Literature survey of contact dynamics modelling
1214G.Gilardi,I.Sharf/Mechanism and Machine Theory37(2002)1213–1239
In general,two di?erent approaches can be distinguished for impact and contact analysis.The ?rst approach assumes that the interaction between the objects occurs in a short time and that the con?guration of impacting bodies does not change signi?cantly.The dynamic analysis is divided mainly in two intervals,before and after impact,and in secondary phases,such as slipping, sticking and reverse motion.To model the process of energy transfer and dissipation,various coe?cients are employed,mainly the coe?cient of restitution and the impulse ratio[3,4].Ap-plication of these methods,referred to as impulse–momentum or discrete methods[5],has been con?ned primarily to impact between rigid bodies.The extension to?exible systems as well as extension to more general cases involving multiple contacts and intermittent contact is quite complicated.The second approach is based on the fact that the interaction forces act in a con-tinuous manner during the impact.Thus,the analysis may be performed in the usual way,by simply adding the contact forces to the equations of motion during their action period.This al-lows a better description of the real behavior of the system,in particular,with respect to friction modeling.More importantly,this approach is naturally suitable for contact modeling and com-plex contact scenarios involving multiple contacts and bodies.This approach is referred to as continuous analysis or force based methods[5].
In the following section,we present basic concepts and de?nitions used in any impact theory. This is followed by a general historical overview of the research on impact and contact dynamics modeling,starting with the initial models of Newton and Poisson through to the modern for-mulations capable of dealing with complex contact scenarios.In the body of the paper,starting with Section2,we allocate one section to each the discrete and continuous models.Given the complexity of impact modeling,it is imperative that results obtained from theoretical analysis are con?rmed with experimental measurements.Furthermore,as in any modeling of reality,the goodness of the model depends on the choice and accuracy of model parameters.Therefore,the last section of the paper is devoted to experimental model validation and identi?cation of impact/ contact parameters.
It is important to emphasize that the literature on contact/impact analysis is vast and spans many diverse disciplines.To narrow the list of citations,our review focuses on contact(and impact)dynamics,rather than contact mechanics treatments of the subject.The latter traditionally aims to solve for stress and displacement distributions in the contact patch,as well as the wave propagation problem.Analytical results are often sought for‘simple’geometry and material combinations of the contacting bodies,such as two spheres with identical elastic constants or impact of a mass on an elastic half space.In addition,contact mechanics solutions are obtained for a known loading condition,as in the case of the classical Cattaneo problem[6,7]where the normal loading is held?xed while the tangential load is increased monotonically.Jaeger[8] presents an excellent overview of several contact mechanics analyses.In distinction,contact dy-namics models tend to deal with,not surprisingly,dynamic quantities such as forces,impulses and velocities of the contacting bodies.Being motivated by space robotic applications,our review favors the works presenting general contact dynamics formulations for multi-body systems.
1.1.Basic impact theory
Impact of two bodies is characterized by large reaction forces and changes in velocities of the two bodies.As a consequence,the bodies are subject to elastic and/or plastic deformation,with