Simmons Ch22 - Geometrical Tolerancing and Datums PDF

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Chapter 22

Geometrical Tolerancing and Datums Geometrical Tolerances The object of this section is to illustrate and interpret in simple terms the advantages of calling for geometrical tolerances on engineering drawings, and also to show that, when correctly used, they ensure that communications between the drawing office and the workshop are complete and incapable of misinterpretation, regardless of any language barrier.

Applications Geometrical tolerances are applied over and above normal dimensional tolerances when it is necessary to control more precisely the form or shape of some feature of a manufactured part, because of the particular duty that the part has to perform. In the past, the desired qualities would have been obtained by adding to drawings such expressions as ‘surfaces to be true with one another’, ‘surfaces to be square with one another’, ‘surfaces to be flat and parallel’, etc., and leaving it to workshop tradition to provide a satisfactory interpretation of the requirements.

Advantages Geometrical tolerances are used to convey in a brief and precise manner complete geometrical requirements on engineering drawings. They should always be considered for surfaces which come into contact with other parts, especially when close tolerances are applied to the features concerned. No language barrier exists, as the symbols used are in agreement with published recommendations of the International Organization for Standardization (ISO) and have been internationally agreed. BS 8888 incorporates these symbols. Caution e It must be emphasized that geometrical tolerances should be applied only when real advantages result, when normal methods of Manual of Engineering Drawing. DOI: 10.1016/B978-0-08-096652-6.00022-X Copyright Ó 2012 Elsevier Ltd. All rights reserved.

dimensioning are considered inadequate to ensure that the design function is kept, especially where repeatability must be guaranteed. Indiscriminate use of geometrical tolerances could increase costs in manufacture and inspection. Tolerances should be as wide as possible, as the satisfactory design function permits.

General Rules The symbols relating to geometrical characteristics are shown in Fig. 22.1(a) with additional symbols used in tolerancing in Fig. 22.1(b). Examination of the various terms e flatness, straightness, concentricity, etc. e used to describe the geometrical characteristics shows that one type of geometrical tolerance can control another form of geometrical error. For example, a positional tolerance can control perpendicularity and straightness; parallelism, perpendicularity, and angularity tolerances can control flatness. The use of geometrical tolerances does not involve or imply any particular method of manufacture or inspection. Geometrical tolerances shown in this book, in keeping with international conventions, must be met regardless of feature size unless modified by one of the following conditions: (a) Maximum material condition, denoted by the symbol, describes a part, which contains the maximum amount of material, i.e. the minimum size hole or the maximum size shaft. (b) Least material condition, denoted by the symbol, describes a part, which contains the minimum amount of material, i.e. the maximum size hole or the minimum size shaft.

Theoretically Exact Dimensions (TEDs) These dimensions are identified by enclosure in rectangular boxes, e.g. 50 60 Ø30 and are commonly 183

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Type of tolerance

Form

Characteristics to be toleranced

Applications

No

A straight line. The edge or axis of a feature.

Flatness

No

A plane surface.

Roundness

No

The periphery of a circle. Cross-section of a bore, cylinder, cone or sphere.

Cylindricity

No

The combination of circularity, straightness and parallelism of cylindrical surfaces. Mating bores and plungers.

Profile of a line

No

The profile of a straight or irregular line.

No

The profile of a straight or irregular surface.

Parallelism

Yes

Parallelism of a feature related to a datum. Can control flatness when related to a datum.

Perpendicularity

Yes

Surfaces, axes, or lines positioned at right angles to each other.

Angularity

Yes

The angular displacement of surfaces, axes, or lines from a datum.

Profile of a line

Yes

The profile of a straight or irregular line positioned by theoretical exact dimensions with respect to datum plane(s).

Profile of a surface

Position

Location

Datum needed

Straightness

Profile of a surface

Orientation

Symbol

Yes

See note below

The profile of a straight or irregular surface positioned by theoretical exact dimensions with respect to datum plane(s). The deviation of a feature from a true position.

