An investigation of the dynamic stability of a slider-crank mechanism with link and drive train flexibility

Abstract

Abstract Symbolic and numerical techniques are used to model and analyze the dynamic behavior of a slider-crank mechanism with a flexible coupler and drive train. The equations of motion are generated using a symbolic algorithmic procedure based on the principle of virtual work. The flexibility of the drive train, when combined with the flexibility of the coupler, leads to coupling between the rigid and elastic motions of the mechanism and, therefore, a set of non-linear dynamic equations with time varying parameters. The linearized equations obtained by restricting the analysis to crank to coupler ratios of less than 0.3 are analyzed using Floquet theory. Stability charts are plotted by tracing the boundaries of the unstable regions. The method of multiple scales is then used to obtain analytical expressions that explain the sensitivity of the shape and location of the unstable regions to combinations of system parameters. The results show that for the coupler to crank ratios considered, the flexibility of the drive train does not appreciably affect the dynamic behavior of the mechanism. In addition, the flexibility of the coupler and of the drive train independently affect the system stability.