Answer to Question #120980 in Mechanical Engineering for Ayush

Question

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

Answer 1

Given

d₁ = 220 mm on x₁ = 110 mm

d₂ = 160 mm on x₂ = 80 mm

W = 570 N , K₁ = 200 mm = 0.2 m

M₁ = 800 kg , M₂ = 1300kg

k₂ =180 mm = 0,18 m

miu = 0.35 ,N₁ = 1250 rpm

angular 1 = (pie *1250/60)

= 131 rad/sec

Final speed

let angular 3 be final speed

I₁ = m₁(k₁)² = 800*0.2² = 32kgm²

and moment of friction for rotor

I₂ = m₂(k₂)² = 1300 * 0.18² = 42.12kgm²

Therefore

I₁w₁ + I₂w₂ = (I₁ + I₂)w₃

32*131 +I₂*0 = (32+42.12)w₃

w₃ = 56.56rad/sec