1

Design of machine elements --

2

(Design of Machine Elements) -- () . ( )

3

1. 4 2 14 3 25 4 (Static Strength) 32 5 37 6 47

4

1

1.1 1.1.1 (Rigid) 1.1.2 1.1

1.

5

1.1 2.

3. 4. 3

6

(Standard part) (Drawing) (Detail drawing) (Assemble drawing) () 5. 1.1

6. (report) 1.2

1. 2.

3.

7

4.

5. () () () ()

6. 7.

8. 1.3 1.3.1 (cold working ) (recrystallization temperature)

8

(quenching ) ( aging age hardening ) ( decarburization ) (hot rolled) (forging) (heat treatment) (elasticity) (malleability) (ductility) (toughness) (hardness) (stiffness) (free carbon) (temper carbon) (Killed steel) (hardening) (Transformation range) (austenite) (Machinability) (Tempering) (tempered) (normalizing) (Normalizing) 38 C

9

(Plasticity) (Rimmed steel) (Annealing) 1.3.2 (Wrought iron) (Slag) 1% 3% 1.5% 3.5% 1.1 1.1 ,

(() 3.25%

, N/mm2 , N/mm2 (200mm),% ,%

290 360 180 240 25 40 40 55

380 415 380 345 25 30 35 45

(Cast iron) 2.5 4 % (Compressive strength) (White cast iron) (Cementite) (Malleable cast iron) 880 C

10

(Gray cast iron) 2.5% 4.0% 2% (Nodular) (cerium) (creep) 1.3.3 (Bush)

1. 2.

3.

4.

11

5. (martensitic)

6.

7.

8.

9.

10. ()

11.

12

3.5% 8.5% 250 ASTM SAE 2 (bronze) ( 20 % ) (phosphor bronze) (silicon bronze) (aluminium bronze) (manganese bronze) ASTM A Z K M H E rare earth 500 B 1112 100

13

1105C (Saturated) (Unsaturated) 2 (Thermosetting) (Thermoplastic) (Filler) 2

14

2

2.1 (Stress ) (Strain ) 2.1.1 (Stresses) (Strains) ()

AF=

2 (tensile stresses) 2.1(a) (compressive stresses) 2.1 (b) (+) (-) (Shear stresses) 2.1 (c) 3 (Principal stresses) 2 ( ) 0 90 2.1

2.1

15

Residual stresses residual stresses Bearing stresses () (projected area) A = LD ( L ) 2.2 Bering stresses b = LD

FAF =

2.2 Bearing stresses

Elastic deformation plastic deformation Elastic Plastic Elastic Plastic Yield point plastic deformation Elastic Plastic Elastic Plastic Yield point

16

Stress Strain diagram 2.3 Stress Strain diagram Elastic Plastic Yield stress, Y Ultimate stress, u Y u 2.3 Stress Strain diagram Yield point Yield point 0.1 0.2% offset yield stress yield stress 2.3

2.3 Stress Strain diagram (Mild steel) Brinell hardness number (BHN) 400 Yield stress Ultimate stress y 0.6 y u 0.6u

Youngs modulus Youngs modulus Modulus of elasticity E =

t

17

t elastic ( t

18

0.0127 (0.5) (Allowance) 0.0508 (2 )

y

(Variable load) (Fatigue)

(Endurance limit) n y n u u (Safety factor Design factor) y

2.2 2.2.1

(Working stress) (Design stress) 700 MN/m2 420 MN/m2 140 MN/m2

5140700 ==uN

3140420N y ==

N u = .

19

N y =

1.

2. 3. 4.

5.

2.1 2.1

Ny Nu Nu

1.5 2 3 - 4 3 6 4 8 5 7 10 - 15

5 6

7 8 10 12

15 20

(Repeated, one direction) (Repeated and reversed) (Dead load)

20

2.2.2 2.4 AISI C 1020 30 kN h = 1.5 b ) ) ) 0 30 kN

2.4 AISI C1020

2y

2u

331N/mm)(48)(6.89548ksi517N/mm)(75)(6.89575ksi

======

) 1.3 Ny = 1.5

2td 220.70N/mm1.5331 ==

)5.1)(( bbF

bhF

AF

t ===

2b5.11000x3070.220 =

b = 9.52 mm. h = (1.5)(9.52) = 14.28 mm.

