Approximate analytical model for fluid film force of finite length plain journal bearing

2011 ◽  
Vol 226 (5) ◽  
pp. 1345-1355 ◽  
Author(s):  
Y L Wang ◽  
Z S Liu ◽  
W J Kang ◽  
J J Yan
Keyword(s):  
Analytical Model ◽  
Finite Length ◽  
Journal Bearing ◽  
Separation Of Variables ◽  
Current Model ◽  
Dynamic Performance ◽  
Journal Bearings ◽  
Force Model ◽  
Oil Film ◽  
Proposed Model

Non-linear dynamic performance of rotor–bearing systems supported by plain journal bearings strongly depends on the mathematical oil film force model. In this article, the analytical solution of oil film pressure for finite length plain journal bearing is obtained by employing the separation of variables method to analytically solve the Reynolds equation based on dynamic Gümbel boundary conditions. The analytical expression of oil film force is then derived by applying the integral method. The expression of the pressure is analysed to investigate the pressure distribution. The oil film force of the analytical model is compared with the results from other methods, namely, long bearing approximation, short bearing approximation, as well as the finite difference method. The results clearly validate the current model. The proposed model also proved to be efficient for analysing the dynamic characteristics of a rigid rotor supported by plain journal bearings.

Approximate Analytical Model for Oil Film Force of Finite Length Squeeze Film Damper Under Low Reynolds Number

2013 ◽  
Author(s):  
Yongliang Wang ◽  
Yu Gao ◽  
Jingjun Zhong ◽  
Ling Yang ◽  
Huawei Lu
Keyword(s):  
Reynolds Number ◽  
Analytical Model ◽  
Finite Length ◽  
High Speed ◽  
Low Reynolds Number ◽  
Separation Of Variables ◽  
Squeeze Film ◽  
Force Model ◽  
Oil Film ◽  
Low Reynolds

Squeeze film dampers (SFDs) are widely used in aero-engines and other high speed rotating machines as damping elements, owing to their remarkable damping effect. The oil-film force model of SFDs is the key to investigate the dynamic characteristics of the rotor-bearing systems involving SFDs. In this paper, the analytical solution of the oil film pressure of a finite length SFD is obtained by employing the separation of variables method to solve the Reynolds equation (at low Reynolds number) based upon the dynamic π boundary condition. The analytical expression of the oil film force is then derived by applying the integral method. The oil film force from the analytical model is compared with the results from other well-known methods, i.e. the long bearing approximation, the short bearing approximation and the finite difference method. The results clearly show that within a wider length-diameter ratio range, the newly proposed model can accurately predict the oil film characteristics of the SFDs at low Reynolds numbers.

scholarly journals Establishment of Approximate Analytical Model of Oil Film Force for Finite Length Tilting Pad Journal Bearings

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Yongliang Wang ◽  
Yu Gao ◽  
Ying Cui ◽  
Zhansheng Liu
Keyword(s):  
Finite Length ◽  
High Speed ◽  
Journal Bearing ◽  
Dynamic Stiffness ◽  
Nonlinear Effects ◽  
Journal Bearings ◽  
Force Model ◽  
Oil Film ◽  
Tilting Pad ◽  
Tilting Pad Journal Bearings

Tilting pad bearings offer unique dynamic stability enabling successful deployment of high-speed rotating machinery. The model of dynamic stiffness, damping, and added mass coefficients is often used for rotordynamic analyses, and this method does not suffice to describe the dynamic behaviour due to the nonlinear effects of oil film force under larger shaft vibration or vertical rotor conditions. The objective of this paper is to present a nonlinear oil force model for finite length tilting pad journal bearings. An approximate analytic oil film force model was established by analysing the dynamic characteristic of oil film of a single pad journal bearing using variable separation method under the dynamicπoil film boundary condition. And an oil film force model of a four-tilting-pad journal bearing was established by using the pad assembly technique and considering pad tilting angle. The validity of the model established was proved by analyzing the distribution of oil film pressure and the locus of journal centre for tilting pad journal bearings and by comparing the model established in this paper with the model established using finite difference method.

