chapter 07 dimensioning and tolerancing

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Thai Nguyen University of Technology Introduction to Engineering Drawing Division of English Taught Mechanical Engineering ME11- 3 Credits Eng. Phan Thi Phuong Thao 1 Email: [email protected] CHAPTER 7: DIMENSIONING AND TOLERANCING I. Dimensioning The purpose of adding size information to a drawing is known as dimensioning, and standard dimensioning practices have been established for this purpose. There are different standards for different types of drawings. In this chapter, the focus will be on mechanical drawings. - Dimensioning is the process of specifying part’s information by using of lines, number, symbols and notes. In a basic information, dimensioning shows sizes, location of the object’s features; Type of materials; Number of piece required to assemble into a single unit of a product (or machine). In higher level information, dimensioning is represented by tolerances: size and geometric; surface roughness; manufacturing or assemble process description. 1. Dimensioning components (1)- Dimension the numerical value that defines the size, shape, location, surface texture, or geometric characteristic of a feature. Normally, dimension text is 3mm (0.125’’) high, and the space between lines of text is 1.5mm (0.0625’’). In metric dimensioning, when the value less than one, a zero precedes the decimal point. In decimal inch dimensioning, a zero is not used before the decimal point. Figure 7.1: Dimensioning lines

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  • Thai Nguyen University of Technology Introduction to Engineering Drawing Division of English Taught Mechanical Engineering ME11- 3 Credits

    Eng. Phan Thi Phuong Thao 1 Email: [email protected]

    CHAPTER 7: DIMENSIONING AND TOLERANCING

    I. Dimensioning

    The purpose of adding size information to a drawing is known as dimensioning, and

    standard dimensioning practices have been established for this purpose. There are

    different standards for different types of drawings. In this chapter, the focus will be

    on mechanical drawings.

    - Dimensioning is the process of specifying parts information by using of lines,

    number, symbols and notes. In a basic information, dimensioning shows sizes,

    location of the objects features; Type of materials; Number of piece required to

    assemble into a single unit of a product (or machine). In higher level information,

    dimensioning is represented by tolerances: size and geometric; surface roughness;

    manufacturing or assemble process description.

    1. Dimensioning components

    (1)- Dimension the numerical value that defines the size, shape, location,

    surface texture, or geometric characteristic of a feature. Normally, dimension text is

    3mm (0.125) high, and the space between lines of text is 1.5mm (0.0625). In

    metric dimensioning, when the value less than one, a zero precedes the decimal

    point. In decimal inch dimensioning, a zero is not used before the decimal point.

    Figure 7.1: Dimensioning lines

  • Thai Nguyen University of Technology Introduction to Engineering Drawing Division of English Taught Mechanical Engineering ME11- 3 Credits

    Eng. Phan Thi Phuong Thao 2 Email: [email protected]

    (2)- Basic dimension- A numerical value defining the exact size, location,

    profile, orientation of feature relative to a coordinate system. Basic dimensions have

    no tolerance.

    (3)- Reference dimension- provided for information only and not directly used

    in the fabrication of the part.

    (4)- Dimension line- a thin, solid line that shows the extent and direction of a

    dimension.

    (5)- Arrows- symbols placed at the

    ends of dimension lines to show the limits

    of the dimension, leaders, and cutting

    plane lines. Arrowheads on engineering

    drawings are represented by freehand

    curves and can be filled, closed or open, as

    shown in the figure.

    (6)- Extension line- a thin, solid line

    perpendicular to a dimension line,

    indicating which feature is associated with

    the dimension.

    Figure 7.2: Dimensioning lines

    Figure 7.3: Arrowheads

  • Thai Nguyen University of Technology Introduction to Engineering Drawing Division of English Taught Mechanical Engineering ME11- 3 Credits

    Eng. Phan Thi Phuong Thao 3 Email: [email protected]

    (7)- Visible gap- there should be a visible gap of 1mm (1/16) between the

    features corners and the end of the extension line.

