Tolerances

Introduction

In engineering and manufacturing, it is impossible to produce parts with exactly one hundred percent precise and perfect dimensions due to variations in machining processes, material properties, and the environment. Tolerance is the total acceptable amount of deviation for a given dimension, meaning the difference between the maximum limit and the minimum limit of that dimension.

Defining appropriate tolerances allows engineers to ensure that parts assemble and function correctly, without unnecessarily increasing manufacturing costs by specifying excessively high precision.

Principles & Theory

Basic Terminology

• Nominal Size: A general size used for reference and naming, often a round number or simple fraction (e.g., 50 mm).
• Basic Size: The theoretical size used as a starting point for calculating size limits by applying allowances and tolerances.
• Limits of Size: The minimum and maximum acceptable dimensions for a part.
  • Maximum Material Condition (MMC): The size limit that results in the part having the maximum amount of material (e.g., largest shaft size or smallest hole size).
  • Least Material Condition (LMC): The size limit that results in the part having the least amount of material (e.g., smallest shaft size or largest hole size).

Tolerance Calculation

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

Worked Example

An engineer specifies the diameter of a shaft 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 Total Tolerance: $T = 50.05 - 49.95 = 0.10 \text{ mm}$

This means a manufactured shaft can have a dimension anywhere between 49.95 mm and 50.05 mm and still be considered within the specified tolerance.

References