A multi-purpose method for analysis of spur gear tooth loading

A large digitized approach was developed for the static and dynamic load analysis of spur gearing. An iterative procedure was used to calculate directly the "variable-variable" gear mesh stiffness as a function of transmitted load, gear tooth profile errors, gear tooth deflections and gear hub torsional deformation, and position of contacting profile points. The developed approach can be used to analyze the loads, Hertz stresses, and PV for the normal and high contrast ratio gearing, presently the modeling is limited to the condition that for a given gear all teeth have identical spacing and profiles (with or without surface imperfections). Certain types of simulated sinusoidal profile errors and pitting can cause interruptions of the gear mesh stiffness function and, thus, increase the dynamic loads in spur gearing. In addition, a finite element stress and mesh subprogram was developed for future introduction into the main program for calculating the gear tooth bending stresses under dynamic loads

Dynamics of early planetary gear trains

A method to analyze the static and dynamic loads in a planetary gear train was developed. A variable-variable mesh stiffness (VVMS) model was used to simulate the external and internal spur gear mesh behavior, and an equivalent conventional gear train concept was adapted for the dynamic studies. The analysis can be applied either involute or noninvolute spur gearing. By utilizing the equivalent gear train concept, the developed method may be extended for use for all types of epicyclic gearing. The method is incorporated into a computer program so that the static and dynamic behavior of individual components can be examined. Items considered in the analysis are: (1) static and dynamic load sharing among the planets; (2) floating or fixed Sun gear; (3) actual tooth geometry, including errors and modifications; (4) positioning errors of the planet gears; (5) torque variations due to noninvolute gear action. A mathematical model comprised of power source, load, and planetary transmission is used to determine the instantaneous loads to which the components are subjected. It considers fluctuating output torque, elastic behavior in the system, and loss of contact between gear teeth. The dynamic model has nine degrees of freedom resulting in a set of simultaneous second order differential equations with time varying coefficients, which are solved numerically. The computer program was used to determine the effect of manufacturing errors, damping and component stiffness, and transmitted load on dynamic behavior. It is indicated that this methodology offers the designer/analyst a comprehensive tool with which planetary drives may be quickly and effectively evaluated

Vibration in Planetary Gear Systems with Unequal Planet Stiffnesses

An algorithm suitable for a minicomputer was developed for finding the natural frequencies and mode shapes of a planetary gear system which has unequal stiffnesses between the Sun/planet and planet/ring gear meshes. Mode shapes are represented in the form of graphical computer output that illustrates the lateral and rotational motion of the three coaxial gears and the planet gears. This procedure permits the analysis of gear trains utilizing nonuniform mesh conditions and user specified masses, stiffnesses, and boundary conditions. Numerical integration of the equations of motion for planetary gear systems indicates that this algorithm offers an efficient means of predicting operating speeds which may result in high dynamic tooth loads

Propagation of Detonation Waves in Tubes Split from a PDE Thrust Tube

A Pulse Detonation Engine (PDE) combusts a fuel air mixture through detonation. Existing designs require spark plugs in each separate thrust tube to ignite premixed reactants. A single thrust tube could require the spark plug to fire hundreds of times per second for long durations. This paper reports on the use of a continuously propagating detonation wave as both a thrust producer and a single ignition source for a multi-tube system. The goal was to minimize ignition complexity and increase reliability by limiting the number of ignition sources. The work includes a systematic investigation of single tube geometric effects on detonations. These results were subsequently used to further examine conditions for splitting detonations i.e. the division of a detonation wave into two separate detonation waves. Finally a dual thrust tube system was built and tested that successfully employed a single spark to initiate detonation in separate thrust tubes

Dynamic effects of internal spur gear drives

Static analysis, dynamic analysis, and computer programs are discussed. Spur gear formulae and involute profile development and deflection are also discussed

Gamma radiation survey of the LDEF spacecraft

The retrieval of the Long Duration Exposure Facility spacecraft in January 1990 after nearly six years in orbit offered a unique opportunity to study the long term buildup of induced radioactivity in the variety of materials on board. We conducted the first complete gamma-ray survey of a large spacecraft on LDEF shortly after its return to earth. A surprising observation was the Be-7 activity which was seen primarily on the leading edge of the satellite, implying that it was picked up by LDEF in orbit. This is the first known evidence for accretion of a radioactive isotope onto an orbiting spacecraft. Other isotopes observed during the survey, the strongest being Na-22, are all attributed to activation of spacecraft components. Be-7 is a spallation product of cosmic rays on nitrogen and oxygen in the upper atmosphere. However, the observed density is much greater than expected due to cosmic-ray production in situ. This implies transport of Be-7 from much lower altitudes up to the LDEF orbit

