The Application of Newton-Raphson Method to Thermal Elastohydrodynamic Lubrication of Line Contacts

1994 ◽  
Vol 116 (4) ◽  
pp. 733-740 ◽  
Author(s):  
R. Wolff ◽  
A. Kubo
Keyword(s):  
Film Thickness ◽  
Thermal Effects ◽  
Elastohydrodynamic Lubrication ◽  
Numerical Approach ◽  
Heavy Load ◽  
Rolling Velocity ◽  
Line Contacts ◽  
Pressure Spike ◽  
Newton Raphson ◽  
Raphson Method

The Newton-Raphson method was applied to solve the thermal EHD lubrication model of line contacts. By accounting for thermal effects in the Newton-Raphson scheme, a very stable numerical approach was obtained. Two models with viscosity constant and variable across the oil film were developed. The results under extremely heavy conditions of dimensionless load W = 52 * 10−5 (pH = 2 GPa) and dimensionless rolling velocity U = 20 * 10−11 are presented. They show that even for pure rolling, but under heavy load and high rolling velocity conditions, the thermal effects significantly reduce the minimum film thickness. The distributions of pressure, film thickness, and temperature for two rolling velocities and various loads are presented. They indicate that under high rolling velocity conditions the thermal effects have a strong influence on a pressure spike.

Thermal Non-Newtonian Elastohydrodynamic Lubrication of Line Contacts Under Simple Sliding Conditions

1992 ◽  
Vol 114 (2) ◽  
pp. 317-327 ◽  
Author(s):  
Shao Wang ◽  
T. F. Conry ◽  
C. Cusano
Keyword(s):  
Film Thickness ◽  
Surface Temperature ◽  
Thermal Effects ◽  
Elastohydrodynamic Lubrication ◽  
Reduction Factor ◽  
Simple Formulation ◽  
Maximum Surface ◽  
Line Contacts ◽  
Traction Coefficient ◽  
Maximum Surface Temperature

A computationally simple formulation for the stationary surface temperature is developed to examine the thermal non-Newtonian EHD problem for line contacts under simple sliding conditions. Numerical results obtained are used to develop a formula for a thermal and non-Newtonian (Ree-Eyring) film thickness reduction factor. Results for the maximum surface temperature and traction coefficient are also presented. The thermal effects on film thickness and traction are found to be more pronounced for simple sliding than for combined sliding and rolling conditions.

Thermal Non-Newtonian Elastohydrodynamic Lubrication of Rolling Line Contacts

1991 ◽  
Vol 113 (3) ◽  
pp. 481-491 ◽  
Author(s):  
H. Salehizadeh ◽  
N. Saka
Keyword(s):  
Film Thickness ◽  
Contact Region ◽  
Elastohydrodynamic Lubrication ◽  
Pressure Profile ◽  
Shear Stresses ◽  
Hertz Contact ◽  
Minimum Film Thickness ◽  
Line Contacts ◽  
Pressure Spike ◽  
Heavy Loads

The two-dimensional thermal elastohydrodynamic equations were numerically solved for a Ree-Eyring type lubricant under pure rolling conditions. Profiles of lubricant pressure, film thickness, and temperature were obtained for medium to heavy loads and moderate to high rolling speeds. The pressure results generally show a small secondary peak near the outlet, but at the highest load considered no pressure spike is obtained and the pressure profile is almost Hertzian. The film thickness results show an increase in minimum film thickness with increasing rolling speeds, but at a lesser rate than those predicted for a Newtonian fluid under isothermal conditions. It is found that unless the lubricant becomes non-Newtonian in the inlet region, the reduction in minimum film thickness at high rolling speeds is completely due to thermal effect. The lubricant temperature profile and the amount of heat generated and dissipated in the contact region were also calculated. The lubricant temperature reaches a maximum just before the entrance to the Hertz contact region. Both shear and compression heating are found to be important in raising the lubricant temperature in the inlet. As the lubricant enters the Hertz contact zone, the temperature first drops rapidly, because of the rapid heat conduction to the rollers, and then remains almost constant for most of the Hertz contact. Near the exit where the pressure gradients are large, the lubricant temperature drops rapidly below the ambient because of lubricant expansion. The lubricant then heats up rapidly before leaving the contact area as a result of heat generated by shear stresses.

