Handbook of Me Chan 00 Nord

7/30/2019 Handbook of Me Chan 00 Nord

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HANDBOOKof

MECHANICAL DESIGN


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'7

HANDBOOKofMECHANICAL DESIGNBY

GEORGE F. NORDENHOLTEditor of Product EngineeringJOSEPH KERR

Managing Editor of Product EngineeringAND

JOHN SASSOAssociate Editor of Product Engineering

First EditionThird Impression

McGRAW-HILL BOOK COMPANY, Inc.NEW YORK AND LONDON1942


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HANDBOOK OP MECHANICAL DESIGNCksPYRIGHT, 1942, BY THE

McGraw-Hill Book Company, Inc.PRINTED IN THE UNITED STATES OF AMERICA

All rights reserved. This book, orparts thereof, may not be reproducedin any form without permission of

the publishers.

THE MAPLE PRESS COMPANY, YORK, PA.


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PREFACEMany engineering departments, perhaps most, compile and keep up to date amanual which may be called the standards book, reference book, engineering depart-ment standards, or which may be given some other name. Also, many designengineers build their own book or manual. In such books will be found a vast fundof engineering data and many methods of design procedure not found in existinghandbooks.When Product Engineering was launched as a pubhcation to serve the designengineers, it was obvious to the editors that a great service could be rendered to theprofession by gathering and publishing data, information, and design procedures suchas are contained in engineering department manuals. Thus, the first number ofProduct Engineering in January, 1930, contained a reference-book sheet for designcalculations, a feature which has been continued in practically every number. Soonafterward, there was added to Product Engineering's editorial content another regularfeature, a two-page spread illustrating standard constructions, possible variations bywhich to achieve a desired result, and similar design standards covering constructions,drives, and controls.

It was soon found impossible to meet all the requests for additional copies ofreference-book sheets and design standards. The demand continued to increase andnumerous readers suggested that the material be compiled into book form and pub-lished. It was in answer to this demand that the authors compiled this book.

Other than the major portion of the chapter on materials and a few other pagesthat have been added to round out the treatment of certain subjects, all the materialin this book appeared in past numbers of Product Engineering, although some of it hasbeen condensed or re-edited. Very little of the material in this book can be found inthe conventional handbooks, for this Handbook of Mechanical Design contains practi-cally no explanations of theoretical design. It confines itself to practical designmethods and procedures that have been in use in engineering design departments.

The authors wiU welcome suggestions from users of this book and especiallydesire to be notified of any errors.We wish to make special acknowledgment of the material on typical designsappearing in Chapters IV and VI, by Fred Firnhaber, now of Landis Tool Company;the nomograms by Carl P. Nachod, vice-president of the Nachod & U. S. Signal Co.;the standard procedure in the design of springs by W. M. Griffith of Atlas ImperialDiesel Engine Company; the spring charts by F. Franz; the methods for calculatingbelt drives and other nomograms by Emory N. Kemler, now associate professor ofmechanical engineering at Purdue University; the nomograms for engineering calcu-lations by M. G. Van Voorhis, now on the editorial staff of Product Engineering; andto S. A. Kilpatrick and 0. J. Schaefer for their brilliant series of articles, which have


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vi PREFACEbeen included in slightlj^ condensed form, on the design of formed thin-sheet aluminum-alloy sections. Acknowledgment is also made here of data on properties of materialscontributed by the Alimiinum Company of America, United States Steel Corporation,and the American Foundrymen's Association.

Other engineers whose contributions to Product Engineering have been incorpo-rated in this book are H. M. Brayton, 0. E. Brown, E. Cowan, C. Donaldson, R. G. N.Evans, C. H. Leis, A. D. McKenzie, G. A. Schwartz, A. M. Wasbauer, B. B. Ramey,J. W. Harper, H. M. Richardson, G. A. Ruehmling, T. H. Nelson, E. Touceda, W. S.Rigby, R. S. Elberty, Jr., and G. Smiley. George F. Nordenholt,

Joseph Kerr,John Sasso.New York,

April, 1942.


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CONTENTSPa.qe

Preface vCHAPTER I

Charts and Tables for General Arithmetical Calculations 1Arc length versus Central Angle. Chordal Height and Length of Chord. Length of Material for Bends.Circular Segments. Volumes in Tanks, Horizontal Round. Volumes in Tanks, Vertical Round. Volume,Weight, and Cost. Weights of Cylindrical Pieces. Chart of Unit and Total Weights. Chart of Weightsand Volumes. Moment of Inertia of Prisms; Flywheels; Gears and Armatures. Radii of Gyration.Transferring Moments of Inertia to Parallel Axis. WR^ of Symmetrical bodies. Centrifugal Force.Forces in Toggle Joint. Linear Motion. Rotary Motion. Mean Cooling Temperature. Solution ofOhm's Equations. Total Resistance of Parallel Circuits.

CHAPTER IIMaterials 33

Selection of Materials. Cast Irons. Alloy Cast Irons. Effect of Nickel and Chromium on Cast Iron.Malleable Iron Castings. Cast Carbon Steels. High Alloy Cast Steels. Low Alloy Cast Steels. Corro-sion and Heat-resistant Cast Steels. Properties of Stainless Steel. Iron-nickel-chromium Alloys. Alumi-num Base Alloys. Magnesium Base Alloys. Insulating Materials. Plastic Materials. PhenolicLaminated Molded Materials. Steels for Automotive Parts.

CHAPTER IIIBeams and Structures 71

Stress Calculations for Thin Aluminum Sheet Sections. Compression Members. Angles in Compression.Shear Members. Vertical Stiffeners for Shear Resisting Webs. Diagonal Tension Webs. HollowGirders. Box Sections Subjected to Torsion. Chart for Determining Bending Moments. Deflection ofVariously Loaded Beams. Stresses in Cantilever Beams. Tensile Strength of Round Wires. RectangularMoments of Inertia.

CHAPTER IVLatches, Locks and Fastenings 95

Locking Devices. Retaining and Locking Detents. Wire Locks and Snap Rings. Taper-Pin Applications.Hinges and Pivots. Clamping Shoes and Plugs. Lock Bolts and Indexing Mechanisms. MachineClamps. Door and Cover Fastenings. Bolt Diameter, Load, and Stress.

CHAPTER VSprings 121

Designs of Helical Springs. Spring Wire Specifications. Design Stresses. Torsional Moduli. AllowableStresses Based on Endurance Limits. Natural Frequency. Formulas for Helical Springs. PermissibleManufacturing Tolerances. Form for Design Calculations. Standard Drawings for Springs. Table ofWire Gages and Diameters, with Their Squares, Cubes, and Fourth Powers. Inspection and Testing ofSprings. Graphical Solution of Helical Spring Formulas. Helical Spring Charts for Specified Ratio ofLoads and Lengths. Designs of Tension Spring Ends. Graphical Designs of Flat Cantilever Springs.Graphical Designs of Semielliptic Laminated Springs. ,

59376


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viil CONTENTSPageCHAPTER VI

Power Transmission Elements and Mechanisms 151Flexible Couplings. Shaft Diameters for Torsion and Bending. Shaft Diameters for Torsional Deflection.Shaft Diameters for Lateral Deflection. Shaft DiametersA.S.M.E. Code. Two-bearing Shafts ofUniform Strength. Stress in Rotating Disk. Velocity Chart for Gears and Pulleys. Flat-belt Length andPulley Diameter. Flat-belt Speed-Horsepower Charts. Belt Horsepower Charts. Flat-belt HorsepowerCharts. Flat and V-belt Horsepower Charts. V-belt Lengths. Short-center Belt Drives. Chart forCalculating Needle Bearings. Thrust Bearing Friction Moments. Bronze Bearing Alloys. Shaft Seals.Roller-Bearing Seals. Sleeve-bearing Seals. Safety Gears. Shifting Mechanisms. Gibs and Guides.Cam Designs. Variable-speed Devices. Transport Mechanisms. Automatic Feed Hoppers. Glue-applying Mechanisms.

CHAPTER VIIDrwes and Controls 207

Significance of WR^. Analysis of Motor Load. Selection of Motor Type. Inquiry 'Form for ElectricMotors. Winding Connection Diagrams for Multispeed Motors. Electric Control Methods. ElectricallyOperated Values. Automatic Timers. Trigger Switch Mountings. Thermostatic Mechanisms. Auto-matic Stops.

CHAPTER VIIIDesign Data on Production Methods 251

Fusion Welding. Resistance Welding. Furnace Brazing. Flame Hardening. Centrifugal Casting.Permanent Mold Casting. Die Casting. Forging. Flame Cutting. Powdered Metal Pressings.


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HANDBOOK OF MECHANICAL DESIGNCHAPTER I

CHARTS AND TABLESFor General Arithmetical Calculations

The charts and nomograms in this chapter include only those pertaining togeneral arithmetical calculations, as hsted below. Nomograms, charts, and tablesfor use in the design of specific machine elements or structures will be found in thechapters devoted to the design of those elements or structures.

Len^jthPage

Arc Length vs. Central Angle 2Chordal Height and Length of Chord 3Length of Material for Bends 4

AreaCircular Segments 8

VolumeTanks, Horizontal Round 9Tanks, Vertical Round 10Volume, Weight, and Cost 11

WeightCyUndrical Pieces 12Unit and Total Weight 14Weight and Volume 15

Moment of Inertia, Radius of Gyration, and WR-PagePrisms 16Flywheels, Gears, and Armatures 17Radii of Gyration 17Transferring to Parallel Axis 18WR- of Symmetrical Bodies 19

ForceCentrifugal 26Forces in Toggle Joint 27

Force, Velocity, and AccelerationLinear Motion 28Rotary Motion 29

Heat and TemperatureMean Cooling Temperature , 30

ElectricalSolution of Ohm's Equations. 31Total Resistance of Parallel Circuits 32


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HANDBOOK OF MECHANICAL DESIGNARC LENGTH VERSUS CENTRAL ANGLE

(Angle of Bend, Length, and Radius)

Draw a straight hne through the two known points. The answer will be foundat the intersection of this line with the third scale.

Example: For a 6-in. radius and 45-deg. bend, length of arc is 4.7 in.


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CHARTS AND TABLESCHORDAL HEIGHT AND LENGTH OF CHORD

Draw a straight line through the two known points. The answer ^vill be foundat the intersection of this line with the third scale.

Example: Length of chord is 3 in., and radius of circle is 4 in. The height h ofthe chord is 0.29 in.


