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Engineering & Design: Geometric Dimensioning
5
14.1 Conversion of Position (Cylindrical) Tolerance Zones 14.2 Conversion of Position Tolerance Zone 14.3 Conversion of Coordinate Measurements to
- NADCA Product Specification Standards for Die Castings / 2006 5-
- Section Contents NADCA No. Format Page S E C T I O N
- 1 Introduction 5-
- 2 What is GD&T? 5-
- 3 Why Should GD&T be Used? 5-
- 4 Datum Reference Frame 5-
- 4.1 Primary, Secondary, Tertiary Features & Datums 5-
- 4.2 Datum Feature Vs. Datum Plane 5-
- 4.3 Datum Plane Vs. Datum Axis 5-
- 4.4 Datum Target Sizes & Locations 5-
- 5 Feature Control Frame 5-
- 6 Rule #1 – Taylor Principle (Envelope Principle) 5-
- 7 GD&T Symbols/Meanings 5-
- 8 Material Conditions 5-
- 8.1 Maximum Material Condition (MMC) 5-
- 8.2 Least Material Condition (LMC) 5-
- 8.3 Regardless of Feature Size (RFS) 5-
- 9 Location Tolerances 5-
- 9.1 Position Tolerance 5-
- 9.2 Concentricity & Symmetry Tolerances 5-
- 10 Profile Tolerance 5-
- 11 Run Out Tolerances 5-
- 12 Orientation Tolerances 5-
- 13 Form Tolerances 5-
- 13.1 Straightness 5-
- 13.2 Flatness 5-
- 13.3 Circulatity (Roundness) 5-
- 13.4 Cylindricity 5-
- 14 Conversion Charts 5- - 5- to/from Coordinate Tolerance Zones - 5- to/from Coordinate Tolerance Zone - 5- Position Location Measurements
5-2 NADCA Product Specification Standards for Die Castings / 2006
1 Introduction
The concept of Geometric Dimensioning and Tolerancing (GD&T) was introduced by Stanley Parker from Scotland in the late 1930’s. However it was not used to any degree until World War II (WW II) because until then the vast majority of products were made in-house. The designer could discuss with the manufacturing personnel (die designer, foundry foreman, machinist, and inspectors) what features were to be contacted to establish the so called “centerlines” that were used on the drawing to locate features such as holes and keyways. Also when two (2) or more features were shown coaxial or symmetrical around these “centerlines”, the questions that needed to be answered by the designer was, “how concentric or symmetrical do these features have to be to each other”?. During WW II companies had to “farm out” parts because of the quantities/schedules. This meant the new manufacturer had to interpret the drawing hence the “centerlines” were often established by contacting features that were not functional or important and features produced from these incorrect “centerlines” were not at the location required. The parts did not assemble and/or did not function properly hence had to be fi xed or scrapped. GD&T was the solution to this major problem. GD&T provides a designer the tools to have clear, concise, and consistent instructions as to what is required. It eliminates ambiguities hence everyone that is involved with the part will not have to interpret the dimensioning.
2 What is GD&T?
It is compilation of symbols and rules that efficiently describe and control dimensioning & tolerancing for all drawings (castings, machined components,etc.). It is documented in ASME Y14.5M which has the symbols, rules, and simple examples. Also ASME Y14.8 has guidance for casting and forging drawings.
3 Why should GD&T be used?
a. It is a simple and efficient method for describing the tolerancing mandated by the designer of the part.
b. It eliminates ambiguities as to what Datum features are to be contacted to establish the Datum planes and/or Datum axis that are to be used for locating other features. All inspection will result in the same result – the dimension is within or out of tolerance. Fig. 5-1 illustrates a simple example of ambiguities associated with the “old” type drawing. Fig. 5-2 illustrates the same example with GD&T.
c. It simplifies inspection because hard gages can often be utilized and inspection fi xtures are often mandated which simplifies inspection for production quantities.
d. It forces the designer to totally consider function, manufacturing process, and inspection methods. The result is larger tolerances that guarantee function, but reduce manufacturing & inspection costs. Also the “bonus” or extra tolerance for certain conditions can result in significant production cost savings. In addition the time to analyze whether a missed dimen- sion is acceptable is dramatically reduced.
5-4 NADCA Product Specification Standards for Die Castings / 2006
Fig. 5-3 Primary, secondary, tertiary features & datum planes.