The nature of the dense core population in the pipe nebula: core and cloud kinematics from C18O observations

We present molecular-line observations of 94 dark cloud cores identified in the Pipe nebula through near-IR extinction mapping. Using the Arizona Radio Observatory 12m telescope, we obtained spectra of these cores in the J=1-0 transition of C18O. We use the measured core parameters, i.e., antenna temperature, linewidth, radial velocity, radius and mass, to explore the internal kinematics of these cores as well as their radial motions through the larger molecular cloud. We find that the vast majority of the dark extinction cores are true cloud cores rather than the superposition of unrelated filaments. While we identify no significant correlations between the core's internal gas motions and the cores' other physical parameters, we identify spatially correlated radial velocity variations that outline two main kinematic components of the cloud. The largest is a 15pc long filament that is surprisingly narrow both in spatial dimensions and in radial velocity. Beginning in the Stem of the Pipe, this filament displays uniformly small C18O linewidths (dv~0.4kms-1) as well as core to core motions only slightly in excess of the gas sound speed. The second component outlines what appears to be part of a large (2pc; 1000 solar mass) ring-like structure. Cores associated with this component display both larger linewidths and core to core motions than in the main cloud. The Pipe Molecular Ring may represent a primordial structure related to the formation of this cloud.Comment: Accepted to ApJ. 14 pages, 11 figures. Complete table at end of documen

The Luminosity & Mass Function of the Trapezium Cluster: From B stars to the Deuterium Burning Limit

We use the results of a new, multi-epoch, multi-wavelength, near-infrared census of the Trapezium Cluster in Orion to construct and to analyze the structure of its infrared (K band) luminosity function. Specifically, we employ an improved set of model luminosity functions to derive this cluster's underlying Initial Mass Function (IMF) across the entire range of mass from OB stars to sub-stellar objects down to near the deuterium burning limit. We derive an IMF for the Trapezium Cluster that rises with decreasing mass, having a Salpeter-like IMF slope until near ~0.6 M_sun where the IMF flattens and forms a broad peak extending to the hydrogen burning limit, below which the IMF declines into the sub-stellar regime. Independent of the details, we find that sub-stellar objects account for no more than ~22% of the total number of likely cluster members. Further, the sub-stellar Trapezium IMF breaks from a steady power-law decline and forms a significant secondary peak at the lowest masses (10-20 times the mass of Jupiter). This secondary peak may contain as many as \~30% of the sub-stellar objects in the cluster. Below this sub-stellar IMF peak, our KLF modeling requires a subsequent sharp decline toward the planetary mass regime. Lastly, we investigate the robustness of pre-main sequence luminosity evolution as predicted by current evolutionary models, and we discuss possible origins for the IMF of brown dwarfs.Comment: 74 pages, 30 figures, AASTeX5.0. To be published in the 01 July 2002 ApJ. For color version of figure 1 and online data table see http://www.astro.ufl.edu/~muench/PUB/publications.htm

The X-ray Size-Temperature Relation for Intermediate Redshift Galaxy Clusters

We present the first measurements of the X-ray size-temperature (ST) relation in intermediate redshift (z~0.30) galaxy clusters. We interpret the local ST relation (z~0.06) in terms of underlying scaling relations in the cluster dark matter properties, and then we use standard models for the redshift evolution of those dark matter properties to show that the ST relation does not evolve with redshift. We then use ROSAT HRI observations of 11 clusters to examine the intermediate redshift ST relation; for currently favored cosmological parameters, the intermediate redshift ST relation is consistent with that of local clusters. Finally, we use the ST relation and our evolution model to measure angular diameter distances; with these 11 distances we evaluate constraints on Omega_M and Omega_L which are consistent with those derived from studies of Type Ia supernovae. The data rule out a model with Omega_M=1 and Omega_L=0 with 2.5 sigma confidence. When limited to models where Omega_M+Omega_L=1, these data are inconsistent with Omega_M=1 with 3 sigma confidence.Comment: ApJ: submitted April 7, accepted June 28, to appear Dec 1 (vol 544