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

Sizing criterial for traction drives

A simplified traction drive fatigue analysis which was derived from the Lundberg-Palmgren theory is measured and the effects of rotational speed, multiplicity of contacts, and variation in the available traction coefficient on traction drive system life, size, and power capacity was investigated. Simplified equations are provided for determining the 90% survival life rating of steel traction drive contacts of arbitrary geometry. References to life modifying factors for material, lubrication, and traction will be made

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

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

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

Simplified fatigue life analysis for traction drive contacts

A simplified fatigue life analysis for traction drive contacts of arbitrary geometry is presented. The analysis is based on the Lundberg-Palmgren theory used for rolling-element bearings. The effects of torque, element size, speed, contact ellipse ratio, and the influence of traction coefficient are shown. The analysis shows that within the limits of the available traction coefficient, traction contacts exhibit longest life at high speeds. Multiple, load-sharing roller arrangements have an advantageous effect on system life, torque capacity, power-to-weight ratio and size

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

OH-58 helicopter transmission failure analysis

The OH-58 main transmission gearbox was run at varying output torques, speeds, and oil cooling rates. The gearbox was subsequently run to destruction by draining the oil from the gearbox while operating at a speed of 6200 revs per minute and 36,000 inch-pounds output torque. Primary cause of gearbox failure was overheating and melting of the planet bearing aluminum cages. Complete failure of the gearbox occurred in 28 1/2 minutes after the oil pressure dropped to zero. The alternating and maximum stresses in the gearbox top case were approximately 10 percent of the endurance limit for the material. Deflection of the bevel gear at 67000 inch-pounds output torque indicate a marginal stiffness for the bevel gear supporting system

Gearing

Gearing technology in its modern form has a history of only 100 years. However, the earliest form of gearing can probably be traced back to fourth century B.C. Greece. Current gear practice and recent advances in the technology are drawn together. The history of gearing is reviewed briefly in the Introduction. Subsequent sections describe types of gearing and their geometry, processing, and manufacture. Both conventional and more recent methods of determining gear stress and deflections are considered. The subjects of life prediction and lubrication are additions to the literature. New and more complete methods of power loss predictions as well as an optimum design of spur gear meshes are described. Conventional and new types of power transmission systems are presented