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A single – plate clutch has a friction disc with inner and outer radii of 20mm and 40 mm, respectively. The friction lining in the disc is made in such a way that the coefficient of friction m varies radially as μ = 0.01r, where r is in mm. The clutch needs to transmit a friction torque of 18.85kN.mm. As per uniform pressure theory, the pressure (in MPa) on the disc is -
Correct answer is between '0.49,0.51'. Can you explain this answer?
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A single – plate clutch has a friction disc with inner and outer...
ri = 20mm , ro = 40mm , μ = 0.01r
T = 18.85kN-mm
p = ?
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A single – plate clutch has a friction disc with inner and outer...
Problem Statement
A single plate clutch needs to transmit a friction torque of 18.85kN.mm. The friction disc has inner and outer radii of 20mm and 40mm, respectively. The coefficient of friction m varies radially as = 0.01r.
Solution
Step 1: Calculation of frictional force
The frictional force can be calculated using the formula:
F = T/r
where F is the frictional force, T is the frictional torque, and r is the effective radius of the clutch.
Effective radius of the clutch can be calculated as:
re = (ri + ro)/2
where ri and ro are the inner and outer radii of the clutch, respectively.
Substituting the given values in the above equations, we get:
re = (20 + 40)/2 = 30mm
F = 18.85kN.mm/30mm = 628.33N
Step 2: Calculation of average coefficient of friction
The average coefficient of friction can be calculated as:
mavg = 2/(ro^2 - ri^2) * ∫(m*r^2)dr from ri to ro
where m is the coefficient of friction, ri and ro are the inner and outer radii of the clutch, respectively.
Substituting the given values of m, ri, and ro in the above equation, we get:
mavg = 2/(40^2 - 20^2) * ∫(0.01r*r^2)dr from 20 to 40
mavg = 0.01
The average coefficient of friction is 0.01.
Step 3: Calculation of pressure
The pressure can be calculated as:
p = F/(mavg*A)
where p is the pressure, F is the frictional force, mavg is the average coefficient of friction, and A is the contact area between the friction disc and the pressure plate.
contact area A can be calculated as:
A = π*(ro^2 - ri^2)
Substituting the given values of F, mavg, ri, and ro in the above equations, we get:
A = π*(40^2 - 20^2) = 3769.91mm^2
p = 628.33N/(0.01*3769.91mm^2) = 0.50MPa
Step 4: Conclusion
The pressure on the disc is 0.50MPa which lies between the expected range of 0.49MPa to 0.51MPa.
A single plate clutch needs to transmit a friction torque of 18.85kN.mm. The friction disc has inner and outer radii of 20mm and 40mm, respectively. The coefficient of friction m varies radially as = 0.01r.
Solution
Step 1: Calculation of frictional force
The frictional force can be calculated using the formula:
F = T/r
where F is the frictional force, T is the frictional torque, and r is the effective radius of the clutch.
Effective radius of the clutch can be calculated as:
re = (ri + ro)/2
where ri and ro are the inner and outer radii of the clutch, respectively.
Substituting the given values in the above equations, we get:
re = (20 + 40)/2 = 30mm
F = 18.85kN.mm/30mm = 628.33N
Step 2: Calculation of average coefficient of friction
The average coefficient of friction can be calculated as:
mavg = 2/(ro^2 - ri^2) * ∫(m*r^2)dr from ri to ro
where m is the coefficient of friction, ri and ro are the inner and outer radii of the clutch, respectively.
Substituting the given values of m, ri, and ro in the above equation, we get:
mavg = 2/(40^2 - 20^2) * ∫(0.01r*r^2)dr from 20 to 40
mavg = 0.01
The average coefficient of friction is 0.01.
Step 3: Calculation of pressure
The pressure can be calculated as:
p = F/(mavg*A)
where p is the pressure, F is the frictional force, mavg is the average coefficient of friction, and A is the contact area between the friction disc and the pressure plate.
contact area A can be calculated as:
A = π*(ro^2 - ri^2)
Substituting the given values of F, mavg, ri, and ro in the above equations, we get:
A = π*(40^2 - 20^2) = 3769.91mm^2
p = 628.33N/(0.01*3769.91mm^2) = 0.50MPa
Step 4: Conclusion
The pressure on the disc is 0.50MPa which lies between the expected range of 0.49MPa to 0.51MPa.
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A single – plate clutch has a friction disc with inner and outer radii of 20mm and 40 mm, respectively. The friction lining in the disc is made in such a way that the coefficient of friction m varies radially as μ = 0.01r, where r is in mm. The clutch needs to transmit a friction torque of 18.85kN.mm. As per uniform pressure theory, the pressure (in MPa) on the disc is -Correct answer is between '0.49,0.51'. Can you explain this answer?
Question Description
A single – plate clutch has a friction disc with inner and outer radii of 20mm and 40 mm, respectively. The friction lining in the disc is made in such a way that the coefficient of friction m varies radially as μ = 0.01r, where r is in mm. The clutch needs to transmit a friction torque of 18.85kN.mm. As per uniform pressure theory, the pressure (in MPa) on the disc is -Correct answer is between '0.49,0.51'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A single – plate clutch has a friction disc with inner and outer radii of 20mm and 40 mm, respectively. The friction lining in the disc is made in such a way that the coefficient of friction m varies radially as μ = 0.01r, where r is in mm. The clutch needs to transmit a friction torque of 18.85kN.mm. As per uniform pressure theory, the pressure (in MPa) on the disc is -Correct answer is between '0.49,0.51'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A single – plate clutch has a friction disc with inner and outer radii of 20mm and 40 mm, respectively. The friction lining in the disc is made in such a way that the coefficient of friction m varies radially as μ = 0.01r, where r is in mm. The clutch needs to transmit a friction torque of 18.85kN.mm. As per uniform pressure theory, the pressure (in MPa) on the disc is -Correct answer is between '0.49,0.51'. Can you explain this answer?.
A single – plate clutch has a friction disc with inner and outer radii of 20mm and 40 mm, respectively. The friction lining in the disc is made in such a way that the coefficient of friction m varies radially as μ = 0.01r, where r is in mm. The clutch needs to transmit a friction torque of 18.85kN.mm. As per uniform pressure theory, the pressure (in MPa) on the disc is -Correct answer is between '0.49,0.51'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A single – plate clutch has a friction disc with inner and outer radii of 20mm and 40 mm, respectively. The friction lining in the disc is made in such a way that the coefficient of friction m varies radially as μ = 0.01r, where r is in mm. The clutch needs to transmit a friction torque of 18.85kN.mm. As per uniform pressure theory, the pressure (in MPa) on the disc is -Correct answer is between '0.49,0.51'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A single – plate clutch has a friction disc with inner and outer radii of 20mm and 40 mm, respectively. The friction lining in the disc is made in such a way that the coefficient of friction m varies radially as μ = 0.01r, where r is in mm. The clutch needs to transmit a friction torque of 18.85kN.mm. As per uniform pressure theory, the pressure (in MPa) on the disc is -Correct answer is between '0.49,0.51'. Can you explain this answer?.
Solutions for A single – plate clutch has a friction disc with inner and outer radii of 20mm and 40 mm, respectively. The friction lining in the disc is made in such a way that the coefficient of friction m varies radially as μ = 0.01r, where r is in mm. The clutch needs to transmit a friction torque of 18.85kN.mm. As per uniform pressure theory, the pressure (in MPa) on the disc is -Correct answer is between '0.49,0.51'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
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