By Paulo Flores, Hamid M. Lankarani
This ebook analyzes a number of compliant touch strength types in the context of multibody dynamics, whereas additionally revisiting the most matters linked to basic touch mechanics. specifically, it provides a variety of touch strength versions, from linear to nonlinear, from in basic terms elastic to dissipative, and describes their parameters. Addressing the various numerical tools and algorithms for touch difficulties in multibody platforms, the e-book describes the gross movement of multibody structures through the use of a two-dimensional formula according to absolutely the coordinates and employs diversified touch types to symbolize contact-impact occasions. effects for chosen planar multibody mechanical structures are awarded and applied to debate the most assumptions and approaches followed all through this paintings. the fabric supplied right here exhibits that the prediction of the dynamic habit of mechanical platforms related to contact-impact strongly depends upon the alternative of touch strength version. in brief, the booklet presents a entire 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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This e-book analyzes a number of compliant touch strength types in the context of multibody dynamics, whereas additionally revisiting the most concerns linked to primary touch mechanics. specifically, it provides numerous touch strength types, from linear to nonlinear, from merely elastic to dissipative, and describes their parameters.
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Extra info for Contact Force Models for Multibody Dynamics
1992) Bordbar and Hyppänen (2007), Schwager and Poschel (1998) Hu and Guo (2015) 3 3 r v¼ 3 3 FN ¼ Kd2 þ vd2 d_ 3ð1Àc2r Þ K 4 d_ ðÀÞ v% 1Àc2r K cr d_ ðÀÞ FN ¼ Kd2 þ vd2 d_ v¼ 3 3 FN ¼ Kd2 þ vd2 d_ v¼ 3ð1Àc2r Þe2ð1Àcr Þ K 4 d_ ðÀÞ 8ð1Àcr Þ K 5cr d_ ðÀÞ 1 K cr d_ ðÀÞ 3 3 3 3 FN ¼ Kd þ vd d_ 3 1 FN ¼ Kd2 þ vd2 d_ v¼ 3 1 FN ¼ Kd2 þ vd4 d_ v¼a FN ¼ Kd2 þ vd0:65 d_ Empirical 3 2 3 2 3 FN ¼ Kd2 þ vd2 d_ 3 3 2 2 Àg1 Þ v ¼ K3 ð3g 3g þ 2g 2 1 ð1ÀmÞð1À2mÞ Em2 pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ Kmeff rÞ K v ¼ 3ð1Àc 2cr d_ ðÀÞ McWhannell approach (1977), as well as the exact solution (Zhang and Sharf 2004).
Another limitation of the Kelvin-Voigt model is that its damping force component is active with the same damping coefﬁcient during the entire impact time interval. This results in uniform dissipation during the compression and restitution phases, which is not fully consistent with reality (Lankarani and Nikravesh 1994; Marhefka and Orin 1999; Gilardi and Sharf 2002; Bibalan and Featherstone 2009; Koshy et al. 2013; Alves et al. 2015). 2 Nonlinear Hunt and Crossley Contact Model Hunt and Crossley (1975) demonstrated that the linear spring-damper contact force model does not represent the physical nature of the energy transferred during the contact process.
It should be mentioned that with this contact force model, the energy dissipated during the contact is related to material damping of the contacting bodies. In this model, the damping term is expressed as a function of indentation, which sounds reasonable from a physical point of view. 5 6 6 Contact force [kN] Penetration Contact force Contact force [kN] 40 Penetration [µm] 31 4 2 0 0 10 20 30 40 Penetration [µm] Time [ms] Fig. , 2009; Silva et al. 2010; Moreira et al. 2012). For instance, Guess et al.