Hans DeSmidt

Optimized Gore/Seam Cable Actuated Shape Control of Gossamer Membrane Reflectors

This investigation explores the feasibility of using an active gore/seam cable-based control system to reduce global root mean square 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 polyvinylidene-fluorideactuated radial cables, for which the cable lengths and attachment points are designed via genetic algorithm optimization. It is found that throughproper tailoring of the cable lengths, significant global rootmean squarefigureerror reduction is achieved. Specifically, root mean square errors due to on-orbit thermal loading were reduced by approximately 75%with a 104-cable active gore/seam cable-control system that has amass equal to 15% the original reflector. Similarly,W errorswere reduced by approximately 95%with a 104-gore/seam cable-control systemwith a mass ratio of 12%. Finally, to deal with simultaneous W error and thermal loading with uncertain relative magnitudes, a hybrid gore/seam cable-control configuration based on a combination of independently optimized thermal andW-error cable patterns is considered. By adjusting the weights of a hybrid objective function, the gore/ seam cable-control system demonstrated robust shape-control performance for combined loading conditions. Because of the relatively lightweight designs and shape-control effectiveness, the gore/seam cable-shape-control concept seems promising for future gossamer reflector applications.

Limit-Cycle Analysis of Planar Rotor/Autobalancer System Influenced by Alford's Force

In recent years, there has been much interest in the use of so-called automatic balancing devices (ABDs) in rotating machinery. Essentially, ABDs or “autobalancers” consist of several freely moving eccentric balancing masses mounted on the rotor, which, at certain operating speeds, act to cancel rotor imbalance at steady-state. This “automatic balancing” phenomenon occurs as a result of nonlinear dynamic interactions between the balancer and rotor, wherein the balancer masses naturally synchronize with the rotor with appropriate phase and cancel the imbalance. However, due to inherent nonlinearity of the autobalancer, the potential for other, undesirable, nonsynchronous limit-cycle behavior exists. In such situations, the balancer masses do not reach their desired synchronous balanced steady-state positions resulting in increased rotor vibration. In this paper, an approximate analytical harmonic solution for the limit cycles is obtained for the special case of symmetric support stiffness together with the so-called Alfords force cross-coupling term. The limit-cycle stability is assessed via Floquet analysis with a perturbation. It is found that the stable balanced synchronous conditions coexist with undesirable nonsynchronous limit cycles. For certain combinations of bearing parameters and operating speeds, the nonsynchronous limit-cycle can be made unstable guaranteeing global asymptotic stability of the synchronous balanced condition. Additionally, the analytical bifurcation of the coexistence zone and the pure balanced synchronous condition is derived. Finally, the analysis is validated through numerical time- and frequency-domain simulation. The findings in this paper yield important insights for researchers wishing to utilize ABDs on rotors having journal bearing support.

Robust-Adaptive Magnetic Bearing Control of Flexible Matrix Composite Rotorcraft Driveline

Recent studies demonstrate that a key advantage of Flexible Matrix Composite (FMC) shaft technology is the ability to accommodate misalignments without need for segmenting or flexible couplings as required by conventional alloy and graphite/epoxy composite shafts. While this is indeed a very promising technology for rotorcraft driveshafts, the high damping loss-factor and thermal stiffness and damping sensitivities of the urethane matrix, makes FMC shafting more prone to self-heating and whirl instabilities. Furthermore, the relatively low bending stiffness and critical speeds of FMC shafts makes imbalance vibration a significant challenge to supercritical operation. To address these issues and advance the state-of-the-art, this research explores Active

NON-SYNCHRONOUS VIBRATION OF PLANAR AUTOBALANCER/ROTOR SYSTEM WITH ASYMMETRIC BEARING SUPPORT

Due to inherent nonlinearity of the autobalancer, the potential for other, undesirable, non-synchronous limit-cycle vibration exists. In such undesirable situations, the balancer masses do not reach their desired synchronous balanced steady-state positions resulting in increased rotor vibration. Such behavior has been widely studied and is well understood for rotor systems on idealized bearings with symmetric supports. However, a comprehensive study into this non-linear behavior of an imbalanced planar rigid rotor/ABD system mounted on a general bearing holding asymmetric damping and stiffness forces including non-conservative effects cross-coupling ones has not been fully conducted. Therefore, this research primarily focuses on the unstable non-synchronous limit-cycle behavior of and the synchronous balancing condition of system under the influence of the general bearing support. Here, solutions for rotor limit-cycle amplitudes and corresponding whirl speeds are obtained via a harmonic balance approach. Furthermore, the limit-cycle stability is assessed via perturbation and Floquet analysis and all possible responses including undesirable coexistence for the bearing parameters and operating speeds have been thoroughly studied. It is found that, due to asymmetric behavior of bearing support, the multiple limit cycles are encountered in the range of supercritical speeds and more complicate coexistences are invited into the ABD-rotor system compared to the case with idealized symmetric bearing supports. The findings in this paper yield important insights for researchers wishing to utilize automatic balancing devices in more practical rotor systems mounted on a asymmetric general bearing support.

