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William Tandler


The Perfect Imaginary World of GD&T

Smart GD&T workshop No. 3

Published: Wednesday, December 12, 2007 - 22:00

Our original plan for workshop No. 3 was to discuss what are generally referred to as material condition modifiers, namely the encircled letters “M,” “L,” and “S” which sometimes follow tolerance values and sometimes follow datum-feature labels in feature-control frames. The idea was to explain their very different effects as a function of their different locations and as a result, to justify some new names, such as tolerance-zone size modifiers when associated with tolerance values, and tolerance-zone mobility modifiers when associated with datum features. Because of many requests to precede this investigation with a preparatory overview of the most important fundamental concepts of GD&T, we do just that, convinced it will enhance the tolerance-zone size and mobility modifier workshop, which will come next.

This workshop is therefore dedicated to what we call the “Perfect Imaginary World” of GD&T. Let’s start with a definition: GD&T is a symbolic language with which to manage imperfect geometry perfectly, that is, with which to impose permissible limits of imperfection that guarantee the assembly and operation of manufactured parts. To perfectly manage imperfect geometry, we need a set of perfect tools and a language with which to implement them. The most important components of the perfect imaginary world of GD&T are:
  • Tolerance zones

  • Tolerance values

  • Datums

  • Datum reference frames

  • Basic dimensions

  • A symbolic language

Let’s start with tolerance zones. As shown in Figure 1 below, tolerance zones are perfect, imaginary bounded regions of space within which a particular feature component is required to lie. Tolerance zones come in many shapes, of which the most important are cylindrical, tube-like, slab-like and skin-like.

Figure 1. Tolerance Zones

Cylindrical zones, for example, normally serve to constrain the orientation or location of an axis, but can also constrain the straightness of a median line. Tube-like zones can set upper and lower limits on the size of a bore, or, if we allow the zone to expand and contract to adapt to changes in size, serve to constrain only its form (cylindricity). Slab-like zones, on the other hand, can be used to limit the flatness, the orientation and the location of a planar surface by requiring all of its points to lie inside the zone, or can serve to locate the mid-plane of a slot. Skin-like zones, defined only by the surface profile tool, can control the size, form, orientation, and location of compound curved surfaces.

The next most important component of the Perfect Imaginary World of GD&T is the tolerance value, which specifies the size of a tolerance zone. As shown in Figure 2, in the case of the cylindrical zone, the tolerance is its diameter. In the case of the tube-like zone, it’s the wall thickness; in the case of the slab-like zone, the slab thickness; and in the case of the skin-like zone, the skin thickness. Just like tolerance zones, tolerance values are also perfect.

Figure 2. Tolerance Values

Clearly, by defining the size and form of a skin-like tolerance zone, we can control the size and form of a feature. However, if we could also orient and locate skin-like and other tolerance zones, we could control feature orientation and location as well. For starters, we’ll need something relative to which to orient and locate them, for example reference points, lines, and planes. These are exactly what we refer to as datums. Figure 3 illustrates the six alternative datums we might need—a stand-alone point, line, or plane; a point on a line; a line in a plane; and a point on a line in a plane—each of which constrains a different set of degrees of freedom.

Figure 3. Datums

But are datums enough? In fact, we normally use coordinate systems for that purpose, namely a perfect imaginary construct consisting of three perfectly straight, mutually perpendicular axes, three perfectly flat, mutually perpendicular base-planes, and a point, or the origin. Because coordinate systems are outfitted with linear scales and provide a complete frame of reference with which everyone in design, manufacturing and inspection is familiar, we use datums only to establish coordinate systems, and the coordinate systems, in turn, to orient and locate tolerance zones. Because they are so special, coordinate systems established by datums are referred to as “datum reference frames.” See Figure 4.

Figure 4. Datum Reference Frames

Once we have datum reference frames, we need a way to orient and locate tolerance zones relative to them. To clearly differentiate between the toleranced nominal dimensions we use for size control and the fixed dimensions we reserve for orienting and locating tolerance zones, we place the latter inside rectangular frames and refer to them as “basic.” In Figure 5 below, we see a cylindrical tolerance zone that has been oriented by a basic angle of 90° relative to the XY base plane of a datum reference frame, and located by basic linear dimensions relative to its origin.


Figure 5. Basic Dimensions

Finally, to impose the perfect imaginary world of GD&T on imperfect real parts, we a way to express and communicate our requirements. This is done with the symbolic language consisting of feature control frames stuffed with geometry control tool icons such as position and cylindricity, tolerance zone shape modifiers, tolerance values, tolerance zone size modifiers, datum feature labels and tolerance zone mobility modifiers as shown in Figure 6.

Figure 6. The Symbolic Language of GD&T

In the end, GD&T is very simply a set of tools with which to, first, define coordinate systems in real objects, and second, specify the shape, size, orientation, and location of tolerance zones. Figure 7 illustrates a partially GD&T encoded drawing and the tolerance zone forest defined by the indicated feature controls frames.

Figure 7. Tolerance Zone Forests

Future Articles
In January we’ll address the topic of tolerance-zone size and tolerance-zone mobility modifiers, and in February the topic of datums, datum features, datum feature simulators, and the process of datum reference frame establishment.

In later articles we will deal with additional topics including the “Virtual Condition,” the GD&T tool selection process in design, and the effect of GD&T on manufacturing and inspection process management.

We also want to encourage readers to suggest topics on which they want feedback, or which cause problems in their work. We are ready when you are.

Feedback on Article 2
I want to thank Tom Gerhke for his feedback on our second article.

Mr. Gehrke suggests it’s important to understand that GD&T applies to objects manufactured from all materials, not merely metal, but also plastics. And why not silicon, carbon, and stone as well? We agree. He also values the fact that GD&T deals so realistically with reality. For example, in the case of a punched hole, by requiring good form on the “push-in” end (at MMC), but allowing poor form on the “push-out” end (LMC), as well as the ability of GD&T to deal with “draft” in castings and injection molded parts.


About The Author

William Tandler’s picture

William Tandler

William Tandler’s professional experience includes three years at the Hewlett Packard R&D laboratory in Palo Alto, CA, where he helped develop a quadruple mass spectrometer; five years with the laser manufacturer Coherent Inc. as international marketing manager; followed in 1975 by the founding of Multi Metrics Inc.

Tandler is currently a member of the ASME Y14.5.1 Mathematization Committee; a subject matter expert for Working Group 4 of the ASME Y14.5 standard focused on datums; and has been a contributor to ISO TC213 in the realm of datum reference frame construction.