Machine Design Databook Episode 3 part 10 docx

25.86 CHAPTER TWENTY-FIVE Downloaded from Digital Engineering Library @ McGraw-Hill www.digitalengineeringlibrary.com ELEMENTS OF MACHINE TOOL DESIGN... W1 W2 ¼ nPLð1= ut1Þ nPLð2= ut2Þ ¼

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Example: d ¼ 45 mm (1.8 in), kD¼ 785 N/mm2(80 kgf/mm2or 114000 psi)

q ¼ 0:2, forming height ¼ h ¼ 12:5mm:

B¼ 196 N/mm2(20 kgf/mm2or 28500 psi)

Punch force¼ PF¼ 1225 kN (125 tf) [C0-D0-E0] (Fig 25-46)

Blank area¼ FB1¼ 1600 mm2(2.46 in2) [A0-B0-C0]

Body cross-section of product¼ QF¼ 400 mm2(0.62 in2) [A0-L0-M0-N0]

The inside body height¼ h1¼ 125 mm (5 in)

Work done: AF¼ 30896 m N (3150 mm tf or 22785 ft-lbf) [E0-H0and G0-H0]

Press rating¼ Psat¼ 1960 kN (200 tf) [H0-I0-K0]

Cross-section ratio q H,F for extusion moulding and impact extrusion

Height ratio S2 / S1 for stamping and cold working

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Limit curve for rational pressworking

F

E Blank diemeter d mm

5 8 12.5 20 31.5 50 80 125 10

5.3 8 10 12.5 15 20 25 31.5 40 50 65

12.5 16 20 40 50 63 80 100

200 315 500 400 250 160 100 63 40

25

16

8000 6300 5000 4000 3150 2500 2000 1600 1250 1000 800 630 400 315 250 200 160 125 100 80

FIGURE 25-48 Chart for calculating stamping and coining

Courtesy: Heinrich Makelt, Die Mechanischen Pressen, Carl Hanser Verlag, Munich, German Edition, 1961 (Translated by R.Hardbottle, Mechanical Presses, Edward Arnold (Publishers) 1968)

X- projected die area Fp, mm; Y- stamping stroke hp, mm; Z, stamping force Pp, tonnes

Key to Fig 25-49

Equations and Examples:

Forging temperature¼ T ¼ 10008C

Tensile strength of plain carbon steel¼ B¼ 588 N/mm2(60 kgf/mm2or 86000 lbf/in2[point B ] (Fig 25-49)

Static deformation resistance¼ kFg¼ 49 N/mm2(5 kgf/mm2or 7100 lbf/in2) [point C of curve]

The deformation rate¼ w ¼ "r=t(% sec) ¼ 500%/sec [point D]

The arithmetic proportions of upsetting¼ "h¼ 4h=ho¼ ½1 Fo=F1 100%

The dynamic deformation resistance¼ kFd¼ 98 N/mm2(10 kgf/mm2or 14200 psi) [point E of the curve] (Fig 25-49)

¼ 2kFgwhere kFa¼ static strength

The diameter of non-circular upset or forged component is calculated from d111¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið4=ÞF1

p

¼ 1:13pffiffiffiffiffiF1

mm where F1¼ section after forming (upsetting surface)

cross-The ﬂash ratio¼ b=s ¼ 4:8 (point F, scale 11)

The deformation resistance¼ kw¼ 392 N/mm2(40 kgf/mm2or 57000 psi) [point G of the curve]

The upsetting force¼ Ps¼ 24516 kN (2500 tf) [point I of the curve]

A prescribed or theoretical upsetting or die diameter d1[D ¼ 280 mm (11 in)]

The corresponding upsetting or die area F1½Ftot¼ 63000 mm2(96 in2) [point H ]

The maximum diameter D ¼ d1þ 2b of forged component

The crushed ﬂash or the total cross-sectional area¼ Ftot¼ F1þ Ub where U ¼ periphery of crushed area

The mass ratio¼ Ls=Bm¼ 6:3 [point K]

