Ioannis Polyzos and Athanasios Chasalevris
J. Comput. Nonlinear Dynam. Sep 2025, 20(9): 091003
https://doi.org/10.1115/1.4068698

In rotating systems where a shaft is mounted on journal bearings, chaotic dynamic response may occur under specific design and operating conditions. Although chaos does not necessarily prevent the operation of rotating machines, it may result in higher frictional power loss and temperature rise in the bearings, compared to operation with periodic or quasi-periodic responses; it is also likely to compromise the integrity of the system when whirling orbits evolve to a large extent. A rotor-bearing system consisting of a rigid rotor mounted on two journal bearings is used to produce chaotic dynamics, which are detected and verified using numerical tools. This study uses sliding bearings with active geometry, that serves as the control input, and implements the Ott-Grebogi-Yorke (OGY) discrete-time control method, to convert chaotic oscillations to periodic. It is found that the OGY method can control the chaotic response and produce periodic motions of desired periodicity with minimal control effort. This method proves robust to measurement errors and noise, actuation errors as well as model uncertainties in oil viscosity and bearing radial clearance. Performance was further enhanced with the use of a Model Predictive Control (MPC) assisted OGY strategy. The results create potential for smooth periodic motions in high-speed rotating systems.

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.