lecture08-development of surfaces

7/29/2019 Lecture08-Development of Surfaces

1/57

ME119:

Engineering Drawing & Graphics

8. Development of Surfaces

Department of Mechanical Engineering

Indian Institute of Technology Bombay


2/57

Outline

General instructions/ Discussions

Development of Surfaces

Conclusions


3/57



4/57


Many objects of desire have considerable sheet metal parts.Examples: aircraft, automobile, boiler, house-hold vessels, ducts,

pipes, funnels, stapler etc. Simpler examples of sheet products are

cardboard boxes used in packing, paper envelopes, inland letters,

garments, etc. Most of these parts are hollow and their shapes are

curved but the raw material is invariably available in the form of

sheet (metal/ material), i.e., flat surfaces. The required planar

shape, known as Flat Pattern (FP), to produce the part has to be

calculated, cut from the sheet stock optimally using nesting and

then folded or formed. The method of determining the FP for any part is known as

development of the surface of the part.

We shall neglect the thickness of the sheet although it is finite.


5/57

Developability of Surfaces

Note that every surface is not developable. So, let us define thenotion ofdevelopability. A surface, assumed to be of zero

thickness, is said to be developable if and only if there are (i) no

wrinkles or (ii) no tears during development. For a surface with

thickness, these defects translate in terms of variation in its original

thickness after forming as (i) thinning or (ii) thickening or (iii) zero

thickness (tear).

Alternately, a 3D sheet metal surface is said to be developable if

we can identify a straight line along which it can be cut and

opened/ hammered to a planar shape without any variation inthickness.


6/57

Classification of Surfaces

Surfaces

Doubly CurvedSingly Curved (Ruled)

Singly Ruled Multi-Ruled

Developable Non-developable


7/57

Development of Non-Developable Surfaces

They are formed with wrinkles and thinning.

If you cannot tolerate, then other manufacturing processes such as

machining or casting shall be used.


8/57

Methods of Development of Surfaces

1. Parallel line development - for prisms and cylinders

2. Radial line development - for pyramids and cones

3. Triangulation development - for transition pieces

4. Approximate development - for non-developable surfaces

Note: For the purpose of development, it is required to obtain the true

lengths.


9/57

Development of Prismatic Surfaces


10/57

Development of SurfacesExample-1 (Solved Pb. 15-1, pp. 353)

Draw the development of a trimmed cube.


11/57


Draw the development of a trimmed cube.


12/57


Draw the development of a trimmed pentagonal prism.


13/57


Draw the development of a trimmed triangular prism.


14/57


Draw the development of a trimmed hexagonal prism.


15/57


Draw the development of the lateral surface of the truncated prismshown in the figure. Also, draw the front view of the line joining the

points P and Q ( whose projections p, pand q, q are given) along

the surfaces of the prism by the shortest distance.


16/57



17/57


The projections of a square prism with a hole drilled in it are given inthe figure. Draw the development of the lateral surface of the prism.

D l f S f


18/57


D l f S f


19/57


Develop the lateral surface of the truncated cylinder shown in thefigure.

D l t f S f


20/57


D l t f S f


21/57


Draw the development of the lateral surface of the part P of thecylinder shown in the figure.

D l t f S f


22/57




23/57


Draw the development of the lateral surface of the cylinder cut bythree planes as shown in the figure.



24/57




25/57


Draw the development of the lateral surface of the cylinder having asquare hole in it as shown in the figure.



26/57




27/57


Draw the development of the lateral surface of the cylinder cut asshown in the figure.



28/57




29/57


Develop the surface of the three-piece cylindrical pipe elbow shownin the figure.



30/57




31/57


Three cylindrical pipes of50 mm diameter from a

y-piece as shown in the

front view of the figure.

Draw the development of

the surface of each pipe.


