Approching of the Line Concentrated Contact as a Quarter Space Problem - A Review

Concentrated contact frequently occurs between machine elements, leading to the development of various forms of damage: abrasive wear, adhesive wear, and seizure, as well as surface destruction through contact fatigue. Contact fatigue is a typical mode of damage to machine parts (bearings, gears, wheel-track contact, but also cams and valves) under strong and repeated Hertz contact pressure (Kohn and Silva, 2020).

Most concentrated contact problems, where bodies touch at a point or a line, are well described and solved using the assumptions and equations of Hertz’s theory, which associate bodies with elastic half-spaces. In the case of cylindrical bodies of finite length, Hertz’s equations do not correctly describe the state of stresses arising at the boundary. At non-coincidentally concentrated linear contact, these uncompensated stresses lead to the so-called ’end effect’: the pressure increases near the edges of the cylinder of shorter length. These uncompensated stresses have to be taken into account in the geometrical and functional design of machine elements.

In this paper, the main methods of solving the stresses arising at concentrated linear contact with finite length are presented, in approaching the problem as a quarter-space problem.