DIN 3990 MDesign 2016 Esempio Spur Gear, Gear Rack

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With the f ollowing ollowing program based on t he standard ca lculations lculations DIN 3960, t he geometry of spur gears can be calculated. calculated. This This module module has different operations and possibiliti possibilities es f or calculation profile shift. These possibilities are the following:  Automatic calculation calculation and distribution distribution of the total profile shift coefficient according according to DIN 3992 (DIN (DIN 3993) Input of centre distance Input of tota l profile profile shift Input of profile shift    

With the f ollowing ollowing program the st rength ex amination amination (pitting (pitting load capacity, root load capacity , corrosion load capacity) of spur gears will be calculated. Therefore t he calculation base DIN 3990 and also the internat ional ISO 6336 can chose by t he user. With this program standard gauges f or spur gears will will be calculated. The application application of the number number of teet h thickness, spherical dim.-roll dim.-roll diameter diameter DM, dev iations of cente r distance and dev iations of t eeth thickness thickness a re optional.

Groundwork calculations Geometry of the spur gear pair and the gear The standard calculations for this module module are described by DIN 3960, edition March 1987. The following DIN specifications will also be utilized: DIN 780 Module Module sequence f or spur gears DIN 867 edition February 1986 (basic profile) DIN 3960 edition March 1987 (concept and dimension dimension determination determination for spur gear pairs with involute gearing) DIN 3960 supplement supplement 1, edition July 1980 DIN 3992 edition March 1964 (profile displacement displacement f or spur gears with outer gearing) DIN 3993 edition August 1981, part 1 - 4 (geometric design design of cy lindrical lindrical inner inner gear pairs).

     

Strength exam ination of spur gears The standard calculations for this module module are described by the f ollowing ollowing DIN specifications: specifications:                   

DIN 3990 Part 1 edition December December 1987 (general influence fa ctors) DIN 3990 Part 2 edition December December 1987 (calculation of the pitting load capacity) DIN 3990 Part 3 edition December December 1987 (calculation of the root load capacity ) DIN 3990 Part 4 edition December December 1987 (calculation of the corrosion load capacity) DIN 3990 Part 5 edition December December 1987 (f atigue stress values a nd material material qualities) DIN 3990 Part 6 edition December December 1994 (operational stability) stability) DIN 3990 Part 11 edition February 1989 (application standards for industrial gears) DIN 3961 edition August 1961 (ground tolerances) DIN 3962 Part 1 edition August 1978 (tolerances fo r dev iation of individual determined determined dimensions) dimensions) DIN 3962 Part 2 edition August 1978 (tolerances for f lank line line deviations) DIN 50 150, edition December December 1976 1976 (convers ion table for Vickers Vickers - Rockwell- Brinell Brinell hardness and ultimate ultimate strength) ISO 6336 Part 1 edition September September 2006 (Basic principles, principles, influence factors) ISO 6336 Part 2 edition September September 2006 (Calculation of surface durability (pitting)) (pitting)) ISO 6336 Part 3 edition September September 2006 (Calculation (Calculation of tooth bending bending strength) ISO 6336 Part 6 edition September September 2006 (Calculation of serv ice life life under variable load) load) ISO 6336-1 Technical Corrigendum 1 ISO 6336-2 Technical Corrigendum 1 ISO 6336-3 Technical Corrigendum 1 ISO 1328 Part 1 edition August 2005 (Definitions (Definitions and allowable allowable values of deviations)

Gauge Design for Spur Gears The standard calculations for this program are described by DIN 3960, edition March 1987. The following DIN specifications will also be utilized:  DIN 3961 edition August 1978 (tolerances f or spur gearing)  DIN 3962 supplement supplement 1 edition A ugust 1978 (tolerances f or dev iation of individual individual determined determined dimensions) dimensions)  DIN 3964 edition November November 1980 (axis position and Ax is position tolerances of housing for spur gears) hickness dimension, dimension, toot h thickness tolerances)  DIN 3967 edition August 1978 (flank play, tooth t hickness (dimension diameter diameter f or the radial or diametric diametric standard gauge of t he tooth thickness thickness of spur gears  DIN 3977 edition February 1981 (dimension (cylinder (cylinder gears))

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Input data: Spur Gear, Gear Rack 

