This post is a brief introduction to tolerances in the world of mechanical design and construction, trying to clarify what they are, what their usefulness is and why they are important.

The definition and standardization of tolerances arises to respond to the need to generate standardized parts that can be linked to each other and generate sets, mechanisms, or other constructions. It also allows the replacement of deteriorated parts with new parts that comply perfectly while maintaining the operation of the set.

When making a mechanical design, we start with a sketch where we make a visual approximation of the part, then we scale this sketch and give it the necessary measurements for the design to work and generate a three-dimensional model. Although in our “virtual model” the forms are perfect, we must not forget that in reality it is impossible to obtain these perfect forms. The degree of approximation to perfection will be defined by the functional requirements of the part and its manufacturing cost, to obtain more precise parts we need more expensive materials and production processes, which can sometimes be above the limit cost of the part.

On the other hand, it is impossible to manufacture two pieces with absolutely equal dimensions because different factors intervene in their construction, such as: the very nature of the material from which it is manufactured, the characteristics and details of each of the machines. that intervene in the manufacture or the different manufacturing processes that are followed to manufacture it.

To solve this, a series of intervals are stipulated that define whether the part is valid or not, these intervals are defined by the geometric and mechanical needs of the part and are indicated on a plane with respect to the nominal dimension, they are the tolerances .

At a mechanical level, we mainly consider two types of tolerances:

The dimensional tolerances that are defined as the total amount that is allowed to vary in manufacturing a dimension specified in the drawing according to the nominal dimension.

Through these, an upper and a lower limit are established, within which the good pieces must be. According to this criterion, all the desired dimensions, also called nominal dimensions, have to be accompanied by limits, which define a tolerance field. Many plane dimensions carry these explicit limits, following the nominal value.

Annotation example:

50 Nominal height

+0.5 Upper limit

-0.1 Lower limit

Therefore, all values between **49.99 and 50.05** would be admissible.

Dimensional tolerances expressed with letters can also be found, this obeys the ISO dimensioning and is generally used to dimension shafts and holes.

In this case the letters “F” and “h” define the position (upper (positive) or lower (negative)) and the numbers “7” and “6” define the degree of quality (limits).

We must look for these correspondences of the letters and numbers present in the dimension in the ISO tables for this purpose, although in this case of the example it is also specified numerically.

IMPORTANT: the lower case letter will always refer to axes and the upper case to holes.

The **geometric tolerances** are those that limit the shape of the surfaces of the part and the relative position therebetween. They are specified for those parts that have to fulfill important functions in an assembly and on which the reliability of the product may depend.

These tolerances can control individual shapes or define relationships between different shapes. The following classification of these tolerances is usual:

- Primitive shapes: straightness, flatness, roundness, cylindricity
- Complex shapes: profile, surface
- Orientation: paralelism, perpendicularity, inclination
- Location: concentricity, position
- Oscillation: radial, axial or total circular

Geometric tolerance dimensioning structure:

In this dimension we see how an angular tolerance of 0.1 value is required with respect to the reference surface A.

If we assume that the angle between them is 45º, the admissible in this case would be an angularity between 44.9º and 45.1º

Below is a table with the different symbols of geometric characteristics and their correspondences:

Finally, it should be noted that all those dimensions of a plane that do not have a tolerance explicitly indicated are governed by the rule indicated in the drawing box:

**Alfredo Blanco Veiga, Department of Mechanical Design PROBOTEC.**