Excitation of g modes in Wolf-Rayet stars by a deep opacity bump

We examine the stability of l=1 and l=2 g modes in a pair of nitrogen-rich Wolf-Rayet stellar models characterized by differing hydrogen abundances. We find that modes with intermediate radial orders are destabilized by a kappa mechanism operating on an opacity bump at an envelope temperature log T ~ 6.25. This `deep opacity bump' is due primarily to L-shell bound-free transitions of iron. Periods of the unstable modes span ~ 11-21 hr in the model containing some hydrogen, and ~ 3-12 hr in the hydrogen-depleted model. Based on the latter finding, we suggest that self-excited g modes may be the source of the 9.8 hr-periodic variation of WR 123 recently reported by Lefevre et al. (2005).Comment: 5 pages, 3 figures, accepted by MNRAS letter

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

An update on the life analysis of spur gears

An analytical method for predicting surface fatigue life of gears was presented. General statistical methods were outlined, showing the application of the general methods to a simple gear mesh. Experimentally determined values for constants in the life equation were given. Comparison of the life theory with test results and AGMA standards was made. Gear geometry pertinent to life calculations was reviewed

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

Experimental and Analytical Load-Life Relation for AISI 9310 Steel Spur Gears

Life tests were conducted at three different loads with three groups of 8.9 cm pitch diameter spur gears made of vacuum arc remelted VAR AISI 9310 steel. Life was found to vary inversely with load to the 4.3 and 5.1 power at the L10 sub and L50 sub life levels, respectively. The Weibull slope varied linearly with maximum Hertz contact stress, having an average value of 2.5. The test data when compared to AGMA standards showed a steeper slope for the load-life diagram

Study of lubricant jet flow phenomena in spur gears

Lubricant jet flow impingement and penetration depth into a gear tooth space were measured at 4920 and 2560 rpm using a 8.89 cm (3.5 inch) pitch diameter 8 pitch spur gear at oil pressures from 70,000 to 410,000 n/sqm (10 psi to 60 psi). A high speed motion picture camera was used with xenon and high speed stroboscopic lights to slow down and stop the motion of the oil jet. An analytical model was developed for the vectorial impingement dept and for the impingement depth with tooth space windage effects included. The windage effects for oil drop size greater than .0076 cm (.003 inches). The analytical impingement dept compared favorably with experimental results above an oil jet pressure of 70,000 n/sqm (10psi). There was further penetration into the tooth space after impingement, but much of this oil was thrown out of the tooth space without further contacting the gear teeth

Dynamic Capacity and Surface Fatigue Life for Spur and Helical Gears

A mathematical model for surface fatigue life of gear, pinion, or entire meshing gear train is given. The theory is based on a previous statistical approach for rolling-element bearings. Equations are presented which give the dynamic capacity of the gear set. The dynamic capacity is the transmitted tangential load which gives a 90 percent probability of survival of the gear set for one million pinion revolutions. The analytical results are compared with test data for a set of AISI 9310 spur gears operating at a maximum Hertz stress of 1.71 billion N/sq m and 10,000 rpm. The theoretical life predictions are shown to be good when material constants obtained from rolling-element bearing tests were used in the gear life model

NASA transmission research and its probable effects on helicopter transmission design

Transmissions studied for application to helicopters in addition to the more conventional geared transmissions include hybrid (traction/gear), bearingless planetary, and split torque transmissions. Research is being performed to establish the validity of analysis and computer codes developed to predict the performance, efficiency, life, and reliability of these transmissions. Results of this research should provide the transmission designer with analytical tools to design for minimum weight and noise with maximum life and efficiency. In addition, the advantages and limitations of drive systems as well as the more conventional systems will be defined

Centrifugal Breakout of Magnetically Confined Line-Driven Stellar Winds

We present 2D MHD simulations of the radiatively driven outflow from a rotating hot star with a dipole magnetic field aligned with the star's rotation axis. We focus primarily on a model with moderately rapid rotation (half the critical value), and also a large magnetic confinement parameter, $\eta_{\ast} \equiv B_{\ast}^2 R_{\ast}^{2} / \dot{M} V_{\infty} = 600$. The magnetic field channels and torques the wind outflow into an equatorial, rigidly rotating disk extending from near the Kepler corotation radius outwards. Even with fine-tuning at lower magnetic confinement, none of the MHD models produce a stable Keplerian disk. Instead, material below the Kepler radius falls back on to the stellar surface, while the strong centrifugal force on material beyond the corotation escape radius stretches the magnetic loops outwards, leading to episodic breakout of mass when the field reconnects. The associated dissipation of magnetic energy heats material to temperatures of nearly $10^{8}$K, high enough to emit hard (several keV) X-rays. Such \emph{centrifugal mass ejection} represents a novel mechanism for driving magnetic reconnection, and seems a very promising basis for modeling X-ray flares recently observed in rotating magnetic Bp stars like $\sigma$ Ori E.Comment: 5 pages, 3 figures, accepted by ApJ