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William Tandler

Metrology

Clarifying GD&T

A glossary of key terms to better understand geometric dimensioning and tolerancing

Published: Thursday, October 29, 2015 - 21:00

Editor's note: The original version of this “classic” article by William Tandler first appeared in Quality Digest media in June 2008 and was based on the ASME Y14.5 1994 standard. Updated here to address the ASME Y14.5 2009 standard, it is an alphabetically organized primer of the terms that define GD&T, and is extraordinarily valuable as a means to replace common “interpretations” of GD&T with uniquely clear statements of its intent. To learn even more about GD&T, visit online to assess the nine-episode streaming video training series, “SmartGD&T: An Advanced Beginners Guide” developed by Tandler and 360 Performance Circle, Quality Digest's training division.

W hen dealing with geometric dimensioning and tolerancing (GD&T), it soon becomes evident that GD&T is a word- and concept-rich subject. And so it must be, because it deals with two very complex worlds—the code-defined, perfect and imaginary world of GD&T itself, and the imperfect real world of actual parts, along with their associated manufacturing, inspection, and assembly processes.

If one is to succeed with GD&T—i.e., benefit from its power to maximize the fault tolerance of machine part designs and uniquely specify permissible limits of imperfection in order to 1) to guarantee assemblability and operation; 2) minimize manufacturing costs; and 3) turn metrology from a confused set of tribal understandings into a science, clear thinking and clear communication are essential, both of which depend on crystalline definitions. So try these terms on, play with them, share them, try to refine their definitions, and complain about the missing ones. Here we go.

Actual Value. In general, the actual value of a geometric characteristic is the size of the smallest associated tolerance zone that just contains the controlled component of the considered feature. Examples: 1) The actual value of the Flatness (the actual Flatness) of a planar surface is the minimum thickness, orientation, and location-unconstrained, slab-like zone that just contains all the points on its surface. 2) The actual value of the Position (the actual position) of a bore is the diameter of the smallest location-constrained cylindrical zone that just contains the entire, bounded axis of the actual feature. Exceptions: 1) Surface Profile: Although the default actual value of the Surface Profile is the minimum thickness, lasagna-like zone whose median surface coincides with the basic surface of the controlled feature and just contains all the points on the controlled surface, because Surface Profile tolerance zones may be asymetrically imposed, the actual value of the Surface Profile may also be broken down into two components, namely the generally positive in-space actual value, and the generally negative in-material actual value. See also “Measured Value.” 2) Diameter: The Diameter tool always defines two actual values. In the case of a shaft referenced at MMC or RFS, the Actual Mating Size is the diameter of the minimum circumscribed, unconstrained cylinder, which just contains all the points on its surface; the Actual Local Size is the diameter of the largest sphere, which can just pass through its interior.

BASIC Dimension. Basic angular or linear dimensions serve to orient and locate tolerance zones, but only those tolerance zones that can be oriented or located. Size and form tolerance zones can be neither oriented nor located. Orientation tolerance zones can only be oriented. Location tolerance zones can be both oriented and located. See also “Nominal Dimension” and “Reference Dimension.”

Bilateral Tolerance. A pair of equal or unequal numerical values p which, when added to a nominal dimension, specify permissible upper and lower limits for a variable defined by a size tool or by the Dimension Origin tool. See also “Unilateral Tolerance.”

Cartesian Coordinate System. A collection of three perfectly straight, mutually perpendicular lines, called axes, that meet in a point, called the origin, that form three perfectly flat, mutually perpendicular planes, called bases planes, and which are outfitted with linear scales. Cartesian coordinate systems have three degrees of rotational freedom—called pitch, yaw, and roll, and three degrees of translational freedom, called Tx, Ty, and Tz. Cartesian coordinate systems provide the framework for specifying the orientations and locations of tolerance zones. Where functionally more appropriate, Cartesian coordinate systems can be converted into cylindrical and spherical coordinate systems. See also “Datum Reference Frame.”

Considered Feature. A feature currently under consideration, for example, being toleranced.

Datums. 1) What are they? Datums are the minimum mutually embedded set of a single, perfect, imaginary reference point and/or line, and/or plane, which together fully characterize the orientation and location of the datum feature simulator. 2) Where do they come from? Datums are extracted from Datum Feature Simulators. 3) What are they for? Datums serve to constrain the rotational and translational degrees of freedom of a “starter coordinate system” and turn it into a Datum Reference Frame.

Datum Features. 1) What are they? Datum features are specially labeled, imperfect physical surfaces of real objects. 2) What are they for? Datum features serve to constrain an object’s degrees of rotational and translational freedom during manufacturing, inspection, and assembly operations.

