Q$3.$ A petrol engine inlet valve is spring$-$loaded. The valve opens at $360$ N closes at $220$ N $,$ while the corresponding lengths of springs when it is open is $41$ mm and when it is closed is $49$ mm $.$ The maximum inside diameter of the spring is $25$ mm $.$ Assume the shear yield strength in steel as $400$ MPa $,$ shear ultimate strength is $643\mathrm{.}2$ MPa and shear modulus as $\backslash (80\backslash$mathrm$\{$kN$\}/\backslash$mathrm$\{$mm$\}^\{2\}\backslash ).$ Assume the helical compression spring has squared and ground ends, minimum factor of safety, $\backslash (\backslash$boldsymbol$\{$n$\}=1\mathrm{.}5\backslash )$ and spring index, $\backslash ($ C$=5\backslash ).$ Determine for shot$-$peened wires

a$)$ initial compression

$[2$ Marks$]$

b$)$ coil diameter $\backslash ($ d $\backslash )$ using Zimmerli data, Goodman theory and Langer theory. Select standard size of Washburn $\backslash$& Moen wire

$[7$ Marks$]$

c$)$ helical diameter $\backslash ($ D $\backslash )$

$[1$ Marks$]$

d$)$ number of actual turns, $\backslash ($ N$\_\{$a$\}\backslash )$ and total turns, $\backslash ($ N$\_\{$t$\}\backslash )$

$[2$ Marks$]$

e$)$ free length

$[2$ Marks$]$