How GD&T Form Tolerances Affect Hole and Shaft Fits

The relatively new and sometimes confusing world of Geometric Dimensioning and Tolerancing (GD&T) opens up a whole new world of ways for engineers to control the geometry of everything from every day parts to complicated geometric surfaces.

GD&T allows the design engineer to fully control the shape and profile of mating parts on the paper drawing.  The subject can be intimidating because many of the concepts can be difficult to visualize, and many volumes of information have been written in order to fully explain the many faceted aspects of the subject.  However, the basic concepts identified below provide a solid introduction to the topic, highlighting ways in which GD&T can be used to control fits of holes/shafts in order to provide additional control on the fit geometry.

For starters, there are three categories of geometric tolerances:

Form Tolerances: These tolerances control the part or feature geometric shape and include such controls as flatness, straightness, circularity, and cylindricity.

Orientation tolerances: These tolerances control the “tilt” associated with features on the part.  They are identified easily by remembering that all of the orientation tags are associated with an angle dimension.  Common orientation GD&T tolerances are angularity, parallelism and perpendicularity

Location Tolerances:  These tolerances are employed to locate features of size and are are always applied to basic dimensions. These are typically the most commonly employed GD&T tags because they are relatively easy to understand and are also the most powerful modifiers because as feature location is controlled, form and orientation control come along for the ride as well.  Common examples of locational tolerances include profile and position tolerance tags.

Location Tolerances:

  • Position

Probably the most commonly specified geometric controls is the position GD&T callout.  These feature controls are exclusively 3D controls and locate features of size, such as a hole or pin.  The positional tolerance specifies a “zone” within which the center, defining axis of the feature of size, is allowed to deviate from the “true” position on the drawing.  This “true” position is defined using basic dimensions from the drawing datums.  (In short, drawing datums define the basic coordinate frame of the part.)

Tolerance Zones. Rasis, E.P. (2011). Technical Reference Handbook Sixth Edition.

Tolerance Zones. Rasis, E.P. (2011). Technical Reference Handbook Sixth Edition.

The illustration below shows how the actual envelope of the hole can move, as allowed by the specified positional tolerance of the hole.   The advantage of using a GD&T positional tolerance as opposed to an ordinary size tolerance of the hole-such as a simple plus/minus 0.05” diameter- is that the use of the positional GD&T symbol also controls the geometric form of the hole.  With this information, the virtual mating hole size or shaft size can be calculated based on the specified GD&T tolerance value.   A complete discussion on this concept is beyond the scope of this article, but the basic principle is not difficult to grasp: as the center axis of the hole moves as allowed by the geometric position tolerance, the inner and outer size envelopes of the hole move along with the center axis, creating a virtual mating envelope.  Mastering positional GD&T controls, the designer can create components to fit together based on the actual mating envelope of the parts.

PositionGDT

Position. Rasis, E.P. (2011). Technical Reference Handbook Sixth Edition.

  • Profile of a Surface

Profile is another powerful GD&T specification because it controls both the form and location of the surface, as it dictates that the actual part surface must lie within a specified zone.  The actual shape and size of the part can vary as long as every point on the surface lies within that specified tolerance zone.  This geometric tolerance is important to understand because it is typically specified directly on fitting surfaces of parts and therefore must be carefully accounted for during fit and tolerance stack up analysis.

Profileofasurface

Profile of Surface. Rasis, E.P. (2011). Technical Reference Handbook Sixth Edition.

  • Other Location Tolerances: There are other location and form GD&T tags such as Concentricity and Cylindricity that are less commonly specified because they are more difficult to visualize and even more difficult to verify conformity. In most cases, the surface profile and position controls will be more than sufficient to achieve the desired geometric control, and the engineer should carefully consider if these advanced location tolerance controls are really necessary.
Cylindricity. Rasis, E.P. (2011). Technical Reference Handbook Sixth Edition.

Cylindricity. Rasis, E.P. (2011). Technical Reference Handbook Sixth Edition.

Orientation Tolerances:

  • Perpendicularity: This tolerance is specified in relation to two other datums and controls the orientation of the surface as it deviates from 90 degrees. The tolerance zone specifies the envelope within which the surface may vary from a perfectly perpendicular state.
Perpendicularity (002)

Perpendicularity. Rasis, E.P. (2011). Technical Reference Handbook Sixth Edition.

  •  Parallelism: This control dictates that all points on a surface or axis are located within the tolerance range.  The parallelism is similar to the angularity tolerance detailed below, except the angle is always zero degrees.
  • Angularity: In practice, this is the same tolerance as perpendicularity, except that the surface must conform to a specified angle, as it is defined from a datum reference frame.
Angularity (002)

Angularity. Rasis, E.P. (2011). Technical Reference Handbook Sixth Edition.

Although this whirlwind survey barely scratches the surface of GD&T principles, it’s serves as a good introduction to principles that can affect the mating surfaces of fittings.  The fundamental lesson is that the geometry and shape of the mating features matter just as much as the actual sizes of those features, and with enough practice in the basics of GD&T, then engineer can wield far more control over mating features that what was previously possible with simple plus/minus size tolerances.

See the full GD&T standard (ASME Y14.5 2009) for more information: https://www.asme.org/products/codes-standards/y145-2009-dimensioning-and-tolerancing

Referenced Images: Rasis, E.P. (2011). Technical Reference Handbook Sixth Edition.


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