Machine Design_U. C. Jindal

Scilab Textbook Companion for Machine Design by U. C. Jindal1 Created by Vibha Manvi B.E Mechanical Mechanical Engineering Cummins College of Engineering,Pune College Teacher Prof. N.r. Patil Cross-Checked by Ganesh R August 10, 2013

1 Funded

by a grant from the National Mission on Education through ICT, http://spoken-tutorial.org/NMEICT-Intro. This Textbook Companion and Scilab codes written in it can be downloaded from the ”Textbook Companion Project” section at the website http://scilab.in

Book Description Title: Machine Design Author: U. C. Jindal Publisher: Dorling Kindersley (India) Edition: 1 Year: 2010 ISBN: 978-81-317-1659-5

1

Scilab numbering policy used in this document and the relation to the above book. Exa Example (Solved example) Eqn Equation (Particular equation of the above book) AP Appendix to Example(Scilab Code that is an Appednix to a particular Example of the above book) For example, Exa 3.51 means solved example 3.51 of this book. Sec 2.3 means a scilab code whose theory is explained in Section 2.3 of the book.

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Contents List of Scilab Codes

5

3 MECHANICS OF SOLIDS

13

4 MANUFACTURING CONSIDERATIONS

37

5 INTRODUCTION TO PRESSURE VESSELS

42

6 LEVERS

47

7 STRUTS AND COLUMNS

54

8 SPRINGS

59

9 THREADED FASTENERS

74

10 PIPES AND PIPE JOINTS

82

11 RIVETED JOINTS

87

12 WELDED JOINTS

94

13 COTTER AND KNUCKLE JOINTS

101

14 KEYS AND COUPLINGS

106

15 SHAFTS

113

16 POWER SCREWS

119

3

17 SLIDING CONTACT BEARINGS

127

18 ROLLING BEARINGS

134

19 FLYWHEEL

142

20 FLAT BELT DRIVE

149

21 V BELT DRIVE

158

22 FRICTION CLUTCHES

164

23 BRAKES

174

24 ROPE DRIVE

182

25 GEARS

186

26 HELICAL GEARS

193

27 STRAIGHT BEVEL GEARS

198

28 WORM AND WORM WHEEL SET

206

29 GEARBOX

212

30 CHAIN DRIVE

216

31 SEALS PACKING AND GASKETS

220

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List of Scilab Codes Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa

3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 3.14 3.15 3.16 3.17 3.18 3.19 3.20 3.21 3.22 3.23 3.24 3.25 3.26 3.27 3.28

MS1 . MS2 . MS3 . MS4 . MS5 . MS6 . MS7 . MS8 . MS9 . MS10 MS11 MS12 MS13 MS14 MS15 MS16 MS17 MS18 MS19 MS20 MS21 MS22 MS23 MS24 MS25 MS26 MS27 MS28

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13 14 14 15 15 16 17 17 18 19 20 20 21 21 22 22 23 23 24 25 25 26 27 27 28 29 29 30

Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa

3.29 3.30 3.31 3.32 3.33 4.1 4.2 4.3 4.4 5.1 5.2 5.3 5.4 5.5 6.1 6.2 6.3 6.4 6.5 6.6 7.1 7.2 7.3 7.4 7.5 7.6 7.7 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 8.10 8.11

MS29 . MS30 . MS31 . MS32 . MS33 . MF1 . . MF2 . . MF3 . . MF4 . . IPV5 1 IPV5 2 IPV5 3 IPV5 4 IPV5 5 L1 . . . L2 . . . L3 . . . L4 . . . L5 . . . L6 . . . SC1 . . SC2 . . SC3 . . SC4 . . SC5 . . SC6 . . SC7 . . S8 1 . . S8 2 . . S8 3 . . S8 4 . . S8 5 . . S8 6 . . S8 7 . . S8 8 . . S8 9 . . S8 10 . S8 11 .

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30 32 33 34 35 37 38 39 40 42 43 44 44 45 47 48 49 50 51 52 54 55 55 56 56 57 58 59 60 61 61 63 63 64 66 67 68 69


8.12 8.13 8.14 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 9.10 9.11 10.1 10.2 10.3 10.4 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9 12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.9 12.10 12.11

S8 12A S8 13 . S8 14 . TF1 . . TF2 . . TF3 . . TF4 . . TF5 . . TF6 . . TF7 . . TF8 . . TF9 . . TF10 . TF11 . PPJ1 . PPJ2 . PPJ3 . PPJ4 . RJ1 . . RJ2 . . RJ3 . . RJ4 . . RJ5 . . RJ6 . . RJ7 . . RJ8 . . RJ9 . . WJ1 . . WJ2 . . WJ3 . . WJ4 . . WJ5 . . WJ6 . . WJ7 . . WJ8 . . WJ9 . . WJ10 . WJ11 .

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70 71 72 74 74 75 75 76 77 78 79 79 80 81 82 82 84 85 87 87 88 89 90 90 91 92 93 94 94 95 95 96 97 97 98 99 99 100


13.1 13.2 13.3 13.4 14.1 14.2 14.3 14.4 14.5 14.6 14.7 15.2 15.3 15.4 15.5 15.6 15.7 16.1 16.2 16.3 16.4 16.5 16.6 16.7 16.8 17.1 17.2 17.3 17.4 17.5 17.6 17.7 18.1 18.2 18.4 18.5 18.6 18.7

CKJ1 CKJ2 CKJ3 CKJ4 KC1 . KC2 . KC3 . KC4 . KC5 . KC6 . KC7 . S2 . . S3 . . S4 . . S5 . . S6 . . S7 . . PS1 . PS2 . PS3 . PS4 . PS5 . PS6 . PS7 . PS8 . SCB1 SCB2 SCB3 SCB4 SCB5 SCB6 SCB7 RB1 . RB2 . RB4 . RB5 . RB6 . RB7 .

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101 102 103 104 106 107 108 108 109 110 111 113 114 115 116 117 118 119 120 121 122 122 123 124 125 127 128 128 129 130 131 132 134 134 135 136 137 138


18.8 18.9 18.10 19.1 19.2 19.3 19.4 19.5 19.6 19.7 20.1 20.2 20.3 20.4 20.5 20.6 20.7 21.1 21.2 21.3 21.4 21.5 22.1 22.2 22.3 22.4 22.5 22.6 22.7 22.8 22.9 22.10 23.1 23.2 23.3 23.4 23.5 23.6

RB8 . . . RB9 . . . RB10 . . F1 . . . . F2 . . . . F3 . . . . F4 . . . . F5 . . . . F6 . . . . F7 . . . . FBD1 . . FBD2 . . FBD3 . . FBD4 . . FBD5 . . FBD6 . . FBD7 . . VBELT1 VBELT2 VBELT3 VBELT4 VBELT5 FC221 . . FC222 . . FC223 . . FC224 . . FC225 . . FC226 . . FC227 . . FC228 . . FC229 . . FC2210 . B23 1 . . B23 2 . . B23 3 . . B23 4 . . B23 5 . . B23 6 . .

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139 140 141 142 143 144 145 145 146 147 149 150 151 152 153 155 156 158 159 160 161 162 164 165 167 167 168 169 170 171 172 172 174 175 176 177 178 179


23.7 24.1 24.2 24.3 24.4 25.1 25.2 25.3 25.4 25.5 25.6 26.1 26.2 26.3 26.4 27.1 27.2 27.3 27.4 27.5 27.6 27.7 27.8 28.1 28.2 28.3 28.4 28.5 28.6 29.1 29.2 29.3 30.1 30.2 30.3 30.4 31.1 31.2

B23 7 . RD1 . . RD2 . . RD3 . . RD4 . . G1 . . . G2 . . . G3 . . . G4 . . . G5 . . . G6 . . . HG1 . . HG2 . . HG3 . . HG4 . . SBG1 . SBG2 . SBG3 . SBG4 . SBG5 . SBG6 . SBG7 . SBG8 . WWS1 WWS2 WWS3 WWS4 WWS5 WWS6 GB1 . . GB2 . . GB3 . . CD1 . . CD2 . . CD3 . . CD4 . . SPG1 . SPG2 .

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10

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180 182 183 184 184 186 187 188 189 190 191 193 194 195 196 198 199 199 200 201 202 203 205 206 207 207 208 209 210 212 213 214 216 216 217 218 220 221

Exa 31.3

SPG3 . . . . . . . . . . . . . . . . . . . . . . . . . . .

11

222

List of Figures 3.1

MS29 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

32

22.1 FC224 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

168

12

Chapter 3 MECHANICS OF SOLIDS

Scilab code Exa 3.1 MS1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

// sum 3−1 clc ; clear ; d =10; l =1500; m =12; h =50; E =210*10^3; sigut =450; A = %pi * d ^2/4; W = m *9.81; sigi = W / A *(1+ sqrt (1+(2* E * A * h ) /( W * l ) ) ) ; deli = sigi * l / E ; siggradual = W / A ; sigsudden =2* siggradual ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” s i g i i s %f N/mmˆ2 ” , sigi ) ; printf ( ” \n d e l i i s %f mm ” , deli ) ; printf ( ” \n s i g g r a d u a l i s %f N/mmˆ2 ”, siggradual ) ; 13

21 22

// The d i f f e r e n c e i n t h e a n s w e r o f s i g i and s i g g r a d u a l i s due t o round− o f f e r r o r s .

Scilab code Exa 3.2 MS2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

// sum 3−2 clc ; clear ; d =5; A = %pi * d ^2/4; l =100*10^3; W =600; E =210*10^3; w =0.0784*10^ -3; del1 = W * l /( A * E ) ; del2 = w * l ^2/(2* E ) ; del = del1 + del2 ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” d e l i s %f mm ” , del ) ;

Scilab code Exa 3.3 MS3 1 2 3 4 5 6 7 8 9

// sum 3−3 clc ; clear ; m =25; v =3; E =210*10^3; KE =0.5* m * v ^2; d =30; L =2000; 14

10 11 12 13 14 15 16 17

A = %pi * d ^2/4; U = A * L /(2* E ) ; del =4*10^ -5* A ; W = A * del ; sigi = sqrt ( KE *10^3/( W + U ) ) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” d e l i s %f N/mmˆ2 ” , sigi ) ;

Scilab code Exa 3.4 MS4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

// sum 3−4 clc ; clear ; P =40*10^3; A =60*18; sig = P / A ; r1 =12; b1 =60; SCF1 =1.7; sigmax1 = sig * SCF1 ; r2 =24; b2 =60; SCF2 =1.5; sigmax2 = sig * SCF2 ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” s i g m a x 1 i s %f N/mmˆ2 ” , sigmax1 ) ; printf ( ” \n s i g m a x 2 i s %f N/mmˆ2 ” , sigmax2 ) ;

Scilab code Exa 3.5 MS5 1

// sum 3−5 15

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

clc ; clear ; p =2.4; // L e t a x i a l movement o f nut be La La = p *45/360; d =20; D =30; L =500; d1 =18; As = %pi * d1 ^2/4; Ac = %pi *( D ^2 - d ^2) /4; sigt =120/(3.543) ; sigb =1.543* sigt ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” s i g t i s %f N/mmˆ2 ” , sigt ) ; printf ( ” \n s i g b i s %f N/mmˆ2 ” , sigb ) ;

Scilab code Exa 3.6 MS6 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

// sum 3−6 clc ; clear ; delT =100; ab =18*10^ -6; aa =23*10^ -6; delta =(360* ab * delT ) +(450* aa * delT ) ; lc = delta -0.6; Ea =70*10^3; Eb =105*10^3; Aa =1600; Ab =1300; P = lc /((360/( Ab * Eb ) ) +(450/( Aa * Ea ) ) ) ; P = P *10^ -3; // L e t t h e c h a n g e i n l e n g t h be d e l L 16

16 17 18 19 20 21 22

delL =( aa *450* delT ) -( P *10^3*450/( Aa * Ea ) ) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”P i s %f kN ” ,P ) ; printf ( ” \n d e l L i s %f mm ” , delL ) ; // The d i f f e r e n c e i n t h e a n s w e r o f d e l L i s due t o round− o f f e r r o r s .

Scilab code Exa 3.7 MS7 1 2 3 4 5 6 7 8 9 10 11

// sum 3−7 clc ; clear ; a =23*10^ -6; E =70*10^3; l =750; sig =35; delT =(( sig * l / E ) +0.8) /( l * a ) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” d e l T i s %f degC ” , delT ) ;

Scilab code Exa 3.8 MS8 1 2 3 4 5 6 7 8

// sum 3−8 clc ; clear ; OA =60; AB =30; OC = -20; CD = -30; theta =30; 17

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

angBEK =2* theta ; OM =14; KM =49.5; p1 =70; p2 = -30; angBEH = -37; angBEI =143; theta1 = angBEH /2; theta2 = angBEI /2; Tmax =50; angBEL =53; angBEN =233; theta3 = angBEL /2; theta4 = angBEN /2; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” S t r e s s on p l a n e AB i s %f MPa ” , OM ) ; printf ( ” \n S t r e s s on p l a n e AB i s %f MPa ” , KM ) ; printf ( ” \n P r i n c i p a l s t r e s s p1 i s %f MPa ” , p1 ) ; printf ( ” \n P r i n c i p a l s t r e s s p2 i s %f MPa ” , p2 ) ; printf ( ” \n P r i n c i p a l a n g l e t h e t a 1 i s %f deg ”, theta1 ) ; printf ( ” \n P r i n c i p a l a n g l e t h e t a 2 i s %f deg ”, theta2 ) ; printf ( ” \n Maximum s h e a r s t r e s s i s %f MPa ”, Tmax ) ; printf ( ” \n D i r e c t i o n o f p l a n e t h e t a 3 i s %f deg ” , theta3 ) ; printf ( ” \n D i r e c t i o n o f p l a n e t h e t a 4 i s %f deg ” , theta4 ) ; // The a n s w e r s i n t h e book a r e w r i t t e n i n form o f d e g r e e s and m i n u t e s .

18

Scilab code Exa 3.9 MS9 1 2 3 4 5 6 7 8 9 10 11 12 13

// sum 3−9 clc ; clear ; E =200*10^3; v =0.29; E1 =720*10^ -6; E2 =560*10^ -6; p1 =121.76; p2 = -76.69; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” p1 i s %f MN/mmˆ2 ” , p1 ) ; printf ( ” \n p2 i s %f MN/mmˆ2 ” , p2 ) ;

Scilab code Exa 3.10 MS10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

// sum 3−10 clc ; clear ; G =38*10^3; d =10; P =5*10^3; A = %pi * d ^2/4; sig = P / A ; deld =0.0002; // L e t t h e l a t e r a l s t r a i n be E1 E1 = deld / d ; v =2* deld * G /( sig -(2* deld * G ) ) ; E =2* G *(1+ v ) *10^ -3; // p r i n t i n g d a t a i n s c i l a b o / p window printf ( ” v i s %0 . 4 f ” ,v ) ; printf ( ” \n E i s %0 . 3 f kN/mmˆ2 ” ,E ) ; 19

Scilab code Exa 3.11 MS11 1 2 3 4 5 6 7 8 9 10 11 12 13 14

// sum 3−11 clc ; clear ; D =1500; p =1.2; sigt =100; sigc = p * D /2; siga = p * D /4; P = sigc *2*10^3; n =0.75; t = sigc /( n * sigt ) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” t i s %0 . 1 f mm ” ,t ) ;

Scilab code Exa 3.12 MS12 1 2 3 4 5 6 7 8 9 10 11 12

// sum 3−12 clc ; clear ; D =50; t =1.25; d =0.5; n =1/ d ; p =1.5; siga = p * D /(4* t ) ; sigc =20.27; sigw = sigc /0.31416;

20

13 14

// p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” s i g w i s %0 . 2 f N/mmˆ2 ” , sigw ) ;

Scilab code Exa 3.13 MS13 1 2 3 4 5 6 7 8 9 10 11

// sum 3−13 clc ; clear ; R1 =50; p =75; pmax =125; R2 = sqrt (( pmax + p ) * R1 ^2/( pmax - p ) ) ; t = R2 - R1 ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” t i s %0 . 1 f mm ” ,t ) ;

Scilab code Exa 3.14 MS14 1 2 3 4 5 6 7 8 9 10 11 12 13 14

// sum 3−14 clc ; clear ; R1 =40; R2 =60; B =50; E =210*10^3; e =41*10^ -6; sig =2* R1 ^2/( R2 ^2 - R1 ^2) ; p = E * e / sig ; Fr = p *2* %pi * R1 * B ; u =0.2; Fa = u * Fr *10^ -3;

21

15 16

// p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”Fa i s %0 . 2 f kN ” , Fa ) ;

Scilab code Exa 3.15 MS15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

// sum 3−15 clc ; clear ; a1 =10*1.5; x1 =15 -0.75; a2 =1.5*(15 -1.5) ; x2 =(15 -1.5) /2; y1 =(( a1 * x1 ) +( a2 * x2 ) ) /( a1 + a2 ) ; y2 = a1 - y1 ; Ixx =(10*1.5^3) /12+(10*1.5*(5.06 -1.5/2) ^2) +(1.5*13.5^3/12) +(1.5*13.5*(9.94 -6.75) ^2) ; Z1 = Ixx / y1 ; Z2 = Ixx / y2 ; L =3; sigc =50; W = sigc * Z1 / L *10^ -3; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”W i s %0 . 3 f kN ” ,W ) ;

Scilab code Exa 3.16 MS16 1 2 3 4 5 6

// sum 3−16 clc ; clear ; D =22; d =20; r =1; 22

7 K =2.2; 8 sigmax =130; 9 sigmax = sigmax / K ; 10 Z = %pi * d ^3/32; 11 M = sigmax * Z *10^ -3; 12 13 // p r i n t i n g d a t a i n s c i l a b o /p window 14 printf ( ”M i s %0 . 3 f Nm ” ,M ) ;


// sum 3−17 clc ; clear ; A =(12*2) +(12*2) +(30 -4) ; B = sqrt ( A /2) ; D =2* B ; B1 =12; D1 =30; d =26; b =1; Z1 =(( B1 * D1 ^3) -(( B1 - b ) * d ^3) ) /( B1 * D1 /2) ; Zr = B * D ^2/6; // L e t t h e r a t i o o f b o t h t h e s e c t i o n s be x x = Z1 / Zr ; M =30*10^6; sigmax = M /( Z1 *10^3) ; // p r i n t i n g d a t a i n s c i l a b o / p window printf ( ” Z1 / Zr i s %0 . 2 f ” ,x ) ; printf ( ” \n s i g m a x i s %0 . 2 f N/mmˆ2 ” , sigmax ) ;


1 // sum 3−18 2 clc ; 3 clear ; 4 //Tmax=F / ( I ∗b ) ∗ [ B∗ t ( d/2+ t / 2 ) +(b∗d∗d / 8 ) ] ; 5 //T1=F / ( I ∗b ) ∗ [ B∗ t ∗ ( d+t ) / 2 ] ; 6 // Tmean=T1+2/3∗(Tmax−T1 ) ; 7 //T=Tmax−Tmean ; 8 //T=F∗d ˆ 2 / ( 2 4 ∗ I ) ; 9 disp ( ” D i f f e r e n c e b e t w e e n maximum and mean s h e a r

s t r e s s e s i n t h e web i s

,T=F∗d ˆ 2 / ( 2 4 ∗ I ) ” ) ;


// sum 3−19 clc ; clear ; x1 =((13*3*1.5) +(2*15*8) ) /(39+30) ; x2 =13 - x1 ; A =30+39; E =2*10^7; Iyy =995.66; e =54.32; x = x2 -3; sigb = e * x / Iyy ; sigd =1/69; sigr = sigd + sigb ; // L e t t h e s t r a i n be E1 E1 =800*10^ -6; P = E1 * E / sigr ; P = P *10^ -3; // p r i n t i n g d a t a i n s c i l a b o / p window printf ( ”P i s %0 . 2 f kN ” ,P ) ;

24


// sum 3−20 clc ; clear ; H =20; D =5; d =3; rho =21; sigd = rho * H ; p =2; A=D*H; P=p*A; M = P * H /2; Z = %pi *( D ^4 - d ^4) /(32* D ) ; sigb = M / Z ; sigmax =420+ sigb ; sigmin =420 - sigb ; // p r i n t i n g d a t a i n s c i l a b o / p window printf ( ” s i g m a x i s %0 . 2 f kN/mˆ2 ” , sigmax ) ; printf ( ” \n s i g m i n i s %0 . 2 f kN/mˆ2 ” , sigmin ) ;

Scilab code Exa 3.21 MS21 1 2 3 4 5 6 7

// sum 3−21 clc ; clear ; D =30; R =15; T =0.56*10^6; G =82*10^3; 25

8 9 10 11 12 13 14 15 16 17 18

J = %pi * R ^4/2; T1 = T * R / J ; l =1000; theta = T * l /( G * J ) *180/ %pi ; r =10; Tr = T1 * r / R ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”T1 i s %0 . 2 f N/mmˆ2 ” , T1 ) ; printf ( ” \n t h e t a i s %0 . 2 f deg ” , theta ) ; printf ( ” \n Tr i s %0 . 2 f N/mmˆ2 ” , Tr ) ;

Scilab code Exa 3.22 MS22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

// sum 3−22 clc ; clear ; T =8*10^3; d =80; D =110; l =2000; Gst =80*10^3; Gcop = Gst /2; Js = %pi * d ^4/32; Jc = %pi *( D ^4 - d ^4) /32; // Ts = 0 . 7 7 7 ∗ Tc Tc = T /1.777*10^3; Ts =0.777* Tc ; Ts1 = Ts / Js * d /2; Tc1 = Tc / Jc * D /2; // L e t t l be A n g u l a r t w i s t p e r u n i t l e n g t h tl = Ts *10^3/( Js * Gst ) *180/ %pi ; // L e t t h e maximum s t r e s s d e v e l o p e d when t h e Torque i s a c t i n g i n t h e c e n t r e o f t h e s h a f t be Ts2 & Tc2 r e s p . f o r s t e e l and c o p p e r 26

20 Ts2 = Ts1 /2; 21 Tc2 = Tc1 /2; 22 23 // p r i n t i n g d a t a i n s c i l a b o /p window 24 printf ( ” Ts1 i s %0 . 3 f N/mmˆ2 ” , Ts1 ) ; 25 printf ( ” \n Tc1 i s %0 . 1 f N/mmˆ2 ” , Tc1 ) ; 26 printf ( ” \n t h e t a / l e n g t h i s %0 . 3 f deg /m ” , tl ) ; 27 printf ( ” \n Ts2 i s %0 . 3 f N/mmˆ2 ” , Ts2 ) ; 28 printf ( ” \n Tc2 i s %0 . 2 f N/mmˆ2 ” , Tc2 ) ;

Scilab code Exa 3.23 MS23 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

// sum 3−23 clc ; clear ; D =100; d =75; r =6; K =1.45; P =20*746; N =400; w =2* %pi * N /60; T=P/w; Ts =16* T *10^3/( %pi * d ^3) ; Tmax = K * Ts ; // p r i n t i n g d a t a i n s c i l a b o / p window printf ( ”Tmax i s %0 . 3 f MPa ” , Tmax ) ;

Scilab code Exa 3.24 MS24 1 // sum 3−24 2 clc ;

27

3 4 5 6 7 8 9 10 11 12

clear ; G =84*10^3; T =28*10^3; l =1000; theta = %pi /180; J = T * l /( G * theta ) ; d =( J *32/ %pi ) ^(1/4) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” d i s %0 . 1 f mm ” ,d ) ;


// sum 3−25 clc ; clear ; P =2*10^6; N =200; w =2* %pi * N /60; Tm = P / w ; W =5*10^3*9.81; l =1800; Mmax = W * l /4; Tmax =1.8* Tm *10^3; Me =( Mmax + sqrt ( Mmax ^2+ Tmax ^2) ) /2; Te = sqrt ( Mmax ^2+ Tmax ^2) ; sig =60; Ts =40; d1 =(32* Me /( %pi * sig ) ) ^(1/3) ; d2 =(16* Te /( %pi * Ts ) ) ^(1/3) ; // p r i n t i n g d a t a i n s c i l a b o / p window printf ( ” d i s %0 . 1 f mm ” , d2 ) ;

28

Scilab code Exa 3.26 MS26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

// sum 3−26 clc ; clear ; Q =4*10^3; P =8*10^3; sig = P ; T=Q; p1 =( sig /2+ sqrt (( sig /2) ^2+ T ^2) ) ; p2 =( sig /2 - sqrt (( sig /2) ^2+ T ^2) ) ; sigyp =285; FOS =3; siga = sigyp /3; A1 = p1 / siga ; d1 = sqrt (4* A1 / %pi ) ; A2 =( p1 - p2 ) *2/( siga *2) ; d2 = sqrt (4* A2 / %pi ) ; v =0.3; A3 = sqrt ( p1 ^2+ p2 ^2 -(2* v * p1 * p2 ) ) / siga ; d3 = sqrt (4* A3 / %pi ) ; // p r i n t i n g d a t a i n s c i l a b o / p window printf ( ” d1 i s %0 . 2 f mm ” , d1 ) ; printf ( ” \n d2 i s %0 . 1 f mm ” , d2 ) ; printf ( ” \n d3 i s %0 . 2 f mm ” , d3 ) ;

Scilab code Exa 3.27 MS27 1 // sum 3−27 2 clc ; 3 clear ;

29

4 5 6 7 8 9 10 11 12 13 14 15 16 17

sigx = -105; Txy =105; sigy =270; p1 =( sigx /2+ sqrt (( sigx /2) ^2+ Txy ^2) ) ; p2 =( sigx /2 - sqrt (( sigx /2) ^2+ Txy ^2) ) ; p3 =0; Tmax =( p1 - p2 ) /2; siga = sigy /2; if ( Tmax <= siga ) then printf ( ” The component i s s a f e ” ) end // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” \n Tmax i s %0 . 1 f MPa ” , Tmax ) ;

Scilab code Exa 3.28 MS28 1 2 3 4 5 6 7 8 9 10 11 12 13

// sum 3−28 clc ; clear ; rho =0.0078*9.81*10^ -6; sigc =150; g =9.81; V = sqrt ( sigc * g / rho ) *10^ -3; R =1; w=V/R; N = w *60/(2* %pi ) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”N i s %0 . 3 f rpm ” ,N ) ;


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

// sum 3−29 clc ; clear ; R1 =50; R2 =200; N =6*10^3; w =2* %pi * N /60; v =0.28; rho =7800*10^ -9; g =9810; k1 =(3+ v ) /8; k2 =(1+(3* v ) ) /8; W = rho *9.81; x = k1 * w ^2* W *( R1 ^2+ R2 ^2) / g ; y = k1 * w ^2* W *( R1 * R2 ) ^2/ g ; y1 = k1 * w ^2* W / g ; z = k2 * w ^2* W / g ; r = sqrt ( R1 * R2 ) ; sigrmax =x -( y / r ^2) -( r ^2* y1 ) ; r =50:200 n = length ( r ) ; for i =1: n sigr ( i ) =x -( y / r ( i ) ^2) -( r ( i ) ^2* y1 ) end for j =1: n sigc ( j ) = x +( y / r ( j ) ^2) -( r ( j ) ^2* z ) end plot (r , sigr ) ; plot (r , sigc ) ; xtitle ( ’ ’ , ’ r mm’ ) ; ylabel ( ’ s t r e s s N/mmˆ2 ’ ) ; xgrid (2) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” s i g r m a x i s %0 . 1 f MPa ” , sigrmax ) ;

31

Figure 3.1: MS29

Scilab code Exa 3.30 MS30 1 2 3 4 5 6 7 8

// sum 3−30 clc ; clear ; r =500; to =15; N =3500; w =2* %pi * N /60; sig =80; 32

9 10 11 12 13 14 15

w1 =0.07644*10^ -3; g =9810; a = w1 * w ^2* r ^2/(2* sig * g ) ; t = to * exp ( - a ) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” t i s %0 . 3 f mm ” ,t ) ;

Scilab code Exa 3.31 MS31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

// sum 3−31 clc ; clear ; M =60*10^3; y1 =((5*1*2.5) +(6*1*5.5) ) /(5+6) ; y2 =6 - y1 ; R =12; R1 =R - y2 ; R1 =10.136 R2 =11.136; R3 = R1 +6; B =6; b =1; A =( B * b ) +(( B -1) * b ) ; // L e t x= h ˆ2/Rˆ2 x = R / A *(( B * log ( R2 / R1 ) ) +( b * log ( R3 / R2 ) ) ) -1; x =1/ x ; // L e t Maximum c o m p r e s s i v e s t r e s s a t B be s i g B sigB = M /( A * R ) *(1+( x * y1 /( R + y1 ) ) ) *10^ -2; // L e t Maximum t e n s i l e s t r e s s a t A be s i g A sigA = M /( A * R ) *(( y2 * x /( R - y2 ) ) -1) *10^ -2; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” s i g B i s %0 . 1 f MPa ” , sigB ) ; printf ( ” \n s i g A i s %0 . 0 f MPa ” , sigA ) ;

33

26

// The a n s w e r t o Rˆ2/ h ˆ2 i s c a l c u l a t e d i n c o r r e c t l y i n t h e book .

