By Paulo Flores, Hamid M. Lankarani
This e-book analyzes a number of compliant touch strength versions in the context of multibody dynamics, whereas additionally revisiting the most matters linked to primary touch mechanics. specifically, it provides a number of touch strength types, from linear to nonlinear, from simply elastic to dissipative, and describes their parameters. Addressing the several numerical tools and algorithms for touch difficulties in multibody platforms, the publication describes the gross movement of multibody structures by utilizing a two-dimensional formula in line with absolutely the coordinates and employs diverse touch types to symbolize contact-impact occasions. effects for chosen planar multibody mechanical platforms are awarded and applied to debate the most assumptions and techniques followed all through this paintings. the fabric supplied right here shows that the prediction of the dynamic habit of mechanical platforms regarding contact-impact strongly is dependent upon the alternative of touch strength version. in brief, the ebook offers a entire source for the multibody dynamics neighborhood and past on modeling touch forces and the dynamics of mechanical platforms present process contact-impact events.
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Additional resources for Contact Force Models for Multibody Dynamics
In turn, the restitution phase starts at this instant of time and ends when the two spheres separate from each other. 4 illustrates the two different phases of a direct central contact between two solid spheres. The spheres are labeled as bodies i and j and have masses mi and mj. The pre- and post-impact velocities associated with each sphere are denoted as ðÀÞ ðÀÞ ðþÞ ðþÞ vi ; vj ; vi and vj , respectively. At the end of the compression phase, the two ðmaxÞ spheres move with a common instantaneous velocity represented by variable vij .
4 Nonlinear Flores et al. Contact Model 39 Substituting now Eqs. 30) into Eqs. 2 d_ ðÀÞ ¼1 ð3:31Þ which is an equation for an ellipse for the deformation and velocity. Thus, it is possible to express the velocity of deformation as function of the deformation for both compression and restitution phases as _ ðÀÞ d_ ¼ d sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ d 2 1À dmax ð3:32Þ sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ d 2 d_ ¼ d_ ð þ Þ 1 À dmax ð3:33Þ At this stage, it is important to note that the post-impact velocity d_ ð þ Þ is negative because the spheres are separating from each other.
In order to keep this analysis simple, only hysteresis damping factor expressions that explicitly depend on the initial impact velocity are utilized. These are, in fact, the most common contact force approaches used for contact modeling and simulation in the context of multibody mechanical systems. In addition, the ratio between contact stiffness and initial impact velocity is considered to be equal to unity. 9 shows the plots of the Hysteresis damping factor 15 Hunt and Crossley (1975), Marefka and Orin (1999) Herbert and McWhannell (1977) 12 Lee and Wang (1983) Lankarani and Nikravesh (1990) 9 Gonthier et al.