In Metrology, **tolerance** means the limit or acceptable limits of the variations of a physical dimension, a physical property of a manufactured object, of a system, or other measured values such as temperature, humidity, or time. In other words, it is the maximum allowable error in the measurement is specified in terms of some value.

The tolerance in mechanical devices is the deviation deemed acceptable between the dimensions established in the design phase of a component and its actual dimensions; for its proper operation in relation with another piece, i.e., in dimensional coupling.

Tolerance allows the operator to establish a measurement with a confidence interval, even in the presence of imperfections and variables due to influence quantities, without the measurement being compromised.

It is essential for the manufacturer to have an in-depth knowledge of the tolerances to manufacture parts economically but, at the same time, adhere to quality and reliability aspects. Precision is engineered selectively in a product depending on the functional requirements and its application. To achieve increased compatibility between mating parts to enable interchangeable assembly, the manufacturer needs to practice good tolerance principles.

The design of a mechanical part requires that this be assigned a dimension that is inevitably an ideal value. In fact, it can be imagined that the manufacturing processes do not allow the assigned value to be reached precisely. We, therefore, use a nominal dimension to which the zero line is made to coincide.

Absolute precision is not relevant for the manufacture of a mechanical part, especially in large productions; it is instead necessary that the actual size of the workpiece is between a maximum value and a minimum value.

\[d_{min}<d<d_{max}\]

To ensure the correct functionality of a mechanical part and therefore to be able to consider it as accurate, it is adequate that its size lies within two limits, namely the tolerance, which define the dimensional variation allowed in the construction. In the same way, in order to obtain a correct coupling between two pieces, a certain margin of error is necessary, said deviation, positive and negative for the nominal size of the pieces to be assembled, to determine the clearance or the required interference. The tolerance of a dimension is defined as:

\[T=d_{max}-d_{min}\]

Both in the case of holes and shafts, the tolerance zone can be entirely below, entirely above or overlapping the zero line. It is not possible to produce any mechanical object with the exact desired size, called nominal size, because in the production cycle there are errors due to:

- the inaccuracy of machine tools (i.e., tool wear effect during processing);
- possible assembly and equipment inaccuracies;
- inaccuracies of measuring instruments used for dimensional control.

## Tolerance classification

Tolerance can be classified under the following categories:

- Unilateral tolerance
- Bilateral tolerance
- Compound tolerance
- Geometric tolerance

### Unilateral tolerance

When the tolerance distribution is only on one side of the basic size, it is known as unilateral tolerance. In other words, tolerance limits lie wholly on one side of the basic size, either above or below it. For example:

\[1500^{\begin{matrix}

+0.00\\

-0.05

\end{matrix}}\]

Unilateral tolerance is employed when precision fits are required during assembly. This type of tolerance is usually indicated when the mating parts are also machined by the same operator. In this system, the total tolerance as related to the basic size is in one direction only.

Unilateral tolerance is employed in the drilling process wherein dimensions of the hole are most likely to deviate in one direction only, that is, the hole is always oversized rather than undersized.

This system is preferred because the basic size is used for the GO limit gauge. This helps in standardization of the GO gauge, as holes and shafts of different grades will have the same lower and upper limits, respectively. Changes in the magnitude of the tolerance affect only the size of the other gauge dimension, the NOT GO gauge size.

### Bilateral tolerance

When the tolerance distribution lies on either side of the basic size, it is known as bilateral tolerance. In other words, the dimension of the part is allowed to vary on both sides of the basic size but may not be necessarily equally disposed of about it. For example:

\[1500\pm 0.02,\,70^{\begin{matrix}

+0.00\\

-0.05

\end{matrix}}\]

The operator can take full advantage of the limit system, especially in positioning a hole. This system is generally preferred in mass production where the machine is set for the basic size.

In case unilateral tolerance is specified in mass production, the basic size should be modified to suit bilateral tolerance.

### Compound tolerance

When tolerance is determined by established tolerances on more than one dimension, it is known as compound tolerance. In practice, compound tolerance should be avoided as far as possible.

### Geometric tolerance

Geometric tolerance is defined as the total amount that the dimension of a manufactured part can vary. Geometric tolerance underlines the importance of the shape of a feature as against its size.

Geometric tolerances are used to indicate the relationship of one part of an object with another. Normally, tolerances are specified to indicate the actual size or dimension of a feature such as a hole or a shaft.

In order to manufacture components more accurately or with minimum dimensional variations, the manufacturing facilities and the labour required become more cost intensive. Hence, it is essential for the manufacturer to have an in-depth knowledge of tolerances, to manufacture quality and reliable components economically. In fact, depending on the application of the end product, precision is engineered selectively. Therefore, apart from considering the actual size, other geometric dimensions such as roundness and straightness of a shaft have to be considered while manufacturing components.

The tolerances specified should also encompass such variations. However, it is difficult to combine all errors of roundness, straightness, and diameter within a single tolerance on diameter.

Geometric dimensioning and tolerancing is a method of defining parts based on how they function, using standard symbols. This method is frequently used in industries. Depending on the functional requirements, tolerance on diameter, straightness, and roundness may be specified separately. Geometric tolerance can be classified as follows:

**Form tolerances**: are a group of geometric tolerances applied to individual features. They limit the amount of error in the shape of a feature and are independent tolerances. Form tolerances as such do not require locating dimensions. These include straightness, circularity, flatness, and cylindricity.- Orientation tolerances: are a type of geometric tolerances used to limit the direction or orientation of a feature in relation to other features. These are related to tolerances. Perpendicularity, parallelism, and angularity fall into this category.
**Positional tolerances**: are a group of geometric tolerances that controls the extent of deviation of the location of a feature from its true position. This is a three-dimensional geometric tolerance comprising position, symmetry, and concentricity.