Normal Line Contact of Finite-Length Cylinders

Abstract

Abstract. In this paper, the normal contact problem between an elastic half-space and a cylindrical body with the axis parallel to the surface of the half-space is solved numerically by using the Boundary Element Method (BEM). The numerical solution is approximated with an analytical equation motivated by an existing asymptotic solution of the corresponding problem. The resulting empirical equation is validated by an extensive parameter study. Based on this solution, we calculate the equivalent MDR-profile, which reproduces the solution exactly in the framework of the Method of Dimensionality Reduction (MDR). This MDR-profile contains in a condensed and easy-to-use form all the necessary information about the found solution and can be exploited for the solution of other related problems (as contact with viscoelastic bodies, tangential contact problem, and adhesive contact problem.)The analytical approximation reproduces numerical results with high precision provided the ratio of length and radius of the cylinder are larger than 5. For thin disks (small length-to-radius ratio), the results are not exact but acceptable for engineering applications.

Investigation on Dynamic Response of Rubber in Frictional Contact

“…Roller and oscillator of the apparatus are practically two wheels in contact. Such a rolling contact can be modeled more accurately than in the present paper using more than one rheological element with the method of dimensionality reduction, see ; Li and Popov (2017).…”

Design, modeling, and performance of a bidirectional stick-slip piezoelectric actuator with coupled asymmetrical flexure hinge mechanisms

“…For the described case of the cylindrical indenter, which is located on a slider, the function g ( x ) is not known. However, in Li and Popov (2017), the function g ( x ) was found for a cylinder of finite length that is indented into a half-space. The form of this function is defined as follows…”

“…In practical applications, the typical procedure used to describe frictional contacts is to formulate a suitable law of friction, which is then subsequently applied in a macroscopic simulation of the dynamics, such as LuGre model (Canudas et al, 1995), Elastoplastic friction model (Peng and Chen, 2011), CEIM (Christoph Edeler–Ingo Meyer) friction model (Edeler et al, 2011), and method of dimensionality reduction (MDR; Nguyen et al, 2016). The MDR friction model was proposed by Popov et al (Argatov et al, 2016; Li and Popov, 2017; Nguyen et al, 2016). It provides effective tools for understanding as well as for analytical calculation and numerical simulation of systems with contact interfaces in a broad range of applications (Popov and Heß, 2015).…”