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An automotive plate clutch consists of two pairs of contracting surfaces with an asbestos friction lining. The torque transmitting capacity of the clutch is 600 N-m. The permissible intensity of the pressure is 1 MPa, coefficient of friction is 0.3, and outer diameter of friction disc is 300 mm. Determine the inner diameter of the friction disc using uniform wear theory.
- a)62 mm
- b)206 mm
- c)300 mm
- d)31 mm
Correct answer is option 'D'. Can you explain this answer?
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An automotive plate clutch consists of two pairs of contracting surfac...
To determine the inner diameter of the friction disc using uniform wear theory, we can use the following steps:
1. Understand the problem:
- An automotive plate clutch consists of two pairs of contracting surfaces with an asbestos friction lining.
- The torque transmitting capacity of the clutch is 600 N-m.
- The permissible intensity of the pressure is 1 MPa.
- The coefficient of friction is 0.3.
- The outer diameter of the friction disc is 300 mm.
- We need to determine the inner diameter of the friction disc.
2. Apply the uniform wear theory:
- The uniform wear theory states that the wear on the friction lining is uniform across its entire surface.
- This means that the pressure distribution on the friction lining is also uniform.
3. Calculate the pressure distribution:
- The pressure distribution can be calculated using the formula:
Pressure = Torque / (Frictional force x Friction radius)
- Given that the torque transmitting capacity is 600 N-m, the coefficient of friction is 0.3, and the outer diameter of the friction disc is 300 mm, we can calculate the friction radius:
Friction radius = Outer diameter / 2
= 300 mm / 2
= 150 mm
- Now, we can calculate the pressure:
Pressure = 600 N-m / (Frictional force x 150 mm)
4. Calculate the frictional force:
- The frictional force can be calculated using the formula:
Frictional force = Pressure x Area
- Given that the permissible intensity of the pressure is 1 MPa and the coefficient of friction is 0.3, we can calculate the frictional force:
Frictional force = 1 MPa x (π x (Outer radius^2 - Inner radius^2))
= 1 MPa x (π x ((150 mm)^2 - Inner radius^2))
= 1 x 10^6 N/m^2 x (π x ((150 x 10^-3 m)^2 - Inner radius^2))
5. Solve for the inner diameter:
- Since the wear is uniform, the friction radius remains constant. Therefore, the frictional force remains constant.
- We can equate the frictional force expression from step 4 to the frictional force calculated in step 3:
1 x 10^6 N/m^2 x (π x ((150 x 10^-3 m)^2 - Inner radius^2)) = Torque / Friction radius
- Substitute the given values and solve for the inner radius:
Inner radius = √((150 x 10^-3 m)^2 - (Torque / (1 x 10^6 N/m^2 x π x Friction radius))^2)
= √((150 x 10^-3 m)^2 - (600 N-m / (1 x 10^6 N/m^2 x π x 150 x 10^-3 m))^2)
≈ 31 mm
Therefore, the correct answer is option 'D' (31 mm).
1. Understand the problem:
- An automotive plate clutch consists of two pairs of contracting surfaces with an asbestos friction lining.
- The torque transmitting capacity of the clutch is 600 N-m.
- The permissible intensity of the pressure is 1 MPa.
- The coefficient of friction is 0.3.
- The outer diameter of the friction disc is 300 mm.
- We need to determine the inner diameter of the friction disc.
2. Apply the uniform wear theory:
- The uniform wear theory states that the wear on the friction lining is uniform across its entire surface.
- This means that the pressure distribution on the friction lining is also uniform.
3. Calculate the pressure distribution:
- The pressure distribution can be calculated using the formula:
Pressure = Torque / (Frictional force x Friction radius)
- Given that the torque transmitting capacity is 600 N-m, the coefficient of friction is 0.3, and the outer diameter of the friction disc is 300 mm, we can calculate the friction radius:
Friction radius = Outer diameter / 2
= 300 mm / 2
= 150 mm
- Now, we can calculate the pressure:
Pressure = 600 N-m / (Frictional force x 150 mm)
4. Calculate the frictional force:
- The frictional force can be calculated using the formula:
Frictional force = Pressure x Area
- Given that the permissible intensity of the pressure is 1 MPa and the coefficient of friction is 0.3, we can calculate the frictional force:
Frictional force = 1 MPa x (π x (Outer radius^2 - Inner radius^2))
= 1 MPa x (π x ((150 mm)^2 - Inner radius^2))
= 1 x 10^6 N/m^2 x (π x ((150 x 10^-3 m)^2 - Inner radius^2))
5. Solve for the inner diameter:
- Since the wear is uniform, the friction radius remains constant. Therefore, the frictional force remains constant.
