JNTU B.Tech III Year ENGINEERING METROLOGY Previous Question Paper (August - 2022 - R13)

Given:

Nominal size = 50 mm

Maximum clearance = 0.15 mm

Minimum clearance = 0.05 mm

Hole tolerance (T_H) = 1.5 * Shaft tolerance (T_S)

1. Hole Basis System

In the hole basis system, the hole is kept at the basic size, and the shaft varies within its tolerance.

Maximum clearance = Hole maximum size (H_max) - Shaft minimum size (S_min)

Minimum clearance = Hole minimum size (H_min) - Shaft maximum size (S_max)

Since the hole is at the basic size, H_max = H_min = 50 mm.

So, 0.15 = 50 - S_min => S_min = 50 - 0.15 = 49.85 mm

And, 0.05 = 50 - S_max => S_max = 50 - 0.05 = 49.95 mm

Shaft tolerance, T_S = S_max - S_min = 49.95 - 49.85 = 0.10 mm

Hole tolerance, T_H = 1.5 * T_S = 1.5 * 0.10 = 0.15 mm

Limits for Hole:

H_max = 50 mm

H_min = H_max - T_H = 50 - 0.15 = 49.85 mm

Limits for Shaft:

S_max = 49.95 mm

S_min = 49.85 mm

2. Shaft Basis System

In the shaft basis system, the shaft is kept at the basic size, and the hole varies within its tolerance.

Maximum clearance = Hole maximum size (H_max) - Shaft minimum size (S_min)

Minimum clearance = Hole minimum size (H_min) - Shaft maximum size (S_max)

Since the shaft is at the basic size, S_max = S_min = 50 mm.

So, 0.15 = H_max - 50 => H_max = 50 + 0.15 = 50.15 mm

And, 0.05 = H_min - 50 => H_min = 50 + 0.05 = 50.05 mm

Hole tolerance, T_H = H_max - H_min = 50.15 - 50.05 = 0.10 mm

Shaft tolerance, T_S = 1.5 * T_H (given T_H = 1.5 * T_S, so T_S = T_H / 1.5)

T_S = 0.10 / 1.5 = 0.0667 mm (approx)

Limits for Hole:

H_max = 50.15 mm

H_min = 50.05 mm

Limits for Shaft:

S_max = 50 mm

S_min = S_max - T_S = 50 - 0.0667 = 49.9333 mm (approx)

Tolerance is the total permissible variation allowed in a dimension. It is the difference between the maximum and minimum limits of size.

Allowance is the intentional difference between the maximum material limits of two mating parts. It is the minimum clearance or maximum interference between mating parts.

In simpler terms:

• Tolerance defines the acceptable size variation for a single part.
• Allowance defines the intended space or interference between two mating parts when they are assembled at their extreme limits.

Formulaic Representation:

For clearance fits:

Maximum Clearance = Hole Maximum Size - Shaft Minimum Size

Minimum Clearance = Hole Minimum Size - Shaft Maximum Size

Allowance (for clearance fit) = Minimum Clearance

Tolerance (Hole) = Hole Maximum Size - Hole Minimum Size

Tolerance (Shaft) = Shaft Maximum Size - Shaft Minimum Size