Hans A. DeSmidt

Coupled Torsion-Lateral Stability of a Shaft-Disk System Driven Through a Universal Joint

Understanding the instability phenomena of rotor-shaft and driveline systems incorporating universal joints is becoming increasingly important because of the trend towards light-weight, high-speed supercritical designs. In this paper, a nondimensional, periodic, linear time-varying model with torsional and lateral degrees-of-freedom is developed for a rotor shaft-disk assembly supported on a flexible bearing and driven through a U-joint. The stability of this system is investigated utilizing Floquet theory. It is shown that the interaction between torsional and lateral dynamics results in new regions of parametric instability that have not been addressed in previous investigations. The presence of load inertia and misalignment causes dynamic coupling of the torsion and lateral modes, which can result in torsion-lateral instability for shaft speeds near the sum-type combinations of the torsion and lateral natural frequencies. The effect of angular misalignment, static load-torque, load-inertia, lateral frequency split, and auxiliary damping on the stability of the system is studied over a range of shaft operating speeds. Other than avoiding the unstable operating frequencies, the effectiveness of using auxiliary lateral viscous damping as a means of stabilizing the system is investigated. Finally, a closed-form technique based on perturbation expansions is derived to determine the auxiliary damping necessary to stabilize the system for the least stable case (worst case). ©2002 ASME

On the Robust Stability of Segmented Driveshafts with Active Magnetic Bearing Control

Many researchers and engineers have employed active control techniques, such as active magnetic bearings (AMBs), to suppress imbalance vibration in various subcritical and supercritical speed rotors dynamic applications. One issue that has not yet been addressed in previous AMB driveline control studies is the effect of non-constant velocity (NCV) flexible couplings, such as U-joint or disk-type couplings, present in many segmented drivelines. The NCV effects introduce periodic parametric and forcing terms into the equations of motion that are functions of shaft speed, driveline misalignment, and load-torque, resulting in a linear periodically time-varying system. Previous research has found that both internal damping and NCV terms greatly impact stability; thus, they must be accounted for in the control law design in order to ensure closed-loop stability of any AMB-NCV-driveline system. In this paper, numerical Floquet theory is used to explore the closed-loop stability of a flexible segmented NCV-driveline supported by AMBs with a proportional-derivative (PD) type controller. To ensure robust stability with respect to internal damping and NCV effects, the robust P and D gains and AMB locations are selected based on maximizing a stability index over a range of shaft speeds, driveline misalignments, and load-torques. It is found that maximum robustness occurs within a finite range of P and D gains for several different AMB locations. Finally, the range of robustly stabilizing P gains versus the shaft speed is examined for several misalignment and load-torque bounds.

Gore/Seam Cable Actuated Shape Control of Inflated Precision Gossamer Reflectors - Assessment Study

This investigation explores the feasibility of utilizing an active gore/seam cable based control system to reduce global RMS figure errors due to thermal loading and inflation effects (W-error) in large gossamer inflatable membrane reflectors. Analysis is performed on an inflated spherical membrane with PVDF actuated radial cables, where the cable lengths and attachment points are designed via a Genetic Algorithm optimization. It is found that through proper tailoring of cable lengths and attachment points, significant global RMS figure error reduction is achieved. Specifically, RMS errors due to on-orbit thermal loading were reduced by approximately 75% with a 104 cable active gore/seam cable control system which has a mass equal to 15% the original reflector. Similarly, W-errors were be reduced by approximately 95% with a 104 cable active gore/seam cable control system with a mass ratio of 12%. Finally, to deal with simultaneous W-error and thermal loading conditions, a hybrid gore/seam cable control configuration based on a combination of the optimized thermal and W-error cable patterns is considered. Due to the relatively lightweight designs and shape control effectiveness, the gore/seam cable based shape control concept seems promising for future gossamer reflector applications.

Multi-harmonic adaptive vibration control of AMB-driveline systems with non-constant velocity flexible couplings

Active Magnetic Bearings (AMB) have been proposed by many researchers and engineers as an alternative to replace traditional contact bearings in rotors and driveshafts. Such active, non-contact bearings do not have frictional wear and can be used to suppress vibration in sub- and supercritical rotor dynamic applications. One important issue that has not yet been addressed in previous AMB driveline control studies is the effect of non-constant velocity (NCV) flexible couplings, such as U-Joint or disk-type couplings. The NCV effects introduce periodic parametric and forcing actions that are functions of shaft speed, driveline misalignment and load-torque. Previous research has found that NCV couplings can greatly impact stability and cause significant harmonic excitation at integer multiples of the shaft speed. Thus, to ensure closed-loop stability and acceptable performance of any AMB-driveline with NCV couplings, these effects must be accounted for in the control law design. In this paper, a hybrid control law consisting of an analog PD feedback controller augmented with a slowly updating, multiple harmonic adaptive vibration control (MHAVC) is developed for a U-joint-driveline system supported by AMBs. The function of the PD controller is to ensure closed-loop stability and convergence of the MHAVC, while the MHAVC suppresses the steady-state vibration. Closed-loop stability, convergence, and performance are investigated over a range of shaft speeds for various misalignment and load-torque levels. It is found that there is an optimal range of P and D feedback gains that ensures both convergence of the MHAVC and maximizes the robust stability of the closed-loop system, with respect to NCV effects. Furthermore, it is demonstrated that the MHAVC can effectively suppress the multi-harmonic vibration induced by shaft imbalance and NCV coupling effects without knowledge of the disturbance input distribution.© 2003 ASME

Analysis of Pericyclic Mechanical Transmission with Straight Bevel Gears

A design methodology for a Pericyclic mechanical transmission utilizing straight bevel gears has been presented. By virtue of its very high reduction ratio in a single meshing stage, the pericyclic transmission holds promise for significant transmission weight reduction compared to state-of-the-art concepts. Assembly, gear geometry and kinematics of the drivetrain leading to a high reduction ratio while having a very high contact ratio (~8-10 teeth in contact) has been discussed. Tooth contact behavior has been studied in detail. A load distribution model has been developed that can be easily generalized to any internal-external bevel gear mesh. A rolling/ sliding velocity analysis has also been carried out, taking nutational motion into account. This is further used to determine the elastohydrodynamic lubrication characteristics of the meshing gear pairs. The methodology was applied to a conceptual design, resulting in acceptable levels of predicted contact stress and transmission efficiency.