Nonlinear Dynamics of Breathing Cracked Jeffcott Rotor Under Axial Excitation

The rotor may operate at various working conditions in practice and the crack breathing behavior at different rotating speeds is essential for damage detection and health monitoring of rotor system. In this paper, the coupling of lateral and longitudinal vibration is investigated by building a Jeffcott rotor model with imbalance. By using D’Alambert Principle, four degree-of-freedom equation of motion is derived in fixed coordinate system and the crack model is built based on the fracture mechanics. Zero SIF method is used to determine the crack open area by computing the SIF of opening mode for every point in crack area. The stiffness matrix is updated every time step by integrating compliant coefficients over instantly calculated crack open area. In addition, the breathing behavior of the crack under axial excitation is studied in terms of several eccentricity phases and rotation speeds, which provide effective guidance for damage detection in such scenarios. The paper also explores the coupling effect of external axial loading on the vibration response and its effectiveness for damage detection.Copyright

Nonlinear Breathing Behavior Study of Transverse Crack on a Jeffcott Rotor Under Torsional Excitation

In this paper, Jeffcott rotor model is employed to explore the vibration response of breathing cracked system with unbalance mass. Based on the energy method and Lagrange principle, 6 degree-of-freedom equation of motion is derived in fixed coordinate system. The crack model is established using strain energy release theory of facture mechanics. The stiffness matrix induced by the crack is changing with the variation of crack open area. Zero stress intensity factor (SIF) method is used to determine the crack closure line by computing the SIF for opening mode. By integrating compliant coefficients over newly determined crack open area, the stiffness matrix is updated and vibration response is solved for every time step by Gear’s method. In addition, the breathing behavior of the crack is studied for multiple eccentricity phases and rotation speeds in order to provide effective guidance for damage detection. The paper explores the effect of external torsional loading on the crack breathing behavior. Finally, the coupling of lateral and torsional vibration is investigated to be used as an indicator of damage detection and health monitoring.Copyright

Multiharmonic Adaptive Vibration Control of Misaligned Driveline via Active Magnetic Bearings

Active magnetic bearings (AMBs) have been proposed by many researchers and engineers as an alternative to replace traditional contact bearings in rotor and driveshaft systems. Such active, noncontact 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 by previous AMB-driveline control studies is the effect of driveline misalignment. Previous research has shown that misalignment causes periodic parametric and forcing actions, which greatly impact both driveline stability and vibration levels. Therefore, in order to ensure closed-loop stability and acceptable performance of any AMB controlled driveline subjected to misalignment, these effects must be accounted for in the control system design. In this paper, a hybrid proportional derivative (PD) feedback/multiharmonic adaptive vibration control (MHAVC) feedforward law is developed for an AMB/U-joint-driveline system, which is subjected to parallel-offset misalignments, imbalance, and load-torque operating conditions. Conceptually, the PD feedback ensures closed-loop stability while the MHAVC feedforward suppresses steady-state vibration. It is found that there is a range of P and D feedback gains that ensures both MHAVC convergence and closed-loop stability robustness with respect to shaft internal damping induced whirl and misalignment effects. Finally, it is analytically and experimentally demonstrated that the hybrid PD-MHAVC law effectively adapts to and suppresses multiharmonic vibration induced by imbalance, misalignment, and load-torque effects at multiple operating speeds without explicit knowledge of the disturbance conditions.

Nonlinear dynamics and health monitoring of 6-DOF breathing cracked Jeffcott rotor

Jeffcott rotor is employed to study the nonlinear vibration characteristics of breathing cracked rotor system and explore the possibility of further damage identification. This paper is an extension work of prior study based on 4 degree-of-freedom Jeffcott rotor system. With consideration of disk tilting and gyroscopic effect, 6-dof EOM is derived and the crack model is established using SERR (strain energy release rate) in facture mechanics. Same as the prior work, the damaged stiffness matrix is updated by computing the instant crack closure line through Zero Stress Intensity Factor method. The breathing crack area is taken as a variable to analyze the breathing behavior in terms of eccentricity phase and shaft speed. Furthermore, the coupled vibration among lateral, torsional and longitudinal d.o.f is studied under torsional/axial excitation. The final part demonstrates the possibility of using vibration signal of damaged system for the crack diagnosis and health monitoring.

Coupled vibration of nonlinear breathing cracked rotor in lateral, torsional, and longitudinal DOFs

In this paper, finite element model of a shaft-disk system is developed to investigate the nonlinear breathing behavior of transverse cracks in terms of crack location and rotation speed. The crack model is built using the released strain energy concept in fracture mechanics. Zero Stress Intensity Factor (SIF) method is employed to determine the crack closure line at each time step by calculating the stress intensity factor of opening mode for prescribed resolutions in crack area. The stiffness matrix is updated every time step by integrating compliant coefficients over instantly calculated crack open area. With the finite element model of rotor system, the breathing behavior of cracks is explored as a function of eccentricity phase under different rotation speeds. The coupling of lateral, longitudinal and torsional vibration is studied in time and frequency domain, which may indicate the existence of damage.

Gear Fault Modeling and Vibration Response Analysis

This paper investigates a machinery health monitoring method using dynamic gearbox models (DGM) and harmonic wavelet transforms (HWT) for vibration response analysis. Gearbox vibration measurement is typically processed via frequency spectrum analysis to identify faults. However, the gearbox system may operate with varying rotational speed, as in many types of wind turbines. In such applications, harmonic wavelet transform analysis has been shown to capture the physics of events with minimal leakage between frequency bands, good frequency resolution and good time resolution. Implementing HWT signal processing for fault detection requires the development of libraries of healthy and faulty gear states to use with pattern recognition. The development of DGM can help to greatly reduce the library development and provide a physically meaningful connection of fault indicators to the actual fault patterns. In this research, a comprehensive DGM is developed, followed by HWT analyses to illustrate the fault detection and diagnosis procedure and capability.Copyright