The maximum upsetting force¼ Pmax¼ 30890 kN (3150 tf) [point L of the curve]

The upset path¼ h ¼ 16 mm (0.65 in) [point M]

The upsetting work¼ As¼ 348134 mm N (35500 mm tf or 256665 ft-lbf) [line N-O]

25.86 CHAPTER TWENTY-FIVE

Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com)

ELEMENTS OF MACHINE TOOL DESIGN

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Deformation rate w, %/sec

Materials testing machine

Tensile strength

σB kg/mm

2

High-percentage Cr -Ni steels (high-percentage

Cr steels)

High-percentage

Ni steels

Deformation efficiency

C steels

C steels Hydraulic prosses

I Free forging d 1 /h 1m

II Drop forging b/s

III Form upsetting d 1 /2h 1m Forging temperature T …C

Dyn deformation strength kg/mm 2

Upsetting force Ps tonnes

II

V K VI

I

10 16

25

40

6.3 16 40

120

500 500 150 100 50 40 25 15 10 6.3 4

High-forging mm

Upsetting path h to BDC on upsetting mm

500 400 315 250 200

200

× 10 3

160 125

125

100 80

80 50 31.5 20 12.5

/s)

G

8 5

3.15 F

0.63

0.5 0.8

0.4 0.315 0.25 0.2 0.16 0.125 0.1

FIGURE 25-49 Chart for calculating hot upsetting and drop forging

Courtesy: Heinrich Makelt, Die Mechanischen Pressen, Carl Hanser Verlag, Munich, German Edition, 1961 (Translated by R.Hardbottle, Mechanical Presses, Edward Arnold (Publishers) 1968)

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The ratio of weights of two bars of same length whose

weights are W1¼ 1A1l and W2¼ 2A2l

The ratio of weights of two bars of same length

subjected to tensile load F

subjected to torque Mt

subjected to bending Mb

For speciﬁc stiﬀness (in tension)

For comparison of speciﬁc strength and stiﬀness/

rigidity of diﬀerent section having equal cross

sectional area

DESIGN OF FRAMES, BEDS, GUIDES AND

COLUMNS:

For machine frames

For stiﬀening eﬀect of reinforcing ribs

For characteristics of bending and torsional rigidities

of models of various forms

For variations in relative bending and torsional

rigid-ity for models of various forms

For eﬀect of stiﬀener arrangement on torsional

stiﬀ-ness of open structure

Refer to Table 25-64 for unit stiﬀness or speciﬁc ness E=.

W1

W2

¼ nPLð1= ut1Þ nPLð2= ut2Þ ¼

ut2=2

ut1=1

ð25-170Þ where ut= is unit strength under tension

where ut2=3= is an index of the ability of a material

to resist torsion and is known as unit strength under torsion

where 2=3b = is an index of the ability of a material

to resist bending and is known as the unit strength under bending

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For eﬀect of aperture and cover plate design in static

and dynamic stiﬀness of box sections

For typical cross-sections of beds

For classiﬁcation and identiﬁcation of machine tools

For machine tools sliding guides, ball and roller

guides made of cast iron, steels and plastics

For design of spindle units in machine tools

For design of power screws and lead screws of

machine tools

For vibration and chattering in machine tools

For variable speed drives and power transmission

For lubrication of guides, spindles and other parts of

D annual allowance for depreciation, per cent

H number of years required for amortization of

investment out of earnings

I annual allowance for interest on investment, per

cent

Number of pieces required to pay for ﬁxture

Economic investment in ﬁxtures for given production

Number of years required for a ﬁxture to pay for itself

Proﬁt from improved ﬁxture designs

of machine tool slideways, guides, beds, frames and columns subjected to external forces are beyond the scope of this Handbook.

Refer to Chapter 14 on ‘‘Design of shafts’’ in this Handbook.

Refer to Chapter 18 on ‘‘Power screws and fasteners’’

in this handbook, and books on power screw design

of machine tools.

