By Paulo Flores, Hamid M. Lankarani
This ebook analyzes numerous compliant touch strength versions in the context of multibody dynamics, whereas additionally revisiting the most matters linked to basic touch mechanics. specifically, it provides numerous touch strength versions, from linear to nonlinear, from in basic terms elastic to dissipative, and describes their parameters. Addressing different numerical tools and algorithms for touch difficulties in multibody platforms, the booklet describes the gross movement of multibody platforms through the use of 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 systems followed all through this paintings. the fabric supplied the following exhibits that the prediction of the dynamic habit of mechanical structures regarding contact-impact strongly relies on the alternative of touch strength version. in brief, the publication presents a accomplished source for the multibody dynamics group and past on modeling touch forces and the dynamics of mechanical structures present process contact-impact events.
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Extra info for Contact Force Models for Multibody Dynamics
The most general and predominant type of collision is the oblique eccentric collision, which involves both relative normal velocity and relative tangential velocity (Maw et al. 1975; Zukas et al. 1982). 13) form a system of three equations with three unknowns ðþÞ ðþÞ vi , vj and ΔE. 4 Nonlinear Flores et al. Contact Model 37 where m is the equivalent mass of the two spheres given by m¼ mi mj mi þ mj ð3:18Þ As mentioned earlier, at the end of the compression phase, the two spheres move ðmaxÞ with a common instantaneous velocity vij .
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.
3 Externally colliding spheres modeled by Lankarani and Nikravesh contact law: a penetration and contact force versus time; b force-penetration relation force and hysteresis of an impact between two externally spheres in contact are presented. 8 have been utilized for the calculations. The generalized stiffness has again been evaluated based on the material properties and radii of the two spheres, given by Eqs. 14). From the analysis of Fig. 3 it can be observed that the compression and restitution phases of the contact process are not the same due to the differences in the energy dissipation process between these two phases.
Contact Force Models for Multibody Dynamics by Paulo Flores, Hamid M. Lankarani