Calculation method

Spur gear

Calculation variants

All

Calculation standard

DIN 3990

Type of toothing

External toothing

Spur gear geometry Basic data Normal modulus

mn  = 4,5

mm

Helical angle

  : 12

°

Centre distance

a:0

mm

Driving element

Pinion

Input of geometry

z1, z2

Number of teeth (pinion)

z1 = 25

Number of teeth (wheel)

z2 = 63

Translation ratio

i = 2,52 Pinion

Tooth width

Wheel

b = 75

70

Input method for tooth-tip height modification

No input

Tip edge modification

No

mm

 Ad dendu m modification according t o DIN 3992/3993 Input methode profile shift coefficients

Input of x1 and x2

Profile shift coefficient (pinion)

x1 = -0,257

Profile shift coefficient (wheel)

x2 = -0,257

Basic gear rack

Pinion

Wheel

Tip clearance factor

c P * = 0,25

0,25

Root fillet radius factor

 f P* : 0,45

0,45

Pressure angle

 p  = 20

Tooth-tip thickness factor

san* = 0,25 Pinion

Tooth-tip height factor Residual fillet undercut

°

Wheel

haP* = 1

1

spr  : 0

0

mm

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Cutter data

Pinion

Wheel

Number of cutter teeth

z0 : 0

0

Basic gear rack profile shift coefficient

x 0 : 0

0

Spur Gear Calculation - Strength Drive data Load case

Nominal load Pinion

Number of meshed teeth  Application fact or

Wheel

nZE  = 1

1 K   A  = 1

Dynamic factor

Kv  : 0  

Performance

P = 15

kW

Rotation speed (pinion)

n1 = 3000

1/min

Required lifetime

Lh  = 10000

h

Lubrication  Viscosity class for 40°

 oil = 32

cSt

 Viscosity class for 100°

 oil = 1

cSt

Density for 15°C

 oil = 885

kg/m³

Oil temperature

oil = 30

°C

Force level (according to FZG-test) Type of oil distribution

3 Splash lubrication

Material selection Pinion - materials (strength values) according to International materials

 MDESIGN database no

Material designation

16MnCr5

Material number

1.7131

Material group

Casehardening steel

Heat treatment / State

trial hardened

Standard dimension

dNm = 16

mm

Standard dimension

dNp  = 16

mm

R mN = 1000

N/mm²

R pN  = 695

N/mm²

Tooth root strength

Flim = 430

N/mm²

Surface durability (pitting)

Hlim = 1500

N/mm²

Ultimate strengt h for d Nm  Yield po int fo r dNp

Type of Material

4

Modulus of elasticity

E = 210000

Poisson' s ratio

  = 0,3

Hardness scale

HB

Hardness

N/mm²

=0

Density

  = 7850

kg/m³

Linear expansion factor

  = 12

10^-6/K  

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Temperature

T = 20

Wheel - materials (strength values) according t o

°C

 MDESIGN database

International materials

no

Material designation

16MnCr5

Material number

1.7131

Material group

Casehardening steel

Heat treatment / State

trial hardened

Standard dimension

dNm = 16

mm

Standard dimension

dNp  = 16

mm

R mN = 1000

N/mm²

R pN  = 695

N/mm²

Tooth root strength

Flim = 430

N/mm²

Surface durability (pitting)

Hlim = 1500

N/mm²

Ultimate strengt h for d Nm  Yield po int fo r dNp

Type of Material

4

Modulus of elasticity

E = 210000

Poisson' s ratio

  = 0,3

Hardness scale

HB

Hardness

N/mm²

=0

Density

  = 7850

kg/m³

Linear expansion factor

  = 12

10^-6/K  

Temperature

T = 20

°C

Spur gear calculation material Structure factor The rmal conduct ivity

Pinion

Wheel

XW  = 1

1

 = 50

50

N/(s*K)

Heat capacity

c M = 485

485

N*m/(kg *K)

Root roughness

Rz =  1,6

1,6

µm

Tooth flank roughness

Rz =  1,6

1,6

µm

Data width load factor Tooth modification

No

Face load factor (root stress)

KF   : 0

Face load factor (contact stress)

KH  : 0

Face load factor (scuffing load)

KB  : 0

Bearing span

l = 200

mm

Eccentricity (pinion)

s:0

mm

Shaft diameter at pinion Factor Type of helical toothing

dsh = 30

mm

K' = 0.48 Simple

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Transverse load factors Transverse load factor (root stress)