Scilab code Exa 3.32 MS32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

// sum 3−32 clc ; clear ; R1 =24; R2 =30; R3 =50; R4 =54; F =200; y1 =((16*4*2) +(2*20*14*4) +(24*6*27) ) /((16*4) +(2*20*4) +(24*6) ) ; y2 =30 - y1 ; R =24+ y2 ; A =(24*6) +(2*4*20) +(4*16) ; // L e t x= h ˆ2/Rˆ2 x = R / A *((24* log ( R2 / R1 ) ) +(2*4* log ( R3 / R2 ) ) +(16* log ( R4 / R3 ) ) ) -1; x =1/ x ; M = F *(60+ R ) ; sigd = F / A ; // L e t b e n d i n g s t r e s s a t a be s i g A sigA = M /( A * R ) *(( y2 * x /( R - y2 ) ) -1) ; // L e t b e n d i n g s t r e s s a t b be s i g B sigB = M /( A * R ) *(1+( x * y1 /( R + y1 ) ) ) ; // L e t r e s u l t a n t a t a be Ra Ra =( sigA + sigd ) *10; // L e t r e s u l t a n t a t b be Rb Rb =( sigB - sigd ) *10; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”Ra i s %0 . 2 f N/mmˆ2 ” , Ra ) ; printf ( ” \n Rb i s %0 . 2 f N/mmˆ2 ” , Rb ) ; 34

29 30

// The d i f f e r e n c e i n t h e a n s w e r s a r e due t o r o u n d i n g − off of values .

Scilab code Exa 3.33 MS33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

// sum 3−33 clc ; clear ; F =50; B1 =4; B2 =8; D =12; y1 = D /3*( B1 +(2* B2 ) ) /( B1 + B2 ) ; y2 =12 - y1 ; R =6+ y2 ; A =( B1 + B2 ) /2* D ; // L e t x= h ˆ2/Rˆ2 a =( B1 +(( B2 - B1 ) *( y1 + R ) / D ) ) * log (( R + y1 ) /( R - y2 ) ) x = R /( A ) *( a -( B2 - B1 ) ) ; x =x -1; x =1/ x ; KG = y2 +8; M = F * KG ; sigd = F / A ; // L e t b e n d i n g s t r e s s a t a be s i g A sigA = M /( A * R ) *(1+( x * y1 /( R + y1 ) ) ) ; // L e t b e n d i n g s t r e s s a t b be s i g B sigB = M /( A * R ) *(( y2 * x /( R - y2 ) ) -1) ; sigA =( sigA - sigd ) *10; sigB =( sigB + sigd ) *10; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” s i g A i s %0 . 2 f MPa ” , sigA ) ; printf ( ” \n s i g B i s %0 . 2 f MPa ” , sigB ) ;

35

30

// The d i f f e r e n c e i n t h e a n s w e r s a r e due t o rounding −o f f o f v a l u e s .

36

Chapter 4 MANUFACTURING CONSIDERATIONS

Scilab code Exa 4.1 MF1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

// sum 4−1 clc ; clear ; d =70; dmin =50; dmax =80; D = sqrt ( dmin * dmax ) ; D =63; i =0.458*( D ^(1/3) ) +(0.001* D ) ; // s t a n d a r d t o l e r a n c e f o r H8 i s ST1 ST1 =25* i ; ST1 = ST1 *10^ -3; // s t a n d a r d t o l e r a n c e o f s h a f t f o r g r a d e g7 i s ST2 ST2 =16* i ; ST2 = ST2 *10^ -3; es = -(2.5*( D ^0.333) ) ; es = es *10^ -3; ei = es - ST2 ; 37

20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

// Lower l i m i t f o r h o l e i s LLH // Upper l i m i t f o r h o l e i s ULH // Upper l i m i t f o r s h a f t i s ULS // Lower l i m i t f o r s h a f t i s LLS LLH = d ; ULH = LLH + ST1 ; ULS = LLH + es ; LLS = ULS - ST2 ; //Maximum c l e a r a n c e i s Cmax // minimum c l e a r a n c e i s Cmin Cmax = ULH - LLS ; Cmin = LLH - ULS ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”LLH i s %0 . 1 f mm ” , LLH ) ; printf ( ” \n ULH i s %0 . 3 f mm ” , ULH ) ; printf ( ” \n ULS i s %0 . 2 f mm ” , ULS ) ; printf ( ” \n LLS i s %0 . 2 f mm ” , LLS ) ; printf ( ” \n Cmax i s %0 . 3 f mm ” , Cmax ) ; printf ( ” \n Cmin i s %0 . 3 f mm ” , Cmin ) ;

Scilab code Exa 4.2 MF2 1 2 3 4 5 6 7 8 9 10 11 12

// sum 4−2 clc ; clear ; d =25; // Lower l i m i t // Upper l i m i t // Upper l i m i t // Lower l i m i t ULH = d +0.021; LLH = d +0; ULS = d +0.041; LLS = d +0.028;

for for for for

hole hole shaft shaft

i s LLH i s ULH i s ULS i s LLS

38

13 14 15 16 17 18 19 20

//Maximum i n t e r f e r e n c e i s Cmax // minimum i n t e r f e r e n c e i s Cmin Cmax = ULS - LLH ; Cmin = LLS - ULH ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”Cmax i s %0 . 3 f mm ” , Cmax ) ; printf ( ” \n Cmin i s %0 . 3 f mm ” , Cmin ) ;

Scilab code Exa 4.3 MF3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

// sum 4−3 clc ; clear ; d =50; Es =0.039; Ei =0; es = -9*10^ -3; ei = -34*10^ -3; // S h a f t d i a i s D D = d + es ; // Lower l i m i t f o r h o l e // Upper l i m i t f o r h o l e // Upper l i m i t f o r s h a f t // Lower l i m i t f o r s h a f t ULH = d + Es ; LLH = d + Ei ; ULS = d + es ; LLS = d + ei ; //Maximum i n t e r f e r e n c e // minimum i n t e r f e r e n c e Cmax = ULH - LLS ; Cmin = LLH - ULS ;


i s Cmax i s Cmin

// p r i n t i n g d a t a i n s c i l a b o /p window 39

25 26 27 28 29 30 31

printf ( ”ULH i s %0 . 3 f mm ” , ULH ) ; printf ( ” \n LLH i s %0 . 3 f mm ” , LLH ) ; printf ( ” \n ULS i s %0 . 3 f mm ” , ULS ) ; printf ( ” \n LLS i s %0 . 3 f mm ” , LLS ) ; printf ( ” \n Cmax i s %0 . 3 f mm ” , Cmax ) ; printf ( ” \n Cmin i s %0 . 3 f mm ” , Cmin ) ; disp ( ’ T h e r e f o r e , H8g7 i s e a s y r u n n i n g f i t ’ ) ;

Scilab code Exa 4.4 MF4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

// sum 4−3 clc ; clear ; d =30; Es =0.025; Ei =0; es =11*10^ -3; ei = -5*10^ -3; // S h a f t d i a i s D D = d + es ; // Lower l i m i t f o r h o l e // Upper l i m i t f o r h o l e // Upper l i m i t f o r s h a f t // Lower l i m i t f o r s h a f t ULH = d + Es ; LLH = d + Ei ; ULS = d + es ; LLS = d + ei ; //Maximum i n t e r f e r e n c e // minimum i n t e r f e r e n c e Cmax = ULH - LLS ; Cmin = ULS - LLH ;;


i s Cmax i s Cmin

// p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”ULH i s %0 . 3 f mm ” , ULH ) ; 40

26 27 28 29 30

printf ( ” \n printf ( ” \n printf ( ” \n printf ( ” \n printf ( ” \n

LLH i s %0 . 3 f ULS i s %0 . 3 f LLS i s %0 . 3 f Cmax i s %0 . 3 Cmin i s %0 . 3

mm ” , LLH ) ; mm ” , ULS ) ; mm ” , LLS ) ; f mm ” , Cmax ) ; f mm ” , Cmin ) ;

41

Chapter 5 INTRODUCTION TO PRESSURE VESSELS

Scilab code Exa 5.1 IPV5 1 // sum 5−1 clc ; clear ; p =2; Rm =220; // t e n s i l e hoop o r c i r c u m f e r e n t i a l s t r e s s = s i g t sigr = -2; // s i g t =(p∗Rm) / t ; Sa =230/2; // t 1=t h i c k n e s s a c c o r d i n g t o maximum p r i n c i p a l s t r e s s theory 11 // t 2=t h i c k n e s s a c c o r d i n g t o maximum s h e a r s t r e s s theory 12 t1 =( p * Rm ) / Sa ; 13 t2 =( p * Rm ) /( Sa + sigr ) ; 1 2 3 4 5 6 7 8 9 10

14 15 16 17

// p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” t 1 i s %0 . 2 f mm ” , t1 ) ; printf ( ” \n t 2 i s %0 . 3 f mm ” , t2 ) ; 42

Scilab code Exa 5.2 IPV5 2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

// sum 5−2 clc ; clear ; // E l a s t i c l i m i t = s i g e sige =310; // i n s i d e d i a m e t e r=d i di =300; p =1.8; FOS =2; // d e s i g n s t r e s s =s i g d ; sigd = sige /2; c =0.162; d =380; // c o v e r p l a t e t h i c k n e s s=t ; t = d * sqrt ( c * p / sigd ) ; t =17; M = di * p * t /4; z =(1/6) *1* t ^2; // b e n d i n g s t r e s s =s i g b ; sigb = M / z ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” t i s %0 . 1 fmm ” ,t ) ; printf ( ” \n M i s %0 . 1 fmm ” ,M ) ; printf ( ” \n s i g b i s %0 . 1 fmm ” , sigb ) ; if ( sigb <= sigd ) then disp ( ’ s i g b i s b e l o w a l l o w a b l e s i g d . ’ ) end

43

Scilab code Exa 5.3 IPV5 3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

// sum 5−3 clc ; clear ; sige =220; v =0.29; Ri =175; FOS =3; Sa = sige /3; p =10; // t 1=t h i c k n e s s a c c o r d i n g t o maximum p r i n c i p a l s t r e s s theory // t 2=t h i c k n e s s a c c o r d i n g t o maximum s h e a r s t r e s s theory x = Sa +( p *(1 -(2* v ) ) ) ; y = Sa -( p *(1+ v ) ) ; t1 =( sqrt ( x / y ) -1) * Ri ; t1 =24; // t 1 =(( s q r t ( ( Sa+(p ∗(1 −(2∗ v ) ) ) ) ) / ( Sa −(p ∗(1+ v ) ) ) ) −1)∗ Ri ; t2 = Ri *(( sqrt ( Sa /( Sa -(2* p ) ) ) ) -1) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” t 1 i s %0 . 1 fmm ” , t1 ) ; printf ( ” \n t 2 i s %0 . 3 fmm ” , t2 ) ; // The a n s w e r t o t 2 i s n o t c a l c u l a t e d i n t h e book .

Scilab code Exa 5.4 IPV5 4 1 // sum 5−4 2 clc ; 3 clear ; 4 p =16;

44

5 6 7 8 9 10 11 12 13 14

Ri =250; // Y i e l d s t r e n g t h =s i g y ; sigy =330; v =0.3; FOS =3; Sa = sigy /3; t = Ri *(( sqrt ( Sa /( Sa -(2* p ) ) ) ) -1) ; t =50; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” t i s %0 . 1 fmm ” ,t ) ;

Scilab code Exa 5.5 IPV5 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

// sum 5−5 clc ; clear ; d =15; Eg =480; t =3; // f l a n g e t h i c k n e s s= f t ; ft =12; A = %pi * d ^2/4; l = d + t +( ft /2) ; E =210; kb = A * E / l ; // e f f e c t i v e a r e a o f g a s k e t=Ag ; Ag = %pi *((( ft + t + d ) ^2) -( d ^2) ) /4; kg = Ag * Eg / t ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” kb i s %0 . 3 f N/mm ” , kb ) ; kb = kb *10^ -3; kg = kg *10^ -3; if ( kb <= kg ) then printf ( ” \n The c o m b i n e s s t i f f n e s s o f b o l t and g a s k e t i s %0 . 3 f kN/mm” , kg ) 45

22 end 23 24 // The d i f f e r e n c e

i n t h e v a l u e o f kb i s due t o rounding −o f f the value o f A

46

Chapter 6 LEVERS

Scilab code Exa 6.1 L1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

// sum 6−1 clc ; clear ; del =10; k =500; W = k * del ; // L e t l o a d arm be l 1 l1 =200; // L e t e f f o r t arm be l 2 l2 =500; P = W * l1 / l2 ; Ro = sqrt ( W ^2+ P ^2) ; Ta =40; d = sqrt ( Ro *4/(2* %pi * Ta ) ) ; d =10; pb =10; d1 = sqrt ( Ro /( pb *1.5) ) ; d1 =20; l =1.5* d ; t =10; T = Ro *4/(2* %pi * d1 ^2) ; 47

22 M =( Ro /2*( l /2+ t /3) ) -( Ro /2* l /4) ; 23 sigb =32* M /( %pi * d1 ^3) ; 24 sigmax =( sigb /2) + sqrt (( sigb /2) ^2+ T ^2) ; 25 P = Ro /( l * d1 ) ; 26 D =2* d1 ; 27 28 // p r i n t i n g d a t a i n s c i l a b o /p window 29 printf ( ” d1 i s %0 . 1 f mm ” , d1 ) ; 30 printf ( ” \n D i s %0 . 1 f mm ” ,D ) ;

Scilab code Exa 6.2 L2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

// sum 6−2 clc ; clear ; d1 =80; p =0.981; Ta =40; siga =80; pa =15; W = %pi *( d1 ^2) * p /4; P = W /8; Ws =W - P ; d = sqrt ( W *4/( %pi *2* Ta ) ) ; l =1.5* d ; D =2* d ; T = W /(2* %pi * pa ^2/4) ; M1 = P *(700 -87.5 -( D /2) ) ; h =50; b = h /4; Z = b * h ^2/6; sigb = M1 / Z ; pmax =80; T =2465.6/ h ^2; pmax =( sigb /2) + sqrt (( sigb /2) ^2+ T ^2) ; 48

24 25 26 27 28 29

// p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” h i s %0 . 2 f mm ” ,h ) ; printf ( ” \n pmax i s %0 . 2 f MPa ” , pmax ) ; // The d i f f e r e n c e i n t h e v a l u e o f pmax i s due t o rounding −o f f the d i g i t s .

Scilab code Exa 6.3 L3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

// sum 6−3 clc ; clear ; P =((4*360) +(2*360) ) /900; Fv =4 -2; Fh = P ; Fr = sqrt ( Fv ^2+ Fh ^2) ; P1 =4*0.36/0.9; Rf = sqrt (4^2+1.6^2) ; d = sqrt ( Rf *10^3/(15*1.25) ) ; d =16; l =1.25* d ; T = Rf *10^3*4/(2* %pi * d ^2) ; D =2* d ; M1 = Rf *10^3*(360 -( D /2) ) ; pa =15; h =80; b = h /4; Z = b * h ^2/6; sigb = M1 / Z ; T =4310/( b * h ) ; pmax =( sigb /2) + sqrt (( sigb /2) ^2+ T ^2) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”P i s %0 . 1 f KN ” ,P ) ; 49

26

printf ( ” \n pmax i s %0 . 2 f MPa

” , pmax ) ;

Scilab code Exa 6.4 L4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

// sum 6−4 clc ; clear ; l =360; P =400; Mh =2* P * l /3; sigb =50; l1 =60; d =( Mh *32/( %pi * l1 ) ) ^(1/3) ; d =30; L =420; siga =60; H =20; B = H /3; Mx = P *( L - H /2) ; Tx =2* P * l /3; sigb1 = Mx *18/ H ^3; Td = P /( B * H ) ; Tr =17.17* Tx / H ^4; T = Tr + Td ; sigmax =( sigb1 /2) + sqrt (( sigb1 /2) ^2+ T ^2) ; Tmax = sqrt (( sigb1 /2) ^2+ T ^2) ; T=P*L; M = P *( l1 +(2/3* l ) ) ; Te = sqrt ( T ^2+ M ^2) ; Ta =40; D =( Te *16/( %pi * Ta ) ) ^(1/3) ; D =30; // Rounding o f f t o n e a r e s t w h o l e number // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” d i s %0 . 1 f mm ” ,d ) ; 50

32

printf ( ” \n D i s %0 . 1 f mm

” ,D ) ;

Scilab code Exa 6.5 L5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

// sum 6−5 clc ; clear ; l2 =300; l =450; P =400; Mx =2* P * l2 /3; siga =80; dh =( Mx *32/( %pi * siga ) ) ^(1/3) ; dh =22; L =(2* l2 /3) + l ; T=P*L; Ta =40; d =( T *16/( %pi * Ta ) ) ^(1/3) ; d =35; d1 =1.6* d ; Th = T *16* d1 /( %pi *( d1 ^4 - d ^4) ) ; l1 =1.5* d ; My = P *( L -( d1 /2) ) ; B = dh ; H = sqrt (3.66*75) ; H =30; Mz = P * l1 /2; Te = sqrt ( T ^2+ Mz ^2) ; d2 =( Te *16/( %pi * Ta ) ) ^(1/3) ; d2 =32; b = d /4; b =9; // Rounding o f f t o n e a r e s t w h o l e number t = d /6; t =6; // Rounding o f f t o n e a r e s t w h o l e number

51

32 33 34 35 36 37 38 39

// p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” d i s %0 . 1 f mm ” ,d ) ; printf ( ” \n dh i s %0 . 1 f mm ” , dh ) ; printf ( ” \n d1 i s %0 . 1 f mm ” , d1 ) ; printf ( ” \n l 1 i s %0 . 1 f mm ” , l1 ) ; printf ( ” \n d2 i s %0 . 1 f mm ” , d2 ) ; printf ( ” \n b i s %0 . 1 f mm ” ,b ) ; printf ( ” \n t i s %0 . 1 f mm ” ,t ) ;

Scilab code Exa 6.6 L6 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

// sum 6−6 clc ; clear ; L =450; P =700; T=P*L; Ta =50; d =( T *16/( %pi * Ta ) ) ^(1/3) ; d =32; d1 =1.6* d ; d1 =52; // Rounding o f f t o n e a r e s t w h o l e number l1 =1.25* d ; My = P *( L - d1 /2) ; sigb =65; H =( My *18/ sigb ) ^(1/3) ; H =45; B = H /3; T1 = P /( B * H ) ; sigmax =( sigb /2) + sqrt (( sigb /2) ^2+ T ^2) ; Mx = P * l1 /2; Te = sqrt (( T ) ^2+( Mx ^2) ) ; d2 =( Te *16/( %pi * Ta ) ) ^(1/3) ; d2 = d2 +6; d2 =38; // Rounding o f f t o n e a r e s t w h o l e number 52

25 26 27 28 29 30 31 32

// p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” d i s %0 . 1 f mm ” ,d ) ; printf ( ” \n d1 i s %0 . 1 f mm ” , d1 ) ; printf ( ” \n l 1 i s %0 . 1 f mm ” , l1 ) ; printf ( ” \n B i s %0 . 1 f mm ” ,B ) ; printf ( ” \n H i s %0 . 1 f mm ” ,H ) ; printf ( ” \n d2 i s %0 . 1 f mm ” , d2 ) ;

53

Chapter 7 STRUTS AND COLUMNS

Scilab code Exa 7.1 SC1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

// sum 7−1 clc ; clear ; sigc =550; FOS =4; sigw = sigc / FOS ; l =4000; le = l /2; A = %pi *(1 -0.7^2) /4; K =(1+0.7^2) /16; Pr =800*10^3; a =1/1600; D =130; // Rounding o f f t o n e a r e s t w h o l e number d = D *0.7; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”D i s %0 . 1 f mm ” ,D ) ; printf ( ” \n d i s %0 . 1 f mm ” ,d ) ;

54

Scilab code Exa 7.2 SC2 1 2 3 4 5 6 7 8 9 10 11 12 13 14

// sum 7−2 clc ; clear ; l =500; E =70*10^3; P =20*10^3; FOS =2; d = P *2*12*4* l ^2/(( %pi ) ^2* E ) ; d =( sqrt (8) * d ) ^0.25; b = d / sqrt (8) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” d i s %0 . 2 f mm ” ,d ) ; printf ( ” \n b i s %0 . 2 f mm ” ,b ) ;

Scilab code Exa 7.3 SC3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

// sum 7−3 clc ; clear ; Ixx =(2*1696.6) +115.4; Iyy =1696.6+(2*115.4) +(2*25.27*10.27^2) ; A =3*25.27; Kmin = sqrt ( Ixx /75.81) ; L =600; k = L / Kmin ; sigc =110; c =1/200; sigw = sigc *(1 -( c * k ) ) ; Pw = sigw * A ; a =1/7500; sigc1 =320; Pr =( sigc1 * A ) /(1+( a *( L / Kmin ) ^2) ) ; 55

17 FOS = Pr / Pw ; 18 19 // p r i n t i n g d a t a i n s c i l a b o /p window 20 printf ( ”FOS i s %0 . 2 f ” , FOS ) ;

Scilab code Exa 7.4 SC4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

// sum 7−4 clc ; clear ; Iyy =193.4+(2*1.2*1.5^3/12) ; E =200*10^3; l =500; Pe =( %pi ^2) * E * Iyy *10^5/( l ^2) ; A =35.53+(2*1.2*15) ; sige = Pe /7530; k = sqrt ( Iyy / A ) ; xc =75; sig =80; sigo =20.875; A = A *100; P = sigo * A ; P = P *10^ -3; // p r i n t i n g d a t a i n s c i l a b o / p window printf ( ”P i s %0 . 1 f kN ” ,P ) ; // The d i f f e r e n c e i n t h e v a l u e o f P i s due t o rounding −o f f the d i g i t s .

Scilab code Exa 7.5 SC5 1

// sum 7−5 56

2 3 4 5 6 7 8 9 10 11 12 13 14 15

clc ; clear ; sigc =330; a =1/7500; t =4; A =14.5* t ^2; l =300; Kx = sqrt (1.4626* t ^2) ; Pr = sigc * A /(1+( a *( l / Kx ) ^2) ) ; FOS =2; P = Pr / FOS *10^ -3; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”P i s %0 . 4 f KN ” ,P ) ;

Scilab code Exa 7.6 SC6 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

// sum 7−6 clc ; clear ; P =1500; FOS =2; Pd = FOS * P ; l =280; E =207*10^3; I = Pd * l ^2/( %pi ^2* E ) ; D =(64* I /( %pi *(1 -0.8^4) ) ) ^(1/4) ; D =8; d =6.4; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”D i s %0 . 1 f mm ” ,D ) ; printf ( ” \n d i s %0 . 1 f mm ” ,d ) ;

57

Scilab code Exa 7.7 SC7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

// sum 7−7 clc ; clear ; D =500; p =0.3; E =208*10^3; sigc =320; a =1/7500; l =2000; le = l /2; W = %pi * D ^2* p /4; FOS =4; Wd = W * FOS ; I = Wd * l ^2/( %pi ^2* E ) ; d =(64* I / %pi ) ^(1/4) ; A = %pi * d ^2/4; k = d /4; d =45; // Rounding o f f t o n e a r e s t w h o l e number // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” d i s %0 . 1 f mm ” ,d ) ;

58

Chapter 8 SPRINGS

Scilab code Exa 8.1 S8 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

// sum 8−1 clc ; clear ; d =5; D =30; G =84*(10^3) ; Na =15; // A x i a l Load W W =300; // S p r i n g i n d e x C C =30/5; // S h e a r s t r e s s Augmentation f a c t o r Ks Ks =((2* C ) +1) /(2* C ) ; // Wahl ’ s f a c t o r Kw Kw =(((4* C ) -1) /((4* C ) -4) ) +(0.615/ C ) ; // C u r v a t u r e c o r r e c t i o n f a c t o r Kc Kc = Kw / Ks ; // S p r i n g s t i f f n e s s k k =( G *( d ^4) ) /(8*( D ^3) * Na ) ; // A x i a l d e f l e c t i o n d e l t a delta = W / k ; 59

22 23 24 25 26 27 28

// p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”Ks i s %0 . 4 f ” , Ks ) ; printf ( ” \n Kw i s %0 . 4 f ” , Kw ) ; printf ( ” \n Kc i s %0 . 3 f ” , Kc ) ; printf ( ” \n The S p r i n g S t i f f n e s s i s %0 . 1 f N/mm” ,k ) ; printf ( ” \n The A x i a l d e f l e c t i o n i s %0 . 3 f mm” , delta ) ;

Scilab code Exa 8.2 S8 2 1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20 21 22 23

// sum 8−2 clc ; clear ; W =196.2; lenthofscale =50; k =196.2/50; C =8; Ks =(1+(0.5/ C ) ) ; // L e t u s c h o o s e o i l t e m p e r e d w i r e 0 . 6 − 0 . 7 %C. R e f e r t o T a b l e 8−4 f o r c o n s t a n t s A and m, r e l a t i n g strength wire // d i a m e t e r . G =77.2*(10^3) ; A =1855; m =0.187; // e q u a t i n g Tmax=0.5∗ s i g ( u t ) . // Ks ∗ ( 8 ∗W∗D/ ( p i ∗ ( d ˆ 3 ) ) ) =0.5∗A/ ( d ˆ 2 ) d1 =( Ks *(8* W * C /( %pi * A *0.5) ) ) ; d = d1 ^(1/1.813) ; D=C*d; Na = G *( d ^4) /(8*( D ^3) * k ) ; // S o l i d l e n g t h = SL SL =( Na -1) * d

60

24 25 26 27 28 29 30

// p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” w i r e d i a m e t e r i s %0 . 3 f mm ” ,d ) ; printf ( ” \n mean d i a m e t e r i s %0 . 3 f mm ” ,D ) ; printf ( ” \n Number o f a c t i n g c o i l s a r e %0 . 3 f ” , Na ) ; // The d i f f e r e n c e i n t h e v a l u e s o f d , D and Na i s due to rounding −o f f the d i g i t s .

Scilab code Exa 8.3 S8 3 1 2 3 4 5 6 7 8 9 10 11 12 13

// sum 8−3 clc ; clear ; d =1.626; A =2211; m =0.145; rm =3; ri =( rm -( d /2) ) ; sigma = A /( d ^ m ) ; W =( sigma * %pi *( d ^3) * ri ) /(32*( rm ^2) ) ;

// p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” U l t i m a t e t e n s i l e S t r e n g t h i s %0 . 1 f MPa ” , sigma ) ; 14 printf ( ” \n F o r c e a t which t h e s p r i n g hook f a i l s i s %0 . 1 f N ” ,W ) ; 15 16

// The d i f f e r e n c e i n t h e v a l u e s o f s i g m a and W i s due to rounding −o f f the d i g i t s .

