Industrial Engineering Chapter 7 Derive Max Without Necking What Should The Minimum Value The Material Referring

ing 0.5-mm-thick 5052-O aluminum foil in the

shape of a square hole 30 mm on each side.

mm, and the thickness is given as t=0.5 mm.

7.72 A straight bead is being formed on a 1-mm-

sidering springback, calculate the outside diam-

RiY

ET =(0.009)(150)

(70,000)(0.001) = 0.0193

0.942 =9 mm

0.942 = 9.55 mm

7.73 Inspect Eq. (7.10) and substituting in some nu-

merical values, show whether the first term in

the equation can be neglected without signifi-

lem 7.72 where it was shown that

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required to develop a pressure of 10,000 psi on

the surface of the workpiece. Use a standoff of

7.75 Estimate the limiting drawing ratio (LDR) for

the materials listed in Table 7.3.

Cold-rolled Al-killed 1.4-1.8 2.5-2.6

steel

Aluminum alloys 0.6-.8 2.2-2.3

Copper and brass 0.6-0.9 2.3-2.4

7.77 A cup is being drawn from a sheet metal that

has a normal anisotropy of 3. Estimate the

maximum ratio of cup height to cup diameter

π

4D2

o−D2

p=πDph

7.78 Obtain an expression for the curve shown in

Fig. 7.56 in terms of the LDR and the average

normal anisotropy, ¯

R(Hint: See Fig. 2.5b).

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LDR = 2.3¯

R0.14

7.79 A steel sheet has Rvalues of 1.0, 1.5, and 2.0 for

the 0◦, 45◦and 90◦directions to rolling, respec-

tively. If a round blank is 150 mm in diameter,

4= 1.5

The limiting-drawing ratio can be obtained

7.80 In Problem 7.79, explain whether ears will form

and, if so, why.

on p. 399. Thus, the minor axis will have the

dimension

x−4 mm

4 mm =−0.125

A=π5 mm

Fig. 7.61.

The coordinate system is shown in the accom-

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7.83 In Example 7.4, assume that the stretching is

done by two equal forces F, each at 6 in. from

αmax = 50◦without necking, what should be

the minimum value of nof the material?

(1) Refer to Fig. 7.31 on p. 373 and note the

following: (a) For two forces Fat 6 in. from

each end, the dimensions of the edge portions

Consequently, the tensile force, which is uni-

form throughout the stretched part, is

(2) For α= 50◦, we have the total length of the

stretched part as

Lf= 2 6 in.

Thus, 304 annealed stainless steel, phosphor

bronze, or 70-30 annealed brass would be suit-

7.84 Derive Eq. (7.5).

tral axis) be lo, we note that

lo=R+T

a 0.5-in. thick annealed 304 stainless-steel plate

that has a diameter of 12 in. on a conical man-

drel of α= 30◦. The mandrel rotates at 100

Ft=utofsin α

In order to determine u, we need to know

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in. diameter, hence

T= (3190 lb) 12 in.

2= 19,140 in-lb

or T= 1590 ft-lb. Thus the maximum power

required is

7.86 Obtain an aluminum beverage can and cut it in

half lengthwise with a pair of tin snips. Using a

micrometer, measure the thickness of the bot-

0.0120 in. thick. The wall thickness reduction

in ironing is then

= 0.1767 in3

0.1767 in3=πd2

4to=πd2

4(0.012 in)

or d= 4.33 in.

7.87 What is the force required to punch a square

hole, 150 mm on each side, from a 1-mm-thick

5052-O aluminum sheet, using ﬂat dies? What

would be your answer if beveled dies were used

instead?

= 0.7(190 MPa)(0.001 m)(0.60 m)

= 79,800 N = 79.8 kN

blanks if the clearance between blanks is one

tenth of the radius of the blank. Consider sin-

illustration is shown below.

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2R

0.1R

2.1R

The area of the unit cell is A=

4.62R2×100 = 32%

7.89 Plot the final bend radius as a function of ini-

tial bend radius in bending for (a) 5052-O alu-

minum; (b) 5052-H34 Aluminum; (c) C24000

the following data is compiled:

5052-H34 210 73

C24000 Brass 265 127

AISI 304 SS 265 195

Rf/Ri

5052-H34

C24000 Brass

304 SS

5052-O

1.05

1.10

1.15

1.2

1.25

profile that will define the mandrel shape in a

spinning operation. Determine the equation of

12 in.

(a) at x= 0, dy

dx = 0.

dy

dx = 2ax +b

Therefore,

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and

9a+c= 1

Thus, a=1

9and c= 0, so that the equation for

7.91 For the mandrel needed in Problem 7.90, plot

the sheet-metal thickness as a function of radius

if the part is to be produced by shear spinning.

Is this process feasible? Explain.

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7.93 Consider several shapes (such as oval, triangle,

L-shape, etc.) to be blanked from a large ﬂat

sheet by laser-beam cutting, and sketch a nest-

ing layout to minimize scrap.

7.94 Give several structural applications in which

diffusion bonding and superplastic forming are

used jointly.

7.95 On the basis of experiments, it has been

suggested that concrete, either plain or rein-

forced, can be a suitable material for dies in

sheet-metal forming operations. Describe your

7.96 Metal cans are of either the two-piece variety

For a three-piece can, should the seam be (a) in

the rolling direction, (b) normal to the rolling

direction, or (c) oblique to the rolling direction

of the sheet? Explain your answer, using equa-

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7.97 Investigate methods for determining optimum

shapes of blanks for deep-drawing operations.

This is a topic that continues to receive consid-

erable attention. Finite-element simulations, as

two different directions, comment on relevant

manufacturing considerations. Include factors

such as anisotropy of the cold-rolled sheet, its

surface texture, the bend directions, the nature

of the sheared edges, and the method by which

the handle is snapped in for assembly.

produced by bending only because of this notch.

As such, the important factors are bendabil-

7.99 Design a box that will contain a 4 in. ×6 in. ×3

in. volume. The box should be produced from

7.101 In opening a can using an electric can opener,

you will note that the lid often develops a scal-

loped periphery. (a) Explain why scalloping

occurs. (b) What design changes for the can

opener would you recommend in order to min-

imize or eliminate, if possible, this scalloping

effect? (c) Since lids typically are recycled or

discarded, do you think it is necessary or worth-

while to make such design changes? Explain.

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7.103 Lay out a roll-forming line to produce any three

Stage 7

7.104 Obtain a few pieces of cardboard and carefully

cut the profiles to produce bends as shown in

ment on the difference in strain states between

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