A Thermal Elastohydrodynamic Lubrication Model for Crowned Rollers and Its Application on Apex Seal–Housing Interfaces

2019 ◽  
Vol 141 (4) ◽  
Author(s):  
Zhong Liu ◽  
David Pickens III ◽  
Tao He ◽  
Xin Zhang ◽  
Yuchuan Liu ◽  
...  
Keyword(s):  
Temperature Rise ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Frictional Heating ◽  
Elastohydrodynamic Lubrication ◽  
Design Equation ◽  
Rotary Engine ◽  
Influence Coefficients ◽  
Heavy Loads ◽  
Thermal Ehl

This paper presents a thermal elastohydrodynamic lubrication (EHL) model for analyzing crowned roller lubrication performances under the influence of frictional heating. In this thermal EHL model, the Reynolds equation is solved to obtain the film thickness and pressure results while the energy equation and temperature integration equation are evaluated for the temperature rise in the lubricant and at the surfaces. The discrete convolution fast Fourier transform (DC-FFT) method is utilized to calculate the influence coefficients for both the elastic deformation and the temperature integration equations. The influences of the slide-to-roll ratio (SRR), load, crowning radius, and roller length on the roller lubrication and temperature rise are investigated. The results indicate that the thermal effect becomes significant for the cases with high SRRs or heavy loads. The proposed thermal EHL model is used to study the thermal-tribology behavior of an apex seal–housing interface in a rotary engine, and to assist the design of the apex seal crown geometry. A simplified crown design equation is obtained from the analysis results, validated through comparison with the optimal results calculated using the current crowned-roller thermo-EHL (TEHL) model.

A Generalized Thermal EHL Model for Point Contact Problems

2008 ◽  
Author(s):  
Yuchuan Liu ◽  
Q. Jang Wang ◽  
Dong Zhu ◽  
Fanghui Shi
Keyword(s):  
Surface Temperature ◽  
Thermal Model ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Contact Problems ◽  
Three Dimensions ◽  
Thermal Ehl ◽  
Generalized Reynolds Equation

A generalized thermal elastohydrodynamic lubrication (TEHL) model for point contact problems is developed based on an isothermal generalized Newtonian elastohydrodynamic (EHL) model recently developed. The thermal model couples FDM for lubricant energy equation and the DC-FFT method for surface temperature integration. A generalized Reynolds equation is derived considering the change of viscosity with respect to temperature, pressure and shear in three dimensions. Numerical cases are conducted to verify the model.

Analysis of Thermal Effect on Elastohydrodynamic Lubrication in Angular Contact Ball Bearing

2015 ◽  
Vol 741 ◽  
pp. 443-448
Author(s):  
Bao Ming Wang ◽  
Xia Lun Yun ◽  
Xing Yao Liao ◽  
Xue Song Mei
Keyword(s):  
Temperature Rise ◽  
High Speed ◽  
Ball Bearing ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Oil Viscosity ◽  
Angular Contact Ball Bearing ◽  
Scanning Method ◽  
Lubrication Performance ◽  
Thermal Ehl

Based on the theory of point contact thermal elastohydrodynamic lubrication (EHL),the mathematical models for the thermal EHL of high-speed angular contact ball bearing are established. Multi-grid method and multigrid integration method are respectively used to calculate out the film pressure and film thickness respectively,and the column-by-column scanning method is used to calculate temperature rise of isothermal EHL and thermal EHL. The calculation results show that, under the pure rolling condition, temperature rise of oil film temperature is mainly caused by the compression work and shear heat at inlet and the heat in contact zone mainly comes from the inlet and the heat conduction around; the temperature rise results in oil viscosity lower and the lubricating film thinner ,in this way it reduces the lubrication performance in contact pair.

Analysis of Heavily Loaded Tilted Pads Thrust Bearings With Large Dimensions Under TEHD Conditions

1988 ◽  
Vol 110 (3) ◽  
pp. 467-476 ◽  
Author(s):  
L. A. Abdel-Latif
Keyword(s):  
Reynolds Equation ◽  
Energy Equation ◽  
Iterative Scheme ◽  
Equation System ◽  
Successive Approximation Method ◽  
Heavy Load ◽  
Thrust Bearings ◽  
Characteristic Values ◽  
Heavy Loads ◽  
Bearing Characteristic

Huge thrust bearings with centrally pivoted and tilted pads operating under heavy loads are analzyed using the (thermoelastohydrodynamic) TEHD-theory. The Reynolds equation, the energy equation of the oil film, and the heat conduction equation of the bearing, all are coupled with the deflection equation and solved simultaneously in order to determine the bearing characteristic values. The first three equations are transformed by means of finite difference method and the last equation is solved using the method of Ritz-Galerkin. Based on successive approximation method a new iterative scheme is presented to apply the heavy load incrementally which provides a successful convergence of the equation system. In order to find the equilibrium state of the pad, another iterative scheme based on a controlled change of the pad tilts is applied. The tilts are changed as a function of the offset of the hydrodynamic resultant force from the pivot location. It is proved that the new scheme is quite efficient in successful convergence of the equation system and in saving CPU time.