Scilab code Exa 8.4 S8 4 61

1 2 3 4 5 6 7 8 9 10 11

// sum 8−4 clc ; clear ; Do =25; // mean c o i l d i a m e t e r D=25−d W =150; T =800; G =81000; // S u b s t i t u t i n g v a l u e s i n e q u a t i o n T=8∗W∗D/ ( %pi ∗ ( d ˆ3) ) // t h e r e f o r e , t h e e q u a t i o n becomes d ˆ3 + 0 . 4 7 7 ∗ d = 11.936 // c o n s i d e r d =2.2mm, ( d can be t a k e n b e t w e e n 2 . 2 − 2 . 3 mm) d =2.337; // ( n e a r e s t a v a i l a b l e w i r e g a u g e ) C =9.5; D =22.2; Do = D + d ; Ks =1+(0.5/ C ) ; Tmax = Ks *8* W * D /( %pi *( d ^3) ) ; // c h e c k f o r s a f e t y − Tmax
12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 N = Na +2; 28 Ls = N * d ; 29 Lo = Ls +(1.15* delta ) ; 30 31 // p r i n t i n g d a t a i n s c i l a b o /p window 32 printf ( ” d i s %0 . 3 fmm ” ,d ) ; 33 printf ( ” \n D i s %0 . 2 f mm” ,D ) ; 34 printf ( ” \n Ls i s %0 . 2 f mm” , Ls ) ; 35 printf ( ” \n Lo i s %0 . 2 f mm” , Lo ) ;

62

36 37

if ( Do <=25) disp ( ’ The d i a m e t e r i s w i t h i n s p a c e c o n s t r a i n t s ’ ); 38 end

Scilab code Exa 8.5 S8 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

// sum 8−5A clc ; clear ; Di =15; Do =20; d =2.3; D =17.5; C=D/d; Ks =1+(0.5/ C ) ; Wmax =100; Tmax = Ks *8* Wmax * D /( %pi *( d ^3) ) ; G =81000; delmax =67.7/2.366; k =100/28; Na = G *( d ^4) /(8* k *( D ^3) ) ; Ls = Na +1; // ( f o r p l a i n e n d s ) delmax =28; //TL= t o t a l w o r k i n g l e n g t h TL = Ls + delmax +(0.15* delmax ) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” d i s %0 . 1 fmm ” ,d ) ; printf ( ” \n C i s %0 . 1 f ” ,C ) ; printf ( ” \n Na i s %0 . 1 f ” , Na ) ;

Scilab code Exa 8.6 S8 6 63

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

// sum 8−6 clc ; clear ; // 18 SWG= 1 . 2 1 9MM i n d i a d =1.219; E =198.6*10^3; G =80.7*10^3; m =0.19; A =1783; sig = A /( d ^ m ) ; Tys =(0.4* sig ) ; Do =12.5; D = Do - d ; C=D/d; Ks =((2* C ) +1) /(2* C ) ; W =( Tys * %pi *( d ^3) ) /(8* D * Ks ) ; Nt =13.5; Na = Nt -2; del =(8* W *( D ^3) * Na ) /( G *( d ^4) ) ; Ls =( Nt -1) * d ; Lo = Ls + del +(0.15* del ) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” Tys i s %0 . 1 f MPa ” , Tys ) ; printf ( ” \n W i s %0 . 1 f N ” ,W ) ; printf ( ” \n d e l i s %0 . 3 f mm ” , del ) ; printf ( ” \n Ls i s %0 . 4 f mm ” , Ls ) ; printf ( ” \n Lo i s %0 . 2 f mm ” , Lo ) ; // Answers i n t h e book f o r T o r s i o n a l y e i l d s t r e n g t h have b e e n rounded − o f f t o t h e n e a r e s t w h o l e number .

Scilab code Exa 8.7 S8 7

64

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

// sum 8−7 clc ; clear ; d =1.016; A =2211; m =0.145; G =81000; Nt =16; Na =16 -2; sig = A /( d ^ m ) ; Tys =0.45* sig ; Do =12.6; D = Do - d ; C=D/d; Ks =1+(0.5/ C ) ; W =( Tys * %pi *( d ^3) ) /(8* D * Ks ) ; k =( G *( d ^4) ) /(8*( D ^3) * Na ) ; del = W / k ; Ls =( Nt -1) * d ; Lo = Ls +(1.15* del ) ;

// p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” Tys i s %0 . 1 f MPa ” , Tys ) ; printf ( ” \n Do i s %0 . 1 f N ” , Do ) ; printf ( ” \n W i s %0 . 1 f N ” ,W ) ; printf ( ” \n k i s %0 . 3 f N ” ,k ) ; printf ( ” \n d e l i s %0 . 2 f mm ” , del ) ; printf ( ” \n Ls i s %0 . 2 f mm ” , Ls ) ; printf ( ” \n Lo i s %0 . 3 f mm ” , Lo ) ; if (( Lo / D ) >=5.26) disp ( ’ The s p r i n g w i l l end

f a i l under b u c k l i n g ’ );

// V a l u e s a f t e r t h e d e c i m a l p o i n t h a s n o t b e e n c o n s i d e r e d f o r answer o f T o r s i o n a l y e i l d s t r e n g t h i n t h e book , w h e r e a s a n s w e r s f o r d e f l e c t i o n and 65

f r e e −l e n g t h i s d i f f e r e n t a s e n t i r e v a l u e o f v a r i a b l e s i s taken f o r c a l c u l a t i o n in the code .

Scilab code Exa 8.8 S8 8 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

// sum 8−8 clc ; clear ; d =2; Do =20; D = Do - d ; C=D/d; Na =9; // M a t e r i a l h a r d drawn s p r i n g s t e e l A =1783; m =0.19; G =81000; sig = A /( d ^ m ) ; Tys =0.45* sig Kf =1.5; Ta = Tys / Kf ; Ks =1+(0.5/ C ) ; W =( Ta * %pi *( d ^3) ) /(8* D * Ks ) ; k =( G *( d ^4) ) /(8*( D ^3) * Na ) ; del = W / k ; Lo =(( Na +1) * d ) +(1.15* del ) ; p =( Lo - d ) / Na ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” k i s %0 . 3 f N/mm ” ,k ) ; printf ( ” \n W i s %0 . 1 f N ” ,W ) ; printf ( ” \n Lo i s %0 . 3 f mm ” , Lo ) ; printf ( ” \n p i s %0 . 3 f mm ” ,p ) ;

66

31 if (( Lo ) >=47.34) 32 disp ( ’ The s p r i n g w i l l f a i l u n d e r b u c k l i n g ’ ) ; 33 end 34 35 // The a n s w e r f o r v a l u e o f s p r i n g r a t e ’ k ’ i s

m i s p r i n t e d i n t h e book . Due t o t h i s a l l s u b s e q u e n t v a l u e s o f d e l , Lo , p i s c a l u c a t e d i n c o r r e c t l y i n t h e book .

Scilab code Exa 8.9 S8 9 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

// sum 8−9 clc ; clear ; // f o r m u s i c w i r e d1 =11.5; A =2211; d =1.5; m =0.145; sigut = A /( d ^ m ) ; sigy =0.78* sigut ; Do =16; E =2*(10^5) ; Nb =4.25; D = Do - d ; C=D/d; Ki =((4*( C ^2) ) -C -1) /(4* C *( C -1) ) ; Mmax =( sigy * %pi *( d ^3) ) /(32* Ki ) ; kc =(( d ^4) * E ) /(10.8* D * Nb ) ; theta3 = Mmax / kc ’; l1 =20; l2 =20; Ne =( l1 + l2 ) /(3* %pi * D ) ; Na = Nb + Ne ; k =(( d ^4) * E ) /(10.8* Na * D ) ; 67

25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

thetat = Mmax /k ’; ke =(3* %pi *( d ^4) * E ) /(10.8*( l1 + l2 ) ) ; // a n g d i s p=t h e t a 1+t h e t a 2=Mmax/ ke ; angdisp = Mmax / ke ; //D1 i s f i n a l c o i l d i a m e t e r D1 =( Nb * D ) /( Nb + theta3 ) ; // IRC= I n i t i a l r a d i a l c l e a r a n c e IRC =(( D - d ) - d1 ) /2; //FRC=F i n a l r a d i a l c l e a r a n c e FRC =(( D1 - d ) - d1 ) /2;

// p r i n t i n g d a t a i n s c i l a b o / p window printf ( ”Maximum Torque i s %0 . 2 f Nmm ” , Mmax ) ; printf ( ” \n t h e t a 3 i s %0 . 3 f t u r n s ” , theta3 ) ; printf ( ” \n Ne i s %0 . 3 f t u r n s ” , Ne ) ; printf ( ” \n ke i s %0 . 1 f N/mm ” , ke ) ; printf ( ” \n t h e t a 1+t h e t a 2 i s %0 . 4 f t u r n s ” , angdisp ) ; printf ( ” \n D1 i s %0 . 2 f mm ” , D1 ) ; printf ( ” \n IRC i s %0 . 2 f mm ” , IRC ) ; printf ( ” \n FRC i s %0 . 2 f mm ” , FRC ) ;

Scilab code Exa 8.10 S8 10 1 2 3 4 5 6 7 8 9 10 11

// sum 8−10 clc ; clear ; A =1783; m =0.190; d =1.5; D =15; M =300; E =20800; k =30; // s i g u l t = u l t i m a t e s t r e n g t h o f t h e m a t e r i a l 68

12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

// s i g y= y i e l d s t r e n g t h o f t h e m a t e r i a l sigult = A /( d ^ m ) ; sigy =0.7* sigult ; // s i g a= a l l o w a b l e y i e l d s t r e n g t h o f t h e m a t e r i a l siga = sigy /2; C=D/d; Ki =(4*( C ^2) -C -1) /(4* C *( C -1) ) ; Z = %pi *( d ^3) /32; // s i g b=b e n d i n g s t r e n g t h o f t h e m a t e r i a l ; sigb = Ki * M / Z ; while ( sigb >= siga ) d = d +0.15; D =15; C=D/d; sigult = A /( d ^ m ) ; sigy =0.7* sigult ; siga = sigy /2; Ki =(4*( C ^2) -C -1) /(4* C *( C -1) ) ; Z = %pi *( d ^3) /32; sigb = Ki * M / Z ; end d =2; // r o u n d i n g o f f t h e v a l u e o f t h e d i a m e t e r . D; Na =( d ^4) * E /(64* D * k ) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” d i s %0 . 1 f mm ” ,d ) ; printf ( ” \n D i s %0 . 1 f mm ” ,D ) ; printf ( ” \n Na i s %0 . 2 f mm ” , Na ) ;

Scilab code Exa 8.11 S8 11 1 // sum 8−11 2 clc ; 3 clear ;

69

4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

L =1180; W =40*(10^3) ; Nf =2; Ng =8; E =207*(10^3) ; // s i g u t i s u l t i m a t e s t r e n g t h sigut =1400; FOS =2; // s i g a= a l l o w a b l e y i e l d s t r e n g t h o f t h e m a t e r i a l siga =1400/2; // s i g b f =b e n d i n g s t r e n g t h i n f u l l l e n g t h sigbf =700; b =75; t =((4.5* W * L ) /(((3* Nf ) +(2* Ng ) ) * sigbf ) ) ^(0.5) ; t =14; I =( Nf * b *( t ^3) ) /12; Wf =(3* Nf * W ) /((3* Nf ) +(2* Ng ) ) ; del =( Wf *( L ^3) ) /(48* E * I ) ;

// p r i n t i n g d a t a i n s c i l a b o / p window printf ( ” t i s %0 . 0 f mm ” ,t ) ; printf ( ” \n Wf i s %0 . 0 f N ” , Wf ) ; printf ( ” \n I i s %0 . 0 f mmˆ4 ” ,I ) ; printf ( ” \n d e l i s %0 . 1 f mm ” , del ) ;

Scilab code Exa 8.12 S8 12A 1 2 3 4 5 6 7

// sum 8−12A clc ; clear ; W =80000; sigbfr =500; L =1100; Nf =3; 70

8 9 10 11 12 13 14 15 16 17 18 19 20 21

Ng =10; N = Nf + Ng ; t =((1.5* W * L ) /( N *6* sigbfr ) ) ^(1/3) ; t =15; b =6* t ; E =207*10^3; deli =( W *( L ^3) ) /(8* E * N * b *( t ^3) ) ; Wi =( W * Nf * Ng ) /( N *((3* Nf ) +(2* Ng ) ) ) ;

// p r i n t i n g d a t a i n s c i l a b o / p window printf ( ” t i s %0 . 1 f mm ” ,t ) ; printf ( ” \n d e l i i s %0 . 1 f mm ” , deli ) ; printf ( ” \n Wi i s %0 . 0 f N ” , Wi ) ;

Scilab code Exa 8.13 S8 13 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

// sum 8−13 clc ; clear ; // u l t i m a t e s t r e n g t h=s i g u t sigut =1500; C =7; d =3; D=C*d; Ks =1+(0.5/ C ) ; Kw =(((4* C ) -1) /((4* C ) -4) ) +(0.615/ C ) ; Pmax =120; Pmin =40; Pm =80; Tm =( Ks *8* Pm * D ) /( %pi *( d ^3) ) ; Ta =( Kw *8* Pmin * D ) /( %pi *( d ^3) ) ; Tse =0.22* sigut ; Tys =0.45* sigut ; x =( Tys -(0.5* Tse ) ) /(0.5* Tse ) ; 71

19 y =(( x ) * Ta ) + Tm ; 20 FOS =( Tys / y ) ; 21 22 // p r i n t i n g d a t a i n s c i l a b o /p window 23 printf ( ”Tm i s %0 . 2 f MPa ” , Tm ) ; 24 printf ( ” \n Ta i s %0 . 1 f MPa ” , Ta ) ; 25 printf ( ” \n FOS i s %0 . 3 f ” , FOS ) ;

Scilab code Exa 8.14 S8 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

// sum 8−14 clc ; clear ; Tse =360; Tys =660; d =25; P =0.03; m =40; Pmin =(( %pi *( d ^2) * P ) /4) +( m *9.81/1000) ; k =6; // A d d i t i o n a l l o a d= Padd=k ∗ f u r t h e r c o m p r e s s i o n i n spring Padd = k *10; Pmax = Padd + Pmin ; Pm =( Pmax + Pmin ) /2; Pa =( Pmax - Pmin ) /2; d =2; D =12; C =6; Ks =1+(0.5/ C ) ; Ks =1.083; Kw =(((4* C ) -1) /((4* C ) -4) ) +(0.615/ C ) ; Ta =( Kw *8* Pa * D ) /( %pi *( d ^3) ) ; Tm =( Ks *8* Pm * D ) /( %pi *( d ^3) ) ; x =( Tys -(0.5* Tse ) ) /(0.5* Tse ) ; 72

25 y =(( x ) * Ta ) + Tm ; 26 FOS =( Tys / y ) ; 27 28 // p r i n t i n g d a t a i n s c i l a b o /p window 29 printf ( ”Tm i s %0 . 2 f MPa ” , Tm ) ; 30 printf ( ” \n Ta i s %0 . 3 f MPa ” , Ta ) ; 31 printf ( ” \n FOS i s %0 . 2 f ” , FOS ) ;

73

Chapter 9 THREADED FASTENERS

Scilab code Exa 9.1 TF1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

// sum 9−1 clc ; clear ; p1 =2; d =16; dt1 =d -(0.93825* p1 ) ; At1 = %pi * dt1 ^2/4; p2 =1.5; d =16; dt2 =d -(0.93825* p2 ) ; At2 = %pi * dt2 ^2/4; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” At1 i s %0 . 1 f mmˆ2 ” , At1 ) ; printf ( ” \n At2 i s %0 . 1 f mmˆ2 ” , At2 ) ;

Scilab code Exa 9.2 TF2

74

1 2 3 4 5 6 7 8 9 10 11

// sum 9−2 clc ; clear ; W =20*10^3; n =4; // L e t t h e l o a d on e a c h b o l t be W1 W1 = W / n ; At = W1 /80; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” At i s %0 . 1 f mmˆ2 ” , At ) ;

Scilab code Exa 9.3 TF3 // sum 9−3 clc ; clear ; d =18; p =2.5; dr =d -(1.2268* p ) ; dm =( d + dr ) /2; alpha = atan ( p /( %pi * dm ) ) ; theta = %pi *30/180; u1 =0.15; u2 =0.13; x =( tan ( alpha ) +( u1 / cos ( theta ) ) ) /(1 -( tan ( alpha ) * u1 / cos ( theta ) ) ) ; 13 K = dm * x /(2* d ) +(0.625* u2 ) ; 1 2 3 4 5 6 7 8 9 10 11 12

14 15 16

// p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”K i s %0 . 5 f ” ,K ) ;

Scilab code Exa 9.4 TF4 75

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

// sum 9−4 clc ; clear ; d =20; t =4; Lg =84; Ad = %pi * d ^2/4; Eb =205*10^3; Ed =105*10^3; kb = Ad * Eb / Lg ; lg =80; x =5*( lg +(0.5* d ) ) /( lg +(2.5* d ) ) ; kp = %pi * Ed * d /(2* log ( x ) ) ; At =245; sigb =105; Pe =20*10^3; Pb = Pe * kb /( kb + kp ) ; sigad = Pb / At ; finalst = sigb + sigad ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” f i n a l s t r e s s i s %0 . 2 f N/mmˆ2 finalst ) ;

Scilab code Exa 9.5 TF5 1 2 3 4 5 6 7 8 9

// sum 9−5 clc ; clear ; Eb =207*10^3; Ec =105*10^3; sigp =650; At =115; Pi =0.75* sigp * At ; F = sigp * At ; 76

”,

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

// L e t t h e a d d i t i o n a l l o a d Fadd Padd =F - Pi ; d =14; Ad = %pi * d ^2/4; Lg =63; kb = Ad * Eb / Lg ; lg =60; x =5*( lg +(0.5* d ) ) /( lg +(2.5* d ) ) ; km = %pi * Ec * d /(2* log ( x ) ) ; C = kb /( kb + km ) ; Pe = Padd / C ; K =0.2; Ti = Pi * K * d *10^ -3; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” Ti i s %0 . 2 f Nm ” , Ti ) ;

Scilab code Exa 9.6 TF6 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

// sum 9−6 clc ; clear ; d =20; sigp =600; At =245; Pi =120*10^3; Pe =30*10^3; C =0.35; Pb = C * Pe ; P = Pi + Pb ; sigi = Pi / At ; sigf = P / At ; K =0.18; T = K * d * Pi *10^ -3; E1 = sigi / sigp ; 77

17 E2 = sigf / sigp ; 18 19 // p r i n t i n g d a t a i n s c i l a b o /p window 20 printf ( ” s i g i i s %0 . 1 f MPa ” , sigi ) ; 21 printf ( ” \n s i g i i s %0 . 2 f MPa ” , sigf ) ; 22 printf ( ” \n T i s %0 . 0 f Nm ” ,T ) ; 23 printf ( ” \n E1 i s %0 . 3 f ” , E1 ) ; 24 printf ( ” \n E2 i s %0 . 3 f ” , E2 ) ; 25 26 // V a l u e u p t o t e n t h t h p l a c e i s c o n s i d e r e d i n t h e

book f o r v a l u e o f f i n a l

s t r e s s in bolt ,

’ sigf ’

Scilab code Exa 9.7 TF7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

// sum 9−7 // The sum s e q u e n c e i s numbered i n c o r r e c t l y i n t h e book , from t h i s sum ownwards . clc ; clear ; p =2; d =16; dt =d -(0.938* p ) ; At = %pi * dt ^2/4; r =60* sqrt (2) ; Td =1/(4* At ) ; Ta =120; T =8.722*10^ -3; P = Ta / T *10^ -3; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”P i s %0 . 3 f kN ” ,P ) ; // V a l u e u p t o h u n d r e d t h p l a c e i s c o n s i d e r e d i n t h e book f o r v a l u e o f p e r m i s s i b l e l o a d , ’P ’

78

Scilab code Exa 9.8 TF8 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

// sum 9−8 clc ; clear ; sigyp =460; FOS =2; Ts =0.577* sigyp / FOS ; At =245; r =100; P = Ts * At /1.453*10^ -3; // Open p r o b 9 p 8 . t x t f i l e fid = mopen ( ’ p r o b 9 p 8 . t x t ’ , ”w” ) ; // e r r o r m e s s a g e if ( fid == -1) error ( ’ c a n n o t open f i l e f o r w r i t i n g ’ ) ; end mfprintf ( fid , ” Problem 9 . 8 S o l u t i o n : \ nThe e c c e n t r i c l o a d i s %f N ” ,P ) ; mclose ( fid ) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”P i s %0 . 3 f kN ” ,P ) ; // V a l u e o f t h o u s a n d t h p l a c e o f e c c e n t r i c l o a d , i s m i s p r i n t e d i n t h e book .

Scilab code Exa 9.9 TF9 1 // sum 9−9 2 clc ;

79

’P ’

3 4 5 6 7 8 9 10 11 12 13 14 15 16

clear ; P =4*10^3; e =200; l1 =150; l2 =550; sigyp =420; FOS =3; siga = sigyp /3; M=P*e; At =12.5; At =14.2; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” At i s %0 . 1 f mmˆ2 ” , At ) ;

Scilab code Exa 9.10 TF10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

// sum 9−10 clc ; clear ; Pi =10*10^3; sigyp =420; FOS =2; sige = sigyp / FOS ; K1 =0.85; K2 =0.74; K4 =0.868; SCF =2.4; K3 =1/ SCF ; sige = sige * K1 * K2 * K3 * K4 ; Pe =10*10^3/3; Pmax = Pi + Pe ; Pmin = Pi ; Pa =( Pmax - Pmin ) /2; Pm =( Pmax + Pmin ) /2; 80

19 theta = atan ( Pa / Pm ) ; 20 siga =21.132; 21 At = Pa / siga ; 22 At =84.2; 23 24 // p r i n t i n g d a t a i n s c i l a b o /p window 25 printf ( ” At i s %0 . 1 f mmˆ2 ” , At ) ; 26 disp ( ’ M12 c o a r s e −p i t c h b o l t w i t h 1 . 7 5 mm p i t c h

used ’ );

Scilab code Exa 9.11 TF11 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

// sum 9−11 clc ; clear ; Pi =15; Pmax =15+3.75; Pmin =15+1.25; Pa =( Pmax - Pmin ) /2; Pm =( Pmax + Pmin ) /2; K1 =0.85; K2 =0.7; K4 =0.897; SCF =2.4; K3 =1/ SCF ; sige =900/4* K1 * K2 * K3 * K4 ; siga =28.115; At = Pa *10^3/ siga ; At =58; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” At i s %0 . 0 f mmˆ2 ” , At ) ;

81

is

Chapter 10 PIPES AND PIPE JOINTS

Scilab code Exa 10.1 PPJ1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

// sum 10−1 clc ; clear ; sigta =140/2; nt =0.75; // L e t t h e f l o w r a t e be Q Q =0.25; v =1.2; D =1.13* sqrt ( Q / v ) ; D =520; p =0.7; C =9; t =( p * D ) /(2* sigta * nt ) + C ; // p r i n t i n g d a t a i n s c i l a b o / p window printf ( ” t i s %0 . 1 f mm ” ,t ) ;

Scilab code Exa 10.2 PPJ2 82

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

// sum 10−2 clc ; clear ; p =3*8; sigta =60; d =150; t = d /2* sqrt ((( sigta + p ) /( sigta - p ) ) -1) ; t =75* sqrt ((84/36) -1) ; t =40; do = d +(2* t ) ; D = d +(2* t ) +20; w =10; Ds = d +(2* w ) ; P = %pi *( Ds ^2) *8/4; sigp =310; FOS =4; sigb =77.5; At = P /( sigb *2) ; At =1300; D =250; db =45; b=D; a =1.8* b ; CD = D +(2* db *1.2) ; sigp =310; Pr =0.75* sigp * At ; Pr = Pr *10^ -3; t =40; D1 = d +(2* t ) +20; D2 = D1 +(4.6*31) ; CD = D2 -((3* t ) +20) ; // p r i n t i n g d a t a i n s c i l a b o / p window printf ( ” Pr i s %0 . 2 f kN ” , Pr ) ; printf ( ” \n D1 i s %0 . 0 f mm ” , D1 ) ; printf ( ” \n D2 i s %0 . 1 f mm ” , D2 ) ; printf ( ” \n CD i s %0 . 1 f mm ” , CD ) ;

83

Scilab code Exa 10.3 PPJ3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

// sum 10−3 clc ; clear ; p =14; d =50; sigyp =270; FOS =3; sigta = sigyp / FOS ; pt =2* p ; t = d /2* sqrt ((( sigta + pt ) /( sigta - pt ) ) -1) ; t =10; D1 = d +(2* t ) ; Ds = D1 +20; P = %pi *( Ds ^2) * p /4; sigba =380/4; At = P /(4* sigba ) ; At =245; db =20; Dd =70+(2*20) +5; R = db +2.5; B =( Dd / sqrt (2) ) +(2*( db +2.5) ) ; B =127; Y = Dd /(2* sqrt (2) ) ; Rm =34.12; M =( P * Y /2) +( P * Rm / %pi ) ; sigfa =250/5; b =127/70; Z = b /6; tf = sqrt ( M /( sigfa * Z ) ) ; tf =44; // p r i n t i n g d a t a i n s c i l a b o / p window 84

33 34 35 36 37 38

printf ( ” d i s %0 . 0 f mm ” ,d ) ; printf ( ” \n t i s %0 . 0 f mm ” ,t ) ; printf ( ” \n B i s %0 . 0 f mm ” ,B ) ; printf ( ” \n R i s %0 . 1 f mm ” ,R ) ; printf ( ” \n Y i s %0 . 2 f mm ” ,Y ) ; printf ( ” \n t f i s %0 . 0 f mm ” , tf ) ;

Scilab code Exa 10.4 PPJ4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

// sum 10−4 clc ; clear ; p =1.25; D =200; nt =0.75; C =9; sigta =20; t =( p * D ) /(2* sigta * nt ) + C ; t =18; D1 = D +(2* t ) ; dr = D1 +10; sigp =310; sigba = sigp /4; db =16; Db = dr +32+5; Do = Db +(2* db ) ; P = %pi *(251+ db ) ^2*1.25/4; n =6; Y =( Db - dr ) /2; M=P/n*Y; Z = dr * tand (30) /6; tf = sqrt ( M /( sigta * Z ) ) ; tf =22; Deff = dr + db +5;

85

27 28 29 30 31 32

// p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”D i s %0 . 0 f mm ” ,D ) ; printf ( ” \n t i s %0 . 0 f mm ” ,t ) ; printf ( ” \n Y i s %0 . 1 f mm ” ,Y ) ; printf ( ” \n t f i s %0 . 0 f mm ” , tf ) ; printf ( ” \n D e f f i s %0 . 0 f mm ” , Deff ) ;

86

Chapter 11 RIVETED JOINTS

Scilab code Exa 11.1 RJ1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

// sum 11−1 clc ; clear ; t =20; p =100; d =25; sigt =40; P =( p - d ) * t * sigt ; Ts =(4* P ) /( %pi * d ^2) ; sigb = P /( d * t ) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”P i s %0 . 0 f N ” ,P ) ; printf ( ” \n Ts i s %0 . 2 f MPa ” , Ts ) ; printf ( ” \n s i g b i s %0 . 0 f MPa ” , sigb ) ;

Scilab code Exa 11.2 RJ2

87

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

// sum 11−2 clc ; clear ; t =22; t1 =5* t /8; d =30; p =100; sigt =75; P =( p - d ) * t * sigt ; Ts =(2* P ) /( %pi * d ^2) ; sigb = P /( d * t ) ; P = P *10^ -3 // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”P i s %0 . 1 f kN ” ,P ) ; printf ( ” \n Ts i s %0 . 1 f MPa ” , Ts ) ; printf ( ” \n s i g b i s %0 . 0 f N/mmˆ2 ” , sigb ) ;

Scilab code Exa 11.3 RJ3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

// sum 11−3 clc ; clear ; t =15; t1 =5* t /8; d =25; n =2; Ta =80; sigta =100; sigba =120; Ps = n *1.875* %pi * d ^2* Ta /4; Pb = n * d * t * sigba ; p = Pb /( t * Ta ) + d ; Pp = p * t * Ta ; n = Pb / Pp ;

88

17 18 19 20

// p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” p i s %0 . 0 f mm ” ,p ) ; printf ( ” \n n i s %0 . 2 f ” ,n ) ;

Scilab code Exa 11.4 RJ4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

// sum 11−4 clc ; clear ; b =200; t =16; d =6* sqrt ( t ) ; sigta =80; Ta =60; sigba =100; Pt =( b - d ) * t * sigta ; Ps =1.875* %pi * d ^2* Ta /4; Pb = d * t * sigba ; n1 = Pt / Pb ; n1 =6; Pt2 =(( b -(2* d ) ) * t * sigta ) + Pb ; Pt3 =(( b -(3* d ) ) * t * sigta ) +(3* Pb ) ; Pp = b * t * sigta ; n2 = Pt / Pp ; n2 = n2 *100; // p r i n t i n g d a t a i n s c i l a b o / p window printf ( ” d i s %0 . 0 f mm ” ,d ) ; printf ( ” \n n1 i s %0 . 0 f ” , n1 ) ; printf ( ” \n Pt i s %0 . 0 f N ” , Pt ) ; printf ( ” \n Pt2 i s %0 . 0 f N ” , Pt2 ) ; printf ( ” \n Pt3 i s %0 . 0 f N ” , Pt3 ) ; printf ( ” \n n2 i s %0 . 0 f ” , n2 ) ;

89

29

// Answer t o s t r e n g t h o f r i v e t i n b e a r i n g ’ Pb ’ i s c a l c u l a t e d i n c o r r e c t l y i n t h e book , h e n c e Pt2 , Pt3 i s c a l c u l a t e d s u b s e q u e n t l y i n c o r r e c t .