Datum Feature Simulators. 1) What are they? Datum Feature Simulators are conceptually perfect and physically almost perfect, inverse datum features. 2) What are they for? Datum Feature Simulators serve as a bridge from the imperfect real world of Datum Features to the perfect, imaginary world of Datums and Datum Reference Frames. It is from Datum Feature Simulators that we extract Datums, it is in Datum Feature Simulators that we establish Datum Reference Frames, and it is with Datum Feature Simulators that we transfer Datum Reference Frames to actual parts. Examples: gauge pins, granite surface plates, collets, machinist vises, manufacturing fixtures, and hard gauges.

Datum Reference Frames. 1) What are they? Datum Reference Frames are Cartesian (or cyclindrical, or spherical) coordinate systems established in real parts. 2) What are they for? Datum Reference Frames serve to orient and locate tolerance zones. 3) How are they established? Datum Reference Frames are established in a six-step process using the Datums extracted from a set of Datum Feature Simulators to constrain a starter coordinate system.

Effective Tolerance. The sum of the Specified Tolerance and an authorized, tolerance zone size bonus. See also “Specified Tolerance” and “Tolerance Zone Size Bonus.”

Feature. A collection of associated points that form a continuous surface separating solid matter from free space, and are bounded by other similar constructs. Examples: 1) the surface of bore bounded by the opposed planar surfaces of a slab; 2) one surface of a propeller blade.

Feature Component. Any physical or conceptual geometric entity associated with a feature, such as the straight and circular surface lines, the axis and the median line, or all the points on the surface of a cylinder.

Feature Control Frame. A rectangular frame containing up to three major compartments, the first for specifying a Geometry Control Tool, the second for specifying the shape and size of a tolerance zone along with appropriate Tolerance Zone Size (material condition) and other modifiers, and the third for listing the Datum Features and their Tolerance Zone Mobility (material boundary) modifiers responsible for establishing the required Datum Reference frame.

Feature of Size (Type I). A collection of associated surface points that are nominally equidistant 1) from a point (forming a sphere), 2) from a straight line (forming a cylinder), or 3) from a plane (forming a slab or a slot), and whose associated normal vectors are exclusively oriented toward or away from said point, line, or plane.

Feature of Size (Type II). A collection of associated points that are nominally equidistant 1) from a compound curved line (example: a bent pipe), or 2) from a compound curved surface (example: a curved wall), and whose associated normal vectors are exclusively oriented toward or away from said line or surface.

Geometric Characteristic. A concept characterizing the size, form, orientation, or location of a feature or of a feature component. Examples include diameter, flatness, parallelism, and/or position. See also “Geometry Control Tool.”

Geometric Entity. Any imaginary or real, two- or three-dimensional geometric construct, thus a point, straight or curved line, plane, or curved surface.

Geometry Control Tool. A conceptual tool for imposing limits on the imperfection in the size, form, orientation, or location of a feature of a physical object. Examples include Position, Cylindricity, Circular Runout, etc. See also “Geometric Characteristic.”

In-Material Boundary. The form perfect boundary representing the region inside the surface of a feature, beyond which one can be guaranteed to find material. There are both virtual and actual in-material boundaries, which can be either unconstrained, orientation-constrained, or orientation- and location-constrained. Virtual in-material boundaries are also referred to as Virtual Least Material Boundaries (LMB). See also “In-Space Boundary.”

In-Space Boundary. The form perfect boundary representing the region outside the surface of a feature, beyond which one can be guaranteed to find no material. There are virtual and actual in-space boundaries, which can be either unconstrained, orientation-constrained, or orientation- and location-constrained. Virtual in-space boundaries are also referred to as Virtual Maximum Material Boundaries (MMB). See also “In-Material Boundary.”

(L). The “Least Material Condition” (LMC) or “Least Material Boundary” (LMB) modifier. 1) When placed behind the tolerance value in a feature control frame, (L) serves as a Tolerance Zone Size Modifier, and expands the tolerance zone by the difference between the unconstrained in-material actual mating size of the considered feature and its LMC size, as the feature departs from LMC toward MMC. 2) When placed behind a Datum Feature label in a Feature Control Frame, (L) serves as a Tolerance Zone Mobility modifier and forecasts potential Datum Reference Frame (L)ability (instability) as the Datum Feature departs from its Least Material Boundary.

LBM. The “Least Material Boundary,” the extreme in-material boundary of a feature as a result of all constraints imposed on its size, form, orientation, and location. See also “In-Material Boundary.”

LMC. The “Least Material Condition,” the effective in-material size of a feature in which it contains the least material allowed by limits on its size.

LMC Envelope. The form-perfect in-material boundary of a feature at its “least material condition” as imposed by the envelope rule in the presence of the Tolerance Zone Size modifier (L).

(M). The “Maximum Material Condition” (MMC) of “Maximum Material Boundary” (MMB) modifier. 1) When placed behind the tolerance value in a Feature Control Frame (M), serves as a Tolerance Zone Size modifier, and expands the tolerance zone by the difference between the unconstrained in-space actual mating size of the considered feature and its MMC size, as the feature departs from MMC toward LMC. 2) When placed behind a Datum Feature label in a feature control frame (M), serves as a Tolerance Zone Mobility modifier and forecasts potential Datum Reference Frame (M)obility as the feature departs from its Maximum Material Boundary.