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HANDBOOK OF MECHANICAL DESIGNLENGTH OF MATERIAL FOR 90-DEG. BENDS

As shown in Fig. 1, when a sheet or flat bar is bent, the position of the neutral plane with respect to the outer andinner surfaces will depend on the ratio of the radius of bend to the thickness of the bar or sheet. For a sharp corner,the neutral plane will lie one-third the distance from the inner to the outer surface. As the radius of the bend isincreased, the neutral plane shifts until it reaches a position midway between the inner and outer surfaces. Thisfactor should be taken into consideration when calculating the developed length of material required for formed pieces.The table on the following pages gives the developed length of the material in the 90-deg. bend. The followingformulas were used to calculate the quantities given in the table, the radius of the bend being measured as the distancefrom the center of curvature to the inner surface of the bend.

1 . For a sharp corner and for any radius of bend up to T, the thickness of the sheet, the developed length L fora 90-deg. bend will be

L = 1.5708 (-D2. For any radius of bend greater than 2T, the length L for a 90-deg. bend will be

L = 1..5708 (r + ^^3. For any radius of bend between IT and 2T, the

value of L as given in the table was found by interpolation

.

The developed length L of the material in any bendother than 90 deg. can be obtained from the followingformulas:

1. For a sharp corner or a radius up to T:L = 0.0175 (li + t) X degrees of bend

2. For a radius of 2T or more:

R= Inside radius

H ^ -M h-T= Stock thickness

Neutralline1t-5*>2 irl

T ESharp corner R=Torless R=iTto2T

Fig. 1.R= 2T or more

L = 0.01755(S+|) X degrees of bendFor double bends as shown in Fig. 2, if fii -|- Ss is greater than B:

X = V2BiR, +Ri- B/2)With Ri, Ri, and B known:

fl, -t- flo - B""^ ^ = rT+rTL = 0.0175(S, + R2)Awhere A is in degrees and L is the developed length.

If Ri + Ri is less than B, as in Fig. 3,Y = B cosec A {Ri + fl2)(cosec A cotan A)

The value of X when B is greater than Ri + Ri will beX = B cot A -h {Ri + 7S2) (cosec A - cotan A)

The total developed length L required for the material in the straight section plus that in the two arcs will beL = Y + 0.0175(^1 4- R2)A '

To simplify the calculations, the table on this page gives the equations for X, Y, and the developed length forvarious common angles of bend. The table on following pages gives L for values of R and T for 90-deg. bends.

EQUATIONS FOR X, Y, AND DEVELOPED LENGTHSAngle A,

deg.


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CHARTS AND TABLESDEVELOPED LENGTH IN INCHES OF MATERIAL REQUIRED FOR 90-DEG. BEND


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6 HANDBOOK OF MECHANICAL DESIGNDEVELOPED LENGTH IN INCHES OF MATERIAL REQUIRED FOR 90-DEG. BEND {Continued)


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CHARTS AND TABLES 7DEVELOPED LENGTH IN INCHES OF MATERIAL REQUIRED FOR 90-DEG. BEND (Continued)


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8 HANDBOOK OF MECHANICAL DESIGN

F-2

oc

1^ 10.9

rO.8-0.7

0.5

0.5

0.4"

-0.3

-0.25

-0.2

-0.15

0.1

AREAS OF CIRCULAR SEGMENTS-70005,000

- 3,000- 2,000

- 1,000500300-200

~ 100

E-30i-20

10

A= 0.01745 R^arc cos -~ - (R-H)Vh('2R-H)Note: The ang/e is expressed in degrees


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CHARTS AND TABLESVOLUMES IN HORIZONTAL ROUND TANKS WITH FLAT ENDS

F-30

/Turning line

Notes: Shift decimal point on volumescale two' points for a one-point sliift ondiameter scale; one point for a one-pointshift on length scale.

Example: Tank is 6 ft. in diameter and 15 ft.' long. H = 0.9 ft. H/D = 0.15. Join 0.15 onH/D scale with 6 on diameter scale. From point of intersection with turning line, draw line to15 ft. on the length scale. The volume scale shows 300 gal. If D had been 0.6 ft., H 0.09 ft.,and length the same, the answer would be 3.00 gal.


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10 HANDBOOK OF MECHANICAL DESIGNVOLUMES IN VERTICAL ROUND TANKS WITH FLAT BOTTOMS10 r^'OOO f-io-9

-8

'-7

r6

^5

-2

r4,000

r- 3,000

-2,000

- 1,000800

^600

^9

-6

-5

r80f-60

4030

-20

r-10

^6

Draw a straight line through the two knownpoints. The answer will be found at theintersection of this line with the third scale.In reading the answer on the volume scale,shift decimal point on volume scale two placesfor one-place shift on diameter scale, andone place for one-place shift on height scale.

Example: Diameter of tank is 4 ft. Depthof liquid is 2.5 ft. Volume as read is 230 gal.If diameter of tank is 0.4 ft. and depth 2.5 ft.,volume is 2.3 gal.


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CHARTS AND TABLES 11VOLUME, WEIGHT, AND COST CHART


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CHARTS AND TABLESWEIGHTS OF CYLINDRICAL PIECES, POUNDS PER INCH OF LENGTH (Continued)

13

Diam-


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14 HANDBOOK OF MECHANICAL DESIGNUNIT AND TOTAL WEIGHTS

Draw a straight linethrougli the two knownpoints. The answer will befound at the intersection ofthis line with the third scale.

Example: Given 7 piecesper pound or 0.143 lb. perpiece; 15 pieces weigh 2.15 lb. - 1 1 -


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CHARTS AND TABLES 15WEIGHT AND VOLUME

1.7

- 1.5

- 1.2

0.06 >,--0,05

Q0300.025

H- 0.020

0.015

0.010

Q09ZAluminum

0.065 Magnesium

Mercury 0.5 i0.50 -|-Q05 Fiber

Cl

0.40Monel mefai 1Copper IMckel \\Pfios. bronze J \ 0.35

Brass 0.3/Steel 0.285Castiron K,^, ^'^'^Roiledzinc 1 0-253 - - - y^^

0.22-1

0.20

017

0.15

012

QIO -IDraw a straight line through the two known points. The answer will be foundat the intersection of this line with the third scale.Exam-pie: 4 cu. in. of aluminum weighs 0.37 lb.


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16 HANDBOOK OF MECHANICAL DESIGNMOMENT OF INERTIA OF A PRISM ABOUT THE AXIS aa


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CHARTS AND TABLESRADII OF GYRATION FOR ROTATING BODIES

17

KC-1

l-c-1

ril^c-M

y

Solidcylinderabout itsown axisHollowcylinderabout itsown axisRectan-gularprismaboutaxis

throughcenterRectan-gularprismaboutaxis atone endRectan-gularprismaboutoutside

2 =

ii2 = 7-2i -j- r'^.

R^ = 12

fl2 = 4b^ + c'12

R' = 462 -I- c2 -f 12bd + 12d-12


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18 HANDBOOK OF MECHANICAL DESIGNCHART FOR TRANSFERRING MOMENT OF INERTIA

7 = 7o + WX'-

0.5 0.75r T

X- Distance Be+ween the Parallel Axes- in Inches1 1.2 1.4 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2\5I I I I IIIIIII 1II r 2.6 2.7 2.8 2.9


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CHARTS AND TABLES 19WR^ OF SYMMETRICAL BODIES

For computing WR'^ of rotating masses of weight per unit volume p, by resolving the body intoelemental shapes. See page 208 for effect of WR^ on electric motor selection.

Note: p in pounds per cubic incli and dimensions in inches give WR'^ in Ib.-in. squared.1. Weights per Unit Volume of Materials.

Weight, Lb.Material per Cu. In.Cast iron . 260Cast-iron castings of heavy section i.e., flywheel rims . 250Steel 0.283Bronze 0.319Lead 0.410Copper 0.318

2. Cylinder, about Axis Lengthwise through the Center of Gravity.\o\Mme = '^L{D\- D\)4

(a) For any material:WR-' = ~ pL{D\ - DS)

where p is the weight per unit volume.(6) For cast iron: L{D\ - DS)WR'- = 39.2(c) For cast iron (heavy sections)

:

_ LjDS - PS)^^ ~ 40.75(d) For steel

:

WR^ = LjDh - D\)36.03. Cylinder, about an Axis Parallel to the Axis through Center of Gravity.

Volume = I L{D\ - D\)^g (a) For any material:

(6) For steel:

*^""-"" 4.50 V 8 ^yj4. Solid Cylinder, Rotated about an Axis Paredlel to a Line that Passes through the Center of

Gravity and Is Perpendicular to the Center Line.

IfV11 r ^

Volume = ^ D'-L4(a) For any material:

(b) For steel:+ ' WR "'" 4.50 Vl2 ^ 16 ^ /


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20 HANDBOOK OF MECHANICAL DESIGN5. Rod of Rectangular or Elliptical Section, Rotated about an Axis Perpendicular

to and Passing through the Center Line.For rectangular cross sections:

K, = }U; K, = 1For elliptical cross sections:

Volume = K^abL(a) For any material

IT4

WR 'x'-x' = pahLU ^ + T,{n + L) + K,a'}(b) For a cast-iron rod of elliptical section (p = 0.260)

:

= 4:90 [y + ''^^^^ + ^) + leJwm6. Elliptical Cylinder, about an Axis Parallel to the Axis through the Center of

Gravity.Volume = 7 abL4

(a) For any material:

(b) For steel:16

abL /a- + b'-OOV 167. Cylinder with Frustum of a Cone Removed

Volume =

WR\_a =2(Di - >.,)

irpL8(Di - D2)

8. Frustum of a Cone with a CyUnder Removed.

Volume = ttL2(Z)i - D2)WP2 = '^wa,_, 8(i)i - D2)

2

4

{D\

^ iD\\{D\ -D\)\


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CHARTS AND TABLES9. Solid Frustum of a Cone.

V uiumt; =

21

Volume = 12 (Di - D,)TTpL {D\ - D\)160 (Di - D2)

10. Chamfer Cut from Rectangular Prism Having One End Turned about aCenter.

f^ Distance to center of gravity, where A = R2/R1 and B = C/2RihC -H

ii2S5volume X {1 A)+ ^[1 - A -A log,

(A' - 3A + 2)>2 / 1 \^(^1 - A -A log. jj + Af(^^-2^ + l)

+ J^^(3A^-4A^+l)672 A ^Volume jR\B?^{


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22 HANDBOOK OF MECHANICAL DESIGN13. Inside Part of a Torus.

