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# A multi-plate clutch is to transmit 10 kW at 1200 rev/min??? WordPress

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A multi-plate clutch is to transmit 10 kW at 1200 rev/min. The inner and outer diameters of the plates are 100 mm and 200 mm respectively and the maximum spring force is limited to 1 kN. If u is 0.3, determine the necessary number of pairs of surfaces, assuming uniform wear and what will be the actual necessary axial force?

2015-07-17

Hi, let me refresh my physics and give it a try ;-)

``` Problem: --------- Find n and F Assume the following formulas: ---------------------------- Torque T_max = n * mu * F_max * (R_inner + R_outer) / 2 Power P_max = T_max * angular_velocity Find angular velocity: ------------------- angular_velocity = 1200 rpm = 1200 * 2 * PI / 60 [rad/s] = 2400 * PI / 60 [rad/s] = 40 * PI [rad/s] Find n: -------- n = P_max / ( mu * F_max * (R_inner + R_outer) / 2 ) = 2 * P_max / ( mu * W_max * (R_inner + R_outer) * angular_velocity ) = 2 * 10.000 [W] / ( 0.3 * 1000[N] * ( 0.1[m] + 0.2[m] ) * 40 * PI [rad/s] ) = 20.000 [W] / ( 0.3 * 0.3 * 40000 PI [Nm rad/s] ) = 20.000 [Nm rad/s] / 11.310 [Nm rad/s] = 1.77 n_ceil = ceil( 1.77 ) = 2 Find F: ------- F = P_max / ( n_ceil * mu * (R_inner + R_outer) / 2 ) * angular_velocity ) = 10.000 [W] / ( 2 * 0.3 * 0.15 [m] * 40 * PI [rad/s] ) = 10.000 [Nm rad/s] / 11.31 [m rad/s] = 884.2 [N] ```

ps: I updated the answer with dimensional analysis in brackets [].

[[LINK href="http://webpages.dcu.ie/~youngpa/mm203/clututsol.htm"]]This reference helped me with the formulas[[/LINK]]

2015-07-17