chapter 07 dimensioning and tolerancing

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



(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



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

feature’s 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



- 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



- 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



3. Dimensioning the object’s 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



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



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



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



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



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



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



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 d–g, 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



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



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 children’s 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



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.



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



+ 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



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



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



- 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



- 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



Fig

ure

7.3

8a:

Th

e m

etri

c pre

ferr

ed h

ole

bas

ic o

f fi

ts



Fig

ure

7.3

8a:

Th

e m

etri

c p

refe

rred

sh

aft

bas

ic o

f fi

ts



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



- 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



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.



Fig

ure

7.4

1:

Surf

ace

tex

ture

sy

mbols

and

co

nst

ruct

ion

F

igu

re 7

.42:

Sp

ecia

l su

rfac

e te

xtu

re l

ay s

ym

bo

ls



Figure 6.43: Special surface values and related symbols

Figure 7.44: Application of surface symbols to a simple part

chapter 07 dimensioning and tolerancing

Documents

minus dimension

dimension text

dimensioning lines figure

reference dimension

ends of dimension lines

dimensioning components

metric dimensioning

size information