Spring Connected Double Rigid Bar Containing The Painleve Paradox Of Friction Oblique Collision Problem Research

In the analyses of non-smooth dynamics, oblique impact of rough bodies in an unsymmetrical configuration can result in self-locking or "jam" at the sliding contact if the coefficient of friction is sufficiently large; this has been termed, Painleve’s paradox. This phenomenon extensively exists in mechanical engineering, aerospace engineering, vehicle engineering, process of chemistry response, biology engineering and etc. on the one side, we need to avoid the occurrence of this phenomenon to ensure the mechanism can work smoothly and to lower the yawp of friction; on the other side, this phenomenon is required to make the mechanism self-lock.In the range of configurations and coefficients of friction where Painleve’s paradox occurs, analyses based on rigid body dynamics give results indicating that either there are multiple solutions or the solution is nonexistent. In this thesis, to resolve the conundrum, a slender bar oblique impacts against a rough rigid ground is taken for example. Firstly, I studied the hybrid analytical model, it’s a model that combined a completely rigid slender bar with a compliant contact model considering both normal and tangential compliance around the contact point is applied to account for the contact effect, a contact dynamic model which considers the whole compliance of the bar is established finally. Then, I build a model which including two rigid rod and there are two parallel line springs between them to study a slender bar with compliance. The software Visual C++is used to write program to simulate the self-lock process of a single rigid bar and two rigid bars linked with springs. The influence of the compliance of the whole bar and the compliance of the local contact region on the self-lock time is analyzed. Numerical results show that in the studies of the two rigid bars linked with springs, when the coefficients of friction is small, it’s outside the self-lock region, it shows gross slip. When the coefficients of friction on the edge of the self-lock region, it’s very different from the model of a single rigid bar, it shows gross slip resulted from the momentary stick after the initial slip. When the coefficients of friction in the self-lock region, it also shows three processes, initial slip, stick and terminal slip. So it is also shown that the compliances of whole bar and the local contact zone have the same significance to the self-lock time.