Ch. 2. Threaded Fasteners & Power Screws - · PDF fileCh. 2. Threaded Fasteners & Power Screws...

1

oct. 2005 1/63 Traian CICONE

Ch. 2. Threaded Fasteners & Power Screws

Dedicated threaded components (fasteners) - screws, bolts, studs, pins, nuts

Various parts, threaded - caps, housings, wheels, etc

THREAD the ridge (channel) usually of uniform section, in the form of a helix on the external or internal surface of a cylinderor in the form of a conical spiral on the external or internal surface of a cone or frustrum of cone

d1(d3)d2d

p

α1

π d1(d3)

π d2π d2

π d

αα2α1

directrix helix

directrix cylinder

generating profile


Eye bolt Threaded pin (setscrew/grub screw)

Threaded oil sight glass cap

Typical threaded elements I

2


Typical threaded elements IIClamping screw

F

Bolt

Hex Nut

Split lock washer

Clamped parts

Fan blade


Jack ScrewConvert rotary motion of either the screw or the nut into translation of the mating member along the screw axis.

Also called

Lead screws

Translation screws

Linear actuators

Power screws I

3


Micrometer

Rigger’s viceSwivel basc vice

Turnbuckle

Power screws applications


Power screws II• Rotating screw – Translating screw• Rotating nut – Translating screw• Rotating nut – Translating nut• Rotating screw – Translating nut

4


FUNCTIONS

INFOWWW.BOLTSCIENCE.COM

• To locate/join parts (FASTENERS)

• To measure length

• To exert/transmit a force

• To convert rotational motion to linear motion (or vice versa)

(POWER SCREWS)

Screw Mechanism = Self locking Mechanism


0.12p p

60°

0.61p

Unified National (inch size)

55°

pR=0.137p

R

Whitworth Standard

p/2p

60°

0.87p

Sharp V

0.12p p

60°0.54p

ISO Metric(a) (b) (c) (d)

pp/2

p/2

Square

p/2p

29°

0.37p

ACME (Trapezoidal)

p/2

p 0.16p7°

45°

Buttress

0.66p

pp/2p/2

Knuckle(e) (e) (f) (g)

Screw thread forms

POWER SCREWS

trapezoidsquare

reduced stress concentrator

arc of circle

triangle

one directional loading

5


d2

Centre axis

Mean (pitch) dia,

Root (minor) dia

Crest (major) dia (NOMINAL DIA)

Pitch, p

d1 (d3 )

d STANDARD

Screw thread dimensions


Centre axis


Mean (pitch) dia

D2

Crest (minor) dia

Root (major) dia

D1

D4

Pitch, p

d2 = D2

6



External thread

Centre axis

Internal thread

Mean (pitch) dia

Clearance


H/4

H/8

60°

H/16

H

H/2D

screw & nut axis

d2=D2

D1H/6

dd1

H2

p

H1=5H/8=0.541p

H=0.866pH1

H2=H1-H/16=0.487p

screw

nut

Metric screw standard dimensions

THREAD SPECIFICATION

M 40 × 1.5 LHd p

Type Other details•Helix direction•Class of tolerances•No of starts

7


Metric screw classification

end of thread

(a) Single thread – right hand

p l

α2

end of thread

(b) Double thread – left hand

pl

α2 end of thread

Pitch, p Pas aparentLead, l Pas

• Single thread• Double thread

Number of starts• Left hand• Right hand

Helix direction• Coarse• Fine• Extra-fine

Thread series (pitch)


Screw head

Shank

Runout (end of thread)

Fillet

Helix angle, α

Major (nominal) diameter, d

Minor(root) diameter, d1 (d3)

Shank diameter- d0 usually about same as

nominal diameter

Pitch, p Thread

Screw body

Crest

Root

Tip

Thread: type, d2 & p, details

Body: type, length, (d0)

Head & Tip type

Reduced shank Elasticized bolt

d0 < d d0 > d

Enlarged shank Shoulder bolt

(fitted bolt)

FASTENERS - Terminology I

8


Threaded fasteners - Terminology I

(c) Stud & nut (d) Threaded rod & nuts

(a) Screw (b) Bolt & nut

length of engagement

length of engagement

grip

grip

washer

clearance

clearance

length of the screw


Threaded fasteners

Flat head screw

Oval head screw

Fillister head screw

Hexagon-socket head screw

Cross-recessed (Phillips) head screw

Hex head screw

Hex flange head screw

Square head screw

Round head screw

Round head square neck screw

9


Types of screw head


Socket Setscrews & Tapping Screws

Cone point Flat point Oval point Half-dog point Cup point

Thread cutting screws

Thread forming screws

10


Types of nuts

Square nut Weld nut Hex plain nut(Jam nut)

Speciality nut Serrated nut

Anchor nut Cap (acorn) nut

Panel nut Flanged nut Spring nut

Wing nut Speed nut Palnut nut Barrel prong nut

Castle nut


WashersFlat washer External tooth

countersunk lockwasher

Coil spring washer

Helical spring/Split spring/ Lockwasher

Internal tooth lockwasher

Conical spring (Belleville)

Conical washer with hardened teeth.

