A Full Numerical Solution for the Thermoelastohydrodynamic Problem in Elliptical Contacts

1984 ◽  
Vol 106 (2) ◽  
pp. 246-254 ◽  
Author(s):  
Dong Zhu ◽  
Shi-zhu Wen
Keyword(s):  
Steady State ◽  
Temperature Distribution ◽  
Numerical Solution ◽  
Pressure Distribution ◽  
Three Dimensional ◽  
Thermal Action ◽  
Film Pressure ◽  
Rolling Velocity ◽  
Friction Factors

In this paper a full numerical solution for the thermoelastohydrodynamic problem in elliptical contacts is presented, and the method of computation is also described. The film pressure, thickness, and film shape, the three dimensional temperature distribution within both the film and the bounding solids, as well as the coefficients of the sliding and rolling frictions have all been determined for different rolling velocities and slide-roll ratios. The results obtained indicate the film temperature increases as the rolling velocity or slide-roll ratio increases. The effects of thermal action on the pressure distribution, the film shape and thickness, and the friction factors are also given. The problem studied in this paper is steady-state, the lubricant is assumed to be Newtonian.

Experimental Measurements of Temperature Distribution in Three Dimensional Stacked Package

2007 ◽  
Author(s):  
Anand Desai ◽  
James Geer ◽  
Bahgat Sammakia
Keyword(s):  
Experimental Study ◽  
Heat Conduction ◽  
Steady State ◽  
Temperature Distribution ◽  
Numerical Model ◽  
Analytical Solution ◽  
Three Dimensional ◽  
Power Input ◽  
Experimental Measurements ◽  
Steady State Heat

This paper presents the results of an experimental study of steady state heat conduction in a three dimensional stack package. The temperatures are measured at different interfaces within the stacked package. Delphi devices are used in the experiment which enables controlled power input and surface temperature of the devices. The experiment is carried out for three different boundary conditions on the package. The power input in varied to study its effects. A numerical model is created to compare to the experimental results. The results are also compared with the analytical solution presented in Desai et al [5] and Geer et al [6]. The results indicate that the experimental, numerical and analytical solutions follow the same trend. The agreement between the experimental and numerical results improves when the lateral losses are taken into account.

Numerical Solution to a Two-Dimensional Conduction Problem Using Rectangular and Cylindrical Body-Fitted Coordinate Systems

1981 ◽  
Vol 103 (4) ◽  
pp. 753-758 ◽  
Author(s):  
A. Goldman ◽  
Y. C. Kao
Keyword(s):  
Temperature Distribution ◽  
Coordinate System ◽  
Numerical Solution ◽  
Rectangular Plate ◽  
Three Dimensional ◽  
Cylindrical Body ◽  
Two Dimensional ◽  
Coordinate Systems

The temperature distribution in a rectangular plate with a circular void at the center was calculated using a body-fitted coordinate system. Three different transformed geometries were considered: rectangular-rectangular, cut-line, and cylindrical. Problems involving insulated outer surfaces could not be solved using the rectangular-rectangular transformation but could be solved with both the cut-line and cylindrical transformations. The cylindrical transformation also appears to have the capability of being extended to three-dimensional problems.

scholarly journals Analytical study of the temperature distribution in solids subjected to nonuniform moving heat sources

2013 ◽  
Vol 17 (3) ◽  
pp. 687-694 ◽  
Author(s):  
Mohamed Hamraoui ◽  
Mounir Chbiki ◽  
Najib Laraqi ◽  
Luis Roseiro
Keyword(s):  
Steady State ◽  
Temperature Distribution ◽  
Power Dissipation ◽  
Relative Velocity ◽  
Analytical Study ◽  
Three Dimensional ◽  
Total Power ◽  
Heat Sources ◽  
Reference Case ◽  
Made In

We propose in this paper an analytical study of the temperature distribution in a solid subjected to moving heat sources. The power dissipated by the heat sources is considered nonuniform. The study was made in steady state. The model is three-dimensional. It is valid regardless of the relative velocity of the source. We have considered three cases of semi-elliptic distribution of the power with: (i) the maximum at the center of the source, (ii) the maximum at the inlet of the source, (iii) the maximum at the output of the source. These configurations simulate the conformity imperfection of contact due to wear and / or the non-uniformity of contact pressure in frictional devices. We compare the temperature change for these different scenarios and for different relative velocities, considering the same total power dissipation. The reference case is that of a uniform source dissipating the same power.

