Multi Clamp

What is the Clamping Force Required?
A multi-plate clutch has 4 pairs of friction surfaces, each of internal diameter 120mm and external diameter 200mm. If the coefficient of friction is 0.32 and uniform pressure condition can be assumed, what is the required clamping force in the axial direction when the discs transmit 30 kW at 1440 rpm?
Power = F * V = integrate (mu * pressure * r W dA)
W = 1440 * 2 * PI/60 : rad/S
V = r W: M/S
integrate (mu Pressure * 2 pi r * r W dr) from Ri to Ro
Energy = 1440/60* mu * Pressure * 4 pi^2 *(Ro^3 - ri^3)/3 = 30000
where Ro = .2 and Ri = .120
mu = .32
and solve for Pressure.
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