(Serrated washer)

11


Materials

Normal application - low or medium carbon steel

M40 × 15 - 6.8 SCREW

Power screw - power & motion transmission ACME/Square/Buttress

Fasteners - assembly Metric - M

σY = min 6×8 × 10MPa

STEEL / Cast iron, bronzeHARD / SOFT - to prevent excessive wear and seizure at high speed

Important application - alloy steel (Mo, Ti, Ni-Cr)

Special application - brass, high-resistance plastics

MATERIAL SPECIFICATION

SCREW

NUT Phosphorous wrought steel, alloy steel, plastics

M40 - 6 NUT

σu = min 6×100MPa


Technology I• Chip removal (cutting)

Tap Drill

(Drill bit)

Drilling Reaming Counterboring Threading

Taper Tap

L

d0

60°

≈ minor diameter of the thread

drill depth

l

d crest diameter c×45°

chamfer

12


Technology II• Thread milling • Thread cutting (lathe)


Technology III

• Thread rolling = cold forming process • External thread cutting with die

• Plastic deformation (rolling or forming)

13


Forces and moments acting in a screw pair I

22tan

dp

πα =

• p - pitch

• α2 – mean lead angle

• d2 - mean diameter

d1(d3)d2d

p

α1

π d1(d3)

π d2π d2

π d

αα2α1

directrix helix

directrix cylinder

generating profile


Forces and moments acting in a screw pair - II

c) screwing up(tightening)

b) unwind thread

a) detail of a square threadwith a part of a nut

Ff

F

N

T

α2

α2

α2

TF

d2

d1

d

N

T

F

µϕ =)tan(

NFf µ=

0=+++ FNFT f

rrrr

=−+−=−−

0cossin0sincos

22

22

αααµα

FNTFNT

( )ϕα += 2tanFT

load displacement

friction between threads

14


Screwing down (loosening)

Forces and moments acting in a screw pair

Ff

F

N

Tα2

α2( )ϕα −−= 2tanFT

ϕα <2Self-locking condition

(No overhauling)

β

N N*

β/2

( )2cos*

βµµ NNFf ==

( )2cos*

βµµ = **tan µϕ =

( )*2tan ϕα ±= FT

Inclined flank of the thread β

*2 ϕα <

( )*2

221 tan

22ϕα ±==

dFdTMtTightening torque


S

Do


( )*2

221 tan

22ϕα ±==

dFdTMt1) Tightening torque

2) Friction torque

a) Collar (constant contact pressure)

20

2

30

32

22 3

d20

DSDSFrrrpM c

S

Dct

−

−⋅== ∫ µπµ(i)

mct FRM µ=2 40DSRm

+=(ii)

F

r

dr

p=const.

15



( )3

d2 02

02

0 dFrrprM c

d

ct µπµ == ∫

b) Bearing surface (constant contact pressure)F

d0d0

mbt FRM µ=2 4DdRm

+=

c) Rolling element bearing

Rm

D

d

F

2) Friction torque


Conclusions

aSF )10060( ÷= The thread is an important force amplifier(a)

(b) The total axial load acting upon the screw can not be accurately known

awtot SLKFM ==

Lw

Sa

( )dLw 1512÷≈( )dK 20.015.0 ÷≈

FKMMM tttot =+= 21Total torque

16


0,0

10,0

20,0

30,0

40,0

50,0

0 10000 20000 30000 40000 50000

Axial force F , [N]

Tigh

teni

ng T

orqu

e, M

t` [N

m]

µ =0.01

µ =0.05

µ =0.2

µ =0.1

µ =0.4

no friction

Mt1≈23Nm

F ≈ 19 kN ! F ≈ 46 kN !

