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5/25/2018 design.pdf

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1

Design of machine elements

--


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(Design of Machine Elements) --

().( )


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


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1

1.1 1.1.1

(Rigid)

1.1.2

1.1 1.


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1.1

2.

3.

4. 3


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(Standard part) (Drawing) (Detail drawing) (Assembledrawing) ()

5.

1.1

6.

(report)

1.2

1. 2.

3.


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7

4.

5. ()()()()

6. 7.

8.

1.3 1.3.1

(cold working )

(recrystallization temperature)


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(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


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(Plasticity)

(Rimmed steel)

(Annealing)

1.3.2

(Wrought iron) (Slag) 1% 3%

1.5% 3.5% 1.11.1,

(()

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


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(Gray cast iron)

2.5% 4.0% 2%

(Nodular) (cerium)

(creep)

1.3.3

(Bush)

1. 2.

3.

4.


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5. (martensitic)

6. 7.

8.

9.

10. ()

11.


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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


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1105C

(Saturated) (Unsaturated) 2 (Thermosetting) (Thermoplastic)

(Filler) 2


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2

2.1 (Stress ) (Strain )2.1.1

(Stresses) (Strains)

()

A

F=

2 (tensilestresses) 2.1(a) (compressive stresses) 2.1 (b)

(+) (-) (Shear stresses) 2.1 (c)

3 (Principal stresses) 2 () 0 90 2.1

2.1


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Residual stresses residual stresses

Bearing stresses () (projected area)A = LD ( L ) 2.2

Bering stresses b=LD

F

A

F=

2.2 Bearing stresses

Elastic deformation

plasticdeformation

Elastic Plastic Elastic PlasticYield point

plastic deformationElastic Plastic

Elastic Plastic Yield point


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Stress Strain diagram 2.3

Stress Strain diagram Elastic Plastic Yield stress, YUltimate stress, uY

u 2.3

Stress Strain diagram

Yield point Yield point 0.1 0.2% offset yield stressyield stress 2.3

2.3 Stress Strain diagram

(Mild steel)

Brinell hardness number (BHN)

400 Yield stress Ultimate stress

y 0.6y u 0.6u

Youngs modulus

Youngs modulus Modulus of elasticity

E =

t


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t elastic ( t


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0.0127 (0.5) (Allowance) 0.0508 (2 )

y

(Variableload) (Fatigue)

(Endurance limit) n y

n u u

(Safety factor Design factor) y

2.2 2.2.1

(Working stress) (Designstress) 700 MN/m

2 420 MN/m2

140 MN/m2

5140700 ==uN

3140

420N y ==

Nu= .


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Ny=

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)


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2.2.2 2.4 AISI C 1020 30 kN h = 1.5 b

) ) )

0 30 kN

2.4

AISI C1020

2

y

2

u

331N/mm)(48)(6.89548ksi

517N/mm)(75)(6.89575ksi

===

===

) 1.3 Ny = 1.5

2

td220.70N/mm

1.5

331==

)5.1)(( bb

F

bh

F

A

Ft ===

2b5.1

1000x3070.220 =

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


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) Nu = 3 2

td mm/N30.1723

517==

2

2tmm/N30.172

b5.1

F ==

172.30 = 30x1000

1.5b2

b = 10.77 mm. h = (1.5)(10.77) = 16.16 mm.

) Ny = 3 331/3

2b5.1

1000x30

3

331 =

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

) )

) b = 10 mm. h = 14 mm.

) (Fatigue)

2.2.3 (torque)

GJ

TL=

T L J (Polar area moment of inertia)

J =4

d32


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J = ( )idd32

44

d di

J

Tr=

r

nT2TWp ==

pW WT Nm

red/sn rev/s

hp =63000

Tn

T in lbn rev/min

(Thin walled tube) R 2.5

2.5


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= GRt2 2TL3

=2

Rt2

3T

2.2.4

1/10 2.6 () ()

. . 2.6

F = pLDi p Tangential stress , St

St = A

F

= 2tL

pLDi

= 2t

pDi


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F = pD 2i / 4 A = (D0+ Di) t / 2

