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A 24-tooth pinion with a diametral pitch of 6 teeth per inch drives a 60-tooth gear in a high precision machine. The gears have face width of 3 inches and a pressure angle of 20 degree. Pinion is fabricated from AISI 4340 steel (Su = 108 ksi, Sy = 68 ksi, and Brinell hardness number HB= 217); while gear is fabricated from AISI 4130 steel (Su = 81 ksi, Sy = 52 ksi, and Brinell hardness number HB= 156). If the gear set operates at a constant pitch line velocity of 1000 feet per minute, using a reliability of 99% and a safety factor of 3, estimate the maximum allowable horsepower that can be transmitted for infinite fatigue life, based on the following conditions: (a) gear tooth bending fatigue failure; and (b) gear tooth surface fatigue failure. Assume i). The source of power is uniform and there is a moderate shock in the machine. ii). The mountings are accurate. iii). There is no load sharing between the gear teeth.