Asynchronous partial contact motion due to internal resonance in multiple degree-of-freedom rotordynamics

Sudden onset of violent chattering or whirling rotorstator contact motion in rotational machines can cause significant damage in many industrial applications. It is shown that internal resonance can lead to the onset of bouncing-type partial contact motion away from primary resonances. These partial contact limit cycles can involve any two modes of an arbitrarily high degree-of-freedom system, and can be seen as an extension of a synchronisation condition previously reported for a single disc system. The synchronisation formula predicts multiple drivespeeds, corresponding to different forms of mode-locked bouncing orbits. These results are backed up by a brute-force bifurcation analysis which reveals numerical existence of the corresponding family of bouncing orbits at supercritical drivespeeds, provided the dampingis sufficiently low. The numerics reveal many overlapping families of solutions, which leads to significant multi-stability of the response at given drive speeds. Further secondary bifurcations can also occur within each family, altering the nature of the response, and ultimately leading to chaos. It is illustrated how stiffness and damping of the stator have a large effect on the number and nature of the partial contact solutions, illustrating the extreme sensitivity that would be observed in practice

Normal form analysis of bouncing cycles in isotropic rotor stator contact problems

This work considers analysis of sustained bouncing responses of rotating shafts with nonlinear lateral vibrations due to rotor stator contact. The insight that this is an internal resonance phenomena makes this an ideal system to be studied with the method of normal forms, which assumes that a system may be modelled primarily in terms of just its resonant response components. However, the presence of large non smooth nonlinearities due to impact and rub mean that the method must be extended. This is achieved here by incorporating an alternating frequency/time (AFT) step to capture nonlinear forces. Furthermore, the presence of gyroscopic terms leads to the need to handle complex modal variables, and a rotating coordinate frame must be used to obtain periodic responses. The process results in an elegant formulation that can provide reduced order models of a wide variety of rotor systems, with potentially many nonlinear degrees of freedom. The method is demonstrated by comparing against time simulation of two example rotors, demonstrating high precision on a simple model and approximate precision on a larger model

Dynamic similarity design method for an aero-engine dualrotor test rig

This paper presents a dynamic similarity design method to design a scale dynamic similarity model (DSM) for a dual-rotor test rig of an aero-engine. Such a test rig is usually used to investigate the major dynamic characteristics of the full-size model (FSM) and to reduce the testing cost and time for experiments on practical aero engine structures. Firstly, the dynamic equivalent model (DEM) of a dual-rotor system is modelled based on its FSM using parametric modelling, and the first 10 frequencies and mode shapes of the DEM are updated to agree with the FSM by modifying the geometrical shapes of the DEM. Then, the scaling laws for the relative parameters (such as geometry sizes of the rotors, stiffness of the supports, inherent properties) between the DEM and its scale DSM were derived from their equations of motion, and the scaling factors of the above-mentioned parameters are determined by the theory of dimensional analyses. After that, the corresponding parameters of the scale DSM of the dual-rotor test rig can be determined by using the scaling factors. In addition, the scale DSM is further updated by considering the coupling effect between the disks and shafts. Finally, critical speed and unbalance response analysis of the FSM and the updated scale DSM are performed to validate the proposed method

Two-plane automatic balancing:a symmetry breaking analysis

International audienceWe present an analysis of a two-plane automatic balancing device for rotating machinery. The mechanism consists of a pair of races that contain balancing balls which move to eliminate imbalance due to rotor eccentricity or principal axis misalignment. A model is developed that includes the effect of support anisotropy and rotor acceleration. The symmetry of the imbalance is considered, and techniques from equivariant bifurcation theory are used to derive a necessary condition for the stability of balanced operation. The unfolding of the solution structure is explored and we investigate mechanical systems in which either the supports or the automatic ball balancer is asymmetric. Here it is shown that, provided the imbalance is small, the balanced state is robust to the considered asymmetries

Investigation of a multi-ball automatic dynamic balancing mechanism for eccentric rotors,

This paper concerns an analytical and experimental investigation into the dynamics of an automatic dynamic balancer (ADB) designed to quench vibration in eccentric rotors. This fundamentally nonlinear device incorporates several balancing masses that are free to rotate in a circumferentially mounted ball race. An earlier study into the steady state and transient response of the device with two balls is extended to the case of an arbitrary number of balls. Using bifurcation analysis allied to numerical simulation of a fully nonlinear model, the question is addressed of whether increasing the number of balls is advantageous. It is found that it is never possible to perfectly balance the device at rotation speeds comparable with or below the first natural, bending frequency of the rotor. When considering practical implementation of the device, a modification is suggested where individual balls are contained in separate arcs of the ball race, with rigid partitions separating each arc. Simulation results for a partitioned ADB are compared with those from an experimental rig. Close qualitative and quantitative match is found between the theory and the experiment, confirming that for sub-resonant rotation speeds, the ADB at best makes no difference to the imbalance, and can make things substantially worse. Further related configurations worthy of experimental and numerical investigation are proposed

Bilinear amplitude approximation for piecewise-linear oscillators

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/97069/1/AIAA2012-1793.pd

Regular and chaotic vibration in a piezoelectric energy harvester

We examine regular and chaotic responses of a vibrational energy harvester composed of a vertical beam and a tip mass. The beam is excited horizontally by a harmonic inertial force while mechanical vibrational energy is converted to electrical power through a piezoelectric patch. The mechanical resonator can be described by single or double well potentials depending on the gravity force from the tip mass. By changing the tip mass we examine bifurcations from single well oscillations, to regular and chaotic vibrations between the potential wells. The appearance of chaotic responses in the energy harvesting system is illustrated by the bifurcation diagram, the corresponding Fourier spectra, the phase portraits, and is confirmed by the 0–1 test. The appearance of chaotic vibrations reduces the level of harvested energy

Bostonia: The Boston University Alumni Magazine. Volume 12

Founded in 1900, Bostonia magazine is Boston University’s main alumni publication

Allogeneic hematopoietic stem cell transplantation for severe, refractory juvenile idiopathic arthritis.

Patients with juvenile idiopathic arthritis (JIA) can experience a severe disease course, with progressive destructive polyarthritis refractory to conventional therapy with disease-modifying antirheumatic drugs including biologics, as well as life-threatening complications including macrophage activation syndrome (MAS). Allogeneic hematopoietic stem cell transplantation (allo-HSCT) is a potentially curative immunomodulatory strategy for patients with such refractory disease. We treated 16 patients in 5 transplant centers between 2007 and 2016: 11 children with systemic JIA and 5 with rheumatoid factor-negative polyarticular JIA; all were either refractory to standard therapy, had developed secondary hemophagocytic lymphohistiocytosis/MAS poorly responsive to treatment, or had failed autologous HSCT. All children received reduced toxicity fludarabine-based conditioning regimens and serotherapy with alemtuzumab. Fourteen of 16 patients are alive with a median follow-up of 29 months (range, 2.8-96 months). All patients had hematological recovery. Three patients had grade II-IV acute graft-versus-host disease. The incidence of viral infections after HSCT was high, likely due to the use of alemtuzumab in already heavily immunosuppressed patients. All patients had significant improvement of arthritis, resolution of MAS, and improved quality of life early following allo-HSCT; most importantly, 11 children achieved complete drug-free remission at the last follow-up. Allo-HSCT using alemtuzumab and reduced toxicity conditioning is a promising therapeutic option for patients with JIA refractory to conventional therapy and/or complicated by MAS. Long-term follow-up is required to ascertain whether disease control following HSCT continues indefinitely