n the previous article, we saw that all geometric tolerance specifications control a particular component of the considered feature.

Now we will see that a geometric tolerance specification also defines a tolerance zone, that the controlled component must conform to.  The tolerance zone has well-defined shape, size, and degree of freedom constraints.  This article will focus on the shape and size aspects.

Tolerance Zone Shape

For almost all geometric tolerance specifications, the shape of the tolerance zone directly follows the shape of the controlled component:
• Boundaries are formed by bilaterally offsetting the nominal (theoretically perfect) controlled component
• The tolerance zone is the volume or area contained inside the boundaries
• For controlled components defined in 3D space, the boundaries are 3D entities and the tolerance zones are 3D volumes
• For controlled components defined in 2D space (cross sections of a feature), the boundaries are 2D entities and the tolerance zones are 2D areas

The following are examples of common tolerance zone shapes and boundary geometry:
• Cylindrical (volume inside a cylindrical boundary)
• Slabular (volume between two parallel plane boundaries)
• Tubular (volume between two coaxial cylindrical boundaries)
• Irregular Shell (volume between two irregular surface boundaries)
• Annular (area between two concentric circular boundaries)
• Spherical (volume inside a spherical boundary)

Tolerance Zone Size

The size of the tolerance zone is primarily determined by the tolerance value specified in the feature control frame.  The tolerance zone dimension that the size applies to depends on the geometry of the zone itself:

• Thickness (for slabular and irregular shell zones)
• Diameter (for cylindrical zones)
• Radial thickness (for tubular and annular zones)
• Width (for strip-like zones)
• Spherical Diameter (for spherical zones)

For geometric tolerances referenced at MMC or LMC, the size of the tolerance zone depends on the as-produced size of the feature.  This allows the size of the tolerance zone to be increased with what is commonly referred to as “bonus” tolerance.
The following table provides examples of the tolerance zone shapes and sizes that can result from various geometric tolerance specifications.  The first group applies Perpendicularity to different considered features, and the tolerances, and the second group applies several geometric characteristics to a cylindrical considered feature:

As can be seen in the above table, different geometric tolerances can result in the same tolerance zone shape for a given controlled component.  For example, Circularity, Total Runout, and Surface Profile all result in a tubular tolerance zone when applied to a cylindrical surface.

The distinction between each of these geometric controls lies in the different degree-of-freedom constraints that they impose on the tolerance zone.  This will be discussed in future articles.

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