Modeling and simulation of the nonsmooth planar rigid multibody systems with frictional translational joints
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Modeling and simulation of the nonsmooth planar rigid multibody systems with frictional translational joints Fangfang Zhuang · Qi Wang
Received: 4 January 2012 / Accepted: 21 July 2012 / Published online: 24 August 2012 © Springer Science+Business Media B.V. 2012
Abstract The main purpose of this paper is to present a modeling and simulation method for the rigid multibody system with frictional translational joints. The small clearance between a slider and guide is considered. The geometric constraints of the translational joints are treated as bilateral constraints and the impacts between sliders and guides are neglected when the clearance sizes of the translational joints are very small. The contact situations of the normal forces acting on the sliders are described by inequalities and complementarity conditions, while the frictional contacts are characterized by a set-valued force law of the type of Coulomb’s law for dry friction. The dynamic equations of the multibody systems with normal and tangential contact forces are written on the acceleration-force level using the Lagrange multiplier technique. The problem of the transitions of the contact situation of the normal forces acting on sliders and the transitions of the stick-slip of the sliders in the system is formulated as a horizontal linear complementarity problem (HLCP), which is solved by event-driven method. Baumgarte’s stabilization method is used to decrease the constraint drift. Finally, two typical mechanisms are considered as demonstrative application examples. The numerical results obtained show some dynamical behaviors of the systems with frictional translational joints and constraint stabilization effect. Keywords Multibody systems · Bilateral constraints · Lagrange multipliers · Horizontal linear complementarity problem (HLCP) · Coulomb friction 1 Introduction Over the last few years, extensive work has been done to study the modeling and simulation of nonsmooth multibody systems with unilateral constraints [1–10]. One approach to model these nonsmooth multibody systems results in a set of nonlinear ordinary differential F. Zhuang () · Q. Wang School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, 100191 Beijing, P.R. China e-mail: [email protected] Q. Wang e-mail: [email protected]
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F. Zhuang, Q. Wang
equations of second order, complemented by inequality constraints due to unilateral contacts [11]. The main difficulty in solving these equations results from instantaneous changes in the contact forces at transitions from sliding to sticking or transitions from sticking to sliding. One way to solve the planar frictional contact problem is given by transforming it to a complementarity problem [12–14]. The nonsmooth dynamics approach is usually used to model the type of multibody systems with frictional unilateral constraints, due to its simplicity and ability to deal with all possible different contact configurations in a unified manner. Flores et al. [15] used the nonsmooth dynamics approac
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