Non-Smooth Dynamics of Coil Contact in Valve Springs

This contribution describes the dynamic simulation of the contact of coils of a valve spring within a multi-body system application. The spring is described by a multi-mass model. Contacting spring coils influence the dynamical properties of a valve spring significantly. The possible interaction between adjacent coils is modeled by means of non-smooth mechanics. Signorini conditions on displacement level are imposed on contact candidates. The set of inequality constraints is transformed into a set of equations by introducing a nonlinear complementarity function, which contains the semi-smooth maximum function. The set of equations of motion together with the contact constraints are integrated in time by a Backward Differentiation Formula (BDF) scheme. In each time step, the resulting nonlinear algebraic equation system is solved by a semi-smooth Newton method. The approach is evaluated by two examples. The first model represents a cylindrical helical spring. The performance of the algorithm is compared to an approach, where the coil contact is modeled by using spring-damper elements in between possible contact nodes. The proposed approach is not only running much faster, but also avoids the need of artificial parameters to calibrate the spring-damper elements. The second example deals with a full model of a single valvetrain system, demonstrating that the valve train dynamics is widely affected by the vibrational characteristics of the valve springs.