MEM05 Metal and Engineering
Training Package
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MEM05039B
Perform advanced geometric
development - conical
Learner guide
SA
Version 1
Training and Education Support
Industry Skills Unit
Meadowbank
Product Code: 5805
MEM05039B Perform advanced geometric development - conical
Acknowledgement
The TAFE NSW Training and Education Support Industry Skills Unit, Meadowbank would like to
acknowledge the support and assistance of the following people in the production of this learner
resource guide:
Writer:
Prepared by Jim Miles from existing TAFE pulbilications
Reviewers:
Stephen Davies
Education Programs Manager
TAFE NSW
Enquiries
Enquiries about this and other publications can be made to:
Training and Education Support Industry Skills Unit, Meadowbank
Meadowbank TAFE
Level 3, Building J,
See Street,
MEADOWBANK NSW 2114
Fax: 02-9942 3257
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Tel: 02-9942 3200
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Project Manager:
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Nathan Gilbert (South Western Sydney Institute)
Stephen Davies (TES Industry Skills Unit)
© The State of New South Wales, Department of Education and Training, TAFE NSW,
Training and Education Support Industry Skills Unit, Meadowbank, 2013.
Copyright of this material is reserved to TAFE NSW Training and Education Support, Industry Skills
Unit Meadowbank. Reproduction or transmittal in whole or in part, other than for the purposes
of private study or research, and subject to the provisions of the Copyright Act, is prohibited
without the written authority of TAFE NSW Training and Education Support, Industry Skills Unit
Meadowbank.
ISBN 978-1-74236-513-8
© TAFE NSW (Training & Education Support, Industry Skills Unit Meadowbank) 2013
MEM05039B Perform advanced geometric development - conical
Table of Contents
Introduction........................................................................................................... 7
1. General introduction.......................................................................................................... 7
2. Using this learner guide ..................................................................................................... 7
3. Prior knowledge and experience.......................................................................................... 8
4. Unit of competency overview.............................................................................................. 8
5. Assessment.................................................................................................................... 10
Topic 1: Principles of radial line development used in the
Intersection of cone with cylindrical branch................................................................. 46
Job 6:
Intersection of cone with square branch (duct)............................................................ 48
Job 7:
Intersection of cone with rectangular branch (duct)...................................................... 50
Answers to review questions................................................................................ 52
Sample assessment (Theory)................................................................................................ 53
Answers to sample assessment (Theory)................................................................................ 55
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Student organiser............................................................................................................... 12
Job 5:
Terms and definitions........................................................................................... 56
metal fabrication industry....................................................................... 13
Resource evaluation form..................................................................................... 57
Pattern development........................................................................................................... 13
Radial line development terminology...................................................................................... 14
Uses of oblique cones.......................................................................................................... 17
Determination of true length of lines (TL)............................................................................... 18
Pattern and templates......................................................................................................... 25
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Computerised development.................................................................................................. 25
Review questions................................................................................................................ 26
Topic 2: Application of radial line development to produce
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complex patterns for conical intersections.............................................. 27
Pattern development for right cones...................................................................................... 27
Conical lobsterback bends (tapered)...................................................................................... 30
Method to mark out pattern of conical intersections................................................................. 35
Suggested practical jobs and projects.................................................................. 38
Job 1:
Conical pipe connector............................................................................................. 38
Job 2:
Offset flaring transition............................................................................................. 40
Job 3:
Intersection of square duct with conical branch............................................................ 42
Job 4:
Intersection of cylinder with conical branch................................................................. 44
© TAFE NSW (Training & Education Support, Industry Skills Unit Meadowbank) 2013
MEM05039B Perform advanced geometric development - conical
Topic 1: Principles of radial line development used in the
metal fabrication industry
Pattern development
Objectives
Methods of pattern development
There are three common methods of developing patterns/templates. These include:
To demonstrate competence at the end of this topic you will be able to:
•
Pattern development is used to produce templates or to develop a single pattern which is then cut,
formed, joined, finished and installed to become a completed article.
identify occupational areas in the metal fabrication industry which use the radial line development
method to produce patterns
define terms commonly used in radial line development
•
identify types of cones and their application
•
identify the principles and applications of complex radial line development for right and oblique
cones and conic sections
•
correctly label and identify points and lines used in the layout of views and patterns
•
describe the use of templates, identification and storage
•
develop patterns for truncated and oblique conical sections on paper/sheetmetal to a tolerance of
±0.5 mm.