21

) Nu = 3 2td mm/N30.1723

517 == 2

2t mm/N30.172b5.1F ==

172.30 = 30x1000 1.5b2 b = 10.77 mm. h = (1.5)(10.77) = 16.16 mm.

) Ny = 3 331/3

2b5.11000x30

3331 =

b = 13.50 mm. h = (1.5)(13.50) = 20.20 mm.

) ) ) b = 10 mm. h = 14 mm.

) (Fatigue)

2.2.3 (torque)

GJTL=

T L J (Polar area moment of inertia) J = 4d

32

22

J = ( )idd32

44 d di

JTr=

r nT2TWp == pW W T Nm red/s n rev/s hp = 63000

Tn T in lb n rev/min (Thin walled tube) R 2.5

2.5

23

= GRt22TL

3 = 2Rt2

3T

2.2.4 1/10 2.6 () ()

. .

2.6 F = pLDi p Tangential stress , St

St = AF = 2tL

pLDi = 2t

pDi

24

F = pD 2i / 4 A = (D0 + Di) t / 2 Transverse stress, Stv

Stv = FA = p 2

iD4

/ 2)tD(D

i0+

= )tD2(DD

i0

2i

p

Transverse Stress tangential stress

=

(Effective wall thickness) th N Np t = S2

NpDi t = )SD(D2

NpDii

0+

S

25

3

3.1 3.1.1 (Combined Stress) 3.1 F () () P Torque (T) (Torsional Sharing Stress )

3.1 2 F P X x T xy X = b + t X = 3d

32M + 2d

4F , xy = 3d

16T

X = -b + t X = - 3d

32M + 2d

4F , xy = 3d

16T

26

3.2 () F Fa F X = b + t , xy = 0 X = 3d

32M + 2d

4F

X = -b + t , xy = 0 X = 3d

32M + 2d

4F

() ()

3.2 3.2 () F Fa F X = - b - c , xy = 0 X = - 3d

32M - 2d

4F

X = b - c , xy = 0 X = 3d

32M - 2d

4F

27

=

yx

xy

2tan2 1

3.1.2 (Differentiate) n (Principal Stress) 2

+= + 2xy

2

22, yxyx21

1 x x 45 - 1 45

3.2 3.2.1 Stress Element 35 P F Stress Element 3.5 3.6 T P Stress Element

Stress Element Stress Element

3.5 3.6

28

3.2.2 3 2 (Mohr s circle) 1. () 2. (x, xy) (y, -xy) , 3. 2 c 3.7 4. 2 3.7 xy .......... ...........

3.7 1 2 3 max(1)

29

221 +

max = 21

22

max = 2 minmax

1 2 () 1 2 max = 2 21

.......... ...........

1 2 1 2 max = 2 31

= 2

1

3.8

x y 0 3.8

30

= + 22 22

, 21

1 2

= + 22 2max

3.2.3 Stress Element Mohr s circle 3.9

x = 80 MPa xy = 50 MPa Stress Element () ()

3.9

3.9 () 1 0 1 = 104 MPa 2 0 2 = -24 MPa

31

max 1 C E = 64 MPa () 2 C F = -64 MPa () 1 x 2 51.8 1 25.9 1 Mohr 2 = 38.2 x = 19.1 3.10 () ()

.......... ...........

() ()

3.10 Stress Element

32

4 (Design for Static Strength)

4.1 (Failure Theories) 4.1.1 (The Maximum Normal Stress Theory ) (Maximum absolute value) (3 = 0) N 1 = - N

y 21 > 2 = - N

y 12 > x =

y 1 y =

y 2

x = 1 , y = 2 4.1 ()

() ()

4.1

33

4.1.2 (The Maximum Shear-Stress Theory) (Trescas criterion) 45 max y / 2

221 = 2

y

2

1 = 2y

2

2 = 2y

21 = y

1 = y

2 = y

x-y = 1 , x= 1 , y = 1

x y

max = y

1 =

2/122

+

yy

y = y/2

34

4.1.3 (Octahedral ShearStress Theory) (distortion energy theory) (plasticity) von Mises (Octahedral plane) ABC 4.2 (directional cosine) 3/1 oc

