Capillary and Viscoelastic Effects on Elastohydrodynamic Lubrication in Roller Nips

1996 ◽  
Vol 118 (4) ◽  
pp. 872-879 ◽  
Author(s):  
M. S. Carvalho ◽  
L. E. Scriven
Keyword(s):  
Reynolds Equation ◽  
Film Flow ◽  
Viscoelastic Behavior ◽  
Elastohydrodynamic Lubrication ◽  
Deborah Number ◽  
Capillary Effects ◽  
Simple Set ◽  
Viscoelastic Effects ◽  
Liquid Movement ◽  
Film Splitting

A viscocapillary model of liquid movement and film-splitting in deformable nips between an elatomer-covered roll and a hard roll is presented here. This “soft” elastohydrodynamic regime is described by Reynolds’ equation of lubrication flow and a simple set of spring-and-dashpot elements for the viscoelastic behavior of elastomeric roll covers. Capillary effects around the film-split are accounted for with an augmented Young-Laplace equation from film-flow theory. Effects of the liquid’s surface tension (via capillary number) and the elastomeric cover’s relaxation time (via Deborah number) are predicted and compared with available experiments. Application to the flows through the multiple roller nips of printing press systems is discussed.

Elastohydrodynamic lubrication of soft viscoelastic materials in line contact

1997 ◽  
Vol 211 (3) ◽  
pp. 185-194 ◽  
Author(s):  
C. J. Hooke ◽  
P Huang
Keyword(s):  
Film Thickness ◽  
Energy Loss ◽  
Elastohydrodynamic Lubrication ◽  
Soft Materials ◽  
Deborah Number ◽  
Line Contact ◽  
Hertz Contact ◽  
Contact Width ◽  
Minimum Film Thickness ◽  
Viscoelastic Effects

The paper discusses the influence of viscoelasticity in elastohydrodynamic lubrication (EHL). It is shown that viscoelastic effects, particularly in soft materials such as rubber and polymers, may significantly affect the lubrication process. The variations of the pressure and film thickness with viscoelasticity are discussed, as is the internal energy loss in the material. Two effects are present. The first, controlled by the Deborah number based on the Hertz contact width, determines the width of the contact, the overall pressure distribution and the energy loss. The second, controlled by the Deborah number based on the entrainment length, largely determines the thickness of the entrained film and the minimum film thickness.

On the Measurement of Dynamic Properties of Lubricants under E. H. L. Conditions Using a Disc Machine

1974 ◽  
Vol 16 (5) ◽  
pp. 331-338 ◽  
Author(s):  
J. M. Davies ◽  
K. Walters
Keyword(s):  
Viscoelastic Properties ◽  
Dynamic Properties ◽  
Elastohydrodynamic Lubrication ◽  
Deborah Number ◽  
Theoretical Treatment

Johnson and Roberts (1)‡ have recently shown how a simple adaptation of the conventional disc machine can be used to measure the viscoelastic properties of lubricants under conditions of elastohydrodynamic lubrication. The present paper contains a theoretical treatment of the problem and derives operating formulae pertinent to conditions of low, finite and high Deborah number.

Two Dimensional Modified Reynolds Equation Including Pressure Dependent Viscosity Effect

2012 ◽  
Author(s):  
Jung Gu Lee ◽  
Alan Palazzolo
Keyword(s):  
Reynolds Equation ◽  
Elastohydrodynamic Lubrication ◽  
Fluid Film ◽  
Maximum Pressure ◽  
Elastic Solids ◽  
Pressure Distributions ◽  
Pressure Dependent Viscosity ◽  
Modified Reynolds Equation ◽  
Dependent Viscosity ◽  
Modified Equation

The Reynolds equation plays an important role for predicting pressure distributions for fluid film bearing analysis, One of the assumptions on the Reynolds equation is that the viscosity is independent of pressure. This assumption is still valid for most fluid film bearing applications, in which the maximum pressure is less than 1 GPa. However, in elastohydrodynamic lubrication (EHL) where the lubricant is subjected to extremely high pressure, this assumption should be reconsidered. The 2D modified Reynolds equation is derived in this study including pressure-dependent viscosity, The solutions of 2D modified Reynolds equation is compared with that of the classical Reynolds equation for the ball bearing case (elastic solids). The pressure distribution obtained from modified equation is slightly higher pressures than the classical Reynolds equations.