Material Condition. A measure of the amount of material associated with a feature as its size varies between its upper and lower limits known as the Maximum and Least Material Condition.

Maximum Material Boundary. See “In-Space Boundary.”

Measured Value. An approximation of the actual value of a geometric characteristic, limited by the uncertainty of a measurement process.

MMB. “Maximum Material Boundary,” the extreme in-space boundary of a feature as a result of all constraints imposed on its size, form, orientation, and location. See also “In-Space Boundary.”

MMC. “Maximum Material Condition,” the effective in-space size of a feature which contains the most material allowed by limits on its size.

MMC Envelope. The form-perfect, in-space boundary of a feature at its MMC, as imposed by the envelope rule in the presence of the Tolerance Zone Size modifiers (S) or (M).

Nominal Dimension. A numerical value that, together with upper and lower tolerances, specifies the permissible upper and lower limits of a dimension. Toleranced nominal dimensions should only be used in conjunction with size tools, including the Radius and Spherical Radius tools, with the Depth tool, and with the Dimension Origin tool. See also “Basic Dimension” and “Reference Dimension.”

Reference Dimension. An untoleranced dimension placed inside parentheses that serves as a general reminder of scale. See also “Basic Dimension” and “Nominal Dimension.”

Resultant Condition. A no-longer recommended ASME Y14.5M 1994 term for the in-material virtual boundary of a feature. See also “In-Material Boundary” and “Least Material Boundary (LMB).”

RFS. “Regardless of Feature Size,” the requirement imposed by the Tolerance Zone Size modifier (S) that the size of a Considered Feature shall have no influence on the size of an associated form, orientation, or location-constrained tolerance zone. See also “(S), the Regardless of Feature Size modifier.”

RMB. “Regardless of Material Boundary,” the requirement imposed by the Tolerance Zone Mobility modifier (S) that the size or location of the referenced Datum Feature shall have no influence on the mobility of the associated tolerance zone, namely that the Datum Feature shall be simulated (S)tably, regardless of its in-space boundary. See also “(S), the Regardless of Feature Size modifier.”

(S). The “Regardless of Feature Size” or “Regardless of Material Boundary” (RMB) modifier. 1) When placed behind the tolerance in a Feature Control Frame (S), serves as a Tolerance Zone Size modifier and requires the tolerance value to be (S)tuck at the stated value regardless of departures from its MMC or LMC. 2) When placed behind a Datum Feature label in a Feature Control Frame (S), serves as a Tolerance Zone Mobility modifier and requires the associated Datum Reference Frame to be (S)table relative to the specified datum feature, regardless of its size. Note: The ASME Y14.5M 1994 standard makes the RFS modifier (S) the default in the absence of an explicit (M) or (L) modifier, but still allows its explicit use. The ASME Y14.5 2009 standard makes (S) the default, but no longer permits its explicit use.

Specified Tolerance. The tolerance specified in a feature control frame. See also “Effective Tolerance” and “Tolerance Zone Size Bonus.”

Third Angle Projection. An elevation view of a part generated by “sliding” the plan view of a part up inside of a bowl by 90°.

Tolerance. The numerical size of a tolerance zone.

Tolerance Zone. A bounded region of space within which a specific component of a feature must lie, which can be unconstrained or oriented and located by Basic dimensions.

Tolerance Zone Size Bonus. The additional tolerance authorized by a tolerance zone size modifier (M) or (L), and generated by a deviation of the actual in-space or actual in-material mating size of the considered feature from its size and form constrained maximum material (M) or least material (L) boundary. See also “Effective Tolerance” and “Specified Tolerance.”

Tolerance Zone Mobility Bonus. The residual orientation and location mobility of Tolerance Zones enabled by Datum Features referenced at MMB or LMB, which have departed from their Maximum or Least Material Boundaries, representing “play” between them and their mating Datum Features.

Unilateral Tolerance. One of a pair of tolerance values associated with a nominal dimension, of which the other is zero, therefore permitting deviations from nominal in one direction only. Also an explicitly unidirectional tolerance imposed by the surface profile tool using the Unequally Disposed modifier (U). See also “Bilateral Tolerance.”

The power of words

GD&T is a symbolic language for specifying and communicating permissible limits of imperfection for machine part features to guarantee assembly and operation prior to drawing release. Applied to 2D engineering drawings or, better, to 3D CAD models, it is the only basis for truly functional tolerance stack-up analysis, and for get-it-right-the-first-time manufacturing and coordinate metrology.

Because of its complexity, most GD&T is largely “decorative” and requires “interpretation,” making it dangerous, tending toward useless. To actually deliver its amazing gifts, it must be carefully “encoded” and uniquely “decoded,” which are the foundation concepts in correct terminology and comprehensive training.

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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.