Inverse Solution of Reynolds’ Equation of Lubrication Under Point-Contact Elastohydrodynamic Conditions

1981 ◽  
Vol 103 (4) ◽  
pp. 539-546 ◽  
Author(s):  
H. P. Evans ◽  
R. W. Snidle
Keyword(s):  
Film Thickness ◽  
Pressure Distribution ◽  
Reynolds Equation ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Hydrodynamic Pressure ◽  
Inverse Solution ◽  
Heavy Loads

The paper describes a technique for solving the inverse lubrication problem under point contact elastohydrodynamic conditions, i.e. the calculation of a film thickness and shape corresponding to a given hydrodynamic pressure distribution by an inverse solution of Reynolds’ equation. The effect of compressibility and influence of pressure upon viscosity are included in the analysis. The technique will be of use in solving the point contact elastohydrodynamic lubrication problem at heavy loads.

Thermoelastohydrodynamic Analysis of Journal Bearings With Non-Newtonian Carreau Fluids

2009 ◽  
Author(s):  
M. Mongkolwongrojn ◽  
C. Aiumpornsin
Keyword(s):  
Reynolds Equation ◽  
Energy Equation ◽  
Initial Conditions ◽  
Elastohydrodynamic Lubrication ◽  
Viscosity Model ◽  
Maximum Temperature ◽  
Approximation Technique ◽  
Low Elastic Modulus ◽  
Modified Reynolds Equation ◽  
Transient Thermal

The paper focuses on the solution of a numerical model to explore the journal bearing performance under transient thermal elastohydrodynamic lubrication with non-Newtonian lubricants based on Carreau viscosity model. The newly derived time-dependent modified Reynolds equation and the adiabatic energy equation have been formulated using a non-Newtonian Carreau viscosity model. The simultaneous systems consisting of the modified Reynolds equation, elasticity equation and energy equation with initial conditions were solved numerically using the multi-grid multi-level method with full approximation technique. The analysis showed that the fluid characteristics as defined by the Carreau model, led to large differences in minimum film thickness and maximum temperature rise for bearing liners with low elastic modulus.

A Numerical Model to Predict Dynamic Performance of Layered Gears at Starved Lubrication

2019 ◽  
Author(s):  
Qingbing Dong ◽  
Jing Wei ◽  
Yan Li ◽  
Lixin Xu
Keyword(s):  
Reynolds Equation ◽  
Dynamic Performance ◽  
Three Dimensional ◽  
Elastohydrodynamic Lubrication ◽  
Material System ◽  
Stress Concentrations ◽  
Damage Resistance ◽  
Influence Coefficients ◽  
Load Carrying ◽  
Potential Energy Method

Abstract Gears of modern industry are required to have a good fatigue performance to transmit power and motion through the contact interfaces. Composite layered surfaces can effectively improve the damage resistance of gears and decrease the friction coefficients. However, improper surface modification may induce intensive stress concentrations at the joint interfaces of the strengthening layers and cause unexpected damages to the flanks. Furthermore, the amount of lubricant at the inlet may probably be insufficient to establish fully flooded condition, which may result in starvation and accelerate damages to the gear sets. In this study, a starved elastohydrodynamic lubrication (EHL) model in three-dimensional (3D) line contact for layered gears is developed. The potential energy method is employed to determine the load distribution along the action line. The loading force is assumed to be balanced by the lubrication pressure, which is derived by discretizing the dimensional Reynolds equation into a solvable matrix with the consideration of the enforced boundary conditions due to the inlet oil supply. The transient evolution of lubrication is investigated to evaluate the load-carrying capability of the lubricant film at various starvation conditions. The influence coefficients related to the displacements and stresses of the layered material system are determined with the assistance of the fast Fourier transform (FFT) algorithm, and the effects of the layer properties and the fabrication methods are evaluated. Such analysis may provide insightful information for the optimization of material systems with fabricated layers and engineering design of gears.

The elastohydrodynamic lubrication of point contacts at heavy loads

1982 ◽  
Vol 382 (1782) ◽  
pp. 183-199 ◽  
Keyword(s):  
Present Method ◽  
Reynolds Equation ◽  
Pressure Coefficient ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Engineering Practice ◽  
Point Contacts ◽  
Pressure Distributions ◽  
Heavy Loads ◽  
Coefficient Of Viscosity

A method of solving the elastohydrodynamic point contact problem at heavy loads is presented. Earlier solutions based upon straightforward iterative techniques have been restricted to relatively light loads. The present method makes use of the inverse solution of the two-dimensional Reynolds equation and is similar in principle to the well known line contact elastohydrodynamic solution of Dowson and Higginson. The method is applicable to the heavily loaded point contacts found in engineering practice. Material combinations of steel–glass and steel–steel have been considered and results have been obtained at maximum Hertzian pressures of 0.7 GPa and 1.4 GPa respectively. Solutions are presented showing the effect of speed and the influence of the pressure coefficient of viscosity of the lubricant on film thickness and pressure distributions at these heavy loads.