KF   : 0

Transverse load factor (contact stress)

KH    : 0

Transverse load factor (scuffing load)

KB  : 0

General input

Pinion

Wheel

Gearing quality

6

6

Design

Disk

Disk

 

Inner diameter of rim

di : 0

0

mm

Tooth modification, base relief

Ca : 0

0

µm

Loading type

Pulsating

Stress ratio

 = 0

Pulsating 0

Minimal root safety

SFmin = 1

Minimal flank safety

SHmin = 1

Minimal scuffing load safety

S Bmin  = 1

Standard gauge spur gear General data

Pinion

Wheel

Deviation of teeth thickness (DIN 3967)

b

b

Tolerances of teeth thickness (DIN 3967)

24

24

Number of teeth dimension Spherical dimension- and roll diameter

k:0

0

DM : 0

0

Deviation of centre distances (DIN 3964)

mm

-

Free input deviations

Pinion

Wheel

Upper deviation of teeth thickness

A sne    : 0

0

µm

Lower deviation of teeth thickness

A sni    : 0

0

µm

q:0

mm

Upper deviation of centre distances

A ae  : 0,01

µm

Lower deviation of centre distances

A ai :   0

µm

Machining allowance

Results: General data Effective number of teeth ratio

u

=

2,52

Effective translation ratio

i

=

2,52

Transverse pressure angle

t

=

20,41

°

Pressure angle at pitch cylinder

 wt

=

18,455

°

Ground lead

b

=

11,267

°

Zero centre distance

ad

=

202,423

mm

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Centre distance

a

=

200,001

Profile shift coefficient (pinion)

x1

=

-0,257

Profile shift coefficient (wheel)

x2

=

-0,257

Sum profile shift coefficient

xs

=

-0,514

Length of path of contact

g

=

21,695

mm

Length of recess path

ga

=

7,844

mm

Length of approach path

gf 

=

13,851

mm

Transverse cont act ratio



=

1,602

Overlap ratio



=

1,029

Total contact ratio



=

2,631

Number of teeth

z

=

25

zn

=

26,573

66,963

Reference diameter

d

=

115,013

289,834

mm

Base diameter

db

=

107,793

271,638

mm

Pitch diameter

dw

=

113,637

286,365

mm

Root diameter

df 

=

101,45

276,271

mm

dv

=

112,7

287,521

mm

Tip diameter

da

=

121,482

296,302

mm

Theoretical tip diameter

d a th

=

121,7

296,521

mm

Tip utility diameter

d Na

=

119,534

296,302

mm

Root form circle diameter

d Ff 

=

108,156

280,469

mm

Root form diameter

dNf 

=

108,11

280,664

mm

Interference utility

cF

=

-0,023

0,097

mm

Specific sliding at point A 

 A 

=

-4,677

0,824

Specific sliding at point E

E

=

0,424

-0,737

T oot h t hickness on t he t ip cylinder

san

=

3,651

3,774

mm

Tooth depth

h

=

10,016

10,016

mm

 Addendum

ha

=

3,234

3,234

mm

Dedendum

hf 

=

6,782

6,782

mm

Root fillet radius factor

 f P*

=

0,45

0,45

Root fillet radius

F

=

2,025

2,025

mm

Theoretical bottom clearance

c

=

1,125

1,125

mm

ctat

=

1,125

1,125

mm

Tooth – tip height modification

k

=

-0,1092

-0,1092

mm

Normal base pitch

p en

=

13,285

mm

Transverse base pitch

pet

=

13,546

mm

Normal pitch on base cylinder

p bn

=

13,285

mm

T ransverse pit ch on base cylinder

pbt

=

13,546

mm

 Virtual numbe r of t ee th of helical gear

mm

63

Geometrical data

 V-circle diamet er

 Ac tu al to pland play

Note:

