Numerical Analysis of Contact Mechanics between a Spherical Slider and a Flat Disk with Low Roughness Considering Lennard–Jones Surface Forces

Abstract

Although analytical and numerical analyses of the contact mechanics of a completely smooth sphere–flat contact have been done, the analysis of a realistic sphere–flat contact with a surface roughness whose mean height planes have a spacing greater than the atomic equilibrium distance has not been done thoroughly. This paper is a fundamental study of the elastic contact mechanics due to Lennard–Jones (LJ) intermolecular surface forces between a spherical slider and a flat disk with low roughness whose height is larger than equilibrium distance z ₀. First, neglecting the effect of the attractive force at contacting asperities, adhesion contact characteristics of a 2-mm-radius glass slider with a magnetic disk are presented in relation to the asperity spacing σ between mean height planes. Results showed that the contact behavior at a small asperity spacing of ∼0.5 nm cannot be predicted either by the Johnson–Kendall–Roberts or Derjaguin–Muller– Toporov theories. Second, contact characteristics of a 1-μm-radius sphere on a flat disk are presented to examine how LJ attractive force at contacting asperities can be evaluated. It was found that the adhesion force of contacting asperity is a function of separation in general, but it becomes almost constant when σ = ∼z ₀. A simple equation to evaluate the LJ attractive pressure of contacting asperities is presented for the rough contact analysis. Third, numerical calculation methods for a sphere–flat contact including LJ attractive forces between the mating mean height planes and contacting asperities are presented. Then, adhesion characteristics of a 2-mm-radius glass slider and magnetic disk are calculated and compared with the previous experimental results of dynamic contact test. It is shown that the calculated LJ adhesion force is much smaller than the experimental adhesion force, justifying that the adhesion force observed at the separation of contact is caused by meniscus force rather than by vdW force.