Problem $14\mathrm{.}025-$ Fatigue Design in Gears

A speed$-$reducer has $20$ full$-$depth teeth, and the single$-$reduction

spur$-$gear gearset has $22$ and $60$ teeth. The diametral pitch is $4$

teeth$/$in and the face width is $3\mathrm{.}25$ in $.$ The pinion shaft speed is

$1,650re\frac{v}{m}in.$ The life goal of $5-$year $24-$hour$-$per$-$day service is about

$3({10}^9)$ pinion revolutions. The absolute value of the pitch variation is

such that the quality number is $6.$ The materials are $4340$ through$-$

hardened grade $1$ steels, heat$-$treated to $250$ Brinell, core and case,

both gears. The load is moderate shock and the power is smooth. For

a reliability of $0\mathrm{.}990,$ rate the speed reducer for power. Assume that

the gear is a commercial enclosed unit and is uncrowned. Use

$(Y_N{)}_P=1\mathrm{.}6831(3({10}^9){)}^{-0\mathrm{.}0323}$ and

$(Z_N{)}_P=1\mathrm{.}4488(3({10}^9){)}^{-0\mathrm{.}023}$

Problem $14\mathrm{.}025.$b $-$ Transmitted Load and Bending Stress

Determine the value of the transmitted load,

$W^t,$ and the achievable power based on the allowable bending stress calculated in

the previous question.

The value of the transmitted load is

Ibf.

The achievable power based on the allowable bending stress is

$|$hp$.$