Some fundamentals of coefficient of friction of threaded fasteners. Focused on bolts in the automotive industry. ISO 16047 description and requirements in the automotive industry

1. 1
Presentation
Coefficient of friction on
threaded fasteners in the
automotive industry
Erik Galdames
Bach. of Eng., Chem.
Xativa, Spain
01

2. 2
Contents
Introduction
Standards and specs
Symbols
Test of coefficient of friction
Formula of Kellermann-Klein
Origin of formula of coefficient of friction
Total coefficient of friction
Bearing surface under the head of the bolt
Influencing factors on coefficient of friction
Coating systems
ISO 16047
Standards and specs of coefficient of friction
Requirements of coefficient of friction
International basic vocabulary

3. 3
Introduction
Fricción
debajo de
cabeza
50%
Fricción en
rosca
40%
Fuerza de
apriete
10%
10% generates
clamping force
40% used in
overcoming
friction on the
thread
50% used in
overcoming
friction under
the head
Tightening process

4. 4
Introduction
Coefficient of friction of bolted joints is determined measuring force and torque. It is a standardized
method that uses a formula in which F and T mainly and dimensional characteristics of the bolt/nut to be
studied
Mating surfaces and reference bolts/nuts are to be the same and agreed so that results are reproducible
and used for comparison
This test is not suitable to predict behaviour of assembly problems but can give some hints of how the
tightening will be
Variations of this test under real conditions in the automotive industry can be used in order to predict
behaviour at the assembly (e.g. VDA 235-203)
T F
F
Tb
Tth = T – Tb
Reference nut
Bolt
Measuring
cells
Bearing plate
Nut holder

5. 5
Introduction
The method of calculation is the linear relationship between clamping force and torque
below the yield point of the bolt
An axial force is produced when a bolt is tightened against a bearing surface and a nut by
means of a pair of forces (torque). This force elongates the bolt and compresses the
bearing surfaces in contact, i.e. two opposite forces are produced
Not all torque is used to generate clamping; most of the torque applied is used to overcome
friction
50% of torque is used in overcoming friction under the head of the bolt, 40% on the thread
and only 10% is used to generate clamping force
Compression/Elongation Equilibrium of forces

6. 6
Standards and specs
DIN 946
(withdrawn)
Bestimmung der Reibungszahlen von Schrauben und Muttern unter festgelegten
Bedindungen
ISO 16047 Fasteners – Torque/Clamp force testing
Renault 01-50-005 Eléments de fixation – Contrôle du coefficient de frottement
PSA C10 0054 Vis goujons écrous – Aptitude au frottement
Ford WZ100 and
WZ101
Steel Metric Threaded Fasteners Torque/Clamping Force Performance
VDI 2230 Systematische Berechnung hochbeanspruchter Schraubenverbindungen Zylindrische
Einschraubverbindungen
EN 14399-2 Aptitud de uniones atornilladas HV. Ensayo de fuerza y par de apriete
ISO 2320 Prevailing torque type steel nuts. Mechanical and performance properties

7. 7
Symbols
ISO 16047:2005
d Nominal diameter Fu Ultimate clamp force
d2 Thread flank diameter (basic pitch diameter of
thread)
Fy Yield clamp force
d4 Hole diamater of equipment T Torque
dh Hole diameter of the washer or support plate Tth Thread torque
Do Outer diameter of the bearing surface Tb Bearing surface torque (bearing surface and
under the head of the bolt/nut)
Dp Diameter of plain area of bearing plate P Pitch
Db Diameter of bearing surface under nut or bolt
head for friction (theoretical or measured)
Rotating angle
LC Clamp length th Coefficient of friction on the thread
Lt Length of complete thread between bearing
surfaces
b Coefficient of friction on the bearing surface and
under bolt head/nut
F Clamping force tot Total coefficient of friction
FP Proof load acc. to ISO 898-1, ISO 898-2 o ISO
898-6

8. 8
Test of coefficient of friction
A torque is applied to a bolted joint made of a bolt, a nut and a bearing surface to generate a clamping
force with a rotating unit driven by an encoder motor
Torque and clamping force are measured by the measuring head
Normally, only clamping force, total torque and torque on the bearing surface under the bolt head can be
directly measured. Torque on the thread is calculated through a formula. A graph representing force and
torque is represented. The coefficient of friction is represented through the relation between these two
values
0 10 20 30 40 50 60 70 80 90 100
Clamping Force/Fv [kN]
Torque/Ma[Nm]
0
20
40
60
80
100
120
140
160
Ma/Fv-_001.PRB
µges_UL-_001.PRB
µges_LL-_001.PRB
Ma/Fv-_002.PRB
µges_UL-_002.PRB
µges_LL-_002.PRB
Ma/Fv-_003.PRB
µges_UL-_003.PRB
µges_LL-_003.PRB
Ma/Fv-_004.PRB
µges_UL-_004.PRB
µges_LL-_004.PRB
Ma/Fv-_005.PRB
µges_UL-_005.PRB
µges_LL-_005.PRB
Ma/Fv-_006.PRB
µges_UL-_006.PRB
µges_LL-_006.PRB
Ma/Fv-_007.PRB
µges_UL-_007.PRB

9. 9
Formula of Kellermann-Klein
The formula for determination of
coefficient of friction is base on the work of
Kellermann-Klein
This formula of Kellermann-Klein was
published in 1956 by Rudolf Kellermann
and Hans Christof Klein in the essay
“Berücksichtigung des Reibungszustandes
bei der Bemessung hochwertiger
Schraubenverbindungen”
(10)
4154,1
154,1
2
1
2
2 ho
b
th
th dD
d
P
dP
FT