Scilab code Exa 11.5 RJ5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

// sum 11−5 clc ; clear ; a =50; b =75; P =36*10^3; d =24; Ta =60; n =9; A = %pi * d ^2/4; Td = P /( n * A ) ; theta = atan ( b / a ) ; Ts =54.64; r2 =90.184; e = A *29575.7/ P ; // p r i n t i n g d a t a i n s c i l a b o / p window printf ( ” e i s %0 . 1 f mm ” ,e ) ;

Scilab code Exa 11.6 RJ6 1 // sum 11−6 2 clc ; 3 clear ; 4 P =12*10^3; 5 Tmax =100; 6 n =6;

90

7 8 9 10 11 12 13 14 15 16 17 18

e =50+50+(5/2) ; T=P*e; Td = P / n ; ra =125; k = T /((2*125^2) +(2*75^2) +(2*25^2) ) ; Tr =( k * ra ) + Td ; A = Tr / Tmax ; d = sqrt ( A *4/ %pi ) ; d =12; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” d i s %0 . 0 f mm ” ,d ) ;

Scilab code Exa 11.7 RJ7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

// sum 11−7 clc ; clear ; t =15; d =6* sqrt ( t ) ; d =24; sigta =75; sigba =105; Ta =60; n =4; Pt = n * %pi * d ^2* Ta /4; x = d * t * sigta ; y =2* t * sigta ; p =( Pt + x ) / y ; p =60; C =4.17; pmax =( C * t ) +41.28; Pt1 =( y * p ) -x ; Ps = n * %pi * d ^2* Ta /4; Pb = n * d * t * sigba ; 91

21 S =2* p * t * sigta ; 22 n = Pt1 / S ; 23 n = n *100; 24 25 // p r i n t i n g d a t a i n 26 printf ( ” n i s %0 . 0 f

s c i l a b o /p window ” ,n ) ;

Scilab code Exa 11.8 RJ8 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

// sum 11−8 clc ; clear ; D =1500; p =2; nt =0.75; sigut =420; FOS =5; sigta = sigut / FOS ; t = p * D /(2* sigta * nt ) ; t =24; d =6* sqrt ( t ) ; d =30; Ta =330/5; sigba =640/5; Ps =2*1.875* %pi *( d ^2) * Ta /4; p =( Ps /( t * sigta ) ) + d ; p =117; t1 =5* t /8; Pt =( p - d ) * t * sigta ; Pp = p * t * sigta ; Pb =2* d * t * sigba ; n = Ps / Pb ; n = n *100; // p r i n t i n g d a t a i n s c i l a b o / p window 92

27

printf ( ” n i s %0 . 0 f

” ,n ) ;

Scilab code Exa 11.9 RJ9 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

// sum 11−9 clc ; clear ; D =1200; p =2.5; sigba =110; Pa = %pi * D ^2* p /4; nt =0.8; sigta =80; t = p * D /(2* sigta * nt ) ; t =24; d =6* sqrt ( t ) ; d =30; Ta =55; Ps = %pi *( d ^2) * Ta /4; Np = Pa / Ps ; Np =74; nr = Np /2; p = %pi *( D + t ) / nr ; pb =2* d ; m =1.5* d ; Pt =( p - d ) * t * sigta ; Ps =2* Ps ; Pb =2* d * t * sigba ; Pp = p * t * sigta ; n = Ps / Pp ; n = n *100; // p r i n t i n g d a t a i n s c i l a b o / p window printf ( ” n i s %0 . 0 f ” ,n ) ;

93

Chapter 12 WELDED JOINTS

Scilab code Exa 12.1 WJ1 1 2 3 4 5 6 7 8 9 10 11

// sum 12−1 clc ; clear ; h =8; F =100*10^3; t =0.707* h ; A =4*60* t ; T=F/A; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”T i s %0 . 1 f MPa ” ,T ) ;

Scilab code Exa 12.2 WJ2 1 // sum 12−2 2 clc ; 3 clear ; 4 FOS =3;

94

5 6 7 8 9 10 11 12

Ta =95/ FOS ; P =350*10^3; h =12.5; t =0.707* h ; l = P /(2* t * Ta ) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” l i s %0 . 0 f mm ” ,l ) ;

Scilab code Exa 12.3 WJ3 1 2 3 4 5 6 7 8 9 10 11 12

// sum 12−3 clc ; clear ; h =12; t =0.707* h ; l =60; Ta =80; P =2* l * t * Ta ; P = P *10^ -3; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”P i s %0 . 3 f kN ” ,P ) ;

Scilab code Exa 12.4 WJ4 1 2 3 4 5 6 7

// sum 12−4 clc ; clear ; P =6*10^3; e =150+(100/2) ; T=P*e; A =200; 95

8 9 10 11 12 13 14 15 16 17 18 19 20

Td = P / A ; r = sqrt (2*50^2) ; Ixx =2*(100*50^2) ; Iyy =2*100^3/12; IG = Ixx + Iyy ; Ts = r * T / IG ; Tmax = sqrt (( Ts * sind (45) ) ^2+( Td +( Ts * cosd (45) ) ) ^2) ; Ta =80; t = Tmax / Ta ; h = sqrt (2) * t ; h =3; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” h i s %0 . 0 f mm ” ,h ) ;

Scilab code Exa 12.5 WJ5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

// sum 12−5 clc ; clear ; h =10; t =10/ sqrt (2) ; Ta =80; x =((50*25) +(50*0) ) /(50+50) ; y=x; ra = sqrt ( x ^2+37.5^2) ; Ixx =(7.07*50^3/12) +(50*7.07*(12.5^2) ) +(50*7.07*12.5^2) ; IG =2* Ixx ; e =100+(50 -12.5) ; Tr =16.09*10^ -3; P = Ta / Tr ; P = P *10^ -3; // p r i n t i n g d a t a i n s c i l a b o / p window printf ( ”P i s %0 . 3 f KN ” ,P ) ; 96


// sum 12−6 clc ; clear ; P =16*10^3; l =300; r =50; M=P*l; A =2* %pi * r ; Ixx = %pi * r ^3; sigb = M * r / Ixx ; Td = P / A ; Tmax = sqrt (( sigb /2) ^2+( Td ^2) ) ; Ta =90; t = Tmax / Ta ; h = sqrt (2) * t ; h =5; // p r i n t i n g d a t a i n s c i l a b o / p window printf ( ” h i s %0 . 0 f mm ” ,h ) ;

Scilab code Exa 12.7 WJ7 1 2 3 4 5 6 7 8

// sum 12−7 clc ; clear ; sigut =415; sige = sigut /3; Ka =0.5; Kb =0.85; Kc =0.897; 97

9 10 11 12 13 14 15 16 17 18 19

SCF =1.5; Kd =1/ SCF ; FOS =2; sige1 = sige * Ka * Kb * Kc * Kd / FOS ; Pa =50*10^3; h =10; t =0.707* h ; l = Pa /(2* sige1 * t ) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” l i s %0 . 0 f mm ” ,l ) ;

Scilab code Exa 12.8 WJ8 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

// sum 12−8 clc ; clear ; l =300; P =30*10^3; T = P /(2* l ) ; Ta =124; t1 = T / Ta ; h1 = sqrt (2) * t1 ; M=P*l; Ixx =2*100*110^2; sigb = M / Ixx *110; // L e t t h e a l l o w a b l e b e n d i n g s t r e s s Tab =200; t2 = sigb / Tab ; h2 = t2 /0.707; h2 =3;

i s Tab

// p r i n t i n g d a t a i n s c i l a b o / p window printf ( ” h i s %0 . 0 f mm ” , h2 ) ;

98

Scilab code Exa 12.9 WJ9 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

// sum 12−9 clc ; clear ; Ta =60; l1 =60; l2 =40; P1 = Ta *0.707* l1 ; P2 = Ta *0.707* l2 ; P =80*10^3; h = P /( P1 + P2 ) ; h =20; a =( P2 *100) /( P1 + P2 ) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” h i s %0 . 0 f mm ” ,h ) ; printf ( ” \n a i s %0 . 0 f mm ” ,a ) ;

Scilab code Exa 12.10 WJ10 1 2 3 4 5 6 7 8 9 10 11

// sum 12 −10 clc ; clear ; P =300*10^3; l =500; A =2* l ; Td = P / A ; T =(350 -250) * P ; IG =( l ^3*2/12) +( l *2*5^2) ; r = sqrt (250^2+5^2) ; Ts = T * r / IG ; 99

12 13 14 15 16 17 18 19

Ts = Ts + Td ; Ta =110; t = Ts / Ta ; h = t /0.707; h =9; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” h i s %0 . 0 f mm ” ,h ) ;


// sum 12 −11 clc ; clear ; t =30; sigut =417; sige = sigut /2; Ka =0.5; Kb =0.85; Kc =0.897; SCF =1.2; Kd =1/ SCF ; FOS =1.5; sige1 = sige * Ka * Kb * Kc * Kd / FOS ; Pa =60*10^3; l = Pa /( sige1 * t ) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” l i s %0 . 1 f mm ” ,l ) ;

100

Chapter 13 COTTER AND KNUCKLE JOINTS

Scilab code Exa 13.1 CKJ1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

// sum 13−1 clc ; clear ; F =25*10^3; sigat =50; Ta =40; pa =80; d = sqrt ((4* F ) /( %pi * sigat ) ) ; d =26; t = d /4; t =7; d1 =1.2* d ; d1 =32; pc = F /( d1 * t ) ; t =10; c =0.75* d ; c =20; d2 =44; tw =( d2 - d1 ) /2; 101

20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

b = F /(2* t * Ta ) ; b =34; a =0.5* d ; d3 =( F /( pa * t ) ) + d1 ; d3 =64; e = F /( Ta *( d3 - d1 ) ) ; d4 = sqrt (( F *4/( %pi * pa ) ) + d1 ^2) ; d4 =40; f =0.5* d ; sigbc =3* F * d3 /( t * b ^2*4) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” d i s %0 . 0 f mm ” ,d ) ; printf ( ” \n d1 i s %0 . 0 f mm ” , d1 ) ; printf ( ” \n d2 i s %0 . 0 f mm ” , d2 ) ; printf ( ” \n d3 i s %0 . 0 f mm ” , d3 ) ; printf ( ” \n d4 i s %0 . 0 f mm ” , d4 ) ; printf ( ” \n s i g b c i s %0 . 1 f MPa ” , sigbc ) ;

Scilab code Exa 13.2 CKJ2 1 2 3 4 5 6 7 8 9 10 11 12 13 14

// sum 13−2 clc ; clear ; P =40*10^3; sigut =490; FOS =4; sigts = sigut / FOS ; sigcs =1.4* sigts ; sigs =0.8* sigts ; d = sqrt ((4* P ) /( %pi * sigts ) ) ; d =21; sigcc =1.4*330/4; Tc =0.8*330/4; t = d /3; 102

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

b = P /(2* t * Tc ) ; b =31; t =10; d1 =28; d2 =40; c = d /2; c =15; a = P /(2*( d2 - d1 ) *98) ; a =20; L =(2* a ) +(2* b ) +(2* c ) +(2*3) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” d i s %0 . 0 f mm ” ,d ) ; printf ( ” \n d1 i s %0 . 0 f mm ” , d1 ) ; printf ( ” \n t i s %0 . 0 f mm ” ,t ) ; printf ( ” \n b i s %0 . 0 f mm ” ,b ) ; printf ( ” \n d2 i s %0 . 0 f mm ” , d2 ) ; printf ( ” \n L i s %0 . 0 f mm ” ,L ) ;

Scilab code Exa 13.3 CKJ3 1 2 3 4 5 6 7 8 9 10 11 12 13 14

// sum 13−3 clc ; clear ; P =40*10^3; sigt =60; sigc =125; T =45; a = sqrt ( P *3/(2* sigt ) ) ; a =33; t = a /3; b = P /(4.5* t * T ) ; b =20; b1 =1.25* b ; t1 = P *3/(4* a * sigt ) ; 103

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

t1 =16; l2 = P /(2*2* T * t1 ) ; l2 =14; l1 = P /(2* a * T ) ; l1 =14; l3 =(0.6* a ) ; l3 =20; l4 =11; sigcr = P /( t * a ) ; sigcr1 = P /(2* t1 * t ) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” a i s %0 . 0 f mm ” ,a ) ; printf ( ” \n t i s %0 . 0 f mm ” ,t ) ; printf ( ” \n t 1 i s %0 . 0 f mm ” , t1 ) ; printf ( ” \n b i s %0 . 0 f mm ” ,b ) ; printf ( ” \n b1 i s %0 . 0 f mm ” , b1 ) ; printf ( ” \n l 1 i s %0 . 0 f mm ” , l1 ) ; printf ( ” \n l 2 i s %0 . 0 f mm ” , l2 ) ; printf ( ” \n l 3 i s %0 . 0 f mm ” , l3 ) ; printf ( ” \n l 4 i s %0 . 0 f mm ” , l4 ) ; printf ( ” \n s i g c r i s %0 . 1 f MPa ” , sigcr ) ; printf ( ” \n s i g c r 1 i s %0 . 1 f MPa ” , sigcr1 ) ;

Scilab code Exa 13.4 CKJ4 1 2 3 4 5 6 7 8 9

// sum 13−4 clc ; clear ; P =50*10^3; sigp =380; FOS =4; sigca =80; Ta =50; sigta = sigp / FOS ; 104

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

At = P / sigta ; d =30; d1 =1.5* d ; t = P /( sigca * d1 ) ; t =14; A =( %pi *( d1 ^2) /4) -( d1 * t ) ; // l e t t e a r i n g s t r e s s be s i g t sigt = P / A ; b = P /(2* t * Ta ) ; b =36; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” d i s %0 . 0 f mm ” ,d ) ; printf ( ” \n s i g t i s %0 . 1 f MPa ” , sigt ) ; printf ( ” \n b i s %0 . 0 f mm ” ,b ) ; // The a n s w e r t o t e a r i n g s t r e s s i n b o l t c a l c u l a t e d i n c o r r e c t l y i n t h e book .

105

’ sigt ’ is

Chapter 14 KEYS AND COUPLINGS

Scilab code Exa 14.1 KC1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

// sum 14−1 clc ; clear ; d =40; r = d /2; P =6*10^3; N =350; sigyt =380; A = %pi *12^2/2; theta = %pi -(2* atan (4/12) ) ; alpha =180 -( theta * %pi /180) ; l =2*12* cosd (19.5) ; A1 = l *4/2; Abcd =( A *141/180) - A1 ; A2 =A - Abcd ; A3 =8* l ; w =2* %pi * N /60; T=P/w; Pt = T *10^3/ r ; sigb = Pt / A2 ; // L e t s h e a r s t r e s s d e v e l o p e d i n key Tk 106

22 Tk = Pt / A3 ; 23 FOS1 = sigyt / sigb ; 24 FOS2 =0.577* sigyt / Tk ; 25 26 // p r i n t i n g d a t a i n s c i l a b o /p window 27 printf ( ”FOS1 i s %0 . 3 f ” , FOS1 ) ; 28 printf ( ” \n FOS2 i s %0 . 2 f ” , FOS2 ) ;

Scilab code Exa 14.2 KC2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

// sum 14−2 clc ; clear ; n =12; phi =360* %pi /(180*12*2) ; R1 =45/2; R2 =50/2; l =60; Rm =( R1 + R2 ) /2; p =6.5; Pn =( R2 - R1 ) * l * p ; T = Pn * Rm ; T=T*n; N =400; w =2* %pi * N /60; P=T*w; A =( %pi * R1 * l ) / n ; Ts = Pn / A ; Ah =( %pi * R2 * l ) / n ; Th = Pn / Ah ; // p r i n t i n g d a t a i n s c i l a b o / p window printf ( ” Ts i s %0 . 2 f N/mmˆ2 ” , Ts ) ; printf ( ” \n Th i s %0 . 2 f N/mmˆ2 ” , Th ) ;

107

Scilab code Exa 14.3 KC3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

// sum 14−3 clc ; clear ; N =360; w =2* %pi * N /60; sigyt =380; r =25; P =40*10^3; FOS =3; T=P/w; Pt = T *10^3/(2* r ) ; siga =380/3; Ta =0.577*380/3; l1 = Pt /( sqrt (2) *12* Ta ) ; l2 = Pt * sqrt (2) /( siga *12) ; // p r i n t i n g d a t a i n s c i l a b o / p window printf ( ” l 1 i s %0 . 0 f mm ” , l1 ) ; printf ( ” \n l 2 i s %0 . 2 f mm ” , l2 ) ;

Scilab code Exa 14.4 KC4 1 2 3 4 5 6 7 8

// sum 14−4 clc ; clear ; N =300; w =2* %pi * N /60; P =12*10^3; Ks =1.25; Pd = P * Ks ; 108

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

T = Pd / w ; Tas =50; d =16* T *10^3/( %pi * Tas ) ; d = d ^(1/3) ; d =40; Ts =10; d1 =(2* d ) +13; x =( d1 ^4 - d ^4) / d1 ; // L e t t h e s h e a r s t r e s s i n t h e key be Tsh Tsh = T *10^3*16/( %pi * x ) ; l =3.5* d ; Ft = T *2*10^3/ d ; l1 =70; sigak =50; b = Ft /( l1 * sigak ) ; t =2* Ft /(100* l1 ) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” d i s %0 . 0 f mm ” ,d ) ; printf ( ” \n Tsh i s %0 . 2 f MPa ” , Tsh ) ; printf ( ” \n b i s %0 . 0 f mm ” ,b ) ; printf ( ” \n t i s %0 . 0 f mm ” ,t ) ;

Scilab code Exa 14.5 KC5 1 2 3 4 5 6 7 8 9 10

// sum 14−5 clc ; clear ; P =36*10^3; N =200; w =2* %pi * N /60; T=P/w; Tas =45; d =16* T *10^3/( %pi * Tas ) ; d = d ^(1/3) ; 109

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

d =60; d1 =(2* d ) +13; l =3.5* d ; Ftk = T *2/ d ; lk = l /2; Tak =40; sigack =90; b = Ftk *10^3/( lk * Tak ) ; t =2* Ftk *10^3/( sigack * lk ) ; n =4; sigatb =60; u =0.25; dr =16* T *10^3/( u * %pi ^2* sigatb * n * d ) ; dr = sqrt ( dr ) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” d i s %0 . 0 f mm ” ,d ) ; printf ( ” \n b i s %0 . 1 f mm ” ,b ) ; printf ( ” \n t i s %0 . 0 f mm ” ,t ) ; printf ( ” \n d r i s %0 . 3 f mm ” , dr ) ;

Scilab code Exa 14.6 KC6 1 2 3 4 5 6 7 8 9 10 11 12

// sum 14−5 clc ; clear ; P =16*10^3; N =1000; w =2* %pi * N /60; T=P/w; Ks =1.4; Td = T * Ks ; Tas =40; d =16* T *10^3/( %pi * Tas ) ; d = d ^(1/3) ; 110

13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

d =32; d1 =2* d ; l =1.5* d ; ds =1.5* d ; Tak =40; sigack =70; Ftk = Td *2/ d ; b = Ftk *10^3/( l * Tak ) ; t =2* Ftk *10^3/( sigack * l ) ; Taf =10; tf = Td *10^3*2/( %pi * Taf * d1 ^2) ; Ftb = Td *10^3/(1.5* d *4) ; Tab =40; db = sqrt ( Ftb *4/( Tab * %pi ) ) ; D =4* d ; trp = d /6; Ftb1 = Td *10^3/(45*4) ; db1 = sqrt ( Ftb1 *4/( Tab * %pi ) ) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” d i s %0 . 0 f mm ” ,d ) ; printf ( ” \n b i s %0 . 0 f mm ” ,b ) ; printf ( ” \n t i s %0 . 0 f mm ” ,t ) ; printf ( ” \n db i s %0 . 2 f mm ” , db ) ; printf ( ” \n db1 i s %0 . 2 f mm ” , db1 ) ; // The a n s w e r t o Key t h i c k n e s s i n c o r r e c t l y i n t h e book .

Scilab code Exa 14.7 KC7 1 // sum 14−5 2 clc ; 3 clear ; 4 P =30*10^3;

111

’t ’ is calculated

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

N =1440; w =2* %pi * N /60; T=P/w; d =36; d1 =30; d2 =2* d ; d3 = d1 *2; l =1.5* d ; Dp =3.5* d ; n =6; Ft =(2* T ) /( Dp * n ) ; p =0.5; A = Ft / p ; Lf = d ; dp = A / Lf ; M = Ft *10^3*(5+( Lf /2) ) ; db =(32* M /( %pi *40) ) ^(1/3) ; db =15; T =(4*526) /( %pi * db ^2) ; sigb =32* M /( %pi * db ^3) ; sigmax =( sigb /2) + sqrt ((( sigb /2) ^2) +( T ^2) ) ; b = d /4; t =6; Lf =36; La =10; Do =126+30+(2*(5+1) ) +(2*6) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” s i g m a x i s %0 . 2 f MPa ” , sigmax ) ; printf ( ” \n b i s %0 . 0 f mm ” ,b ) ; printf ( ” \n t i s %0 . 0 f mm ” ,t ) ; printf ( ” \n L f i s %0 . 0 f mm ” , Lf ) ; printf ( ” \n Do i s %0 . 0 f mm ” , Do ) ;

112

Chapter 15 SHAFTS

Scilab code Exa 15.2 S2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

// sum 15−2 clc ; clear ; dA =150; dB =250; alpha =20* %pi /180; W =400; sigyt =400; sigut =500; Kb =1.5; Kt =2; T = W * dA /2; Pt = T /( dB /2) ; Pr1 = W * tan ( alpha ) ; Pr2 = Pt * tan ( alpha ) ; RDH =(( W *120) -( Pt *320) ) /440; RcH =W - RDH - Pt ; //RcH=400+65.5 −240; McH =0; MAH = RcH *120; MBH = RDH *120; 113

22 23 24 25 26 27 28 29 30 31 32 33

RDV =(( Pr1 *120) -( Pr2 *320) ) /440; RcV = Pr1 - RDV - Pr2 ; MAV = RcV *120; MBV = RDV *120; Mmax = sqrt (( MAH ^2) +( MAV ^2) ) ; T =30*10^3; Ta =0.135* sigut ; d =16* sqrt (( Kb * Mmax ) ^2+( Kt * T ) ^2) /( %pi * Ta ) ; d = d ^(1/3) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” d i s %0 . 2 f mm ” ,d ) ;

Scilab code Exa 15.3 S3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

// sum 15−3 clc ; clear ; P =16*746; N =3000; w =2* %pi * N /60; T = P / w *10^3; sigy =400; Ty = sigy /2; FOS =2; Ta = Ty / FOS ; d = T *16/( %pi * Ta ) ; d1 = d ^(1/3) ; r =3; D = d1 +(2* r ) ; SCF =1.196 Tys = Ta / SCF ; d = T *16/( %pi * Tys ) ; d2 = d ^(1/3) ; d =14; 114

21 D = d +(2* r ) ; 22 23 // p r i n t i n g d a t a i n s c i l a b o /p window 24 printf ( ” d1 i s %0 . 2 f mm ” , d1 ) ; 25 printf ( ” \n d2 i s %0 . 2 f mm ” , d2 ) ;

Scilab code Exa 15.4 S4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

// sum 15−4 clc ; clear ; P1 =24*10^3; P2 =10*10^3; sigyt =460; Tya = sigyt *0.3; SCF =2.84; Ta = Tya / SCF ; N =400; w =2* %pi * N /60; T1 = P1 / w ; T2 = P2 / w ; d1 = T1 *16*10^3/( %pi * Ta ) ; d1 = d1 ^(1/3) ; d2 = T2 *16*10^3/( %pi * Ta ) ; d2 = d2 ^(1/3) ; theta1 = %pi /3600; l1 =120; G =84*10^3; d3 = T1 *10^3* l1 *32/( %pi * G * theta1 ) ; d3 = d3 ^(1/4) ; d4 = T2 * l1 *10^3*32/( %pi * G * theta1 ) ; d4 = d4 ^(1/4) ; // p r i n t i n g d a t a i n s c i l a b o / p window printf ( ” d1 i s %0 . 2 f mm ” , d1 ) ; 115

28 29 30

printf ( ” \n d2 i s %0 . 2 f mm printf ( ” \n d3 i s %0 . 1 f mm printf ( ” \n d4 i s %0 . 2 f mm

Scilab code Exa 15.5 S5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

// sum 15−5 clc ; clear ; d =200; r = d /2; N =300; P =5000; D =500; R = D /2; u =0.3; E =205*10^3; G =84*10^3; Ta =60; Kb =1.5; Kt =2; w =2* %pi * N /60; beta1 =20* %pi /180; V=r*w; v=R*w; // L e t T1−T2 =T T=P/V; x = u * %pi / sin ( beta1 ) ; T2 = T /(( exp ( x ) -1) ) ; T1 = T2 * exp ( x ) ; t=P/v; y = u * %pi ; T3 = t /(( exp ( x ) -1) ) ; T4 = T3 * exp ( x ) ; T=P/w; 116

” , d2 ) ; ” , d3 ) ; ” , d4 ) ;

30 31 32 33 34 35 36 37 38 39 40 41 42 43

Rc =2612;; RA =645.1; MB =96.76; MC = -208.96; d =16*10^3* sqrt (( Kb * MC ) ^2+( Kt * T ) ^2) /( %pi * Ta ) ; d = d ^(1/3) ; l =380; J = %pi * d ^4/32; theta = T *10^3* l /( G * J ) ; theta = theta *180/ %pi ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” d i s %0 . 1 f mm ” ,d ) ; printf ( ” \n t h e t a i s %0 . 2 f deg ” , theta ) ;

Scilab code Exa 15.6 S6 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

// sum 15−6 clc ; clear ; T =400; Pt =4800; Pg =3600; sigyt =360; E =205*10^3; G =80*10^3; Kb =2; Kt =1.5; FOS =3; RC =(( Pt *90) +( Pg *200) ) /140; RA =8400 - RC ; MB = RA *0.9; MC = Pg *0.045; Te = sqrt (( Kb * MC ) ^2+( Kt * T ) ^2) ; Ta =0.577* sigyt / FOS ; 117

19 20 21 22 23 24 25 26 27 28 29

d =16*10^3* Te /( %pi * Ta ) ; d = d ^(1/3) ; L =110; J = %pi * d ^4/32; T =400; theta = T *10^3* L /( G * J ) ; theta = theta *180/ %pi ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” d i s %0 . 0 f mm ” ,d ) ; printf ( ” \n t h e t a i s %0 . 4 f deg ” , theta ) ;

Scilab code Exa 15.7 S7 1 2 3 4 5 6 7 8 9 10 11 12 13 14

// sum 15−7 clc ; clear ; T =47*10^3; M =32*10^3; d =20; siga =32* M /( %pi * d ^3) ; Tm =16* T /( %pi * d ^3) ; sige =75; Tys =165; n =1/ sqrt (( siga / sige ) ^2+( Tm / Tys ) ^2) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” n i s %0 . 2 f ” ,n ) ;

118

Chapter 16 POWER SCREWS

Scilab code Exa 16.1 PS1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

// sum 16−1 clc ; clear ; d =30; W =20*10^3; r1 =8; r2 =16; p =6; u1 =0.2; u2 =0.15; dm =d -( p /2) ; alpha = atan ( p /( %pi * dm ) ) ; phi = atan ( u1 ) ; rm =( r1 + r2 ) /2; Ttr = W *(( dm * tan ( alpha + phi ) /2) +( u2 * rm ) ) ; Ttr = Ttr *10^ -3; // p r i n t i n g d a t a i n s c i l a b o / p window printf ( ” Ttr i s %0 . 3 f Nm ” , Ttr ) ; // The a n s w e r t o Ttr i s

slightly 119

d i f f e r e n t than i n

t h e book due t o r o u n d i n g − o f f o f v a l u e s .

