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
oct. 2005 2/63 Traian CICONE
Eye bolt Threaded pin (setscrew/grub screw)
Threaded oil sight glass cap
Typical threaded elements I
2
oct. 2005 3/63 Traian CICONE
Typical threaded elements IIClamping screw
F
Bolt
Hex Nut
Split lock washer
Clamped parts
Fan blade
oct. 2005 4/63 Traian CICONE
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
oct. 2005 5/63 Traian CICONE
Micrometer
Rigger’s viceSwivel basc vice
Turnbuckle
Power screws applications
oct. 2005 6/63 Traian CICONE
Power screws II• Rotating screw – Translating screw• Rotating nut – Translating screw• Rotating nut – Translating nut• Rotating screw – Translating nut
4
oct. 2005 7/63 Traian CICONE
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
oct. 2005 8/63 Traian CICONE
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
oct. 2005 9/63 Traian CICONE
d2
Centre axis
Mean (pitch) dia,
Root (minor) dia
Crest (major) dia (NOMINAL DIA)
Pitch, p
d1 (d3 )
d STANDARD
Screw thread dimensions
oct. 2005 10/63 Traian CICONE
Centre axis
Screw thread dimensions
Mean (pitch) dia
D2
Crest (minor) dia
Root (major) dia
D1
D4
Pitch, p
d2 = D2
6
oct. 2005 11/63 Traian CICONE
Screw thread dimensions
External thread
Centre axis
Internal thread
Mean (pitch) dia
Clearance
oct. 2005 12/63 Traian CICONE
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
oct. 2005 13/63 Traian CICONE
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)
oct. 2005 14/63 Traian CICONE
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
oct. 2005 15/63 Traian CICONE
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
oct. 2005 16/63 Traian CICONE
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
oct. 2005 17/63 Traian CICONE
Types of screw head
oct. 2005 18/63 Traian CICONE
Socket Setscrews & Tapping Screws
Cone point Flat point Oval point Half-dog point Cup point
Thread cutting screws
Thread forming screws
10
oct. 2005 19/63 Traian CICONE
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
oct. 2005 20/63 Traian CICONE
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
oct. 2005 21/63 Traian CICONE
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
oct. 2005 22/63 Traian CICONE
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
oct. 2005 23/63 Traian CICONE
Technology II• Thread milling • Thread cutting (lathe)
oct. 2005 24/63 Traian CICONE
Technology III
• Thread rolling = cold forming process • External thread cutting with die
• Plastic deformation (rolling or forming)
13
oct. 2005 25/63 Traian CICONE
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
oct. 2005 26/63 Traian CICONE
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
oct. 2005 27/63 Traian CICONE
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
oct. 2005 28/63 Traian CICONE
S
Do
Forces and moments acting in a screw pair
( )*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
oct. 2005 29/63 Traian CICONE
Forces and moments acting in a screw pair
( )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
oct. 2005 30/63 Traian CICONE
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
oct. 2005 31/63 Traian CICONE
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
oct. 2005 32/63 Traian CICONE
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
oct. 2005 33/63 Traian CICONE
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
oct. 2005 34/63 Traian CICONE
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
oct. 2005 35/63 Traian CICONE
Solutions to increase efficiency II
(iii) Ball screw
95.0...85.0=η
Multiple circuit ball screw
oct. 2005 36/63 Traian CICONE
Solutions for increased efficiency III
(iv) Rolling element power screw (Planetary roller-screw)
19
oct. 2005 37/63 Traian CICONE
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
oct. 2005 38/63 Traian CICONE
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
oct. 2005 39/63 Traian CICONE
Joint stiffness – FEM analysisF=24 kNDi=17 mmDo=20 mm
pm=275 MPapmax=347 MPa
60°
Simplified model
FEM model
oct. 2005 40/63 Traian CICONE
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
oct. 2005 41/63 Traian CICONE
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
oct. 2005 42/63 Traian CICONE
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
oct. 2005 43/63 Traian CICONE
Joint diagram Applied force
F0
F
δ*F
∆l
F
F′0
δ
∆ls
Ft
F″0
F*t
F′0
oct. 2005 44/63 Traian CICONE
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
oct. 2005 45/63 Traian CICONE
Elastic bolts for connecting rod big end
oct. 2005 46/63 Traian CICONE
F
∆l
Joint diagram Joint embedding
Amount of joint deformation due to embedding
F0
Preload after embedding
24
oct. 2005 47/63 Traian CICONE
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%
oct. 2005 48/63 Traian CICONE
Bolt failures
www.boltscience.com
25
oct. 2005 49/63 Traian CICONE
Bolt failures Vise Power Screw
oct. 2005 50/63 Traian CICONE
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
oct. 2005 51/63 Traian CICONE
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
oct. 2005 52/63 Traian CICONE
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
oct. 2005 53/63 Traian CICONE
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≈
oct. 2005 54/63 Traian CICONE
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
oct. 2005 55/63 Traian CICONE
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
oct. 2005 56/63 Traian CICONE
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
oct. 2005 57/63 Traian CICONE
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
oct. 2005 58/63 Traian CICONE
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
oct. 2005 59/63 Traian CICONE
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
oct. 2005 60/63 Traian CICONE
Lock nuts
Castle nutSlotted nut
Nut and split spring washers
31
oct. 2005 61/63 Traian CICONE
Thread insertRepairing solution
oct. 2005 62/63 Traian CICONE
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
oct. 2005 63/63 Traian CICONE
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