T Volume = 2irr-g D

i WR\^, = TTpr^ 4 \2D-A'):

14. Circular Segment about an Axis through Center of Circle.

'^ 12 X area -^ 4r""

Gravityaxis

-i!

ca = 2 sin ^ ;^^ deg.ZKArea = i2=a c114.59 2 i^- 4

(a) Any material

:

FE^_. = pT(5) For steel:

229:2 " 6 r^"^ ~ 2 / 2 V^ 4 _

WP2 = i 229:2 ~ 6 V^' ~ Y; 2 V^ 415. Circular Segment about Any Axis Parallel to an Axis through the Center of

the Circles. (Refer to 14 for Figure.)WR%.-.' = WR\_. + weight {r' - r^)

16, Rectangular Prism about an Axis Parallel to the Axis through the Center ofGravity.

Volume = WLT-WAT (a) For any material:

L

y-j-x

WR\_. = pWLT [^' ^"^ + if)(h) For steel:

^^^-- = 3:534 1-^2 + n


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CHARTS AND TABLES17. Isosceles Triangular Prism, Rotated about an Axis through Its Vertex.

23

f- axisVolume = CUT2pCHT

\2 12/

18. Isosceles Triangular Prism, Rotated about Any Axis Parallel to an Axisthrough the Vertex.

Volume = CHTWK.._^. 2 \2 12 9^+V

19. Prism with Square Cross Section and Cylinder Removed, along Axis throughCenter of Gravity of Square.

Volume = L {h- - '^)WR\^, = "^ {l.miH' - D')

20. Any Body about an Axis Parallel to the Gravity Axis, When WR"^ about theGravity Axis Is Known.

g -y-en'^/A>'*-/i WR\^, = WR\_, + weight X r^^Pc

'-


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24 HANDBOOK OF MECHANICAL DESIGN22. WR^ of a Connecting Rod, Effective at the Cylinder Center Line, about the

Crankshaft Center Line.WR^ = r' (- i + Tf4J + 8L2-

where r = crank radius W2 = weight of the upper or reciprocating partL = center-to-center length of connecting of the rod = WrLi/Lrod Wr = Wi + W2, the weight of the complete rod

Wi = weight of the lower or rotating part of Li = distance from the center line of the crank-the rod = [Wr(L Li)]/L pin to the center of gravity of the con-

necting rod

23. Mass Geared to a Shaft.The equivalent flyvi^heel effect at the shaft inquestion is

WR^ = hîWR'Ywhere h = gear ratio

_ r.p.m. of mass geared to shaftr.p.m. of shaft

(WR"^)' = flywheel effect of the body in questionabout its own axis of rotation

24. Mass Geared to Main Shaft and Connected by a Flexible Shaft.The effect,^2)' r>*-j^~Driven gear of the mass (TTî?-)' at the position of the drivingC^^^^j . gear on the main shaft is'""^^ '^^^ TI7P2 _ ^KWR'^y^Mainshaff VVK ("TFTP'VP

^^n r..nr ^ " 9.775CDriving gearwhere h = gear ratio / = natural torsional frequency of the shafting

_ r.p.m. of driven gear system, in vibrations per sec."" r.p.m. of driving gear C = torsional rigidity of flexible connecting{WR^y = flywheel effect of geared-on mass shaft, in pound-inches per radian

25. Belted Drives.The equivalent flywheel effect of the driven mass at theL L -^1 driving shaft is

/HS T\^ WR^ = ^'^'^'V4^ Vi^y " 9.775CDriven \ ^ Drivingpuiiey pulleywhere h = Rx/R C = RÂE/L

r.p.m. of pulley belted to shaft A = cross-sectional area of belt, in sq. in.~ r.p.m. of shaft E = modulus of elasticity of belt material in[WR-y = flywheel effect of the driven body tension, in lb. per sq. in.

about its own axis of rotation R = radius of driven pulley, in in./ = natural torsional frequency of the L = length of tight part of belt which is clear

system, in vibrations per sec. of the pulley, in in.


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CHARTS AND TABLES 2526. Effect of the FlexibiUty of Flywheel Spokes on WR^ of Rim.The effectiveWR^ of the rim is ^

mWR' = iWR')'{WRyp

9.775(7where (WR^)' = flywheel effect of the rim

/ = natural torsional frequency ofthe system of which the fly-wheel is a member, in vibra-tions per sec.

C = torque required to move therim through one radian relativeto the hub

^ _ 12Eka^bR ( L , R \where g = number of spokesE = bending modulus of elasticity of the

spoke materialk = 7r/64 for elliptical, and h = }^2 for

rectangular section spokesAll dimensions are in inches.

For cast-iron spokes of elliptical section:E = 15 X lO*^ lb. per sq. in.ga'bR XIO'/L . R A Ib.-in.C = 0.1132L2 (i+!-0 radians

Note: It is found by comparative calculations that with spokes of moderate taper very little error is involved inassuming the spoke to be straight and using cross section at mid-point for area calculation.

Section A-A

Note: Since the beads at the ends of the spokes comprisebut a small part of the flywheel WR', very little errorwill result in assuming them to be of rectangular crosssection. Also, because of the effect of the clampingbolts, the outer hub will be considered a square equalto the diameter. The spokes will be assumed straightand of mid-point cross section.

Partof flywheel

TYPICAL EXAMPLEThe flywheel shown below is used in a

Diesel engine installation. It is requiredto determine effective WR- for calculationof one of the natural frequencies of tor-sional vibration. The anticipated nat-ural frequency of the system is 56.4vibrations per sec.

(o)

(b)

(r)

(rf)

ie)

if)

Formula IFie=

2f

2616a

neglecting/ ir^ + L^\\ 12 y

56

26

19

10[(52)^ - (43)^]40.75 = 955,300

2.375[(43)- - (39)


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26 HANDBOOK OF MECHANICAL DESIGNCHART FOR DETERMINING CENTRIFUGAL FORCEF = 0.000341 M^i^n^

F7 10,000r-8iOOO'- 6,000

-4,0003,000

2,000

4 5 6 8 10 15 20 30 40 50 60 80 100R= Radius of Gyration in Ft.


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CHARTS AND TABLES 27FORCES IN TOGGLE JOINT WITH EQUAL ARMS

P ^ S^F 4/i

10,000 -8,000 -:6,000 -:5,000 H4,000 -:

I 1 1 II i|iiii|i ii i [ I iii|ii i i|iii i | I I i | i | i l I I I I I ' i"| i " ' l"" | " " | ""|"" | M ' I ' ' ' I0.1 0.2 0.3 0.4 0.5 0.6 0.8 I 2 3 4 5 6 8 10h in in.

Example: Use mutually perpendicular lines drawn on tracing cloth or celluloid.In the example given for S = 10 in. and h = 1 in., a force F of 10 lb. exerts pressuresPof 25 lb. each.


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28 HANDBOOK OF MECHANICAL DESIGNACCELERATED LINEAR MOTION

2S V V 32.16FT- 2S W = G

3 4 5 6 7 8 i9 10 20 30 40 50 60 80 100 120 140I I I,...i,..,l,.., I I I , r , I ,

ft per sec. per sec. ^100WLb.* = turning pointF = velocity at time T, in ft. per sec.(S . = distance passed thi-ough, in ft.T = time during which force acts, in sec.F accelerating force, in lb.W weight of moving body, in lb.G = constant acceleration, in ft. per sec.


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30 HANDBOOK OF MECHANICAL DESIGNMEAN COOLING TEMPERATURE

e;-l


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CHARTS AND TABLES 31SOLUTION OF OHM'S EQUATIONS

Volts

10 100

50100

Draw a straight line through the two known points.The values of the two unknowns will be found at theintersections of this line with the other two scales.Use boldface scales or lightface scales according toposition of decimal point.

Ohms100 1 1000

500

aoi'0.1


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32 HANDBOOK OF MECHANICAL DESIGNTOTAL RESISTANCE OF PARALLEL CIRCUITS

1J_+ ++ + ...Ri R2 Rz RiFor convenience, list the resistances of the different parallel circuits in descending order

of magnitude. Locate Ri on the diagonal scale and connect it with ^2 on the hori-zontal scale. The total resistance is found at the intersection with the Total Resistancediagonal. For more than two parallel circuits, project horizontally from the intersec-tion point on the Total Resistance diagonal to the diagonal Resistance Ri, draw aline to i? 3 on the horizontal scale, and the answer will again be found at theintersection with the Total Resistance diagonal. Repeat successively foradditional resistances Rt, Ri, etc.

The light dashed lines indicate the procedure for finding the totalresistance of five parallel circuits, Ri =100, R^ = 60, Rs = 40,Ri = 30, Rti = 25. The answer as given by the chart is 8.0.

Conversely, the resistances of individual parallel cir-cuits to give a desired total resistance can be determinedfrom this chart.

f ir|ll l l|llll | ll l l |ll l Ol l M|llll|l ll l[ lll l|ll ll|I UI| lll lpl l l| l ll l | l lll|ll l l|nil |l l ll |N I I|l lll|MII|lll

10 20 30 40 50 60 70 80 90 100 110 12050 60 70 80Resisi'ances, R2,R3,R4""


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CHAPTER IIMATERIALS

PageSelection of Materials 34Cast Irons 35Alloy Cast Irons 36Effect of Nickel and Chromium on Cast Iron

.

38Malleable Iron Castings 39Cast Carbon Steels 40High Alloy Cast Steels 42Low Alloy Cast Steels 44Corrosion and Heat-resistant Cast Steels .... 46

PageProperties of Stainless Steel 50Iron-Nickel-Chromium Alloys 52Wrought Brasses and Bronzes 54Corrosion-resisting Metals and Alloys 58Aluminum Base Alloys 60Magnesium Base Alloys 64Insulating Materials 65Plastic Materials 66Phenolic Laminated Molded Materials 68Steels for Automotive Parts 70

33


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34 HANDBOOK OF MECHANICAL DESIGNSELECTION OF MATERIALS

The universal problem in engineering design is the selection of the materials from which thevarious parts of the device, machine, or product are to be made. It is also the first problem becausethe material selected will govern the allowable stresses, the types of construction that might beadopted, the manufacturing methods employed, the assembly operations, the finishes that might beapplied, and, of greatest importance, the cost and sales appeal of the product. In many designs,the commercial success or failure will be determined definitely by the materials selected.

In practically every design, the physical and other properties required will determine whichmaterials might be used. But the relative importance of the different properties will vary consider-ably for different types of design. The unit strength of the material is practically always a factorthough often a minor one.

For constructions subjected to only a steady tension, the yield point on the stress-strain curveor the yield strength of the material, i.e., the unit tension it can withstand with a specified elongation,will be the first consideration. But for a compression-loaded column, both the tensile strength andthe elastic modulus must be considered. For vibratory or repeated stresses, the endurance limit ofthe material becomes the governing strength consideration, whereas for low-temperature service andshock loads the impact values are of great importance. And, of course, there is also to be consideredthe compressive strength or the shear strength, according to the type of stresses to which the mem-ber will be subjected.

