The transition region of elastohydrodynamic lubrication

1991 ◽  
Vol 432 (1886) ◽  
pp. 467-479 ◽  
Keyword(s):  
Film Thickness ◽  
Transition Region ◽  
Parameter Space ◽  
Elastohydrodynamic Lubrication ◽  
Line Contact ◽  
Series Method ◽  
Chebyshev Series ◽  
Pressure Spike ◽  
Constant Coefficients ◽  
Dimensional Parameters

A semi-analytic approach is presented for the elastohydrodynamic lubrication problem of two cylinders in line contact. The model takes account of the effects of elastic deformation and piezo-viscosity in the transition region (the area of parameter space where the pressure spike emerges and develops). Following Poritsky, pressure and displacement are expressed as Chebyshev series and Fejér’s method is used to deal with the sharp crease in the film shape that is a feature of piezoviscous contacts. It is shown that the film thickness depends solely upon two non-dimensional parameters and can be accurately represented by an equation of the form: H = a 0 g 3 a 1 g 1 + a 2 g 3 a 3 , where the a i = 0, 1, 2, 3) are constant coefficients. Important features of this Chebyshev series method include accurate representations for the emerging pressure spike and the associated sharp crease in the film shape together with film thickness predictions which smoothly link those areas of parameter space on either side of the transition region.

The line contact problem of elastohydrodynamic lubrication - I. Asymptotic structure for low speeds

1989 ◽  
Vol 424 (1867) ◽  
pp. 393-407 ◽  
Keyword(s):  
Asymptotic Solution ◽  
Contact Problem ◽  
Film Thickness ◽  
Numerical Solutions ◽  
Elastohydrodynamic Lubrication ◽  
Thin Layers ◽  
Line Contact ◽  
Asymptotic Regime ◽  
Lubricating Film ◽  
Pressure Spike

This paper reports the first formal asymptotic solution to the line contact problem of elastohydrodynamic lubrication (EHL), a fundamental problem describing the elastic deformation of lubricated rolling elements such as roller bearings, gear teeth and other contacts of similar geometry. The asymptotic régime considered is that of small λ , a dimensionless parameter proportional to rolling speed, viscosity and the elastic modulus. The solution is shown to possess four regions: a zone where the lubricating film is both thin and slowly narrowing and which is closely related to the contact area that occurs in the absence of lubricant, an upstream inlet zone of low pressure, and two thin layers on either side of the contact zone. The solutions in the first two just-mentioned zones are given by simple analytical expressions. The solutions in the two thin layers are obtained from two universal functions obtained by Bissett & Spence ( Proc. R. Soc. Lond . A 424, 409 (1989)). Although these two functions, related to the local film thickness, are obtained by numerical techniques by Bissett & Spence, it should be emphasized that all cases in the asymptotic régime considered are hereby solved definitively without recourse to further computation. Although some features of this structure have been suggested by other solution approaches, generally, these are numerical or ad hoc approximations. See the texts by Johnson ( Contact Mechanics , pp. 328 (1985)) and Dowson & Higginson ( Elasto-hydrodynamic lubrication (1977)), this work provides a formal mathematical basis for understanding most of the principal features of EHL. The solution provides a simple formula for minimum film thickness and displays the sharp narrowing of the lubricating film in the thin layer near the exit. In the basic asymptotic solution provided here, the dimensionless pressure-viscosity coefficient, α , is assumed to be O (1), and in this parameter régime, no pressure spike will occur. By comparing with the work of Hooke ( J. mech. Engng Sci . 19(4), 149 (1977)), we can show that an incipient pressure spike occurs when α becomes as large as O ( λ -1/5 ). However, asymptotic solutions in this latter parameter régime require new numerical solutions for each case of interest and are not pursued here.

scholarly journals Fast Approach for Calculating Film Thicknesses and Pressures in Elastohydrodynamically Lubricated Contacts at High Loads

1986 ◽  
Vol 108 (3) ◽  
pp. 411-419 ◽  
Author(s):  
L. G. Houpert ◽  
B. J. Hamrock
Keyword(s):  
High Pressure ◽  
Film Thickness ◽  
Line Contact ◽  
Elastic Deformations ◽  
New Approach ◽  
Lubricated Contacts ◽  
Fast Approach ◽  
Pressure Spike

The film thicknesses and pressures in elastohydrodynamically lubricated contacts have been calculated for a line contact by using an improved version of Okamura’s approach. The new approach allows for lubricant compressibility, the use of Roelands viscosity, a general mesh (nonconstant step), and accurate calculations of the elastic deformations. The new approach is described, and the effects on film thickness, pressure, and pressure spike of each of the improvements are discussed. Successful runs have been obtained at high pressure (to 4.8 GPa) with low CPU times.

