Torsional Instabilities and Nonlinear Oscillation of a System incorporating a Hooke's Joint: 2DOF-model

摘要

Hooke's joint is a commonly used element in drive trains to transmit twisting moment from an input shaft to an output shaft. The kinematic relation between the input and output angles induces periodically varying velocity ratios and it is known that this can cause violent torsional oscillations of the torsionally flexible shafts within certain ranges of rotating speed. Previous studies adopting one degree-of-freedom model show that parametric and external resonances can occur to give nonlinear phenomena such as jump. Two degree-of-freedom model has been adopted to study subharmonic and combination resonances numerically. Two degree-of-freedom model is adopted to study the torsional instabilities of the nonlinear system analytically. Two linearly-and nonlinearly-coupled second-order differential equations are transformed to the four-dimensional weakly-nonlinear system which is appropriate for a further perturbation analysis. Applying the method of averaging leads to the identifications of possible occurrences of various subharmonic and combination resonances, and the reduced amplitude- and phase-equations of motion are analyzed to give bifurcation diagrams and sets.