4.2

oc = [ ] [ ] [ ][ ] 2/121323222131 ++ (4.1) 2 3 1 = y (4.1) 2 = 3 = 0 1 = y

= y32 = 471.0 y (4.2)

oc = 2 y2 = [ ] [ ] [ ]213232221 ++ (4.3)

35

3 = 0 N (4.3)

2

y = 222112 + (4.4 )

1 = 22 + 2 3/2

4.2

4.2 A B C D E F GH () 4.2

y = [ ] 2/122 3 +

1 =

2/1223

+

yy

36

y = 3y = 0.577 y

2/122

1

+

= yy

(Maximum principal strain theory) (Maximum strain energy theory)

37

5

5.1 5.1.1 (Fatigue) 5.1.2 (Discontinuity) F F max ( 0 = F/A) (Stress concentration factor)

K = 0

max

38

5.1 (Microscopic) 5.2 5.2.1 (Fatigue limit) (Reversed stress) 8 mm

. .

5.2 . .

F

F

39

5.2.2 3 (Reversed bending) 5.2 .

5.3

A 5.3 () 8 mm A 50% (Iinfinite life) 1 5.2.3

A

40

( 50%)

n = 0.5u n = 690 N / mm2 n = 0.4 u n = 0.35 u ( 106 ) n = 0.45 u n = 0.38 u 275

N/mm2 ( 5x108 ) n = 0.16 u 345

N/mm2 ( 5x108 )

5.3 5.3.1 (Surface factor) ka 5.4

41

5.4 (Surface factor) ka

5.3.2 (Size factor) kb 8 mm

kb = 1.00 d < 8 mm kb = 0.85 8 < d < 50 mm kb = 0.75 d > 50 m (hb)0.808d = h b kb = (d/7.62) -0.1133

42

5.3.3 (Load factor) kc kc = 1.00 kc = 0.80 kc = 0.60

5.3.4 (Temperature factor) kd

kd =1 {t350 c} kd =0.5 {350

43

q = 0 Kf = 1 q = 1 Kf = Kt Kf = Kt () Kf = Kt Kf

4.5 q

5.4 5.4.1 (Soderbergs Criterion) () () ()

44

()

5.6

(Sinusoidal) 5.6 () () 5.6 () 5.6 ()

R = maxmin

min max R = 0 5.6 () R = -1 5.6 ()

5.4.2 (Soderbergs Criterion)

a = 2min-max (Stress amplitude)

m = 2minmax + (Mean stress)

a m

a = AaF

ICaM A

Fa a = JraT

45

m = AmF

ICmM A

mF m = JrmT

Fa, Ma, Ta, Fm, Mm Tm Fa = 2

Fmin-Fmax

Ma = 2Mmin-Mmax

Ta = 2Tmin-Tmax

.......... ...........

Fm = 2

FminFmax + Mm = 2

MminMmax + Tm = 2

TminTmax + AB a m AB AB N GE

4.7 GE DEF ABC AC

DF = BCEF

46

na

= y

m-/Ny

N

1 = ym

+ na

(Proof stress) (Goodman) B 4.7

N1 =

um +

na

Kf a m

N1 =

ym

+ n

afK

N1 =

um +

nafK

(Gerber)

N1 =

ym

+

nafsK

Kfs

1) - q(K 1 K tsfs +=

47

6

6.1 6.1.1 (Shaft) (Axle) (Spindle) (Head stock spindle) (Stub Shaft) (Head Shaft) (Line Shaft) (Power transmission shaft) (Main Shaft) (Flexible Shaft) (Cable) (Wire rope) (Rigidity) (Deflection) (Critical speed) (Ball bearing) (Misalignment)

48

6.1.2 (mild steel) AISI 1347 3140 4150 4340 90 mm. (Nominal size) ISO/R 775-1969 6.1 6.1 ISO/P 775-1969

mm. 6 7 8 9 10 12 14 18 20

25 30 35 40 45 50 55 60 65

70 75 80 85 90 95 100 110 120

130 140 150 160 170 180 190 200 220

240 260 280 300 320 340 360 380

6.1.3 ASME (Cam shaft ) 0.3 1 m. 1 20

49

0.5 (Clearance) (Contact ratio) 0.08 mm./m. (Spur gear) 0.125 mm. 0.286 (Bevel gear) 0.075 mm. (Double integration) (Moment area) ASME ..2497 (ASME) ASME (Static design method) 6.1 di d

