Problem $1$: $P=15kW,n_p=1460rpm,z_p=18,C-60$ steel, ${}_u=750$MPa,$=15,{}_n=20,C_s=1\mathrm{.}5,$ fos$=3,$ and $\frac{b}{m}=x=12.$ Find out standardized module $(mm),$ number of teeth and pitch circle diameter, face width, blank diameter and circular pitch. Consider it is a single stage helical gear drive.

Problem $2$: $P=35kW,n_p=1450rpm,n_g=290rpm,z_p=18.$ For gear material: ${}_u=940$MPa,$={15}^0,{}_n=20,C_s=1\mathrm{.}5,$ fos $=3,$ and $\frac{b}{m}=x=12.$ Find out $($a$)$ normal module $($mm$),($b$)$ face width, $($c$)$ centre distance for the helical gear.