Tolerances

Introduction

In engineering and manufacturing, it is impossible to manufacture a part to an exact dimension due to variations in machining processes, material properties, and environmental conditions. Tolerance is the total amount a specific dimension is permitted to vary. It is the difference between the upper limit and the lower limit of a dimension.

By setting the right tolerances, engineers make sure parts fit together and work properly without making manufacturing more expensive than necessary.

Principles & Theory

Basic Terms

• Nominal Size: The general size used to identify a part, typically a round number or simple fraction (e.g., 50 mm).
• Basic Size: The exact theoretical size used as the starting point for calculating limits by applying allowances and tolerances.
• Limits of Size: The largest and smallest sizes allowed for a feature.
  • Maximum Material Condition (MMC): The limit of size that results in the part containing the maximum amount of material (e.g., the largest shaft limit or the smallest hole limit).
  • Least Material Condition (LMC): The limit of size that results in the part containing the minimum amount of material (e.g., the smallest shaft limit or the largest hole limit).

Calculating Tolerance

The tolerance $T$ of a dimension is the difference between the upper limit ($U_{limit}$) and the lower limit ($L_{limit}$):

Worked Example

An engineer specifies a shaft diameter as $50.00 \pm 0.05$ mm.

1. Calculate the Upper Limit: $U_{limit} = 50.00 + 0.05 = 50.05 \text{ mm}$

2. Calculate the Lower Limit: $L_{limit} = 50.00 - 0.05 = 49.95 \text{ mm}$

3. Calculate the Total Tolerance: $T = 50.05 - 49.95 = 0.10 \text{ mm}$

This means the shaft can be anywhere between 49.95 mm and 50.05 mm and still be within tolerance.

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