Refer to Chapter 22 on ‘‘Mechanical vibrations’’ in this Handbook.

Refer to Chapter 23 on ‘‘Gears’’ and Chapter 25 on

‘‘Miscellaneous machine elements’’ in this Handbook Refer to Chapter 24 on ‘‘Design and bearings and Tribology’’ in this Handbook and other books on lubrication.

M annual allowance for repairs, per cent

N number of pieces manufactured per year

S yearly cost of setup

t percentage of overhead applied on labour saved

T annual allowances for taxes, per cent

V yearly operating proﬁt over ﬁxed charges

V ¼ Nað1 þ tÞ CðI þ T þ D þ MÞ S ð25-176Þ

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PROCESS—COST COMPARISONS:

Symbols:

c value of each piece, dollars

Cx, Cytotal unit cost for methods Y and Z

respectively

d hourly depreciation rate for the ﬁrst machine

(based on machine hours for the base years

period)

D hourly depreciation rate for the second

machine (based on machine hours for the base

years period)

k annual carrying charge per dollar of

inventory, dollar

l labor rate for the ﬁrst machine, dollar

L lot size, pieces

labor rate for the second machine, dollar

m monthly consumption, pieces

Nt total number of parts to be produced in a

single run

Number of parts for which the unit costs will be equal

for each of two compared methods Y and Z

(‘‘break-even point’’)

Total unit cost for methods Y

Total unit cost for method Z

Quantity of pieces at break-even point

Relatively simple formula for calculation of economic

lot size, pieces

MACHINING COST:

Machining time cost per work piece

Non-productive time cost per work piece

Tool change time cost per work piece

Tool cost per work piece

Nb number of parts for which the unit costs will

be equal for each of two compared methods Y and Z (break-even point)

p number of pieces produced per hour by the ﬁrst machine

P number of pieces produced per hour by the second machine

Py unit tool process cost for method Y

Pz unit tool process cost for method Z

Q quantity of pieces at break-even point

Ty total tool cost for method Y

Tz total tool cost for method Z

s setup hours required on the ﬁrst machine

S setup hours required on the second machine

V ratio of machining time piece

L ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 24mS kcð1 þ mvÞ

60 ð25-183Þ

Cc¼ tmtcR 60t1

ð25-184Þ

Ct¼ Ct1

1 þ nsþ

tshtmR 60t1

ð25-185Þ

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Total cost of machining

Total tool cost per workpiece

Ctot¼ Cmþ Cnþ Ccþ Ct ð25-186Þ

Cn¼ Ccþ Ct ð25-187Þ where

tm¼ machining time per workpiece, min

tL¼ loading and unloading time per workpiece, min

ts¼ setting time per batch, min

tt¼ tool life, min

tc¼ tool charge time, min

tsh¼ tool sharpening time, min

R ¼ cost rate per hour

nb¼ number of batch

ns¼ number of resharpening

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TABLE 25–64

Unit stiﬀness/rigidity of some materials

b, weight density; w is also the symbol used for unit weight of materials

Source: K Lingaiah and B R Narayana Iyengar, Machine Design Data Handbook, Volume I (SI and Customary Metric Units), Suma Publishers,Bangalore, India and K Lingaiah, Machine Design Data Handbook, Volume II, (SI and Customary Metric Units), Suma Publishers, Bangalore,India, 1986

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Sectionmodulus

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TABLE 25-66

Machine Frames

Simple frames and beds of horizontal machines

Simple frames and beds of vertical machines

Portal frames

Circular frames, housings

Frames of piston machines, banks of cylinders

Frames of conveying machines

Moment ofinertia I

Sectionmodulus

BH312ð1 3Þ

BH26ð1 3Þ

0:083 1 3ð1 Þ2 0:166 1 3

64.Z/Zaand I/Iafor solid and hollow stock having identical cross sectional area in ﬂexure