32/57

Development of Pyramidal Surfaces



33/57


Draw the development ofthe lateral surface of the

part P of the triangular

pyramid shown in the

figure. The line o1 in the

front view is the true lengthof the slant edge because

it is parallel to xy in the top

view. The true length of the

side of the base is seen in

the top view.



34/57



frustum of the square


figure.



35/57



part P of the square


figure.



36/57



pentagonal pyramid, the

lower part of which is

removed as shown in the

figure.



37/57

e e op e t o Su acesExample-19 (Solved Pb. 15-19, pp. 363)

Draw the development of the lateral

surface of the part P of the

pentagonal pyramid as shown in

the figure.



38/57

pExample-20 (Solved Pb. 15-20, pp. 363)

Draw the development of the lateral surface of the part P of the

hexagonal pyramid shown in the figure.



39/57




40/57


A frustum of a

square pyramid has

its base 50 mm

side, top 25 mm

side and height 75

mm. Draw thedevelopment of its

lateral surface.



41/57


Draw the

development

of the lateral

surface of

the

truncatedcone shown

in the figure.

Note:

Sector angle =r/l



42/57


Draw the development of the lateral surface of the truncated cone

shown in the figure.



43/57

Example-24 (Solved Pb. 15-24, pp. 366)

Draw the development of the lateral surface of the part P of the cone




44/57


Draw the development of the lateral surface of the part P of the cone




45/57


Draw the projections of a cone

resting on the ground on its

base and show on them, the

shortest path by which a point

P, starting from a point on the

circumference of the base andmoving around the cone will

return to the same point. Base

of cone 61 mm diameter; axis

75 mm.

Note:

The shortest path between two points on a

surface is knows as geodesic curve,which

is not straight on the body!.



46/57


Draw the development of the

lateral surface of the part of

the cone, the front view of

which is shown in the figure.



47/57


The development of the conical surface is a sector of the semi-

circular plane. The radius of the sector is 75mm and the angle

subtended by the arc at the centre is 120. Construct the cone and

draw its projections when the apex is 35 mm above the H.P. and its

axis is parallel to the V.P.



48/57


Development of SurfacesE l 29 (S l d Pb 1 29 3 0)


49/57


Draw the shape of the sheet metal required for the funnel shown in

the figure.

Development of SurfacesE l 30 (S l d Pb 15 30 370)


50/57


The projection of a solid composed of a truncated half-cylinder and

cut a half-prism are given in the figure. Draw the development of itslateral surface.



51/57


Draw the

development ofthe lateral

surface of the

solid shown in

two views

(drawn in first-

angle

projection).



52/57


In air-conditioning

system a rectangularduct of 100 mm X50

mm connects

another rectangular

duct of 50 mm X 25

mm through the

transition piece as


Neglecting thickness

of a metal sheet,develop the lateral

surface of the

transition piece.



53/57


An air-conditioning

duct of squarecross-section 70 mm

x 70 mm connects a

circular pipe of 40

mm diameter

through the

transition piece.

Draw the projection

and develop the

lateral surface of thetransition piece.

Development of SurfacesExample 34 (Solved Pb 15 34 pp 374)


54/57


A steam pipe bends

at certain angle isconnected by a

transition piece as


Draw the

development of

lateral surface of the

transition piece A.

Development of SurfacesExample 35 (Solved Pb 15 35 pp 374)


55/57


The orthogonal

projection of anexhaust pipe

required for an

engine is shown in

the figure. Draw the

development of the

transition connector

by triangulation

method.

Conclusions


56/57

Roughly work out all the problems given to you. Only if you comeprepared, you will be able to complete all problems of the sheet in

the drawing session.

Thank You!


57/57

Thank You!

K.P. Karunakaran

Professor

Department of Mechanical EngineeringIndian Institute of Technology Bombay

Powai, Mumbai-400076, INDIA

Tel.: 022-25767530/ [email protected]

www.me.iitb.ac.in/~karuna

lecture08-development of surfaces

Documents