Chaos intensity: Using Lyapunov exponent and uniformity to judge the intensity of mechanism chaos based on a planar slider–crank mechanism with multi-clearance joints

Abstract

Abstract Mechanism chaos, a real nonlinear dynamic phenomenon arises from a mechanism with nonlinear characteristics, whose chaotic behavior can directly affect the performance of machinery. For general mechanism, it will cause undesired impact and vibration, furthermore, reducing the life span of the machine, and then it should be suppressed or controlled. For some special applications, however, it is beneficial to improve the performance of the mechanism, and then it should be excited or enhanced. In addition, there is a coupling of several nonlinear factors existing in the mechanism. In all these circumstances, it is necessary to establish a method to judge chaos intensity (MJCI). However, there has not been widely accepted and effective MJCI until now. To satisfy the need, this paper focuses on the establishment of MJCI. To verify the correctness of this method, Logistic mapping, Duffing chaotic oscillator, and Lorenz system are used. Finally, the MJCI is used to analyze the chaos intensity of a planar slider–crank mechanism with a single or two clearance joints, the results show that with the change of clearance sizes or driving speeds, the chaos intensity can be suppressed or excited, and the practicability of MJCI in mechanism is proved.