Life analysis of helical gear sets using Lundberg-Palmgren theory

A mathematical model is developed for surface fatigue life of helical gears. The expected fatigue life of a pinion, gear, or gear set may be calculated from the model. An equation for the dynamic capacity of a gear set was also derived. 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 equations, when simplified by setting the helix angle to zero, reduce to the results which were previously developed for spur gears. A sample calculation is given which illustrates the use of the new fatigue life model

Some limitations in applying classical EHD film-thickness formulae to a high-speed bearing

Elastohydrodynamic film thickness was measured for a 20 mm ball bearing using the capacitance technique. The bearing was thrust loaded to 90, 448, and 778 N. The corresponding maximum stresses on the inner race were 1.28, 2.09, and 2.45 GPa. Test speeds ranged from 400 to 14,000 rpm. Film thickness measurements were taken with four different lubricants: (1) synthetic paraffinic; (2) synthetic paraffinic with additives; (3) neopentylpolyol (tetra) ester; and (4) synthetic cycloaliphatic hydrocarbon traction fluid. The test bearing was mist lubricated. Test temperatures were 300, 338, and 393 K. The measured results were compared to theoretical predictions and are presented

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

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

Life analysis of restored and refurbished bearings

An analysis of the potential life of refurbished and restored bearings was performed. The sensitivity of 10-percent life and mean-time-between-failure to the effects of cumulative fatigue damage and the amount of stressed volume removed in the restoration process were examined. A modified Lundberg-Palmgren theory was used to predict that the expected 10-percent life of a restored bearing, which is dependent on the previous service time and the volume of material removed from the race surfaces, can be between 74 and 100 percent of the new bearing life. Using renewal theory, it is found that the mean time between failure ranged from 90 to 100 percent of that for a new bearing

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

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

Fatigue life analysis for traction drives with application to a toroidal type geometry

A contact fatigue life analysis for traction drives was developed which was based on a modified Lundberg-Palmgren theory. The analysis was used to predict life for a cone-roller toroidal traction drive. A 90-percent probability of survival was assumed for the calculated life. Parametric results were presented for life and Hertz contact stress as a function of load, drive ratio, and size. A design study was also performed. The results were compared to previously published work for the dual cavity toroidal drive as applied to a typical compact passenger vehicle drive train. For a representative duty cycle condition wherein the engine delivers 29 horsepower at 2000 rpm with the vehicle moving at 48.3 km/hr (30 mph) the drive life was calculated to be 19,200 km (11 900 miles)

Space Station/Shuttle Orbiter dynamics during docking

Mathematical models of a reference space station configuration (Power Tower) and a Space Shuttle Orbiter are developed and used to study the dynamic behavior of the Space Station/Orbiter system just prior to and subsequent to an impulsive docking of the two spacecraft. The physical model of the space station is a collection of rigid and flexible bodies. The orbiter is modeled as a rigid body. An algorithm developed for use in digitally simulating the dynamics of the system is described and results of its application are presented

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