    (8) Leader line- a thin solid line used to indicate the feature with which a

    dimension, note or symbol is associated.

    (9)- Limits of size- the largest acceptable size and the minimum acceptable

    size and feature.

    (10)- Plus and minus dimension- the allowable positive and negative variance

    from the dimension specified. The plus and minus values may or may not be equal.

    (11)- Diameter symbol- indicate the diameter of a circle ()

    (12)- Radius symbol- indicate the radius of circle (R)

    (13)- Tolerance- the amount that a particular dimension is allowed to vary.

    The tolerance is the difference between the maximum and minimum limits.

    2. Recommended practice

    a. Extension line

    - Always leave a visible gap ( 1 mm) from a view or center lines before start

    drawing a line. Extend the lines beyond the (last) dimension line 2-3 mm.

    Figure 7.4: Extension lines

  • Thai Nguyen University of Technology Introduction to Engineering Drawing Division of English Taught Mechanical Engineering ME11- 3 Credits

    Eng. Phan Thi Phuong Thao 4 Email: [email protected]

    - Do not break the extension lines as they cross any line types, e.g. visible line,

    hidden line or center line, i.e. extension line always a continuous line.

    b. Dimension lines

    - Dimension lines should be

    appropriately spaced apart from each

    other and the view.

    c. Dimension number

    - Lettered with 2H or HB pencil. The height of numbers is suggested to be 2.5~3

    mm. Place the numbers at about 1 mm above and at a middle of a dimension line.

    Figure 7.5: Extension lines can cross to mark a theoretical point

    Figure 7.6: Dimension lines

  • Thai Nguyen University of Technology Introduction to Engineering Drawing Division of English Taught Mechanical Engineering ME11- 3 Credits

    Eng. Phan Thi Phuong Thao 5 Email: [email protected]

    - Length dimension is expressed in

    millimeters without a necessity to specify

    a unit symbol mm. Angular dimension

    is expressed in degree with a symbol o

    places behind the number (and if

    necessary minutes and seconds may be

    used together).

    - If there is not enough space for number

    or arrows, put it outside either of the

    extension lines.

    - Orientation: Prefer aligned method

    c. Local notes

    - Lettered with 2H or HB pencil and the height of 2.5~3 mm.

    Must be used in a combination with a leader line. Place near

    to the feature which they apply but should be placed outside

    the view. Placed above the bent portion of a leader line.

    Always be lettered horizontally.

    Figure 7.7: Dimension number

    Figure 7.8: Aligned method

    Figure 7.9: Local notes

  • Thai Nguyen University of Technology Introduction to Engineering Drawing Division of English Taught Mechanical Engineering ME11- 3 Credits

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    3. Dimensioning the objects features

    a. Length- Information to be dimensioned: length of

    an edge, distance between features.

    b. Angle- Information to be dimensioned: Angles are dimensioned by specifying the

    angle in degrees and a linear dimension

    c. Arcs - Information to be dimensioned: radius, location of its center

    The letter R is written in front of a

    number to emphasize that the

    number represents radius of an arc.

    Leader line must be aligned with a

    radial line and has an inclined angle

    between 30 ~ 60 degrees to the

    horizontal.

    The note and the arrowhead should

    be placed in a concave side of an arc,

    whenever there is a sufficient space

    Figure 7.10: Length

    Figure 7.11: Angle

    Figure 7.12: Angle

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    If the arc has its center lies outside the sheet or interfere with other views, use

    the foreshortened radial dimension line.

    d. Curve (A combination of arcs) - Information to be

    dimensioned: radius, location of its center.

    Figure 7.13: Sufficient space

    Figure 7.14: Foreshortened radial dimension line

    Figure 7.15: Curve

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    e. Fillets and Rounds- Information to be dimensioned: A circular arc is

    dimensioned in the view where its true shape in seen by giving the value for its radius

    preceded by the abbreviation R. Individual fillets and rounds are dimensioned like

    other arcs.

    - Counter bored hole with a fillet radius specified.

    - When a fillet radius is specified for a spot face

    dimension, the fillet radius is added to the outside of

    the spot face diameter.

