Problem $14\mathrm{.}022-$ Fatigue Design in Gears

A commercial enclosed gear drive consists of a $16-$tooth helical pinion

with a $20$ normal pitch angle, a helix angle of $30,$ and a normal

diametral pitch of $6$ teeth $\frac{?}{in}.$ The pinion drives a $48-$tooth gear. The

pinion speed is $300re\frac{v}{m}in$ and the face width is $2$ in $.$ The gears are

grade $1$ steel, through$-$hardened at $200$ Brinell, made to number $6$

quality standards, uncrowned, and are to be accurately and rigidly

mounted. Assume a pinion life of ${10}^8$ cycles and a reliability of $0\mathrm{.}920.$

Use $(Y_N{)}_P=1\mathrm{.}3558({10}^8{)}^{-0\mathrm{.}0178}$ and

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

Problem $14\mathrm{.}022.$b $-$ Factors of Safety

If $5$ hp is to be transmitted corresponding factors of safety for a pinion life of ${10}^8$

cycles and a reliability of $0\mathrm{.}920,$ determine the factor of safety against bending and

pitting stress for the pinion and gear. $($Round the final answers to three decimal

places.$)$

a$.(S_F{)}_P$

b$.(S_F{)}_G$

c$.(S_H{)}_P$

d$.(S_H{)}_G$

The factor of safety against bending and pitting stress for the pinion and gear is as

follows:

a$.(S_F{)}_P=$

b$.(S_F{)}_G=$

c$.(S_H{)}_P=$

d$.(S_H{)}_G=$