Stability of a segmented supercritical driveline with non-constant velocity couplings subjected to misalignment and torque

With the trend toward high-speed, lightweight, supercritical drivelines, it is increasingly important to understand all instability phenomena associated with realistic driveline configurations. Furthermore, it is important to understand the interaction between different instability mechanisms. One well-known phenomenon that occurs with supercritical shafts is whirl instability due to internal (rotating-frame) shaft damping. Whirl instability occurs at shaft speeds above the first critical speed and is related to the internal/external-damping ratio. Another less explored instability phenomena is parametric instability caused by non-constant velocity flexible couplings, e.g., U-joint couplings or disk couplings, combined with driveline misalignment and load-torque. Previous research examined stability of various single U-joint/shaft systems without shaft internal damping. However, it is difficult to fully understand the stability of more realistic multi-U-joint/flexible shaft drivelines based on the single U-joint studies due to the more complicated shaft speed kinematics and misalignment configurations of multi-U-joint systems. In this paper, the non-dimensional, linear, periodically time-varying equations-of-motion for a segmented triple-U-joint driveline with shaft internal damping are derived. Torsional and lateral shaft flexibly and their effects on the shaft speed kinematics are included in the model. Numerical Floquet theory is used to explore the effects of internal/external damping ratio, misalignment, load-inertia and load-torque on the stability of the driveline operating at both sub and supercritical speeds. It is discovered that misalignment and load-torque have both stabilizing and destabilizing effects. On one-hand, misalignment and load-torque tend to stabilize internal damping-induced whirl, however, they cause instability at speeds near bending-bending and bending-torsion sum-type combination frequencies. Finally, it is shown that external damping is not always effective for stabilizing the misalignment and torque induced parametric instabilities.