    Figure 7.16: Fillets and rounds

    Figure 7.17: Counter bores

    Figure 7.18: Spot faces

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    Eng. Phan Thi Phuong Thao 9 Email: [email protected]

    f. Cylinder- Information to be dimensioned:

    Cylinders are usually dimensioned by giving

    the diameter and length where the cylinder

    appears as a rectangle.

    g. External chamfer- Information to be dimensioned: Linear distance, angle

    Figure 7.19: Cylinder

    Figure 7.20: External chamfer

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    h. Hole- Information to be dimensioned:

    Diameter, depth, location of its center,

    number of holes having an identical

    specification.

    The leader of a note should point to the

    circular view of the hole, if possible.

    Countersunk, counter bored, spot

    faced and tapped holes are usually

    specified by standard symbols or

    abbreviations.

    i. Tapers

    - A taper is a conical surface on a shaft or in a hole. The usual method of

    dimensioning a taper is to give the amount of taper in a note, such as TAPER 0.167

    ON DIA (with TO GAGE often added), and then give the diameter at one end with

    the length or give the diameter at both ends and omit the length. Taper on diameter

    means the difference in diameter per unit of length.

    Figure 7.21a: Hole

    Figure 7.21b: Hole

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    Eng. Phan Thi Phuong Thao 11 Email: [email protected]

    j. Chamfers- A chamfer is a beveled or sloping edge. It is dimensioned by giving

    the length of the offset and the angle. A 45 chamfer also may be dimensioned.

    k. Keyways- The preferred method of dimensioning the depth of a keyway is to give

    the dimension from the bottom of the keyway to the opposite side of the shaft or

    hole.

    Figure 7.22: Tapers

    Figure 7.23: Chamfers

    Figure 7.24: Keyways

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    l. Knurls- is a roughened surface to provide a better handgrip or to be used for a

    press fit between two parts. For handgrip purposes, it is necessary only to give the

    pitch of the knurl, the type of knurling, and the length of the knurled area.

    m. Finish marks

    - A finish mark is used to indicate that a surface is to be machined, or finished,

    as on a rough casting or forging. To the patternmaker or diemaker, a finish mark

    means that allowance of extra metal in the rough work piece must be provided for

    the machining.

    Figure 7.26: Finish marks

    Figure 7.25: Knurls

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    Eng. Phan Thi Phuong Thao 13 Email: [email protected]

    n. Sheet metal bends

    - In sheet metal dimensioning, allowance must be made for bends. The

    intersection of the plane surfaces adjacent to a bend is called the mold line, and this

    line, rather than the center of the arc, is used to determine dimensions.

    o. Rounded-end shapes

    - For accuracy, in parts dg, overall lengths of rounded-end shapes are given,

    and radii are indicated, but without specific values. The center-to-center distance

    may be required for accurate location of some holes. In part g, the hole location is

    more critical than the location of the radius, so the two are located.

    Figure 7.27: Sheet marks

    Figure 7.28: Rounded-end shapes

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    Eng. Phan Thi Phuong Thao 14 Email: [email protected]

    p. Notes

    - It is usually necessary to supplement the direct dimensions with notes. Notes

    should be brief and carefully worded to allow only one interpretation. Notes should

    always be lettered horizontally on the sheet and arranged systematically. They

    should not be crowded and should not be placed between views, if possible. Notes

    are classified as general notes when they apply to an entire drawing and as local

    notes when they apply to specific items.

    Figure 7.29: Notes

  • Thai Nguyen University of Technology Introduction to Engineering Drawing Division of English Taught Mechanical Engineering ME11- 3 Credits

    Eng. Phan Thi Phuong Thao 15 Email: [email protected]

    q. Mating dimensions- Mating dimensions should be given on the multi-view

    drawings in the corresponding locations.

