Thermal and Roughness Effects in a Slider Bearing Considering Conduction Through Both the Pad and the Slider

2008 ◽  
Author(s):  
Prawal Sinha ◽  
Getachew Adamu
Keyword(s):  
Heat Conduction ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Momentum Equation ◽  
Regular Domain ◽  
Slider Bearing ◽  
Irregular Domain ◽  
Temperature Dependent ◽  
Roughness Effects ◽  
Different Characteristics

This paper analyses the thermal and roughness effects on different characteristics of an infinitely long tilted pad slider bearing considering heat conduction through both the pad and slider. The roughness is assumed to be stochastic, Gaussian randomly distributed. Density and viscosity are assumed to be temperature dependent. The irregular domain of the fluid due to roughness is mapped to a regular domain so that the numerical method can be easily applied. The modified Reynolds equation, momentum equation, continuity equation, energy equation and the heat conduction equations on the pad and slider are coupled and solved using finite difference method to yield various bearing characteristics. The solutions with respect to different pad and slider boundary conditions are elaborated through tables and figures.

Numerical Solution of Heat Conduction in a Heterogeneous Multiscale Material With Temperature-Dependent Properties

2016 ◽  
Vol 138 (6) ◽  
Author(s):  
James White
Keyword(s):  
Heat Conduction ◽  
Numerical Solution ◽  
Time Scales ◽  
Thermal Energy ◽  
Energy Equation ◽  
Three Dimensional ◽  
Homogeneous Material ◽  
Time Level ◽  
Temperature Dependent ◽  
Temperature Dependent Properties

Numerical solution of heat conduction in a heterogeneous material with small spatial and time scales can lead to excessive compute times due to the dense computational grids required. This problem is avoided by averaging the energy equation over the small-scales, which removes the appearance of the short spatial and time scales while retaining their effect on the average temperature. Averaging does, however, increase the complexity of the resulting thermal energy equation by introducing mixed spatial derivatives and six different averaged conductivity terms for three-dimensional analysis. There is a need for a numerical method that efficiently and accurately handles these complexities as well as the other details of the averaged thermal energy equation. That is the topic of this paper as it describes a numerical solution for the averaged thermal energy equation based on Fourier conduction reported recently in the literature. The solution, based on finite difference techniques that are second-order time-accurate and noniterative, is appropriate for three-dimensional time-dependent and steady-state analysis. Speed of solution is obtained by spatially factoring the scheme into an alternating direction sequence at each time level. Numerical stability is enhanced by implicit algorithms that make use of the properties of tightly banded matrices. While accurately accounting for the nonlinearity introduced into the energy equation by temperature-dependent properties, the numerical solution algorithm requires only the consideration of linear systems of algebraic equations in advancing the solution from one time level to the next. Computed examples are included and compared with those for a homogeneous material.

Forced Cooling of a Slider Bearing With Wedge Film

1968 ◽  
Vol 90 (1) ◽  
pp. 297-304 ◽  
Author(s):  
H. Tahara
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Heat Flow ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Heat Flow Rate ◽  
Slider Bearing ◽  
The Mean ◽  
Forced Cooling ◽  
Generalized Reynolds Equation

This paper deals with the forced cooling problem of a slider bearing with wedge film of finite length, where most of the heat generated in the lubricant film is removed by a coolant which flows under the surface of the bearing pad. Analysis was made on the generalized Reynolds’ equation, including viscosity variations with temperature throughout the film and the energy equation. Simultaneous solutions of these equations seemed to be supported by experiments. From the analysis, calculations were made on the heat flow rate into the coolant, the temperature difference between slider and pad surfaces, bearing characteristics using the representative viscosity, and the mean heat transfer coefficient of the wedge film.