50

6.1

)(4

22i

a ddF=

)(

3244i

b ddMd

IMc

==

)(

1644i

xy ddTd

JTr

== (buckling)

)(

422i

a ddF=

ASME (Fatigue factor)

Cm = Ct =

6.2 Cm Ct

: :

1.0

1.5-2.0

1.5 1.5-2.0 2.0-3.0

1.0

1.5-2.0

1.0 1.0-1.5 1.5-3.0

51

ba +=

/ddK i= F

K = di/d = 0 ASME 1= F

( ))/0044.011

kL= 115kL 6.1

( )nEkLy

2

2/

= 115>kL 6.2

n = 1.00 SS

n = 2.25 CC

xy2

2

max 2 +

=

( ) ( ) 22243 81116

+++= MCKFd(TC

)K(d mt

( ) ( )2243 116 MCTC

)K(d mt +=

( ) ( )223 16 MCTC

d mt +=

52

n = 1.60 (partially restrained) L = 6.1 (Straight line formula)

6.2 ASME

d = 55 N/mm 2 d = 41 N/mm 2

7.3

d = 0.3y d = 0.18y 6.3 75 % 6.3

6.2 6.2.1 (Pulley) (Friction Wheel) (Gear)

6.2

(y)

watcharpRectangle

53

EIFLy

48

3

max = EIFLy3

3

max = y mm.

E = 200 kN /mm2 I = 80 x103 mm4 6.3

6.3

EIFLy

48

3

max =

)1080)(10200(48

600)10(1033

33

max xxxy =

81.2max =y mm.

6.2.2

. .

(Critical speed) nc

54

6.4

6.4 W1 W2 W3 y1 y2 y3

++++= 2

332

222

11

332211945yWyWyWyWyWyW

nc

m

=

2945 WyWy

nc

m W N y mm

nc rpm

() 25 %

55

6.2 6.2.1 6 6

1. 6.5 (A) 2. 6.1 (B) 3. 6.5 (C) 4. (Bearing Crushing) 6.5(D) 5. 6.5 (E) 6. 6.5 (F)

6.5 6

6

6.2.2 ()

=

6.4

56

(t) t =

td2pD 6.5

p D td 6.3

6.3

50-60 60-75 65-80 55-65 65-80 80-88 90-95

6.2.3 ASME Boiler Code 1. ASME Boiler Code 6.4

57

6.4

(D) (mm)

(t) (mm) 900

925-1350 1375-1800 1800

6.00 7.90 9.40 12.50

6.4 6.4 6.4 t 6.4 BS DD5 ( mm)

6 8 10 12 15 18 20 22 25 28 30 32 35 38 40 45 50 55 60

ut = 380 N/mm2 uc = 655 N/mm2 u = 300 N/mm2

5

58

6.5 (mm) (mm)

600-1800 900-2100 1500-2700

5-12 8-25 9-23

d = 6.6 t 6.6

t mm (Solid plate) 6.3 () 6.5 () 6.3 () (6.5) 6.4 () (6.6) () ()

59

6.3 6.3.1

mm mm x

16 mm () M16

20 mm 2 mm M20x2 M30-LH (LH = Left Hand )

ISO/R 261-1969 (E) 1. 1 2 2.

