The Best and Worst Feed Directions in Milling Chatter

In this paper, a 2D milling stability analysis is reduced to a 1D problem by performing a modal analysis on an oriented transfer function matrix under a given feed direction. The oriented frequency response function (FRF) of the oriented transfer matrix are obtained as explicit functions of the radial immersion and feed direction. At different feed directions in most of the lower immersion range, the process is demonstrated to be the least stable when the modal direction of the directional matrix is oriented at 45° and 225° and in the −45° and 135°, yielding a local minimum critical depth of cut, regardless of up or down cuts. At higher immersion, the worst critical depth of cut is dominated by the lower frequency mode, and becomes a constant, independent of the feed direction at full cut. When the modal direction is oriented along the x or y axes, the process has a local maximum critical depth of cut.

Thermoacoustic Oscillations in Multipath Heated Fuel Circuits

Pressure oscillations in supercritical jet-A fuel flowing through four parallel heated tubes connected to common manifolds have been observed in this study. Tests were performed with fuel inlet temperatures ranging from 70 °F to 700 °F, and fuel pressures ranging from 360 to 700 psi. Total fuel flow rate ranged from 5 to 55 lb/h. Tubes were heated by blowing 800–950 °F nitrogen over them. Acoustic-mode oscillations, typically ranging from 100 to 500 Hz, occurred only when a large temperature gradient was created inside the heated fuel tubes. Pressure oscillation amplitudes ranged from 0.1 to 1.0 psi. Oscillations at the inlet and outlet manifolds that were caused by a mode with the characteristic length of a single fuel tube were separated by a phase lag that was a function of the manifold cross-passage diameter. A lower frequency mode was also observed, which had a characteristic length based on the summed lengths of a single fuel tube and a single manifold passage. An acoustic simulation using the comsol acoustics module was performed to predict frequencies based on geometry and flow conditions of the experiment.

Effects of Ions on the Propagation of Langmuir Oscillations in Cold Quantum Electron-Ion Plasmas

The effects of ions on the propagation of Langmuir oscillations are investigated in cold quantum electron-ion plasmas. It is shown that the higher and lower frequency modes of the Langmuir oscillations would propagate in cold quantum plasmas according to the effects of ions. It is also shown that these two propagation modes merge into one single propagation mode if the contribution of ions is neglected. It is found that the quantum effect enhances the phase and group velocities of the higher frequency mode of the propagation. In addition, it is shown that the phase velocity of the lower frequency mode is saturated with increasing the quantum wavelength and further that the group velocity of the lower frequency mode has a maximum position in the domains of the wave number and quantum wavelength.

Structural Dynamics and Response of Roof Tiles Under Wind Loading: Effect of Vibration on Scattering

This study has investigated the nature and source of the vibrating and scattering behavior of roof tiles with the aim of providing a better insight to the mechanism. The 100 roof tiles were set up on 10 lines and 10 lows on the pitched roof in the downstream of the flow from the wind tunnel. These experiments were followed by series of tests where the slope angle of the roof tiles was changed. The vibrations of the roof tiles were simultaneously measured by the two accelerometers, and the motions of the vibration and scattering were observed by the high-speed video camera. The frequency response function and coherence function of roof tile were measured by impact hammer test under no flow condition. Just before scattering of the roof tiles, both vibrations of higher frequency mode and vibrations of lower frequency mode appeared simultaneously in roof tiles. The values of the higher frequencies were corresponding to the values of resonant frequencies of the roof tiles. It was thought that the scattering of roof tiles was influenced by the vibration of the lower frequency mode. The frequencies of the vibration were measured by the high-speed video camera system. The values of the lower frequencies were 10 Hz ∼ 20 Hz. The mechanism of scattering of roof tiles could be understood by means of the information from the accelerations and the images of roof tiles.

Self Excited Multi-Mode Vibrations of Aircraft Brakes With Nonlinear Negative Damping

This paper shows how vibratory modes of a brake/landing gear system can interact strongly when there is nonlinear negative damping being generated at the brake’s friction interface. The approach first considers the normal modes of the linearized system. The nonlinear frictional interface force is then added to the modal equations of motion. The energy added to each of the modes, per cycle of the lowest frequency mode, is then determined. From these functions an amplitude path map and limit cycle amplitudes are determined. Multiple limit cycles are found to exist for certain combinations of damping. Amplitude modulation of the higher-frequency mode at multiples of the lower frequency mode is explained. Time solutions of the motion are obtained and compared to computer simulation results. Results compare closely. The method yields a global view of the stability and modal interactions caused by nonlinear negative damping at the brake’s friction interface.

Phonon Dispersion in Suspensions of Hard Sphere Colloids*

ABSTRACTWe use Brillouin scattering to measure the dispersion of the propagating acoustic modes in a suspension of hard sphere colloids. We find two distinct longitudinal modes when the sound wavelength becomes comparable to the sphere diameter. The higher frequency mode has a velocity intermediate between those of the pure solid and the pure liquid phases, and its velocity increases with increasing volume fraction, ø. The lower frequency mode has a velocity less than the velocities in either the pure fluid or pure solid phases, and its velocity decreases with increasing ø. We interpret the higher frequency mode as a compressional wave which propagates through both the solid and the fluid, as expected for a composite medium. The lower frequency mode has not been observed before, and is interpreted as a surface acoustic mode, which propagates between adjacent spheres through a decaying portion of the excitation in the fluid.

A note on the damping and oscillations of a fluid drop moving in another fluid

The oscillations of a drop moving in another fluid medium have been studied at low values of Reynolds number and Weber number by taking into consideration the shape of the drop and the viscosities of the two phases in addition to the interfacial tension. The deformation of the drop modifies the Lamb's expression for frequency by including a correction term while the viscous effects split the frequency into a pair of frequencies—one lower and the other higher than Lamb's. The lower frequency mode has ample experimental support while the higher frequency mode has also been observed. The two modes almost merge with Lamb's frequency for the asymptotic cases of a drop in free space or a bubble in a dense viscous fluid but the splitting becomes large when the two fluids have similar properties. Instead of oscillations, aperiodic damping modes are found to occur in drops with sizes smaller than a critical size ($\sim\hat{\rho}\hat{\nu}^2/T $). With the help of these calculations, many of the available experimental results are analyzed and discussed.