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Required Information

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 dlametral

pitch is $4$ teeth$/$in and the face width is $3\mathrm{.}25$ in $.$ The pinion shaft speed is $1,600re\frac{v}{m}in.$ The life goal of $5-$year $24-$hour$-$

per$-$day service is about $3({10}^9)$ pinion revolutions. The absolute value of the pitch varlation 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 reliablity 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 $14\mathrm{.}025.$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 achlevable 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, $l,$ is

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

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

sII.

The value of the transmitted load, $W^t,$ is

lbf$.$

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

hp$.$