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.

scholarly journals Nonlinear dynamic analysis of low viscosity fluid-lubricated tilting-pad journal bearing for different design parameters

Friction ◽  
2019 ◽  
Vol 8 (5) ◽  
pp. 930-944 ◽  
Author(s):  
Yingze Jin ◽  
Fei Chen ◽  
Jimin Xu ◽  
Xiaoyang Yuan
Keyword(s):  
Dynamic Analysis ◽  
Nonlinear Dynamic ◽  
Load Capacity ◽  
Nonlinear Dynamic Analysis ◽  
Design Parameters ◽  
Clearance Ratio ◽  
Low Viscosity ◽  
Nonlinear Design ◽  
Tilting Pad ◽  
Viscosity Fluid

Abstract To reveal nonlinear dynamic rules of low viscosity fluid-lubricated tilting-pad journal bearings (TPJBs), the effects of design parameters on journal center orbits and dynamic minimum film thicknesses of water-lubricated TPJBs with and without static loads are investigated. The hydrodynamic bearing force used in the nonlinear dynamic analysis is an approximate analytical solution including the turbulence effect. The results reveal the methods for vibration suppression and load capacity improvement and give an optimal pivot offset and clearance ratio that can maximize the minimum film thickness. The results also show that four-pad TPJBs with loads between pads are preferred due to good dynamic performance and load capacity. This study would provide some guidance for nonlinear design of low viscosity fluid-lubricated TPJBs under dynamic loads.

Analysis on Dynamic Performance of Hydrodynamic Tilting-Pad Gas Bearings Using Partial Derivative Method

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Yang Lihua ◽  
Qi Shemiao ◽  
Yu Lie
Keyword(s):  
Analytical Method ◽  
Gas Turbines ◽  
High Speed ◽  
Dynamic Performance ◽  
Gas Bearings ◽  
Dynamic Coefficients ◽  
Tilting Pad ◽  
Dynamic Performances ◽  
Perturbation Frequency ◽  
San Andres

Tilting-pad gas bearings are widely used in high-speed rotating machines due to their inherent stability characteristics. This paper advances the analytical method for prediction of the dynamic performances of tilting-pad gas bearings. The main advantage of the analytical method is that the complete set of dynamic coefficients of tilting-pad gas bearings can be obtained. The predictions show that the perturbation frequency has the strong effects on the dynamic coefficients of gas bearings. In general, at lower perturbation frequency, the equivalent direct stiffness coefficients increase with frequency, whereas equivalent direct damping coefficients dramatically reduce. For higher perturbation frequency, the dynamic coefficients are nearly independent of the frequency. Moreover, the equivalent dynamic coefficients of four-pad tilting-pad gas bearing obtained by the method in this paper are in good agreement with those obtained by Zhu and San Andres [(2007), “Rotordynamic Performance of Flexure Pivot Hydrostatic Gas Bearings for Oil-Free Turbomachinery,” ASME J. Eng. Gas Turbines Power, 129(4), pp. 1020–1027] in the published paper. The results validate the feasibility of the method presented in this paper in calculating the dynamic coefficients of gas-lubricated tilting-pad bearings.

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.

Turbulence effect on dynamic performance of non-circular floating ring bearing

2020 ◽  
pp. 135065012091605
Author(s):  
Sandeep Soni
Keyword(s):  
Dynamic Performance ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Well Performance ◽  
Hydrodynamic Bearing ◽  
Continuity Equations ◽  
Analytical Work ◽  
Turbulence Effect ◽  
Stiffness Characteristics ◽  
The Impact

The current work scrutinizes the impact of turbulence on the dynamic performance of the novel variation of hydrodynamic bearing, especially “Non-Circular Floating Ring Bearing”. A bearing comprises of a shaft, floating ring, and non-circular outer housing. The journal and floating ring are cylindrical, whilst the outer housing is noncircular. The noncircular designs of journal bearing provide better stiffness characteristics. The well-established Navier–Stokes and continuity equations (cylindrical coordinates) have been adequately utilized with the linear turbulence lubrication theory. Dynamic characteristics of modified floating ring bearing have been scrutinized at different numerical values of film eccentricity ratio (outer) and Reynolds numbers up to 9000. The current analytical work envisages satisfactorily well performance of modified floating ring bearing in the regime of turbulence.

