It was found that the gear pair described in Problem $72$ wore out when driven by a $25-$hp engine. Propose a redesign that would be expected to give $15000$ hr life under the conditions described

problem $72$:

Determine the power$-$transmitting capacity for a pair of spur gears having $20,$ full$-$depth teeth, a diametral pitch of $6,35$ teeth in the pinion, $100$ teeth in the gear, a face width of $2\mathrm{.}00$ in$,$ and an AGMA quality class of A$11.$ A gasoline engine drives the pinion at $1500$ rpm$.$ The gear drives a conveyor for crushed rock in a quarry. The pinion is made from SAE $1040$ WQT $800.$ The gear is made from gray cast iron, ASTM A$48-83,$ class $30.$ Design for $15000$ hr life.