Size effect on thermal elastohydrodynamic lubrication of industrial chain bush-pin hinge pair

2019 ◽  
Vol 71 (9) ◽  
pp. 1080-1085 ◽  
Author(s):  
Mingyu Zhang ◽  
Jing Wang ◽  
Yi Liu ◽  
Longjie Dai ◽  
Zhaohua Shang
Keyword(s):  
Friction Coefficient ◽  
Film Thickness ◽  
Temperature Rise ◽  
Elastohydrodynamic Lubrication ◽  
Curvature Radius ◽  
Line Contact ◽  
Content Type ◽  
Oil Film ◽  
Industrial Chain ◽  
Infinite Line

Purpose The purpose of this paper is to use elastohydrodynamic lubrication (EHL) theory to study the variation of the equivalent curvature radius “R” on the change of oil film thickness, pressure, temperature rise and friction coefficient in the contact zone between bush-pin in industrial chain drive. Design/methodology/approach In this paper, the contact between bush and pin is simplified as infinitely long line contact. The lubrication state is studied by numerical simulation using steady-state line contact thermal EHL. The two constitutive equations, namely, Newton fluid and Ree–Eyring fluid are used in the calculations. Findings It is found that with the increase of equivalent curvature radius, the thickness of oil film decreases and the temperature rise increases. Under the same condition, the friction coefficient of Newton fluid is higher than that of Ree–Eyring fluid. When the load increases, the oil film thickness decreases, the temperature rise increases and the friction coefficient decreases; and the film thickness increases with the increase of the entraining speed under the condition “R < 1,000 mm”. Research limitations/implications The infinite line contact assumption is only an approximation. For example, the distances between the two inner plates are 5.72 mm, by considering the two parts assembled into the inner plates, the total length of the bush is less than 6 mm. The diameter of the pin and the bore diameter of the bush are 3.28 and 3.33 mm. However, the infinite line contact is also helpful in understanding the general variation of oil film characteristics and provides a reference for the future study of finite line contact of chain problems. Originality/value The change of the equivalent radius R on the variation of the oil film in the contact of the bush and the pin in industrial chain drive was investigated. The size effect influences the lubrication characteristic greatly in the bush-pin pair.

A thermal EHL investigation on plate-pin hinge pairs in silent chains using a narrow finite line contact

2020 ◽  
Vol 72 (10) ◽  
pp. 1139-1145
Author(s):  
Mingyu Zhang ◽  
Jing Wang ◽  
Jinlei Cui ◽  
Peiran Yang
Keyword(s):  
Film Thickness ◽  
Temperature Rise ◽  
Elastohydrodynamic Lubrication ◽  
Radius Of Curvature ◽  
Line Contact ◽  
Equivalent Radius ◽  
Content Type ◽  
Finite Line Contact ◽  
Pressure Peak ◽  
Finite Line

Purpose The purpose of this paper is to numerically study the variations of oil film pressure, thickness and temperature rise in the contact zone of plate-pin pair in silent chains. Design/methodology/approach A steady-state thermal elastohydrodynamic lubrication (EHL) model is built using a Ree–Eyring fluid. The contact between the plate and the pin is simplified as a narrow finite line contact, and the lubrication state is examined by varying the geometry and the plate speed. Findings With increase in the equivalent radius of curvature, the pressure peak and the central film thickness increase. Because the plate is very thin, the temperature rise can be neglected. Even when the influence of the rounded corner region is less, a proper design can beneficially increase the minimum film thickness at both edges of the plate. Under a low entraining speed, strong stress concentration results in close-zero film thickness at both edges of the plate. Originality/value This study reveals the EHL feature of the narrow finite line contact in plate-pin pairs for silent chains and will support the future works considering transient effect, surface features and wear.

scholarly journals Analysis of Line Contact Elastohydrodynamic Lubrication with the Particles under Rough Contact Surface

