Stability analysis for nonlinear valve train systems in automotive engines
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REVIEW
Martin Busch
Stability analysis for nonlinear valve train systems in automotive engines
Received: 18 June 2020 / Accepted: 16 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In the present paper, the structural stability of a valve train system is investigated. Valve trains are applied in automotive combustion engines to accomplish the alternation of load. Regarding the efficiency of the engine, a stable system is favorable since it produces less oscillations and less friction. Further, the stability behavior is important from simulative perspective since model instabilities are challenging for the numerical solvers. The system behavior is described with a simplified pendulum replacement model. The stable and unstable equilibria are calculated by means of the effective potential energy. The analysis reveals a subcritical pitchfork bifurcation which changes the stability and friction behavior depending on the cam-shaft velocity. The analytically calculated results are validated with comprehensive numerical simulations. Keywords Stability analysis · Valve train · Friction · Bifurcation · Kapitza pendulum · Automotive engine
1 Introduction The dynamic behavior in automotive engines is rather complex and far from trivial. The components undergo high-frequency oscillations which can induce different kinds of nonlinearities, such as self-excited vibrations, state-dependent eigenvalues or instabilities. In order to optimize the engine’s emissions and friction, it is crucial to understand the nonlinear vibration behavior in detail. The paper at hand deals with the nonlinearities in valve train systems as they are crucial with regard to friction, see, e.g., Refs. [7,20]. Valve trains are applied in automotive combustion engines to accomplish the alternation of load. By means of a rotating cam, a roller-finger follower is driven which opens and closes a valve to control the fuel/air mixture supply. The friction in the valve train system depends on the orientation between cam-shaft and roller-finger follower, more precisely, if the valve train is mounted in a so-called pulled or in a pushed orientation, see Sect. 2 for a detailed explanation. In Fig. 1, a representative valve train is investigated on a friction test rig. The measurements show the overall friction torque at the cam shaft at different temperatures for the pushed and the pulled configuration. It can be seen that the pushed valve train generates higher friction at low speeds. Further, the friction of both approaches converges at higher speed. The reason for this behavior is still not exactly clarified in engineering science. The valve train friction is addressed in various studies. In Ref. [13], a simulative friction comparison of the different contacts in the valve train can be found. According to this study, the overall friction at low speed is mainly generated in the cam-shaft plain bearings. Indeed, the plain bearings seem to influence the absolute friction torque in Fig. 1, as the temperature affects the visco
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