Characteristics evaluation of gas film in the aerostatic thrust bearing within rarefied effect

2016 ◽  
Vol 231 (2) ◽  
pp. 149-157 ◽  
Author(s):  
Dongju Chen ◽  
Shuai Zhou ◽  
Jihong Han ◽  
Jinwei Fan ◽  
Qiang Cheng
Keyword(s):  
Machine Tool ◽  
Reynolds Equation ◽  
Thrust Bearing ◽  
Film Flow ◽  
Machining Accuracy ◽  
Aerostatic Bearing ◽  
Supply Pressure ◽  
Slip Regime ◽  
Key Factor ◽  
Gas Supply

The characteristic of gas film is a key factor in the performance of the aerostatic bearing. Because the gas film flow is in the slip regime, influence of the rarefied effect is significant. The modified Reynolds equation suitable for compressible gas in the rarefied effect is deduced through introducing the flow factor in the rarefied effect to the Reynolds equation. Pressure distribution, capacity, and stiffness of the gas film under the rarefied effect are analyzed. With the increase of gas pressure, the gas film capacity and stiffness of bearing would also increase. However, the greater the gas supply pressure, the more intense the gas film vibration, so it was important to select a reasonable gas supply pressure for achieving the optimal gas film characteristic. Finally, the gas rarefied effect is verified by the experiment indirectly, which agreed well with the analytical results and provided a theoretical guidance for the machining accuracy of the machine tool.

Study on the Influence of Non-Newtonian Characteristics on Robots for Medical Application

2010 ◽  
Vol 29-32 ◽  
pp. 857-861
Author(s):  
Jian Ping Liu ◽  
Xin Yi Zhang ◽  
Qing Xuan Jia
Keyword(s):  
Film Thickness ◽  
Elastic Deformation ◽  
Reynolds Equation ◽  
Traction Force ◽  
Elastohydrodynamic Lubrication ◽  
Medical Application ◽  
Lubrication Theory ◽  
Newtonian Model

Considering lumen elastic deformation, Reynolds equation is deduced based on non-Newtonian model in this paper. Traction force and hydrodynamic mucus film thickness are calculated according to elastohydrodynamic lubrication theory. Compared with results based on Newtonian model and experiments, analysis based on non-Newtonian model reflects practical condition well. Lumen elastic deformation has some influence on traction force and mucus film thickness.

scholarly journals From the Phan–Thien–Tanner/Oldroyd-B Non-Newtonian Model to the Double Shear Thining Rabinowisch Thin Film Model

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
Guy Bayada ◽  
Laurent Chupin ◽  
Sébastien Martin
Keyword(s):  
Thin Film ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Solvent Mixture ◽  
Deborah Number ◽  
Fluid Viscosity ◽  
Three Dimensional Model ◽  
Bulk Fluid ◽  
Double Shear ◽  
Viscoelastic Effects

In this paper, an asymptotic expansion is used to derive a description of Phan–Tien– Tanner (PTT)/Oldroyd-B flows in the thin film situation without the classical “upper convective maxwell”(UCM) assumption. We begin with a short presentation of the Phan–Thien–Tanner/Oldroyd-B models, which introduce viscoelastic effects in a solute–solvent mixture. The three-dimensional flow is described using five parameters, namely the Deborah number (De) (or the relaxation parameter λ), the viscosity ratio r, the bulk fluid viscosity η, the material slip parameter a related to the “convected derivative” and an elongation number κ. Then we focus on the thin film assumption and the related asymptotic analysis that allows us to derive a reduced model. A perturbation procedure for “not too small” values of κ allows us to obtain further results such as an asymptotic “effective viscosity/ shear rate” law, which appears to be a perturbation of the double Rabinowisch model, whose parameters are completely defined by those of the original three-dimensional model. And last a numerical procedure is proposed based on a penalized Uzawa method, to compute the corresponding solution. This algorithm can also be used for any generalized double Newtonian shear thinning Carreau law.

Theoretical Investigation in Transient Elastohydrodynamic Lubrication of Reciprocating Motion in Air Compressor Piston Pin

2012 ◽  
Vol 622-623 ◽  
pp. 1821-1825
Author(s):  
Khanittha Wongseedakaew
Keyword(s):  
Friction Coefficient ◽  
Reynolds Equation ◽  
Initial Conditions ◽  
Elastohydrodynamic Lubrication ◽  
Approximation Technique ◽  
Air Compressor ◽  
Compressor Piston ◽  
Minimum Film Thickness ◽  
Bearing Materials ◽  
Lubricant Viscosity

This paper presents the effect of squeeze motion to elastohydrodynamic lubrication (EHL) in piston pin of air compressor with non-Newtonian lubricants based on a Carreau viscosity model. The time dependent modified Reynolds equation and elasticity with initial conditions were formulated and solved numerically using a multigrid multilevel with full approximation technique for a piston pin. Effects of bearing materials and liquid properties were examined. The results show that minimum film thickness and friction coefficient increases when lubricant viscosity increases. At the same time, for increasing of elastic modulus of bearing bushing the friction coefficient decreases.