Measurement and Prediction of the Journal Circumferential Temperature Distribution for the Rotordynamic Morton Effect

2017 ◽  
Vol 140 (3) ◽  
Author(s):  
Xiaomeng Tong ◽  
Alan Palazzolo
Keyword(s):  
Steady State ◽  
Temperature Distribution ◽  
Hot Spot ◽  
Angular Position ◽  
Three Dimensional ◽  
3D Fem ◽  
Transient Model ◽  
Morton Effect ◽  
Tilting Pad Journal Bearing ◽  
Prediction Approach

The journal is the part of a shaft that is inside a fluid film bearing and is usually assumed to be circumferentially isothermal. Recent work has shown that under certain vibration conditions, a significant temperature difference (ΔT) can develop around the journal circumference. The ΔT may cause the shaft to bend leading to a synchronous vibration instability problem, termed the “Morton effect” (ME). A test rig was developed to verify the asymmetric journal temperature of the ME and its prediction using a five-pad tilting pad journal bearing (TPJB) operating with an eccentric shaft to replicate a circular vibration orbit. The bearing is tested at various conditions including: supply oil temperature at 28 °C and 41 °C, bearing operating eccentricities of zero and 32%Cb, and rotor speed up to 5500 rpm. The journal temperature distribution is recorded with 20 sensors located around the journal circumference, and the measurements provide a benchmark for predictions from a time transient model with the three-dimensional (3D) fluid and solid finite element method (FEM), and with a simplified ME prediction approach using only steady-state results. The test results follow the predictions exhibiting a sinusoidal-like temperature profile around the circumference with an angular lag of the hot spot location behind the high spot location (angular position on the rotor that arrives at the minimum film thickness condition each rotation) by a speed-dependent angle. Increasing the supply oil temperature reduced the journal ΔT, while increasing the bearing operating eccentricity increased the journal ΔT. The agreement between the test and predicted results is significantly better for the 3D FEM transient model than for the steady-state-based model in terms of journal ΔT and hot spot position. An improved version of the latter approach is proposed and yields significantly better correlation with the test measurements.

On the Field of Temperatures in Lubricating Films

1967 ◽  
Vol 89 (4) ◽  
pp. 483-491 ◽  
Author(s):  
N. Tipei ◽  
Al. Nica
Keyword(s):  
Temperature Distribution ◽  
Pressure Distribution ◽  
Energy Equation ◽  
Three Dimensional ◽  
Journal Bearings ◽  
Dimensional Case ◽  
Experimental Measurements ◽  
Lubricating Film ◽  
Good Agreement

The temperature distribution in the lubricating film of journal bearings for the three-dimensional case is obtained by using the results already known regarding the pressure distribution in the film and by integrating the energy equation. Relations for the divergent and convergent zones of the bearing are established by taking into account the viscosity and the side leakage; the distribution of the temperature along the bearing width is also considered. Comparisons between the theoretical values and experimental measurements are also performed, resulting in good agreement.

Analysis of the Effect of Heating Control Conditions on Temperature Distribution in a Wafer During Rapid Thermal Processing With Lamp Heaters

2001 ◽  
Author(s):  
Shigeki Hirasawa ◽  
Tadashi Suzuki ◽  
Shigenao Maruyama ◽  
Yuhei Takeuchi
Keyword(s):  
Steady State ◽  
Temperature Distribution ◽  
Thermal Processing ◽  
Radiative Heat ◽  
Rapid Thermal Processing ◽  
Three Dimensional ◽  
Heating Process ◽  
Computation Technique ◽  
Shielding Ring ◽  
Optimum Heating

Abstract To unify temperature distribution in a wafer during rapid thermal processing, we calculated the effect of the heating control conditions on temperature distributions in the wafer during heat-up and at steady state by using a program for analyzing three-dimensional radiative heat transfer. We calculated optimum monitoring positions on the wafer in order to minimize the temperature distribution in the wafer. The effects of rotating the wafer, the spacing between the wafer and the shielding ring, the number of monitoring positions, and the initial non-uniform temperature distribution were also calculated. The minimum steady temperature distribution in the wafer at the optimum condition was calculated as ±0.1 K during 100 K/s heat-up and ±0.02 K at 1273 K steady state. We also developed a rapid parallel-computation technique to find the optimum heating control conditions for the whole heating process.

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