Question $4($clutches$)$

A clutch has $4$ plates on the driving shaft and $3$ plates on the driven shaft. Each plate has an inside diameter of $130$ mm and an outside diameter of $200$ mm $.$ When the clutch is new it can transmit $33$ kW at $\backslash (4500\backslash$mathrm$\{$r$\}/\backslash$mathrm$\{$min$\}\backslash ).$ Coefficient of friction can be considered as $0\mathrm{.}25.$

i$)$ Determine the axial spring load pressing the plates together

$($Hint: $\backslash ($ N$=\backslash$sum $\backslash )$ Plates $-1\backslash ()\backslash )$

If there are six $(6)$ springs, each with a stiffness of $\backslash (16\backslash$mathrm$\{$kN$\}/\backslash$mathrm$\{$m$\}\backslash ),$ and each of the contact surfaces has worn by $0\mathrm{.}1$ mm $,$

ii$)$ Calculate the maximum torque that can be transmitted at the same speed. Coefficient of friction can be considered to be $0\mathrm{.}25.$