60

P

() () (.) 1 2 1.00 0.25 0.838 0.693 0.729 0.4561.20 0.25 1.038 0.893 0.929 0.7301.60 0.35 1.373 1.170 1.221 1.2702.00 0.40 1.740 1.509 1.567 2.0702.50 0.45 2.208 1.948 2.013 3.3903.00 0.50 2.675 2.387 2.459 5.0303.50 0.60 3.110 2.764 2.850 6.7804.00 0.70 3.545 3.141 3.242 8.7804.50 0.75 4.013 3.580 3.688 11.3005.00 0.80 4.480 4.019 4.134 14.2006.00 1.00 5.350 4.773 4.917 20.1008.00 1.25 7.183 6.466 6.647 36.600(9) 1.25 8.188 7.466 7.647 48.100

10.00 1.50 9.026 8.160 8.376 58.000(11) 1.50 10.026 9.160 9.376 72.300

12.00 1.75 10.863 9.830 10.106 84.30014.00 2.00 12.701 11.546 11.835 115.00016.00 2.00 14.701 13.546 13.835 157.00018.00 2.50 16.376 14.933 15.294 192.00020.00 2.50 18.376 16.933 17.294 245.00022.00 2.50 20.376 18.933 19.294 303.00024.00 3.00 22.051 20.319 20.752 353.00027.00 3.00 25.051 23.319 23.752 459.00030.00 3.50 27.727 25.706 26.211 561.00033.00 3.50 30.727 28.706 29.211 694.00036.00 4.00 33.402 31.093 31.670 817.00039.00 4.00 36.402 34.093 34.670 976.00042.00 4.50 39.077 36.479 37.129 1120.00045.00 4.50 42.077 39.479 40.129 1300.00048.00 5.00 44.752 41.866 42.587 1470.00052.00 5.00 48.752 45.866 46.587 1760.00056.00 5.50 52.428 49.252 50.046 2030.00060.00 5.50 56.428 53.252 54.046 2360.00064.00 6.00 60.103 56.639 57.050 2680.00068.00 6.00 64.103 60.639 61.505 3060.000

6.6

6.3.2 1. (Bolt and nut) 2. (Cap Screw)

61

3. (Stud bolt) 4. (Machine screw) 5. (Set Screw) 1.

. . .

. . 6.6

2. 6.6 ()

62

3. 6.6 () . . . 4. 6.6 () 5. 6.6 () d D d = 0.125D + 8 mm 6.3.3

1. 2. 3. 4. 5.

63

6.4 6.4.1

1. 2.

1. ISO/R 773 6.8 (hub) (Feather key)

A B C

6.8

6.8 2.

64

2 ISO 2491 1:10 ISO 2492 3. (Saddle key) 6.9 () 6.9 ()

. . 4. (Woodruff key ) 6.10 (A) b ISO 3912 6.10 (B) h2 = 0.8 h1 75 mm.

5. (Tangential key ) 6.11

ISO 3117 2 2 180

6.9

6.10

65

6.11 6. (spline) 6.12 ISO /R 14

6.12

7. (Overload ) (shear pin) 6.4.2 2 1. 2.

66

(Torsional stiffness) 6.13 ()

. . 6.13

. .

6.14 6.14 F F F F

242FdhdFT

+=

67

, 6.7

T F d b

l , 6.8 h cd

6.7 6.8 1/2 = 0.5y b = h

22dblFdT ==

ldbT

AF

..2==

lhdT

AF

c ..4==

42dhlFdT c==

42dhldbl c =

162

3 ddblT ==

bdl

8

2=

watcharpRectangle

68

d/4

1.57 (6.1 ) (6.2) 6.7 6.7 2 180 (6.1) (6.2)

6.7

(6.8) (6.1) (6.9) (Effective length) le

6.9 le

ddl 57.12

==

6 8 10 12 14 16 18 20 22 25 28 32 36 40 45 50 56 63 70 80 90 100 110 125 140 160 180 200 220 250 280 320 360 400

lhdT

cd ..4=

cde hd

Tl ..4=

watcharpRectangle

watcharpHighlight

watcharpHighlight

watcharpHighlight

watcharpHighlight

watcharpHighlight

watcharpHighlight

watcharpHighlight

watcharpHighlight

watcharpHighlight

watcharpHighlight

watcharpHighlight

watcharpHighlight

watcharpHighlight

watcharpHighlight

watcharpHighlight

watcharpHighlight

watcharpHighlight

watcharpHighlight

watcharpHighlight

69

cd (6.9) 25 % 6.4.3 75 %

l dm = (D+d)/2 h = (D-d)/2 Ny Ny = 1.5 Ny = 2.5 Ny = 4.5

600 N/mm2 ISO 600 N/mm2

cdm

c zlhdT =

75.0.2

cdm zhdTl 75.0

2

y

ycd N

=

70

38 mm 70 mm 600 N/mm2 320 N/mm2 900 Nm 38 mm ISO/R 774-A10 x 8 3.5 cd = 320/3.5 = 91.43 N/mm2

2 70 mm ISO/R 774-A10x8x70 2

6.4.5 (Pins)

1.

