Non-smooth dynamics of coil contact in valve springs

• Published in: Zeitschrift für angewandte Mathematik und Mechanik Vol. 94; no. 11; pp. 957 - 967
• Main Authors: Haslinger, J., Offner, G., Sopouch, M.
• Format: Journal Article
• Language: English
• Published: Berlin WILEY-VCH Verlag 01.11.2014; WILEY‐VCH Verlag; Wiley Subscription Services, Inc
• Subjects: Automobile racing; Coil contact; Coiling; Contact; Dynamical systems; Dynamics; Mathematical analysis; Mathematical models; Nonlinear programming; semi-smooth Newton method; Signorini condition; Springs (elastic); Valves
• ISSN: 0044-2267; 1521-4001
• DOI: 10.1002/zamm.201300254

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. 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.