In addition to the unit strength considerations, any one or a group of almost innumerable otherproperties must be considered. If, as in most machine tools, it is important to have little or novibration, a material with a high vibration damping capacity, such as cast iron, might be consideredfirst. Hardness, wear resistance, porosity, and ductility are some of the other properties that maybe of major importance.

In addition to physical properties; corrosion resistance, heat conductivity, electrical conduc-tivity, dielectric strength, frictional properties, and many others may enter into the problem.

There is no formula or equation by which the most suitable material from the standpoint ofproperties can be selected. Nor is il always advisable to use the material that has the highest valuesfor the properties desired. Invariably the final selection must be a compromise largely because twoother important factors enter into the problem, namely, the workability of the material and its cost.When a number of different materials have been selected, each of which possesses the desiredproperties to a satisfactory degree, the next step toward the final selection is the determination ofthe manufacturing methods that might be employed. Aluminum, zinc, and many of the non-ferrous alloys naturally suggest die-casting, stamping, and forging. Iron, steel, aluminum, and someother metals offer great possibilities bj^ virtue of their weldability. Casting is suitable for almostall metals and alloys. Plastics are mostly molded; some are sheet-laminated or are in the form ofsheets; a few are extruded. To mention only a few other manufacturing processes, we have impactextrusion, die extrusion, drawn shapes and rolled shapes, and roll-formed sheet sections.

After it has been determined what types of construction might be used, the design must beanalyzed with reference to such things as the use of inserts, consolidating different parts into onepiece, use of standard purchased parts, and similar possibilities.

Hand in hand with the types of construction that might be employed are the costs of machining,grinding, and other operations, which will vary greatly. Included in this category may be pimch-ing, hand reaming, riveting, buffing, and polishing.

Not until all the factors discussed above have been studied closely and analyzed should anyconsideration be given to the cost per pound of the material. A complete analysis may often revealthat aluminum at 30 cts. per lb. or zinc at 10 cts. per lb. is cheaper to use than gray iron at 5 cts.per lb.A complete analysis of all the items to be considered in the selection of materials and the associ-ated problems of types of constructions and workability considerations would require volumes andeven then would obscure the problem rather than clarify it. In the final analysis, nothing can besubstituted for clear engineering thinking based on broad experience and knowledge.


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MATERIALS 35CAST IRONSGRAY IRON

Per CentChemical Composition by Weight

Graphitic carbon 2 -3Combined carbon 0.8 max.Iron 93.7 -94.3Silicon 0.25-0.3Manganese. : 0.5 - 1Sulphur 0.07- 0.12Phosphorus 0. 10- 1.05

Average Physical Properties Lb. per Sq. In.Tensile strength 21,000- 42,000Shear strength 36,000- 60,000Compressive strength 70,000-200,000Modulus of elasticity 15,000,000

Gray iron ordinarily is easily machinable.WHITE IRON

Per CentChemical Composition by Weight

Graphitic carbon TraceCombined carbon 3 . 30Iron...... 94.93Silicon 0.60Manganese . 52Sulphur 0.15Phosphorus 0. 50

Average Physical Properties Lb. per Sq. In.Tensile strength 20,000-70,000Modulus of elasticity 20 ,000 ,000

White iron is difficult to machine. When not heat-treated, white iron has greatresistance to wear bj^ abrasion.

MOTTLED IRONPer Cent

Chemical Composition by WeightGraphitic carbon 1 . 50Combined carbon 1 . 80Iron 95.07Silicon 0.92Manganese . 36Sulphur 0. 13Phosphorus 0. 22

Mottled iron is a mixture of gray iron and white iron.ChUled cast iron are those parts of castings which after pouring are cooled

quickly by chills in order to retain the carbon in the iron carbide form found in whiteiron, whereas other parts of the casting cool slowly to form gray iron.


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36 HANDBOOK OF MECHANICAL DESIGNALLOY CAST IRONS

To obtain exceptional properties such as high tensile strength, hardness, wear resistance, corro-sion resistance, and heat resistance, many alloys of cast iron with other elements have been developed.The effect of various alloying additions are indicated in the accompanying table.

EFFECTS OF ALLOYING ADDITIONS ON CAST IRONAddition


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MATERIALS 37EFFECT OF ALLOYS ON CAST IRON280

ro


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38 HANDBOOK OF MECHANICAL DESIGNEFFECT OF NICKEL AND CHROMIUM ON CAST IRON

Addition of Nickel.1. Increases strength and elasticity when composition of the iron is adjusted,

especially the sUicon content.2. Refines the grain and reduces porosity.3. Increases hardness.4. Eliminates hard spots and thus improves machinability when nickel additions

amount to K to 4 per cent depending upon the sUicon content and sectionthickness.

5. Decreases the amount of sihcon needed to keep castings gray and machinable.6. Increases wearing quahties.7. Improves impact resistance.8. Improves heat and corrosion resistance.9. Raises electrical resistance.Addition of Chromium.1. Improves tensile strength.2. Refines the grain.3. Increases hardness. Produces hard spots when used alone or in excessive

amounts.4. Increases chilling power, depth of chill, and the combined carbon.5. Increases heat resistance.6. Increases wear resistance.7. Increases corrosion resistance.8. Decreases machinability.Addition of Nickel and Chromium Together.1. By using two or three parts of nickel to one of chromium, the chilling action of

chromium is restrained and the beneficial effects of chromium are retained.2. Increases strength and hardness. Amounts needed to obtain maximum

machining qualities, and also hardness and strength, in castings of varioussection thickness are shown in the accompanying table.

Applications for Nickel and Nickel-chromium Cast Iron.Cylinders, cams, gears, hardware, bushings, machine frames, liners, and plates.

NICKEL AND CHROMIUM IN CAST IRON FOR MAXIMUM MACHINABILITYSections }/i-}>4 in. thick


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MATERIALS 39MALLEABLE IRON CASTINGSAVERAGE MECHANICAL PROPERTIES

Tensile strength, lb. per sq. in 54 ,000Yield point in tension, lb. per sq. in 36 ,000Elongation in 2 in 18 per centReduction in area (see note 1) 19 per centModulus of elasticity in tension, lb. per sq. in 25,000,000Compressive strength (see note 2)Ultimate shearing strength, lb. per sq. in. (see note 3) 48,000Yield point in shear, lb. per sq. in 23 ,000Modulus of elasticity in shear, lb. per sq. in 12,500,000Yield point in torsion, lb. per sq. in 24 ,000Modulus of rupture in torsion, lb. per sq. in. 58,000Brinell hardness number 100-140Charpy impact value, ft.-lb. (see note 4) 16.5Wedge test for impact (see note 4)Fatigue endurance limit (no definite data, probably about 25,000 to 26,000

lb. per sq. in.)Effect of temperature (see note 5)

PHYSICAL CONSTANTSSpecific gravity 7 . 15-7 . 45Shrinkage allowance, in. per ft M~^l6Coefficient of thermal expansion per deg. F . 0000066Specific heat, c.g.s. units 0. 122

ELECTRICAL AND MAGNETIC PROPERTIESResistivity, microhms per cc 28-37Magnetization properties (see note 6)Magnetic hysteresis (see note 6)

Notes on Malleable Iron Castings1. Reduction of Area.^The elongation usually is spread quite evenly over the entire gage length, instead of being

restricted locally. This may be construed to mean that cohesion is more uniform in malleable iron than in otherferrous metals.

2. Compressive Strength.In ductile ferrous metals, the yield point in compression so closely approximates that intension that testing for the latter, being much more easily determined, avoids the necessity of testing for the former.Also, it is impractical to determine the compressive strength of such products, because once the yield point has beenpassed the specimen flattens out, yielding no well-marked fracture.

3. Shear and Torsion Tests.In determining shear by the "direct method," approximate results only can besecured because a certain amount of distortion caused by the combined effect of compression and bending during thetest can not be avoided. Consequently, shearing properties are better studied from torsion tests. The number oftwists per foot of length will furnish an estimate of the toughness of the material, and their distribution yields someindication of the variation in hardness which tends to cause an uneven localization of the twists, there being lessdistortion at planes of greater hardness.

4. The wedge test will furnish a more accurate idea of what can be expected of castings that are to be subjected toshock and occasional overload in service than will a notched bar test, wherein the stresses are concentrated at the rootof the notch.

5. Effect of Temperature.If malleable iron is heated to a temperature in excess of its critical range, the tempercarbon will start to revert back to the combined form, and if heated to around 1600F. practically all of it wOl bereverted. Malleable iron can be heated to around 800F. without loss in tensile properties.

6. Magnetization Properties.When high permeability is required in iron, the carbctn should be in the form oftemper carbon, whereas combined carbon or free cemenite should be absent. Malleable iron possesses high inductionand permeability and low hysteresis loss.


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40 HANDBOOK OF MECHANICAL DESIGNCAST CARBON STEELS

Chemical composition Mechanical properties

Car-bon,percent

0.11

0.11

0.150.170.180.20-0.25

0.19

0.220.220.220.24

Man-ga-nese,per

0.73

0.810.670.830.70-0.80

0.03

0.700.680.670.78

0.260.270.270.270.270.28

0.28

0.25 0.68

0.840.710.720.750.690.65

0.79

Sili-con,percent

0.27

0.40

0.200.230.30

0.25-0.35

0.320.280.340.28

0.32

0.370.410.320.310.260.27

Sul-phur,percent

0.027

Under0.03

0.031

0.0300.0300.029

0.0340.0340.0320.032

Phos-phoruspercent

Tensilestrength,lb. persq. in.

Yieldpoint, lb.per sq. in.