Scilab code Exa 16.2 PS2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

// sum 16−2 clc ; clear ; d =50; W =20*10^3; r1 =10; r2 =30; p =7; u1 =0.12/ cosd (15) ; u2 =0.15; dm =d -( p /2) ; alpha = atan (3* p /( %pi * dm ) ) ; phi = atan ( u1 ) ; rm =( r1 + r2 ) /2; Tr = W *(( dm * tan ( alpha + phi ) /2) +( u2 * rm ) ) ; Tr = Tr *10^ -3; Te = W *(( dm * tan ( phi - alpha ) /2) +( u2 * rm ) ) ; Te = Te *10^ -3; n = dm /2* tan ( alpha ) /( dm * tan ( alpha + phi ) /2+( u2 * rm ) ) ; L =0.30; Ph = Tr / L ; // p r i n t i n g d a t a i n s c i l a b o / p window printf ( ” Tr i s %0 . 2 f Nm ” , Tr ) ; printf ( ” \n Te i s %0 . 3 f Nm ” , Te ) ; printf ( ” \n n i s %0 . 4 f ” ,n ) ; printf ( ” \n Ph i s %0 . 2 f N ” , Ph ) ; // The a n s w e r s t o Tr , Te and Ph i s s l i g h t l y d i f f e r e n t t h a n i n t h e book due t o r o u n d i n g − o f f of values . 120

Scilab code Exa 16.3 PS3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

// sum 16−3 clc ; clear ; d =30; W =5*10^3; p =5; rm =45/2; u1 =0.15/ cosd (14.5) ; u2 =0.15; dm =d -( p /2) ; alpha = atan ( p /( %pi * dm ) ) ; phi = atan ( u1 ) ; Tr1 = W *(( dm * tan ( alpha + phi ) /2) +( u2 * rm ) ) ; Tr1 = Tr1 *10^ -3; n1 = dm /2* tan ( alpha ) /( dm * tan ( alpha + phi ) /2+( u2 * rm ) ) ; T1 = W *(( dm * tan ( phi - alpha ) /2) +( u2 * rm ) ) ; T1 = T1 *10^ -3; n2 = dm /2* tan ( alpha ) /( dm * tan ( phi - alpha ) /2+( u2 * rm ) ) ; u2 =0.02; Tr2 = W *(( dm * tan ( alpha + phi ) /2) +( u2 * rm ) ) ; Tr2 = Tr2 *10^ -3; n3 = dm /2* tan ( alpha ) /( dm * tan ( alpha + phi ) /2+( u2 * rm ) ) ; Te = W *(( dm * tan ( phi - alpha ) /2) +( u2 * rm ) ) ; Te = Te *10^ -3; n4 = dm /2* tan ( alpha ) /( dm * tan ( phi - alpha ) /2+( u2 * rm ) ) ; // p r i n t i n g d a t a i n s c i l a b o / p window printf ( ” Tr1 i s %0 . 3 f Nm ” , Tr1 ) ; printf ( ” \n n1 i s %0 . 4 f ” , n1 ) ; printf ( ” \n T1 i s %0 . 3 f Nm ” , T1 ) ; printf ( ” \n n2 i s %0 . 4 f ” , n2 ) ; printf ( ” \n Tr2 i s %0 . 3 f Nm ” , Tr2 ) ; 121

33 34 35 36 37

printf ( ” \n n3 i s %0 . 4 f printf ( ” \n Te i s %0 . 3 f Nm printf ( ” \n n4 i s %0 . 4 f

” , n3 ) ; ” , Te ) ; ” , n4 ) ;

// The a n s w e r t o T1 i s m i s p r i n t e d i n t h e book .


// sum 16−4 clc ; clear ; d =28; P =300; L =180; p =8; r1 =16; r2 =46; rm =( r1 + r2 ) /2; u1 =0.12; u2 =0.15; dm =d -( p /2) ; alpha = atan ( p /( %pi * dm ) ) ; phi = atan ( u1 ) ; T=P*L; F = T /(( dm * tan ( alpha + phi ) /2) +( u2 * rm ) ) ; F = F *10^ -3; // p r i n t i n g d a t a i n s c i l a b o / p window printf ( ”F i s %0 . 3 f kN ” ,F ) ;

Scilab code Exa 16.5 PS5 1

// sum 16−5 122

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

clc ; clear ; d =25; p =8; F =392.4; L =250; l = p *2; u =0.14; dm =d -( p /2) ; alpha = atan ( l /( %pi * dm ) ) ; phi = atan ( u ) ; T = dm * tan ( alpha + phi ) /2; M=F*L; P = M / T *10^ -3; // p r i n t i n g d a t a i n s c i l a b o / p window printf ( ”P i s %0 . 1 f kN ” ,P ) ;

Scilab code Exa 16.6 PS6 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

// sum 16−6 clc ; clear ; d =52; W =2.2*10^3; p =8; r1 =15; r2 =30; rm =( r1 + r2 ) /2; u1 =0.15/ cosd (14.5) ; dm =d -( p /2) ; alpha = atan ( p /( %pi * dm ) ) ; phi = atan ( u1 ) ; Ts = W * dm * tan ( alpha + phi ) /2; u2 =0.12; 123

16 17 18 19 20 21 22 23 24 25 26

Tc = u2 * W * rm ; T =10^ -3*( Ts + Tc ) ; N =40; w =2* %pi * N /60; P = T * w *10^ -3; To = W * dm /2* tan ( alpha ) ; n = To /( T *10^3) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”P i s %0 . 2 f KW ” ,P ) ; printf ( ” \n n i s %0 . 4 f ” ,n ) ;


// sum 16−7 clc ; clear ; alpha = atan (2*0.2/( %pi *0.9) ) ; u1 =0.15; phi = atan ( u1 ) ; P =200; L =250; Tt = P * L ; W =10*10^3; u2 =0.15; x = Tt / W ; d = x /0.1716; d =30; p =6; dr =0.8* d ; d =24; p =5; dr =d - p ; dm =d -( p /2) ;

124

22 23 24

// p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” d i s %0 . 0 f mm ” ,d ) ; printf ( ” \n p i s %0 . 0 f mm ” ,p ) ;

Scilab code Exa 16.8 PS8 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

// sum 16−8 clc ; clear ; FOS =3; sigut =380; Ta =0.577* sigut / FOS ; d =25; Tus =460; Ps = %pi * d * Tus ; siga =127; dr = sqrt ( Ps *4/( %pi * siga ) ) ; d =30; p =6; dr =d - p ; dm =d -( p /2) ; u1 =0.15; alpha = atan ( p *2/( %pi * dm ) ) ; phi = atan ( u1 ) ; T = Ps * dm * tan ( alpha + phi ) /2; T1 =16* T /( %pi * dr ^3) ; sigc =4* Ps /( %pi * dr ^2) ; sigmax = sigc /2+ sqrt (( sigc /2^2) +( T1 ^2) ) ; Tmax = sqrt (( sigc /2^2) +( T1 ^2) ) ; n = tan ( alpha ) / tan ( alpha + phi ) ; Uo = Ps /2; Ui = Uo / n ; wav = %pi /2; wmax =2* wav ; I = Ui *2/ wmax ^2; 125

30 31 32 33 34 35 36 37 38 39 40 41 42 43

k =0.4; Ir =0.9* I *10^ -3; m = Ir / k ^2; R =0.4; rho =7200; a = sqrt ( m /(2* %pi * R * rho ) ) ; T = T *10^ -3; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”T i s %0 . 3 f Nm ” ,T ) ; printf ( ” \n n i s %0 . 4 f ” ,n ) ; printf ( ” \n a i s %0 . 5 f mm ” ,a ) ; // The d i f f e r e n c e i n t h e a n s w e r s o f T i s due t o rounding −o f f o f v a l u e s .

126

Chapter 17 SLIDING CONTACT BEARINGS

Scilab code Exa 17.1 SCB1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

// sum 17−1 clc ; clear ; Ta =22; u =7/10^9; nj =20; r =25; l =2* r ; Ao =30000; Uo =15.3/10^3; c =0.025; // s p e c i f i c w e i g h t o f t h e m a t e r i a l i s r h o rho =8.46*(10^ -6) ; Cp =179.8; Tf = Ta +(16* %pi ^3* u * nj ^2* l * r ^3/( Uo * Ao * c ) ) ; // avg mean f i l m t e m p e r a t u r e i s Tav Tav =( Tf - Ta ) /2; x = l * c * rho * %pi * r * nj * Cp *10^3; y = Ao * Tav * Uo ; 127

20 21 22 23 24

delT = y / x ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”Tav i s %0 . 2 f degC ” , Tav ) ; printf ( ” \n d e l T i s %0 . 1 f degC ” , delT ) ;

Scilab code Exa 17.2 SCB2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

// sum 17−2 clc ; clear ; l =60; d =60; r = d /2; ho =0.008; c =0.04; S =0.0446; nj =1260/60; W =6000; p = W /( l * d ) ; u = S *( c / r ) ^2* p / nj ; u = u *10^9; // p r i n t i n g d a t a i n s c i l a b o / p window printf ( ” u i s %0 . 3 f cP ” ,u ) ;

Scilab code Exa 17.3 SCB3 1 // sum 17−3 2 clc ; 3 clear ; 4 d =60; 5 r =30;

128

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

l =60; c =0.8*10^ -3* r ; ho =0.2* c ; W =21000/2; p = W /( l * d ) ; S =0.0446; nj =1440/60; u = S *( c / r ) ^2* p / nj ; u = u *10^9; // s i n c e Q/ ( r ∗ n j ∗ l ) =4.62 Q =4.62* r * c * nj * l ; Q = Q *60/10^6; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” u i s %0 . 3 f cP ” ,u ) ; printf ( ” \n Q i s %0 . 4 f lpm ” ,Q ) ;

Scilab code Exa 17.4 SCB4 // sum 17−4 clc ; clear ; l =60; d =60; r = d /2; W =3000; p = W /( l * d ) ; u =30*10^ -9; c =0.06; nj =1440/60; S =( r / c ) ^2* u * nj / p ; // For r a t i o l / d =1 , v a l u e s o f d i f f e r e n t p a r a m e t e r s are given in matrix A corresponding to S 14 A =[1 0.264 0.6 5.79 3.99 15 1 0.121 0.4 3.22 4.33]; 1 2 3 4 5 6 7 8 9 10 11 12 13

129

16 // l e t ho / c=x 17 x =( A (1 ,3) ) -(( A (1 ,3) -( A (2 ,3) ) ) *(( A (1 ,2) ) -S ) /(( A (1 ,2) ) 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

-( A (2 ,2) ) ) ) ; // l e t y= ( r / c ) ∗ f=CFV y =( A (1 ,4) ) -(( A (1 ,4) -( A (2 ,4) ) ) *(( A (1 ,2) ) -S ) /(( A (1 ,2) ) -( A (2 ,2) ) ) ) ; // l e t z=Q/ ( r ∗ c ∗ n j ∗ l )=FV z =( A (1 ,5) ) -(( A (1 ,5) -( A (2 ,5) ) ) *(( A (1 ,2) ) -S ) /(( A (1 ,2) ) -( A (2 ,2) ) ) ) ; f=y*c/r; ho = x * c ; Q = z * r * c * nj * l ; Q = Q *60/10^6; delT =8.3* p * y / z ; // l e t power l o s t i n f r i c t i o n be Pf Pf =2* %pi * nj * f * W * r /10^6; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” f i s %0 . 5 f ” ,f ) ; printf ( ” \n ho i s %0 . 3 f mm ” , ho ) ; printf ( ” \n Q i s %0 . 3 f lpm ” ,Q ) ; printf ( ” \n d e l T i s %0 . 1 f degC ” , delT ) ; printf ( ” \n Pf i s %0 . 4 f KW ” , Pf ) ;

Scilab code Exa 17.5 SCB5 1 2 3 4 5 6 7 8 9

// sum 17−5 clc ; clear ; W =22000; nj =960/60; p =2.4; u =20*10^ -9; d = sqrt ( W / p ) ; d =96; 130

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

r = d /2; l=d; S =0.0446; pact = W /( l * d ) ; // x=r / c ; x = sqrt ( S * pact /( u * nj ) ) ; c=r/x; ho =0.2* c ; Q = r * c * nj * l *4.62; Q = Q *60/10^6; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” d i s %0 . 0 f mm ” ,d ) ; printf ( ” \n l i s %0 . 0 f mm ” ,l ) ; printf ( ” \n ho i s %0 . 4 f mm ” , ho ) ; printf ( ” \n Q i s %0 . 3 f lpm ” ,Q ) ; // The d i f f e r e n c e i n a n s w e r t o Q i s due t o r o u n d i n g −o f f the value of c .

Scilab code Exa 17.6 SCB6 1 2 3 4 5 6 7 8 9 10 11 12 13

// sum 17−6 clc ; clear ; W =400*10^3; Ro =200; Ri =160; ho =0.1; t =150; // s p e c i f i c g r a v i t y i s r h o rho =0.86; pi =2* W * log ( Ro / Ri ) /( %pi *( Ro ^2 - Ri ^2) ) ; zk =(0.22* t ) -(180/ t ) ; z = rho * zk ; 131

14 u = z /(10^9) ; 15 Q = %pi * pi * ho ^3/(6* u * log ( Ro / Ri ) ) ; 16 Q = Q *60/10^6; 17 18 // p r i n t i n g d a t a i n s c i l a b o /p window 19 printf ( ” p i i s %0 . 3 f MPa ” , pi ) ; 20 printf ( ” \n Q i s %0 . 2 f lpm ” ,Q ) ; 21 22 // The d i f f e r e n c e i n a n s w e r t o Q i s due t o r o u n d i n g

−o f f of values .

Scilab code Exa 17.7 SCB7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

// sum 17−7 clc ; clear ; // l e t number o f p a d s be n n =4; W =100*10^3; Ro =125; Ri =50; t =200; ho =0.15; pi =2* W * log ( Ro / Ri ) /( %pi *( Ro ^2 - Ri ^2) ) ; zk =(0.22* t ) -(180/ t ) ; // s p e c i f i c g r a v i t y i s r h o rho =0.86; z = rho * zk ; u = z /(10^9) ; Q = %pi * pi * ho ^3/(6* u * log ( Ro / Ri ) ) ; Q = Q *60/10^6; // p r i n t i n g d a t a i n s c i l a b o / p window printf ( ” p i i s %0 . 2 f MPa ” , pi ) ; printf ( ” \n Q i s %0 . 3 f lpm ” ,Q ) ; 132

133

Chapter 18 ROLLING BEARINGS

Scilab code Exa 18.1 RB1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

// sum 18−1 clc ; clear ; Pr =16*10^3; u =0.0011; F = u * Pr ; r =20*10^ -3; // L e t f r i c t i o n a l moment be M M=F*r; N =1440; w =2* %pi * N /60; Pf = M * w ; // p r i n t i n g d a t a i n s c i l a b o / p window printf ( ” Pf i s %0 . 2 f W ” , Pf ) ;

Scilab code Exa 18.2 RB2

134

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

// sum 18−2 clc ; clear ; C =5590; Ca =2500; Pa =625; Pr =1250; V =1; X =0.56; Y =1.2; P1 =( X * V * Pr ) +( Y * Pa ) ; L1 =( C / P1 ) ^3; V =1.2; P2 =( X * V * Pr ) +( Y * Pa ) ; L2 =( C / P2 ) ^3; // p r i n t i n g d a t a i n s c i l a b o / p window printf ( ” L1 i s %0 . 1 f m i l l i o n r e v o l u t i o n s printf ( ” \n L2 i s %0 . 2 f m i l l i o n r e v o l t i o n s ;

Scilab code Exa 18.4 RB4 1 2 3 4 5 6 7 8 9 10 11

// sum 18−4 clc ; clear ; P =20*10^3; Co =22400; C =41000; Ln =( C / P ) ^3; Lh = Ln *10^6/(720*60) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”Lh i s %0 . 3 f h r s ” , Lh ) ;

135

” , L1 ) ; ” , L2 )

Scilab code Exa 18.5 RB5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

// sum 18−5 clc ; clear ; R1x =120; R1y =250; R2x =300; R2y =400; Lh =8000; N =720; Ln = Lh *60* N *10^ -6; R1 = sqrt ( R1x ^2+ R1y ^2) ; R2 = sqrt ( R2x ^2+ R2y ^2) ; // L e t l o a d f a c t o r be Ks Ks =1.5; P1 = R1 * Ks ; P2 = R2 * Ks ; C1 = P1 *( Ln ^(1/3) ) ; C2 = P2 *( Ln ^(1/3) ) ; // l e t d e s i g n a t i o n , d , D, B , C a t b e a r i n g B1 be De1 , d1 , D1 , B1 , C1 d1 =25; D1 =37; B1 =7; C1 =3120; De1 =61805; // l e t d e s i g n a t i o n , d , D, B , C a t b e a r i n g B2 be De2 , d2 , D2 , B2 , C2 d2 =25; D2 =47; B2 =8; C2 =7620; De2 =16005; 136

31 32 33 34 35 36 37 38 39 40 41 42 43 44

// p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” D e s i g n a t i o n o f B e a r i n g B1 i s %0 . 0 f De1 ) ; printf ( ” \n d1 i s %0 . 0 f mm ” , d1 ) ; printf ( ” \n D1 i s %0 . 0 f mm ” , D1 ) ; printf ( ” \n B1 i s %0 . 0 f mm ” , B1 ) ; printf ( ” \n C1 i s %0 . 0 f N ” , C1 ) ; printf ( ” \n D e s i g n a t i o n o f B e a r i n g B2 i s %0 . 0 f ” , De2 ) ; printf ( ” \n d2 i s %0 . 0 f mm ” , d2 ) ; printf ( ” \n D2 i s %0 . 0 f mm ” , D2 ) ; printf ( ” \n B2 i s %0 . 0 f mm ” , B2 ) ; printf ( ” \n C2 i s %0 . 0 f N ” , C2 ) ;

disp ( ’ B e a r i n g 6 1 8 0 5 a t B1 and 1 6 0 0 5 a t B2 can be installed . ’)


”,

// sum 18−6 clc ; clear ; P =7500; N =1440; w =2* %pi * N /60; T=P/w; r =0.2; // L e t T1−T2=t t=T/r; T2 = t /2.5; T1 =3.5* T2 ; R =0.125; Ft = T / R ; Fr = Ft * tan (20* %pi /180) ; 137

16

17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43

// RD & RA a r e r e a c t i o n f o r c e s c a l c u l a t e d i n v e r t i c a l and h o r i z o n t a l d i r e c t i o n s from FBD by force equilibrium RDv =186.5; RAv =236.2; RDh =36.2; RAh =108.56; RA = sqrt ( RAv ^2+ RAh ^2) ; RD = sqrt ( RDv ^2+ RDh ^2) ; Ks =1.4; P1 = RA * Ks ; P2 = RD * Ks ; // l e t d e s i g n a t i o n , d , D, B , C a t b e a r i n g B1 be De1 , d1 , C1 d1 =25; C1 =3120; De1 =61805; // l e t d e s i g n a t i o n , d , D, B , C a t b e a r i n g B2 be De2 , d2 , C2 d2 =25; C2 =2700; De2 =61804; L1 =( C1 / P1 ) ^3; Lh1 = L1 *10^6/(720*60) ; L2 =( C2 / P2 ) ^3; Lh2 = L2 *10^6/(720*60) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” Lh1 i s %0 . 0 f h r s ” , Lh1 ) ; printf ( ” \n Lh2 i s %0 . 0 f h r s ” , Lh2 ) ; // I n c o r r e c t v a l u e o f P2 i s t a k e n i n t h e book w h i l e c a l c u l a t i n g L2 .

Scilab code Exa 18.7 RB7 1

// sum 18−7 138

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

clc ; clear ; P =3500; Lh =6000; N =1400; R98 =0.98; R90 =0.9; L98 = Lh *60* N /10^6; x =( log (1/ R98 ) / log (1/ R90 ) ) ^(1/1.17) ; L90 = L98 / x ; C = P * L90 ^(1/3) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”C i s %0 . 0 f N ” ,C ) ; // The d i f f e r e n c e i n t h e v a l u e o f C i s due t o rounding −o f f o f value o f L .


// sum 18−8 clc ; clear ; n =3; P =3; // L e t R e l i a b i l i t y o f s y s t e m be R R =0.83; L94 =6; R94 =( R ) ^(1/ n ) ; x =( log (1/ R94 ) / log (1/0.90) ) ^(1/1.17) ; L90 = L94 / x ; C = P * L90 ^(1/3) ; // p r i n t i n g d a t a i n s c i l a b o / p window printf ( ”C i s %0 . 3 f kN ” ,C ) ; 139

16 17

// The d i f f e r e n c e i n t h e v a l u e o f C i s due t o rounding −o f f o f value o f L .

Scilab code Exa 18.9 RB9 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

// sum 18−9 clc ; clear ; P1 =3000; P2 =4000; P3 =5000; N1 =1440; N2 =1080; N3 =720; t1 =1/4; t2 =1/2; t3 =1/4; n1 = N1 * t1 ; n2 = N2 * t2 ; n3 = N3 * t3 ; N =( n1 + n2 + n3 ) ; Pe =((( n1 * P1 ^3) +( n2 * P2 ^3) +( n3 * P3 ^3) ) / N ) ^(1/3) ; Lh =10*10^3; L = Lh *60* N /10^6; C = Pe * L ^(1/3) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”C i s %0 . 0 f N ” ,C ) ; // The d i f f e r e n c e i n t h e v a l u e o f C i s due t o r o u n d i n g − o f f o f v a l u e o f Pe

140

Scilab code Exa 18.10 RB10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

// sum 18 −10 clc ; clear ; Co =695; C =1430; Pa1 =200; Pr1 =600; x = Pa1 / Co ; y = Pa1 / Pr1 ; e =0.37+((0.44 -0.37) *0.038/0.28) ; X =1; Y =0; P1 =600; Pa2 =120; Pr2 =300; X =0.56; Y =1.2 -(0.2*0.042/0.12) ; P2 =( X * Pr2 ) +( Y * Pa2 ) ; N1 =1440; N2 =720; t1 =2/3; t2 =1/3; n1 = N1 * t1 ; n2 = N2 * t2 ; N =( n1 + n2 ) ; Pe =((( n1 * P1 ^3) +( n2 * P2 ^3) ) / N ) ^(1/3) ; L =( C / Pe ) ^3; Lh = L *10^6/( N *60) ; // p r i n t i n g d a t a i n s c i l a b o / p window printf ( ”Lh i s %0 . 2 f h r s ” , Lh ) ; // The d i f f e r e n c e i n t h e v a l u e o f Lh i s due t o r o u n d i n g − o f f o f v a l u e o f Pe

141

Chapter 19 FLYWHEEL

Scilab code Exa 19.1 F1 // sum 19−1 clc ; clear ; R =1200; b =300; t =150; N =500; m =7100*10^ -9* b * t ; Ar = b * t ; Aa = Ar /4; C =(20280/ t ^2) +0.957+( Ar / Aa ) ; w =2* %pi * N /60; V = w * R *10^ -3; siga =2*10^3* m * V ^2/( C * Aa *3) ; theta =30* %pi /180; alpha =30* %pi /180; x1 =10^3* m *( V ^2) /( b * t ) ; y1 = cos ( theta ) /(3* C * sin ( alpha ) ) ; z1 =2000* R *10^ -3/( C * t ) *((1/ alpha ) -( cos ( theta ) / sin ( alpha ) ) ) ; 20 sigrr1 = x1 *(1 - y1 + z1 ) ; 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

142

21 theta =0* %pi /180; 22 x2 =10^3* m *( V ^2) /( b * t ) ; 23 y2 = cos ( theta ) /(3* C * sin ( alpha ) ) ; 24 z2 =2000* R *10^ -3/( C * t ) *((1/ alpha ) -( cos ( theta ) / sin (

alpha ) ) ) ; 25 sigrr2 = x2 *(1 - y2 - z2 ) ; 26 27 28 29 30 31 32

// p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” a x i a l s t r e s s i s %0 . 2 f MPa ” , siga ) ; printf ( ” \n t e n s i l e s t r e s s f o r t h e t a =30 deg i s %0 . 1 f MPa ” , sigrr1 ) ; printf ( ” \n t e n s i l e s t r e s s f o r t h e t a =0deg i s %0 . 2 f MPa ” , sigrr2 ) ; // The d i f f e r e n c e i n t h e v a l u e o f s i g r r 1 and s i g r r 2 i s due t o r o u n d i n g − o f f o f v a l u e s .

