A Simple Mechanical Model for a Wiper Blade Sliding and Sticking Over a Windscreen

From the mechanical standpoint, wiper blades may be thought of as belonging to a category of systems in which some components are forced to slide with friction over each other or over some rough surface. Such systems, which are in widespread use in all areas of modern engineering, exhibit complex dynamic behavior, even when only a small number of degrees of freedom are involved. In this paper we reconsider a well-known, simple mechanical model in which a rigid block connected to a linear spring is free to slide over a rough surface. The surface moves according to a prescribed sinusoidal law. The model, despite its apparent simplicity, proves to be quite useful for studying the main dynamic features of such systems. In particular, herein the equations of motion are solved analytically and the exact sequence of sticking and sliding phases found. The influence on the solution of three dimensionless parameters chosen to describe the system is investigated, and some early indications provided on the set of possible long-term system responses. Lastly, a first evaluation of the different limit cycles for the block’s motion is illustrated