scholarly journals Numerical Modelization of the Oil Film Pressure for a Hydrodynamic Tilting-Pad Thrust Bearing

2020 ◽  
Vol 30 (7) ◽  
pp. 25-30
Author(s):  
Anh Dung Le ◽  
Thi Thanh Hai Tran
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Thrust Bearing ◽  
Hydrodynamic Characteristic ◽  
The Finite Element Method ◽  
Equilibrium Equations ◽  
Tilting Pad ◽  
Inclination Angles ◽  
High Pressure Zone ◽  
Force Equilibrium

This study analyses the hydrodynamic characteristic of the tilting pad thrust bearing. Research content is simultaneously solving the Reynolds equation, force equilibrium equation, and momentum equilibrium equations. Reynolds equation is solved by utilizing the finite element method with Galerkin weighted residual, thereby determines the pressure at each discrete node of the film. Force and momentums are integrated from pressure nodes by Gaussian integral. Finally, force and momentum equilibrium equations are solved using Newton-Raphson iterative to achieve film thickness and inclination angles of the pad at the equilibrium position. The results yielded the film thickness, the pressure distribution on the whole pad and different sections of the bearing respected to the radial direction. The high-pressure zone is located at the low film thickness zone and near the pivot location.

Static Characteristics of Gas Foil Thrust Bearing Based on Gas Rarefaction Model

2015 ◽  
Author(s):  
Jiajia Yan ◽  
Guanghui Zhang ◽  
Zhansheng Liu ◽  
Fan Yang
Keyword(s):  
Film Thickness ◽  
Optimization Design ◽  
Reynolds Equation ◽  
Thrust Bearing ◽  
Rarefied Gas ◽  
Load Capacity ◽  
Structural Parameters ◽  
Lubricating Film ◽  
Lift Off ◽  
Foil Thrust Bearing

A modified Reynolds equation for bump type gas foil thrust bearing was established with consideration of the gas rarefaction coefficient. Under rarefied gas lubrication, the Knudsen number which was affected by the film thickness and pressure was introduced to the Reynolds equation. The coupled modified Reynolds and lubricating film thickness equations were solved using Newton-Raphson Iterative Method and Finite Difference Method. By calculating the load capacity for increasing rotor speeds, the lift-off speed under certain static load was obtained. Parametric studies for a series of structural parameters and assembled clearances were carried out for bearing optimization design. The results indicate that with gas rarefaction effect, the axial load capacity would be decreased, and the lift-off speed would be improved. The rarefied gas has a more remarkable impact under a lower rotating speed and a smaller foil compliance coefficient. When the assembled clearance of the thrust bearing rotor system lies in a small value, the lift-off speed increases dramatically as the assembled clearance decreases further. Therefore, the axial clearance should be controlled carefully in assembling the foil thrust bearing. It’s worth noting that the linear uniform bump foil stiffness model is not exact for large foil compliance ∼0.5, especially for lift-off speed analysis, due to ignoring the interaction between bumps and bending stiffness of the foil.

An Experimental Investigation of a Tilting-Pad, Compliant-Surface, Thrust Bearing

1976 ◽  
Vol 98 (1) ◽  
pp. 95-110 ◽  
Author(s):  
Glenn K. Rightmire ◽  
Vittorio Castelli ◽  
Dudley D. Fuller
Keyword(s):  
Experimental Investigation ◽  
Film Thickness ◽  
Thrust Bearing ◽  
Lubricant Film ◽  
Film Pressure ◽  
Compliant Surface ◽  
Pressure Fields ◽  
Tilting Pad ◽  
Typical Range

Results are provided for an investigation of a compliant-surface, tilting-shoe bearing, when operating in oil. Two values of elastomer durometer were used on shoes as well as seven different pivot locations. The investigation included measurements of lubricant film pressure fields and film-thickness profiles under the shoes during operation. Friction and overall stiffness were also recorded for a typical range of speeds, loads, and pivot positions.

Steady State Performance Characteristics of a Tilting Pad Thrust Bearing

2000 ◽  
Vol 123 (3) ◽  
pp. 608-615 ◽  
Author(s):  
Sergei B. Glavatskikh
Keyword(s):  
Steady State ◽  
Film Thickness ◽  
Thrust Bearing ◽  
Operating Conditions ◽  
Performance Characteristics ◽  
Shaft Speed ◽  
Oil Film ◽  
Tilting Pad ◽  
Bearing Load ◽  
Steady State Performance

The paper reports results of the experimental investigation into the steady state performance characteristics of a tilting pad thrust bearing typical of design in general use. Simultaneous measurements are taken of the pad and collar temperatures, the pressure distributions, oil film thickness, and power loss as a function of shaft speed, bearing load, and supplied oil temperature. The effect of operating conditions on bearing performance is discussed. A small radial temperature variation is observed in the collar. A reduction in minimum oil film thickness with load is approximately proportional to p−0.6, where p is an average bearing pressure. It has also been found that the oil film pressure profiles change not only due to the average bearing load but also with an increase in shaft speed and temperature of the supplied oil.