    II. Tolerance

    Interchangeable manufacturing, by means of which parts can be made in widely

    separated localities and then be brought together for assembly, where the parts will

    all fit together properly, is an essential element of mass production. Without

    interchangeable manufacturing, modern industry could not exits, and without

    effective size control by the engineer, interchangeable manufacturing could not be

    achieved. For example, an automobile manufacturer not only subcontracts the

    manufacture of many parts of a design to other companies but also must make

    provision for replacement parts. All parts in each category must be near enough alike

    so that any one of them will fit properly in any assembly. Unfortunately, it is

    impossible to make anything to exact size. Parts can be made to very close

    dimensions, even to a few millionths of an inch or thousandths of a millimeter, but

    such accuracy is extremely expensive.

    However, exact sizes are not needed, only varying degree of accuracy according to

    functional requirements. A manufacturer of childrens tricycle would soon go out of

    business if the parts were made with jet-engine accuracy, as no one would be willing

    to pay the price. So what is needed is a means of specifying dimensions with

    whatever degree of accuracy may be required. The answer to the problem is the

    specification of a tolerance on each dimension.

    Figure 7.30: Mating dimensions

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    Eng. Phan Thi Phuong Thao 16 Email: [email protected]

    1. Important terms

    - Nominal size: a dimension used to describe the general size, usually expressed in

    common fractions. The slot in figure below has a nominal size of (1/2) inch.

    - Basic size: The theoretical size used as a starting point for the application of

    tolerances. The basic size of the slot in figure below is .500

    - Actual size: The measured size of the finished part after machining. In the figure

    below, the actual size is .501

    - Limits: the maximum and the minimum sizes shown by the tolarenced dimension.

    The slot in figure below has limits of .502 and .498, and the mating part has limits

    of .495 and .497. The larger value for each part is the upper limit, and the smaller

    value is the lower limit.

    - Allowance: The minimum clearance or the maximum interference between parts,

    or the tightest fit between two mating parts. In the figure below, the allowance is

    .001, meaning that the tightest fit occurs when the slot is machined to its smallest

    allowable size of .498 and the mating part is machined to its largest allowable size

    of .497. The different between .498 and .497, or .001, is allowance.

    - Tolerance: the total allowable variance in a dimension; the different between the

    upper and the lower limits. The tolerance of the slot below is .004 inch = .502- .498

    and the tolerance of the mating part is .002 inch = .497- .495

    - Maximum material condition (MMC): The condition of a part when it contains

    the greatest amount of material. The MMC of an external feature, such as a shaft, is

    the upper limit. The MMC of an internal feature, such as a hole, is the lower limit.

    - Least material condition (LMC): The condition of a part when it contains the

    least amount of material possible. The LMC of an external feature is the lower limit.

    The LMC of an internal feature is the upper limit.

    - Piece tolerance: The different between the upper and the lower limits of a single

    part.

    - System tolerance: the sum of all the piece tolerances.

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    Eng. Phan Thi Phuong Thao 17 Email: [email protected]

    2. Fit types:

    - The degree of tightness between mating parts is called the fit. There are three most

    common types of fir found in industry.

    + Clearance fit: occurs when two toleranced mating parts will always leave a space

    or a clearance when assembled. In the bellowing figure, the largest that shaft A can

    be manufactured is .999 and the smallest the hole can be is 1.000. The shaft always

    will be smaller than the hole, resulting in a minimum clearance of +.001, also called

    allowance. The maximum clearance occurs when the smallest shaft (.998) is mated

    with the largest hole (1.001), resulting in a difference of +.003

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    + Interference fit: occurs when two toleranced mating parts always will interfere

    when assembled. An interference fit fixes or anchors one part into the other, as

    though the two parts were one. In the figure above, the smallest that shaft B can be

    manufactured is 1.002, and the largest the hole can be manufactured is 1.001. This

    means that the shaft always will be large than the hole, and the minimum interference

    is -.001. The maximum interference would occur when the smallest hole (1.000) is

    mated with the largest shaft (1.003), resulting in an interference of -.003. In order to

    assemble the parts under this condition, it would be necessary to stretch the hole or

    shrink the shaft or to use force to press the shaft into the hole. Having an interference

    is a desirable situation for some design applications. For example, it can be used to

    fasten two parts together without the use of mechanical fasteners or adhesive.

