$14-23$ A spur gearset has $17$ teeth on the pinion and $51$ teeth on the gear. The pressure angle is $20$ and the overload factor $K_o=1.$ The diametral pitch is $6$ teeth$/$in and the face width is $2$ in $.$ The pinion speed is $1120re\frac{v}{m}in$ and its cycle life is to be ${10}^8$ revolutions at a reliability $R=0\mathrm{.}99.$ The quality number is $5.$ The material is a throughhardened steel, grade $1,$ with Brinell hardnesses of $232$ core and case of both gears. For a design factor of $2,$ rate the gearset for these conditions using the AGMA method.