05/13/2016 11:45:35 Page 6/17

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Condition for running without interference(c F1 > 0) is not met Cutter data of gear rack  Cutter data pinion type cutter Number of teeth

z0

=

0

0

Profile shift coefficient

x0

=

0

0

Topland height factor

haP0*

=

1,25

1,25

Root height factor

hfP0*

=

1

1

Reference diameter

d0

=

0

0

mm

Base diameter

d b0

=

0

0

mm

Tip diameter

d a0

=

11,25

11,25

mm

Dedde ndum diamet er (ge ne rat ion)

dfE

=

101,45

276,271

mm

Centre distance

a0

=

56,241

143,724

mm

Zere centre distance

ad0

=

57,507

144,917

mm

Pressure angle at pitch cylinder

 wt0

=

16,602

19,091

Transverse tangential load at reference cylinder

Ft

=

830,277

N

Transverse tangential load at pitch cylinder

Ftw

=

840,333

N

Radial load at pitch cylinder

Frw

=

280,446

N

Faw

=

176,481

N

Tooth load at pitch cylinder

Fw

=

903,302

N

Moment (pinion)

T1

=

47,746

N*m

Moment (wheel)

T2

=

120,321

N*m

=

11,861

N/mm

°

Results of calculation strength Forces, moment, speed

 Axial load at pitch cylinde r

Line load Peripheral speed at reference cylinder

v

=

18,066

m/s

Peripheral speed at pitch cylinder

vw

=

17,85

m/s

Rotation speed (pinion)

n1

=

3000

1/min

Rotation speed (wheel)

n2

=

1190,476

1/min

Number of loading cycle (pinion)

NL1

=

1800000000

Number of loading cycle (wheel)

NL2

=

714285714

Note: The lineload is < 100 N/mm so the risk of bad load distribution and vibrations is available ! General factors Hekix slope deviation

fH 

=

10

10

µm

Transverse pitch deviation

fpe  

=

9

10

µm

Profile form deviation

ff  

=

10

10

µm

Effect ive meshing slope deviat ion

fpe   eff 

=

9,287

µm

Effective profile form deviation

ff   eff 

=

9,25

µm

Flank line deviation

f x 

=

10,271

µm

Manufact uring - flank line de viat ion

fma  

=

10

µm

Flank line deviation through pinion def.

f sh

=

0,204

µm

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Reduced mass / tooth width

mred

=

0,035

kg/mm

Individual spring rigidity

c'

=

1,469

N/(mm*µm)

Meshing spring rigidity

c

=

2,132

N/(mm*µm)

Resonance velocity (pinion)

nE1

=

2965,243

1/min

Resonance velocity (gear)

nE2

=

1176,684

1/min

Basic velocity

NR 

=

1,012

Dynamic factor

Kv  

=

2,016

Face load factor (root stress)

KF 

=

1,326

Face load factor (contact stress)

KH  

=

1,389

Face load factor (scuffing load)

KB 

=

1,389

T ransve rse lo ad fact or ( roo t st re ss)

KF  

=

1,165

Transverse load factor (contact stress)

K H

=

1,165

Transverse load factor (scuffing load)

K B

=

1,165

Helix angle factor

KB 

=

1,245

Zone factor

ZH

=

2,587

Elasticity factor

ZE

=

191,646

Contact ratio factor

Z

=

0,79

Helix angle factor

Z

=

0,989

Work hardening factor

ZW

=

1

Lubricant factor

ZL

=

0,922

-

Zv

=

1,017

-

Roughness factor

ZR 

=

1,071

-

Life factor for contact stress

Z NT

=

1

1,019

Size factor

ZX

=

1

1

Single pair tooth contact factor

ZB

=

1

Pitting stress limit

HG

=

1507,76

1536,617

N/mm²

HP

=

1507,76

1536,617

N/mm²

Contact stress

H

=

265,68

265,68

N/mm²

Safety factor for pitting

SH

=

5,675

5,784

Lh

=

fat. strength

Overlapping factor (root stress)

Y  

=

0,7

Helix angle factor

Y  

=

0,9

Deep tooth factor

Y DT 

=

-

Rim thickness factor

Y B 

=

-

-

Tooth form factor

YF  

=

1,494

1,362

Stress correction factor

Y S 

=

1,71

1,874

Relativ notch sensitivity factor

Y  relT

=

0,946

0,966

Relativ survace factor

Y RrelT  

=

1,024

1,024

Size factor

YX  

=

1

1

Life factor for tooth root stress

Y NT  

=

1

1

Mean stress influence factor

Y M 

=

1

1

Pitting load capacity

 Ve locity fact or

 Allowable flank pressure

 At tainable lifet ime

Z D =

1,000

fat. strength

Root load capacity

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To ot h root stress limit

FG

=

833,799

850,981

N/mm²

FP

=

833,799

850,981

N/mm²

Toot h root stress

F

=

17,629

17,624

N/mm²

Safety factor for tooth breakage

SF

=

47,297

48,284

Lh

=

X

=

0,95

XS

=

1

Load distribution factor

X

=

0,333

Flash factor

XM

=

50,235

Geometry factor

XB

=

0,264

Tangential line force at weigth

w Bt

=

48,194

N/mm

Scuffing temperature



=

99,42

°C

Corrosion safety factor

SB

=

25,759

Flash factor

XM

=

50,235

Geometry factor (pinion tip)