Concentricity and coaxiality

Yes

The relationship between two circles having a common centre or two cylinders having a common axis.

Symmetry

Yes

The symmetrical position of a feature related to a datum.

Profile of a line

Yes

The profile of a straight or irregular line positioned by theoretical exact dimensions with respect to datum plane(s).

Yes

The profile of a straight or irregular surface positioned by theoretical exact dimensions with respect to datum plane(s).

Circular runout

Yes

The position of a point fixed on a surface of a part which is rotated 360° about its datum axis.

Total runout

Yes

The relative position of a point when traversed along a surface rotating about its datum axis.

Profile of a surface

Runout

FIGURE 22.1a

Chapter | 22

Additional symbols Symbols

Description

Toleranced feature indication

A

Geometrical Tolerancing and Datums

Minor diameter

LD

Major diameter

MD

Pitch diameter

PD

Line element

LE

Not convex

NC

Any cross section

ACS

A

Datum feature indication

Unilateral or unequally disposed tolerance Ø2 A1

Median feature

Theoretically exact dimension

50

Between (two points)

Projected tolerance zone

P

Maximum material requirement

M

Least material requirement

L

Free state condition (non-rigid parts)

F

Datum target indication

185

UZ

All around (profile)

From … to (two points) Counterbore or Spotface

All around profile

Envelope requirement

E

Common zone

CZ

Minor diameter

LD

Major diameter

MD

Pitch diameter

PD

Line element

LE

Not convex

NC

Any cross-section

ACS

SF

Countersink Deep / Depth Intersection plane

A

A

Orientation plane

A

A

Direction feature

A

A

Collection plane

A

A

A A A A

FIGURE 22.1c

FIGURE 22.1b

known as boxed dimensions or true position dimensions. They define the true position of a hole, slot, boss profile, etc. TEDs are never individually toleranced but are always accompanied by a positional or zone tolerance specified within the tolerance frame referring to the feature (see Fig. 22.2). Note: If two or more groups of features are shown on the same axis, they shall be considered to be a single pattern when not related to a datum.

Definitions Limits: The maximum and minimum dimensions for a given feature are known as the limits; for example, 20  0.1. The upper and lower limits of size are 20.1 and 19.9 mm, respectively. Tolerance: The algebraic difference between the upper and lower limit of size is known as the tolerance. In the example above, the tolerance is 0.2 mm. The tolerance is the amount of variation permitted. Nominal dimension: Limits and tolerances are based on ‘nominal dimensions’, which are target dimensions. In practice there is no such thing as a nominal dimension, since no part can be manufactured to a theoretical exact size. The limits referred to above can be set in two ways: (a) unilateral limits e limits set wholly above or below the nominal size; (b) bilateral limits e limits set partly above and partly below the nominal size.

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6 × Ø20 Ø 0.2 A B B

60

0.1 A

30

60°

A

30

60

60

30

A

FIGURE 22.2

Geometrical tolerance: These tolerances specify the maximum error of a component’s geometrical characteristic, over its whole dimensioned length or surface. Defining a zone in which the feature may lie does this. Tolerance zone: A tolerance zone is the space in which any deviation of the feature must be contained, for example: e the space within a circle; e the space between two concentric circles; e the space between two equidistant lines or two parallel straight lines; e the space within a cylinder; e the space between two coaxial cylinders; e the space between two equidistant surfaces or two parallel planes; e the space within a sphere. The tolerance applies to the whole extent of the considered feature unless otherwise specified.

Method of Indicating Geometrical Tolerances on Drawings Geometrical tolerances are indicated by stating the following details in compartments in a rectangular frame: (a) the characteristic symbol, for single or related features; (b) the tolerance value; (i) preceded by Ø if the zone is circular or cylindrical, (ii) preceded by SØ if the zone is spherical;

(c) letter or letters identifying the datum or datum systems. Figure 22.3 shows examples.

