Mathcad - Bolt Loading VDI M39 01

Bolt Loading VDI M39 01.xmcd

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MARYLAND METRICS -- THREAD DATA CHART: Metric Thread -- Coarse Pitch

Nominal Size

ISO M

Thread Form Type

Major Diameter

mm d=D

Pitch mm p

Root Radius

mm r

Pitch Diameter

mm d2=D2

Minor Diameter Male Thd.

d3

Minor Diameter

Female Thd. D1

Thread Height

Male Thd. h3

Thread Height

Female Thd. H1

Tap Drill

Diameter mm

20.00 M 20.00 2.50 0.361 18.376 16.933 17.294 1.534 1.353 17.50 copyright maryland metrics-- all rights reserved filnam:isomlee.xls ver t3a

Fastner size M20

Diameter at stress cross-section A.s (Minor dia of male thread) DS 16.933 mm⋅:=

Shank diameter of bolt neck DT 16.933 mm:=

Effective diameter for friction at the contact of the head of the driven fastner Dkm 26 mm⋅:=

Outside diameter of the consact area under the head of the driven fastner DW 30 mm⋅:=

Assembly preload, bolt tensile load at tightning FM :=

Allowable bolt preload, bolt tensile loat at shich the equivelent stressconsidering tension and torsion is vRp0.2

FM.v :=

Effective tensile stress cross-section of the bolt thread AS 245 mm2⋅:=

Pitch of the bolt thread P 2.5 mm⋅:=

Ry 450 MPa⋅:=Actual proof stress of the bolt

Minimum 2% Proof stess fo bolt material ISO 898 Rp.0.2 450 MPa⋅:=

Outside diameter of bolt at the smallest cross section d0 16.933 mm:=

Pitch diameter of the bolt thread d2 18.376 mm⋅:=

Minor Diameter of bolt thread d3 16.933 mm⋅:=

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Minimum cross section area of the bolt A0

π d02⋅

4225.194 mm

2⋅=:=

Inside diameter of the contact area under the head of driven fastner dh :=

Half flank angle of blt threadβth

π

60.524=:=

Coefficien of friction between bolt and nut thread μG 0.14:=

Mimimum coefficien of friction between the bolt and nut thread μG.min 0.1:=

Maximum coefficien of friction between the bolt and nut thread μG.max 0.14:=

Coefficien of friction at the contact of the driven head μK 0.14:=

Mimimum coefficien of friction at the contact of the driven head μK.min 0.14:=

Maximum coefficien of friction at the contact of the driven head μK.max 0.14:=

Degree of explotiaiton of bolt yield stress desired at max assembly condition ν 90%:=

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lK 520 mm⋅:=

Bolt clamp Length

Shank length l1 lK:=

Hole diameter

Joint coefficientw 1:=

Clamped parts hole diameter dh 22 mm⋅:=

dw 30 mm⋅:=

DA 110 mm⋅:=

φ atan 0.6( ) 30.964 deg⋅=:=

Rp.0.2.min 450 MPa⋅:=

Esteel 200 GPa⋅:=

Econc 30 GPa⋅:=

Ep Econc:=

Maximum assembly preloadexpected from tightening to specifiedtorque

FM.Tab

AS ν⋅ Rp.0.2⋅

1 34

1d3

d2+

P

π d2⋅

μG.min

cos βth( )+

⋅

2

⋅+

86.112 kN⋅=:=

Note this is not with in the VDI spec and should normally be taken from tables

A Minimum clamping force required FA.max 45 kN⋅:=

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R1 tightening factor in acordance with table 8 αA 1.7:=

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bolt diameter to clamping lengthlK

d030.709=

For friction coefficient class BFKRmin 50 kN⋅:=

R2 Required minimum clamp load.

The joint is symetrically clamped

FKerf FKRmin:=FKerf 5 10

4× N=

R3 Splitting the working load, elastic resilience and load introduction factor

δS

lK

AS Esteel⋅:=

δS 1.061 105−×

mm

N⋅=

δP

2

w dh⋅ tan φ( )⋅ln

dw dh+( ) DA dh−( )⋅

dw dh−( ) DA dh+( )⋅

⋅2

DA2

dh2−

lK DA DW−( )−

w tan φ( )⋅

⋅+

Ep π⋅:=

δP 3.697 106−×

mm

N⋅=

Load facto with the application under the bolt head

ΦK

δP

δP δS+0.258=:=

Φ ΦK:=

fZ 3.5 μm⋅:= fZ 3.5 106−× m=R4 Preload changes

See table 5.4/1 P64FZ

fZ 2⋅

δP δS+489 N=:= 2 no interfaces

R5 Determinine the minimum assembly preload

No temperature reqirements∆FVth 0 N⋅:=

FM.min FKerf 1 Φ−( ) FA.max⋅+ FZ+ ∆FVth+:=

FM.min 84 kN⋅=

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R6 Determine maximum assembly preload

FM.max αA FM.min⋅:=

FM.max 143 kN⋅=

R7 Determine the assembly stressσred.Mzul ν Rp.0.2.min⋅:=

σred.Mzul 405 MPa⋅=

FMzul

A0 ν⋅ Rp.0.2.min⋅

1 33

2

d2

d0⋅

P

π d2⋅1.55 μG.min⋅+

⋅

+

:=

FMzul 65 kN⋅=

FM.max 142.567 kN⋅=

Φ FA.max⋅ 11.626 kN⋅=

0.1 Rp.0.2.min⋅ AS⋅ 11.025 kN⋅=

R8 Determine the working stress

Φ FA.max⋅ 11.626 kN⋅=

FS.max FMzul Φ FA.max⋅+:=

FS.max 76.632 kN⋅=

σZ.max

FS.max

A0:=

σZ.max 340.295 MPa⋅=

τmax

Mg

Wp:=

Mgd ??????????

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FS.max 76.632 kN⋅=

FM.max 142.567 kN⋅=

FM.min 83.863 kN⋅=

FA

GS.max.x

FS.max− δS⋅

0 mm⋅

FS.max δP⋅

:=GM.max.x

FM.max− δS⋅

0 mm⋅

FM.max δP⋅

:=GM.min.x

FM.min− δS⋅

0 mm⋅

FM.min δP⋅

:=

GS.max.y

0 kN⋅

FS.max

0 kN⋅

:=GM.max.y

0 kN⋅

FM.max

0 kN⋅

:=GM.min.y

0 kN⋅

FM.min

0 kN⋅

:=

GZ.x

FM.min− FZ+( ) δS⋅

0 mm⋅

FM.min FZ+( ) δP⋅

:=

GKerf.x

FKerf−( ) δS⋅

0 mm⋅

FKerf( ) δP⋅

:=

GZ.y

0 kN⋅

FM.min FZ−( )0 kN⋅

:=

GKerf.y

0 kN⋅

FKerf( )0 kN⋅

:=

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2− 1− 0 1

50

100

150

GS.max.y

kN

GM.max.y

kN

GM.min.y

kN

GZ.y

kN

GKerf.y

kN

GS.max.x

mm

GM.max.x

mm,

GM.min.x

mm,

GZ.x

mm,

GKerf.x

mm,

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FKerf

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Mathcad - Bolt Loading VDI M39 01

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