XBE

=

0,264

Pitch factor

XQ

=

1

Tip relief factor

XCa

=

1

Contact ratio factor

X

=

0,337

Mass temperature

M

=

31,535

°C

Integral temperature

int

=

34,823

°C

Scuffing integral temperature

intS

=

99,42

°C

Corrosion safety factor

SintS

=

2,855

Scuffing load safety factor

SSL

=

14,394

 Allowable roo t stress

 At tainable lifet ime

fat. strength

fat. strength

Scuffing load capacity  Angle fact or Lubricant factor Flash temperature calculation way

Integral calculation way

Ultimate strengt h for pinion

Rm 

=

684,7

N/mm²

Ultimate strength for gear

Rm 

=

545,7

N/mm²

 Yielding point fo r pinion

R e

=

475,9

N/mm²

 Yielding point fo r gear

R e

=

379,3

N/mm²

(for d eff = (for d eff =

107,79

mm

)

271,64

mm

)

(for d eff = (for d eff =

107,79

mm

)

271,64

mm

)

Results check gauge Case centre distance

a

=

200,001

mm

Maximum case centre distance

amax

=

200,001

mm

Minimum case centre distance

amin

=

200,001

mm

Theoretical backlash

jt

=

0,396

mm

Maximum theoretical backlash

jt max

=

0,429

mm

Minimum theoretical backlash

jt min

=

0,363

mm

Upper deviat ion of t eet h t hickness

A sne  

=

-125

-230

µm

Low er deviat ion of t eet h t hickness

Asni  

=

-150

-270

µm

Tolerance of teeth thickness

T sn

=

25

40

µm

Fluctuation of teeth thickness

Rs 

=

14

18

µm

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Nominal teeth thickness (theoretical)

snth

=

6,227

6,227

mm

Nominal teeth thickness

sn

=

6,227

6,227

mm

Maximum nominal teeth thickness

sn max

=

6,102

5,997

mm

Minimum nominal teeth thickness

sn min

=

6,077

5,957

mm

Base tangent lengt h (theoretical)

W kth

=

34,099

89,788

mm

Base tangent length

W k 

=

34,099

89,788

mm

Maximum base tangent length

W k max

=

33,981

89,572

mm

Minimum base tangent length

W k min

=

33,958

89,534

mm

Number of teeth dimension

k

=

Measure roller diameter

DM

=

Radial gauge spheres/roller

Mrk 

=

61,165

148,419

mm

Maximum radial gauge spheres/roller

Mrk e

=

61,182

148,447

mm

Minimum radial gauge spheres/roller

Mrk i

=

61,147

148,391

mm

Diametral gauge spheres

Mdk 

=

122,103

296,748

mm

Diametral gauge roller

MdR 

=

122,329

296,838

mm

max. Diametral gauge spheres

Mdk e

=

122,137

296,804

mm

min. Diametral gauge spheres

Mdk i

=

122,068

296,693

mm

max. Diametral gauge roller

MdRe

=

122,364

296,894

mm

min. Diametral gauge roller

MdRi

=

122,294

296,783

mm

Factor of deviation of base tangent lengthA w

=

0,94

0,94

Factor of deviation radial spheres/roller

A mr

=

1,39

1,391

Fact or of de viat ion diamet ral rolle r

A md  

=

2,78

2,782

Factor of deviation diametral spheres

A md

=

2,774

2,781

3

7

7,5

7,5

mm

Specific sliding accor d. t o DIN 3960 Kg

External toothing



5,2 1,114

3,9 Kg1  A

0,442 0,341 0,246

2,6

E 1,3

C

0 -0,246 -0,341 -0,442

-1,3 2 1

Kg2

-2,6 -3,9

-1,114 -5,2

0

6,331

18,994

31,657

44,320

56,983

x1 x2 xs

= -0,257 = -0,257 = -0,514

ga gf g

= 7,844 = 13,851 = 21,695

Kga1 Kga2 Kgf1 Kgf2

= = = =

0,246 0,341 0,341 0,246

spec. sliding: pinion   A E

= -4,677 = 0,424

spec. sliding: gear  A   E

= 0,824 = -0,737

[mm]