Multigrid method for the solution of EHL point contact with bio-based oil as lubricants for smooth and rough asperity

2018 ◽  
Vol 70 (4) ◽  
pp. 599-611 ◽  
Author(s):  
Vishwanath B. Awati ◽  
Shankar Naik ◽  
Mahesh Kumar N.
Keyword(s):  
Design Methodology ◽  
Reynolds Equation ◽  
Multigrid Method ◽  
Approximation Scheme ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Alternative Source ◽  
Content Type ◽  
Longitudinal Roughness ◽  
Isothermal Case

Purpose The purpose of this paper is to study the elastohydrodynamic lubrication point contact problem with bio-based oil as lubricants for an isothermal case. The simulation of the problem is analyzed on smooth and rough asperity. Design/methodology/approach The modified Reynolds equation is discretized using finite difference and multigrid method with full approximation scheme (FAS), applied for its solution with varying load and speed. Findings This paper traces out the comparison of minimum and central film thickness with the standard formulation of Hamrock and Dowson. The effect of longitudinal roughness on surfaces is investigated by means of numerical simulations. Originality/value The results obtained are comparable with the standard results, and are shown by graphs and tables. Bio-based products bring out an alternative source of lubricant to reduce energy crises.

Effect of changing geometrical characteristics for different shapes of a single ridge passing through elastohydrodynamic of point contacts

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mohamed Abd Alsamieh
Keyword(s):  
Film Thickness ◽  
Pressure Distribution ◽  
Reynolds Equation ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Point Contacts ◽  
Time Step ◽  
Content Type ◽  
Geometrical Characteristics ◽  
Different Shapes

Purpose The purpose of this paper is to study the behavior of a single ridge passing through elastohydrodynamic lubrication of point contacts problem for different ridge shapes and sizes, including flat-top, triangular and cosine wave pattern to get an optimal ridge profile. Design/methodology/approach The time-dependent Reynolds’ equation is solved using Newton–Raphson technique. Several shapes of surface feature are simulated and the film thickness and pressure distribution are obtained at every time step by simultaneous solution of the Reynolds’ equation and film thickness equation, including elastic deformation. Film thickness and pressure distribution are chosen to be the criteria in the comparisons. Findings The geometrical characteristics of the ridge play an important role in the formation of lubricant film thickness profile and the pressure distribution through the contact zone. To minimize wear, friction and fatigue life, an optimal ridge profile should have smooth shape with small ridge size. Obtained results are compared with other published numerical results and show a good agreement. Originality/value The study evaluates the performance of different surface features of a single ridge with different shapes and sizes passing through elastohydrodynamic of point contact problem in relation to film thickness and pressure profile.

Analysis of Non-Newtonian Effects in Dynamically Loaded Finite Journal Bearings Including Mass Conserving Cavitation

1992 ◽  
Vol 114 (4) ◽  
pp. 736-744 ◽  
Author(s):  
R. S. Paranjpe
Keyword(s):  
Reynolds Equation ◽  
Relaxation Times ◽  
Shear Thinning ◽  
Limited Range ◽  
Engine Oils ◽  
Dynamically Loaded ◽  
Viscoelastic Effects ◽  
Oil Flow ◽  
Thinning Effect ◽  
Generalized Reynolds Equation

Non-Newtonian effects of multigrade engine oils in dynamically loaded crankshaft bearings are analyzed. The main focus of this work is on the shear-thinning effect. Viscoelastic effects are also considered over a limited range of the relaxation time. It has been shown that the same generalized Reynolds equation used in the Thermohydrodynamic (THD) analysis can be used for analyzing the shear-thinning effects as well. Consequently the shear thinning effect and the THD effect can be treated together. A mass conserving cavitation algorithm developed earlier for doing the THD analysis is used to solve the generalized Reynolds equation. Non-Newtonian shear-thinning significantly affects the power loss, film thickness, and oil flow of a multigrade oil as compared with a Newtonian oil. Over the range of relaxation times considered, no viscoelastic effects were discernible for crankshaft bearings lubricated with multigrade oils.

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