Transverse stress, Stv

Stv

=F

A= p

2

iD

4

/

2

)tD(Di0

+ =

)tD2(D

D

i0

2

i

p

Transverse Stress tangential stress

=

(Effective wall thickness) th N Np

t =S2

NpDi

t =)SD(D2

NpDi

i

0+

S


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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 = - 3d32M

+2

d4F

, xy= 3d

16T


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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


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=

yx

xy

2tan2 1

3.1.2 (Differentiate) n

(Principal Stress)

2

+= + 2xy

2

22

,yxyx

21

1x x 45 - 145

3.2 3.2.1 Stress Element

35 P F Stress Element 3.5 3.6T PStress Element

Stress Element Stress Element

3.5 3.6


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3.2.2 3

2 (Mohr s circle)

1. ()

2. (x,

xy) (

y, -

xy) ,

3. 2

c

3.74. 2 3.7

xy

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

3.7

123

max(1)


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2

21 +

max = 2

1

2

2

max =2

minmax

12 ()

1

2

max =2

21

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

12 1 2

max = 2 31

=21

3.8

x y 0 3.8


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= + 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


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31

max 1 C E = 64 MPa ()

2 C F = -64 MPa ()

1x 251.8 1 25.9

1 Mohr 2= 38.2 x = 19.1

3.10 () ()

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

() () 3.10 Stress Element


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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


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4.1.2 (The Maximum Shear-Stress Theory)

(Trescas criterion)

45

max

y/ 2

2

21 =

2

y

2

1 =

2

y

2

2 =

2

y

21 = y

1 = y

2 =

y

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

x y

max = y

1

=

2/122

+

yy

y= y/2


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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 = [ ] [ ] [ ][ ]2/12

13

2

32

2

213

1 ++ (4.1)

2

3

1 = y (4.1) 2= 3= 0 1= y

= y3

2= 471.0 y (4.2)

oc

=

2 y2 = [ ] [ ] [ ]213

2

32

2

21 ++ (4.3)


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3= 0

N (4.3) 2

y= 2

2

2112 + (4.4 )

1 = 22 +

2 3/2

4.2

4.2A B C D E F GH

()

4.2

y

= [ ] 2/122 3 +

1

=

2/122

3

+

yy


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y =3

y= 0.577 y

2/122

1

+

= yy

(Maximumprincipal strain theory) (Maximum strain energy theory)


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5

5.1 5.1.1

(Fatigue)

5.1.2 (Discontinuity)

F

F

max (

0 = F/A) (Stress concentration factor)

K =0

max


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5.1

(Microscopic)

5.2 5.2.1

(Fatigue limit) (Reversed stress) 8 mm

. .

5.2 . .

F

F


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5.2.2 3

(Reversed bending) 5.2 .

5.3

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

5.2.3

A


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(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 275N/mm

2(5x108)

n = 0.16 u 345N/mm

2(5x108)

5.3 5.3.1 (Surface factor) ka

5.4


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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


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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


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q = 0 Kf= 1

q = 1 Kf= Kt

Kf= Kt () K

f= K

t

Kf

4.5 q

5.4 5.4.1

(Soderbergs Criterion) ()

() ()


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()5.6

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

R =

max

min

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

5.4.2 (Soderbergs Criterion)

a =2

min-max (Stress amplitude)

m =2

minmax + (Mean stress)

am

a = A

aF

IC

aM

AFa

a = J

ra

T


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m=A

mF

I

Cm

M

A

mF

m =J

rm

T

Fa, M

a, T

a, F

m, M

mT

m

Fa =2

Fmin-Fmax

Ma =2

Mmin-Mmax

Ta =

2

Tmin-Tmax

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

Fm =

2

FminFmax +

Mm

=2

MminMmax +

Tm =2

TminTmax +

AB

am AB AB N GE

4.7 GE DEF ABC

AC

DF=

BC

EF


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n

a

=

y

m-/N

y

N

1=

y

m

+

n

a

(Proof stress) (Goodman) B 4.7

N

1=

u

m

+

n

a

Kf

a

m

N1 =

y

m

+

n

af

K

N

1=

u

m

+

n

afK

(Gerber)

