Machine Kinematics Multiple Choice Questions on “Laws of Fluid Friction”.
1. A multiple disc clutch has five plates having four pairs of active friction surfaces. If the intensity of pressure is not to exceed 0.127 N/mm2, find the power transmitted at 500 r.p.m. The outer and inner radii of friction surfaces are 125 mm and 75 mm respectively. Assume uniform wear and take coefficient of friction = 0.3.
a) 17.8 kW
b) 18.8 kW
c) 19.8 kW
d) 20.8 kW
Answer: b
Clarification: n1 + n2 = 5 ; n = 4 ; p = 0.127 N/mm2 ; N = 500 r.p.m. or ω = 2π × 500/60 = 52.4 rad/s ; r1 = 125 mm ; r2 = 75 mm ; μ = 0.3
Since the intensity of pressure is maximum at the inner radius r2, therefore
p.r2 = C or C = 0.127 × 75 = 9.525 N/mm
We know that axial force required to engage the clutch,
W = 2 π C (r1 – r2) = 2 π × 9.525 (125 – 75) = 2990 N
and mean radius of the friction surfaces,
R = r1 + r2/2 = 125 + 75/2 = 100 mm = 0.1 m
We know that torque transmitted,
T = n.μ.W.R = 4 × 0.3 × 2990 × 0.1 = 358.8 N-m
∴ Power transmitted,
P = T.ω = 358.8 × 52.4 = 18 800 W = 18.8 kW.
2. A single plate clutch, with both sides effective, has outer and inner diameters 300 mm and 200 mm respectively. The maximum intensity of pressure at any point in the contact surface is not to exceed 0.1 N/mm2. If the coefficient of friction is 0.3, determine the power transmitted by a clutch at a speed 2500 r.p.m.
a) 61.693 kW
b) 71.693 kW
c) 81.693 kW
d) 91.693 kW
Answer: a
Clarification: Given : d1 = 300 mm or r1 = 150 mm ; d2 = 200 mm or r2 = 100 mm ; p = 0.1 N/mm2 ; μ = 0.3 ; N = 2500 r.p.m. or ω = 2π × 2500/60 = 261.8 rad/s
Since the intensity of pressure ( p) is maximum at the inner radius (r2), therefore for uniform wear,
p.r2 = C or C = 0.1 × 100 = 10 N/mm
We know that the axial thrust,
W = 2 π C (r1 – r2) = 2 π × 10 (150 – 100) = 3142 N
and mean radius of the friction surfaces for uniform wear,
R = r1 + r2/2 = 150 + 100/2 = 125 mm = 0.125m
We know that torque transmitted,
T = n.μ.W.R = 2 × 0.3 × 3142 × 0.125 = 235.65 N-m …( n = 2,for both sides of plate effective)
∴ Power transmitted by a clutch,
P = T.ω = 235.65 × 261.8 = 61 693 W = 61.693 kW.
3. A 60 mm diameter shaft running in a bearing carries a load of 2000 N. If the coefficient of friction between the shaft and bearing is 0.03, find the power transmitted when it runs at 1440 r.p.m.
a) 171.4 W
b) 271.4 W
c) 371.4 W
d) 471.4 W
Answer: b
Clarification: Given : d = 60 mm or r = 30 mm = 0.03 m ; W = 2000 N ; μ = 0.03 ; N = 1440 r.p.m.
or ω = 2π × 1440/60 = 150.8 rad/s
We know that torque transmitted,
T = μ.W.r = 0.03 × 2000 × 0.03 = 1.8 N-m
∴ Power transmitted, P = T.ω = 1.8 × 150.8 = 271.4 W.
4. The force of friction is inversely proportional to the normal load between the surfaces.
a) True
b) False
Answer: b
Clarification: The force of friction is directly proportional to the normal load between the surfaces.
5. The force of friction is dependent of the area of the contact surface for a given normal load.
a) True
b) False
Answer: b
Clarification: The force of friction is independent of the area of the contact surface for a given normal load.
6. The force of friction depends upon the material of which the contact surfaces are made.
a) True
b) False
Answer: a
Clarification: Following are the laws of solid friction :
1. The force of friction is directly proportional to the normal load between the surfaces.
2. The force of friction is independent of the area of the contact surface for a given normal load.
3. The force of friction depends upon the material of which the contact surfaces are made.
4. The force of friction is independent of the velocity of sliding of one body relative to the other body.
7. The force of friction is dependent of the velocity of sliding of one body relative to the other body.
a) True
b) False
Answer: b
Clarification: The force of friction is independent of the velocity of sliding of one body relative to the other body.
8. The force of friction is almost dependent of the load.
a) True
b) False
Answer: b
Clarification: The force of friction is almost independent of the load.
9. The force of friction is dependent of the substances of the bearing surfaces.
a) True
b) False
Answer: b
Clarification: The force of friction is independent of the substances of the bearing surfaces.
10. The force of friction is _____________ for different lubricants.
a) same
b) different
c) zero
d) none of the mentioned
Answer: a
Clarification: The force of friction is different for different lubricants.