Performance characteristics of two-axial groove journal bearing for different groove angles

2018 ◽  
Vol 70 (2) ◽  
pp. 432-443
Author(s):  
K.R. Kadam ◽  
S.S. Banwait
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Heat Conduction ◽  
Pressure Distribution ◽  
Heat Conduction Equation ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Journal Bearing ◽  
Three Dimensional ◽  
Content Type

Purpose Different groove angles are used to study performance characteristics of two-axial groove journal bearing. In this study two grooves are located at ±90º to the load line. The various angles of grooves have been taken as 10° to 40° in the interval of 5°. Different equations such as Reynolds equation, three-dimensional energy equation and heat conduction equation have been solved using finite element method and finite difference method. Pressure distribution in fluid is found by using Reynolds equation. The three-dimensional energy equation is used for temperature distribution in the fluid film and bush. One-dimensional heat conduction equation is used for finding temperature in axial direction for journal. There is a very small effect of groove angle on film thickness, eccentricity ratio and pressure. There is a drastic change in attitude angle and side flow. Result shows that there is maximum power loss at large groove angle. So the smaller groove angle is recommended for two-axial groove journal bearing. Design/methodology/approach The finite element method is used for solving Reynolds equation for pressure distribution in fluid. The finite difference method is adopted for finding temperature distribution in bush, fluid and journal. Findings Pressure distribution in fluid is found out. Temperature distribution in bush, fluid and journal is found out. There is a very small effect of groove angle on film thickness, eccentricity ratio and pressure. Research limitations/implications The groove angle used is from 10 to 40 degree. The power loss is more when angle of groove increases, so smaller groove angle is recommended for this study. Practical implications The location of groove angle predicts the distribution of pressure and temperature in journal bearing. It will show the performance characteristics. ±90° angle we will prefer that will get before manufacturing of bearing. Social implications Due to this study, we will get predict how the pressure and temperature distribute in the journal. It will give the running condition of bearing as to at what speed and load we will get the maximum temperature and pressure in the bearing. Originality/value The finite element method is used for solving the Reynolds equation. Three-dimensional energy equation is solved using the finite difference method. Heat conduction equation is also solved for journal. The C language is used. The code is developed in C language. There are different equations which depend on each other. The temperature is dependent on pressure viscosity of fluid, etc. so C code is preferred.

scholarly journals Nonlinear Solution to a Non-Fourier Heat Conduction Problem in a Slab Heated by Laser Source

2016 ◽  
Vol 63 (1) ◽  
pp. 129-144
Author(s):  
Mohammad Javad Noroozi ◽  
Seyfolah Saedodin ◽  
Davood Domiri Ganji
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Adomian Decomposition Method ◽  
Laser Source ◽  
Temperature Dependent ◽  
Conduction Model ◽  
Non Linear Equation ◽  
Adomian Decomposition ◽  
Non Linear ◽  
Fourier Heat Conduction

Abstract The effect of laser, as a heat source, on a one-dimensional finite body was studied in this paper. The Cattaneo-Vernotte non-Fourier heat conduction model was used for thermal analysis. The thermal conductivity was assumed temperature-dependent which resulted in a non-linear equation. The obtained equations were solved using the approximate-analytical Adomian Decomposition Method (ADM). It was concluded that the non-linear analysis is important in non-Fourier heat conduction problems. Significant differences were observed between the Fourier and non-Fourier solutions which stresses the importance of non-Fourier solutions in the similar problems.

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.

DDC Lubrication: A New Concept in Tribology

1992 ◽  
Vol 114 (1) ◽  
pp. 181-185 ◽  
Author(s):  
K. To̸nder
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Gap Function ◽  
Upper And Lower Bounds ◽  
Roughness Effects ◽  
Cavity Depth ◽  
Roughness Amplitude ◽  
Previously Treated ◽  
The Mean ◽  
Expansion Scheme

A new lubrication concept is presented, Deep Disconnected Cavities. It differs from the lubrication of microcavities, previously treated by other authors, by the deepness of the cavities. The validity of Reynolds’ equation and nonturbulent conditions are assumed. By a Taylor expansion scheme, it is shown that the roughness effects are expressible in terms of roughness factors modifying the Reynolds equation, similar to those proposed by Patir and Cheng (1978). Unlike those established for ordinary roughness, the DDC factors are independent of local film thickness and roughness amplitude (cavity depth), and may therefore be used to modify standard hydro-dynamic parameters. By a different mathematical approach, involving upper and lower bounds on the various hydrodynamic quantities, it is found that Reynolds’ equation and all the other hydrodynamic expressions may be written just as for smooth surfaces, with the following modifications: 1. The film thickness should be expressed by the minimum gap function, and not by the mean gap function. 2. There are, in general, three effective viscosities, lower than the physical one, two of which are associated with the x and y directions respectively and appear in the modified Reynolds equation as well as in the flow terms. The third one appears only in the expression for shear stress.

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