N

1=

y

m

+

n

afsK

Kfs

1)-q(K1Ktsfs

+=


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6

6.1 6.1.1

(Shaft) (Axle)

(Spindle) (Head stock spindle)(Stub Shaft) (Head Shaft)

(Line Shaft) (Power transmission shaft) (MainShaft)

(Flexible Shaft) (Cable) (Wire rope)

(Rigidity) (Deflection) (Criticalspeed) (Ball bearing)

(Misalignment)


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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


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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


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50

6.1

)(

422

i

add

F

=

)(

3244

i

bdd

Md

I

Mc

==

)(16

44

i

xydd

TdJTr

==

(buckling)

)(

422

i

add

F

=

ASME (Fatigue factor)

Cm = C

t=

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


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ba +=

/ddK i= F

K = di/d = 0

ASME

1= F

( ))/0044.011

kL= 115

k

L 6.1

( )

nE

kLy

2

2/

= 115>

k

L 6.2

n = 1.00 SS

n = 2.25 CC

xy2

2

max2

+

=

( ) ( )

22

24

3

8

1

1

16

+

++= MC

KFd(TC

)K(d mt

( ) ( )224

3

1

16MCTC

)K(d mt +

=

( ) ( )22316

MCTC

d mt +=


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

6.2 ASME

d = 55 N/mm2

d = 41 N/mm2

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)


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53

EI

FLy

48

3

max= EI

FLy

3

3

max =

y mm.

E = 200 kN /mm2 I = 80 x103mm4 6.3

6.3

EI

FLy

48

3

max=

)1080)(10200(48

600)10(1033

33

maxxx

xy =

81.2max=y mm.

6.2.2

. .

(Critical speed) nc


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6.4

6.4 W1 W2 W3 y1y2 y3

++

++=

2

33

2

22

2

11

332211945yWyWyW

yWyWyWnc

m

=

2

945Wy

Wync

m W Ny mmn

c rpm

() 25 %


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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


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(t)

t =

td2

pD

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

ASMEBoiler Code

1. ASME Boiler Code 6.4


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6.4

(D) (mm)

(t) (mm)

900925-1350

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


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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)()

()


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59

6.3

6.3.1

mm mm x

16mm () M16

20mm 2 mm M20x2

M30-LH (LH = Left Hand )

ISO/R 261-1969 (E)

1. 1 2

2.


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60

P

() () (.) 1 2 1.00 0.25 0.838 0.693 0.729 0.456

1.20 0.25 1.038 0.893 0.929 0.730

1.60 0.35 1.373 1.170 1.221 1.270

2.00 0.40 1.740 1.509 1.567 2.070

2.50 0.45 2.208 1.948 2.013 3.390

3.00 0.50 2.675 2.387 2.459 5.030

3.50 0.60 3.110 2.764 2.850 6.780

4.00 0.70 3.545 3.141 3.242 8.780

4.50 0.75 4.013 3.580 3.688 11.300

5.00 0.80 4.480 4.019 4.134 14.200

6.00 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 84.300

14.00 2.00 12.701 11.546 11.835 115.000

16.00 2.00 14.701 13.546 13.835 157.000

18.00 2.50 16.376 14.933 15.294 192.000

20.00 2.50 18.376 16.933 17.294 245.000

22.00 2.50 20.376 18.933 19.294 303.000

24.00 3.00 22.051 20.319 20.752 353.000

27.00 3.00 25.051 23.319 23.752 459.000

30.00 3.50 27.727 25.706 26.211 561.000

33.00 3.50 30.727 28.706 29.211 694.000

36.00 4.00 33.402 31.093 31.670 817.000

39.00 4.00 36.402 34.093 34.670 976.000

42.00 4.50 39.077 36.479 37.129 1120.000

45.00 4.50 42.077 39.479 40.129 1300.000

48.00 5.00 44.752 41.866 42.587 1470.000

52.00 5.00 48.752 45.866 46.587 1760.000

56.00 5.50 52.428 49.252 50.046 2030.000

60.00 5.50 56.428 53.252 54.046 2360.000

64.00 6.00 60.103 56.639 57.050 2680.000

68.00 6.00 64.103 60.639 61.505 3060.000

6.6

6.3.2

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


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61

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

1.