Torque - Axial Load Relationship

M10×1.5


66%

28%16%

9% 5%

19%

41%48%

52% 54%

14%

31% 36% 39% 41%

0%

20%

40%

60%

80%

100%

Torq

ue

Friction in threads

Useful Torque

Friction on collar

µ =0.01 µ =0.05 µ =0.2µ =0.1 µ =0.4

M10×1.5

Total Torque Efficiency

17


0

0.2

0.4

0.6

0.8

1

0 10 20 30 40 50 60Pitch angle, α 2

Efii

cien

cy, η

square threadISO Metric thread

µ =0.2 (ϕ =11.3o)

µ =0.1 (ϕ =5.7o)µ =0.05 (ϕ =3o)

µ =0.01 (ϕ =0.6o)

Efficiency of a threaded pair

( )*2

2

2 tantan

ϕαα

πη

+==

TdFp

FpLu =useful work

toti ML π2=input worki

u

LL

=η

( ) °÷= 4241max2α

( ) °÷= 622 typicalα

t1i ML π2=only for threaded pair


Solutions to increase efficiency I

(ii) Hydrostatic screw(i) Multiple start screw

22tan

dπα l

= For the same pitch, p, α2 increases Very low friction coefficient

( )*2

2

2 tantan

ϕαα

πη

+==

TdFp

0

0.2

0.4

0.6

0.8

1

0 10 20 30 40 50 60Pitch angle, α 2

Efii

cien

cy, η

square threadISO Metric thread

µ =0.2 (ϕ =11.3o)

µ =0.1 (ϕ =5.7o)µ =0.05 (ϕ =3o)

µ =0.01 (ϕ =0.6o)

18


Solutions to increase efficiency II

(iii) Ball screw

95.0...85.0=η

Multiple circuit ball screw


Solutions for increased efficiency III

(iv) Rolling element power screw (Planetary roller-screw)

19


p

F=0F0≠0

b)

∆lf

∆ls

F0

Preloaded fasteners in tensionF≠0 F0≠0

δ

δ

c)

F=0 F0=0

a)

F

2. Operation, F

1. Preloading=tightening F0

F0


Joint stiffness

confined“O”-ring

unconfinedgasket

∑=i ii

i

s/f AEkl1

Equivalent stiffness l1

l2

d0

d

+= 2

2

220

1 4411ddEks ππllExample

BOLT STIFFNESS

CLAMPED PARTS STIFFNESS

20


Joint stiffness – FEM analysisF=24 kNDi=17 mmDo=20 mm

pm=275 MPapmax=347 MPa

60°

Simplified model

FEM model


Joint diagram Preload

s

0s k

F=∆l

f

0f k

F=∆l

Bolt extension line

ψs

∆ls

ψf

Joint compression

line

∆lf

F0

F

Extension

Compression

∆l∆l

)tan( ssk ψ=)tan( ffk ψ=

ψf

21


Joint diagram Applied force

ss

z

kF

kF 0′′==δ 0FFF z ′′+=

F′0Residual clamping force

F

∆l

F

δ

F0

∆ls

ψs

FtTotal force in the bolt

F″0 Joint clamp force decrease

Fz

Bolt force increase

zt FFF += 0 000 FFF ′′−=′

∆lf

ψf

p

F=0F0≠0

b)

∆lf

∆ls

F0

F≠0 F0≠0

δ

δ

c)

F=0F0=0

a)

F


Total force in the boltfs

szt kk

kFFFFF+

+=+= 00

fs

f

kkk

FFFFF+

−=′′−=′ 0000Residual clamping force

fs

sz kk

kFF+

=Bolt force increase

fs

f

kkk

FF+

=′′0Joint clamp force decrease

Joint diagram Forces & Practical conclusions

Objectives

⇑′0Ff

sfs

f

kkkk

k

+=

+ 1

1High residual force in the joint

⇓tFLow force in the bolt

s

ffs

s

kkkk

k

+=

+ 1

1

CONTRADICTION⇓

⇓

22


Joint diagram Applied force

F0

F

δ*F

∆l

F

F′0

δ

∆ls

Ft

F″0

F*t

F′0


Joint diagram Variable loading & Practical conclusions

Elastic bolts

Rigid clamped parts

0F ′′

F

∆lψs ψf

Ft

F0

Fz

F

0F ′

Reduced shank down to the stressdiameter of the bolt in this regions

to reduce the bolt stiffness

23


Elastic bolts for connecting rod big end


F

∆l

Joint diagram Joint embedding

Amount of joint deformation due to embedding

F0

Preload after embedding

24


Bolt failures

Stripping of the external or internal thread

Rupture of the turns

Wear of the mating surfaces Failure of the threaded part

Failure through the shank or threaded section of the fastener

Stress concentrators

Plastic deformation of the turns

65% 15%

σaverage

σtrue

20%


Bolt failures

www.boltscience.com

25


Bolt failures Vise Power Screw


Thread Strength Calculation - Bearing Pressure

ASSUMPTION Uniform load repartition among the engaged turns zFP /=

d2 (D2)