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Keying Chen ◽  
Liangcai Zeng ◽  
Juan Chen ◽  
Xianzhong Ding
Keyword(s):  
Film Thickness ◽  
Rough Surface ◽  
Thickness Distribution ◽  
Traction Force ◽  
Elastohydrodynamic Lubrication ◽  
Equation System ◽  
Line Contact ◽  
Equivalent Inclusion Method ◽  
Equivalent Inclusion ◽  
The Matrix

A numerical solution for line contact elastohydrodynamic lubrication (EHL) occurring on the rough surface of heterogeneous materials with a group of particles is presented in this study. The film thickness disturbance caused by particles and roughness is considered into the solution system, and the film pressure between the contact gap generated by the particles and the surface roughness is obtained through a unified Reynold equation system. The inclusions buried in the matrix are made equivalent to areas with the same material as that of the matrix through Eshelby’s equivalent inclusion method and the roughness is characterized by related functions. The results present the effects of different rough topographies combined with the related parameters of the particles on the EHL performance, and the minimum film thickness distribution under different loads, running speeds, and initial viscosities are also investigated. The results show that the roughness morphology and the particles can affect the behavior of the EHL, the traction force on a square rough surface is smaller, and the soft particles have more advantages for improving the EHL performance.

Effect of Roughness Orientation on the Elastohydrodynamic Lubrication Film Thickness

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Dong Zhu ◽  
Q. Jane Wang
Keyword(s):  
Film Thickness ◽  
Stochastic Models ◽  
Deterministic Model ◽  
Elastohydrodynamic Lubrication ◽  
Contact Problems ◽  
Operating Conditions ◽  
Orientation Effect ◽  
Line Contact ◽  
Lubrication Film ◽  
Dry Contact

Effect of roughness orientation on lubricant film thickness has been an important issue of surface design, attracting much attention since the 1970 s. A systematical study, however, is still needed for various contact types in an extended range of operating conditions, especially in mixed lubrication cases with film thickness to roughness ratio (λ ratio) smaller than 0.5. The present study employs a deterministic mixed elastohydrodynamic lubrication (EHL) model to investigate the performance of lubricating films in different types of contact geometry, including the line contact, circular contact, and elliptical contacts of various ellipticity ratios. The speed range for analyzed cases covers 11 orders of magnitude so that the entire transition from full-film and mixed EHL down to dry contact (corresponding λ ratio from about 3.5 down to 0.001 or so) is simulated. Three types of machined surfaces are used, representing transverse, longitudinal, and isotropic roughness, respectively. The line contact results are compared with those from the stochastic models by Patir and Cheng (“Effect of Surface Roughness Orientation on the Central Film Thickness in EHD Contacts,” Proc. 5th Leeds-Lyon Symp. on Tribol., 1978, pp. 15–21) and the influence of roughness orientation predicted by the deterministic model is found to be less significant than that by the stochastic models, although the basic trends are about the same when λ > 0.5. The orientation effect for circular or elliptical contact problems appears to be more complicated than that for line contacts due to the existence of significant lateral flows. In circular contacts, or elliptical contacts with the ellipticity ratio smaller than one, the longitudinal roughness may become more favorable than the isotropic and transverse. Overall, the orientation effect is significant in the mixed EHL regime where theλratio is roughly in the range from 0.05 to 1.0. It is relatively insignificant for both the full-film EHL (λ > 1.2 or so) and the boundary lubrication/dry contact (λ < 0.025 ∼ 0.05).

Influence of lubrication starvation and surface waviness on the oil film stiffness of elastohydrodynamic lubrication line contact

2016 ◽  
Vol 24 (5) ◽  
pp. 924-936 ◽  
Author(s):  
Yuanyuan Zhang ◽  
Huaiju Liu ◽  
Caichao Zhu ◽  
Chaosheng Song ◽  
Zufeng Li
Keyword(s):  
Film Thickness ◽  
Contact Stiffness ◽  
Elastohydrodynamic Lubrication ◽  
Force Balance ◽  
Line Contact ◽  
Surface Waviness ◽  
Regular Surface ◽  
Normal Contact ◽  
Oil Film ◽  
Film Stiffness

Stiffness properties of interfacial engineering surfaces are of great importance to the dynamic performance of relevant mechanical systems. Normal contact stiffness and oil film stiffness of line contact problems are studied in this work analytically and numerically. The Hertzian contact theory and the Yang–Sun method are applied to predict the contact stiffness, while the empirical elastohydrodynamic lubrication (EHL) film thickness method and the complete numerical EHL model are used to predict the oil film stiffness. The numerical model mainly consists of the Reynolds equation; the film thickness equation, in which the regular surface roughness is taken into consideration; the force balance equation; and the viscosity-pressure equation. The effects of the normal load, rolling speed, regular surface waviness, and starved lubrication level on the oil film stiffness are investigated.