Scilab code Exa 19.2 F2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

// sum 19−2 clc ; clear ; N =350; theta1 = asin ( sqrt ((3 -0.6) /4) ) ; theta1 = theta1 *180/ %pi ; theta2 =(180) - theta1 ; // Ti =16000+6000∗ s i n d ( 3 ∗ t h e t a ) ; //To=16000+3600∗ s i n d ( t h e t a ) ; a = -3600*( cosd ( theta2 ) - cosd ( theta1 ) ) ; b =2000*( cosd (3* theta2 ) - cosd (3* theta1 ) ) ; c=a+b; delU = c ; Ks =0.05; w =2* %pi * N /60; I = delU /( Ks * w ^2) ; 143

17 18 19 20 21 22 23 24 25 26 27 28

V =25; Ir = I *0.95; R=V/w; Mr = Ir / R ^2; rho =7150; t = sqrt ( Mr *(10^6) /(2* %pi * R *2* rho ) ) ; b =2* t ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” t i s %0 . 2 f mm ” ,t ) ; printf ( ” \n b i s %0 . 2 f mm ” ,b ) ; printf ( ” \n R i s %0 . 3 f m ” ,R ) ;

Scilab code Exa 19.3 F3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

// sum 19−3 clc ; clear ; N =300; Ks =0.03; rho =7150; Kr =0.9; w =2* %pi * N /60; WD =(300*2* %pi ) +(4* %pi *200/4) ; Tm =400; delU = %pi *200/16; Ir = Kr * delU /( w ^2* Ks ) ; R = Ir /( rho *1.5*0.1*0.1*2* %pi ) ; R = R ^(1/5) ; t =0.1* R *1000; b =1.5* t ; // p r i n t i n g d a t a i n s c i l a b o / p window printf ( ” t i s %0 . 2 f mm ” ,t ) ; printf ( ” \n b i s %0 . 2 f mm ” ,b ) ; 144

21

printf ( ” \n R i s %0 . 4 f m

” ,R ) ;

Scilab code Exa 19.4 F4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

// sum 19−4 clc ; clear ; d =20; t =12; Tus =450; Pmax = %pi * d * t * Tus ; WD = Pmax * t /2*10^ -3; n =0.95; Wi = WD / n ; delU =5* Wi /6; N =300; w =2* %pi * N /60; Ks =0.2; I = delU /( Ks * w ^2) ; Ir = I *0.9; R =0.5; m = Ir / R ^2; rho =7150; t = sqrt ( m *10^6/( rho *2* %pi * R *2) ) ; b =2* t ; // p r i n t i n g d a t a i n s c i l a b o / p window printf ( ” t i s %0 . 1 f mm ” ,t ) ; printf ( ” \n b i s %0 . 1 f mm ” ,b ) ; printf ( ” \n R i s %0 . 1 f m ” ,R ) ;

Scilab code Exa 19.5 F5 145

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

// sum 19−5 clc ; clear ; U =(500*2* %pi ) +(3* %pi *500/2) ; Tm = U /(2* %pi ) ; delU =2.25* %pi *125/2; Ks =0.1; N =250; w =2* %pi * N /60; I = delU /( Ks * w ^2) ; t =0.03; rho =7800; R =( I *2/( %pi * rho * t ) ) ^(1/4) ; V=R*w; v =0.3; sigmax = rho * V ^2*(3+ v ) /8*10^ -6; // p r i n t i n g d a t a i n s c i l a b o / p window printf ( ”R i s %0 . 3 f m ” ,R ) ; printf ( ” \n s i g m a x i s %0 . 2 f MPa ” , sigmax ) ;

Scilab code Exa 19.6 F6 // sum 19−6 clc ; clear ; N =1.5*8*60; l =200; t =1.5/2; W =350*10^3; WD =0.15* l * W *10^ -6; n =0.9; // s i n c e f r i c t i o n a l o f s y s t e m i s 90% 10 Wi = WD / n ; 11 L =400; 1 2 3 4 5 6 7 8 9

effect

146

i s 10%, e f f c i e n c y

12 13 14 15 16 17 18 19 20 21 22 23 24 25

delU =( L -(0.15* l ) ) /( L ) *10^3* Wi ; Ks =0.12; w =2* %pi * N /60; I = delU /( Ks * w ^2) ; Ir = I *0.9; R =0.7; m = Ir / R ^2; rho =7150; t = sqrt ( m *10^6/( rho *2* %pi * R *1.5) ) ; b =1.5* t ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” t i s %0 . 1 f mm ” ,t ) ; printf ( ” \n b i s %0 . 1 f mm ” ,b ) ;

Scilab code Exa 19.7 F7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

// sum 19−7 clc ; clear ; N =144; // L e t n be no . o f p u n c h e s / min n =8; // L e t t be t i m r f o r 1 punch t =60/ n ; theta = N /60*2* %pi *0.6; T =2.1; U = T * theta ; // L e t U1 be r e v o l u t i o n o f c r a n k s h a f t i n t s e c U1 = t * N /60*2* %pi ; delU =( U1 - theta ) / U1 * U *10^3; w =2* %pi *1440/60; Ks =0.1; I = delU /( Ks * w ^2) ; Ir = I *0.9; 147

19 20 21 22 23 24 25 26 27 28 29 30 31

rho =7100; R = Ir /( rho *0.2*0.1*2* %pi ) ; R = R ^(1/5) ; t =0.1* R *1000; b =0.2* R *10^3; t =40; b =80; R =400; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” t i s %0 . 0 f mm ” ,t ) ; printf ( ” \n b i s %0 . 0 f mm ” ,b ) ; printf ( ” \n R i s %0 . 0 f mm ” ,R ) ;

148

Chapter 20 FLAT BELT DRIVE

Scilab code Exa 20.1 FBD1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

// sum 20−1 clc ; clear ; b =0.2; P =50*10^3; v =20; m =1.95; d =0.3; D =0.9; C =5.8; u =0.4; // L e t d e n s i t y be r h o rho =1000; E =40; // L e t T1−T2 = T T=P/v; // L e t t h e c e n t r i f u g a l t e n s i o n be Tc Tc = m * v ^2; alpha = asind (( D + d ) /(2* C ) ) ; theta =180+(2* alpha ) ; theta = theta * %pi /180; 149

22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

x = exp ( u * theta ) ; T2 =(((1 - x ) * Tc ) -T ) /(1 - x ) ; //T1=T+T2 ; T1 = T + T2 ; t = m /( b * rho ) *10^3; // L e t maximum s t r e s s be s i g m a x b =200; d =300; sigmax =( T1 /( b * t ) +(( E * t ) / d ) ) ; sigmin =( T2 /( b * t ) ) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”T1 i s %0 . 1 f N ” , T1 ) ; printf ( ” \n T2 i s %0 . 1 f N ” , T2 ) ; printf ( ” \n t i s %0 . 2 f mm ” ,t ) printf ( ” \n t h e t a i s %0 . 2 f r a d ” , theta ) printf ( ” \n s i g m a x i s %0 . 2 f N/mmˆ2 ” , sigmax ) ; printf ( ” \n s i g m i n i s %0 . 3 f N/mmˆ2 ” , sigmin ) ; // The a n s w e r f o r T1 i s m i s c a l c u l a t e d i n t h e book .

Scilab code Exa 20.2 FBD2 1 2 3 4 5 6 7 8 9 10 11 12

// sum 20−2 clc ; clear ; P =12*10^3; d =0.2; D =0.5; C =2; sigmax =2*10^6; t =8*10^ -3; // L e t d e n s i t y be r h o rho =950; u =0.38; 150

13 14 15 16 17 18 19 20 21 22 23 24 25 26

N =1500; // L e t a n g l e o f c o n t a c t = t h e t a d thetad =180 -(2* asind (( D - d ) /(2* C ) ) ) ; thetad = thetad * %pi /180; thetaD =(2* %pi ) - thetad ; v =(2* %pi * N * d ) /(60*2) ; // L e t T1−T2=T T=P/v; x = exp ( u * thetad ) ; b =( T * x ) /((1 - x ) * t *(( rho * v ^2) -( sigmax ) ) ) ; b = b *10^3; // L e t b r e a d t h o f t h e p u l l e y be b1 b1 = b *10^3+13; // T a b l e 20−3 L = sqrt ((4* C ^2) -( C *( D - d ) ^2) ) +(( D * thetaD ) +( d * thetad ) ) /2; 27 // L e t p u l l e y crown f o r d=h1 , D=h2 28 h1 =0.6; // T a b l e 20−4 29 h2 =1; 30 31 32 33 34 35 36

// p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” b i s %0 . 2 f mm ” ,b ) printf ( ” \n L i s %0 . 2 f m ” ,L ) printf ( ” \n b1 i s %0 . 2 f mm ” , b1 ) ; printf ( ” \n h1 i s %0 . 1 f mm ” , h1 ) ; printf ( ” \n h2 i s %0 . 1 f mm ” , h2 ) ;

Scilab code Exa 20.3 FBD3 1 2 3 4 5 6 7

// sum 20−3 clc ; clear ; P =11; N =1440; n =480; C =2.4; 151

8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

// L e t power t r a n s m i t t e dfrom h i g h s p e e d b e l t =P1 P1 =0.0118; V =5; Ks =1.2; v =15; d = v *10^3*60/(2* %pi * N ) ; d =0.2; D=N/n*d; // L e t a n g l e o f c o n t a c t =t h e t a A thetaA =180 -(2* asind (( D - d ) /(2* C ) ) ) ; thetaA = thetaA * %pi /180; v =(2* %pi * N * d ) /(60*2) ; // L e t t h e a r c o f c o n t a c t c o r r e c t i o n f a c t o r be Ka Ka =1.05; Pd = P * Ka * Ks ; // L e t c o r r e c t e d l o a d r a t i n g=Pc Pc = P1 * v / V ; b = Pd /( Pc *4) ; thetaB =(2* %pi ) - thetaA ; L = sqrt ((4* C ^2) -((D - d ) ^2) ) +(( d * thetaA /2) +( D * thetaB ) /2) ;

// p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” v i s %0 . 2 f m/ s ” ,v ) printf ( ” \n b i s %0 . 3 f mm ” ,b ) printf ( ” \n L i s %0 . 4 f m ” ,L ) ;

Scilab code Exa 20.4 FBD4 1 // sum 20−4 2 clc ; 3 clear ; 4 N =1440; 5 i =2.5;

152

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

C =3600; // l e t l o a d f a c t o r be LF LF =1.3; P =12*10^3; n=N/i; V =16; d = V *10^3*60/(2* %pi * N ) ; d =220; D=d*i; V =2* %pi * N * d /(2*60*1000) ; v =5; // L e t power t r a n s m i t t e dfrom h i g h s p e e d b e l t =P1 P1 =0.0118; // L e t LR be t h e l o a d r a t i n g o f b e l t LR = P1 / v * V ; theta =180+(2* asind (( D - d ) /(2* C ) ) ) ; theta = theta * %pi /180; // L e t Arc o f c o n t a c t c o n n e c t i o n f a c t o r be CF CF =1 -(0.03/2) ; Pd = P * LF * CF ; b = Pd /( LR *5) ; b =80; L = sqrt ((4* C ^2) -( D + d ) ^2) +( theta *( D + d ) /2) ; L = L *10^ -3; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”V i s %0 . 1 f m/ s ” ,V ) printf ( ” \n b i s %0 . 0 f mm ” ,b ) printf ( ” \n L i s %0 . 3 f m ” ,L ) ;

Scilab code Exa 20.5 FBD5 1 // sum 20−5 2 clc ; 3 clear ;

153

4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

i =3.6; N =1440; d =220; Ks =1.2; Kf =1.1; C =5000; u =0.8; D=i*d; // From t a b l e 20 −7 , t h e f o l l o w i n g d a t a i s a v a i l a b l e t =5; b =120; Fa =30.64; // l e t w e i g h t d e n s i t y be w w =0.106*10^5; Cp =0.71; // From t a b l e 20−6 Cv =1; T1 = Fa * b * t * Cp * Cv ; m = w * b * t /10^6; V =2* %pi * N * d /(2*60*1000) ; Tc = m * V ^2/9.81; theta =180+(2* asind (( D - d ) /(2* C ) ) ) ; theta = theta * %pi /180; x = u * theta ; T2 = Tc +(( T1 - Tc ) / exp ( x ) ) ; Pd =( T1 - T2 ) * V *10^ -3; P = Pd /( Ks * Kf ) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”V i s %0 . 2 f m/ s ” ,V ) ; printf ( ” \n Pd i s %0 . 2 f KW ” , Pd ) ; printf ( ” \n P i s %0 . 1 f KW ” ,P ) ; // The v a l u e o f T2 i s c a l c u l a t e d i n c o r r e c t l y , t h e r e f o r e there i s a d i f f e r e n c e in the values o f Pd and P .

154

Scilab code Exa 20.6 FBD6 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

// sum 20−6 clc ; clear ; i =2.5; C =4500; N =960; P =20*10^3; Ks =1.15; Kf =1.10; t =8; // l e t w e i g h t d e n s i t y be w w =0.110*10^5; m = w * t /10^6; Fa =8.75; d =200; D=i*d; u =0.4; V =2* %pi * N * d /(2*60*1000) ; Pd = P * Ks * Kf ; Cp =1; Cv =0.6; // t o f i n d b T1 = Fa * t * Cp * Cv ; Tc = m * V ^2/9.81; theta =180 -(2* asind (( D - d ) /(2* C ) ) ) ; theta = theta * %pi /180; x = u * theta ; T2 = Tc +(( T1 - Tc ) / exp ( x ) ) ; T = Pd / V ; b = T /( T1 - T2 ) ; // b =90; L = sqrt ((4* C ^2) -( D + d ) ^2) +( theta *( D + d ) /2) ; 155

33 L = L *10^ -3; 34 35 // p r i n t i n g d a t a i n s c i l a b o /p window 36 printf ( ”V i s %0 . 2 f m/ s ” ,V ) 37 printf ( ” \n b i s %0 . 3 f mm ” ,b ) 38 printf ( ” \n L i s %0 . 3 f m ” ,L ) ;

Scilab code Exa 20.7 FBD7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

// sum 20−7 clc ; clear ; b =160; t =7; P =3*10^3; Ks =1.2; d =160; N =1440; D =480; C =2400; w =11200; u =0.4; Fa =7.2; m = w * b * t /10^6; V =2* %pi * N * d /(2*60*1000) ; Tc = m * V ^2/9.81; Cp =0.6; // from t a b l e 20−6 Cv =0.98; // from t a b l e 20−7 Ta = Fa * b * Cp * Cv ; T=P/V; theta =180 -(2* asind (( D - d ) /(2* C ) ) ) ; theta = theta * %pi /180; x = u * theta ; //T2=Tc +((T1−Tc ) / exp ( x ) ) ; T2 =( T +(( exp ( x ) * Tc ) - Tc ) ) /( exp ( x ) -1) ; 156

27 28 29 30 31 32 33 34 35 36 37 38 39

T1 = T + T2 ; Kf = Ta / T1 ; Pd = P * Ks * Kf ; Pd = Pd *10^ -3; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”Tc i s %0 . 0 f N ” , Tc ) ; printf ( ” \n T1 i s %0 . 2 f N ” , T1 ) ; printf ( ” \n T2 i s %0 . 2 f N ” , T2 ) ; printf ( ” \n Kf i s %0 . 2 f ” , Kf ) ; printf ( ” \n Pd i s %0 . 1 f KW ” , Pd ) ; // The d i f f e r e n c e i n v a l u e s o f T1 and T2 i s due t o rounding −o f f o f v a l u e s .

157

Chapter 21 V BELT DRIVE

Scilab code Exa 21.1 VBELT1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

// sum 21−1 clc ; clear ; P1 =12*10^3; d =0.3; D =0.9; C =0.9; A =230*10^ -6; // d e n s i t y i s r h o rho =1100; N =1500; //Maximum s t r e s s i s s i g sig =2.1*10^6; // s e m i g r o o v e a n g l e i s b b =20* %pi /180; u =0.22; m = rho * A ; v =2* %pi * N * d /(60*2) ; Tc = m * v ^2; T1 = A * sig ; // wrap a n g l e i s t h e t a A 158

22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

ang =( D - d ) /(2* C ) ; thetaA = %pi /180*(180 -(2* asind ( ang ) ) ) ; thetaB =((2* %pi ) - thetaA ) ; x = u * thetaB ; T2 = Tc +(( T1 - Tc ) / exp ( x ) ) ; P2 =( T1 - T2 ) * v ; n = P1 / P2 ; n =3; // ( r o u n d i n g o f f t o n e a r e s t w h o l e number ) // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”Tc i s %0 . 1 f N ” , Tc ) ; printf ( ” \n T1 i s %0 . 0 f N ” , T1 ) ; printf ( ” \n T2 i s %0 . 1 f N ” , T2 ) ; printf ( ” \n P2 i s %0 . 0 f W ” , P2 ) ; printf ( ” \n n i s %0 . 0 f ” ,n ) ;

Scilab code Exa 21.2 VBELT2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

// sum 21−2 clc ; clear ; D =0.6; d =0.3; C =0.9; m =0.193; n =2; N =1500; u =0.3; v =2* %pi * N /60* d /2; P =150*10^3; Tc = m * v ^2; // l e t T1−T2=T T = P /( n * v ) ; thetaA = %pi /180*(180 -(2* asind (( D - d ) /(2* C ) ) ) ) ; thetaB =((2* %pi ) - thetaA ) ; 159

// Groove a n g l e=b b =17.5* %pi /180; x = u * thetaA / sin ( b ) ; y = exp ( x ) ; c =( Tc *(1 - y ) ) ; T2 =( T +( Tc *(1 - y ) ) ) /( y -1) ; //T2=(T−y ) /Tc ; T1 = T + Tc ; Lp =2* sqrt (( C ^2) -((D - d ) /2) ^2) +( thetaA * d /2) +( thetaB * D /2) ; 27 v = sqrt ( T /(3* m ) ) ; 18 19 20 21 22 23 24 25 26

28 29 30 31 32 33 34 35 36 37

// p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”Tc i s %0 . 2 f N ” , Tc ) ; printf ( ” \n T1 i s %0 . 0 f N ” , T1 ) ; printf ( ” \n T2 i s %0 . 2 f N ” , T2 ) ; printf ( ” \n Lp i s %0 . 3 f m ” , Lp ) ; printf ( ” \n v i s %0 . 2 f m/ s ” ,v ) ; printf ( ” \ nThe d e s i g n a t i o n o f t h e b e l t i s B−3251−45 ”); // The d i f f e r e n c e i n v a l u e s o f T1 and T2 i s due t o rounding −o f f o f v a l u e s .

Scilab code Exa 21.3 VBELT3 1 2 3 4 5 6 7 8 9

// sum 21−3 clc ; clear ; C =1; m =0.35; d =0.25; P =22*10^3; // L e t t h e s m a l l e r p u l l e y d i a be n // L e t t h e l a r g e r p u l l e y d i a be N 160

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

n =1000; N =400; D=d*n/N; v =2* %pi * n * d /(60*2) ; Tc = m * v ^2; topwidth =22; h =14; bottomwidth = topwidth -(2* h * tand (20) ) ; A =( topwidth + bottomwidth ) /2* h ; // l e t a l l o w a b l e t e n s i o n be Ta Ta =2.2; T1 = A * Ta ; u =0.28; thetaA = %pi /180*(180 -(2* asind (( D - d ) /(2* C ) ) ) ) ; thetaB =((2* %pi ) - thetaA ) ; // Groove a n g l e=b=19 b =19* %pi /180; x = u * thetaA / sin ( b ) ; T2 = Tc +(( T1 - Tc ) / exp ( x ) ) ; n = P /(( T1 - T2 ) * v ) ; Lp =2* sqrt (( C ^2) -((D - d ) /2) ^2) +( thetaA * d /2) +( thetaB * D /2) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”Tc i s %0 . 2 f N ” , Tc ) ; printf ( ” \n T1 i s %0 . 1 f N ” , T1 ) ; printf ( ” \n T2 i s %0 . 1 f N ” , T2 ) ; printf ( ” \n n i s %0 . 1 f ” ,n ) ; printf ( ” \n Lp i s %0 . 3 f m ” , Lp ) ; printf ( ” \ nThe d e s i g n a t i o n o f t h e b e l t i s C−3414−47 ”); // d i f f e r e n c e i n v a l u e o f Lp i s due t o r o u n d i n g − o f f t h e v a l u e s o f t h e t a A and t h e t a B .

161

Scilab code Exa 21.4 VBELT4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

// sum 21−4 clc ; clear ; P =12*10^3; Ks =1.1; Pd =12*10^3* Ks ; N =1440; B =17; t =11; d =200; i =3; D=i*d; C =1000; // s i n c e a n g l e o f c o n t a c t t h e t a i s v e r y s m a l l theta =( D - d ) / C ; theta = theta *180/ %pi ; Kc =0.8; Lp =(2* C ) +( %pi /2*( D + d ) ) +((( D - d ) ^2) /(4* C ) ) ; Li = Lp -45; Ki =1.1; // l e t number o f v−b e l t s r e q u i r e d = n // l e t t h e KW r a t i n g be KWR KWR =5.23; n =( P * Ks ) /( KWR * Ks * Ki *10^3) ; n =3; // p r i n t i n g d a t a i n s c i l a b o / p window printf ( ”D i s %0 . 1 f mm ” ,D ) ; printf ( ” \n C i s %0 . 1 f mm ” ,C ) ; printf ( ” \n n i s %0 . 3 f ” ,n ) ; printf ( ” \n L i i s %0 . 0 f mm ” , Li )

Scilab code Exa 21.5 VBELT5 162

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

// sum 21−5 clc ; clear ; N =800; P =20; i =2.5; Ks =1.5; // ( from t a b l e f o r 3−5 h r s / day ) Pd = P * Ks ; d =250; D=i*d; C =1.6* D ; Lp =(2* C ) +( %pi *( D + d ) /2) +(( D - d ) ^2) /(4* C ) ; Li = Lp +74; Listd =3454; Lp = Listd +74; p =[1 -1.0768 0.0175]; function r = myroots ( p ) a = coeff ( p ,0) ; b = coeff ( p ,1) ; c = coeff ( p ,2) ; r (1) =( -b + sqrt ( b ^2 -4* a * c ) ) /(2* a ) ; r (2) =( -b - sqrt ( b ^2 -4* a * c ) ) /(2* a ) ; endfunction z = roots ( p ) ; KW =9.4; Kc =0.795; K1 =1; n = Pd /( KW * Kc * K1 ) ;

// p r i n t i n g d a t a i n s c i l a b o / p window printf ( ”C i s %0 . 4 f m ” ,z ) ; printf ( ” \n Pd i s %0 . 0 f KW ” , Pd ) ; printf ( ” \n n i s %0 . 2 f KW ” ,n ) ;

163

Chapter 22 FRICTION CLUTCHES

Scilab code Exa 22.1 FC221 // 22−1 clc ; clear ; u =0.28 // ( c o e f f i c i e n t o f f r i c t i o n ) N =300 // ( E n g i n e rpm ) I =7.2 Pmax = 0.1; R1 =70; R2 =110; n =2; // ( Both s i d e s o f t h e p l a t e a r e e f f e c t i v e ) // U s i n g Uniform Wear Theory // A x i a l F o r c e W W = n * %pi * Pmax * R1 *( R2 - R1 ) ; // F r i c t i o n a l Torque Tf Tf = u * W *( R1 + R2 ) /2*(10^ -3) ; w =2* %pi * N /60; // Power P P = Tf * w ; // Torque = Mass moment o f i n e r t i a ∗ a n g u l a r acceleration 20 a = Tf / I ;

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

164

21 t = w / a ; 22 // A n g l e t u r n e d by d r i v i n g 23 24 25 26 27 28 29 30 31 32

s h a f t t h e t a 1 t h r o u g h which slipping takes place theta1 = w * t ; // a n g l e t u r n e d by d r i v e n s h a f t t h e t a 2 theta2 = a *( t ^2) /2; E = Tf *( theta1 - theta2 ) ;

// p r i n t i n g printf ( ” \ nThe printf ( ” \ nThe printf ( ” \ nThe printf ( ” \ nThe ˆ2 ” ,a ) ; 33 printf ( ” \ nThe 34 printf ( ” \ nThe 35 36

d a t a i n s c i l a b o /p window f o r c e i s %0 . 1 f N” ,W ) ; Torque i s %0 . 2 f Nm” , Tf ) ; Power i s %0 . 0 f W” ,P ) ; a n g u l a r a c c e l e r a t i o n i s %0 . 2 f r a d / s e c t i m e t a k e n i s %0 . 1 f s e c ” ,t ) ; e n e r g y i s %0 . 2 f Nm” ,E ) ;

// The d i f f e r e n c e i n t h e a n s w e r o f e n e r g y ’E ’ i s due to rounding −o f f o f v a l u e s .

Scilab code Exa 22.2 FC222 1 2 3 4 5 6 7 8 9 10 11 12 13

// 22−2 clc ; clear ; // Power P P =80*10^3; // ( Watt ) N =3000; // ( E n g i n e rpm ) w =2* %pi *3*10^3/60 Tf =8*10^4/ w ; Rm =100; // (mm) p =0.2 //N/mmˆ2 u =0.22 // l e t w i d t h b= ( R1−R2 ) . // A x i a l f o r c e W=2∗ p i ∗Rm∗b∗p 165

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

// Torque T=u∗W∗Rm b = Tf /( u *2* %pi *( Rm ^2) * p ) ; b =50; R2 = Rm + b ; R1 = Rm - b ; Di =2* R1 ; // i n n e r d i a m e t e r W =2* %pi * Rm * b * p ; n =8; // n i s number o f s p r i n g s // A x i a l f o r c e p e r s p r i n g W1 W1 = W / n ; W1 = W1 +15; // a x i a l d e f l e c t i o n d e l del =10; // s t i f f n e s s k k = W1 / del ; // S p r i n g i n d e x C C =6; // number o f c o i l s n1 n1 =6; // Assumption d = k * n * n1 *( C ^3) /(80*10^3) ; d =11; // Rounding o f f t o n e a r e s t s t a n d a r d v a l u e D=C*d; clearance =2; FL =(( n1 +2) * d ) +(2* del ) + clearance ; // two end c o i l s , t h e r e f o r e (2∗ del ) // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” \ nThe printf ( ” \ nThe printf ( ” \ nThe printf ( ” \ nThe ; printf ( ” \ nThe printf ( ” \ nThe printf ( ” \ nThe printf ( ” \ nThe

Torque i s %0 . 2 f Nm” , Tf ) ; w i d t h i s %0 . 0 f mm” ,b ) ; f o r c e i s %0 . 0 f N” ,W ) ; A x i a l f o r c e p e r s p r i n g i s %0 . 0 f N” , W1 ) S p r i n g s t i f f n e s s i s %0 . 0 f N/mm” ,k ) ; S p r i n g w i r e d i a m e t e r i s %0 . 0 f mm” ,d ) ; Mean c o i l d i a m e t e r i s %0 . 0 f mm” ,D ) ; F r e e l e n g t h i s %0 . 0 f mm” , FL ) ;

166

Scilab code Exa 22.3 FC223 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

// 22−3 clc ; clear ; // Power P P =40*10^3 // Watt n1 =100; // rpm n2 =400; // rpm // Speed f a c t o r Ks Ks =0.9+0.001* n2 ; // C l u t c h power Pc Pc = P * n2 /( n1 * Ks ) *10^ -3; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” \ nThe Speed f a c t o r i s %0 . 1 f ” , Ks ) ; printf ( ” \ nThe c l u t c h p o w e r i s %0 . 0 f KW” , Pc ) ;

Scilab code Exa 22.4 FC224 1 2 3 4 5 6 7 8 9 10

// 22−4 clc ; clear ; // p l o t Torque v s Ro/ Ri // x=Ro/ Ri // A c c o r d i n g t o Uniform Wear t h e o r y x =[0 0.2 0.4 0.577 0.6 0.8 1.0]; n = length ( x ) ; for i =1: n Tf ( i ) =( x ( i ) -( x ( i ) ^3) ) ; 167

Figure 22.1: FC224 11 end 12 plot (x , Tf ) ; 13 xtitle ( ’ ’ , ’ Ro/ Ri ’ ) ; 14 ylabel ( ’ Tf ’ ) ; 15 xgrid (2) ;

Scilab code Exa 22.5 FC225 1 2 3 4 5 6 7 8

// 22−5 clc ; clear ; n1 =4; n2 =3; n =( n1 + n2 -1) ; R2 =80; R1 =50; 168

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

// A c c o r d i n g t o Uniform P r e s s u r e Theory //W=p∗ p i ∗ ( ( R2 ˆ 2 ) −(R1 ˆ 2 ) ) T=n ∗2∗ u∗W∗ ( ( R2 ˆ 3 ) −(R1 ˆ 3 ) ) / ( ( ( R2 ˆ 2 ) −(R1 ˆ 2 ) ) ∗ 3 ) P =15*10^3; N =1400; u =0.25; w =2* %pi * N /60; T=P/w; W = T *3*(( R2 ^2) -( R1 ^2) ) /( n *2* u *(( R2 ^3) -( R1 ^3) ) ) *10^3; p = W /( %pi *(( R2 ^2) -( R1 ^2) ) ) ; // p r i n t i n g printf ( ” \ nThe printf ( ” \ nThe printf ( ” \ nThe printf ( ” \ nThe

d a t a i n s c i l a b o /p window a n g u l a r s p e e d i s %0 . 2 f r a d / s e c ” ,w ) ; Torque i s %0 . 3 f Nm” ,T ) ; u n i f o r m p r e s s u r e i s %0 . 3 f N/mmˆ2 ” ,p ) ; F o r c e i s %0 . 1 f N” ,W ) ;

Scilab code Exa 22.6 FC226 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

//FRICTION CLUTCHES // PAGE 5 8 4 , 22−6 clc ; P =5*10^3; N =1000; w =2* %pi * N /60; Rm =50; pm =0.3; Tf = P / w ; u =0.1; R2 =50*2/(0.6+1) ; R1 =0.6* R2 ; // A c c o r d i n g t o u n i f o r m Wear t h e o r y W = pm * Rm *( R2 - R1 ) *2* %pi ; n = Tf *(10^3) /( u * W * Rm ) ; pmax = pm * Rm / R1 ; 169

17 18 19 20 21 22 23

// p r i n t i n g printf ( ” \ nThe printf ( ” \ nThe printf ( ” \ nThe printf ( ” \ nThe printf ( ” \ nThe ” ,n ) ; 24 printf ( ” \ nThe

d a t a i n s c i l a b o /p window a n g u l a r s p e e d i s %0 . 2 f r a d / s e c ” ,w ) ; Torque i s %0 . 3 f Nm” , Tf ) ; I n n e r r a d i u s i s %0 . 1 f mm” , R1 ) ; Outer r a d i u s i s %0 . 1 f mm” , R2 ) ; number o f c o n t a c t i n g s u r f a c e s i s %0 . 0 f max . p r e s s u r e i s %0 . 1 f N/mmˆ2 ” , pmax ) ;

Scilab code Exa 22.7 FC227 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

// 22−7 clc ; clear ; P =12*10^3; N =750 // Speed=N w =2* %pi * N /60; Tf = P / w ; p1 =0.12; a =12.5; // Semi−c o n e a n g l e u =0.3; k = u *0.18246*1.121/0.21644; R1 =( Tf *(10^3) / k ) ^(1/3) ; R2 = R1 *1.242; Rm =1.121* R1 ; W =2* %pi * p1 * R1 *( R2 - R1 ) ; // p r i n t i n g printf ( ” \ nThe printf ( ” \ nThe printf ( ” \ nThe printf ( ” \ nThe printf ( ” \ nThe printf ( ” \ nThe

d a t a i n s c i l a b o / p window a n g u l a r s p e e d i s %0 . 2 f r a d / s e c ” ,w ) ; Torque i s %0 . 1 f Nm” , Tf ) ; I n n e r r a d i u s i s %0 . 1 f mm” , R1 ) ; Outer r a d i u s i s %0 . 1 f mm” , R2 ) ; mean r a d i u s i s %0 . 2 f mm” , Rm ) ; a x i a l f o r c e i s %0 . 0 f N” ,W ) ; 170

24 25

// The d i f f e r e n c e i n t h e a n s w e r i s due t o r o u n d i n g − off of values .