Third compartment: datum identification letter(s)

Left-hand compartment: symbol for characteristic

Ø0.03

0.2

X

Second compartment: total tolerance value in the unit used for linear dimensions

FIGURE 22.3

Methods of Applying the Tolerance Frame to the Toleranced Feature Figures 22.4 and 22.5 illustrate alternative methods of referring the tolerance to the surface or the plane itself. Note that in Fig. 22.5 the dimension line and frame leader line are offset. The tolerance frame as shown in Fig. 22.6 refers to the axis or median plane only of the dimensioned feature.

FIGURE 22.4

Chapter | 22

Geometrical Tolerancing and Datums

187

4 × Ø10 Ø 0.01

FIGURE 22.8 6× Ø0.1

FIGURE 22.5

FIGURE 22.9

Indications qualifying the feature within the tolerance zone should be written under the tolerance frame (see Fig. 22.10). If it is necessary to specify more than one tolerance characteristic for a feature, the tolerance specification should be given in tolerance frames positioned one under the other as shown in Fig. 22.11.

FIGURE 22.6

0.3

Figure 22.7(a) illustrates the method of referring the tolerance to the axis or median plane. Note that the dimension line and frame leader line are drawn in line. Figure 22.7(b) illustrates an alternative way of referring to an axis or median feature; this has been introduced to aid the annotation of 3D models (see Chapter 28). In this method the tolerance frame is connected to the feature by a leader line terminating with an arrowhead pointing directly at the surface, but with the addition of the modifier symbol (median feature) placed at the right-hand end of the second compartment of the tolerance frame. (a)

NC

FIGURE 22.10 0.01 0.06 B

FIGURE 22.11

The Application of Tolerances to a Restricted Length of a Feature Figure 22.12 shows the method of applying a tolerance to only a particular part of a feature. The tolerance frame in Fig. 22.13 shows the method of applying another tolerance, similar in type but smaller in magnitude, on a shorter length. In this case, the whole flat surface must lie between parallel planes 0.2 apart, but over any length of 180 mm, in any direction, the surface must be within 0.05. 0.01

(b) ∅0,1 A ∅0,1

A

FIGURE 22.7

FIGURE 22.12

Procedure for Positioning Remarks which are Related to Tolerance Remarks related to the tolerance, for example ‘6 x’, should be written above the frame (see Figs 22.8 and 22.9).

Tolerance of whole feature

0.2 0.05/180 Tolerance value

Length applicable

FIGURE 22.13

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0.02/100

Ø0, 2 A

FIGURE 22.14 A

Figure 22.14 shows the method used to apply a tolerance over a given length; it allows the tolerance to accumulate over a longer length. In this case, straightness tolerance of 0.02 is applicable over a length of 100 mm. If the total length of the feature was 800 mm, then the total permitted tolerance would accumulate to 0.16.

(a) 0,2 A B

A 0,1 A B

Tolerance Zones The width of the tolerance zone is in the direction of the leader line arrow joining the symbol frame to the toleranced feature unless the tolerance zone is preceded by the symbol Ø. An example is given in Fig. 22.15(a). If two tolerances are given, then they are considered to be perpendicular to each other, unless otherwise stated. Figure 22.15(b) shows an example. Figure 22.15(c) gives an example where a single tolerance zone is applied to several separate features. In the tolerance frame the symbol ‘CZ’ is added. CZ is the standard abbreviation for ‘Common Zone’. Figure 22.15(d) gives an example where individual tolerance zones of the same valve are applied to several separate features.