25.94

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TABLE 25-67

Characteristics of Bending and Torsional Rigidities for Models of Various Forms

Model No Model form

Relativerigidity inbendingSb

Relativerigidity intorsionSt

Pillars, brackets, pedestals, hangers, etc

Tables, slide blocks, carriages

Crossheads, slides, jibs

Lids and casings

Source: Courtesy: Dobrovolsky, V., etl., ‘‘Machine Elements’’, Mir Publishers, Moscow, 1974

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TABLE 25-28

Variations in Relative Bending and Torsional Rigidity for Models of Various Forms

Relative rigidity in bending Relative rigidity in torsion

Model No

Relative weight ofbox-like section With ribs

With thicker

With thickerwalls

Relativeweight

Relative torsionalstiﬀness perunit weight

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TABLE 25-70

Eﬀect of aperture and cover plate design on static and dynamic stiﬀness of box section3

Relative stiﬀness about

Relative natural frequency ofvibrations about

Relative damping ofvibrations about

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FIGURE 25-51B Principal shapes of sliding guides (a) ﬂat

ways; (b) prismatic ways; (c) dovetail ways; (d) cylindrical

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P P

2r 2r

FIGURE 25-51D Rolling guides (a) open type; (b) closed type

TABLE 25-71

Traversing Force Calculations – Typical Cases

1

y452r 2r cos 45

3 In the type 4 ways only the feed force Pxand the preload force Ppare taken into consideration

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fC

Y

O

GAcosα

FIGURE 25-52 Forces acting on the Slidways of a Lathe – A Typical Case

Source: Courtesy: Acherkan, N., ‘‘Machine Tool Design’’, Mir Publishers Moscow, 1968

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Open ﬂat belts

Crossed ﬂat belts

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Boring spindles with faceplates

Two-direction jaw clutches

Cone clutches

Single disk clutches

Twin disk clutches

TABLE 25-72

Classiﬁcation and Identiﬁcation code of Machine Tools – Kinematic Diagram (Cont.)

Single-direction overrunningclutches

Two-direction overrunningclutches

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1 Lingaiah, K., Machine Design Data Handbook, McGraw-Hill Publishing Company, New York, 1994.

2 Lingaiah, K., Machine Design Data Handbook, Vol I, Suma Publishers, Bangalore, India, 1986.

3 Merchant, M E., Trans Am Soc Mech Engrs., 66, A-168, 1944.

4 Ernst, H., and M E Merchant, Chip Formation, Friction and Finish, Cincinneti Milling, Machine Company, USA.

5 American Society of Tool and Manufacturing Engineers (ASTME), Tool Engineers Handbook, 2nd ed.,

F W Wilson, Editor, McGraw-Hill Book Publishing Company, New York, 1959.

6 Cyril Donaldson, George H Lecain and V.C Goold, Tool Design, Tata-McGraw-Hill Publishing Company Ltd., New Delhi, India, 1976.

7 Frank W Wilson, Editor-in-Chief, American Society of Tool and Manufacturing Engineers (ASTME), Fundamentals of Tool Design, Prentice Hall, New Delhi, India, 1969.

8 Kuppuswamy, G., Center for Continuing Education, Department of Mechanical Engineering, Indian tute of Technology, Madras, India, August 12, 1987.

Insti-9 Sen, G C., and A B Bhattacharyya, Principles of Machine Tools, New Central Book Agency, (P) Ltd., Calcutta, India, 1995.

10 Geoﬀrey Boothroyd, Fundamentals of Metal Machining and Machine Tools, McGraw-Hill Publishing pany, New York, 1975.

Com-11 Koenigsberger, F., Design Principles of Metal Cutting Machine Tools, the MacMillan Company, New York, 1964.

12 Shaw, M C., and C J Oxford, Jr., (1) ‘‘On the Drilling Metals’’ (2) ‘‘The Torque and Thrust in Milling’’, Trans ASME., 97:1, January 1957.

13 Hindustan Machine Tools, Bangalore, Production Technology, Tata-McGraw-Hill Publishing Company Ltd., New Delhi, India, 1980.

