External diameter of the clutch facing is limited to 120 mm and the inner diameter may be assumed to be 0.3 times the external diameter. Assume uniform wear theory. What is the effective mean radius?

Solution (By Examveda Team)

The clutch facing is the friction material (like a special brake pad) on the clutch disc. It's designed to create friction to transmit power from the engine to the gearbox. When you push the clutch pedal, these facings disengage, and when you release it, they engage.

Now, let's talk about the 'uniform wear theory'. When a clutch works over time, its friction material starts to wear out. There are different ways to model how this wear happens. The 'uniform wear theory' assumes that the amount of wear is the same everywhere across the clutch facing surface. This is a common and practical assumption, especially for older or worn clutches, because as wear occurs, the pressure distribution changes to keep wear uniform.

We need to find the effective mean radius (Rm). This is like an "average" radius that engineers use in calculations to determine things like how much torque the clutch can handle under this uniform wear condition.

Let's solve the problem step-by-step:

1. We are given the External diameter (Do) = 120 mm.
To find the External radius (Ro), we divide the diameter by 2:
Ro = Do / 2 = 120 mm / 2 = 60 mm.

2. We are told the Inner diameter (Di) is 0.3 times the external diameter.
Di = 0.3 * Do = 0.3 * 120 mm = 36 mm.
To find the Inner radius (Ri), we divide this diameter by 2:
Ri = Di / 2 = 36 mm / 2 = 18 mm.

3. For uniform wear theory, the formula to calculate the effective mean radius (Rm) is very straightforward:
Rm = (Ro + Ri) / 2
This formula effectively takes the average of the outer and inner radii.

Now, let's put our calculated radii into the formula:
Rm = (60 mm + 18 mm) / 2
Rm = 78 mm / 2
Rm = 39 mm

So, the effective mean radius for this clutch facing, according to the uniform wear theory, is 39 mm.

Comparing our result with the given options, Option B: 39 is the correct answer.