B

(b) 0,1 CZ

(c) 0,1

Projected Toleranced Zone Figure 22.16(a) shows a part section through a flange where it is required to limit the variation in perpendicularity of each hole axis. The method used is to apply a tolerance to a projected zone. The enlargement shows a possible position for the axis through one hole. Each hole axis must lie somewhere within a projected cylinder of Ø0.02 and 30 deep. As an alternative to indicating the projected tolerance zone using supplemental geometry, the length of projection can also be specified indirectly by adding the value, after the P symbol, in the tolerance frame (Fig. 22.16(b)). This method of indication is only applicable to blind holes. Note: Projected tolerance zones are indicated by the symbol P . Note that the zone is projected from the specified datum.

(d) FIGURE 22.15

Datums and Datum Systems Datums and Datum Systems are used as the basis for establishing the geometric relationship of related features of a workpiece.

Definitions Single datum: A theoretical exact point, axis, line, plane or a combination of the same (see Figs 22.17 to 22.24). Common datum: A datum established from two or more datum features considered simultaneously (see Fig. 22.25).

Chapter | 22

(a)

Geometrical Tolerancing and Datums

A

8 × Ø24 Ø0.02 P A B

FIGURE 22.19

A

B

Ø

P 30

B

A

Ø160

FIGURE 22.20 Possible altitude of axis

30

B

Projected tolerance zone

FIGURE 22.21

Enlargement through one hole

(b)

Ø 0,9 P 30

A

B

A

FIGURE 22.22

FIGURE 22.16

10.2 10.0

A

B

A

–

0.05

FIGURE 22.23

FIGURE 22.17 B A

FIGURE 22.18

FIGURE 22.24

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R-S

A (a) Single datum used alone

(b) Common datum used alone

B A (c) Two single datums used in a system

G P S (d) Three single datums used in a system

A U-V (e) A single datum and a common datum used in a system

FIGURE 22.25

Primary

Tertiary C

A

M Secondary

FIGURE 22.26

Datum system: Datum established from two or more datum features considered in a specific order (see Fig. 22.26). Datum target: A portion of a datum feature which can be a line, point or an area (see Fig. 22.38)

Datums A datum surface on a component should be accurately finished, since other locations or surfaces are established by measuring from the datum. Figure 22.17 shows a datum surface indicated by the letter A. In this example, the datum edge is subject to a straightness tolerance of 0.05, shown in the tolerance frame.

Methods of Specifying Datum Features A datum is designated by a capital letter enclosed by a datum box. The box is connected to a solid or a blank datum triangle. There is no difference in understanding between solid or blank datum triangles. Figures 22.18 and 22.19 show alternative methods of designating a flat surface as Datum A. Figure 22.20 illustrates alternative positioning of datum boxes. Datum A is designating the main outline of the feature. The shorter stepped portion Datum B is positioned on an extension line, which is clearly separated from the dimension line. Figure 22.21 shows the datum triangle placed on a leader line pointing to a flat surface. Figures 22.22, 22.23, and 22.24 illustrate the positioning of a datum box on an extension of the dimension line, when the datum is the axis or median plane or a point defined by the dimensioned feature.

Note: If there is insufficient space for two arrowheads, one of them may be replaced by the datum triangle, as shown in Fig. 22.24. Examples of indicating datums in the tolerance frame are shown in Fig. 22.25.

Datum Systems In a datum system the primary datum is indicated in the third compartment of the tolerance frame; the secondary datum is indicated in the fourth compartment and the tertiary datum is indicated in the fifth compartment (Fig. 22.26). Figures 22.27 to 22.31 explain the concept, specification and interpretation of a datum system.

Common Datums Figure 22.32 illustrates two datum features of equal status used to establish a single datum axis. The reference letters, separated by a hyphen, are placed in the third compartment of the tolerance frame. Figure 22.33 shows an application where a geometrical tolerance is related to two separate datum surfaces indicated in order of priority. If a positional tolerance is required as shown in Fig. 22.34 and no particular datum is specified, then the individual feature to which the geometrical-tolerance frame is connected is chosen as the datum. Figure 22.35 illustrates a further positionaltolerance application where the geometrical requirement is related to a...