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

A spurgearset has $17$ teeth on the pinion and $51$ teeth on the gean The pressure angle is $20$ and the overload factor

$K_0=1$ 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

with Brinell hardnesses of $232$ core and case of both gears. For a design factor of $2\mathrm{.}500,$ 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 $14\mathrm{.}023.$a $-$ Parameters for a Pinion

Determine the value of each of the following:

a$.$ The stress$-$cycle factor, pinion. $(Y_N{)}_P$

b$.$ The pitch$-$line velocity, $V$

c$.$ The allowable bending stress on the pinion, ${}_{\text{a}\text{l}\text{l}}$

d$.$ The dynamic factor $K_v$

e$.$ The pinion size factor $KSP$

f$.$ The load$-$distribution factor, $K_m$

The design factor of safety and the factor of safety for bending are the same. Assume that the size factor for the pinion is $1.$

The stress$-$cycle factor, pinion. $(Y_N{)}_P,$ is $0\mathrm{.}929.($Round the final answer to three decimal places.$)$

The pitch$-$line velocity, $V.$ is $1482\mathrm{.}5f\frac{t}{m}in.$

The allowable bending stresson the pinion, ${}_{\text{a}\text{l}\text{l}},$ is $p$ si$.($Round the final answer to the nearest whole number.$)$

The dynamic factor $Kv$ is $($Round the final answer to three decimal places.$)$

The pinion size factor, $K_{SP}$ Tis $($Round the final answer to three decimal places.$)$

The load$-$distribution factor, $K_m,$ is $1300.($Round the final answer to three decimal places.$)$