0.028

Under0.03

0.028

0.0240.0250.024

0.0270.0290.0270.027

62,00064,00073.00067,00070,00070,00071,50074 , 50062,00063 , 500

71,00072,00073,50071,00067,00077,00077,000

75,00072,00082,50074,50076,00074 , 000

68,00069,000

75,00076,00084 , 00095,000108,000119,000130,000

26,00024.00035,00035,000

35,000

34,00037,00036 , 50046 , 50048,00042,00044,000

37.00043.00043,500

27,00044,00043,000

44.50040 , 00041,50043,000

42,00043 , 500

36,00042,00057,00068,00079,00090,000100,000

Elon-gation,percent

33.013.228.229.531.034.028.534.014.026.533.034.032.036.539.0

33.032.533.028.022.030.5

33.032.928.035.028.028.0

33.337.8

19.525.530.024.019.0

14.09.0

Re-duc-

tion ofarea,percent

36.030.053.059.554.052.540.249.018.631.651.258.055.1

59.867.0

53.552.449.747.833.051.0

54.257.647.745.744.842.0

51.1

63.3

29.031.565.057.046.033.018.0

Im-pact

3.7'2.1

15.0'13.7'

3.7''

15'36'

16/24/26/

0164'

Hard-nessnum-bers"

20.1/32.6/32.0/

34.0/

35. 5

37.5'

45.5'

126B119B116B126B

137B139B143B

149B149B156B

119B136B136B

133B

163B153B156B

156B143B160B192B220B238B250B

Treatment of steel**

Annealed in commercial furnaceAs cast1475^. (800C.) (6), furnace cooled1650F. (900C.) (6), furnace cooled1825F. (995-0.) (6). furnace cooled

Annealed1650F. (900C.) (5). furnace cooledAnnealedAs castleoO-F. (870''C.), furnace cooledAs cast1650F. (900C.) (1), air cooled16S0r. (900C.) (1), furnace cooled

leSOT. (900''C.) (1). furnace cooled1700F. (930C.) (1), air cooled1600F. C870''C.) (1). air cooled1200F. (650


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MATERIALSCAST CARBON STEELS (Conlinued)

41

Chemical composition


54/296

42 HANDBOOK OF MECHANICAL DESIGNHIGH ALLOY CAST STEELS

Manganese Steel.1. Contains 10 to 14 per cent manganese with less than 1.5 per cent carbon.2. Extremely hard, strong, and tough, with high resistance to wear.3. Usually cast to form, but can be forged at a yellow heat.4. Difficult to machine, can be partly softened by quenching from about 1830F.5. Hardness is restored by heating to about 1380F. and coohng slowly in air.

Nickel Steel.1. Contains ordinarily 0.52 to 3 per cent nickel with 0.15 to 0.60 per cent carbon.2. Has high elastic limit and tensUe strength.3. Corrosion resistance increases mth the nickel content.

Chrome Steel.i

1. Contains usually 0.5 to 3.5 per cent of chromium with 0.2 to 0.6 per centcarbon.

2. Has high elastic limit, tensile strength, and hardness.3. Up to 1 per cent of chromium has httle effect on steel. With 1 per cent car-

bon and 2 per cent chromium, great toughness is attained.4. Low-carbon chrome steels can be forged with as high as 12 per cent chromium

present, but the alloy becomes brittle as the carbon increases.5. Chrome steel attains great hardness when quenched in water.6. Steels with about 15 per cent chromium are relatively corrosion resistant.

Vanadium Steel.1. Small percentages of vanadium combined with chromium and manganese in

steel result in an alloy that has high tensUe strength and elastic hmit.2. Vanadium makes nickel steel more homogeneous and decreases the fragility;

it is seldom used with more than 8 per cent nickel.3. Additions of 0.15 to 0.25 per cent vanadium to chrome steel counterbalances

the extreme hardness of chromium and produces an alloy with better machin-ing properties.

Tungsten Steel.1. Is very hard and brittle, difficult to forge, and cannot be welded when the

tungsten exceeds 2 per cent.2. Can be worked at a red heat, but is usually cast in the form of tools and ground

to the desired form.3. Addition of tungsten to steel produces a close and uniform structure.4. High-carbon tungsten steel retains high magnetism.5. Steel alloys with 5 to 8 per cent tungsten are self-hardening.


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MATERIALS 43Molybdenum Steel.

1. Effect of molybdenum on steel is between that of tungsten and chromium.2. Molybdenum in chrome steel improves the forging qualities.

High-speed Steels.1 . Derive their properties from selected combinations of the several metals listed

above.2. Cobalt, uranium, titanium, and silver are also used in high-speed steels.3. A typical high-speed steel analysis is iron, 68.79 per cent; carbon, 0.51;

manganese, 0.26; silicon, 0.14; phosphorus, 0.02; sulphur, 0.04; chromium,7.08; tungsten, 22.68; and molybdenum, 0.48 per cent.


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0-T3O V(NX!

lO^ 'O oIs. C iQO if3

C C


57/296

MATERIALS 45

wmHPia(^oPi

Q


58/296

46 HANDBOOK OF MECHANICAL DESIGNPROPERTIES OF CORROSION- AND HEAT-


59/296

MATERIALS 47RESISTANT CAST STEELS

CoeflBcient ofthermal expansion


60/296

48 HANDBOOK OF MECHANICAL DESIGNPROPERTIES OF CORROSION- AND HEAT-


61/296

MATERIALS 49RESISTANT CAST STEELS (Continued)


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50 HANDBOOK OF MECHANICAL DESIGNPROPERTIES OF U.S.S. STAINLESS STEEL

AUoy

Typical chemical composition

CarbonManganesePhosphorusSulphurSiliconChroniiumNickelTitaniumColumbium

Physical propertiesDensity. lb. per cu. inSpecific electrical resistance at 68r.:Microhms per ccMicrohms per cu. inLow-carbon steel = 1.00Melting range, deg. FStructureMagnetic permeability;As annealedAfter 10 per cent reduction of area. . . .

Specific heat:B.t.u./deg. F./lb., at 32-212FLow-carbon steel = 1.00 (0-100C.)..Thermal conductivity:B.t.u./sq. ft./hr./deg. F./in., at212rLow-carbon steel = 1.00, at 100C. . .B.t.u./sq. ft./hr./deg. F./in., at 932F

Coefficient of thermal expansion:Per deg. F. X 10 (32-212F.)Per deg. F. X 10 (32-932F.)

U.S.S. 18-8

Type 302*

. 08/201 .25 max.0.03 max.0.03 max.0.75 max.18.0/20.08.0/10.0

0.28670 (cold worked,70-82)27.6 (cold worked.27 . 6-32 . 3)6.42550-2590Austenitic

= 1= 1 003100.121.1

1130.1509.

10.

33

Type 304

0.08 max.2.00 max.0.03 max.0.03 max.0.75 max.18.0/20.08.0/10.0

0.28670 (cold worked,70-82)

27 . 6 (cold worked,27 . 6-32 . 3)6.42550-2590Austenitic

00310

0.1.

1130.1509.610.2

U.S.S. stabihzed 18-8

Type 321

0.10 max.2.00 max.0.03 max.0.03 max.0.75 max.17.0/20.07.0/10.04 X C min.

0.28571286.52550-2590

Austenitic^ = 1 . 003ji = 1.10

0.121.1

1120.321539.310.3

Type 347

. 10 max.2.00 max.0.03 max.0.03 max..75 max.17.0/20.08.0/12.010 X C

0.28571

2550-2590Austeniticn = 1 . 003It = 1.100.121.1

1120.321539.310.3

Mechanical properties at room\

temperatures Annealed Coldworked Annealed Coldworked Annealed Coldworked Annealed Coldworked

Tensile strength, 10^ lb. per sq. inYield point, 10' lb. per sq. inModulus of elasticity. 10^ lb. per sq. inElongation in 2 in., per centReduction of area, per centCharpy impact strength, ft.-lbIzod impact strength, ft.-lbEndurance Umit (fatigue), 10 lb. per sq. in.Brinell hardness numberRockwell hardness number _.Stress causing 1 per cent elongation (creep)

in 10,000 hr.:At 1000F., lb. per sq. inAt 1200F., lb. per sq. inAt 1350F., lb. per sq. inAt 1500F.. lb. per sq. in.Scaling temperature, deg. F. (approx.)Initial forging temperature, deg. FFinishing temperature, deg. F.A.nneaUng treatment.

80- 9535- 452955- 6055- 65

105-300t60-25029- 2650- 265- 30

80- 9535- 452955- 6055- 6575-11035135-185B75-B90

90- 95170-460C5-C4775-110

35138-185B75-B90

105-300t60-25029- 2650- 265- 30

90- 95170-460C5-C47

Cold forming, drawing, stampingMachinabilityWelding (arc. gas. resistance, atomic hydro.geK)

Precautions (see notes)

17,0007.0003.0008501,6502.200f Not under\ 1600-1700f 1900-2000F.I and quench

ExcellentFair toughVery good, annealafter welding for maxi-mum corrosionresistance

(A)

17,0007.0003,0008501,6502,200Not under1600-17001900-2000F.and quenchGoodFair toughVery good, anneal

heavier than J-s in.for maximum corro-sion resistanceU)

80- 9535- 452950- 5555- 657745135-185B75-B90

105-300t60-25029- 2650- 265- 30

90- 95170^60C5-C4717,0007.0003.0008501,6502,200Not under1600-17001900-2000F.and quenchGoodFair toughVery good, not

necessary to anneal(B)

80- 9535- 452950- 5555- 657745135-185B75-B90

105-300t60-25029- 2650- 265- 3090- 95170-460C5-C47

17,0007,0003,000i

8501.6502.200Not under1600-17001900-2000F.and quenchi Good[Fair toughVery good,; notnecessary to anneal

(B)

* U.S.S. 18-8 free machining. Type 303. same as 302 except S or Se 0.07 min. or molybdenum 0.60 max.t Commercial grades, thin gages of sheet and strip

i-i Hard = 125.000 lb. per sq. in.i-i Hard = 150.000 lb. per sq. in.% Hard = 175.000 lb. per sq. in.Full hard = 185.000 lb. per sq. in.


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MATERIALSPROPERTIES OF U.S.S. STAINLESS STEEL (Continued)

51

Alloy

Typical chemical composition

CarbonManganese.

.

Phosphorus. .SulphurSiliconChromium. . .NickelMolybdenum

Physical propertiesDensity, lb. per cu. inSpecific electrical resistance at 6S''F.:Microhms per ccMicrohms per cu. inLow-carbon steel = 1.00Melting range, deg. FStructureMagnetic permeabihty:As annealedAfter 10 per cent reduction of area. .Specific heat:B.t.u./deg. F./lb. at 32-212FLow-carbon steel = 1.00 (0-100C.)

.

Thermal conductivity:B.t.u./sq. ft./hr./deg. F./in., at 212FLow-carbon steel = 1.00, at 100C. . .B.t.u./sq. ft./hr./deg. F./in., at932F

Coefficient of thermal expansion:Per deg. F. X 10= (32-212F.)Per deg. F. X 10= (32-932''F.)

