LIMITS, FITS AND TOLERANCES Free study notes

1. Introduction

In manufacturing, it is impossible to produce components with exact dimensions due to machine errors, tool wear, and environmental factors. Therefore, a permissible variation is allowed. This concept is called tolerance.

The system of limits, fits, and tolerances ensures interchangeability, proper assembly, and smooth functioning of machine parts. It is standardized globally by organizations such as the International Organization for Standardization.

External Resource

2. Basic Terminology

2.1 Nominal Size

Nominal size refers to a standardized or approximate dimension used to identify and classify an object, rather than its exact physical measurement.

Example:
A shaft of 50 mm.

2.2 Actual Size

Actual size refers to the exact length, diameter, width, thickness, or other dimension obtained by measurement.

Example:
A wooden board sold as 2 × 4 inches actually measures about 1.5 × 3.5 inches.

2.3 Basic Size

In engineering metrology and limits & fits, the basic size is the size specified on the drawing and serves as the reference for calculating upper and lower limits.

Difference Between Nominal Size, Basic Size, and Actual Size

Parameter	Nominal Size	Basic Size	Actual Size
Definition	A convenient designation or name used to identify a component.	The exact theoretical size from which limits and tolerances are assigned.	The size obtained by actual measurement of the finished component.
Purpose	Identification and classification.	Basis for determining limits and fits.	Verification of the manufactured part.
Used In	Catalogs, standards, and commercial descriptions.	Engineering drawings and tolerance calculations.	Inspection and quality control.
May Vary?	Can differ from the true dimension.	Fixed reference dimension.	Varies within specified limits due to manufacturing tolerances.
Example	“50 mm shaft” (general designation).	50.000 mm (size specified on drawing).	49.98 mm, 50.01 mm, etc. (measured value).

2.4 Limit

The two extreme permissible sizes between which the actual size lies. Limits are the maximum and minimum permissible sizes of a component.

• Upper Limit: Largest permissible size.
• Lower Limit: Smallest permissible size.

Example

For a shaft of 50 ± 0.02 mm:

• Lower Limit = 49.98 mm
• Upper Limit = 50.02 mm

2.5 Tolerance

The difference between maximum and minimum limits. Tolerance is the total permissible variation in a dimension.

Formula

$$\text{Tolerance} = \text{Upper Limit} – \text{Lower Limit}$$

Example

For the shaft above:

• Upper Limit = 50.02 mm
• Lower Limit = 49.98 mm

Tolerance = 50.02 − 49.98 = 0.04 mm

Types of Tolerance

• Bilateral Tolerance: Variation on both sides (e.g., 50 ± 0.02 mm)
• Unilateral Tolerance: Variation on one side only (e.g., 50 +0.02/0 mm)

2.6 Allowance

Allowance is the intentional difference between the maximum material limits of mating parts.

It is the minimum clearance or maximum interference between two mating parts.

Formula

For clearance fit:

$\text{Allowance}=\text{Minimum Hole Size}-\text{Maximum Shaft Size}$

Example

• Hole: 50.00 to 50.04 mm
• Shaft: 49.96 to 49.98 mm

Allowance = 50.00 − 49.98 = 0.02 mm

Difference Between Limits, Tolerance & Allowance

Term	Meaning	Purpose
Limits	Maximum and minimum permissible sizes	Define acceptable size range
Tolerance	Difference between upper and lower limits	Control manufacturing variation
Allowance	Intentional difference between mating parts	Ensure desired fit (clearance or interference)

3. Need for Limits and Tolerances

1. To allow for manufacturing variations.
2. To reduce production cost.
3. To ensure interchangeability.
4. To facilitate mass production.
5. To avoid rejection of parts.
6. To maintain proper functioning of machine parts.

4. Types of Tolerances

4.1 Unilateral Tolerance

Variation is allowed only on one side of the basic size.

Example:
50 +0.02 / 0.00 mm.

Advantages:

• Easy inspection.
• Suitable for automated production.

4.2 Bilateral Tolerance

Variation is allowed on both sides of the basic size.

Example:
50 ±0.01 mm.

Advantages:

• Uniform distribution of error.

5. System of Fits

Fit is the relationship between two mating parts such as a shaft and a hole.

It determines whether the parts will be loose, tight, or intermediate.

6. Types of Fits

6.1 Clearance Fit

6.2 Interference Fit

The shaft is always larger than the hole.

Requires force or heating/cooling for assembly.
No relative motion.

Applications:

• Permanent joints.
• Railway wheels.

6.3 Transition Fit

May result in either clearance or interference.

Sometimes tight, sometimes loose.

Applications:

• Precision assemblies.

7. Hole Basis and Shaft Basis System

7.1 Hole Basis System

The hole size is kept constant, and the shaft is varied.

Most commonly used.

Reasons:

• Standard tools are available for holes.
• Easier manufacturing.

7.2 Shaft Basis System

The shaft size is constant, and the hole is varied.

Used when:

• Standard shaft is required.

8. Limits and Fits According to ISO System

The ISO system uses letters and numbers.

Example:
50 H7/g6

Capital letters → Hole
Small letters → Shaft
Number → Tolerance grade.

9. Tolerance Grades

Tolerance grades are designated as IT01, IT0, IT1 to IT16.

Lower number → Higher precision
Higher number → Lower precision.

Example:

• IT5 → Precision engineering
• IT12 → General engineering.

10. Advantages of Limit System

✔ Ensures interchangeability.
✔ Reduces scrap and wastage.
✔ Improves product quality.
✔ Reduces manufacturing cost.
✔ Facilitates mass production.

11. Applications

✔ Automobile industries
✔ Aerospace
✔ Machine tools
✔ Bearings
✔ Gear assemblies
✔ Construction equipment.

---