Q$4$ a$)$ A pair of Helical Gear is used to transmit $10kW$ power from a multiple clutch to a constant mesh gear box. The clutch rotates at $7200rpm,$ which further reduce the speed to $2400mm.$ Assume number of teeth on pinion as $20,$ pressure angle as $20$ and helix angle as $25.$ Desigr the gear. Material for both pinion and gear is $C_8.$ Surface hardness is $300$ BHN for pinion. ${}_{ut}=600$MPa,FOS$=2,Cs=1,5.$ For initial design, consider a velocity factor as $Cv=\frac{5\mathrm{.}6}{5\mathrm{.}6+\sqrt[\phantom{2}]{7}}.$

The gear and pinion are nude of Grade $4$ for which following data is to be used. Take: $e=(3\mathrm{.}2+0\mathrm{.}25)m$ and $=m_n+0\mathrm{.}25\sqrt[\phantom{2}]{d}C=11,400MPC$