Problem $14\mathrm{.}023-$ Fatigue Design in Gears

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 $2,000re\frac{v}{m}in$ 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

through$-$hardened steel, grade $1,$ with Brinell hardnesses of $232$ core

and case of both gears. For a design factor of $2\mathrm{.}200,$ rate the gearset

for these conditions using the AGMA method. Use

$(Y_N{)}_P=1\mathrm{.}6831({10}^8{)}^{-0\mathrm{.}0323}$ and $(Z_N{)}_P=1\mathrm{.}4488({10}^8{)}^{-0\mathrm{.}023}$

Problem $14\mathrm{.}023.$c $-$ Contact Stress Factors and Power Rating

Determine the value of the transmitted load, $W^t,$ the stress$-$cycle factor for pitting

resistance $($pinion$),$ the geometry factor for pitting resistance, the allowable contact

stress, and the achievable power based on the allowable pitting stress.

The stress$-$cycle factor for pitting resistance $($pinion$),Z_N,$ is

$($Round the

final answer to three decimal places.$)$

The geometry factor for pitting resistance, $1,$ is

$($Round the final answer to

four decimal places.$)$

The allowable contact stress, ${}_c,$ all, is

psi.

The value of the transmitted load, $W_t,$ is

Ibf.

The achievable power based on the allowable pitting stress, $H,$ is

hp$.$

$($Round the final answer to three decimal places.$)$