Nonlinear Dynamics of a Three-Degree-of-Freedom Shaft Driveline Coupled With a Series of Universal Joints With Clearances

Junaid Ali, Gregory Shaver, and Anil K. Bajaj
J. Comput. Nonlinear Dynam. Sep 2025, 20(9): 091007
https://doi.org/10.1115/1.4068930

This study presents an extended investigation into the dynamic behavior of a multidegree-of-freedom (DOF) driveline interconnected by a series of universal joints (U-joints). While previous studies have focused on the effects of rotational-type clearance within a single U-joint in a 2DOF shaft system—revealing bifurcation phenomena such as period-doubling routes to chaos and various crisis bifurcations—this work extends the analysis to a 3DOF driveline coupled with two U-joints arranged in a Z-type configuration, with a π/2 rad phase difference, which is previously not explored. The presence of multiple U-joints introduces additional holonomic constraints and nonsmooth nonlinearities, resulting in more complex dynamical behavior. This study highlights the significant influence of U-joint phasing on the dynamics of multijointed drivelines, particularly in the context of clearance-induced nonlinearities. Numerical bifurcation diagrams are constructed for driveline output states as functions of system parameters, and Poincaré mapping is used to characterize the presence of periodic and coexisting attractors, as well as strange chaotic attractors exhibiting fractal-like properties. The boundaries between periodic and chaotic regions are identified through the computation of basins of attraction for coexisting attractors and 2D parameter space. Furthermore, the study demonstrates that the driveline exhibits greater sensitivity to mechanical clearances in the downstream U-joint compared to the upstream joint, highlighting the critical role of U-joint phasing in torsional instability mitigation. These findings provide new insights into the nonlinear dynamics of driveline systems with multiple U-joints and clearances, paving the way for more accurate modeling and the development of robust design strategies.