# GD&T Workshop: The Perfect Imaginary World of GD&T

January 31, 2012

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Discover the important components of the perfect imaginary world of GD&T.

Let’s start with a definition. Geometric dimensioning and tolerancing (GD&T) is a symbolic language with which to manage imperfect geometry perfectly, that is, with which to impose fault tolerant, permissible limits of imperfection, which guarantee the assembly and operation of manufactured parts and keep costs down. In order to manage imperfect geometry perfectly, we need a set of perfect tools and a perfect language beholden to perfect rules 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 and a symbolic language.

Cylindrical zones, for example, as defined by the position tool, normally serve to constrain the orientation and location of a perfectly straight axis, but also can constrain the straightness of a potentially bent median line. Tube-like zones can set upper and lower limits on the size as well as the form of a bore using the diameter or the surface profile tool. If we impose a constant wall thickness but allow a tube-like zone to expand and contract in order to accommodate changes in the size of a bore, it serves only to constrain its form, namely its cylindricity.

Slab-like zones, on the other hand, can be used to limit the flatness and the orientation and the location of a planar surface using the surface profile tool, or can serve to orient and locate the mid-plane of a slot using the position tool.

Finally, compound curved skin-like zones defined by the surface profile tool, can control the size, form, orientation and location of compound curved surfaces, such as an automobile fender. Tolerance zones are form-perfect by definition.

2. Tolerance values. 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 1, in the case of the cylindrical zone, the tolerance value defines its diameter. In the case of the tube-like zone, the tolerance value defines the wall thickness; in the case of the slab-like zone, the thickness of the slab; and in the case of the skin-like zone, the thickness of the skin. Just like tolerance zones, tolerance values are also perfect.

Thus, coordinate systems have to be established, and the tools for doing so are called datums, namely the perfect, imaginary reference points, lines and planes we extract from the datum features of a machine part. Figure 2 illustrates the six alternative datums we will need, namely 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.

With a set of datums in hand, we can constrain the six degrees of freedom of a coordinate system-namely pitch, yaw, roll and translation in x, y and z. By outfitting the axes with linear scales, we can provide a complete frame of reference with which to orient and locate tolerance zones. Because they are established using datums, said coordinate systems are referred to as datum reference frames. (See Figure 3.)

Let’s start with a definition. Geometric dimensioning and tolerancing (GD&T) is a symbolic language with which to manage imperfect geometry perfectly, that is, with which to impose fault tolerant, permissible limits of imperfection, which guarantee the assembly and operation of manufactured parts and keep costs down. In order to manage imperfect geometry perfectly, we need a set of perfect tools and a perfect language beholden to perfect rules 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 and a symbolic language.

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

Cylindrical zones, for example, as defined by the position tool, normally serve to constrain the orientation and location of a perfectly straight axis, but also can constrain the straightness of a potentially bent median line. Tube-like zones can set upper and lower limits on the size as well as the form of a bore using the diameter or the surface profile tool. If we impose a constant wall thickness but allow a tube-like zone to expand and contract in order to accommodate changes in the size of a bore, it serves only to constrain its form, namely its cylindricity.

Slab-like zones, on the other hand, can be used to limit the flatness and the orientation and the location of a planar surface using the surface profile tool, or can serve to orient and locate the mid-plane of a slot using the position tool.

Finally, compound curved skin-like zones defined by the surface profile tool, can control the size, form, orientation and location of compound curved surfaces, such as an automobile fender. Tolerance zones are form-perfect by definition.

2. Tolerance values. 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 1, in the case of the cylindrical zone, the tolerance value defines its diameter. In the case of the tube-like zone, the tolerance value defines the wall thickness; in the case of the slab-like zone, the thickness of the slab; and in the case of the skin-like zone, the thickness of the skin. Just like tolerance zones, tolerance values are also perfect.

3. Datums. By merely defining the size and form of a skin-like tolerance zone, we can control the size and form of a feature. But if we could also orient and locate the zone, we could control the feature’s orientation and location as well. We always control the orientations and location of geometric entities using a coordinate system, but the question then arises, what coordinate system?

Thus, coordinate systems have to be established, and the tools for doing so are called datums, namely the perfect, imaginary reference points, lines and planes we extract from the datum features of a machine part. Figure 2 illustrates the six alternative datums we will need, namely 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.

4. Coordinate systems. Coordinate systems consist of three perfectly straight, mutually perpendicular axes [x], [y] and [z], which intersect to create an origin [xyz], and which act in pairs to form three perfectly flat, mutually perpendicular base-planes [xy], [yz] and [zx].

With a set of datums in hand, we can constrain the six degrees of freedom of a coordinate system-namely pitch, yaw, roll and translation in x, y and z. By outfitting the axes with linear scales, we can provide a complete frame of reference with which to orient and locate tolerance zones. Because they are established using datums, said coordinate systems are referred to as datum reference frames. (See Figure 3.)

5. Basic dimensions. After we have established a datum reference frame, we need a way to orient and locate tolerance zones relative to them. In order 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 4, we see a cylindrical tolerance zone which has been oriented by the implied basic angle of 90 degrees relative to the XY base plane, and located by the explicit basic linear dimensions of 50 and 70 millimeters relative to the X and Y axes of the datum reference frame established using datums A, B and C.

6. Symbolic language. Finally, in order to impose the perfect imaginary world of GD&T on imperfect real parts, we need a way to express and communicate our requirements. This is done with the symbolic language consisting of rectangular feature control frames which we stuff with geometry control tool icons like those for position and cylindricity, followed by tolerance zone shape modifiers such as the Ø symbol, followed by tolerance values, followed by tolerance zone size modifiers, namely the symbols (S), (M) and (L) associated with said tolerance values, followed by datum feature labels, namely A, B and C, finally followed by tolerance zone mobility modifiers, namely the symbols (S), (M) and (L) associated with said labels, all shown in Figure 5. In the end, GD&T is very simply a set of symbolic tools with which to define coordinate systems in real objects and with which to specify the shape, size, orientation and location of tolerance zones. Figure 6 illustrates a partially GD&T encoded drawing and the tolerance zone forest defined by the indicated feature control frames.

*Editor’s Note: Visit www.qualitymag.com (keyword: GD&T Workshop) to view the explanation for the first of the three drawings in the January GD&T Workshop. Comments on the remaining two drawings will follow once we have an adequate GD&T foundation.*
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