword(s):  
Reynolds Equation ◽  
Dynamic Performance ◽  
Slip Flow ◽  
Tangential Velocity ◽  
Continuum Theory ◽  
Transient State ◽  
Velocity Slip ◽  
Journal Bearings ◽  
The Stability ◽  
Coupled Stress

The objective of the present investigation is to study theoretically, using the finite-difference techniques, the dynamic performance characteristics of finite-hydrodynamic porous journal bearings lubricated with coupled stress fluids. In the analysis based on the Stokes micro-continuum theory of the rheological effects of coupled stress fluids, a modified form of Reynolds equation governing the transient-state hydrodynamic film pressures in porous journal bearings with the effect of slip flow of coupled stress fluid as lubricant is obtained. Moreover, the tangential velocity slip at the surface of porous bush has been considered by using Beavers-Joseph criterion. Using the first-order perturbation of the modified Reynolds equation, the stability characteristics in terms of threshold stability parameter and whirl ratios are obtained for various parameters viz. permeability factor, slip coefficient, bearing feeding parameter, and eccentricity ratio. The results show that the coupled stress fluid exhibits better stability in comparison with Newtonian fluid.

Nonlinear Dynamic Oil-Film Forces in Infinite-Short Journal Bearings

2011 ◽  
Author(s):  
Lihua Yang ◽  
Weimin Wang ◽  
Lie Yu
Keyword(s):  
Nonlinear Dynamic ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Analytic Solutions ◽  
Journal Bearings ◽  
Oil Film ◽  
Dynamic Coefficients ◽  
Representation Model ◽  
Linear And Nonlinear

In this paper, the analytic solutions of oil-film forces in infinite-short cylindrical journal bearing are calculated by solving its corresponding Reynolds equation. On this base, the linear and nonlinear dynamic coefficients of the bearing are predicted. By comparing the dynamic oil-film forces approximately represented by dynamic coefficients with the analytic solutions, the accuracy of this representation model is investigated. The results show that more orders of dynamic coefficients are included in representation model, the obtained approximate oil-film forces are more close to their analytic solutions. This can be a reference to illustrate the feasibility and applicability of representing oil-film forces by applying the dynamic coefficients of bearings.

A Review of Journal Bearing Induced Nonlinear Rotordynamic Vibrations

2021 ◽  
Vol 143 (11) ◽  
Author(s):  
Sitae Kim ◽  
Dongil Shin ◽  
Alan B. Palazzolo
Keyword(s):  
High Performance ◽  
Journal Bearing ◽  
Dynamic Performance ◽  
Journal Bearings ◽  
Thermally Induced ◽  
Frequency Domain Methods ◽  
Vibration Responses ◽  
Numerical Tools ◽  
Rotordynamic Forces ◽  
Solution Methodology

Abstract Nonlinear elements found in fluid film journal bearings and their surrounding structures are known to induce sub- and super-synchronous, chaos and thermally induced instability responses in rotor-bearing systems. The current review summarizes the literature on journal bearing induced nonlinear, rotordynamic forces, and responses. Nonlinear, thermo-elasto-hydrodynamic (TEHD) aspects of journal bearings has become increasingly important in high-performance turbomachines. These have significant influence on bearing dynamic performance and thermally induced, rotordynamic instability problems. Techniques for developing TEHD bearing models are discussed in the second section. Nonlinear solution methodology, including bifurcation determination and time and frequency domain methods such as harmonic balance, shooting and continuation, etc., is presented in the third section. Numerical tools to determine nonlinear vibration responses, including chaos, along with examples of bearing induced nonlinear vibrations are presented in the fourth and fifth sections, respectively.

The Rolling-Pad Journal Bearing: A Promising Antiwhirl Configuration

1981 ◽  
Vol 23 (3) ◽  
pp. 131-141
Author(s):  
M. Malik ◽  
R. Sinhasan ◽  
D. V. Singh
Keyword(s):  
Journal Bearing ◽  
Dynamic Performance ◽  
Journal Bearings ◽  
Operating Conditions ◽  
Performance Characteristics ◽  
Tilting Pad ◽  
The Comparative Study ◽  
Tilting Pad Journal Bearing ◽  
Tilting Pad Journal Bearings ◽  
Theoretical Performance

The rolling-pad journal bearing is a kinematic variation of the well-known tilting-pad journal bearing. In rolling-pad bearings, the pads, instead of tilting about fixed pivots, roll at their back surfaces on the inside surface of a common sleeve to accommodate changes in the operating conditions of the bearing. This paper presents a comparison of the theoretical performance characteristics of rolling-pad journal bearings with those of tilting-pad journal bearings. The comparative study indicates that the dynamic performance characteristics of the rolling-pad bearing configuration are superior to those of the tilting-pad bearing.

