Abstract
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.
Highlights
Windshield wiper systems are fundamental, albeit simple devices, nowadays mounted on all motor vehicles
In this paper we have studied the dynamic response of wiper systems viewed as an assemblage of elements that can slide one over the other in the presence of significant friction
We have studied a first elementary model in which a rigid block connected to an elastic spring is free to slide over a rough surface moving according to a sinusoidal law of motion
Summary
Windshield wiper systems are fundamental, albeit simple devices, nowadays mounted on all motor vehicles. The full list of contributions is too lengthy to cite here, some relevant work on the issues at hand include, by way of example, the study of Parnes [5], in which a single degree of freedom model is used to represent the contact between the soil and a buried pipe during a seismic event, the work of Marui and Kato [6], which addresses the dynamics of an excited single degree of freedom system through the introduction of the “stopping region of motion”, that of Shaw [7] in which the results of Den Hartog are extended to the case that the static friction coefficient is different from the dynamic one, that of Hong and Liu [8], which illustrates some analytical solutions for a mass-spring system subjected to harmonic forces and free to slide over a fixed plane with friction, Andreaus and Casini [9], which instead analyzes the dynamics of a friction oscillator subjected to both ground base motion and a driving force and, more recently, Gibert et al [10], which analyses the stick-slip dynamics in ultrasonic additive manufacturing, and Butikov [11], which studies the free and forced oscillations of a torsion spring pendulum damped by viscous and dry friction. The preliminary results deduced in this way, by no means exhaustive, can be compared with some of the analytical and numerical results available in the literature
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