Problem $2(55$ pts$)$

In the gear reduction unit shown in Fig. $2,$ gear A receives power from another gear with the transmitted force $F_A$ applied at the $20$ pressure angle. The power is transmitted through the shaft and delivered through gear $B$ through a transmitted force $F_B$ at the pressure angle of $25.$ The unit has been analyzed for static loading condition by the manufacturer and the critical stresses are reported as $=300\mathrm{.}0$MPa and $=100\mathrm{.}0$MPa. The shaft is made of cold$-$drawn AISI $1018$ steel. The unit is designed to operate at $300C$ with $90\%$ reliability.

a$)$ Determine the alternative and mean stresses. $(10$ pts$)$

b$)$ Determine equivalent mean and alternating stresses $(10$ pts $)$

c$)$ Determine marine factors. $(10$ pts$)$

d$)$ Find endurance limit $(5$ pts$)$

e$)$ Determine the safety factor using yield line. $(5$ pts$)$

f$)$ Using Goodman criterion, determine the minimum factor of safety for fatigue based on infinite life. $(5$ pts$)$

g$)$ If infinite life is infinite life is predicted $($safety factor is less than $1),$ then estimate the number of cycles to failure. $(10$ pts$)$