Scilab code Exa 22.8 FC228 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

// 22−8 clc ; clear ; // semi −c o n e a n g l e i s g i v e n a s 15 d e g r e e k = sin (15* %pi /180) ; u =0.3; W =300; Rm =90/2; Tf = u * W * Rm / k ; Tf = Tf *(10^ -3) ; I =0.4; a = Tf / I ; N =1440; w =2* %pi * N /60; t=w/a; // D u r i n g S l i p p i n g theta1 = w * t ; theta2 = theta1 /2; U = Tf *( theta1 - theta2 ) ;

// p r i n t i n g printf ( ” \ nThe printf ( ” \ nThe ˆ2 ” ,a ) ; 24 printf ( ” \ nThe 25 printf ( ” \ nThe 26 printf ( ” \ nThe );

d a t a i n s c i l a b o / p window Torque i s %0 . 3 f Nm” , Tf ) ; a n g u l a r a c c e l e r a t i o n i s %0 . 3 f r a d / s e c a n g u l a r s p e e d i s %0 . 1 f r a d / s e c ” ,w ) ; t i m e t a k e n i s %0 . 2 f s e c ” ,t ) ; Energy l o s t i n f r i c t i o n i s %0 . 0 f Nm” ,U

171

Scilab code Exa 22.9 FC229 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

// 22−9 clc ; clear ; P =15*10^3; Ka =1.25; N =1500; w =2* %pi * N /60; Tf = P / w ; d =( Tf *16/(50* %pi ) ) ^(1/3) ; d =25; Rm =5* d ; Pav =0.12; u =0.22; b = Tf /( %pi * u * Pav *( Rm ^2) ) ; b =40; R1 = Rm -( b * sin (15* %pi /180) /2) ; R2 = Rm +( b * sin (15* %pi /180) /2) ; // p r i n t i n g printf ( ” \ nThe printf ( ” \ nThe printf ( ” \ nThe printf ( ” \ nThe printf ( ” \ nThe

d a t a i n s c i l a b o / p window Torque i s %0 . 2 f Nm” , Tf ) ; s h a f t d i a m e t e r i s %0 . 0 f mm” ,d ) ; w i d t h i s %0 . 0 f mm” ,b ) ; I n n e r r a d i u s i s %0 . 1 f mm” , R1 ) ; Outer r a d i u s i s %0 . 1 f mm” , R2 ) ;

Scilab code Exa 22.10 FC2210 1 // 22 −10 2 clc ; 3 clear ;

172

4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

w2 =2* %pi *1400/60; w1 =0.8* w2 ; P =40*10^3; T = P / w2 ; n =4; T1 = T /4; R =0.16; // I n n e r r a d i u s o f drum r =0.13; // r a d i a l d i s t a n c e o f e a c h s h o e from a x i s o f rotation u =0.22; // c o e f f i c i e n t o f f r i c t i o n x = u * r * R *(( w2 ^2) -( w1 ^2) ) m = T1 / x ; l = R * %pi /3; N = T1 /( R * u ) ; p =1*10^5; b = N /( p * l ) *10^3; // p r i n t i n g printf ( ” \ nThe printf ( ” \ nThe ; printf ( ” \ nThe printf ( ” \ nThe printf ( ” \ nThe printf ( ” \ nThe printf ( ” \ nThe l); printf ( ” \ nThe

d a t a i n s c i l a b o /p window f u l l s p e e d i s %0 . 1 f r a d / s e c ” , w2 ) ; e n g a g e m e n t s p e e d i s %0 . 2 f r a d / s e c ” , w1 ) number o f s h o e s i s %0 . 0 f ” ,n ) ; Torque i s %0 . 1 f Nm” ,T ) ; Torque p e r s h o e i s %0 . 1 f Nm” , T1 ) ; mass p e r s h o e i s %0 . 2 f kg ” ,m ) ; l e n g t h o f f r i c t i o n l i n i n g i s %0 . 5 f m” , w i d t h i s %0 . 1 f mm” ,b ) ;

173

Chapter 23 BRAKES

Scilab code Exa 23.1 B23 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

// sum 23−1 clc ; clear ; W =20 e3 ; m = W /9.81; // d i a m e t e r o f b r a k e drum Db =0.6; p =1; Vi =1; Vf =0; D =1; R =0.5; wi = Vi / R ; wf =0; w =1; Vav =0.5; S =2; t = S / Vav ; // a n g l e t u r n e d by by h o i s t drum=t h e t a theta =0.5* wi * t ; K . E =0.5* m * Vi ^2; 174

22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43

P . E =2* W ; T.E=K.E+P.E; T = T . E / theta ; P = wi * T *10^ -3; Rb = Db /2; Ft =0.5* T * p / Rb ; u =0.35; N = Ft / u ; // c o n t a c t a r e a o f b r a k e l i n i n g =A A=N/p; b =0.3* Db ; L = A *10^ -6/( b ) ; // a n g l e s u b t e n d e d a t b r a k e drum c e n t r e=t h e t a 2 theta2 =2*( asin ( L / Db ) ) ; theta2 = theta2 *180/ %pi ; // c o n v e r t i n g r a d i a n t o degree // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”T i s %0 . 1 f Nm ” ,T ) ; printf ( ” \n P i s %0 . 4 f kW ” ,P ) ; printf ( ” \n b i s %0 . 2 f m ” ,b ) ; printf ( ” \n L i s %0 . 3 f m ” ,L ) ; printf ( ” \n t h e t a 2 i s %0 . 0 f deg ” , theta2 ) ;

Scilab code Exa 23.2 B23 2 1 2 3 4 5 6 7 8 9

// sum 23−2 clc ; clear ; b =80; t =2; theta =225* %pi /180; u =0.22; // F1/F2=e ˆ ( u∗ t h e t a ) // l e t F1/F2=x ; 175

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

x = exp ( u * theta ) ; //maximum t e n s i l e s t r e s s i n s t e e l t a p e i s s i g a siga =60; A=b*t; F1 = siga * A ; F2 = F1 / x ; r =0.2; T =( F1 - F2 ) * r ; OA =30; OB =100; OC =350; P =(( F2 * OB ) +( F1 * OA ) ) / OC ; OA = F2 * OB / F1 ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”F1 i s %0 . 0 f N ” , F1 ) ; printf ( ” \n F2 i s %0 . 1 f N ” , F2 ) ; printf ( ” \n T i s %0 . 2 f Nm ” ,T ) ; printf ( ” \n OA i s %0 . 2 f mm ” , OA ) ;

Scilab code Exa 23.3 B23 3 1 2 3 4 5 6 7 8 9 10 11 12 13

// sum 23−3 clc ; clear ; theta = %pi /3; r =160; u =0.3; pmax =0.9; b =40; R =(4* r * sin ( theta ) ) /((2* theta ) + sin (2* theta ) ) ; // f r i c t i o n a l t o r q u e i s T T =2* u * pmax * b *( r ^2) * sin ( theta ) ; T =2* T *10^ -3; Rx =0.5* pmax * b * r *((2* theta ) +( sin (2* theta ) ) ) *10^ -3; 176

14 Ry = u * Rx ; 15 16 // p r i n t i n g d a t a i n s c i l a b o /p window 17 printf ( ”T i s %0 . 2 f Nmm ” ,T ) ; 18 printf ( ” \n R i s %0 . 3 f mm ” ,R ) ; 19 printf ( ” \n Rx i s %0 . 3 f kN ” , Rx ) ; 20 printf ( ” \n Ry i s %0 . 2 f kN ” , Ry ) ;

Scilab code Exa 23.4 B23 4 // sum 23−4 clc ; clear ; d =320; r = d /2; b =50; u =0.3; pmax =1; c =115*2; // From t o f i g . 23 −9 , d i s t a n c e OA=R i s c a l c u l a t e d . R = sqrt (115^2+66.4^2) ; C =115*2; theta1 =0; theta2 =120* %pi /180; theta0 =120* %pi /180; thetamax = %pi /2; Tr = u * pmax * b * r ^2*( cos ( theta1 ) - cos ( theta2 ) ) / sin ( thetamax ) *10^ -3; 18 // t h e n o t a t i o n ’ r ’ i s u s e d f o r moments o f r i g h t hand shoe , s i m i l a r l y ’ l ’ f o r the l e f t shoe . 19 Mfr = u * pmax * b * r *(4* r *( cos ( theta1 ) - cos ( theta2 ) ) +( R *( cos (2* theta1 ) - cos (2* theta2 ) ) ) ) /(4* sin ( thetamax ) ) *10^ -3; 20 Mpr = pmax * b * r * R *((2* theta0 ) -( sin (2* theta2 ) -( sin ( theta1 ) ) ) ) /(4* sin ( thetamax ) ) *10^ -3;

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

177

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F =( Mpr - Mfr ) / c *10^3; // Mpl+Mfl=F∗ c ; x = F * c *10^ -3; y =( Mpr / pmax ) +( Mfr / pmax ) ; pmax2 = x / y ; Tl = pmax2 * Tr ; Mpl = pmax2 * Mpr ; Mfl = pmax2 * Mfr ; T = Tl + Tr ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” Tr i s %0 . 0 f Nm ” , Tr ) ; printf ( ” \n Mf i s %0 . 2 f Nm ” , Mfr ) ; printf ( ” \n Mp i s %0 . 2 f Nm ” , Mpr ) ; printf ( ” \n Tl i s %0 . 1 f Nm ” , Tl ) ; printf ( ” \n Mfl i s %0 . 2 f Nm ” , Mfl ) ; printf ( ” \n Mpl i s %0 . 2 f Nm ” , Mpl ) ; printf ( ” \n F i s %0 . 1 f N ” ,F ) ; printf ( ” \n T i s %0 . 1 f Nm ” ,T ) ; // The d i f f e r e n c e i n t h e a n s w e r s a r e due t o rounding −o f f o f v a l u e s .

Scilab code Exa 23.5 B23 5 1 2 3 4 5 6 7 8 9 10

// sum 23−5 clc ; clear ; m =1100; V =65*5/18; t =4; r =0.22; mb =12; C =460; S =0.5* V * t ; 178

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

// T o t a l k i n e t i c e n e r g y TE=K . E( v e h i c l e )+K. E( r o t a t i n g parts ) . TE =((0.5* m *( V ^2) ) +(0.1*0.5* m *( V ^2) ) ) ; E = TE /4; w=V/r; theta = S / r ; T = E / theta ; delT = E /( mb * C ) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” S i s %0 . 2 f m ” ,S ) ; printf ( ” \n E i s %0 . 2 f Nm ” ,E ) ; printf ( ” \n T i s %0 . 2 f Nm ” ,T ) ; printf ( ” \n d e l T i s %0 . 2 f ” , delT ) ; // The d i f f e r e n c e i n t h e a n s w e r s a r e due t o r o u n d i n g − off of values .

Scilab code Exa 23.6 B23 6 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

// sum 23−6 clc ; clear ; T =35000; u =0.4; p =0.7; r =200; N = T /( u * r ) b = sqrt ( N / p ) ; l=b; // 2 t h e t a = t h e t a 2 theta2 =2* asin ( l /(2* r ) ) ; F=u*N; P =((250* N ) -( u * N *80) ) /550; Ry =N - P ; 179

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Rx = u * N ; R = sqrt ( Rx ^2+ Ry ^2) ; w =2* %pi *100/60; // Rate o f h e a t g e n e r a t e d i s Q Q = u * N * w * r /1000; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”N i s %0 . 1 f N ” ,N ) ; printf ( ” \n b i s %0 . 0 f mm ” ,b ) ; printf ( ” \n P i s %0 . 1 f N ” ,P ) ; printf ( ” \n R i s %0 . 2 f N ” ,R ) ; printf ( ” \n Q i s %0 . 2 f J / s ” ,Q ) ; // The a n s w e r t o Rate o f h e a t g e n e r a t e d ’Q’ i s c a l c u l a t e d i n c o r r e c t l y i n t h e book .

Scilab code Exa 23.7 B23 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

// sum 23−7 clc ; clear ; Vi =20*5/18; Vf =0; m =80; pmax =1; u =0.1; S =50; KE =0.5* m * Vi ^2; N = KE /( u * S *2) ; t = sqrt ( N /( pmax *3) ) ; b =3* t ; // p r i n t i n g d a t a i n s c i l a b o / p window printf ( ”KE i s %0 . 1 f Nm ” , KE ) ; printf ( ” \n N i s %0 . 2 f N ” ,N ) ; 180

18 19 20 21

printf ( ” \n t i s %0 . 1 f mm ” ,t ) ; printf ( ” \n b i s %0 . 1 f mm ” ,b ) ; // The d i f f e r e n c e i n t h e a n s w e r s a r e due t o r o u n d i n g − off of values .

181

Chapter 24 ROPE DRIVE

Scilab code Exa 24.1 RD1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

// sum 24−1 clc ; clear ; P =150000; m =0.4; D =1.8; d =0.6; C =4.2; V =15; Fc = m * V ^2; BL =44.81*10^3; FOS =35; F1 = BL / FOS ; theta = %pi -(2* asin (( D - d ) /(2* C ) ) ) ; beta =22.5* %pi /180; u =0.13; x = u * theta / sin ( beta ) ; F2 =( F1 - Fc ) / exp ( x ) ; n = P /(( F1 - F2 ) * V ) ; n =13;

182

22 23

// p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” n i s %0 . 0 f ” ,n ) ;

Scilab code Exa 24.2 RD2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

// sum 24−2 clc ; clear ; W =1000; m =0.498; BL =78; d =12; Am =0.39* d ^2; dw = sqrt ( Am *4/(6*19* %pi ) ) ; Ew =74.4*10^3; Ds =56* d ; sigb = Ew * dw / Ds ; Wb = sigb * %pi *( d ^2) /4*10^ -3; l =20; Ws = m * l ; a =1.2; Wa = a *( W /2+ Ws ) *10^ -3; // L e t t h e s t a t i c l o a d be Ps Ps =( W /2+ Ws ) *9.81*10^ -3; // l e t t h e e f f e c t i v e l o a d be P e f f Peff = Ps + Wb + Wa ; FOS1 = BL / Peff ; FOS2 = BL /(5+0.612) ; // p r i n t i n g d a t a i n s c i l a b o / p window printf ( ” a n n u a l FOS i s %0 . 2 f ” , FOS1 ) ; printf ( ” \n FOS n e g l e c t i n g b e n d i n g l o a d i s %0 . 1 f ” , FOS2 ) ;

183

Scilab code Exa 24.3 RD3 1 2 3 4 5 6 7 8 9 10 11 12

// sum 24−3 clc ; clear ; d =12; sigut =1960; Pb =0.0025* sigut ; Ds =480; F = Pb * d * Ds /2; W = F *2*10^ -3; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”W i s %0 . 3 f kN ” ,W ) ;

Scilab code Exa 24.4 RD4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

// sum 24−4 clc ; clear ; sigut =1770; Pb =0.0018* sigut ; W =4000; a =2.5/2; Ws =90*0.5; Wa =( W + Ws ) * a /9.81; Weff = W + Wa ; d = sqrt ( Weff *2/(23* Pb ) ) ; d =12; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” d i s %0 . 0 f mm ” ,d ) ; 184

185

Chapter 25 GEARS

Scilab code Exa 25.1 G1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

// sum 25−1 clc ; clear ; Zp =25; Zg =60; m =5; dp = m * Zp ; dg = m * Zg ; CD =( dp + dg ) /2; ha = m ; hf =1.25* m ; c = hf - ha ; r =0.4* m ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” dp i s %0 . 0 f mm ” , dp ) ; printf ( ” \n dg i s %0 . 0 f mm ” , dg ) ; printf ( ” \n CD i s %0 . 1 f mm ” , CD ) ; printf ( ” \n ha i s %0 . 0 f mm ” , ha ) ; printf ( ” \n h f i s %0 . 2 f mm ” , hf ) ; printf ( ” \n c i s %0 . 2 f mm ” ,c ) ; 186

22

printf ( ” \n r i s %0 . 0 f mm

” ,r ) ;

Scilab code Exa 25.2 G2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

// sum 25−2 clc ; clear ; N =800; P =6000; n =200; Cs =1.4; sigb =150; FOS =2; Zp =18; Zg = Zp * N / n ; Y = %pi *(0.154 -(0.912/ Zp ) ) ; p =[1 0 -9.5846 -38.135]; function r = myroots ( p ) a = coeff ( p ,0) ; b = coeff ( p ,1) ; c = coeff ( p ,2) ; d = coeff (p , 3) ; r (1) =( -b + sqrt ( b ^2 -4* a * c ) ) /(2* a ) ; r (2) =( -b - sqrt ( b ^2 -4* a * c ) ) /(2* a ) ; endfunction m = roots ( p ) ; m =4.5; dp = m * Zp ; dg = m * Zg ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” dp i s %0 . 0 f mm ” , dp ) ; printf ( ” \n dg i s %0 . 0 f mm ” , dg ) ;

187

Scilab code Exa 25.3 G3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

// sum 25−3 clc ; clear ; Zp =30; N =1000; Zg =75; m =5; b =60; sigut =450; BHN =350; Cs =1.5; FOS =2; dp = m * Zp ; dg = m * Zg ; v =2* %pi * N * dp /(60*1000*2) ; Cv =3/(3+ v ) ; sigb =450/3; Y =0.358; Sb = m * b * sigb * Y ; Q =(2* Zg ) /( Zp + Zg ) ; K =0.16*( BHN /100) ^2; Sw = b * dp * Q * K ; Pt = Sb * Cv /( Cs * FOS ) ; P = Pt * v ; P = P *10^ -3; // p r i n t i n g d a t a i n s c i l a b o / p window printf ( ” Sb i s %0 . 0 f N ” , Sb ) ; printf ( ” \n Sw i s %0 . 0 f N ” , Sw ) ; printf ( ” \n P i s %0 . 3 f kW ” ,P ) ; // The d i f f e r e n c e i n t h e v a l u e o f Sw i s due t o 188

r o u n d i n g − o f f o f t h e v a l u e o f Q.

Scilab code Exa 25.4 G4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

// sum 25−4 clc ; clear ; n =240; P =8000; N =1200; CD =300; Cs =1.5; alpha =20* %pi /180; G=N/n; dp = CD *2/6; dg =5* dp ; v =2* %pi * N * dp /(60*1000*2) ; Cv =3/(3+ v ) ; Pt = P / v ; Peff = Pt * Cs / Cv ; m =4; b =10* m ; FOS =2; Sb = Peff * FOS ; sigut =600; sigb = sigut /3; Zp = dp / m ; Zg = dg / m ; Q =(2* Zg ) /( Zp + Zg ) ; K = Sb /( b * dp * Q ) ; BHN = sqrt ( K /0.16) *100; BHN =333; // p r i n t i n g d a t a i n s c i l a b o / p window printf ( ”BHN i s %0 . 0 f ” , BHN ) ; 189

Scilab code Exa 25.5 G5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

// sum 25−5 clc ; clear ; alpha =20* %pi /180; N =800; P =6000; sigut =450; i =5; Cs =1.3; v =3.6; FOS =2; Pt = P / v ; Cv =3/(3+ v ) ; sigb = sigut /3; dp =3.6*1000*2*60/(2* %pi * N ) ; dp =86; Sb = Pt * Cs / Cv * FOS ; // L e t x be mˆ2∗Y x = Sb /(10* sigb ) ; m =5; Zp =18; dp = m * Zp ; Zg = i * Zp ; dg = m * Zg ; b =10* m ; phip = m +(0.25* sqrt ( dp ) ) ; ep =32+(2.5* phip ) ; phig = m +(0.25* sqrt ( dg ) ) ; eg =32+(2.5* phig ) ; e = ep + eg ; e = e *10^ -3; Ps = Cs * Pt ; 190

33 34 35 36 37 38 39 40 41 42 43

r1 = dp /2; r2 = dg /2; Pd = e * N * Zp * b * r1 * r2 /(2530* sqrt ( r1 ^2+ r2 ^2) ) ; Q =(2* Zg ) /( Zp + Zg ) ; K = Sb /( b * dp * Q ) ; BHN = sqrt ( K /0.16) *100; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” Ps i s %0 . 2 f N ” , Ps ) ; printf ( ” \n Pd i s %0 . 1 f N ” , Pd ) ; printf ( ” \n BHN i s %0 . 0 f ” , BHN ) ;

Scilab code Exa 25.6 G6 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

// sum 25−4 clc ; clear ; P =9000; N =900; n =150; sigut =750; BHN =300; Cs =1.5; FOS =2; i=N/n; x = sqrt ( i ) ; Zp =18; Zg = x * Zp ; Zg =44; // L e t a c t u a l s p e e d r e d u c t i o n be xa xa = Zg / Zp ; n1 = N / xa ^2; T1 = P *60/(2* %pi * N ) ; i2 = N / xa ; T2 = N / i2 * T1 ; 191

22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

m =6; dp = Zp * m ; dg = m * Zg ; phip = m +(0.25* sqrt ( dp ) ) ; ep =16+(1.25* phip ) ; phig = m +(0.25* sqrt ( dg ) ) ; eg =16+(1.25* phig ) ; e = ep + eg ; e = e *10^ -3; Pt =26000; Ps = Cs * Pt ; r1 = dp /2; r2 = dg /2; b =10* m ; Pd = e * i2 * Zp * b * r1 * r2 /(2530* sqrt ( r1 ^2+ r2 ^2) ) ; Q =(2* Zg ) /( Zp + Zg ) ; sigb = sigut /3; Y =0.308; Sb = b * m * sigb * Y ; K =0.16*( BHN /100) ^2; Sw = b * dp * K * Q ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”m i s %0 . 0 f mm ” ,m ) ; printf ( ” \n Pd i s %0 . 3 f N ” , Pd ) ; printf ( ” \n Sw i s %0 . 0 f N ” , Sw ) ; // The d i f f e r e n c e i n t h e v a l u e s i s due t o r o u n d i n g − o f f of the values .

192

Chapter 26 HELICAL GEARS

Scilab code Exa 26.1 HG1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

// sum 26−1 clc ; clear ; Zp =20; Zg =50; alphan =20* %pi /180; phi =15* %pi /180; mn =4; m = mn / cos ( phi ) ; alpha =180/ %pi * atan ( tan ( alphan ) /( cos ( phi ) ) ) ; dp = Zp * m ; dg = Zg * m ; ha =4; hd =1.25* mn ; // L e t addendum c i r c l e d i a o f p i n i o n be Pa Pa = dp +(2* mn ) ; // L e t dedendum c i r c l e d i a o f p i n i o n be Pd Pd = dp -(2.5* mn ) ; // L e t addendum c i r c l e d i a o f g e a r be Ga Ga = dg +(2* mn ) ; // L e t dedendum c i r c l e d i a o f g e a r be Gd 193

22 Gd = dg -(2.5* mn ) ; 23 b = %pi * mn / sin ( phi ) ; 24 25 // p r i n t i n g d a t a i n s c i l a b o /p window 26 printf ( ”m i s %0 . 2 f mm ” ,m ) ; 27 printf ( ” \n a l p h a i s %0 . 3 f deg ” , alpha ) ; 28 printf ( ” \n Pa i s %0 . 1 f mm ” , Pa ) ; 29 printf ( ” \n Pd i s %0 . 1 f mm ” , Pd ) ; 30 printf ( ” \n Ga i s %0 . 0 f mm ” , Ga ) ; 31 printf ( ” \n Gd i s %0 . 0 f mm ” , Gd ) ; 32 printf ( ” \n b i s %0 . 2 f mm ” ,b ) ;

Scilab code Exa 26.2 HG2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

// sum 26−2 clc ; clear ; P =5000; Zp =25; Zg =50; mn =4; alphan =20* %pi /180; phi =20* %pi /180; N =1200; m = mn / cos ( phi ) ; dp = Zp * m ; dg = Zg * m ; v =2* %pi * N * dp /(60*2*1000) ; Pt = P / v ; Pa = Pt * tan ( phi ) ; Pr = Pt * tan ( alphan ) / cos ( phi ) ; // p r i n t i n g d a t a i n s c i l a b o / p window printf ( ” Pt i s %0 . 2 f N ” , Pt ) ; printf ( ” \n Pa i s %0 . 1 f N ” , Pa ) ; 194

22

printf ( ” \n Pr i s %0 . 2 f N

” , Pr ) ;

Scilab code Exa 26.3 HG3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

// sum 26−3 clc ; clear ; Zp =24; Zg =72; alphan =20* %pi /180; phi =24* %pi /180; N =720; mn =5; b =50; sigut =600; BHN =360; Cs =1.4; FOS =2; sigb = sigut /3; dp = mn * Zp / cos ( phi ) ; Zp = Zp /( cos ( phi ) ) ^3; Zg = Zg /( cos ( phi ) ) ^3; Y =0.358+((0.364 -0.358) *1.48/2) ; Sb = b * mn * sigb * Y ; Q =(2* Zg ) /( Zp + Zg ) ; K =0.16*( BHN /100) ^2; Sw = b * dp * Q * K /( cos ( phi ) ^2) ; v =2* %pi * N * dp /(60*2*1000) ; Cv =5.6/(5.6+ sqrt ( v ) ) ; Peff = Sb / FOS ; Pt = Peff * Cv / Cs ; P = Pt * v ; P = P *10^ -3; // p r i n t i n g d a t a i n s c i l a b o / p window 195

32 33 34

printf ( ”P i s %0 . 3 f kW

” ,P ) ;

// The d i f f e r e n c e i n t h e v a l u e i s due t o r o u n d i n g − o f f of the values .