- We can equate the frictional force expression from step 4 to the frictional force calculated in step 3:
1 x 10^6 N/m^2 x (π x ((150 x 10^-3 m)^2 - Inner radius^2)) = Torque / Friction radius
- Substitute the given values and solve for the inner radius:
Inner radius = √((150 x 10^-3 m)^2 - (Torque / (1 x 10^6 N/m^2 x π x Friction radius))^2)
= √((150 x 10^-3 m)^2 - (600 N-m / (1 x 10^6 N/m^2 x π x 150 x 10^-3 m))^2)
≈ 31 mm
Therefore, the correct answer is option 'D' (31 mm).
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An automotive plate clutch consists of two pairs of contracting surfaces with an asbestos friction lining. The torque transmitting capacity of the clutch is 600 N-m. The permissible intensity of the pressure is 1 MPa, coefficient of friction is 0.3, and outer diameter of friction disc is 300 mm. Determine the inner diameter of the friction disc using uniform wear theory.a)62 mmb)206 mmc)300 mmd)31 mmCorrect answer is option 'D'. Can you explain this answer?
Question Description
An automotive plate clutch consists of two pairs of contracting surfaces with an asbestos friction lining. The torque transmitting capacity of the clutch is 600 N-m. The permissible intensity of the pressure is 1 MPa, coefficient of friction is 0.3, and outer diameter of friction disc is 300 mm. Determine the inner diameter of the friction disc using uniform wear theory.a)62 mmb)206 mmc)300 mmd)31 mmCorrect answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about An automotive plate clutch consists of two pairs of contracting surfaces with an asbestos friction lining. The torque transmitting capacity of the clutch is 600 N-m. The permissible intensity of the pressure is 1 MPa, coefficient of friction is 0.3, and outer diameter of friction disc is 300 mm. Determine the inner diameter of the friction disc using uniform wear theory.a)62 mmb)206 mmc)300 mmd)31 mmCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An automotive plate clutch consists of two pairs of contracting surfaces with an asbestos friction lining. The torque transmitting capacity of the clutch is 600 N-m. The permissible intensity of the pressure is 1 MPa, coefficient of friction is 0.3, and outer diameter of friction disc is 300 mm. Determine the inner diameter of the friction disc using uniform wear theory.a)62 mmb)206 mmc)300 mmd)31 mmCorrect answer is option 'D'. Can you explain this answer?.
An automotive plate clutch consists of two pairs of contracting surfaces with an asbestos friction lining. The torque transmitting capacity of the clutch is 600 N-m. The permissible intensity of the pressure is 1 MPa, coefficient of friction is 0.3, and outer diameter of friction disc is 300 mm. Determine the inner diameter of the friction disc using uniform wear theory.a)62 mmb)206 mmc)300 mmd)31 mmCorrect answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about An automotive plate clutch consists of two pairs of contracting surfaces with an asbestos friction lining. The torque transmitting capacity of the clutch is 600 N-m. The permissible intensity of the pressure is 1 MPa, coefficient of friction is 0.3, and outer diameter of friction disc is 300 mm. Determine the inner diameter of the friction disc using uniform wear theory.a)62 mmb)206 mmc)300 mmd)31 mmCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An automotive plate clutch consists of two pairs of contracting surfaces with an asbestos friction lining. The torque transmitting capacity of the clutch is 600 N-m. The permissible intensity of the pressure is 1 MPa, coefficient of friction is 0.3, and outer diameter of friction disc is 300 mm. Determine the inner diameter of the friction disc using uniform wear theory.a)62 mmb)206 mmc)300 mmd)31 mmCorrect answer is option 'D'. Can you explain this answer?.
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