An Analytic Model of Oil-Film Force on Hydrodynamic Journal Bearing of Finite Length

2008 ◽  
Author(s):  
JinFu Yang ◽  
Ce Chen ◽  
ShengBo Yang ◽  
DaRen Yu ◽  
Ying Cui ◽  
...  
Keyword(s):  
Finite Length ◽  
Journal Bearing ◽  
Slip Boundary Condition ◽  
Analytic Model ◽  
Clearance Ratio ◽  
Oil Film ◽  
Slip Boundary ◽  
Proposed Model ◽  
Speed Up ◽  
Hydrodynamic Journal Bearing

In order to more clearly express the interrelation between the oil-film force on hydrodynamic journal bearing of finite length and the wedging, whiling, and squeezing motions of journals, an analytic model with well-defined physical meaning is proposed in this paper by introducing the non-slip boundary condition for the oil-film velocity gradient without modifying the basic assumption for Reynolds equation to formulate the expression of oil-film pressure distribution, obtaining the analytic solution of oil-film force through integration of circumferential pressure, and defining the effect coefficients for wedging, whirling and squeezing motions, which are related to the clearance ratio and eccentricity ratio of bearings. The proposed model is compared with an existing model to show off its advantage. The proposed model was also applied to a 200MW steam turbine low-pressure rotor-bearing system to simulate the dynamic response of the rotor during the speed-up process. The analytic results of this application proved the validity of the proposed model.

STATIC CHARACTERISTICS OF OFFSET 8-LOBE JOURNAL BEARINGS

Tribologia ◽  
2021 ◽  
Vol 295 (1) ◽  
pp. 39-51
Author(s):  
Stanisław Strzelecki
Keyword(s):  
Laminar Flow ◽  
Equilibrium Position ◽  
Iterative Procedure ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Diameter Ratio ◽  
Static Characteristics ◽  
Oil Film ◽  
Cooling Conditions ◽  
Grinding Machines

The 8-lobe journal bearings have found application in the bearing systems of spindles of grinding machines. The design of bearings and the large number of lobes and oil grooves assures good cooling conditions of bearing. These bearings can be manufactured as the bearings with cylindrical, non-continuous operating surfaces separated by six lubricating grooves, bearings with the pericycloidal shape of the bearing bore, and as offset journal bearing. This paper presents the results of the computation of static characteristics of an offset 8-lobe journal bearing operating under the conditions of an aligned axis of journal and bush, adiabatic oil film, and at the static equilibrium position of journal. Different values of bearing length to diameter ratio, relative clearance, and lobe relative clearance were assumed. Reynolds' energy and viscosity equations were solved by means of an iterative procedure. Adiabatic oil film, laminar flow in the bearing gap, and aligned orientation of journal in the bearing were considered.

Analytical Method for Hydrodynamic Force in Finite-Length Tilting-Pad Journal Bearing Including Turbulence Effect

2020 ◽  
Vol 142 (9) ◽  
Author(s):  
Yingze Jin ◽  
Xiaoyang Yuan
Keyword(s):  
Finite Length ◽  
Analytical Method ◽  
Nonlinear Dynamic ◽  
Separation Of Variables ◽  
Dynamic Performance ◽  
Published Data ◽  
Hydrodynamic Bearing ◽  
Low Viscosity ◽  
Tilting Pad ◽  
Turbulence Effect

Abstract To improve the efficiency in nonlinear dynamic calculation of finite-length tilting-pad journal bearings (TPJBs) under dynamic loads, an analytical method for hydrodynamic bearing forces, which considers the turbulence effect, is proposed using the method of separation of variables under the dynamic Gümbel boundary condition. No thermal effects are considered because this method is designed for the low viscosity case. The infinitely long bearing pressure is introduced as the circumferential pressure, and a general solution of the nonhomogeneous Reynolds equation is derived as the axial pressure. The turbulence model of Ng and Pan is characterized by a linear function of film thicknesses. A complete analytical expression of hydrodynamic bearing forces is derived. The analytical simulation shows slight differences and extremely low time expense in lubricating and dynamic performance compared to published data and finite difference method (FDM) simulation. The analytical method could be used to fast evaluate the nonlinear dynamic performance of a TPJB-rotor system in the low viscosity environment, supporting the nonlinear dynamic design of the system.

Experimentally study of dynamic pressure distribution and oil film forces in journal bearing using ElectroMechanical Film sensor array

2019 ◽  
Vol 234 (4) ◽  
pp. 903-913
Author(s):  
Changmin Chen ◽  
Jianping Jing ◽  
Jiqing Cong ◽  
Chao Ji
Keyword(s):  
Pressure Distribution ◽  
Sensor Array ◽  
Journal Bearing ◽  
Dynamic Pressure ◽  
Vertical Direction ◽  
Journal Bearings ◽  
Film Sensor ◽  
Film Pressure ◽  
Oil Film ◽  
Oil Film Pressure

