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Simulation of a Valve Train Using Non-Smooth Mechanics
Abstract:
Nowadays, multi-body systems theory including bilateral and unilateral constraints is comparatively well established by means of set-valued force laws. Although methods of non-smooth mechanics enable a highly efficient modeling, they are not conventionally used in industrial practice. Therefore in the present paper a valve train including hydraulic elements like a hydraulic lash adjuster is modeled using above mentioned methods.
A main focus is laid upon the treatment of contact problems and two different models are investigated. Contacts in multi-body dynamics are classically described using spring and damper elements minimizing penetration. This approach results in stiff differential equations with unintentional high eigenfrequencies and long computing times as well as uncertainties in the parameters for contact stiffness and damping. Whereas in rigid contact models the contact is supposed to be completely stiff leading to non-smooth systems. The contact forces are subject to set-valued force laws describing the physical properties of the contact, namely the condition of non-penetration. Thus, stiff differential equations can be avoided and efficient models of these systems are obtained. For the rigid model discussed herein, only one interpretable physical parameter describing the dissipation of energy has to be adjusted.
The dynamics of the system are described in terms of a measure differential equation augmented by projection functions representing set-valued force laws. Integration is done by a half-explicit time-stepping scheme. The set-valued laws are solved by methods of convex analysis.
The concepts of non-smooth mechanics are adopted to hydraulic components. Using these methods a hydraulic lash adjuster is modeled and the simulation is compared to experimental results. Finally a non-smooth model of a valve train is investigated briefly and the different contact models are compared.