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

Liquid cryogenic lubricant

Fluorinated polyethers are suitable lubricants for rolling-element bearings in cryogenic systems. Lubrication effectiveness is comparable to that of super-refined mineral oil lubricants operating at room temperature

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

Sigma-model soliton intersections from exceptional calibrations

A first-order `BPS' equation is obtained for 1/8 supersymmetric intersections of soliton-membranes (lumps) of supersymmetric (4+1)-dimensional massless sigma models, and a special non-singular solution is found that preserves 1/4 supersymmetry. For 4-dimensional hyper-K\"ahler target spaces ($HK_4$) the BPS equation is shown to be the low-energy limit of the equation for a Cayley-calibrated 4-surface in \bE^4\times HK_4. Similar first-order equations are found for stationary intersections of Q-lump-membranes of the massive sigma model, but now generic solutions preserve either 1/8 supersymmetry or no supersymmetry, depending on the time orientation.Comment: 21 pages. Version 3: Minor corrections and one further reference: version published in JHE

Dimethylsulfide (DMS) and Dimethylsulfoniopropionate (DMSP) in Relation to Phytoplankton in the Gulf of Maine

Dimethylsulfide (DMS) and its precursor dimethylsulfoniopropionate (DMSP), in both particulate and dissolved forms, were surveyed during the early spring (March and April) and summer (July) of 1991 in coastal and offshore waters of the Gulf of Maine, USA, along with the hydrography, inorganic nutrients, phytoplankton chlorophyll, and phytoplankton taxonomic composition and abundance. Concentrations as high as 15 nM DMS (in April and July), 208 nM particulate DMSP (in April), and 101 nM dissolved DMSP (in July) were recorded. Total DMSP (dissolved plus particulate) reached 293 nM in a patch of the dinoflagellate Katodinium sp. in April. This is the first report of high DMSP concentrations in temperate waters in early spring associated with any organism other than the prymnesiophyte Phaeocystis pouchetii. There were no correlations between phytoplankton biomass, as measured by chlorophyll a, and DMS, and there were only slight correlations between chlorophyll a and DMSP in either dissolved or particulate form. As previously demonstrated by others, concentrations of intracellular (particulate) DMSP were related more to the presence of specific phytoplankton species rather than to overall phytoplankton biomass. The occurrence of high DMSP and DMS levels in early spring, comparable with or higher than those seen in summer maxima, at a time when bacterial activity is minimal and wind speeds are typically high may result in enhanced air-sea-fluxes of DMS

Vibration signature analysis of multistage gear transmission

An analysis is presented for multistage multimesh gear transmission systems. The analysis predicts the overall system dynamics and the transmissibility to the gear box or the enclosed structure. The modal synthesis approach of the analysis treats the uncoupled lateral/torsional model characteristics of each stage or component independently. The vibration signature analysis evaluates the global dynamics coupling in the system. The method synthesizes the interaction of each modal component or stage with the nonlinear gear mesh dynamics and the modal support geometry characteristics. The analysis simulates transient and steady state vibration events to determine the resulting torque variations, speeds, changes, rotor imbalances, and support gear box motion excitations. A vibration signature analysis examines the overall dynamic characteristics of the system, and the individual model component responses. The gear box vibration analysis also examines the spectral characteristics of the support system