A semianalytical method for studying the performances of aerostatic thrust bearing

2018 ◽  
Vol 233 (4) ◽  
pp. 628-637
Author(s):  
Jianbo Zhang ◽  
Chunxiao Jiao ◽  
Donglin Zou ◽  
Na Ta ◽  
Zhushi Rao
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Film Thickness ◽  
Reynolds Equation ◽  
Thrust Bearing ◽  
Separation Of Variables ◽  
Orifice Diameter ◽  
Thrust Bearings ◽  
Supply Pressure ◽  
Semianalytical Method

The solution of Reynolds equation and computational fluid dynamics are widely employed for the lubrication performance analysis of aerostatic thrust bearing. However, the solution of Reynolds equation may be inaccurate and cannot present detailed performance near orifice, while computational fluid dynamics method has low computational efficiency with time consumption in mesh generation and solving Navier–Stokes equations. In order to overcome the drawbacks of Reynolds equation and computational fluid dynamics, based on the method of separation of variables, a semianalytical method is developed for describing the characteristics of aerostatic bearings available. The method of separation of variables considering the initial and viscous effect is more accurate than the Reynolds equation and can present detailed performance near orifice in the aerostatic thrust bearings, while method of separation of variables has great computational efficiency compared to computational fluid dynamics. Meanwhile, the pressure distribution calculated by method of separation of variables is compared to the published experimental data and the results obtained by computational fluid dynamics. The comparative results indicate validity of the method. Furthermore, the influences of flow and geometry parameters, such as supply pressure, orifice diameter, film thickness, and bearing radius, on the characteristics of aerostatic thrust bearings with single orifice are studied. The results show that there exists pressure depression phenomenon near orifice. The depression phenomenon is strengthened with increase of film thickness and supply pressure and decrease of orifice diameter and bearing radius, while the maximum speed increases with strengthening of pressure depression due to decrease of minimum local pressure near orifice. Moreover, the bearing capacity increases with increase of supply pressure, orifice diameter, and bearing radius and decreases with increase of film thickness, while mass flow rate increases with supply pressure, orifice diameter, and film thickness and it is not sensitive to bearing radius.

Analysis of Four Finite Volume Schemes for Plane Stress Problems

2012 ◽  
Vol 204-208 ◽  
pp. 4635-4642
Author(s):  
Yue Ping Qin ◽  
Quan Sun ◽  
Xiao Bin Yang ◽  
Guo Yu Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Volume ◽  
Plane Stress ◽  
Linear Equations ◽  
Finite Volume Scheme ◽  
The Finite Element Method ◽  
Finite Volume Schemes ◽  
Equilibrium Equations ◽  
Volume Method ◽  
Force Equilibrium

In order to compare precisions of different finite volume schemes for plane stress problems, this paper discussed three typical finite volume schemes(FVM2, FVM3 and FVM4) through theoretical deduction and example verification, and introduced a new scheme(FVM1). Force equilibrium equations were obtained, which derived from the principle of the finite volume method (FVM). Using triangular units and in view of internal cells and boundary elements, this paper put forward these four finite schemes linear equations similar to the finite element method(FEM) stiffness equations but with different coefficients. The analyses and numerical example results show that FVM1 is the optimal finite volume scheme, and suggest that in practical civil, architectural and hydraulic engineering calculations, schemes should be selected carefully and FVM1 is a good option.

The Significance of Oil Thermal Properties on the Performance of a Tilting-Pad Thrust Bearing

2001 ◽  
Vol 124 (2) ◽  
pp. 377-385 ◽  
Author(s):  
Sergei B. Glavatskih ◽  
Michel Fillon ◽  
Roland Larsson
Keyword(s):  
Thermal Properties ◽  
Film Thickness ◽  
Thrust Bearing ◽  
Friction Torque ◽  
Temperature Fields ◽  
Outer Diameter ◽  
Oil Film ◽  
Tilting Pad ◽  
Viscosity Grade ◽  
Mineral Base

This paper is a report into an experimental and theoretical investigation of the effect of oil thermal properties on the performance of a tilting-pad thrust bearing. Three oils, namely poly-α-olefin, ester and mineral base, were chosen for this study. These oils all have same viscosity grade (ISO VG46) but differ in their rates of viscosity variation with temperature and in their heat capacity and thermal conductivity values. Mineral base oil of a higher viscosity grade (ISO VG68) was also analyzed for comparison. Experimental data were obtained from an equalizing tilting-pad thrust bearing with an outer diameter of 228.6 mm operating in a flooded lubrication mode. Simultaneous measurements of pad and collar temperatures, friction torque, pressures and oil film thickness were taken. In the tests, oil supply temperature and flow rate were held constant for all load-speed combinations. The theoretical analysis of oil performance was based on a three-dimensional TEHD model. In the analysis, thermal effects were locally taken into account and heat transfer into the pads was considered. The displacements of the active surface of the pads, due to pressure and temperature fields, were determined. The effect of initial pad crowning on the oil film thickness is discussed. Experimental and theoretical results are compared and analyzed in terms of the inlet and outlet oil film thickness, bearing operating temperature and power loss.

