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
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
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
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
Eng. Phan Thi Phuong Thao 6 Email: [email protected]
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
Thai Nguyen University of Technology Introduction to Engineering Drawing Division of English Taught Mechanical Engineering ME11- 3 Credits
Eng. Phan Thi Phuong Thao 7 Email: [email protected]
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
Thai Nguyen University of Technology Introduction to Engineering Drawing Division of English Taught Mechanical Engineering ME11- 3 Credits
Eng. Phan Thi Phuong Thao 8 Email: [email protected]
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
Thai Nguyen University of Technology Introduction to Engineering Drawing Division of English Taught Mechanical Engineering ME11- 3 Credits
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
Thai Nguyen University of Technology Introduction to Engineering Drawing Division of English Taught Mechanical Engineering ME11- 3 Credits
Eng. Phan Thi Phuong Thao 10 Email: [email protected]
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
Thai Nguyen University of Technology Introduction to Engineering Drawing Division of English Taught Mechanical Engineering ME11- 3 Credits
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
Thai Nguyen University of Technology Introduction to Engineering Drawing Division of English Taught Mechanical Engineering ME11- 3 Credits
Eng. Phan Thi Phuong Thao 12 Email: [email protected]
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
Thai Nguyen University of Technology Introduction to Engineering Drawing Division of English Taught Mechanical Engineering ME11- 3 Credits
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 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
Thai Nguyen University of Technology Introduction to Engineering Drawing Division of English Taught Mechanical Engineering ME11- 3 Credits
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 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
Thai Nguyen University of Technology Introduction to Engineering Drawing Division of English Taught Mechanical Engineering ME11- 3 Credits
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.
Thai Nguyen University of Technology Introduction to Engineering Drawing Division of English Taught Mechanical Engineering ME11- 3 Credits
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
Thai Nguyen University of Technology Introduction to Engineering Drawing Division of English Taught Mechanical Engineering ME11- 3 Credits
Eng. Phan Thi Phuong Thao 18 Email: [email protected]
+ 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
Thai Nguyen University of Technology Introduction to Engineering Drawing Division of English Taught Mechanical Engineering ME11- 3 Credits
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
Thai Nguyen University of Technology Introduction to Engineering Drawing Division of English Taught Mechanical Engineering ME11- 3 Credits
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
Thai Nguyen University of Technology Introduction to Engineering Drawing Division of English Taught Mechanical Engineering ME11- 3 Credits
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
Thai Nguyen University of Technology Introduction to Engineering Drawing Division of English Taught Mechanical Engineering ME11- 3 Credits
Eng. Phan Thi Phuong Thao 24 Email: [email protected]
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
Thai Nguyen University of Technology Introduction to Engineering Drawing Division of English Taught Mechanical Engineering ME11- 3 Credits
Eng. Phan Thi Phuong Thao 26 Email: [email protected]
- 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
Thai Nguyen University of Technology Introduction to Engineering Drawing Division of English Taught Mechanical Engineering ME11- 3 Credits
Eng. Phan Thi Phuong Thao 27 Email: [email protected]
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.
Thai Nguyen University of Technology Introduction to Engineering Drawing Division of English Taught Mechanical Engineering ME11- 3 Credits
Eng. Phan Thi Phuong Thao 28 Email: [email protected]
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
Thai Nguyen University of Technology Introduction to Engineering Drawing Division of English Taught Mechanical Engineering ME11- 3 Credits
Eng. Phan Thi Phuong Thao 29 Email: [email protected]
Figure 6.43: Special surface values and related symbols
Figure 7.44: Application of surface symbols to a simple part