ISO 2338 6.8

6.15

cde hd

Tl ..4=

43.9183810009004

xxxxle = 52.129= mm

71

2. 1:50 6.16 ISO 2339 A B

6.16 6.8 ISO 2338

d

l

d

l 0.6 0.8 1.0 1.2 1.5 2.0 2.5 3.0 4.0 5.0

2-6 2-8 4-10 4-12 4-16 6-25 6-25 8-30 8-45 10-50

6.0 8.0 10.0 12.0 16.0 20.0 25.0 30.0 40.0 50.0

12-60 14-80 20-100 25-150 30-180

40 50 60 80 100

3. (Clevis)

6.17 (Split pin) ISO 2340

72

6.17 4. 6.18 ISO 2341

6.18

5. 6.19 6.8

6.19

73

IMc

3dM32

A3V4=

2d d3F8=

AF

cd =

6.2.2 (cotter) ( socket) 6.20

6.20

cd td = =

CD

V = F/2 A

A A = dl A=2ds A

74

s2

1

ddT4

AF

==

sdDT2+

Ny = 2.0 Ny = 2.5 Ny = 3.5

6.21

6.21 F1=T/ds 25 % F 6.21 F =

75

F 6.5 6.5.1 (Outer ring) (Inner ring ) (Rolling element ) (Case) Rolling friction 25-50 % 2 1. Ball bearing 2. Rolling bearing (Cylinder) 1. (Cylindrical roller bearing) 2. (Needle roller bearing) 3. (Taper roller bearing) 4. (Barrel roller bearing) 5. (Spherical roller bearing) 6. (Cylindrical roller thrust bearing) 7. (Spherical roller thrust bearing)

76

6.22

6.5.2 (Diameter series) 8 9 0 1 2 3 4 8 4 (Width series ) 8 0 1 2 3 4 5 6 8 6 51309 5 13 d = 9 x 5 = 45 . NU308 NU 03 d = 8 x 5 = 45 . 6.5.3 ) 90 % B-10 (B-10 life) 3 50 % Plain ball bearing 90 % Survival rpm x 60 x 106 106 90 % Survival 106/(rpm x 60)

) Ball ) Cylinder ) Taper ) Needle ) Spherical ) Barrel

77

1

2

2

1

HH

nn =

n rpm H

1

2

2

1

BB

FFk

k

=

F B k 3 -4 (k=3 ball bearing ,k=3.3 roller bearing needle bearing ) (B) (H)

B = H x rpm x 60

6.6

- - - - 6.6.1 0.5%

78

(helical spring) 12 mm (wound cold) (wound hot) (stress relieved) 260C 15 60 6.6.2 u x

Ad

= n y

Bd

= u N/mm2 n N/mm2 d mm y = 0.60u y = 0.47u 6.6.3 F 6.23 () Do Di D d

79

6.23 F T 6.23 () Tr F

J A = +

2FDT =

4( / 32)/ 2

J dr d

=

3

16d=

2

4dA =

3 2

8 4FD Fd d

= +

C = D/d (Spring index)

38

sFDKd

=

80

KS = 1 + 0.5C KS (Shear stress correction factor) F/A Tr/J (Curvature correction factor) KC K = KCKS 4 1 0.615

4 4CC C= +

K (Wahls factor) = 38FDK d = 2

8FCKd

6.7 6.7.1 4 (Flat belt) (Round belt) (V belt) (Timing belt) 6.7.2

(Open belt) (Close belt) 6.24 (a)

81

6.24 (a) (b)

6.24 (a)

C2dDsin2 1d

=

C2

dDsin2 1D+=

D = d = C = = 2

82

[ ] )dD(21)dD(C4L dD

2/122 ++=

6.24 (b) 2

C2dDsin2 1 +=

[ ] +++= )dD(21)dD(C4L 2/122