Abstract
In order to understand the nonlinear dynamic behavior of a planar mechanism with clearance, the nonlinear dynamic model of the 2-DOF nine-bar mechanism with a revolute clearance is proposed; the dynamic response, phase diagrams, Poincaré portraits, and largest Lyapunov exponents (LLEs) of mechanism are investigated. The nonlinear dynamic model of 2-DOF nine-bar mechanism containing a revolute clearance is established by using the Lagrange equation. Dynamic response of the slider’s kinematics characteristic, contact force, driving torque, shaft center trajectory, and the penetration depth for 2-DOF nine-bar mechanism are all analyzed. Chaos phenomenon existed in the mechanism has been identified by using the phase diagrams, the Poincaré portraits, and LLEs. The effects of the different clearance sizes, different friction coefficients, and different driving speeds on dynamic behavior are studied. Bifurcation diagrams with changing clearance value, friction coefficient, and driving speed are drawn. The research could provide important technical support and theoretical basis for the further study of the nonlinear dynamics of planar mechanism.
Highlights
Clearance joint is unavoidable, thanks to many uncertainties such as manufacturing tolerances, assemblage, material deformation, and wear. e clearance of kinematic pair in mechanical system is universal, and the joint clearance will obviously degrade working performance of the mechanical system. [1,2,3]
It is known that the nonlinear characteristic is one of most important dynamic behaviors of the nonlinear dynamic system, and it can well describe the movement rule of the system [4,5,6]. erefore, it is necessary to investigate the nonlinear dynamic behavior of mechanism with clearance, and it provides important theoretical basis and technical support for the further research of nonlinear dynamics of planar mechanism
Reis et al [7] built the dynamic equation of slider-crank mechanism containing revolute joint clearance. e contact force model based upon the Hertz model considers the dissipative influence related to the contact between the piston and pin
Summary
Thanks to many uncertainties such as manufacturing tolerances, assemblage, material deformation, and wear. e clearance of kinematic pair in mechanical system is universal, and the joint clearance will obviously degrade working performance of the mechanical system. [1,2,3]. Reis et al [7] built the dynamic equation of slider-crank mechanism containing revolute joint clearance. Rahmanian and Ghazavi [23] researched nonlinear dynamic behavior of the crank-slider mechanism including clearance joints. Flores et al [27] used the general methodology to evaluate the effect of the clearance value and friction coefficient on the dynamic response of the rigid crank-slider mechanism containing clearance joints. E Poincaremaps have been used to study the nonlinear characteristics, and influences of different clearance sizes and different driving speeds on dynamic response have been both investigated. Taking 2-DOF nine-bar mechanism as the study object, dynamic response of the kinematics characteristic of the slider, contact force, driving torque, shaft center trajectory, and the penetration depth for 2-DOF nine-bar mechanism are all studied, and chaos phenomenon existed in the mechanism is systematically identified by the phase diagrams, the Poincareportraits, and LLEs, respectively. It is remarkable that revolute clearance joint introduces two extra DOFs which contain horizontal and vertical displacements of center of shaft corresponding to the bearing center. e DOF of the mechanism is changed from 2 to 4
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