Thermal Elastohydrodynamic Lubrication of Heavily Loaded Line Contacts—An Efficient Inlet Zone Analysis

1998 ◽  
Vol 120 (1) ◽  
pp. 119-125 ◽  
Author(s):  
Mihir K. Ghosh ◽  
Raj K. Pandey
Keyword(s):  
Film Thickness ◽  
Thermal Loading ◽  
Elastohydrodynamic Lubrication ◽  
Thermal Reduction ◽  
Reduction Factor ◽  
Computationally Efficient ◽  
Rolling Velocity ◽  
Minimum Film Thickness ◽  
Line Contacts ◽  
Inlet Zone

An inlet zone analysis of TEHD lubrication of heavily loaded line contacts has been done using a computationally efficient and accurate numerical method based on Lobatto quadrature developed by Elrod and Brewe (1986). The results under extremely heavy conditions of dimensionless load W = 5.2*10−4 (pH = 2.0 GPa) and dimensionless rolling velocity U = 2.0*10−10(50 m/s) are presented. Significant reduction in thermal reduction factor (film thickness) at high rolling speeds relative to isothermal conditions have been observed. The results of the present work have been compared with the results of Wilson and Sheu (1983) and Hsu and Lee (1994). A correction formula of the thermal reduction factor for the minimum film thickness has been derived for a range of thermal loading parameters, loads, and slip ratios.

Simple Formulas for Performance Parameters Used in Elastohydrodynamically Lubricated Line Contacts

1989 ◽  
Vol 111 (2) ◽  
pp. 246-251 ◽  
Author(s):  
Ping Pan ◽  
B. J. Hamrock
Keyword(s):  
Film Thickness ◽  
Curve Fitting ◽  
Center Of Pressure ◽  
Operating Parameters ◽  
Performance Parameters ◽  
Practical Applications ◽  
Line Contacts ◽  
Pressure Spike

The film thickness and pressure in elastohydrodynamically lubricated conjunctions have been evaluated numerically for a rather complete range of operating parameters (dimensionless load, speed, and materials parameters) normally experienced in practical applications. From the film thickness and pressure throughout the conjunction a number of performance parameters were evaluated. By curve fitting the data, formulas were obtained that allow easy evaluation of the amplitude and location of the pressure spike, the minimum and central film thicknesses, the value of ρeHe, and the center of pressure.

scholarly journals A thermal resistances-based approach for thermal-elastohydrodynamic calculations in point contacts

2017 ◽  
Vol 232 (11) ◽  
pp. 2088-2102 ◽  
Author(s):  
Eduardo de la Guerra Ochoa ◽  
Javier Echávarri Otero ◽  
Enrique Chacón Tanarro ◽  
Benito del Río López
Keyword(s):  
Friction Coefficient ◽  
Film Thickness ◽  
Thermal Effects ◽  
Good Accuracy ◽  
Computational Cost ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Point Contacts ◽  
New Approach ◽  
Ball On Disc

This article presents a thermal resistances-based approach for solving the thermal-elastohydrodynamic lubrication problem in point contact, taking the lubricant rheology into account. The friction coefficient in the contact is estimated, along with the distribution of both film thickness and temperature. A commercial tribometer is used in order to measure the friction coefficient at a ball-on-disc point contact lubricated with a polyalphaolefin base. These data and other experimental results available in the bibliography are compared to those obtained by using the proposed methodology, and thermal effects are analysed. The new approach shows good accuracy for predicting the friction coefficient and requires less computational cost than full thermal-elastohydrodynamic simulations.

The Effects of Surface Irregularities on the Elastohydrodynamic Lubrication of Sliding Line Contacts. Part II—Wavy Surfaces

1984 ◽  
Vol 106 (1) ◽  
pp. 113-119 ◽  
Author(s):  
P. R. Goglia ◽  
C. Cusano ◽  
T. F. Conry
Keyword(s):  
Shear Stress ◽  
Film Thickness ◽  
Smooth Surface ◽  
Wave Amplitude ◽  
Elastohydrodynamic Lubrication ◽  
Wavy Surface ◽  
Line Contacts ◽  
Surface Irregularities ◽  
Wavy Surfaces ◽  
Octahedral Shear Stress

The micro-EHD effects caused by wavy surfaces have been analytically investigated. The investigation includes the effects of phase, wavelength, and wave amplitude on film thickness, pressure distribution and subsurface octahedral shear stress field. The presence of a wavy surface with a given wavelength produces pressure oscillations of the same wavelength. With increasing wave amplitude and decreasing wavelength, the micro-EHD action increases. This results in a maximum value of the octahedral shear stress which is greater in magnitude and closer to the surface than the corresponding smooth surface case. The slope of the wavy surface in the inlet region determines whether the average film thickness is smaller or larger than the smooth surface value.