    + Transition fit: occurs when two toleranced mating parts are sometimes an

    interference and sometimes a clearance fit when assembled. In the figure below, the

    smallest the shaft can be manufactured is .998 and the largest the hole can be

    manufactured is 1.001, resulting in a clearance of +.003. The largest the shaft can be

    manufactured is 1.002, and the smallest the hole can be is 1.000, resulting in an

    interference of -.002.

    Figure 7.31: Clearance and interference fits

    between two shafts and a hole

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    Eng. Phan Thi Phuong Thao 19 Email: [email protected]

    3. Fit type determination: If feature A of

    one part is to be inserted into or mated

    with feature B of another part, the type of

    fit can be determined by the following

    figure.

    - The loosest fit is the different

    between the smallest feature A and

    the largest feature B.

    - The tightest fit is the different

    between the largest feature A and

    the smallest feature B.

    Figure 7.32: Transition fit between a shaft

    and a hole

    Figure 7.33: Determining fits

  • Thai Nguyen University of Technology Introduction to Engineering Drawing Division of English Taught Mechanical Engineering ME11- 3 Credits

    Eng. Phan Thi Phuong Thao 20 Email: [email protected]

    4. Metric limits and Fits

    The standards used for metric measurements are recommended by the ISO and are

    given in US standard. The terms used in metric tolerancing are as follow:

    - Basic size: the size to which limits of deviation are assigned. The limits must be

    the same for both parts.

    - Deviation: the difference between and the actual size of the part and the basic size.

    - Upper deviation: the difference between the maximum size limit and the basic size.

    - Lower deviation: the difference between the minimum size limit and the basic size.

    Figure 7.34: US standard preferred metric

    sizes used for metric tolerancing

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    Eng. Phan Thi Phuong Thao 21 Email: [email protected]

    - Fundamental deviation: the deviation closest to the basic size. The letter H

    represents the fundamental deviation for the hole, and the letter f indicates the

    fundamental deviation for the shaft.

    - Tolarence: the difference between the maximum and minimum size limits on a

    part.

    - Tolerance zone: the tolerance and its position relative to the basic size.

    - International tolerance grade (IT)- a group of tolerances that vary depending on the

    basic size but have the same level of accuracy within a given grade. The number 7

    and 8 in Figure 7.36 are IT grades. There are 18 IT grades: IT0, IT1, and IT01 to

    IT16. The smaller the grade number, the smaller the tolerance zone.

    Figure 7.35: Important definition used in

    metric tolerancing

  • Thai Nguyen University of Technology Introduction to Engineering Drawing Division of English Taught Mechanical Engineering ME11- 3 Credits

    Eng. Phan Thi Phuong Thao 22 Email: [email protected]

    - Hole basis- the system of fits where the minimum hole size is the basic size. The

    fundamental deviation for a hole basic system is indicated by the uppercase letter H

    (Figure 7.36(a))

    - Shaft basis- the system of fits where the minimum shaft size is the basic size. The

    fundamental deviation for a shaft basic system is indicated by the lowercase letter f

    (Figure 7.36(b))

    Metric tolerance symbol- combining the IT

    grade number and the tolerance position letter

    establishes the tolerance symbol, which

    identifies the actual upper and lower limits of a

    part. The toleranced size of the part is defined by

    the basic size followed by a letter and a number,

    such as 40H8 or 40f7. The internal part is

    preceded by the external part in the symbol. The

    basic callout for a metric fit would appear as

    40H8, where: 40 is the basic size of 40

    millimeters, H is an internal feature (hole), 8 is a

    close running clearance fit.

    Figure below indicates three methods of

    designating metric tolerances on drawings. (The

    values follows US standard)

    Preferred fits- the hole basis system for clearance, interference, and transition fits

    is shown in figure 7.38 Hole basis fits have a fundamental deviation of H on the

    hole, as shown in the figure. The shaft basis system for clearance, interference, and

    transition fits is shown in figure 7.38a Shaft basis fits have a fundamental deviation

    of h on the shaft, as shown in the figure. A description of the hole basis system and

    shaft basic system is given in figure 7.38b.