Effects of a Single Bump or Dent in Time Dependent Thermal Line EHD Lubrication

1994 ◽  
Vol 116 (1) ◽  
pp. 9-20 ◽  
Author(s):  
Farshid Sadeghi ◽  
Kyung-Hoon Kim
Keyword(s):  
Film Thickness ◽  
Elastohydrodynamic Lubrication ◽  
Transient Behavior ◽  
Time Dependent ◽  
Line Contact ◽  
Temperature Distributions ◽  
Ehd Lubrication ◽  
Pure Rolling ◽  
Energy Equations ◽  
Thermal Line

A time-dependent thermal compressible elastohydrodynamic lubrication of line contact model has been developed to investigate the effects of a single bump or dent in heavily loaded rolling/sliding contacts. The results illustrate the transient behavior of the film thickness, pressure and temperature distributions as a bump or a dent travels through the contact. The multigrid multilevel technique was used to simultaneously solve the discretized time dependent Reynolds, elasticity and energy equations. The effects of various loads and speeds have been investigated. Results are presented for the nondimensional loads of W = 1.3 × 10−4, 2.3 × 10−4 and nondimensional speeds ranging from U = 1 × 10−11 to U = 10−10 under pure rolling and rolling/sliding conditions.

The Elastohydrodynamic Lubrication of Heavily Loaded Point Contacts

1980 ◽  
Vol 22 (4) ◽  
pp. 183-187 ◽  
Author(s):  
C. J. Hooke
Keyword(s):  
Exact Solution ◽  
Film Thickness ◽  
Close Agreement ◽  
Numerical Solutions ◽  
Elastohydrodynamic Lubrication ◽  
Substantial Part ◽  
Line Contact ◽  
Point Contacts ◽  
Contact Width ◽  
Inlet Zone

It is shown that the film thickness in heavily loaded point contacts can be accurately calculated by comparing the inlet and exit zones of the contact with those of an equivalent line contact. The results become increasingly accurate as the extent of the inlet and exit regions is reduced and in the limit yields an exact solution. Even for moderately loaded contacts in which the inlet zone occupies a substantial part of the contact width the results are in close agreement with existing numerical solutions.

A Three-Dimensional Model of Line-Contact Elastohydrodynamic Lubrication for Heterogeneous Materials with Inclusions

2016 ◽  
Vol 08 (02) ◽  
pp. 1650014 ◽  
Author(s):  
Kun Zhou ◽  
Qingbing Dong
Keyword(s):  
Film Thickness ◽  
Half Space ◽  
Surface Deformation ◽  
Three Dimensional ◽  
Elastohydrodynamic Lubrication ◽  
Lubricant Film ◽  
Line Contact ◽  
Lubricant Film Thickness ◽  
Equivalent Inclusion Method ◽  
Surface Contact

This paper develops a three-dimensional (3D) model for a heterogeneous half-space with inclusions distributed periodically beneath its surface subject to elastohydrodynamic lubrication (EHL) line-contact applied by a cylindrical loading body. The model takes into account the interactions between the loading body, the fluid lubricant and the heterogeneous half-space. In the absence of subsurface inclusions, the surface contact pressure distribution, the half-space surface deformation and the lubricant film thickness profile are obtained through solving a unified Reynolds equation system. The inclusions are homogenized according to Eshelby’s equivalent inclusion method (EIM) with unknown eigenstrains to be determined. The disturbed half-space surface deformations induced by the subsurface inclusions or eigenstrains are iteratively introduced into the lubricant film thickness until the surface deformation finally converges. Both time-independent smooth surface contact and time-dependent rough surface contact are considered for the lubricated contact problem.

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