mem05039b perform advanced geometric development - … · · 2013-11-27job 4: intersection of...

MEM05 Metal and EngineeringTraining Package

Learner guideVersion 1

Training and Education SupportIndustry Skills Unit

Meadowbank

Product Code: 5805

MEM05039BPerform advanced geometric

development - conical

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© TAFE NSW (Training & Education Support, Industry Skills Unit Meadowbank) 2013

MEM05039B Perform advanced geometric development - conical

AcknowledgementThe 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:Nathan Gilbert (South Western Sydney Institute)Stephen Davies (TES Industry Skills Unit)

Project Manager:Stephen DaviesEducation Programs ManagerTAFE NSW

EnquiriesEnquiries about this and other publications can be made to:

Training and Education Support Industry Skills Unit, MeadowbankMeadowbank TAFELevel 3, Building J,See Street,MEADOWBANK NSW 2114

Tel: 02-9942 3200 Fax: 02-9942 3257

ISBN 978-1-74236-513-8

© 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.

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© TAFE NSW (Training & Education Support, Industry Skills Unit Meadowbank) 2013


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

Student organiser .............................................................................................................. 12

Topic 1: Principles of radial line development used in the metal fabrication industry ......................................................................13

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

Computerised development ................................................................................................. 25

Review questions ............................................................................................................... 26

Topic 2: Application of radial line development to produce 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

Table of Contents

Job 5: 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

Terms and definitions .......................................................................................... 56

Resource evaluation form .................................................................................... 57

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of 60 © TAFE NSW (Training & Education Support, Industry Skills Unit Meadowbank) 2013


Topic 1: Principles of radial line development used in the metal fabrication industry

Objectives

To demonstrate competence at the end of this topic you will be able to:

• 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.

Pattern developmentPattern 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.

Methods of pattern developmentThere are three common methods of developing patterns/templates. These include:

• 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.

Uses of radial line developmentRadial line development is used in the following occupational areas of the metal fabrication industry.

• General manufacture for storage containers, buckets and funnels.• Ventilation and air conditioning ductwork, cowls and hoods.• Stainless steel for kitchenware, food preparation equipment and handrails• Cubicle manufacture for switchboards, cabinets and cupboards• Rainwater fittings such as rainwater heads and roof flashings.

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 (c) 90˚Conical tapering elbow (Lobsterback)

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Radial line development terminologyBefore 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:

Axis is the centreline about which an object may rotateGenerator 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 anotherSeam is where two edges are joined togetherTrue length is the length of a line viewed at right angles to the lineTrue shape (TS) is the shape of an object when viewed at 90˚ to its faceBase is the bottom surface of an objectCurved surface is rolled or formed to a radiusFlat surface has no deviationsTrue shape of section (TSS) is the shape viewed when a prism is cut at 90˚ to its axisPattern blank is the cutting size of the material, including allowances required for the pattern

The above terminology will be referred to in this resource. Some examples are shown here:

true slant height

generator line

base

centre of base

curved surface

axis

apex

Flat surface

Pattern radius orslant height of coneChord

Circumference of base

Right cone Pattern of a right cone

Centre of base

Apex

Generatorlines

Curvedsurface

Flat surface

True

sla

nt h

eigh

ts

Oblique cone Pattern of an oblique cone

Types of conesThere are two types of cones, right cones and oblique cones. Both types have a circular base but the position of the apex varies.

Right conesRight cones are either full right cones or, if the top is removed, the remainder is called a frustum or truncated right cone.

Full right coneA 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.

Apex

Full right cone

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.

Frustum of a right cone

Apex

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.

Truncated right cone

Apex

.

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Oblique cones (offset)

Oblique cones are either full oblique cones or, if they are cut, the remainder is called a frustum or truncated oblique cone.

Full oblique cone

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:

ApexApex Apex

Apex on the base Apex inside the base Apex outside the base of the circle of the circle of the circle

Frustum of oblique coneAn oblique conical frustum is an oblique cone that has been cut by a plane parallel to its base.

Apex

Frustum of an oblique cone

Truncated oblique coneA truncated oblique cone is an oblique cone that has been cut by a plane or planes not parallel to its base.

Apex

Truncated oblique cone

Identification of cones 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:

Example 1: Single view drawingApex

1. 2.

1. Extend the outlines of the single view drawing

to make a triangle with a horizontal base.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.

Single view drawing

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Exercise 1Using the single view drawings shown below determine if the objects are:

(a) □ right cone (b) □ right cone □ offset cone □ offset cone □ neither of the above □ neither of the above

Calculation for cones

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:

Circumference of a circle = C = �D = 2�R D

R

Hypotenuse of a right angled triangle = c = a2 + b2

a

b c

Referring to sketch of the cone opposite;

Pattern radius = PR = H2 + R2

Included angle = IA = C x 180 degrees = 180D PR x � PR

Chord length = CL = 2 x PR x sin(½IA)

Small diameter (d)

Radius of base (R)

Frus

tum

hei

ght

(h)

frus

tum

(sht

) Sl

ant he

ight(S

H)

Slan

t he

ight

(pa

tter

n ra

dius

)

Ape

x he

ight

(H

)

Apex point

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:

• round air duct connectors • funnels• parts of cyclone separators• light poles• covers• exhaust hoods• transit cement mixers• buckets

• cowls• vats• hoppers and chutes• tundishes• flashings• reducers• silos.

Examples of articles based on oblique cones are:

• round pipework connectors• hoppers• chutes• funnels• reducers• silos.

Pattern Radius (PR)

Chord Length (CL)

Included Angle (IA)

Circumference (C)

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Uses of oblique conesOblique 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.

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.

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 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:

TOP VIEW TOP VIEW TOP VIEW

Apex Apex

Obtuse angle FRONT VIEW

Apex

90˚ angleFRONT VIEW

Acute angleFRONT VIEW

Truncations of oblique cones

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.

Top truncated

Base truncated

Top and base truncated

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mem05039b perform advanced geometric development - … · · 2013-11-27job 4: intersection of...

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