A Waved Journal Bearing Concept-Evaluating Steady-State and Dynamic Performance With a Potential Active Control Alternative

1993 ◽  
Author(s):  
Florin Dimofte
Keyword(s):  
Steady State ◽  
Wave Amplitude ◽  
Journal Bearing ◽  
Load Capacity ◽  
Dynamic Stiffness ◽  
Dynamic Performance ◽  
Film Stability ◽  
Dynamic Coefficients ◽  
The Waves ◽  
Compressible Lubricant

Abstract Analysis of the waved journal bearing concept featuring a waved inner bearing diameter for use with a compressible lubricant (gas) is presented. The performance of generic waved bearings having either three or four waves is predicted for air lubricated bearings. Steady-state performance is discussed in terms of bearing load capacity, while the dynamic performance is discussed in terms of fluid film stability and dynamic coefficients. It was found that the bearing wave amplitude has an important influence on both steady-state and dynamic performance of the waved journal bearing. For a fixed eccentricity ratio, the bearing steady-state load capacity and direct dynamic stiffness coefficient increase as the wave amplitude increases. Also, the waved bearing becomes more stable as the wave amplitude increases. In addition, increasing the number of waves (e.g., four waves instead of three waves) reduces the waved bearing’s sensitivity to the direction of the applied load relative to the wave. However, the range in which the bearing performance can be varied decreases as the number of waves increases. Therefore, both the number and the amplitude of the waves must be properly selected to optimize the waved bearing design for a specific application. Another possibility is to use the waved bearing to actively control the rotor-bearing system dynamic coefficients via actively controlling the wave amplitude.

Frequency Effects on Dynamic Characteristics of Tilting-Pad Journal Bearings due to Pivot Flexibility

2017 ◽  
Author(s):  
Tian Jiale ◽  
Yu Lie ◽  
Zhou Jian
Keyword(s):  
Dynamic Characteristics ◽  
High Speed ◽  
Dynamic Performance ◽  
Journal Bearings ◽  
Dynamic Coefficients ◽  
Stability Performance ◽  
Limit Value ◽  
Tilting Pad ◽  
Perturbation Frequency ◽  
Tilting Pad Journal Bearings

The stable working condition of high speed, heavy loaded rotating machinery depends strongly on the stability provided by the journal bearing. Tilting pad journal bearings (TPJB) are widely used under such situation due to their inherent stability performance. However, because of the complexity of the TPJB structure, obtaining a reliable prediction of the journal bearing’s dynamic characteristics has always been a challenging task. In this paper, a theoretical analysis has been done to investigate the dynamic performance of a 4 pad TPJB with ball-in-socket pivot, emphasizing on the frequency dependency due to pivot flexibility. The analytical model containing the complete set of dynamic coefficients of the TPJB is built and the pivot stiffness is calculated and used to evaluate the equivalent dynamic coefficients of the bearing. In general, at lower perturbation frequency, the equivalent stiffness and damping increase with frequency. While for higher perturbation frequency, the dynamic coefficients are nearly independent of the frequency. Moreover, the results also show the limit value of the dynamic characteristics of the TPJB when the perturbation frequency is set to 0+ and ∞.

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.

Effect of Uncertainties in the Estimation of Dynamic Coefficients on Tilting Pad Journal Bearings

2016 ◽  
Author(s):  
Rafael O. Ruiz ◽  
Sergio E. Diaz
Keyword(s):  
Surrogate Model ◽  
Journal Bearing ◽  
Deterministic Model ◽  
Journal Bearings ◽  
Kriging Interpolation ◽  
Manufacturing Tolerance ◽  
Dynamic Coefficients ◽  
Tilting Pad ◽  
Tilting Pad Journal Bearing ◽  
Tilting Pad Journal Bearings

It has been identified that small variations in the pad clearance and preload of a Tilting Pad Journal Bearing lead to important variations in their dynamic coefficients. Although this variation trend is already identified, a more robust statistical analysis is required in order to identify more general tendencies and quantify it. This work presents a framework that helps to identify the relation between the manufacturing tolerance of the bearing (reflected in the pad clearance and preload) and the expected variations on the dynamic coefficients. The procedure underlies the adoption of a surrogate model (based on Kriging interpolation) trained by any deterministic model available to predict dynamic coefficients. The pad clearance and preload are considered uncertain parameters defined by a proper probability density function. All statistical quantities are obtained using stochastic simulation, specifically adopting a Monte Carlo simulation employing the surrogate model. The framework is illustrated through the study of a five pad bearing.

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