Paper 25: Use of Similarity Numbers in Connection with Plain Bearings under Conditions of Varying Temperature and Viscosity

1966 ◽  
Vol 181 (15) ◽  
pp. 144-155 ◽  
Author(s):  
E. Pollmann
Keyword(s):  
Numerical Method ◽  
Approximation Method ◽  
Temperature Rise ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Mean Value ◽  
Similar Form ◽  
Adiabatic Conditions ◽  
Lubricating Film ◽  
Temperature And Pressure

The similarity conditions for the phenomena in a lubricating film follow from the Reynolds equation and from the energy equation. It will be shown that with the aid of some justifiable simplifications the properties of a bearing may be described by two characteristic magnitudes only. From the inlet viscosity, a loading value and a similarly constituted temperature rise value may be derived. Further, since an approximation method is used, the calculation effort has been considerably reduced. (A similar form of approximation was used by Schiebel and Vogelpohl for the finite bearing.) The results obtained for a 360° bearing are compared with those obtained by Motosh, which were calculated from a more complicated numerical method. As an example of the description of the bearing characteristics, calculations are made for a 120° bearing, and the temperature and pressure curves together with the loading and temperature rise values are shown in the form of curves. The limitations on the use of adiabatic conditions are illustrated by an example. Finally, the effects arising from the variation of viscosity with pressure are demonstrated by means of a further example. In the application of the method, it is not necessary to calculate with a mean value of viscosity for the lubricating medium in the lubricating gap, so that more reliable calculations are possible.

scholarly journals Run-Up Simulation of a Semi-Floating Ring Supported Turbocharger Rotor Considering Thrust Bearing and Mass-Conserving Cavitation

Lubricants ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 44
Author(s):  
Christian Ziese ◽  
Cornelius Irmscher ◽  
Steffen Nitzschke ◽  
Christian Daniel ◽  
Elmar Woschke
Keyword(s):  
Reynolds Equation ◽  
Energy Equation ◽  
Thrust Bearing ◽  
Three Dimensional ◽  
Reliable Prediction ◽  
Two Phase ◽  
Hydrodynamic Bearings ◽  
Thrust Bearings ◽  
Run Up ◽  
The Impact

The vibration behaviour of turbocharger rotors is influenced by the acting loads as well as by the type and arrangement of the hydrodynamic bearings and their operating condition. Due to the highly non-linear bearing behaviour, lubricant film-induced excitations can occur, which lead to sub-synchronous rotor vibrations. A significant impact on the oscillation behaviour is attributed to the pressure distribution in the hydrodynamic bearings, which is influenced by the thermo-hydrodynamic conditions and the occurrence of outgassing processes. This contribution investigates the vibration behaviour of a floating ring supported turbocharger rotor. For detailed modelling of the bearings, the Reynolds equation with mass-conserving cavitation, the three-dimensional energy equation and the heat conduction equation are solved. To examine the impact of outgassing processes and thrust bearing on the occurrence of sub-synchronous rotor vibrations separately, a variation of the bearing model is made. This includes run-up simulations considering or neglecting thrust bearings and two-phase flow in the lubrication gap. It is shown that, for a reliable prediction of sub-synchronous vibrations, both the modelling of outgassing processes in hydrodynamic bearings and the consideration of thrust bearing are necessary.

An Assessment of the Value of Theory in Predicting Gas-Bearing Performance

1961 ◽  
Vol 83 (2) ◽  
pp. 195-200 ◽  
Author(s):  
S. Cooper
Keyword(s):  
Steady State ◽  
Slip Velocity ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Experimental Methods ◽  
Experimental Results ◽  
Theoretical Investigations ◽  
Gas Bearing ◽  
Theoretical Results

The object of the paper is to indicate the value of theoretical investigations of hydrodynamic finite bearings under steady-state conditions. Methods of solution of Reynolds equation by both desk and digital computing, and methods of stabilizing the processes of solution, are described. The nondimensional data available from the solutions are stated. The outcome of an attempted solution of the energy equation is discussed. A comparison between some theoretical and experimental results is shown. Experimental methods employed and some difficulties encountered are discussed. Some theoretical results are given to indicate the effects of the inclusion of slip velocity, stabilizing slots, and a simple case of whirl.

Sign in / Sign up

Export Citation Format

Share Document