The accessory drive unit of a large aircraft engine involves an identical pair of 20° full-depth spur gears. The gears have 50 teeth and rotate together at 5000 rpm. The diametral pitch is 12 and the face width 1.5 in. The gears are made of alloy steel, casehardened to 62Rc (680 Bhn). Although the case extends throughout the fillet, it is conservatively decided to use the core hardness of 500 Bhn for calculating bending fatigue strength. The tooth profiles are finished with a fine-grinding operation that gives a degree of precision justifying the use of curve A of Figure 15.24 and the assumption that teeth share the load. The loading involves only very mild shock, justifying the use of Ko = 1.1.

(a). Estimate the horsepower that can be transmitted with 99% reliability, based on tooth bending fatigue.

(b). Estimate the horsepower that can be transmitted for 109 cycles with 90% reliability, based on surface fatigue.