4 Datum Reference Frame (DRF):
The DRF is probably the most important concept of GD&T. In order to manufacture and/or inspect a part to a drawing , the three (3) plane concept is necessary. Three (3) mutually perpendicular (exactly 90° to each other) and perfect planes need to be created to measure from. In GD&T this is called Datum Reference Frame whereas in mathematics it is the Cartesian coordinate system invented by Rene Descartes in France (1596-1650). Often one would express this concept as the need to establish the X,Y, and Z coordinates. The DRF is created by so-called Datum Simulators which are the manufacturing, processing, and inspection equipment such as surface plate, a collet, a three jaw chuck, a gage pin, etc. The DRF simulators provide the origin of dimensional relationships. They contact the features (named Datum Features) which of course are not perfect hence measurements from simulators (which are nearly perfect) provides accurate values and they stabilize the part so that when the manufacturer inspects the part and the customer inspects the part they both get the same answer. Also if the part is contacted during the initial manufacturing setup in the same manner as when it is inspected, a “layout” for assuring machining stock is not required. The final result (assuming the processing equipment is suitable for the tolerancing specified) will be positive.
4.1 Primary, Secondary, and Tertiary Features & Datums:
The primary is the first feature contacted (minimum contact at 3 points), the secondary feature is the second feature contacted (minimum contact at 2 points), and the tertiary is the third feature contacted (minimum contact at 1 point). Contacting the three (3) datum features simultaneously establishes the three (3) mutually perpendicular datum planes or the datum reference frame. If the part has a circular feature that is identified as the primary datum feature then as discussed later a datum axis is obtained which allows two (2) mutually perpendicular planes to intersect the axis which will be the primary and secondary datum planes. Another feature is needed (tertiary) to be contacted in order orientate (fi x the two planes that intersect the datum axis) and to estab- lish the datum reference frame. Datum features have to be specified in an order of precedence to properly position a part on the Datum Reference Frame. The desired order of precedence is obtained by entering the appropriate datum feature letter from left to right in the Feature Control Frame (FCF) (see Section 5 for explanation for FCF). The first letter is the primary datum, the second letter is the secondary datum, and the third letter is the tertiary datum. The letter identi- fies the datum feature that is to be contacted however the letter in the FCF is the datum plane or axis of the datum simulators. See Fig. 5-3 for Datum Features & Planes.
NADCA Product Specification Standards for Die Castings / 2006 5-
Fig. 5-4 Datum feature vs. datum plane.
Fig. 5-5 Datum feature vs. datum axis.
4.2 Datum Feature vs Datum Plane:
The datum features are the features (surfaces) on the part that will be contacted by the datum simulators. The symbol is a capital letter (except I,O, and Q) in a box such as A used in the 1994 ASME Y14.5 or -A- used on drawings made to the Y14.5 before 1994. The features are selected for datums based on their relationship to toleranced features, i.e., function, however they must be accessible, discernible, and of sufficient size to be useful. A datum plane is a datum simulator such as a surface plate. See Fig. 5-4 for a Datum Feature vs a Datum Plane.
4.3 Datum Plane vs Datum Axis:
A datum plane is the datum simulator such as a surface plate. A datum axis is also the axis of a datum simulator such as a three (3) jaw chuck or an expandable collet (adjustable gage). It is important to note that two (2) mutually perpendicular planes can intersect a datum axis however there are an infinite number of planes that can intersect this axis (straight line). Only one (1) set of mutually perpendicular planes have to be established in order to stabilize the part (everyone has to get the same answer – does the part meet the drawing requirements?) therefore a feature that will orientate or “clock” or “stabilize” has to be contacted. The datum planes and datum axis establish the datum reference frame and are where measurements are made from. See Fig. 5-5 for Datum Feature vs Datum Axis.
NADCA Product Specification Standards for Die Castings / 2006 5-
Fig. 5-8 Rule #1.
6 Rule # 1 – Taylor Principle (Envelope Principle):
When only a size tolerance is specified for an individual feature of size the form of this feature shall not extend beyond a boundary (envelope) of perfect form at maximum material condition (MMC). In other words when the size is at MMC the feature has to be perfectly straight. If the actual size is less than the MMC the variation in form allowed is equal to the difference between the MMC and the actual size. The relationship between individual features is not controlled by size limits. Features shown perpendicular, coaxial or symmetrical to each other must be controlled for location or orientation otherwise the drawing is incomplete. In other words Fig. 5- is an incomplete drawing. Fig. 5-8 shows the meaning of Rule #1 for an external cylinder (pin or shaft) and an internal cylinder (hole). Note that a hard gage can be used to inspect this principle or requirement.
