What will be the average pressure in plate clutch when the axial force is 4 kN. The inside radius of the contact surface is 50 mm and the outside radius is 100 mm. Assume uniform wear. 

Concept:

We calculate the average pressure in a plate clutch under uniform wear conditions using the axial force and contact area.

Given:

• Axial force, \( W = 4 \, \text{kN} = 4000 \, \text{N} \)
• Inner radius, \( r_i = 50 \, \text{mm} \)
• Outer radius, \( r_o = 100 \, \text{mm} \)
• Uniform wear condition

Step 1: Calculate Effective Contact Area

For uniform wear, the effective area is the lateral surface area of a truncated cone:

\( A = 2\pi r_i (r_o - r_i) \)

\( A = 2\pi \times 50 \times (100 - 50) \)

\( A = 2\pi \times 50 \times 50 = 5000\pi \, \text{mm}^2 \)

\( A \approx 15708 \, \text{mm}^2 \)

Step 2: Compute Average Pressure

\( P_{avg} = \frac{W}{A} \)

\( P_{avg} = \frac{4000}{15708} \)

\( P_{avg} \approx 0.2546 \, \text{N/mm}^2 \)

Correction:

For uniform wear, the average pressure is actually calculated over the entire annular area:

\( A = \pi (r_o^2 - r_i^2) \)

\( A = \pi (100^2 - 50^2) = \pi (10000 - 2500) = 7500\pi \, \text{mm}^2 \)

\( A \approx 23562 \, \text{mm}^2 \)

\( P_{avg} = \frac{4000}{23562} \approx 0.17 \, \text{N/mm}^2 \)