• parallel line
•
radial line • triangulation
Patterns based on the above methods may also be generated by a range of computer software
packages. The methods used depend upon the geometric form of the article. In this resource we
concentrate on the radial line development method to produce patterns for complex conical shapes.
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Uses of radial line development
Radial line development is used in the following occupational areas of the metal fabrication industry.
•
•
•
•
•
General manufacture Ventilation and air conditioning
Stainless steel Cubicle manufacture Rainwater fittings for storage containers, buckets and funnels.
ductwork, cowls and hoods.
for kitchenware, food preparation equipment and handrails
for switchboards, cabinets and cupboards
such as rainwater heads and roof flashings.
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Applications of radial line development
Radial line development is the common method used in the fabrication industry to develop patterns for
conical articles. To understand how we use the radial line method you must think of the curved surface
of a cone having a series of triangles radiating out from a common point called the apex to equal
divisions on the circular base.
The conic section may be part of either a right cone or an oblique (offset) cone. Complex conical
shapes including hoods, intersections (penetrations), bends and elbows are developed using the radial
line development method.
The following articles are typical of those developed using the principles of radial line development.
(a) Conical hood
(b) Conical intersection
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© TAFE NSW (Training & Education Support, Industry Skills Unit Meadowbank) 2013
(c) 90˚Conical tapering
elbow (Lobsterback)
MEM05039B Perform advanced geometric development - conical
Radial line development terminology
Types of cones
There are two types of cones, right cones and oblique cones. Both types have a circular base but the
position of the apex varies.
Before you start to develop shapes it is important to understand the terminology used to describe
geometrical terms. Terms and definitions commonly used in radial line development include:
Full right cone
A full right cone can be defined as a shape which has a circular
base and a curved sloping surface which radiates from a point
situated vertically above the centre of the base. The point is
called the apex of the cone.
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Axis is the centreline about which an object may rotate
Generator lines are the main dividing lines used in pattern development
(used to determine slant heights around conical shape)
Projection line is drawn from one view to another
Seam is where two edges are joined together
True length is the length of a line viewed at right angles to the line
True shape (TS) is the shape of an object when viewed at 90˚ to its face
Base is the bottom surface of an object
Curved surface is rolled or formed to a radius
Flat surface has no deviations
True shape of section (TSS) is the shape viewed when a prism is cut at 90˚ to its axis
Pattern blank is the cutting size of the material, including allowances required for the pattern
Right cones
Right cones are either full right cones or, if the top is removed, the remainder is called a frustum or
truncated right cone.
The above terminology will be referred to in this resource. Some examples are shown here:
apex
Pattern radius
or
slant height
of cone
Chord
lan
es
tru
axis
e
th
Full right cone
Apex
Frustum of a right cone
(conical frustum)
A conical frustum is a right cone that has been cut by a plane
parallel to its base.
t
M
igh
curved surface
Apex
Flat surface
generator line
centre of base
C irc
u m fere c e of b a s
n
e
Apex
Frustum of a right cone
Truncated right cone
(right conic sections)
A truncated right cone is a right cone that has been cut by a
plane or planes not parallel to its base.
heig
hts
Generator
lines
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base
Right conePattern of a right cone
True
slant
Curved
surface
Apex
Flat surface
Oblique cone
Truncated right cone
Centre of base
Pattern of an oblique cone
.
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© TAFE NSW (Training & Education Support, Industry Skills Unit Meadowbank) 2013
MEM05039B Perform advanced geometric development - conical
Oblique cones (offset)
Identification of cones
Oblique cones are either full oblique cones or, if they are cut, the remainder is called a frustum or
truncated oblique cone.
A single view drawing as shown below, an object may be either a right or offset cone You may use the
following method to determine which it is:
Full oblique cone
Example 1: Single view drawing
Apex
An oblique cone, often referred to as an offset cone, is a three dimensional shape with a circular base
and curved sloping surface that radiates from the apex which is not above the centre of the base. There
are three (3) types of full oblique cones, as shown below:
Apex
Apex
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Apex
1.
2.
