a$)$ Design a dry multi$-$disc flat plate clutch to have a torque capacity, when well worn in$,$ of $400$ Nr

$(3001b-$ft$).$ Assume:

$-$a frictional coefficient of $0\mathrm{.}27$

a maximum peripheral $($tangential$)$ velocity of $30\frac{m}{s}(100f\frac{t}{sec})$ at the clutch's top speed of

$3000$ revimin.

Note: this is a design problem, with many correct answers, You will have to make one or more

assumptions, such as the ratio of inner$-$to$-$outer diameters. Work in either S$.$I, or English units.

Required answers:

$-$inner and outer diameters

number of active clutch surfaces

maximum clutch pressure when new, and when well worn in

the axial force required.

b$)$ The torque capacity changes as the clutch wears in$.$ Find the minimum torque the laboratory

testers should expect, when testing a new clutch.

c$)$ This clutch is designed to be a "slip clutch$*($it brings a very large load up to speed slowly$)$

which reduces the motor size required. Find the time required to accelerate a large rotor

or $\{$:$12\mathrm{.}0db-ft-se{c}^2)$ up to full speed from rest $(0re\frac{v}{m}in).$

d$)($Bonus of $4$ marks for this part$).$

How much mechanical energy will be converted into heat during one acceieration period in $($c$)?$

Assume that the motor remains at a steady $3000re\frac{v}{m}in$ during acceleration of the rotor.