| In order to understand vibro-impact sources in vehicle drivetrains, most prior analyses have focused on the determination of time domain responses under harmonic excitations using cumbersome numerical tools. But, in this dissertation, alternative prediction methods are proposed that examine the nonlinear frequency response characteristics of key torsional sub-systems. Unlike previous methods, the proposed Harmonic Balance Method (HBM) includes adaptive arc-length continuation and stability calculation capabilities to find periodic solutions in multi-valued non-linear frequency response regimes as well as to improve convergence. Essential steps of the proposed HBM calculations are introduced, and it is validated by comparing time and frequency domain predictions with those yielded by numerical solutions, experimental studies, or analog simulations. Then non-linear frequency response characteristics of an oscillator with clearance non-linearity (and under the influence of a mean load) are examined with focus on super- and sub-harmonics. We also explore some issues that are not fully resolved in the literature. For instance, the effect of mean operating point, and the number of harmonic terms required in reliable the HBM calculations have been investigated. Furthermore, several smoothening functions to overcome discontinuities in clearance type non-linearity are proposed and their influences on the non-linear frequency response characteristics of a single degree-of-freedom system are critically compared.; Next, a particular non-linear impact damping model is modeled and analyzed. First, we consider the damping element with a linear spring and examine the non-linear frequency response characteristics of a torsional system. Second, the impact damping is examined along with the clearance non-linearity including the backlash problem. Three semi-analytical methods, the Describing Function Method, Multi-term Harmonic Balance Method and Stochastic Linearization Method, are utilized to investigate the effect of impact damping. Feasibility of such methods is confirmed by comparing predictions with results yielded by a numerical method and an experimental result. Finally, a vehicle drive train case is introduced where the vibro-impacts from an unloaded gear pair are related to those from an engaged set. Linear and non-linear mathematical models of the driveline are developed to understand, quantify and control the rattle problem. Trends predicted by simulations are compared with those observed in experiments. |
