Literature survey of contact dynamics modelling(3)

Literature survey of contact dynamics modelling

dissipation of energy in various forms [9].A generic impact can be represented as shown in Fig.1.The line of impact is a straight line normal to the contacting surfaces at the contact point,1i.e.,normal to the tangential plane at the contact point [1].Four types of impact can be de?ned for single-point collision between two bodies:(a)central or collinear ,if the mass centers of the two bodies are on the line of impact;(b)eccentric ,if the mass centers of one or both bodies are not on the line of impact;(c)direct ,if the initial velocities of the two bodies are along the line of impact;(d)oblique ,if the initial velocities of one or both bodies are not along the line of impact.A class of tangential impacts was introduced by Wang and Mason [10],which is characterized by zero initial relative velocity along the line of impact.

The dynamics of impact is a very complex event,depending on many properties of contacting bodies such as material,geometry and velocity.In general,two phases can be identi?ed:com-pression and restitution ,as shown in Fig.2[2,3,9,10].The ?rst phase begins when the two bodies come in contact at the instant t 0(point O),and ?nishes when the maximum deformation is reached at the instant t m (point A),where the relative normal velocity is zero.The second phase begins at the instant t m and ?nishes when the two bodies separate,i.e.,instant t f (points B,C or

D).For impacts with su?ciently high velocities,not all deformation is recoverable because of the permanent (plastic)deformation and the resulting energy loss.With respect to the latter,impact can also be classi?ed into:(a)perfectly elastic,line O–A–C,where no energy is lost;(b)perfectly plastic,line O–A,where all energy is lost and the deformation is permanent;(c)partially elastic,line O–A–D,with energy loss but no permanent deformation;(d)partially plastic,line O–A–B,with energy loss and permanent deformation.

The objective of impact modeling is to determine the after-impact conditions of the system,given its initial (pre-impact)con?guration.Because of the complex dependencies on many pa-rameters,one possible solution is to use experimentally measured coe?cients.Coe?cient of restitution,de?ned along normal direction,and coe?cients along tangential directions are the most important [3,4].

1.1.1.Coe?cient of restitution

The energy loss due to the motion in the normal direction can be expressed in terms of a co-e?cient,usually denoted by e .To honour the work-energy principle,it should satisfy the con-dition 06e 61with the end conditions corresponding to perfectly elastic ðe ¼1Þand

perfectly

1The de?nition of the line of impact is an approximation since the contacting surfaces can have di?erent normals at the point of contact.G.Gilardi,I.Sharf /Mechanism and Machine Theory 37(2002)1213–12391215

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