Scilab code Exa 26.4 HG4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

// sum 26−4 clc ; clear ; Zp =25; Zg =100; P =5000; N =2000; alphan =20* %pi /180; phi =15* %pi /180; sigut =660; Cs =1.5; FOS =1.8; v =10; Zp1 = Zp /( cos ( phi ) ) ^3; Zg1 = Zg /( cos ( phi ) ) ^3; Y =0.348+(0.74*0.004) ; sigb = sigut /3; Cv =5.6/(5.6+ sqrt ( v ) ) ; // Sb=FOS∗ P e f f mn = FOS * P * Cs *60*1000*2* cos ( phi ) /(2* %pi * N * Cv * Zp *12* sigb * Y ) ; mn = mn ^(1/3) ; mn =2.5; dp = mn * Zp / cos ( phi ) ; Q =(2* Zg ) /( Zp + Zg ) ; b =12* mn ; Sb =12* sigb * Y ; K = Sb *( cos ( phi ) ^2) /( dp * Q * b ) ; 196

28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

BHN = sqrt ( K /0.16) *100; dg = mn * Zg / cos ( phi ) ; phip = mn +(0.25* sqrt ( dp ) ) ; ep =16+(1.25* phip ) ; phig = mn +(0.25* sqrt ( dg ) ) ; eg =16+(1.25* phig ) ; e = ep + eg ; e = e *10^ -3; r1 = dp /2; r2 = dg /2; Pd = e * N * Zp1 * b * r1 * r2 /(2530* sqrt ( r1 ^2+ r2 ^2) ) ; v =2* %pi * N * dp /(60*2*1000) ; // L e t t a n g e n t i a l component be TC TC =( Cs *1845/ mn ) +( Pd * cos ( alphan ) * cos ( phi ) ) ; Sb = b * mn * sigb * Y ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”mn i s %0 . 1 f mm ” , mn ) ; printf ( ” \n TC i s %0 . 0 f N ” , TC ) ; printf ( ” \n Sb i s %0 . 1 f N ” , Sb ) ; // The d i f f e r e n c e i n t h e v a l u e rounding −o f f o f t

197

o f Sb i s due t o

Chapter 27 STRAIGHT BEVEL GEARS

Scilab code Exa 27.1 SBG1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

// sum 27−1 clc ; clear ; P =8000; N1 =400; N2 =200; i = N1 / N2 ; // i =Zg /Zp=dg / dp gamma1 = atan (1/ i ) ; gamma2 =90 - gamma1 ; rp =200; R = rp / sin ( gamma1 ) ; b =0.2* R ; rm1 = rp -( b * sin ( gamma1 ) /2) ; Pt = P *1000*60/(2* %pi * N1 * rm1 ) ; alpha =20* %pi /180; Ps = Pt * tan ( alpha ) ; Pr = Ps * cos ( gamma1 ) ; Pa = Ps * sin ( gamma1 ) ; // p r i n t i n g d a t a i n s c i l a b o / p window printf ( ” Pt i s %0 . 0 f N ” , Pt ) ; 198

22 23 24 25 26

printf ( ” \n Ps i s %0 . 2 f N ” , Ps ) ; printf ( ” \n Pr i s %0 . 2 f N ” , Pr ) ; printf ( ” \n Pa i s %0 . 2 f N ” , Pa ) ; // The d i f f e r e n c e i n t h e v a l u e s i s due t o r o u n d i n g − o f f of the values .

Scilab code Exa 27.2 SBG2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

// sum 27−2 clc ; clear ; alpha =20* %pi /180; Zp =20; Zg =36; m =4; sigut =600; b =25; dp = m * Zp ; rp = dp /2; dg = m * Zg ; rg = dg /2; gamma1 = atan ( rp / rg ) ; Zpv = Zp / cos ( gamma1 ) ; Y =0.33+0.003*0.88; sigb = sigut /3; Sb = m * b * sigb * Y ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” Zpv i s %0 . 2 f ” , Zpv ) ; printf ( ” \n Sb i s %0 . 0 f N ” , Sb ) ;

Scilab code Exa 27.3 SBG3 199

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

// sum 27−3 clc ; clear ; m =6; Zp =30; Zg =45; dp = m * Zp ; rp = dp /2; dg = m * Zg ; rg = dg /2; R = sqrt ( rg ^2+ rp ^2) ; gamma1 =180/ %pi * asin ( rp / R ) ; gamma2 =(90 - gamma1 ) ; ha =6; hf =1.25* ha ; phi =180/ %pi * atan ( ha / R ) ; beta =180/ %pi * atan ( hf / R ) ; // l e t Face Cone A n g l e be FCA FCA =( gamma1 + phi ) ; // L e t Root c o n e a n g l e be RCA RCA =( gamma1 - beta ) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” gamma1 i s %0 . 1 f deg ” , gamma1 ) ; printf ( ” \n gamma2 i s %0 . 1 f deg ” , gamma2 ) ; printf ( ” \n R i s %0 . 2 f mm ” ,R ) ; printf ( ” \n FCA i s %0 . 3 f deg ” , FCA ) ; printf ( ” \n RCA i s %0 . 2 f deg ” , RCA ) ;

Scilab code Exa 27.4 SBG4 1 // sum 27−4 2 clc ; 3 clear ; 4 alpha =20* %pi /180;

200

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

Zp =25; Zg =40; m =5; b =30; BHN =400; dp = m * Zp ; rp = dp /2; dg = m * Zg ; rg = dg /2; gamma1 = atan ( rp / rg ) ; gamma1 =180/ %pi * gamma1 ; gamma2 =(90 - gamma1 ) ; a = cosd ( gamma2 ) ; Zp1 = Zp / cos ( gamma1 ) ; Zg1 = Zg / a ; Q =(2* Zg1 ) /( Zp1 + Zg1 ) ; K =0.16*( BHN /100) ^2; Sw =0.75* b * dp * Q * K / cosd ( gamma1 ) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”Sw i s %0 . 1 f N ” , Sw ) ; // The d i f f e r e n c e i n t h e v a l u e o f Sw i s due t o r o u n d i n g − o f f o f t h e v a l u e o f Q.

Scilab code Exa 27.5 SBG5 1 2 3 4 5 6 7 8

// sum 27−5 clc ; clear ; Zp =20; Zg =36; m =4; b =25; BHN =360; 201

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

Np =750; FOS =1.75; dp = m * Zp ; rp = dp /2; dg = m * Zg ; rg = dg /2; gamma1 = atan ( dp / dg ) ; gamma1 =180/ %pi * gamma1 ; gamma2 =(90 - gamma1 ) ; a = cosd ( gamma2 ) ; Zp1 = Zp / cosd ( gamma1 ) ; Zg1 = Zg / a ; Q =(2* Zg1 ) /( Zp1 + Zg1 ) ; K =0.16*( BHN /100) ^2; R = sqrt ( rp ^2+ rg ^2) ; Y =0.33+0.003*0.86; sigut =600; sigb = sigut /3; Sb = m * b * Y * sigb *(1 -( b / R ) ) ; Sw =0.75* b * dp * Q * K / cosd ( gamma1 ) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” Sb i s %0 . 0 f N ” , Sb ) ; printf ( ” \n Sw i s %0 . 1 f N ” , Sw ) ; // The answwer t o Sb i s c a l c u l a t e d i n c o r r e c t l y i n t h e book .

Scilab code Exa 27.6 SBG6 1 // sum 27−6 2 clc ; 3 clear ; 4 Dp =300; 5 rp =150;

202

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

// L e t t h e a n g u l a r v e l o c i t y r a t i o be i i =2/3; rg = rp / i ; Dg =2* rg ; R = sqrt ( rp ^2+ rg ^2) ; P =15000; N =300; Cs =1.5; FOS =2; sigb =100; gamma1 = atan ( Dp / Dg ) ; gamma1 =180/ %pi * gamma1 ; gamma2 =(90 - gamma1 ) ; v =2* %pi * N * rp /(60*1000) ; Cv =5.6/(5.6+ sqrt ( v ) ) ; Pt = P / v ; Peff = Pt * Cs / Cv ; Sb = Peff * FOS ; b = R /4; // l e t x=m∗Y x = Sb /( b * sigb *(1 -( b / R ) ) ) ; m =6; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”m∗Y i s %0 . 3 f mmˆ2 ” ,x ) ; printf ( ” \n m i s %0 . 0 f mm ” ,m ) ;

Scilab code Exa 27.7 SBG7 1 2 3 4 5 6

// sum 27−7 clc ; clear ; Zp =24; Zg =36; N =1400; 203

7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44

P =11600; Cs =1.4; FOS =2; sigut =600; sigb = sigut /3; gamma1 = atan ( Zp / Zg ) ; gamma1 =180/ %pi * gamma1 ; gamma2 =(90 - gamma1 ) ; a = cosd ( gamma2 ) ; Zp1 = Zp / cosd ( gamma1 ) ; Zg1 = Zg / a ; Q =(2* Zg1 ) /( Zp1 + Zg1 ) ; v =1.76; Pt = P / v ; Cv =5.6/(5.6+ sqrt ( v ) ) ; Peff = Pt * Cs / Cv ; x = Peff * FOS ; Y =0.352+(0.003*0.85) ; y =2* sigb * Y *(1 -(6/21.63) ) ; m = sqrt ( x / y ) ; // D e s i g n i s s a f e f o r m=4 m =4; b =6* m ; dp =24* m ; rp =48; dp = dp / cosd ( gamma1 ) ; v =2* %pi * N * rp /(60*1000) ; Cv =5.6/(5.6+ sqrt ( v ) ) ; Sb = y * m ^2; //Sw=Sb ; K = Sb /(0.75* b * dp * Q ) ; BHN = sqrt ( K /0.16) *100; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”m i s %0 . 0 f mm ” ,m ) ; printf ( ” \n BHN i s %0 . 0 f ” , BHN ) ; // The answwer t o BHN i s c a l c u l a t e d i n c o r r e c t l y i n 204

t h e book .

Scilab code Exa 27.8 SBG8 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

// sum 27−8 clc ; clear ; Zp =40; Zg =60; P =3500; N =600; Cs =1.5; sigb =55; gamma1 = atan ( Zp / Zg ) ; gamma1 =180/ %pi * gamma1 ; gamma2 =(90 - gamma1 ) ; a = cosd ( gamma2 ) ; Zp1 = Zp / cosd ( gamma1 ) ; Zg1 = Zg / a ; Q =(2* Zg1 ) /( Zp1 + Zg1 ) ; // D e s i g n i s s a f e f o r m=6 m =6; b =6* m ; dp = Zp * m ; rp = dp /2; dg = Zg * m ; rg = dg /2; R = sqrt ( rp ^2+ rg ^2) ; // p r i n t i n g d a t a i n s c i l a b o / p window printf ( ”m i s %0 . 0 f mm ” ,m ) ; printf ( ” \n b i s %0 . 0 f mm ” ,b ) ; printf ( ” \n R i s %0 . 0 f mm ” ,R ) ;

205

Chapter 28 WORM AND WORM WHEEL SET

Scilab code Exa 28.1 WWS1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

// sum 28−1 clc ; clear ; Z1 =1; Z2 =30; q =10; m =5; d=q*m; D = m * Z2 ; // l e t t h e s p e e d r e d u c t i o n r a t i o be G G = Z2 / Z1 ; CD =( d + D ) /2; // p r i n t i n g d a t a i n s c i l a b printf ( ”G i s %0 . 0 f ” ,G ) ; printf ( ” \n CD i s %0 . 0 f mm printf ( ” \n d i s %0 . 0 f mm printf ( ” \n D i s %0 . 0 f mm

206

o / p window ” , CD ) ; ” ,d ) ; ” ,D ) ;

Scilab code Exa 28.2 WWS2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

// sum 28−2 clc ; clear ; Z1 =1; Z2 =52; q =10; m =8; i = Z2 / Z1 ; CD =(( m * q ) +( m * Z2 ) ) /2; lambda = atan ( Z1 / q ) ; d=q*m; da = m *( q +2) ; df = m *( q +2 -(4.4* cos ( lambda ) ) ) ; pa = m * %pi ; D = m * Z2 ; Da = m *( Z2 +(4* cos ( lambda ) ) -2) ; Df = m *( Z2 -2 -(0.4* cos ( lambda ) ) ) ; // p r i n t i n g d a t a i n s c i l a b o / p window printf ( ” i i s %0 . 0 f ” ,i ) ; printf ( ” \n CD i s %0 . 0 f mm ” , CD ) ; printf ( ” \n pa i s %0 . 2 f mm ” , pa ) ; printf ( ” \n da i s %0 . 0 f mm ” , da ) ; printf ( ” \n d f i s %0 . 3 f mm ” , df ) ; printf ( ” \n Da i s %0 . 3 f mm ” , Da ) ; printf ( ” \n Df i s %0 . 3 f mm ” , Df ) ;

Scilab code Exa 28.3 WWS3 1

// sum 28−3 207

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

clc ; clear ; Z1 =2; Z2 =60; q =10; m =5; P =6000; N =1440; u =0.08; alpha =20* %pi /180; lambda = atan ( Z1 / q ) ; d=m*q; w =2* %pi * N /60; T=P/w; Ptw = T *10^3/( d /2) ; a = cos ( alpha ) ; b = cos ( lambda ) ; x = sin ( alpha ) ; y = sin ( lambda ) ; Paw = Ptw *((( a * b ) -( u * y ) ) /(( a * y ) +( u * b ) ) ) ; Prw = Ptw * y /(( a * y ) +( u * b ) ) ; //Paw=Ptw ∗ ( ( c o s ( a l p h a ) ∗ c o s ( lambda ) ) −(u∗ s i n ( lambda ) ) ) / ( ( c o s ( a l p h a ) ∗ s i n ( lambda ) ) +(u∗ c o s ( lambda ) ) ) ; 24 // Prw=Ptw ∗ ( ( s i n ( a l p h a ) ) / ( ( c o s ( a l p h a ) ∗ s i n ( lambda ) ) +(u ∗ c o s ( lambda ) ) ) ) ; 25 26 27 28 29 30 31

// p r i n t i n g d a t a i n s c i l a b o / p window printf ( ”Ptw=Pag i s %0 . 1 f N ” , Ptw ) ; printf ( ” \n Paw=Ptg i s %0 . 0 f N ” , Paw ) ; printf ( ” \n Prw=Prg i s %0 . 0 f N ” , Prw ) ; // The d i f f e r e n c e i n t h e v a l u e i s due t o r o u n d i n g − o f f the values .

Scilab code Exa 28.4 WWS4 208

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

// sum 28−4 clc ; clear ; Z1 =2; Z2 =40; q =8; m =5; d=q*m; P =1.2; lambda = atan ( Z1 / q ) ; N =1000; Vt =2* %pi * N *20/(60*1000) ; Vs = Vt / cos ( lambda ) ; u =0.032; alpha =20* %pi /180; x = cos ( alpha ) ; y = tan ( lambda ) ; z =( cos ( lambda ) ) / sin ( lambda ) ; n =( x -( u * y ) ) /( x +( u * z ) ) ; // L e t power o u t p u t be Po Po = P * n ; // L e t power l o s t i n f r i c t i o n be Pf Pf =P - Po ; // p r i n t i n g d a t a i n s c i l a b o / p window printf ( ”P i s %0 . 1 f kW ” ,P ) ; printf ( ” \n Po i s %0 . 3 f kW ” , Po ) ; printf ( ” \n Pf i s %0 . 3 f kW ” , Pf ) ;

Scilab code Exa 28.5 WWS5 1 // sum 28−5 2 clc ; 3 clear ; 4 Z1 =2;

209

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

Z2 =54; q =10; m =8; P =4000; A =1.8; K =16; N =1000; u =0.028; lambda = atan ( Z1 / q ) ; alpha =20* %pi /180; d=m*q; Vt =2* %pi * N * d /(2*60*1000) ; Vs = Vt / cos ( lambda ) ; x = cos ( alpha ) ; y = tan ( lambda ) ; z =( cos ( lambda ) ) / sin ( lambda ) ; n =( x -( u * y ) ) /( x +( u * z ) ) ; delT = P *(1 - n ) /( K * A ) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” n i s %0 . 3 f ” ,n ) ; printf ( ” \n d e l T i s %0 . 2 f deg ” , delT ) ;

Scilab code Exa 28.6 WWS6 1 2 3 4 5 6 7 8 9 10

// sum 28−6 clc ; clear ; Z1 =1; Z2 =30; q =10; m =6; // L e t t h e u l t i m a t e s t r e n g t h o f g e a r i s s i g u t // L e t t h e a l l o w a b l e s t r e n t h o f w h e e l i s s i g b sigut =450; 210

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

sigb =84; N =1200; n = N / Z2 ; alpha =20* %pi /180; d=m*q; D = Z2 * m ; b =3* d /4; V =2* %pi * n * D /(2*60*1000) ; Cv =6/(6+ V ) ; y =0.154 -(0.912/ Z2 ) ; Y = %pi * y ; Sb = sigb * b * Cv * m * Y ; K =0.415; Sw = b * D * K ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” Sb i s %0 . 0 f N ” , Sb ) ; printf ( ” \n Sw i s %0 . 0 f N ” , Sw ) ; // The d i f f e r e n c e i n t h e v a l u e o f Sb i s due t o rounding −o f f the v a l u e s .

211

Chapter 29 GEARBOX

Scilab code Exa 29.1 GB1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

// sum 29−1 clc ; clear ; Ts1 =16; Ts2 =18; Ts3 =20; Ts4 =25; Tr1 =64; Tr2 =63; Tr3 =70; Tr4 =50; // L e t Nr1 / Nr2=G1 G1 =1+( Ts1 / Tr1 ) ; // L e t Nr1 / Ni=G2 G2 =( Ts2 /( Tr2 *(1 -(1/ G1 ) +( Ts2 / Tr2 ) ) ) ) ; // L e t Ni /No=G3 ( t h i r d g e a r ) G3 =(1+( Ts3 / Tr3 ) ) /(( Ts3 / Tr3 ) + G2 ) ; // L e t Ni / Nr1=G4 // The r a t i o c a l c u l a t i o n s a r e done a s a b o v e G4 =1.2857/0.2857; 212

22 // L e t Ni /No =G5 ( s e c o n d g e a r ) 23 G5 = -20/70; 24 // L e t Ni /No=G6 ( f i r s t g e a r ) 25 G6 =1.2857/0.2857; 26 // L e t Ni /No=G7 ( r e v e r s e g e a r ) 27 G7 = -1.7143/0.2857; 28 29 // p r i n t i n g d a t a i n s c i l a b o /p window 30 printf ( ” r a t i o f o r t h i r d g e a r i s %0 . 3 f ” , G3 ) ; 31 printf ( ” \n r a t i o f o r s e c o n d g e a r i s %0 . 4 f ” , G5 ) ; 32 printf ( ” \n r a t i o f o r f i r s t g e a r i s %0 . 1 f ” , G6 ) ; 33 printf ( ” \n r a t i o f o r r e v e r s e g e a r i s %0 . 3 f ” , G7 )

;

Scilab code Exa 29.2 GB2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

// sum 29−2 clc ; clear ; // L e t r e v e r s e s p e e d g e a r be RSG RSG =5.5; // L e t T5/T6 = Z1 T1 =2; // L e t T3/T7 = Z2 Z2 =2.75; T7 =18; T3 = Z2 * T7 ; T3 =50; // L e t T3/T1 =Z3 Z3 =2.5; T1 = T3 / Z3 ; // L e t T4/T2 = Z4 Z4 =2.25/2; T2 =( T1 + T3 ) /( Z4 +1) ; T4 = T1 + T3 - T2 ; 213

20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

// L e t T5/T6=Z5 Z5 =2; T6 =( T1 + T3 ) /3; T5 =( T1 + T3 ) - T6 ; T7 =18; // l e t f i r s t g e a r r a t i o i s G1 G1 =50*47/(20*23) ; // L e t 2 nd g e a r r a t i o i s G2 G2 =37*47/(33*23) ; // L e t 3 r d g e a r r a t i o i s G3 G3 =1; // L e t r e v e r s e g e a r r a t i o i s R R =50*47/(18*23) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”T1 i s %0 . 0 f ” , T1 ) ; printf ( ” \n T2 i s %0 . 0 f ” , T2 ) ; printf ( ” \n T3 i s %0 . 0 f ” , T3 ) ; printf ( ” \n T4 i s %0 . 0 f ” , T4 ) ; printf ( ” \n T5 i s %0 . 0 f ” , T5 ) ; printf ( ” \n T6 i s %0 . 0 f ” , T6 ) ; printf ( ” \n T7 i s %0 . 0 f ” , T7 ) ; printf ( ” \n G1 i s %0 . 3 f ” , G1 ) ; printf ( ” \n G2 i s %0 . 3 f ” , G2 ) ; printf ( ” \n G3 i s %0 . 1 f ” , G3 ) ; printf ( ” \n R i s %0 . 3 f ” ,R ) ;

Scilab code Exa 29.3 GB3 1 // sum 29−3 2 clc ; 3 clear ; 4 // L e t t h e c o n s t a n t g e a r 5 G =2;

r a t i o be G

214

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

x =5.5^(1/3) ; G1 =1; G2 = x ; G3 = x * x ; G4 = x ^3; T7 =18; T8 = T7 *( x ^3) /2; T8 =51; T5 =69/2.558; T6 =69 -27; T4 =69/1.8825; T3 =69 - T4 ; T1 =23; T2 =46; T9 =18; G1 = T2 * T8 /( T1 * T7 ) ; G2 = T2 * T6 /( T1 * T5 ) ; G3 =1; G4 = - T2 * T8 /( T1 * T9 ) ; // p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”T1 i s %0 . 0 f ” , T1 ) ; printf ( ” \n T2 i s %0 . 0 f ” , T2 ) ; printf ( ” \n T3 i s %0 . 0 f ” , T3 ) ; printf ( ” \n T4 i s %0 . 0 f ” , T4 ) ; printf ( ” \n T5 i s %0 . 0 f ” , T5 ) ; printf ( ” \n T6 i s %0 . 0 f ” , T6 ) ; printf ( ” \n T7 i s %0 . 0 f ” , T7 ) ; printf ( ” \n T8 i s %0 . 0 f ” , T8 ) ; printf ( ” \n T9 i s %0 . 0 f ” , T9 ) ; printf ( ” \n G1 i s %0 . 3 f ” , G1 ) ; printf ( ” \n G2 i s %0 . 3 f ” , G2 ) ; printf ( ” \n G3 i s %0 . 3 f ” , G3 ) ; printf ( ” \n G4 i s %0 . 3 f ” , G4 ) ;

215

Chapter 30 CHAIN DRIVE

Scilab code Exa 30.1 CD1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

// sum 30−1 clc ; clear ; n1 =17; n2 =51; C =300; p =9.52; Ln =(2* C / p ) +(( n1 + n2 ) /2) +(((( n2 - n1 ) /(2* %pi ) ) ^2) *( p / C ) ) ; x =( Ln -(( n2 + n1 ) /(2) ) ) ^2; y =8*((( n2 - n1 ) /(2* %pi ) ) ^2) ; z = Ln -(( n1 + n2 ) /2) ; C =( p /4) *( z +( sqrt (x - y ) ) )

// p r i n t i n g d a t a i n s c i l a b o / p window printf ( ”C i s %0 . 2 f mm ” ,C ) ;

Scilab code Exa 30.2 CD2 216

// sum 30−2 clc ; clear ; G =4; n1 =17; n2 = n1 * G ; N1 =2300; Kc =1.2; // from t a b l e 30−2 p =12.7; // fom t a b l e 30−1 D1 = p * n1 ; D2 = p * n2 ; phi =2*10.6; x = tan ( phi /2) ; // p h i /2 = 1 0 . 6 deg , from t a b l e 30−3 Da1 =( p / x ) +(0.6* p ) ; Da2 =( p / x *4) +(0.6* p ) ; Cmin = Kc *(( Da1 + Da2 ) /2) ; Ln1 =(2* Cmin / p ) +(( n1 + n2 ) /2) +(((( n2 - n1 ) /(2* %pi ) ) ^2) *( p / Cmin ) ) ; 18 Ln1 =80; 19 // p r i n t i n g d a t a i n s c i l a b o /p window 20 printf ( ”Ln i s %0 . 0 f ” , Ln1 ) ;

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Scilab code Exa 30.3 CD3 // sum 30−3 clc ; clear ; N1 =1000; N2 =500; P =2.03*10^3; // from t a b l e 30−8 K1 =1.26; Ks =1; // l e t Pc be t h e power t r a n s m i t t i n g c a p a c i t y o f t h e chain 10 Pc = P * K1 / Ks ; 1 2 3 4 5 6 7 8 9

217

11 12 13 14 15 16 17 18 19 20 21

p =9.52; n1 =21; n2 =42; V = n1 * p * N1 /(60*10^3) ; // L e t t h e c h a i n t e n s i o n be T T = Pc / V ; // L e t t h e b r e a k i n g l o a d be BL BL =10700; FOS = BL / T ; C =50* p ; Ln =(2* C / p ) +(( n1 + n2 ) /2) +(((( n2 - n1 ) /(2* %pi ) ) ^2) *( p / C ) ) ; 22 L = Ln * p ; 23 Pc = Pc *10^ -3; 24 25 26 27 28 29 30 31 32

// p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” Pc i s %0 . 2 f KW ” , Pc ) ; printf ( ” \n V i s %0 . 3 f m/ s ” ,V ) ; printf ( ” \n T i s %0 . 1 f N ” ,T ) ; printf ( ” \n FOS i s %0 . 2 f ” , FOS ) ; printf ( ” \n L i s %0 . 2 f mm ” ,L ) ; // The d i f f e r e n c e i n t h e v a l u e o f L and T i s due t o rounding −o f f the v a l u e s .

Scilab code Exa 30.4 CD4 1 2 3 4 5 6 7 8

// sum 30−5 clc ; clear ; G =2; P =5000; Ks =1.7; Pd = P * Ks ; K2 =1.7; 218

9 10 11 12 13 14 15

p =15.88; n1 =17; n2 = n1 * G ; D1 = n1 * p ; D2 = n2 * p ; C =40* p ; Ln =(2* C / p ) +(( n1 + n2 ) /2) +(((( n2 - n1 ) /(2* %pi ) ) ^2) *( p / C ) ) ; 16 L = Ln * p ; 17 18 19 20

// p r i n t i n g d a t a i n s c i l a b o /p window printf ( ”L i s %0 . 2 f mm ” ,L ) ; // The d i f f e r e n c e i n t h e v a l u e o f L i s due t o rounding −o f f the v a l u e s .

219

Chapter 31 SEALS PACKING AND GASKETS

Scilab code Exa 31.1 SPG1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

// sum 31−1 clc ; clear ; d =18; lg =25+25; Eb =210*10^3; Ecl =90*10^3; A = %pi * d ^2/4; kb = A * Eb / lg ; x =(5*( lg +(0.5* d ) ) /( lg +(2.5* d ) ) ) ; km = %pi * Ecl * d /(2* log ( x ) ) ; C = kb /( kb + km ) ; sigp =600; At =192; Pi =0.75* sigp * At ; F =200; C =0.322; Pb = F * C *10^3; FOS =2; 220

20 W = At * sigp ; 21 N = Pb * FOS /( W - Pi ) ; 22 23 // p r i n t i n g d a t a i n 24 printf ( ”N i s %0 . 2 f

s c i l a b o /p window ” ,N ) ;

Scilab code Exa 31.2 SPG2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

// sum 31−2 clc ; clear ; d =16; D =1.5* d ; t =20; tg =4; // L e t G a s k e t d i a m e t e r i n c o m p r e s s i o n z o n e be d1 d1 = D +(2* t ) + tg ; lg =40; E =207*10^3; kb = %pi * d ^2* E /( lg *4) ; Ecl =90*10^3; x =(5*( lg +(0.5* d ) ) /( lg +(2.5* d ) ) ) ; kp = %pi * Ecl * d /(2* log ( x ) ) ; Ag = %pi *( d1 ^2 - d ^2) /4; Eg =480; kg = Ag * Eg / tg ; km = kg * kp /( kg + kp ) ; C = kb /( kb + km ) ; At =157; sigp =600; Pi =0.75* At * sigp /2; FOS =2; Pf = At * sigp / FOS ; W = Pf - Pi ; P=W/C; 221

28 N =5; 29 F = P * N ; 30 p = F *4/( %pi *120^2) ; 31 32 // p r i n t i n g d a t a i n s c i l a b o /p window 33 printf ( ” p i s %0 . 3 f N/mmˆ2 ” ,p ) ;

Scilab code Exa 31.3 SPG3 // sum 31−3 clc ; clear ; sigp =600; FOS =3; siga = sigp / FOS ; d =16; D =1.5* d +60; // L e t G a s k e t d i a m e t e r i n c o m p r e s s i o n z o n e be d1 d1 =(300 -160) /2; // L e t c o m p r e s s i v e s t r e s s i n g a s k e t f o r l e a k p r o o f j o i n t be s i g l 12 sigl =12; 13 At =[1 157; 2 192; 3 245] 14 d =[1 16; 2 18; 3 20]

1 2 3 4 5 6 7 8 9 10 11

15 16 17 18 19 20 21 22 23 24 25

n =3; for ( i =1: n ) Pi (i ,2) = At (i ,2) * d (i ,2) Pc (i ,2) =3* %pi *( d1 ^2 - d (i ,2) ^2) if ( Pi (i ,2) >= Pc (i ,2) ) then printf ( ” The D e s i g n i s s a f e ” ) end end

222

26 27 28

// p r i n t i n g d a t a i n s c i l a b o /p window printf ( ” d i s %0 . 0 f mm ” ,d (i ,2) ) ;

223

Machine Design_U. C. Jindal

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