U.S.S. 18-8 Mo U.S.S. 25-12Type 316

0. 10 max.2 . 00 max.0.03 max.0.03 max.0.75 max.16.0/18.014.0 max.2.00/3.00

0.29172.328.5

2500-2550Austenitic

n = 1.003-fi = 1.10

0.121.11080.311458.49.6

Type 309

0.20 max.2.00 max.0.03 max.0.03 max.0.75 max.22.0/26.012.0/14.0

0.2837830.77.12530-2570Austenitic

1^ = 1.003*i = 1.003

0.121.187-116. 25-0 . 341258.39.6

U.S.S. 12

Type 410J;

0. 15 max.0.75 max.. 03 max.0.03 max.0.75 max.10.0/14.0

0.2765722.45.22750-2790

MartensiticFerromagneticFerromagnetic

0.11i.d1730.501996.17.2

U.S.S. 17

Type 430

0.12 max.0.75 max.0.03 max.0.03 max.0.75 max.14.0/18.0

2.2735923.25.42710-2750Ferritic

FerromagneticFerromagnetic0.111.0

1690.491816.06.7

U.S.S. 27

Type 446

0..35 max.1.00 max.0.03 max.0.03 max.0.75 max.23.0/30.0

0.2706726.46.12710-2750Ferritic

FerromagneticFerromagnetic0.111.0

1450.421695.96.3

Mechanical properties at roomtemperatures

Tensile strength, 10^ lb. per sq. inYield point, 10^ lb. per sq. inModulus of elasticity, 10= lb. per sq. in.Elongation in 2 in., per centReduction of area, per centCharpy impact strength, ft.-lbIzod impact strength, ft.-lbEndurance Umit (fatigue), 10=* lb. per sq.Brinell hardness numberRockwell hardness number _. . .Stress causing 1 per cent elongation

(creep) in 10,000 hr.:At 1000F., lb. per sq. inAt 1200F., lb. per sq. inAt 1350F.. lb. per sq. inAt 1500F., lb. per sq. inScahng temperature, deg. F. (approxi-mate)Initial forging temperature, deg. FFinishing temperature, deg. FAnneahng treatment.

Cold forming, dra\ving, stampingMachinabihtyWelding (arc, gas, resistance, atomichydrogen)

Precautions (see notes)

Annealed

80- 9535- 452950- 5555- 6570-110

43135-185B75-B90

Coldworked

105-300t60-25029- 2650- 265- 30

90- 95170^60C5-C4025,00018,0008,0003,00016502200Not under1600-17001950-2050F.and quench

GoodFair toughVery good, annealfor maximum

corrosionresistance

(A)

Annealed

90-11040- 602935- 5045- 60

53150-185B80-B90

Coldworked

110-27065-23029- 2625- 255- 20

170-375C5-C4017,00011,0003,40085021002150Not under1600-17001950-2050F.and quench

GoodFair toughVery good, annealfor maximum

corrosionresistance

(-4)

Annealed

65- 8535- 452835- 2565- 60100- 60

135-165B75-B85

Quench-ed anddrawn

100-20060-18025- 1065- 25100- 5

293-390C30-C4013,0002,3001,400

13002100Not over 1450

I

Furnace coolfrom 1550-1100F. or aircool from1300-1400F.Fair

FairFairWelding hardensAnneal to restoreductiUty(C)

Annealed

70- 9040- 552930- 2055- 408- 2550145-185B80-B90

Coldworked

100-18065- 302925- 240- 20

185-270B90-B1058,5002,1001,200

15502000Not over 1400Air cool from1500-1400'F.

GoodFairFairWelds are brittlewhen coldShght response

to anneal(fl)

Annealed

75- 9545- 602930- 2050- 40

50140-185B80- 90

Coldworked

85-17555-1552925- 255- 25

150-250C0-C25

1,600400

21002000Not over1400-1450Rapid cool from1650-1550F.

PoorFairFairWelds are brittlewhen coldShght response

to anneal(-D)

X U.S.S. 12 free machining, Type 416, same as 410 except S or Se 0.07 min. or molybdenum 0.60 max.{A) Preheat slowly to 1600F.. then heat rapidly to the forging or annealing temperature. Exposure to temperatures between 800 to1600F. produces marked susceptibihty to intergranular corrosion. If the metal is unattached, this can be cured by repeating the anneahngtreatment.{B) For maximum corrosion resistance in high temperature ser\dce, use following stress reheving operationsheat 2 hr. at 1550F..air cool.(C) Preheat slowly to 1450F., then heat rapidly to 2100F. for forging. Full corrosion resistance is developed only in the heat-treatedcondition. (Temper below 1000F.)(D) In forging, preheat slowly to 1450F. Excessive grain growth takes place above 2000F. Expert welding is required to avoidexcessive grain growth. Prolonged exposure at 850 to 950r. produces cold brittleness. To prevent this, heat to 1650 to 1550F. beforecooling, and quench. Stainless steels cannot be forge hammer welded.


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52 HANDBOOK OF MECHANICAL DESIGNCOMPOSITION AND PROPERTIES OF IRON-NICKEL-CHROMIUM ALLOYS

Group classification, typical composition ofeach type, per cent


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MATERIALSCHARACTERISTICS AND USES OF IRON-NICKEL-CHROMIUM ALLOYS

53


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67/296

MATERIALS 55

CONOmQfe

mHwot)o

oI

(

HftOftOfe

oo


68/296


NaoPinQB

1^owWOs


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MATERIALS 57

MP4NoPipqQOft

o oo rf o"o -^ ^.

-*J CO o Mld 3 CtT g" bCC E C

P. CD JiIB 03 a;

- CD

C d

S 'J "" ^ g " I

1^ -a ^

c3 CDbC 'm

C 03o3

bCC^ O 'ElCO ft P-o3 CO

" ftj3 'i- -^bO '

f_ CD -.-Icu .t ^& 5-^CO -^ ^g .2 m'-3 bD a3^ 2 'Sa1 I3 "^ .SC3 ^ QJ'" S CDCD OJ tift ^ CCCO

bCO


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58 HANDBOOK OF MECHANICAL DESIGNCORROSION-RESISTING

Metal oralloy


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MATERIALS 59METALS AND ALLOYS


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60 HANDBOOK OF MECHANICAL DEÎUN

O

o

3 -- (1) +j""' c^t3 d go u.d ri d-ô o

CO

I g gigs'

acesW 0) g

^ ô cr[fl ' r '1'

^gsi

ma

OS

o a;

HZ

N


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MATERIALS 617* ' M

Oh-l

IS


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to>4-J!

HW-UoQ

owMCOt>Q, complete engage-ment is shown. Rounded corners as at Xand Y should be provided. There should beplenty of clearance as at E to allow for wearbecause of the small angle of the slot. At H isshown an improved form of gear. It assuresclearance and provides for grinding of the,angular surfaces if necessary. If the lock-boltspring is not strong enough to seat the bolt byrotating the plate, vibration will usually com-plete the seating, causing chatter at the cuttingtool or spindle and wear on the bolt and slot.In this type of bolt, the angular sides are alike,hence the direction may be opposite from thatshown.

Fig. 197.More accurate form oflock bolt, which is claimed by manyto be the correct method for thistype of design. The inclined sur-face gets the wear as it seats thethe bolt, whereas the straight orradial side positions the bolt accu-rately. Positions A, B, C, and Dcorrespond to those in Fig. 196, andindicate that the corners X and Yshould be rounded. At H is shownhow the groove is ground. Othernotations are the same as given inFig. 196.

Milled \ Pin pre venisrolaIionFig. 198.

'Tapered gibs perrnii accurole,-D^iJ. n selfinq of boll in bolh side

Fig. 199.


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Tension springkeeps bo/rinengagementFig. 205.

Hand-operated / Projecfion Jnfegral, cam ^ / niin cam engages ^

\ ; sloi- in bolfBoli

BoltBolt engageddisengaged y ^qo

Bolfdisengaged

Boltengaged

Pivof centerlocafion

Swinging loci; boll / Lug j^elease / Cam"t^-" Lock boll

ZA^Hand-operoledlever

, Xy-Lock-boll'Cenlering lugs-' plolePlan

Fig. 207.By using a lock-bolt plate larger than the work, the indexing error is diminished. The swinging lockbolt is released automatically by the spring plunger, which has a predetermined movement, when the hand-operatedlever is moved to the left, as shown by the arrow marked Release, and the cam contacts the rounded top surface of thelock bolt. The ratchet is keyed with the lock-bolt plate to the spindle. As the lock bolt is released and the lever isrotated 30 deg. counterclockwise, the pawl engages the ne.xt tooth in the ratchet wheel at X. The lever is then pulledin the direction of the arrow marked Index, the cam moving the lock bolt downward into the next opening in thelock-bolt plate. The plan view of the bolt shows the two centering lugs between which the lock bolt is additionallysupported.

Spring-backed lock boll,L ock- boll plalekeyed lo spindle ,-- Groove J

---Xfe/K

-Pin-Prong

^ Plale

'Indexinghandle

Locked

ThirdprongProng

Lock-boll operal-ingplale freeforolale

Pin^Groove F'Lock boll

Lock- boll plate ~Fig. 208. Fig. 209.

Fig. 208.The handle is mounted on the plate and is independent of the lock-bolt plate. As the handle is pulled tothe left, the prong pushes against the pin driven into the spring-backed lock bolt, thereby disengaging the bolt. Atthe same time, the second prong contacts the plate at Z. Both plates then move simultaneously, releasing the lockbolt, which rides on the periphery of the lock-bolt plate, and the bolt falls into the next slot. The handle is then pushedback again, clockwise, contacting the plate at R, upon which a third prong pushes against the pin-seating lock boltin a locked position.

Fig. 209.The plate is indexed through a half revolution in one direction and then back again in the opposite direc-tion. The lock-bolt plate is keyed to the spindle. The lock-bolt operating plate is free to rotate on the spindle. Whenthe indexing handle is pushed counterclockwise, as shown at the right, groove F in the plate forces the lock bolt out ofengagement. The pin driven into the plate engages the slot in the plate, thereby lining up groove / with slot K. Uponfurther movement in a counterclockwise direction, the roller on the bolt may slide into groove / and the bolt may enterslot K. The dashed line in both views show the positions when indexing in the opposite directions.


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LATCHES, LOCKS, AND FASTENINGS 115MACHINE CLAMPS

Fig. 210. Fig. 211.Clamping Fig. 212.Spindle clamping bolt. Fig. 213.Clamping slid-Clamping with bolt by spring dovetail. ing table with plate andand bushing. bolt.

Fig. 214.Clamp-ing a spindle with asplit bracket.

Fig. . 215.Sleeve Fig. 216.Example of wedgesplit at ends for clamping,clamping.

Fig. 217.Clampingwith a split bracket.

'

Fig. 218.Clamping with an eccentric. Fig. 219.Clamping a swiveling column.