Meshing Line

05/13/2016 11:45:35 Page 10/17

test version Program

: MDESIGN

Module version : 16.0

User :

Customer :

Date : 13.05.2016

Project

:

Spur Gear, Gear Rack 

Tooth profile (evolvent) pinion

da1

d1 dw 1

df1

Tooth profile (evolvent) gear

da2

d2

dw 2

df2

05/13/2016 11:45:35 Page 11/17

test version Program

: MDESIGN

Module version : 16.0

User :

Customer :

Date : 13.05.2016

Project

:

Spur Gear, Gear Rack 

Gap of tooth (env elope curve, ev olvent) pinion

da1

d1 dw 1

df1

Gap of tooth (envelope curve, evolvent) gear

da2

d2 dw 2

df2

05/13/2016 11:45:35 Page 12/17

test version Program

: MDESIGN

Module version : 16.0

User :

Customer :

Date : 13.05.2016

Project

:

Spur Gear, Gear Rack 

Side view pinion

d f1 d 1 d a1

Side view gear

d f2 d 2 d a2

05/13/2016 11:45:35 Page 13/17

test version Program

: MDESIGN

Module version : 16.0

User :

Customer :

Date : 13.05.2016

Project

:

Spur Gear, Gear Rack 

Front view pinion

df1 d1da1

Front view gear

df2 d2da2

05/13/2016 11:45:35 Page 14/17

test version Program

: MDESIGN

Module version : 16.0

User :

Customer :

Date : 13.05.2016

Project

:

Spur Gear, Gear Rack 

Gear wheel (evolvent) pinion

Gear wheel (evolvent) gear

05/13/2016 11:45:35 Page 15/17

test version Program

: MDESIGN

Module version : 16.0

User :

Customer :

Date : 13.05.2016

Project

:

Spur Gear, Gear Rack 

Pinion, Pitting Bearing Capacity Diagram ma teria l :

HG

16MnCr5

load cycle [-]

[N/mm²]

3000 static 2400 time strength 1800

fatigue strength

lifetime [h]

102

0,00

10

3

0,01

10

4

0,06

10

5

0,56

10

6

5,56

10

7

55,56

10

8

555,56

10

9

5555,56

10

10

55555,56

1200

600

0 102

103

104

105

106

107

108

109

1010

load c ycle

Gear, Pitting Bearing Capacity Diagram ma teria l :

HG

16MnCr5

load cycle [-]

[N/mm²]

3000 static 2400 time strength 1800

fatigue strength

lifetime [h]

102

0,00

10

3

0,01

10

4

0,14

10

5

1,40

10

6

14,00

10

7

140,00

10

8

1400,00

10

9

14000,00

10

10

140000,00

1200

600

0 102

103

104

105

106

107

108

109

1010

load c ycle

05/13/2016 11:45:35 Page 16/17

test version Program

: MDESIGN

Module version : 16.0

User :

Customer :

Date : 13.05.2016

Project

:

Spur Gear, Gear Rack 

Pinion, Root Bearing Capacity Diagram ma teria l :

FG

16MnCr5

load cycle [-]

[N/mm²]

3000

2400

static

1800 time strength

lifetime [h]

102

0,00

10

3

0,01

10

4

0,06

10

5

0,56

10

6

5,56

10

7

55,56

10

8

555,56

10

9

5555,56

10

10

55555,56

1200

fatigue strength

600

0 102

103

104

105

106

107

108

109

1010

load c ycle

Gear, Root Bearing Capacity Diagram ma teria l :

FG

16MnCr5

load cycle [-]

[N/mm²]

3000

2400

static

1800 time strength

lifetime [h]

102

0,00

10

3

0,01

10

4

0,14

10

5

1,40

10

6

14,00

10

7

140,00

10

8

1400,00

10

9

14000,00

10

10

140000,00

1200

fatigue strength

600

0 102

103

104

105

106

107

108

109

1010

load c ycle

05/13/2016 11:45:35 Page 17/17