1. An existing parallel-shaft single-reduction spur gear speed reducer is made up of a 21-tooth 8-pitch input pinion driving a 73-tooth gear mounted on the output shaft. The center distance between pinion and gear is 5.875 inches. The input shaft is driven by a 15-hp, 1725-rpm electric motor operating steadily at full rated capacity. To reduce vibration and noise, it is desired to substitute a helical gearset that can operate on the same center distance and provide approximately the same angular velocity ratio as the existing spur gearset. Study this request and propose a helical gearset that can perform the function satisfactorily at a reliability level of 99 percent for a very long lifetime. Assume that the helical gears will be cut by an 8-pitch 20 full-depth involute hob. The probable material is through-hardened Grade 1 steel with a hardness of BHN 350. Determine the following:

a. Using the spur gear data as a starting point, make a preliminary design proposal for a pair of helical gears with the same center distance and approximately the same angular velocity ratio as the existing spur gear set. Specifically, determine a combination of transverse diametral pitch, number of teeth on the pinion, and number of 698 Chapter 15 / Gears and Systems of Gears teeth on the mating gear that will satisfy specifications on-center distance and angular velocity ratio.

b. Determine the helix angle. Does it lie within the recommended range of values?

 c. Determine the pitch diameter for the pinion and the gear.

 d. Determine the nominal outside diameter of the pinion and the gear.

 e. Estimate an appropriate face width for the helical gear pair.

f. Calculate the existing safety factor for the tentatively selected helical gear pair, based on tooth bending fatigue as a potential failure mode.

 g. Calculate the existing safety factor for the tentatively selected helical gear pair, based on surface fatigue pitting wear as a potential failure mode.

h. Comment on the governing safety factor.