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Research Papers: Elastohydrodynamic Lubrication

# A Three-Dimensional Deterministic Model for Rough Surface Line-Contact EHL Problems

[+] Author and Article Information
Ning Ren

Center for Surface Engineering and Tribology, Northwestern University, Evanston, IL 60208n-ren@northwestern.edu

Dong Zhu

Tri-Tech Solutions, Mount Prospect, IL 60056

W. Wayne Chen, Yuchuan Liu, Q. Jane Wang

Center for Surface Engineering and Tribology, Northwestern University, Evanston, IL 60208

J. Tribol 131(1), 011501 (Dec 02, 2008) (9 pages) doi:10.1115/1.2991291 History: Received February 06, 2008; Revised August 04, 2008; Published December 02, 2008

## Abstract

This paper reports the development of a novel three-dimensional (3D) deterministic model (3D L-EHL) for rough surface line-contact mixed-elastohydrodynamic lubrication (EHL) problems. This model is highly demanded because line contacts are found between many mechanical components, such as various gears, roller and needle bearings, cams and followers, and work rolls and backup rolls in metal-forming equipment. The macro aspects of a line-contact problem can be simplified into a two-dimensional (2D) model; however, the topography of contacting rough surfaces, microasperity contacts, and lubricant flows around asperities are often three-dimensional. The present model is based on Hu and Zhu’s unified 3D mixed-EHL model (Hu and Zhu, 2000, “Full Numerical Solution to the Mixed Lubrication in Point Contacts  ,” ASME J. Tribol., 122(1), pp. 1–9) originally developed for point contacts and the mixed fast Fourier transform (FFT)-based approach for deformation calculation formulated by Chen (2008, “Fast Fourier Transform Based Numerical Methods for Elasto-Plastic Contacts With Normally Flat Surface  ,” ASME J. Appl. Mech., 75(1), 011022-1-11). It is numerically verified through comparisons with results from the line-contact Hertzian theory and the conventional 2D line-contact smooth-surface EHL formulas. Numerical examples involving 3D sinusoidal and digitized machined surfaces are also analyzed. Sample cases indicate that transverse roughness may yield greater film thickness than longitudinal roughness. This observation is qualitatively in agreement with the trend predicted by Patir and Cheng’s stochastic model (1978, “Effect of Surface Roughness on the Central Film Thickness in EHL Contacts  ,” Proceedings of the Fifth Leeds-Lyon Symposium on Tribology, London, pp. 15–21). However, the roughness orientation effect does not appear to be quantitatively as great as that shown in the work of Patir and Cheng for the same range of $λ$ ratio.

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## Figures

Figure 1

Two bodies with rough surfaces in a line-contact; the contact length in the y-direction is infinite, or much greater than the contact width in the x-direction

Figure 10

Film thickness results for cases with sinusoidal roughness. Dashed lines show central film thickness from corresponding smooth-surface solution (currently 220 nm): (a) rms roughness σ=70 nm, film thickness ratio λ=hcs/σ=3.143; (b) rms roughness σ=150 nm, film thickness ratio λ=hcs/σ=1.467; (c) rms roughness σ=300 nm, film thickness ratio λ=hcs/σ=0.733; and (d) rms roughness σ=450 nm, film thickness ratio λ=hcs/σ=0.489.

Figure 2

Sketch of mixed padding; DC-FFT in the motion (x) direction while modified DC-FFT with duplicated padding (DCD-FFT) in the infinite length (y) direction

Figure 3

Sample smooth surface solutions at different speeds

Figure 4

A line contact EHL solution at an ultralow speed (0.0005 m/s); obtained from the 3D L-EHL model, in comparison with that from the line-contact Hertzian theory; (a) 3D view of the deformed surface (film thickness), (b) 3D view of the pressure distribution, (c) pressure and film profiles in the x-direction, (d) pressure and film profiles in the y-direction, and (e) comparison of the L-EHL solution (line) with that from the Hertzian theory (dots)

Figure 5

Comparison with the results from classic line-contact EHL film thickness formulas: (a) central film thickness, and (b) minimum film thickness

Figure 6

Some typical machined surfaces showing 3D topography

Figure 7

3D line contact mixed-EHL solutions for machined surfaces; the composite rms roughness values and contact load ratios are shown. The average film thickness values within the width of ±0.5a from the centerline are 249 nm, 296 nm, 173 nm, and 213 nm for the shaved, ground, honed, and polished surfaces, respectively, while the central film thickness for the corresponding smooth-surface EHL is 215.6 nm

Figure 8

Cases for a honed surface versus a turned surface in longitudinal and transverse orientations; (a) solution for honed versus turned-longitudinal, (b) solution for honed versus turned-transverse, and (c) honed and turned surfaces used

Figure 9

A sample 3D L-EHL solution for a sinusoidal surface sliding on a smooth plane

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