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Nonlinear dynamic behavior analysis of closed-loop self-excited crankshaft model using improved Newmark-β method

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Abstract

The torsional vibration of engine crankshaft is affected by many nonlinear factors, such as unbalanced external force (combustion pressure, friction resistance), nonlinear stiffness, unbalanced moment of inertia and self-excited oscillation considering velocity feedback. In the traditional numerical calculation methods, the simultaneous introduction of multiple nonlinear factors may lead to the divergence of calculation results, which may not be able to accurately evaluate the nonlinear dynamic bifurcation behavior. Therefore, the current researches focus on the influence of a single nonlinear factor on torsional vibration. Motivated by such limitations, dynamic behavior analysis of torsional vibration of an engine crankshaft model considering multiple nonlinear factors is investigated in this work, including the in-cylinder combustion, lubricating oil lubrication, bearing friction, in-cylinder piston ring friction, valve seat percussion, variable inertia and angular displacement as well as angular velocity feedback. For this purpose, a nonlinear crankshaft closed-loop self-excitation coupled oscillation (NCSCO) model is established. On the basis of verifying the correctness of the model through comparison with experiments, an improved Newmark-β integral method which has a better convergence is proposed to solve the model in a longer time domain. The correctness of it is verified through the comparison of results solved using traditional Runge–Kutta method. Based on this, Sobol method is performed for sensitivity analysis and dynamic bifurcation characteristics are explored through a series of numerical simulations. Abundant ‘jumping’ phenomena are obtained and the appropriate range of parameters is given based on bifurcation diagrams.

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Data availability

The datasets analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant nos. 11972125 and 12102101)

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  1. College of Power and Energy Engineering, Harbin Engineering University, Harbin, 150001, People’s Republic of China

    Kai Ma, Jingtao Du & Yang Liu

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  1. Kai Ma
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Correspondence to Yang Liu.

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Ma, K., Du, J. & Liu, Y. Nonlinear dynamic behavior analysis of closed-loop self-excited crankshaft model using improved Newmark-β method. Nonlinear Dyn 111, 5107–5124 (2023). https://doi.org/10.1007/s11071-022-08100-3

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