Статична задача про контакт пружних куль, що мають шорсткі поверхні

Abstract

Досліджено вплив урахування шорсткості поверхонь взаємодіючих пружних куль на контактний тиск. Сформульовані умови, при виконанні яких цим впливом можна знехтувати. Taking into account surface roughness significantly complicates search of solution of a contact problem. Therefore, it is advisable to find conditions under which disregarding the roughness of the surfaces of the compressed objects does not result in a considerable change of the contact area and contact pressures. This study attempts to determine such conditions for two elastic spheres. The problem being considered is a static problem of non-friction contact between two linear-elastic spheres with rough surfaces. The equation for this problem taking into account surface roughness of the interacting objects has the form (1) and that disregarding surface roughness has the form (2). The total of 216 variants of calculation was implemented for different values of the initial parameters. The parameters considered were Poisson's ratio, Young modulus, radii of the interacting spheres, compression force and factors of the power law accounting for the effect of roughness. The distribution of contact pressures in a specific plane area covering the unknown contact area and hard approaching of the objects were found. Based on the outcomes of the numerical experiment, values of the non-dimensional parameter characterizing mutual relative deviation of the solutions to the equations (1) and (2) were established. Additionally, the dependence of this parameter on the one characterizing the relationship of the largest compression of the rough sphere to the total linear-elastic displacement of the points with the largest contact pressure was analysed. The analysis resulted in formulating the conditions fulfilment of which allows disregarding the effect exerted on contact pressure by surface roughness of the interacting objects. In order to apply these conditions practically, it is sufficient to know the hard approaching of the objects, not considering the roughness and micro-irregularities of the surface. These parameters are available in the reference literature, thereby skirting the need to solve the contact problem.