The acquisition of the oil film pressure and forces on the bearing pads through experimentation is crucial to understanding the characteristics of journal bearing. Lots of efforts had been taken in film pressure measurement, and the pressure was obtained at specified position on the bearing pads. However, due to the space and structure constraint, merely very limited number of the point pressure can be obtained with traditional sensors and acquiring the detail pressure field on whole bearing pad surface is still an open challenge. In this paper, a method based on thin-film sensors technique is proposed and employed to measure the pressure distribution and oil film forces of journal bearings. The measurement is conducted on a cylindrical journal bearing with two axial grooves, and ElectroMechanical Film sensor arrays are designed and laid on the surface of the bearing pads. The oil film pressure is acquired at up to 32 measurement points in total along the bearing pads in both circumference and axial directions. The pressure distribution in a wide rotation speed range is obtained successfully by using fitting algorithm. Furthermore, the oil film forces on horizon and vertical direction are obtained through the integration of the measured pressure filed. The test results prove that it is feasible to measure the oil pressure filed of journal bearings using ElectroMechanical Film piezo-film sensor array.

Power Loss of Tilting 5-Pad Journal Bearing Operating With Turbulent Oil Film

2005 ◽  
Author(s):  
S. Strzelecki
Keyword(s):  
Power Loss ◽  
High Speed ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Heavy Duty ◽  
Safe Operation ◽  
Oil Film ◽  
Full Knowledge

Journal bearings of high speed turbocompressors, compressors and heavy duty high speed turbine gearboxes operate at journal peripheral speeds like 150 m/s. The flow of lubricant in such bearings is not laminar but super laminar or turbulent. It results in the increase in power loss and in the decrease of the bearing stability. The ground for the safe operation of high speed journal bearings at proper oil film temperature and with less power loss is the full knowledge of bearing performances at the turbulent oil film.

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.

Stability of Jeffcott Rotor Operating in Tilting 3-Pad Journal Bearings with Turbulent Oil Film

2009 ◽  
Vol 147-149 ◽  
pp. 450-455
Author(s):  
Stanislaw Strzelecki ◽  
Sobhy M. Ghoneam
Keyword(s):  
Theoretical Investigation ◽  
Dynamic Characteristics ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Oil Film ◽  
Temperature Distributions ◽  
Jeffcott Rotor ◽  
Oil Flow ◽  
The Stability ◽  
Oil Film Pressure

This paper introduces the results of theoretical investigation on the dynamic characteristics of tilting 3-pad journal bearing that operates with turbulent oil film. The Reynolds, energy, viscosity and geometry equations determine the oil film pressure, temperature distributions, and oil film resultant force that are the grounds for the dynamic characteristics of bearing. These equations were solved simultaneously on the assumption of adiabatic laminar or adiabatic turbulent oil flow in the bearing gap. The stability and system damping of Jeffcott rotor operating in tilting 3-pad journal bearing was determined.

Effect of Scratches on a Tilting-Pad Journal Bearing

2020 ◽  
Author(s):  
Steven Chatterton ◽  
Paolo Pennacchi ◽  
Andrea Vania ◽  
Mohamed Amine Hassini ◽  
Antoine Kuczkowiak
Keyword(s):  
Film Thickness ◽  
Dynamic Performance ◽  
Journal Bearings ◽  
Hydrodynamic Performance ◽  
Axial Position ◽  
Steam Turbines ◽  
Local Pressure ◽  
Oil Film ◽  
Tilting Pad ◽  
Tilting Pad Journal Bearing

Abstract Many industrial rotating machines are equipped with hydrodynamic journal bearings, such as centrifugal compressors, steam turbines, pumps and motors. After some time from the installation, however, the surface of the bearings often presents imperfections and slight damages mainly caused by the presence of harder particles in the lubricant during start-ups and shut-downs, when the hydrodynamic mechanism is not well developed and the mixed lubrication can occur. The presence of scratches on a bearing can lead to variations of the oil film thickness which, in turn, causes significant degradation of the bearing hydrodynamic performance. For example, the reduction of the minimum oil-film thickness can lead to the increase in the local temperature, to local pressure peaks and, finally, to the failure of the bearing. Experimental data relating to scratches on journal bearings are extremely limited in the literature especially for tilting-pad journal bearings (TPJBs). An experimental activity was carried out to study the effect of artificial scratches on pads on the static and dynamic behaviors of a TPJB. The number of scratches, the depth and the axial position have been investigated and the dynamic coefficients have been estimated as well. The experimental results confirmed a degradation of the dynamic performance of the bearing in case of scratches, that it has has been also confirmed by means of numerical simulations.

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