5-8 NADCA Product Specification Standards for Die Castings / 2006
7 GD&T Symbols / Meanings
Tolerance Type
Geometric Charac- teristics
Symbol Applied To Datum Reference Required
Use L or M Material Condition
Gages Used Feature Surface
Feature of Size Dim. Form Straightness^ ⎯
YES
YES
NO
YES YES***
Flatness Circularity NO NO NO
Cylindricity
Location Positional Tolerance ⁄⁄
NO YES YES
YES YES***
Concentricity NO NO Symmetry ——————— Orientation Perpendicularity ⊥ Parallelism (^) ⁄⁄ YES YES YES YES YES***** Angularity ∠ Profile Profile of a Surface ∩ YES NO YES YES NO* Profile of a Line ∩ Runout Circular Runout (^) YES YES YES NO NO Total Runout * Can be used to control form without a datum reference. ** Datum reference only.
*** – Yes if M is specified for the feature of size being controlled
- No if S or L are specified for the feature of size being controlled.
8 Material Conditions:
Features of size which includes datum features have size tolerances hence the size condition or material (amount of metal) condition can vary from the maximum metal condition (MMC) to the least metal condition (LMC). Consequently if the center planes or axes of a feature of size are controlled by geometric tolerances a modifying symbol can be specified in the feature control frame that applies the tolerance value at either the maximum or the least material condition. It also can be specified for a datum that is a feature of size. If a symbol is not specified the tolerance value applies regardless of material condition which is named regardless of feature size (RFS).
8.1 Maximum Material Condition (MMC):
This is the condition when the actual mating size or envelope size is at the maximum material condition which is maximum size for an external feature such as a cylinder and the minimum
size for an internal feature such as a hole. The symbol is m. The tolerance value specified for the
feature being controlled in the FCF applies only if the actual mating envelope is the MMC size. If the actual mating envelope deviates from MMC an additional tolerance is allowed. The added tolerance is the difference between the actual mating envelope size and the MMC size hence the largest actual mating envelope named virtual condition is equal to the MMC size plus the tolerance specified in the FCF for an external feature and minus for an internal feature. The MMC symbol is used to assure that parts will assemble and it allows the use of so called hard gages (go gages) for quick inspections. An example of position with MMC is shown in Fig. 5-9. It should be noted that actual local size has to meet the size tolerance however the actual local size does not affect the geometric characteristic tolerance.
5-10 NADCA Product Specification Standards for Die Castings / 2006
Fig. 5-10 Position control with LHC.
A
THIS ON THE DRAWING
MEANS THIS
Ø TOLERANCE ZONE
Ø TOLERANCE ZONE
ACTUAL MINIMUM MATING ENVELOPE FEATURE BEING CONTROLLED
DATUM AXIS A (AXIS OF ACTUAL MATING ENVELOPE)
ACTUAL LOCAL SIZE Ø1.00 TO Ø1.
Ø2.00+.
ACTUAL MINIMUM MATING ENVELOPE (AXIS PARALLEL TO DATUM AXIS A)
Ø1. Ø1.
. .
Ø1.00+. Ø.005 L A
8.3 Regardless Of Feature Size (RFS):
There is no symbol in the 1994 Y14.5 whereas it was s for the 1982 Y14.5. It is applicable if the
MMC or the LMC are not specified for individual features of size tolerances or for datum features of size. The tolerance is limited to the specified value in the FCF and if applied to a datum feature of size the actual axis or center plane have to be established regardless of the feature size. It is always used for run out, concentricity, and symmetry controls as will be discussed in those sections. It is also used when targets are specified to establish datum axes and center planes because the targets have to contact the datum features to be useful. Also it is used to control wall thickness variation between external and internal features. Hard gages are not applicable since there is no additional or bonus tolerance as allowed for MMC and LMC. An example of position with RFS is shown in Fig. 5-11.
NADCA Product Specification Standards for Die Castings / 2006 5-
Fig. 5-11 Position control with RFS.
A
THIS ON THE DRAWING
MEANS THIS
Ø TOLERANCE ZONE
Ø TOLERANCE ZONE
ACTUAL MINIMUM MATING ENVELOPE FEATURE BEING CONTROLLED
DATUM AXIS A (AXIS OF ACTUAL MATING ENVELOPE)
ACTUAL LOCAL SIZE Ø1.00 TO Ø1.
Ø2.00+.
ACTUAL MATING ENVELOPE (AXIS NOT PARALLEL TO DATUM AXIS A)
Ø1.
Ø1.