Apex inside the base
of the circle
Frustum of oblique cone
An oblique conical frustum is an oblique cone that
has been cut by a plane parallel to its base.
Apex
Frustum of an
oblique cone
Apex outside the base
of the circle
1. Extend the outlines of the single view drawing
to make a triangle with a horizontal base.
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Apex on the base
of the circle
Truncated oblique cone
A truncated oblique cone is an oblique cone that
has been cut by a plane or planes not parallel to
its base.
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Apex
2. Find the centre of the triangle base and
extend the axis of the object.
• If the three lines go through the same point (apex) then the object is a cone
• if the triangle formed is isosceles (opposite sides equal) or equilateral (all sides equal) then the
object is a right cone
• if the triangle formed is scalene (no sides equal) then the object is an oblique cone.
Note: To accurately mark out a pattern for cones the apex height must be determined either
geometrically or by calculations. If the three lines do not intersect at the same point (apex), as
illustrated below, the radial line development method is unsuitable and another method of development
will need to be used.
Truncated oblique
cone
Single view drawing
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© TAFE NSW (Training & Education Support, Industry Skills Unit Meadowbank) 2013
MEM05039B Perform advanced geometric development - conical
Exercise 1
Using the single view drawings shown below determine if the objects are:
□
□
□
right cone
(b)
offset cone
neither of the above
□
□
□
right cone
offset cone
neither of the above
Calculation for cones
Apex height (H)
n Ra
dius
Included Angle (IA)
(PR)
Chord Length (CL)
Circumference (C)
Radius of base (R)
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To accurately mark out a pattern for a cone, its dimensions must be determined either geometrically or
by calculations.
The calculations relating to cones include:
�D = 2�R
D
R
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Circumference of a circle = C =
c
Hypotenuse of a right angled triangle =
c = a2 + b2
Referring to sketch of the cone opposite;
H2 + R2
Included angle = IA = C x 180 degrees = 180D
PR x � PR
Chord length = CL = 2 x PR x sin(½IA)
b
Pattern radius = PR =
Patte
r
Frustum height (h)
(a)
(sh
Small diameter (d)
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t) S
(SH
lan
) Sl
t he
ant
frus
igh
heig
t
tum
ht (
pat
tern
rad
ius)
Apex point
a
Large diameter (D)
Diameter of base
Applications of cones
Cones have many uses within industry and for domestic purposes. Examples of articles based on right
cones are:
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•
•
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round air duct connectors
funnels
parts of cyclone separators
light poles
covers
exhaust hoods
transit cement mixers
buckets
Examples of articles based on oblique cones are:
•
•
•
•
•
•
round pipework connectors
hoppers
chutes
funnels
reducers
silos.
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© TAFE NSW (Training & Education Support, Industry Skills Unit Meadowbank) 2013
•
•
•
•
•
•
•
cowls
vats
hoppers and chutes
tundishes
flashings
reducers
silos.
MEM05039B Perform advanced geometric development - conical
Uses of oblique cones
Truncations of oblique cones
Oblique conical shapes are used for many applications. The various shapes or types of oblique
cones are used in industry for transporting and storing materials, ventilation systems, large pipeline
transitions and are formed to shape from developed patterns on flat materials.
A truncated oblique cone is the base section of an oblique cone whereby the base or top is cut at an
angle other than 90° to the vertical plane. The sketches below show various front view examples of
truncated oblique cones.
Examples:
• petro-chemical industry: LPG tankers, oil and chemical storage / transfer
• mining industry: ore crushing plant, storage and transfer systems
• power generation plants: hydropipework, ventilation ducting
• domestic uses:
hoods, funnels and flues.
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Oblique cones (offset cones)
Oblique cones are either full oblique cones or, if they are cut, the cone is called a frustum or truncated
oblique cone.
Frustums of oblique cones
Top truncated
Apex
TOP VIEW
Apex
Obtuse angle
FRONT VIEW
TOP VIEW
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TOP VIEW
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A frustum of an oblique cone is the base section below a cutting plane, parallel to the horizontal base.
The following sketches show the three types of frustum of oblique cones:
90˚ angle
FRONT VIEW
Base truncated
Apex
Acute angle
FRONT VIEW
Top and base truncated
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© TAFE NSW (Training & Education Support, Industry Skills Unit Meadowbank) 2013