Question #120980

A rotor is driven by a co-axial motor through a single plate clutch,both sides of the plate being effective.The external and internal diameters of the plate are respectively 220 mm and 160 mm and the total spring load pressing the plates together is 570 N.The motor armature and shaft has mass of 800 kg with an effective radius of gyration of 200 mm.The rotor has a mass of 1300 kg with an effective radius of gyration of 180 mm.The co-efficient of friction for the clutch is 0.35.The driving motor is brought up to a speed of 1250 r.p.m. when the current is switched off and the clutch suddenly engaged.QUESTION 1.The final speed of the motor and rotor

Expert's answer

Given

d_{1} = 220 mm on x_{1} = 110 mm

d_{2} = 160 mm on x_{2} = 80 mm

W = 570 N , K_{1} = 200 mm = 0.2 m

M_{1} = 800 kg , M_{2} = 1300kg

k_{2} =180 mm = 0,18 m

miu = 0.35 ,N_{1} = 1250 rpm

angular 1 = (pie *1250/60)

= 131 rad/sec

Final speed

let angular 3 be final speed

I_{1} = m_{1}(k_{1})^{2} = 800*0.2^{2} = 32kgm^{2}

and moment of friction for rotor

I_{2} = m_{2}(k_{2})^{2} = 1300 * 0.18^{2} = 42.12kgm^{2}

Therefore

I_{1}*w*_{1} + I_{2}*w*_{2} = (I_{1} + I_{2})*w*_{3}

32*131 +I_{2}*0 = (32+42.12)*w*_{3}

*w*_{3} = 56.56rad/sec

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