Rocking-mass gyroscope consists of an assembly of four cantilever beams with a rigid mass attached to them in the middle subjected to base rotations. Due to the gyroscope effect, the beams undergo coupled flexural-torsional vibrations. The main goal of the research is to develop an accurate model of such a system and along this line a detailed mathematical modeling of the gyroscope is developed. The equations of motion clearly show the presence of the gyroscopic couplings in all cantilever beams. A computer simulation model in its most general form has been developed, to analyze the effectiveness of this type of gyroscope. / UOIT

Tool chatter in longitudinal turning is addressed with a new perspective using a complex machining model describing the coupled tool-workpiece dynamics subject to nonlinear regenerative cutting forces, instantaneous depth-of-cut (DOC) and workpiece whirling due to material imbalance. The workpiece is modeled as a system of three rotors: unmachined, being machined and machined, connected by a flexible shaft. The model enables workpiece motions relative to the tool and tool motions relative to the machining surface to be three-dimensionally established as functions of spindle speed, instantaneous DOC, rate of material removal and whirling. Excluding workpiece vibrations from the cutting model is found improper. A rich set of nonlinear behaviors of both the tool and the workpiece including period-doubling bifurcation and chaos signifying the extent of machining instability at various DOCs is observed. Presented numerical results agree favorably with physical experiments reported in the literature. It is found that whirling is non-negligible if the fundamental characteristics of machining dynamics are to be fully understood. The 3D model is explored along with its 1D counterpart, which considers only tool motions and disregards workpiece vibrations. Numerical simulations reveal diverse behaviors for the 3D coupled and 1D uncoupled equations of motion for the tool. Most notably, observations made with regard to the inconsistency in describing stability limits raise the concern for using 1D models to obtain stability charts. The nonlinear 3D model is linearized to investigate the implications of applying linear models to the understanding of machining dynamics. Taylor series expansion about the operating point where optimal machining conditions are desired is applied to linearize the model equations of motion. Modifications are also made to the nonlinear tool stiffness term to minimize linearization errors. Numerical experiments demonstrate inadmissible results for the linear model and good agreement with available physical data in describing machining stability and chatter for the nonlinear model. Effects of tool geometry, feed rate, and spindle speed on cutting dynamics are also explored. It is observed that critical DOC increases with increasing spindle speed and small DOCs can induce cutting instability -- two of the results that agree qualitatively well with published experimental data.

In the present study, effect of satisfying stress boundary conditions, in addition to displacement boundary conditions, in the axisymmetric vibration analysis of circular and annular plates is investigated. A new axisymmetric finite element, which is based on a combination of the conventional displacement-type variational principle and the Reissner¡¦s principle, is proposed. With this formulation, stresses, like displacements, are primary variables, and both displacement and stress boundary conditions can be easily and exactly imposed. Axisymmetric vibration frequencies of some typical circular and annular plates are then obtained with the present approach and are compared with those by the displacement-type axisymmetric finite element. It is found that the conventional finite element, though not satisfying stress boundary conditions, can still obtain sufficiently accurate vibration frequencies of circular and annular plates.

ABSTRACT The flow-induced vibrations of tubes in a rotated triangular array subject to cross flow are investigated numerically and experimentally. The parameters are inlet velocity of cross flow, number of tube, and tube natural frequency. In the study, the instantaneous fluid forces on tube surfaces are computed numerically, the instantaneous displacement of the tubes due to the fluid forces is calculated, and thus the motions of the tubes in cross flow are described. Experiments are also conducted to compare the numerical results. The tube vibrations in a water tunnel are measured by two accelerometers. The amplitudes, spectra, and trace of tube motion are presented. The critical velocities of tube vibrations are then determined. Experimental results show that some tubes vibrate seriously when the flow velocity increases up to a critical value, and hysteresis of the tube vibrations is observed. In case of the seven-tube array, the tubes in the fourth row exhibit the most serious vibration. When the flow velocity is above the critical value, only one dominant frequency of the tube vibrations is detected, comparing to multiple dominant frequencies in subcritical condition. Furthermore, the tube in supercritical condition behaves like a limit cycle, especially when the natural frequency is equal to or near the vortex shedding frequency from the upstream tubes. It is also shown that the critical velocity decreases with more surrounding tubes in the upstream and does not change as more adjacent tubes are added in the downstream. However, the tube number seems to have no effect on the critical velocity when the tube natural frequency is far from the vortex shedding frequency.

Gas foil bearings (GFB) appear to satisfy most requirements for oil-free turbomachinery, i.e. relatively simple in construction, ensuring low drag friction and reliable high speed operation. However, GFBs have a limited load capacity and minimal amounts of damping. A test rig for the rotordynamic evaluation of gas foil bearings was constructed. A DC router motor, 25 krpm max speed, drives a 1.02 kg hollow rotor supported on two bump-type foil gas bearings (L = D = 38.10 mm). Measurements of the test rotor dynamic response were conducted for increasing mass imbalance conditions. Typical waterfalls of rotor coast down response from 25 krpm to rest evidence the onset and disappearance of severe subsynchronous motions with whirl frequencies at ~ 50% of rotor speed, roughly coinciding with the (rigid mode) natural frequencies of the rotor-bearing system. The amplitudes of motion, synchronous and subsynchronous, increase (non) linearly with respect to the imbalance displacements. The rotor motions are rather large; yet, the foil bearings, by virtue of their inherent flexibility, prevented the catastrophic failure of the test rotor. Tests at the top shaft speed, 25 krpm, did not excite subsynchronous motions. In the experiments, the subsynchronous motion speed range is well confined to shaft speeds ranging from 22 krpm to 12 krpm. The experimental results show the severity of subsynchronous motions is related to the amount of imbalance in the rotor. Surprisingly enough, external air pressurization on one side of the foil bearings acted to reduce the amplitudes of motion while the rotor crossed its critical speeds. An air-film hovering effect may have enhanced the sliding of the bumps thus increasing the bearings’ damping action. The tests also demonstrate that increasing the gas feed pressure ameliorates the amplitudes of subsynchronous motions due to the axial flow retarding the circumferential flow velocity development. A finite element rotordynamic analysis models the test rotor and uses predicted bearing force coefficients from the static equilibrium GFB load analysis. The rotordynamic analysis predicts critical speeds at ~8 krpm and ~9 krpm, which correlate well with test critical speeds. Predictions of rotordynamic stability are calculated for the test speed range (0 to 25 krpm), showing unstable operation for the rotor/bearing system starting at 12 krpm and higher. Predictions and experimental results show good agreement in terms of critical speed correlation, and moderate displacement amplitude discrepancies for some imbalance conditions. Post-test inspection of the rotor evidenced sustained wear at the locations in contact with the bearings' axial edges. However, the foil bearings are almost in pristine condition; except for top foil coating wear at the bearing edges and along the direction of applied static load.

Thèse doctorat : Acoustique : INSA LYON : 2003. / Titre provenant de l'écran-titre. Bibliogr. p. 235-543.

Thèse de doctorat : sciences. Acoustique : Ecully, Ecole centrale de Lyon : 2005. / 153 réf.

Thèse de doctorat : sciences. Mécanique : Ecully, Ecole centrale de Lyon : 2005. / 97 réf.

Thèse doctorat : Acoustique : Villeurbanne, INSA : 2004. / Titre provenant de l'écran-titre. Bibliogr. p. 161-165.

Thèse de doctorat : sciences. Mécanique : Ecully, Ecole centrale de Lyon : 2005. / Titre provenant de l'écran-titre. 97 réf.