A Performance Investigation into the Elastically Stepped and Shrouded Thrust Bearing

1967 ◽  
Vol 182 (1) ◽  
pp. 769-782 ◽  
Author(s):  
E. W. Hemingway
Keyword(s):  
Experimental Investigation ◽  
Film Thickness ◽  
Thrust Bearing ◽  
Frictional Resistance ◽  
Oil Film ◽  
Elastic Deflection ◽  
Tilting Pad ◽  
Thrust Pad ◽  
A Performance

An experimental investigation is reported in which a stepped and shrouded thrust pad was formed from an initially plane pad face by elastic deflection caused by pressures generated hydrodynamically in the oil film. The pad shape was optimized experimentally and it produced thicker films than a comparable tilting pad bearing but with higher frictional resistance. Pressure and film thickness contours were investigated and plotted. A comparison is made with stepped pad bearing results. This paper is based on sections of a thesis presented in 1966 for the degree of Ph.D., University of London.

Numerical Calculation and Analysis of Water-Lubricated Stern Bearing Considering Elastic Hydrodynamic

2014 ◽  
Vol 1061-1062 ◽  
pp. 653-657
Author(s):  
Gang Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Calculation ◽  
Film Thickness ◽  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
Water Film ◽  
Polymer Materials ◽  
The Finite Element Method ◽  
Metal Materials

The deformation of marine water-lubricated stern bearing which the lining materials are polymer materials is much bigger than the bearing built with metal materials. So, in order to improve the calculate accuracy of elastic hydrodynamic, it is necessary to consider the deformation of the lining. Both pressure and thickness distributions of water film which contrasts with the hydrodynamic lubrication are presented by the Reynolds equation, and combining with the elastic deformation of the stern bearing solved by using the finite element method theory. The result shows that the stern bearing water film pressure of elastic hydrodynamic lubrication is lower than that of hydrodynamic lubrication, while the water film thickness is larger.

scholarly journals Comparison of measured and calculated water film thickness of a water-lubricated elastically supported tilting pad thrust bearing

2019 ◽  
Vol 7 (4) ◽  
pp. 045010 ◽  
Author(s):  
Xingxin Liang ◽  
Xinping Yan ◽  
Wu Ouyang ◽  
Robert J K Wood ◽  
Fuming Kuang ◽  
...  
Keyword(s):  
Film Thickness ◽  
Thrust Bearing ◽  
Water Film ◽  
Water Film Thickness ◽  
Tilting Pad ◽  
Elastically Supported

The Influence of Injection Pockets on the Performance of Tilting-Pad Thrust Bearings: Part II — Comparison Between Theory and Experiment

2006 ◽  
Author(s):  
Niels Heinrichson ◽  
Axel Fuerst ◽  
Ilmar Ferreira Santos
Keyword(s):  
Film Thickness ◽  
Thrust Bearing ◽  
Three Dimensional ◽  
Leading Edge ◽  
Operating Conditions ◽  
Oil Film ◽  
Thrust Bearings ◽  
Tilting Pad ◽  
High Pressure Injection ◽  
Theoretical Pressure

This is Part II of a two-part series of papers describing the effects of high pressure injection pockets on the operating conditions of tilting-pad thrust bearings. Measurements of the distribution of pressure and oil film thickness are presented for tilting-pad thrust bearing pads of approximately 100 cm2 surface area. Two pads are measured in a laboratory test-rig at loads of approximately 0.5, 1.5 and 4.0 MPa and velocities of up to 33 m/s. One pad has a plain surface. The other pad has a conical injection pocket at the pivot point and a leading edge taper. The measurements are compared to theoretical values obtained using a three dimensional thermoelasto-hydrodynamic (TEHD) numerical model. At low and intermediate loads the theoretical pressure distribution corresponds well to the measured values for both pads although the influence of the pocket is slightly underestimated. At high loads large discrepancies exist for the pad with an injection pocket. It is argued that this is likely to be due to the unevenness of the collar surface. The measured and theoretical values of oil film thickness compare well at low loads. At high loads discrepancies grow to up to 25 %. It is argued that this is due to the accuracy of the measurements.

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