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On the Proportionality Between Area and Load in Line Contacts.

J S van Dokkum¹, M Khajeh Salehani¹, N Irani¹

¹1Department of Materials Science and Engineering, Delft University of Technology, 2628 CD Delft, The Netherlands.

Tribology Letters

|April 9, 2019

Summary

The contact area of rough surfaces increases linearly with reduced pressure. This study reveals that linearity in line contacts depends on measuring the root-mean-square gradient over the actual contact area, not the entire surface.

Keywords:

Contact area Greenwood and Williamson Random rough surface Reduced pressure Root-mean-square gradient

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Area of Science:

Tribology
Surface Mechanics
Contact Mechanics

Background:

The contact area of rough surfaces typically increases linearly with reduced pressure.
The root-mean-square gradient (RMSG) is commonly used to define reduced pressure.
Previous research indicated linearity in Hertzian contacts requires RMSG over the actual contact area.

Purpose of the Study:

To investigate the linearity assumption in line contact problems.
To determine if the proportionality factor for line contacts is constant.
To compare line and surface contact linearity under varying conditions.

Main Methods:

Green's function molecular dynamics simulations were employed.
Analysis focused on the relationship between contact area and reduced pressure.
The root-mean-square gradient (RMSG) was calculated over both the entire and actual contact areas.

Main Results:

The proportionality factor for line contacts is not constant; it depends on reduced pressure and the Hurst exponent.
Linearity holds for line contacts when RMSG is measured over the actual contact area.
The ratio of proportionality factors for line and surface contacts is approximately 0.9.

Conclusions:

The assumption of constant linearity in line contacts is re-evaluated.
Accurate contact mechanics analysis requires RMSG measurement over the actual contact area.
Analytical derivation using the Greenwood and Williamson model supports numerical findings for rough surface contacts.