The optimal design of standard gearsets

A design procedure for sizing standard involute spur gearsets is presented. The procedure is applied to find the optimal design for two examples - an external gear mesh with a ratio of 5:1 and an internal gear mesh with a ratio of 5:1. In the procedure, the gear mesh is designed to minimize the center distance for a given gear ratio, pressure angle, pinion torque, and allowable tooth strengths. From the methodology presented, a design space may be formulated for either external gear contact or for internal contact. The design space includes kinematics considerations of involute interference, tip fouling, and contact ratio. Also included are design constraints based on bending fatigue in the pinion fillet and Hertzian contact pressure in the full load region and at the gear tip where scoring is possible. This design space is two dimensional, giving the gear mesh center distance as a function of diametral pitch and the number of pinion teeth. The constraint equations were identified for kinematic interference, fillet bending fatigue, pitting fatigue, and scoring pressure, which define the optimal design space for a given gear design. The locus of equal size optimum designs was identified as the straight line through the origin which has the least slope in the design region

The optimal design of involute gear teeth with unequal addenda

The design of a gear mesh is treated with the objective of minimizing the gear size for a given gear ratio, pinion torque, pressure angle, and allowable tooth lengths. Tooth strengths considered include scoring, pitting fatigue, and bending fatigue. Kinematic involute interference is avoided. The design variation on standard spur gear teeth called the long and short addendum system, is considered. In this system the mesh center distance and pressure angle are maintained as is the ability to manufacture the teeth with standard tooling. However, the pinion and gear tooth proportions are altered in order to obtain fewer teeth numbers for the same ratio as standard gears without kinematic involute interference. The effect of this nonstandard gearing geometry with on tooth strengths and gear mesh size are studied. For a 2:1 gearing ratio, the optimal nonstandard gear design is compared with the optimal standard gear design

Stability of continuously pumped atom lasers

A multimode model of a continuously pumped atom laser is shown to be unstable below a critical value of the scattering length. Above the critical scattering length, the atom laser reaches a steady state, the stability of which increases with pumping. Below this limit the laser does not reach a steady state. This instability results from the competition between gain and loss for the excited states of the lasing mode. It will determine a fundamental limit for the linewidth of an atom laser beam.Comment: 4 page

A method to study complex systems of mesons in Lattice QCD

Finite density systems can be explored with Lattice QCD through the calculation of multi-hadron correlation functions. Recently, systems with up to 12 $\pi^+$'s or $K^+$'s have been studied to determine the 3-$\pi^+$ and 3-$K^+$ interactions, and the corresponding chemical potentials have been determined as a function of density. We derive recursion relations between correlation functions that allow this work to be extended to systems of arbitrary numbers of mesons and to systems containing many different types of mesons, such as $\pi^+$'s, $K^+$'s, $\bar{D}^0$'s and $B^+$'s. These relations allow for the study of finite-density systems in arbitrary volumes, and for the study of high-density systems.Comment: JLAB-THY-10-1121, NT@UW-10-01, journal versio

A Survey of O VI, C III, and H I in Highly Ionized High-Velocity Clouds

(ABRIDGED) We present a Far-Ultraviolet Spectroscopic Explorer survey of highly ionized high-velocity clouds (HVCs) in 66 extragalactic sight lines. We find a total of 63 high-velocity O VI absorbers, 16 with 21 cm-emitting H I counterparts and 47 ``highly ionized'' absorbers without 21 cm emission. 11 of these high-velocity O VI absorbers are positive-velocity wings (broad O VI features extending asymmetrically to velocities of up to 300 km/s). The highly ionized HVC population is characterized by =38+/-10 km/s and <log N_a(O VI)>=13.83+/-0.36. We find that 81% (30/37) of high-velocity O VI absorbers have clear accompanying C III absorption, and 76% (29/38) have accompanying H I absorption in the Lyman series. The lower average width of the high-velocity H I absorbers implies the H I lines arise in a separate, lower temperature phase than the O VI. We find that the shape of the wing profiles is well reproduced by a radiatively cooling, vertical outflow. However, the outflow has to be patchy and out of ionization equilibrium. An alternative model, consistent with the observations, is one where the highly ionized HVCs represent the low N(H I) tail of the HVC population, with the O VI formed at the interfaces around the embedded H I cores. Though we cannot rule out a Local Group explanation, we favor a Galactic origin. This is based on the recent evidence that both H I HVCs and the million-degree gas detected in X-ray absorption are Galactic phenomena. Since the highly ionized HVCs appear to trace the interface between these two Galactic phases, it follows that highly ionized HVCs are Galactic themselves. However, the non-detection of high-velocity O VI in halo star spectra implies that any Galactic high-velocity O VI exists at z-distances beyond a few kpc.Comment: 36 pages, 14 figures (3 in color), accepted to ApJS. Some figures downgraded to limit file siz

Absorption Line Studies in the Halo

Significant progress has been made over the last few years to explore the gaseous halo of the Milky Way by way of absorption spectroscopy. I review recent results on absorption line studies in the halo using various instruments, such as the Far Ultraviolet Spectroscopic Explorer, the Space Telescope Imaging Spectrograph, and others. The new studies imply that the infall of low-metallicity gas, the interaction with the Magellanic Clouds, and the Galactic Fountain are responsible for the phenomenon of the intermediate- and high-velocity clouds in the halo. New measurements of highly-ionized gas in the vicinity of the Milky Way indicate that these clouds are embedded in a corona of hot gas that extends deep into the intergalactic space.Comment: 7 pages, 1 figure; Invited review at the conference "How does the Galaxy work ?", Granada/Spain, June 200