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116 HANDBOOK OF MECHANICAL DESIGNDOOR AND COVER FASTENINGS

Finger grooves

Knob"Casi-iron com has o spiralrise of abouf^in.jof filecircum ference of Ig in. ouf-sic/e diamefer ofcam. Directionofspiral shouidiie such fhafwifh door hinged on left,knob is fumed ro leff for open-ing door, anci when hingedon fhe right knob is turnedright to open door

Fig. 220.

'KnobI Tapered face ^

Adjustable cam, with threadedhole,the spiral being obtained by taperingone face. Nut locks the cam in placeFig. 221.

Lever-type lock. When placedin vertical position, the weightoflever fends fo lock boltmore securely. Taperedbrocket furnishesbinding action

Suitable for heavy doorssuch OS on motors, chain, orbelt housings

J

%Fig. 222.

, Knurled^

xl;.jx

Alternate''handle, asteelcastinq

Fig. 223

Plain knob

Fig. 224.-tener usingspring.

-Snap-type fas-a flat formed

Lugs hold'- ,spring i. %^control

Fig. 225.Snap-type fastener usinground wire spring.

Pressed steel flanged cap withflat leafspring fastener. A 90-de'i.twist loosens cover Suitable forclosing inspection or adjustmentopenings

Fig. 226.


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LATCHES, LOCKS, AND FASTENINGS' Cover

117

Aliernaie con-sfruc-tion re-quiring /


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^^^^^m.Exfended finger grip

Flush iop^KlU ^Fig. 236.Stove-plate-type cover

held by gravity.

Finger liffWeic/h-f ofex.-iending lug Arunning fullwic/fh ofcoverkeeps if inplace

Fig. 237.A simple coverheld by gravity and requiringno machine work.

Fig. 2 38.Pivoted oil-hole cover.

3 [lis;

Fig. 239.Vertical coverswung on a screw.Weighf of knobkeeps hook in place

Fig. 240.LFig. 241.Plain gravity latch.

Bevel-

16 ^8 ^Co ver is slippedover studanddrops on bodyof The sfuds,being heldbygravify

0.005"clearance

Fig. 242.Positive type of gravity lock.


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LATCHES, LOCKS, AND FASTENINGS 119BOLT DIAMETER,LOAD,AND STRESSU.S. STANDARD 60-DEG.V THREAD

-I

Tol^al Tension Load on BoH" in Pounds (L)


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133/296

CHAPTER VSPRINGS

PageDesign of Helical Springs

Spring Wire Specifications 122Design Stresses 128Torsional Moduli 130Allowable Stresses Based on Endurance

Limits 131Natural Frequenc3r 132Formulas for Helical Springs 133Permissible Manufacturing Tolerances . .

.

134Form for Design Calculations 136Standard Drawings for Springs 137

PageTable of Wire Gages and Diameters, with

Their Squares, Cubes, and Fourth Powers 138Inspection and Testing of Springs 139

Graphical Solution of Helical SpringFormulas 140

Helical Spring Charts for Specified Ratioof Loads and Lengths 141

Designs of Tension Spring Ends 144Flat Cantilever Springs, Graphical Design

of 145Semielliptic Laminated Springs, Graphical

Design of 148

121


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122 HANDBOOK OF MECHANICAL DESIGNDesign of Helical Springs

Condensation of the standard specifications and design procedure adopted by the Atlas Imperial Diesel EngineCompany as set forth by W. M. Griffith, product engineer of that company, in March and April 1937, ProductEngineering.

CLASSES OF SPRING SERVICEClass I. Rapid, continuous deflection over a uniform stress range from zero to amaximum or from an intermediate stress to maximumas in engine valve springs.Class II. Rapid deflections over a variable stress range that may be from zero to

intermediate, intermediate to maximum, or zero to maximumbut with onlyintermittent operationas in springs for engine governors.

Class III. Statically loaded at maximum stress or infrequent deflections withstress range from zero to intermediate, intermediate to maximum, or zero tomaximumbut with only infrequent operationas springs for relief valves.

PURCHASE SPECIFICATIONS FOR SPRING WIREThe minimum physical properties given in these specifications are 95 per cent ofthe average values determined by tests. Thus the minimmn physical properties herespecified are well within commercial limits.

SWEDISH STEEL SPRING WIRE SPECIFICATIONSGenerally used for Class I extension or compression springs and Class II and

Class III extension springs, in wire diameters from 0.1055 in. up to 0.262 in. Thismaterial can be used for springs of larger or smaller wire diameter, but generallymusic wire is used for the smaUer wire diameters and carbon steel for the larger wires.

1. Steel ManufactureThis steel is to be of Swedish manufacture according to approved practice by the

acid open-hearth or electric-furnace process.2. Chemical Composition

Carbon 0.60-0.70 Phosphorus 0.025 max.Manganese 0.45-0.65Silicon 0.15-0.25

Sulphur 0.025 max.

3. Physical Properties

Range of wire diameter, in.

0.1055 and under.0.1205-0.1350...0.1483-0.1920...0.2070-0.2625...0.2812-0.3437...0.3625-0.4375...0.4615-0.5625 .. .

Minimum tensilestrength, lb. per sq. in.Ultimate212,000202,000187,000175,000164,000155,000146,000

Elasticlimit

154,000146,000136,000126,000119,000112,000106,000

Alinimumstrength, lb.

torsionalper sq. in.

Ultimate184,000175,000163,000151,000142,000135,000127,000

Elasticlimit

112,000106,00099,00092,00086,00082,00077,000

Reduction of area, 48 per cent minimum. Elongation in 10 in., 5 per cent minimum.


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SPRINGS 123Twist Test : Samples taken from any part of the bundle of wire must withstand

twisting seven revolutions forward and seven reverse, at a twisting speed not to exceed25 r.p.m., for the number of times as given in the following table, and the ultimatebreak must be clean and square.

Length of wire between grips, 10 in.

:

Diameter of wire, in . .Minimum twistingcycles

0.1055

23

0.1205

20

0.125020

0.135018

0.1483

17

0.1563

16

0.1620

15

0.177014

Length of wire between grips, 15 in.Diameter of wire, in . .Minimum twisting

cycles

0.1875

20

0.1920

19

0.2070

18

0.2188

17

0.2253

16

0.2437

15

0.250015

0.2625

14

Length of wire between grips, 20 in.

:

Diameter of wire, inMinimum twisting cycles

.

0.281318

0.283017

0.306516

0.312516

0.331015

0.343814

0.362514

Length of wire between grips, 30 in.Diarneter of wire, in.Minimum twisting

cycles

0.3750

20

0.3938

19

0.406318

0.4305

17

0.4375

17

0.4615

16

0.4688

16

0.490015

0.500

15

0.5313

14

0.562513

4. Surface ConditionsUpon etching with a hot solution of hydrochloric acid sufficiently to disclose

surface defects, no hairline cracks, seams, pits, gouges, die marks, or other imperfec-tions shall be revealed. Decarburization must be held to a minimum.

5. Limits of Variations in DiameterWire diameter 0.162 in. and lessplus or minus 0.0015 in.Wire diameter 0.1770 in. and overplus or minus 0.002 in.

6. Inspection, Rejections, and ReplacementsAU springs will be rigidly inspected at the plant as received. If more than a

total of 10 per cent of the springs on any one purchase order are made of steel thatfails to comply with the preceding specifications, or with the specifications on thedetail drawing, the entire lot will be rejected. All springs rejected at the plant wHlbe held at the seller's risk for a reasonable length of time, subject to his instructions,and shall be replaced by the seller without further cost to the purchaser.


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124 HANDBOOK OF MECHANICAL DESIGNCARBON-STEEL SPRING WIRE SPECIFICATIONS

Generally used for springs of wire diameter greater than 0.262 in. and also forsquare or rectangular wire ranging from M2 X }i2 in. up to H X H in., advancingby M2 in., and for sizes larger than H X /4 in., advancing by He in.

1. Steel ManufactureThis steel is to be made according to approved practice by the electric-furnace or

open-hearth process.2. Chemical Composition

Carbon 0.60-0.70 Sulphur 0.025 max.Manganese 0.45-0.65 Phosphorus 0.025 max.



0.1055 and under.0.1205-0.1350....0.1483-0.1920....0.2070-0.2625..,.0.2813-0.3438....0.3625-0.4375. . .

.

0.4615-0.5625....

Minimum tensilestrength, lb. per sq. in.

Ultimate

202,000191,000178,000165,000156,000147,000139,000

Elastic limit

132,000125,000117,000108,000102,00097,00091,000

Minimum torsionalstrength, lb. per sq. in.

Ultimate

165,000157,000145,000136,000127,000121,000114,000

Reduction of area 48 per cent minimum. Elongation in 10 in., 5 per cent

Elastic limit

108,000103,00095,00089,00084,00079,00074,000

minimum.

4. Surface ConditionsUpon etching with a hot solution of hydrochloric acid sufficiently to disclose sur-

face defects, no seams, hairline or otherwise, pits, gouges, die marks, or other imper-fections shall be revealed. Decarburization must be held to a minimum.

5. Limits of Variation in DiameterWire diameter 0.1762 in. and lessplus or minus 0.0015 in.Wire diameter 0.177 in. and overplus or minus 0.002 in.

6. Inspection, Rejections, and ReplacementsAll springs will be rigidly inspected at the plants as received. If more than a

total of 10 per cent of the springs on any one purchase order are made of steel thatfails to comply with the above specifications, or with the specifications on the detaildrawing, the entire lot will be rejected. All springs rejected at the plants wUl be heldat the seller's risk for a reasonable length of time, subject to his instructions, and shallbe replaced by the seller without further cost to the purchaser.


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SPRINGS 125CHROME-VANADIUM-STEEL SPRING WIRE, S.A.E. 6150 SPECIFICATIONS

Generally used for same range of sizes of spring wire as covered by carbon-steelspring wire, and where the higher physicals of the chrome-vanadium-steel wire makeits use specially desirable or necessary.

1. Steel ManufactureThis steel is to be made according to approved practice by the electric-furnace or

open-hearth process.2. Chemical Composition

Carbon 0.45-0.55 Sulphur 0.5 max.Manganese 0.50-0.90 Phosphorus 0.04 ma.\.Chromium 0.80-1.10 Sihcon 0.15-0.30Vanadium 0.15 min.




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SPRINGS 127PHOSPHOR BRONZE SPRING WIRES.A.E. 81

Used only for small springs, especially where resistance to moisture or othercorrosion is essential. Can be used in Class I, Class II, or Class III service. Diam-eters are specified in Brown and Sharpe gage numbers. Square or rectangular mate-rial may be used from a minimum size of M2 X M2 in. to a maximum of M X Yi in.,advancing by M2 in.

