Understanding Clutch Torque Calculation Using Uniform Wear Theory

This solution details the calculation for the torque carrying capacity of a single-plate clutch, specifically applying the uniform wear theory. We will identify the given parameters, recall the appropriate formula, and perform the calculation step-by-step.

Given Parameters for the Clutch

• Outer Radius ($R_o$): 50 mm
• Inner Radius ($R_i$): 20 mm
• Axial Clamping Force ($F$): 2 kN
• Coefficient of Friction ($\mu$): 0.4

Concept of Uniform Wear Theory

In clutch design, the uniform wear theory is a common assumption. It posits that the wear rate across the friction surface is constant. Mathematically, this means the product of pressure ($p$) and radius ($r$) is constant ($p \cdot r = \text{constant}$). This condition influences the formula used to calculate the torque capacity.

Formula for Torque Calculation

For a single-plate clutch operating under the uniform wear theory, the torque ($T$) that the clutch can transmit is given by the formula:

Where:

• $T$ is the torque carrying capacity.
• $\mu$ is the coefficient of friction.
• $F$ is the axial clamping force.
• $R_o$ is the outer radius of the friction surface.
• $R_i$ is the inner radius of the friction surface.

Step-by-Step Calculation Process

First, we must ensure all measurements are in consistent SI units. Convert millimeters (mm) to meters (m) and kilonewtons (kN) to Newtons (N):

• Outer Radius ($R_o$) = 50 mm = $\frac{50}{1000}$ m = 0.05 m
• Inner Radius ($R_i$) = 20 mm = $\frac{20}{1000}$ m = 0.02 m
• Axial Clamping Force ($F$) = 2 kN = $2 \times 1000$ N = 2000 N

The coefficient of friction ($\mu$) is given as 0.4.

Now, substitute these converted values into the torque formula:

Calculate the sum of the radii:

Now, continue with the torque calculation:

Final Result

The calculated torque carrying capacity for the single-plate clutch, based on the uniform wear theory, is 28 Nm. This value aligns with one of the options provided.