.
.
Ø1.00+. Ø.005 A
9 Location Tolerances:
These include position, concentricity, and symmetry tolerances. Position is used to control coaxiality of features, the center distance between features, and the location of features as a group. Concentricity and symmetry are used to control the center distance of feature elements. These three (3) tolerances are associated with datum’s because the obvious question is – located from what?
9.1 Position Tolerance:
Positional tolerances are probably used more than any other geometric control. It is used to locate features of size from datum planes such as a hole or keyway and used to locate features coaxial to a datum axis. The tolerance defines a zone that the axis or center plane of a feature of size may vary from. The concept is there is an exact or true position that the feature would be if it was made perfect however since nothing is made perfect a tolerance zone allows deviation from perfection. The exact location of a feature of size is defined by basic dimensions which is shown in a box () and are established from datum planes or axes. Coaxial controls are typically a cylindri-
NADCA Product Specification Standards for Die Castings / 2006 5-
Fig. 5-14 Concentricity tolerancing.
9.2 Concentricity & Symmetry Tolerances:
These both control the median points of a feature of size: concentricity ( ) is applied to circular features whereas symmetry ( ) is applied to non circular features. Both require that the median points of the controlled feature, regardless of its size, to be within the tolerance zone (cylindrical zone for concentricity and two parallel planes for symmetry). The tolerance zone is equally disposed about the datum axis for concentricity and datum plane for symmetry. These controls are not used very often because median points are difficult to establish due to irregularities of form and the only reason to use these controls is for controlling the out of balance that can exist if the mass center is not close to the axis of rotation or center plane. Examples of controlling concentricity and symmetry are shown in Fig. 5-14 & 5-15 respectively.
5-14 NADCA Product Specification Standards for Die Castings / 2006
Fig. 5-15 Symmetry tolerancing.
10 Profile Tolerance:
Profile tolerances can control the location, orientation, and form of a feature that has no size (sur- face). There are two (2) types – profile of a surface (∩) and profile of a line (∩). The exact or true profile of a feature is established by basic dimensions of radii, angular dimensions, and coordinate dimensions established from datums however a profile tolerance can be specified to an individual surface without specifying a datum – see Fig. 16. The elements of a profile (outline of an object in a given plane) are straight lines or arcs. The tolerance is a boundary of two (2) parallel planes disposed (equally – see Fig. 17 or in one direction – see Fig. 16) and normal (perpendicular) along the perfect or true profile within which the entire surface must lie. The profile can be controlled between two (2) points – see Fig 16. Also if datum planes are established by targets – see Fig. 18 the tolerance zone is equally disposed about the datum planes whereas if the datum planes are established by complete contact with the datum features the tolerance zone is unidirectional and ½ the tolerance value in the FCF – see Fig. 17 vs Fig. 18.
5-16 NADCA Product Specification Standards for Die Castings / 2006
Fig. 5-17 Profile control – all around entire part without targets. Notes: 1) All surfaces to be within .02 ± .01 tolerance zone of true or perfect profile.
2) Datum A B and C to be within .01 of datum planes A, B, and C.
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Fig. 5-18 Profile control – all around entire part with targets.
NADCA Product Specification Standards for Die Castings / 2006 5-
Fig. 5-20 total runout with targets.
12 Orientation Tolerances:
There are three (3) separate orientation tolerances however two (2) of the three are specific values of the general tolerance named angularity. The two (2) specific tolerances are named perpendicu- larity (90° to a datum) and parallelism (180° to a datum). These tolerances control the orientation of features to a datum plane or axis. Angularity controls a surface (non feature of size), a center plane or an axis of a feature of size to a specified angle and its symbol is ∠. Perpendicularity symbol is ⊥ and parallelism symbol is ⁄⁄ and they do the same as angularity except the angles are specific as previously stated. The tolerance zone may be either two (2) parallel planes at the specified basic angle from a datum plane or axis within which the surface, center plane or axis must lie or it may be a cylindrical zone within which the axis of the considered feature must lie. Of course if angularity tolerance is specified for a feature of size the material condition modifiers
m or l may be specified. If neither m or l is specified then as always the regardless of feature size
(RFS) is applicable. See Fig’s 5-21 thru 5-23 for examples of ∠, ⊥, and ⁄⁄.
5-20 NADCA Product Specification Standards for Die Castings / 2006
Fig. 5-21 Angularity of a feature of size axis at MMC.
Fig. 5-22 Perpendicularity of a feature of size axis at MMC with datum feature of size at MMC.