    Figure 7.36: Metric symbol

    and their definition

    Figure 7.37: Three method of showing tolerance

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    Eng. Phan Thi Phuong Thao 23 Email: [email protected]

    Fig

    ure

    7.3

    8a:

    Th

    e m

    etri

    c pre

    ferr

    ed h

    ole

    bas

    ic o

    f fi

    ts

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    Fig

    ure

    7.3

    8a:

    Th

    e m

    etri

    c p

    refe

    rred

    sh

    aft

    bas

    ic o

    f fi

    ts

  • Thai Nguyen University of Technology Introduction to Engineering Drawing Division of English Taught Mechanical Engineering ME11- 3 Credits

    Eng. Phan Thi Phuong Thao 25 Email: [email protected]

    Determining the tolerance using the hole basis system

    - Step 1: Given A shaft and a hole, the basis system, clearance fit, and a basic

    diameter of 41mm for the hole.

    - Step 2: Solution: From figure 7.34, assign the basic size of 40 mm to the shaft.

    From figure 7.39, assign the sliding fit H7/g6. Sliding fit is defined in the

    figure.

    - Step 3: Hole: Determine the upper and lower limits of the hole from Appendix

    9, using column H7 and row 40 from the hole basis charts. From the table, the

    limits are 40.025 and 40.000

    Figure 7.39: Description of preferred metric fits

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    - Step 4: Shaft: Determine the upper and lower limits of the shaft from

    Appendix 9, using column g6 and row 40. From the table, the limits are

    39.991 and 39.975.

    5. Tolerance in CAD

    Some tolerancing concepts are unique to CAD. In hand drawing, the graphics are

    imagines of the part, and the dimensions add important information to the drawing.

    In CAD, the graphics can become more descriptive because an accurate

    mathematical definition of the shape of a part is created, whereas in hand drawing,

    the graphics are not as accurate.

    CAD drawings, then, can be considered geometry files rather than simply drawings.

    CAD geometry databases often are translated directly to machining equipment,

    making them considerable more useful than hand drawings. Rather than having a

    machinist interpret the dimension shown on the drawing, the machine tool uses the

    size of the geometric elements encoded in the CAD database. Part geometry should

    Figure 7.40: Example of determining the tolerance using the

    hole basis system

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    be made so that it can be translated directly to a CAM system for machining. In order

    for this to occur, lines must:

    - End exactly at corners.

    - Never be short (even by 0.00002 inch)

    - Never be one on top of another.

    - Have all lengths and angles that are perfect.

    Surface texture symbols

    The surface texture of a finished part is critical for many products, such as

    automobiles and aircraft, to reduce friction between parts or aerodynamics drag

    caused by the friction of air passing over the surface. Standard drawing practices

    relate directly to the grinding process, which is used to produce finished surfaces.

    - The surface finish for a part is specified on an engineering drawing using a

    finish mark symbol similar to a checkmark and variations of these are shown

    in figure below. One leg of the symbol is drawn 1.5 times the height of the

    lettering, the other leg is drawn three times the height of the lettering, and the

    angle between the two legs is 60 degrees.

    - The direction that the machine tools passes over the part can be controlled by

    adding a letter or symbol to the right of the finish mark. For example, the letter

    M means the machine tool is multidirectional.

    - Various applications of surface symbols are shown in figure below.

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    Fig

    ure

    7.4

    1:

    Surf

    ace

    tex

    ture

    sy

    mbols

    and

    co

    nst

    ruct

    ion

    F

    igu

    re 7

    .42:

    Sp

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    l su

    rfac

    e te

    xtu

    re l

    ay s

    ym

    bo

    ls

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    Figure 6.43: Special surface values and related symbols

    Figure 7.44: Application of surface symbols to a simple part