Occurrence of High Pressure Spike in Unidirectional Start–Stop–Start Point Contacts

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
P. Sperka ◽  
J. Wang ◽  
I. Krupka ◽  
M. Hartl ◽  
M. Kaneta
Keyword(s):  
High Pressure ◽  
Film Thickness ◽  
Rolling Contact Fatigue ◽  
Contact Fatigue ◽  
Elastohydrodynamic Lubrication ◽  
Rolling Contact ◽  
Point Contacts ◽  
Pressure Distributions ◽  
Machine Element ◽  
Pressure Spike

The transient film thickness and pressure distributions in point elastohydrodynamic lubrication (EHL) contacts during start–stop–start motion are discussed based on experimental and numerical analyses. When the machine element starts to move after the stopping, where the oil is entrapped between two surfaces, the pressure at the exit area increases very much. The pressure increase depends markedly on the overall film thickness before the stopping of the motion, but is hardly controlled by the acceleration after the stopping. It can be considered that this phenomenon affects the rolling contact fatigue damage.

Uniform Equations in the Inlet and Exit Zones of Heavily Loaded Point and Line Elastohydrodynamically Lubricated Contacts Involved in Various Steady Motions

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
Ilya I. Kudish
Keyword(s):  
Film Thickness ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Point Contacts ◽  
Lubrication Film ◽  
Lubricated Contacts ◽  
Asymptotic Equations ◽  
Line Contacts ◽  
Steady Motions ◽  
Numerical Approaches

Heavily loaded point elastohydrodynamically lubricated (EHL) contacts involved in steady purely transitional, skewed transitional, and transitional with spinning motions are considered. It is shown that in the central parts of the inlet and exit zones of such heavily loaded point EHL contacts the asymptotic equations governing the EHL problem along the lubricant flow streamlines for the above types of contact motions can be reduced to two sets of asymptotic equations: one in the inlet and one in the exit zones. The latter sets of equations are identical to the asymptotic equations describing lubrication process in the inlet and exit zones of the corresponding heavily loaded line EHL contact (Kudish, I. I., 2013, Elastohydrodynamic Lubrication for Line and Point Contacts: Asymptotic and Numerical Approaches, Chapman and Hall/CRC). For each specific motion of a point contact, a separate set of formulas for the lubrication film thickness is obtained. For different types of contact motions, these film thickness formulas differ significantly (Kudish, I. I., 2013, Elastohydrodynamic Lubrication for Line and Point Contacts: Asymptotic and Numerical Approaches, Chapman and Hall/CRC). For heavily loaded contacts, the discovered relationship between point and line EHL problems allows to apply to point contacts most of the results obtained for line contacts (Kudish, I. I., 2013, Elastohydrodynamic Lubrication for Line and Point Contacts: Asymptotic and Numerical Approaches, Chapman and Hall/CRC; Kudish, I. I., and Covitch, M. J., 2010, Modeling and Analytical Methods in Tribology, Chapman and Hall/CRC).

Effect of Load Variation on Elastohydrodynamic Lubrication Film Collapse

2014 ◽  
Vol 592-594 ◽  
pp. 1366-1370
Author(s):  
Tapash Jyoti Kalita ◽  
Punit Kumar
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Elastohydrodynamic Lubrication ◽  
Transient Behavior ◽  
Computer Code ◽  
Practical Situation ◽  
Lubrication Film ◽  
Newton Raphson ◽  
Simulation Results ◽  
Film Collapse

Elastohydrodynamic line contact simulations have been carried out in the present study. A practical situation of transient EHL film collapse has been analyzed. The aim is to observe the effect of variation of maximum Hertzian pressure (PH) on transient behavior of EHL film thickness (H).The analysis is based upon classical Reynolds equation considering time variation. The simulation results pertaining to EHL film thickness calculated using linear pressure-viscosity relationship have been compared for different values of load. It has been observed that film thickness reduces with increase in load. Similar results are obtained using exponential pressure-viscosity relationship and compared with those for linear pressure-viscosity. The EHL equations are solved by discretizing Reynolds equation and load equilibrium equation along with other equations using Newton-Raphson technique with the help of a computer code.

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