1. Chemical CompositionTin .. .. 4.00-6.00 Iron, max 0.10Phosphorus 0.03-0.40 Lead, max 0. 10Zinc, max . 20 Copper remainder

2. Tensile Strength

Range of WireDiameter, In.Up to 0.06250.0625-0.12500.1250-0.25000.2500-0.3750

MinimumTensile Strength,

Lb. per Sq. In.130,000120,000110,000100,000

3. Bend TestThe wire should be capable of being bent through an angle of 180 deg. flat back

on itself without fracture on the outside of the bent portion.4. Appearance

The wire shall be uniform in quality and temper, cylindrical in shape, and smoothand free from injurious defects.

5. Dimensional TolerancesThe wire shaU not vary from the specified diameter by more than the following:Sizes over 0.050 in., by plus or minus 1 per centSizes 0.050 to 0.025 in., by plus or minus 0.0005 in.Sizes under 0.025 in., by plus or minus 0.00025 in.

BRASS SPRING WIRE, S.A.E. 80This material may be used for the same types and classes of springs for whichphosphor bronze is suitable. It is available in two grades, as given below, Grade A

for use where the requirements are especially severe and Grade B for use underordinary conditions. Grade B will be furnished unless otherwise specified.


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128 HANDBOOK OF MECHANICAL DESIGN2. Physical Properties

This wire shall have a tensile strength of at least 100,000 lb. per sq. in. but shouldbe capable of being bent through an angle of 180 deg. around a ware of the samediameter without breaking.

3. AppearanceThe wire shall be uniform in quaUty and temper, cyhndrical in shape, and smooth

and free from injurious defects.4. Dimensional Tolerances

The wire shall not vary from the specified diameter by more than the following:Sizes over 0.050 in., by plus or minus 1 per centSizes 0.050 to 0.025 in., by plus or minus 0.0005 in.Sizes under 0.025 in. by plus or minus 0.00025 in.

DESIGN CALCULATIONSClass I springs, i.e., springs subjected to rapid continuous deflections over a uni-

form stress range from zero to maximum or from an intermediate stress to maximum,as in engine valve springs, must be designed on the basis of the endurance hmit ofthe material. Class II and Class III springs, respectively, springs that operate onlyintermittently or springs that are statically loaded are designed on the basis of thestatic strength of the material.

Because the static strength of wire of a given material increases with decreasedwire diameter, as shown in Figs. 243 to 247, a larger permissible stress can be used forthe smaller wires. The following table gives the maximum permissible workingstresses for springs for Class II and Class III service.

MAXIMUM


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SPRINGS 129250

150

100

50

1 1Chemical analysis

Carbon O65-Q70Manganese 0.45-0,65Silicon Q 15- 0.25Phosphorous Q025max.''^^ Sulphur Q025n-iax,

^//',

01 0.2 03 0.4 05 06Diam.of Wire in InchesFig. 243.Swedish steel wire. Relation of wirediameter to physical properties.

02 03 04Diam.of Wire in InchesFig. 244.Carbon-steel wire, S.A.E. 1065. Relationof wire diameter to physical properties.

02 03 0.4niam. of Wire in Inches

Fig. 245.Chrome-vanadium-steel wire, S.A.E. 6150.Relation of wire diameter to physical properties.

0.1 0.2 0.3Diom. of Wire in Inches

Fig. 246.Music wire, S.A.E.1095. Relation of wire diameterto physical properties.


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0.2 0.3 0.4Diam. of Wire in InchesFig. 247.Phosphor bronze wire, S.A.E. 81. Relation of wire diameter to physical properties.

WAHL CORRECTION FACTORAs the spring index, i.e., the ratio of coU diameter to wire diameter, decreases,

the maximum stress developed becomes increasingly greater than that as calculatedby the conventional formulas. To compensate for this in the design calculations,the Wahl correction factor must be applied. The accompanying chart (Fig. 248)

2.0

1.9

1.8>-fel.7-*-Ui 16

I 1.5O3-13iL2

II

1.0


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144/296

132 HANDBOOK OF MECHANICAL DESIGNIn calculating Class I springs, the procedure is similar except that the permissible

working stress must be based on the endurance value of the material. A tentativeallowable stress is assumed, and the wire diameter is calculated by following the sameprocedure as outlined above for Class I and Class II springs. The calculated wirediameter is then checked against the endurance charts as given in Figs. 249 to 253 forthe various materials.

As an example of the use of the endurance charts, assume a valve spring had beencalculated to be made of Swedish steel wire 0.177 in. diameter and the wire calculatedto be stressed to 62,000 lb. per sq. in. when the valve is closed and 81,000 lb. per sq. in.


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SPRINGS 133TABLES FOR CALCULATING HELICAL SPRINGS

COMPRESSION SPRING FORMULASSpring index = -r or -r- = 5 (minimum)

Round-FL-^

AUdw =

F =

0.3927Sd'(D - d)YMWL - (2.25d)

l.lOd

SP(D - d)3(maximum)

Gd'Fv = FNFL =Fn + MWL

FL - {2.25d)NitchLoad per inch of deflection = P/FnSolid length = (iV + 2.25)d

MWL = (l.lOdiV) + (2.25d)

Square

-K -i^kd

_ 0A44Sd'"^ ~ (.D - d)Y

-'^^- (o^d +5.58P(0 - d)'

Gd'Fa = FNFL =Fn + MWL

(maximum)

Pitch = --[


146/296

134 HANDBOOK OF MECHANICAL DESIGNTABLES FOR CALCULATING HELICAL SPRINGS

TORSION SPRING FORMULASPitch = FLIN

Hound


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SPRINGS 135proportional to the number of active turns. In a compression spring, the number ofactive turns mil be the total number of turns less 2K turns, assuming IM dead turnsat each end of the spring.

DEFLECTIONCalculate the deflection per turn and total deflection by the formulas given in

the tables on pages 133 and 134. For compression springs, the number of active oreffective turns N will be the total number of turns less 2M turns. ;

GENERAL SPECIFICATIONSCompression Springs.Ends must be ground square. Minimum and maximum

inside and outside diameters will be determined by the space restrictions imposed bythe application. Both ends of the compression spring should be guided on either theoutside or inside or both. All compression springs should be wound right handexcept where they operate inside one another, in which case they should be woundoppositely. Minimum working length of the spring under compression should allow aminimum clearance between effective turns equal to 10 per cent of the wire diameter.Additional compression beyond this minimum working should not be permitted.

Extension Springs.They may be close wound with or without initial tension,or they may ]5e open wound. They should always be wound without initial tensionwhen load capacity is an important factor. All extension springs should be woundright hand unless required otherwise. Maximum working length determines theposition of the spring beyond which additional extension should not be permitted.

FINISHESSteel springs to resist moisture or atmospheric corrosion should be cadmium

plated. For appearance, they may be enameled, lacquered, or japanned. Springsmade of nonferrous metals are usually not finished in any manner.

STANDARD DESIGN PROCEDUREBy using a form such as given on page 136, the procedure in designing springs

can be standardized. The data relating to the actual dimensions and characteristicsof the spring are obtained from the inspection or test department.

STANDARD DRAWINGSExamples of standard drawings on sheets 83-2 X 11 in. for the three types of heh-cal springs, compression, tension, and torsion, are shown on page 137. Drawing need

not be to scale. Wire sizes should be specified in inches, not gage numbers. Usedecimals for specifying wire diameters and fractions of inches for rectangular materials.Also dimension the thickness of rectangular wire so as to indicate how the wire is to bewound. Indicate finish, if any. In dimensioning the drawing, indicate the permissi-ble manufacturing tolerances as given in table above, but tolerances as large as per-missible should always be specified. Load tolerances should be indicated as plus orminus, the mean value to correspond with the specific rate.

The notations and dimensions as given in the drawings show^n here should begiven.


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149/296

SPRINGS 137STANDARD DRAWINGS FOR SPRINGS

I4 deadcoilsateach end.Grind endssquarewifii C.L.

Rote -390 lb. per inchToleronce -5 7oMateriol MS-IZSize -0.250 diom.Hand -RightFinish -Block Japon

Minimum worIdng iengihJj2max. JJ2 minr"Free iengfii

Springs musf be sfraigiif and compressiblefo minimum working length without coilstouching or taking a permanentset

ono^ Close wound with-out initialtension

Rate- 1601b per inchTolerance -t 57oMaterial- MS-13Size- 0.135 diom.Hond- RightFinish- Block Japon

Free iengthMaximum working length

-4i *llength between endsSprings must be straight andcapable ofextensionto maximum working length without taking apermanent set Ends must be neatly made andwithout mutilation of wire

{'Maximum deflect-ion 180 degrees --22 -Free lengthRoteToleronceMateriol-S.A.E.81Size- 0.125 diom.Hand -Right

I Finish-None

Sp^'hgs musf be straight andcapable ofwithstanding maximum deflection withouttaking a permanen t set Ends must beneatly made and without mutilation of wire

Examples of standard spring drawings. At the top is a compression spring; inthe middle is shown an extension spring; at the bottom is a torsion spring.


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138 HANDBOOK OF MECHANICAL DESIGNWire Gages, Diameters, and Their Squares, Cubes, and Fourth Powers

STEEL WIRE SIZES MONEL, BRONZE, AND BRASS WIRE(Washburn & Moen gage) (Brown & Sharpe gage)

No.


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SPRINGS 139The spring end construction of tension and torsion springs should be given in

detail by showing all necessary views. See page 144 for typical spring ends.INSPECTION

All springs received shall be carefully inspected, tested, and marked, whererequired, for identification.

Inspection shall cover all specification requirements noted on the spring drawingsand on the material specification sheets. Particular care should be exercised ininspecting the material to make certain all defects noted on the material specificationsheets are absent. In case of doubt, one or two springs from the shipment in questionshould be etched in a 30 per cent solution of boUing hydrochloric acid for a sufficientlength of time to reduce the diameter 0.002 to 0.003 in. After etching, aU materialor manufacturing defects are readily discernible.A sufficient number of springs from each shipment shall be tested to determine ifthe spring rate is within the limits specified on the drawing. The amount of set, ifany, when compressed to the minimum working length must also be determined.

All springs failing to meet the requirements referred to above shall be rejected.If more than 10 per cent of the springs on any one order are rejected, the entire ship-ment shall be rejected.

Springs constructed of music wire, Monel metal, phosphor bronze, or brass shallnot be marked in any way for identification. Springs made of steel shaU have one ortwo coUs at one end painted a color corresponding to that indicated as follows : Swed-ish steel, blue; carbon steel, orange; chrome vanadium steel, red. The paint usedshall be quick-drying, oilproof, heat-resisting lacquer.


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