Nut

Bolt

D4

d

d1(d3)d1(d3)

P=F/z

D1

a

H1

1. Contact stress

Contact surface - plane & annular

( ) akk HdzF

Dd

zF σππσ <=

−=

1221

2

/

4

/

=mobile MPafixed MPa

ak 3058030

K

Kσ

πd2

h

F/z

h/2

26


3. Shear stress (Stripping)

g

abb gd

ddzF

σπ

σ <

−

=

6

22

)3(1

)3(12Screw

abb gD

DDzF

σπ

σ <

−

=

6

22

4

24Nut

2. Bending stress Cantilever beam

ass gDzF τ

πτ <=

1

/ Nutass gdzF τ

πτ <=

)3(1

/ Screw

atsbeq στσσ <+= 22 4Compound stress

Thread Strength Calculation - Bending & Shear

πd2

h

F/z

h/2

d2 (D2)

Nut

Bolt

D4

d

d1(d3)d1(d3)

P=F/z

D1

a

H1


P

Stress Repartition

nutbolt

clampedmemeber

Force flow lines

Elasticized nut

50%

30%

20%

Uniform load repartition among the engaged turns - CRITICIZABLE

Number of mating threads z=max 10

27


Thread Strength Calculation

REMARKS

No need to calculate standard fastening screws

dm 8.0≈

Contact stress → length of engagement

d

≈ m

m

D0

dD 7.10 ≈

Number of mating threads z=max 10

Length of engagement =max (1.5-2) d

( )dp 2.01.0 K≈


A. Centrally loaded Critical cross-section - threaded zone

Effective cross-section - root diameter

1. Traction/Compression ( )catctd

F,

2)3(1

,

4

σπσ ==

3)3(1

1

16d

Mtπτ =2. Torsion

ateq στσσ <+= 22 4Compound stress

Screw Body Strength Calculation - Static loading

28


0F ′′

F

∆lψs ψm

0F ′F

Ft

F0

Fz

F

Screw Body Strength Calculation - Time variable loading

0FFmin =

zmax FFF += 0

20z

mFFF +=

2z

vFF =

2)3(1

4dFm

m πσ = 2

)3(1

4dFv

v πσ =

3)3(1

16dMt

m πτ = 0=vτ

Torque is constant during variable loading

Tension - fluctuating cycle

c

mvKc

σσ

σσ

εγβσ

σ+

=

−1

1m

ccττ

τ =

22v

veq

cc

ccc+

=σ

σ


Screw Dimensioning

A. Statically loaded Total torque Mtot not known -- estimated with γ

cat1(3)

Fd,

4πσ

γ> 5.12.1 ÷=γ Typical value γ=1.3

B. Variable (dynamically) loaded

( )

÷=

48.06.0

21dF Y0

πσ

29


Fasteners in shear

min0k d

Tl

=σ1. Bearing pressure

20

s dT

πτ 4

=2. Shear stress

µTF =

A) Clearance

d0l2

l1

B) Close fit

FT

T

T

T

σk


Locking devices

Prevail screw loosening (nuts, washers or else)

Principle of the operation(A) Solutions which exert supplementary forces into

the assembly – nut and jam nut, split-lock washer, spring head, etc.

(B) Solutions which do not exert supplementary loads into the assembly (which use the shape or the friction force in order to lock the assembly) –cotter pin and castle nut, pin-lock nut, distortion nut, etc.

Prevailing –torque locknuts

Free-spinning locknuts

30


LocknutsElliptical or polygon locknut

(b) (c) (d) (a)

(e) (f)

(g) (h) (i) (j) (k)

Split locknut Distorted threadsAdhesive

Nylon insertPin locknut

Spring-top nutNut & jam-nut Spring nut Nut & twisted-tooth washer


Lock nuts

Castle nutSlotted nut

Nut and split spring washers

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Thread insertRepairing solution


CONCLUSIONS I

Operating Features / Applications

High force amplifier for clamping, sealing, tensioning, lifting, etc.

Adjustment of relative position (“leading screw”) in positioning devices

Transformation of the motion (rotation ⇔ translation)

Length measurement

32


CONCLUSIONS IIPositive Features

High clamping load with moderate tightening force

Small overall dimensions

Great variety of design solutions, adapted to all types of applications

Simple technology

ShortcomingsHigh stress concentration in the threaded zone (Kσ ≈ 2...4)

Difficult to control exactly the clamping load

Requires supplementary solutions to secure clamping

Low mechanical efficiency

Does not ensure centering of the assembled parts

Does not provide sealing

Ch. 2. Threaded Fasteners & Power Screws - · PDF fileCh. 2. Threaded Fasteners & Power Screws...

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