14 Central Machine Tool Institute, Machine Tool Design Handbook, Bangalore, India, 1988.

15 Acherkan, A., General Editor, V Push, N Ignatyev, A Kakoilo, V Khomyakov, Y U Mikheyev, N Lisitsyn, A Gavryushin, O Trifonov, A Kudryashov, A Fedotyonok, V Yermakov, V Kudinov, Machine Tool Design, Vol 1 to 4, Mir Publishers, Moscow, 1968-69.

16 Milton C Shaw, Metal Cutting Principles, Clarendon Press, Oxford, 1984.

17 Martelloti, M E., Trans Am Soc Mech Engrs., 63, 677, 1941.

18 Kovan, V M., Technology of Machine Building, Mashgiz, Moscow, 1959.

19 Basu, S R., and D K Pal, Design of Machine Tools, 2nded., Oxford and IBH Publishing Company, New Delhi, 1983.

20 Heinrich Makelt, Die Mechanischen Pressen, Carl Hanser Verlag Muchen, 1961 (in German) Translated to English by R Hardbottle, Mechanical Presses, Edward Arnold (Publishers) Ltd., 1968.

21 Dobrovolsky, K Zablonsky, S Mak, Radchik, L Erlikh, Machine Elements, Mir Publishers, Moscow, 1968.

22 Rivin, E I., Stiﬀness and Damping in Mechanical Design, Marcel Dekker, Inc., New York, 1999.

23 Machine Tool Design and Numerical Control.

24 Chernov, N., Machine Tools, Translated from Russian to English by Falix Palkin, Mir Publishers, Moscow, 1975.

25 Greenwood, D C., Engineering Data for Product Design, McGraw-Hill Publishing Company, New York, 1961.

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26

RETAINING RINGS AND CIRCLIPS

SYMBOLS

a acceleration of retained parts, m/s2(ft/s2or in/s2)

Ch actual chamfer, m (in)

Chmax listed maximum allowable chamfer, m (in)

CF conversion factor (refer to Table 26-1)

d depth of groove, m (in)

D shaft or housing diameter, m (in)

f frequency of vibration, cps

Ftg allowable static thrust load on the groove wall, kN (lbf)

Fig allowable impact load on groove, kN (lbf)

Frt allowable static thrust load of the ring, kN (lbf)

Fir allowable impact load on a retaining ring, kN (lbf)

F0r listed allowable assembly load with maximum corner radius or

chamfer, kN (lbf)

F00r allowable assembly load when cornor radius or chamfer is less

than the listed, kN (lbf)

Ftrr allowable thrust load exerted by the adjacent part, kN (lbf)

Fsg allowable sudden load an groove, kN (lbf)

Fsr allowable sudden load on ring, kN (lbf)

l distance of the outer groove wall from the end of the shaft or

bore as shown in Fig 26-2, m (in)

n factor of safety (about 2 to 4 may be assumed)

nmax maximum safe speed, rpm

q reduction factor from Fig 26-1.

r actual corner radius or chamfer, m (in)

rmax listed maximum allowable corner radius, m (in)

t ring thickness, m (in)

T largest section of the ring, m(in)

w weight of retained parts, kN (lbf)

ðwaÞg allowable vibratory loading on groove, kN (lbf)

ðwaÞr allowable vibratory loading on ring, kN (lbf)

xo amplitude of vibration, m (in)

sy tensile yield strength of groove material, Table 26-2, MPa (psi)

saw maximum working stress of ring during expansion or

contraction of ring, MPa (psi)

s shear strength of ring material, MPa (psi) (refer to Table 26-3)

coeﬃcient of friction between ring and retained parts whichever

is the largest.

26.1

Source: MACHINE DESIGN DATABOOK

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Ctẳ...

Ctẳ Ct1

1 ỵ nsỵ

tshtmR 60t1... Ccỵ Ct 25-186ị

Cnẳ Ccỵ Ct 25-187ị where

tmẳ machining

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