Lateral nonlinear vibration of the camshaft considering the structural clearance and load force

Abstract

To reveal the influence of variations in dynamic characteristics on the working performance of the camshaft, the lateral nonlinear vibration of the camshaft considering the structural clearance and load force is studied. By using the Magnus series expansion method, the response of lateral nonlinear vibration is solved, and the numerical computation scheme applied to the global evolution characteristics of attractors and their basins is developed, which solves the problems of inadequate accuracy and long-term numerical unreliability in numerical solutions and simulations. By analyzing the attractors and basins, single-parameter bifurcation, and bi-parameter dynamic characteristics, the influence of different parameters on the nonlinear dynamic characteristics of the camshaft system is revealed. The results show that as the structural clearance increases, the attraction basins of both periodic and chaotic attractors exhibit tongue-shaped fractal features, and the camshaft system changes from the coexistence of two types of period-3 attractors to chaotic attractors, which reveals the mechanism of global vibration instability of the camshaft system. In addition, when the camshaft system evolves from the flutter to forced vibration conditions, the period-doubling bifurcation behavior occurs, and the parameter ranges for stable operation of the system increase. More importantly, the bi-parameter dynamic characteristics confirm that the parameter ranges for the periodic motion of the system are enlarged when the load force increases, and there exist multi-parameter optimal matching solutions for the stable motion of the camshaft system. The research results reveal the evolution mechanism of the lateral nonlinear vibration of the camshaft, which can provide a theoretical reference for suppressing the vibration and improving the working performance.