Proposal of nonlinear dynamic analytical method taking account of effects of local buckling damage

2009 ◽  
Vol 96 (10) ◽  
pp. 31-40
Author(s):  
Toshitaka Yamao ◽  
Akito Morimitsu ◽  
Atavit Sujaritpong ◽  
Faizal Chandra
Keyword(s):  
Analytical Method ◽  
Nonlinear Dynamic ◽  
Local Buckling

Investigation of slip/no-slip surface for two-dimensional large tilting pad thrust bearing

2017 ◽  
Vol 69 (6) ◽  
pp. 995-1004 ◽  
Author(s):  
Zhixiang Song ◽  
Fei Guo ◽  
Ying Liu ◽  
Songtao Hu ◽  
Xiangfeng Liu ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Slip Surface ◽  
Load Capacity ◽  
Slip Condition ◽  
Optimized Design ◽  
Two Dimensional ◽  
Boundary Slip ◽  
Content Type ◽  
Tilting Pad ◽  
Turbulence Effect

Purpose This paper aims to present the slip/no-slip design in two-dimensional water-lubricated tilting pad thrust bearings (TPTBs) considering the turbulence effect and shifting of pressure centers. Design/methodology/approach A numerical model is established to analyze the slip condition and the effect of turbulence according to a Reynolds number defined in terms of the slip condition. Simulations are carried out for eccentrically and centrally pivoted bearings and the influence of different slip parameters is discussed. Findings A considerable enhancement in load capacity, as well as a reduction in friction, can be achieved by heterogeneous slip/no-slip surface designs for lubricated sliding contacts, especially for near parallel pad configurations. The optimized design largely depends on the pivot position. The load capacity increases by 174 per cent for eccentrically pivoted bearings and 159 per cent for centrally pivoted bearings for a suitable design. When slip zone locates at the middle of the radial direction or close to the inner edge, the performance of the TPTB is better. Research limitations/implications The simplification of slip effect on the turbulence (definition of Reynolds number) can only describe the trend of the increasing turbulence due to slip condition. The accurate turbulence expression considering the boundary slip needs further explorations. Originality/value The shifting of pressure center due to the slip/no-slip design for TPTBs is investigated in this study. The turbulence effect and influence of slip parameters is discussed for large water-lubricated bearings.

Analysis on the Dynamic Performance of Vehicles

2021 ◽  
Vol 42 ◽  
pp. 71-78
Author(s):  
Oana Victoria Oțăt ◽  
Ilie Dumitru ◽  
Laurenţiu Racilă ◽  
Dragoș Tutunea ◽  
Lucian Matei
Keyword(s):  
Initial Data ◽  
Analytical Method ◽  
Dynamic Performance ◽  
Automotive Sector ◽  
Vehicle Dynamic ◽  
Car Model ◽  
Dynamic Performances

The current accelerated developments within the automotive sector have triggered a series of performance, comfort, safety and design-related issues. Hence, oftentimes manufacturers are challenged to combine various elements so as to achieve an attractive design, without diminishing the vehicle’s dynamic performance. In order to determine the vehicle dynamic performances we carried out an analysis by two methods. In the first part of the paper, we have used the analytical method to establish the dynamic performances of a vehicle. The second part of our study addresses another method to determine the star performances of the vehicle by means of computerized simulations. The first test aimed to determine vehicle starting performances for two vehicle models, with similar technical configuration, but with the same initial data. In the second test, we aimed at determining the start performance for the same car model, with the same initial data, but for different adhesion coefficients

Rotor Damped Natural Frequencies and Stability Under Reduced Oil Supply Flow Rates to Tilting-Pad Journal Bearings

2018 ◽  
Vol 140 (12) ◽  
Author(s):  
Bradley R. Nichols ◽  
Roger L. Fittro ◽  
Christopher P. Goyne
Keyword(s):  
Experimental Data ◽  
Natural Frequencies ◽  
Dynamic Performance ◽  
Operating Conditions ◽  
System Stability ◽  
Flow Rates ◽  
Oil Supply ◽  
Pressure Profiles ◽  
Tilting Pad ◽  
Identification Technique

Reduced oil supply flow rates in fluid film bearings can cause cavitation, or lack of a fully developed film layer, over one or more of the pads due to starvation. Reduced oil flow has the well-documented effects of higher bearing operating temperatures and decreased power losses; however, little experimental data are available on its effects on system stability and dynamic performance. The study looks at the effects of oil supply flow rate on dynamic bearing performance by comparing experimentally identified damped natural frequencies and damping ratios to predictive models. A test rig consisting of a flexible rotor and supported by two tilting pad bearings in flooded housings is utilized in this study. Tests are conducted over a range of supercritical operating speeds and bearing loads while systematically reducing the oil supply flow rates provided to the bearings. Shaft response measured as a magnetic actuator is used to perform sine sweep excitations of the rotor. A single-input, multiple-output system identification technique is then used to obtain frequency response functions (FRFs) and modal parameters. All experimental results are compared to predicted results obtained from bearing models based on thermoelastohydrodynamic (TEHD) lubrication theory. Both flooded and starved model flow assumptions are considered and compared to the data. Differences in the predicted trends of the models and the experimental data across varying operating conditions are examined. Predicted pressure profiles and dynamic coefficients from the models are presented to help explain any differences in trends.

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