Dynamic behavior of a slider-crank mechanism with a flexible coupler and drive train

Symbolic, analytical, and numerical techniques are used to model and analyze the dynamic behavior of a slider-crank mechanism with a flexible damped coupler/connecting rod and flexible damped drive train. The equations of motion are generated using the Newton-Euler approach. The flexibility of the drive train when combined with the flexibility of the coupler, leads to interaction between the rigid and elastic motions of the mechanism and therefore to a set of highly nonlinear dynamic equations with time varying parameters. The linear equations obtained by linearization with respect to zero solutions are analyzed using Floquet theory. Stability charts of zero solutions are plotted by tracing the boundaries of the unstable regions. The Method of Multiple Scales is used to obtain nonzero steady state solutions of the nonlinear equations. The locus of instabilities of the periodic approximate solutions in the amplitude-frequency parameter space are plotted. The predictions are verified by numerical integration using {dollar}rm 4sp{lcub}th{rcub}{dollar} order Runge-Kutta method.; 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. The length ratio of crank to coupler turns out to be the parameter which has the most direct influence on the system response. The magnitude of the response and the strength of the nonlinearity both depend on this parameter. The mass ratio of slider to coupler is proved to be the strongest source of nonlinearity. The presence of the larger mass ratio makes the system behave like a system possessing a softening type of nonlinearity. Damping mechanisms have a favorable effect on the overall response. Comparisons of nonlinear results with linear analysis results indicate that a linear model is sufficiently accurate to identity stable and unstable regions of operation of a mechanism.; Nonlinear phenomena identified in the course of this study include jump resonances associated with the super-harmonic, sub-harmonic, and primary resonances. Strange behavior in the vicinity of the boundary between stability and instability has also been recorded.