A model of a simple parallel-shaft, spur-gear transmission is presented. The model is developed to simulate dynamic loads in power transmissions. Factors affecting these loads are identified. Included are shaft stiffness and inertia, load and power source inertia, tooth geometry, tooth stiffness, local compliance due to contact stress, load sharing, and friction. Governing differential equations are developed and a solution procedure is outlined. A parameter study of the solutions is presented in Part 2.
A mathematical model for surface fatigue life of gear, pinion, or entire meshing gear train is given. The theory is based on the statistical approach used by Lundberg and Palmgren for rolling-element bearings. Also 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 were compared with test data for a set of AISI 9310 spur gears operating at a maximum Hertz stress of 1.71 × 109 N/m2 (248,000 psi) and 10,000 rpm. The theoretical life predictions were very good when material constants obtained from rolling-element bearing tests were used in the gear life model.
An analysis of tooth profile changes in the transverse plane of circular-cut, spiral-bevel crown gears is presented. The analysis assumes a straight-line profile in the midtransverse plane. The profile variation along the centerline is determined by using expressions for the variation of the spiral angle along the tooth centerline, together with the profile description at the midtransverse plane. It is shown that the tooth surface is a hyperboloid and that significant variations in the pressure angle are possible.
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