. . .

. . 6.6

2. 6.6 ()


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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.


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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.


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64

2 ISO2491 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


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6.11

6. (spline) 6.12

ISO /R 14

6.12

7. (Overload ) (shear pin)

6.4.2

2 1.

2.


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66

(Torsional stiffness)

6.13 ()

. .

6.13

. .

6.14

6.14 F F F F

242

FdhdFT

+=


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67

, 6.7

T F d b l

, 6.8

h

cd 6.7 6.8

1/2 = 0.5y

b = h

22

dblFdT

==

ldb

T

A

F

..

2==

lhd

T

A

Fc

..

4==

42

dhlFdT c

==

42dhldbl c =

162

3 ddblT ==

b

dl

8

2=


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68

d/4

1.57

(6.1 ) (6.2)

6.7 6.7 2180

(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

lhd

Tcd

..

4=

cd

ehd

Tl

..

4=


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69

cd

(6.9) 25 %

6.4.3

75 %

l dm = (D+d)/2h = (D-d)/2

NyNy = 1.5 Ny = 2.5 Ny = 4.5

600 N/mm2ISO

600 N/mm2

cd

m

czlhd

T =

75.0.

2

cdm zhd

Tl

75.0

2

y

y

cdN

=


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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

cd

ehd

Tl

..

4=

43.91838

10009004

xx

xxle = 52.129= mm


71/82

71

2. 1:506.16 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

40506080100

3. (Clevis) 6.17 (Split pin) ISO 2340


72/82

72

6.17

4. 6.18 ISO 2341

6.18

5. 6.19 6.8

6.19


73/82

73

I

Mc3d

M32

A3

V4=

2d d3

F8

=

A

Fcd =

6.2.2 (cotter) ( socket) 6.20

6.20

cd td = =

CD

V = F/2 A

A A= dl

A=2d

s

A


74/82

74

s

2

1

dd

T4

A

F

==

sdD

T2

+

N

y = 2.0

Ny = 2.5 N

y = 3.5

6.21

6.21 F

1=T/d

s

25 %

F 6.21

F =


75/82

75

F

6.5 6.5.1

(Outer ring) (Innerring ) (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)


76/82

76

6.22

6.5.2

(Diameter series) 8 9 0 12 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


77/82

77

1

2

2

1

H

H

n

n=

n rpmH

1

2

2

1

B

B

F

F

k

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%


78/82

78

(helical spring) 12 mm

(wound cold) (wound hot)

(stress relieved) 260C 15 60

6.6.2

u x

A

d =

n y

B

d =

u N/mm2

n N/mm2

d mm

y = 0.60u

y = 0.47u

6.6.3 F 6.23 ()

Do Di D d


79/82

79

6.23

F T 6.23 ()

Tr F

J A= +

2

FDT=

4( / 32)

/ 2

J d

r d

=

3

16

d=

2

4

dA

=

3 2

8 4FD F

d d

= +

C = D/d (Spring index)

3

8s

FDK

d

=


80/82

80

KS = 1 +0.5

C

KS (Shear stress correction factor) F/A

Tr/J (Curvature correction factor) KC

K = KCK

S

4 1 0.615

4 4

C

C C

= +

K (Wahls factor)

=3

8FDK

d

=2

8FCK

d

6.7 6.7.1

4(Flat belt) (Round belt) (V belt) (Timing belt)

6.7.2 (Open belt) (Close belt)

6.24 (a)


81/82

81

6.24 (a) (b)

6.24 (a)

C2

dDsin2 1d

=

C2

dDsin2 1D

+=

D = d = C = =

2


82/82

82

[ ] )dD(2

1)dD(C4L dD

2/122 ++=

6.24 (b) 2

C2

dDsin2 1

+=

[ ] +++= )dD(2

1)dD(C4L

2/122

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