10. 10
Origin of the formula of coefficient of friction
When clamping force is below the yield point of the
bolt, coefficient of friction is directly proportional to
torque and inversely proportional with clamping
force
When coefficient of friction is higher, torque is
higher, clamping force is lower
When coefficient of friction is lower, torque is lower,
clamping force is higher
Tightening process of a bolt can be decomposed as
an object moving upwards through a slope. Formula
of Kellermann-Klein is determined through the study
of this movement
Tightening of a bolt
Pitch
1/2xPitch
Unfolded helix
Pitch angle
Pitch
Helix
Cifcumference of the circle

11. 11
Total coefficient of friction
Kellermann-Klein’s formula is too complicated to use
it as it is and it is simplified for practical usage
It is assumed that friction under the head and friction
on the bearing surface is the same, making the
formula easier to use
The general method for calculation simplifies partial
coefficient of friction under the head and on the
thread through
µtot = µth + µb)/2
µtot = µth = µb
Uncertainty of 1% to 2%
To determine coefficient of friction it will be necessary
to know:
T, Tb, F, measured by equipment
Tth is calculated through T = Tb + Tth then, Tth = T -
Tb
P, d2 y Db Dimensional parameters of the bolt/nut
Target values of T and F are obtained through a table
for the different dimensions of bolts/nuts
– It is necessary to know the characteristics of the
bolt (diameter, pitch, flank diameter, PC)
– Clamping force applied is 75% of proof load acc. to
ISO 16047
F values are determined through ISO 898-1, ISO
898-2 (ISO 16047)
(5)
2
577,0
2
2
b
tot
D
d
P
F
T

12. 12
Bearing surface under the head of the bolt
Do
dh
Do
dh
Do
dh
Hex bolt Hex bolt with washer Hex flange bolt
2
3 22
0
33
0
ho
b
h
h
b
dD
D
dD
dD
D

13. 13
Influencing factors on coefficient of friction
Lubricants adjust coefficient of friction and reduce variability of friction. They
adjust coefficient of friction on a certain window so that friction is more regular.
Their action relies on the interfering action caused by the molecules of lubricant
between the mating surfaces and thus, friction is reduced
Modern coating systems incorporate solid lubricants in their formulation. Thus,
not only corrosion protection is obtained; lubrication is additionally among their
properties
In practice, the following factors have an influence on coefficient of friction:
– Surface treatment. Type of coating (metallic, zinc flake coatings, lubrication, layer
thickness, dirt)
– Bearing surface. Hard surface (e.g. roughness, heat treated, non-heat treated steel,
aluminium, KTL)
– Geometry of the head. Pan head screw, hexagonal bolt, hex flange bolt, diameter of
the head, washer
– Thread of the mating nut. With coating, without coating, with or without oil.
Manufacturing process of the nut
– Testing conditions. Temperature, humidity, speed of rotation
Values of coefficient of friction can be adjusted but these factors may influence
their predictible behaviour dramatically if out of control or when there is too much
variation

14. 14
Influencing factors on coefficient of friction
Lubricants based on emulsions in water can be applied such as waxes, oils and solid
lubricants in water mixes (e.g. PE, PTFE, PAK, molybdenum bisulfide). They are dried after
application and they provide a stable coefficient of friction
Solid lubricants or sealers with solid integrated lubricants provide less variation of
coefficient of friction than liquid or lubricants in water emulsions and provide better results
in automated assembly
Solid lubricants also provide better repeated assembly
Variation of coefficient of friction will be higher when working with µ > 0,14. The tend to
scatter more
Values under µ < 0,08 are difficult to adjust and are not desirable, since self-loosening
effect may appear
Values over 0,25 do not produce sufficient tightening, so there is a high risk of fatigue
fracture
Values under 0,06 can lead to ultimate clamping load. High risk of fracture.
There are some bolted unions that request coefficient of friction of 0,06 to 0,09
Uncontrolled lubrication such as oil spraying on the workshop could lead to lower
coefficient of friction and unsafe bolted unions. This may lead to ultimate clamping force
and thus, bolt fracture. This situation must be avoided

15. 15
Coatings
Coatings and lubricants help improving friction behaviour and offer less variation
of values of coefficient of friction
Coatings for bolted joints in the automotive industry consist mainly on:
– Phosphate + post-treatment
– Electroplated Zn or Zn alloys (ZnNi, ZnFe) + post-treatment
– Zinc flake coatings + post-treatment
As post-treatments, the following materials are available:
– Lubricants
Waxes
Oils
PTFE
MoS2
– Sealers with integrated lubricants
Anorganic sealers
Organic and anorganic sealers
– Organic coatings with integrated lubricants
Sealers with integrated lubricants offer corrosion resistance and temperature
resistance besides lubrication properties

16. 16
ISO 16047
Uncertainty 2%
Room temperature, 10ºC to 35ºC, 24 h after coating application
Applied clamping force, 75% of proof load 0,75·FP (see ISO 898-1, ISO 898-2)
Rotation speed = 10 a 40 rpm (M1,6 to M16), 5 to 15 rpm (M16 to M39)
Bearing plate or washer type HH or HL
– Roughness Ra = 0,5 0,3 µm (Ra < 1,6 µm and Ra < 3,2 µm washer type HL)
– Tolerance of flatness acc. to ISO 4759-3, section 3.5.3
– Surface
a) Blank and degreased
b) Zinc plating A1J acc. to ISO 4042 and degreased
– Minimum thickness according to ISO 7093-1
– Hardness 50 to 60 HRc (200 to 300 HV for washer type HL)
– Hole diameter dh, acc. to ISO 273, medium series, without chamfering
Reference nuts for bolt testing
– A) ISO 4032 and ISO 8673 class 10 uncoated nuts and degreased.
– B) Zinc plated nuts A1J ISO 4042 and degreased
Reference bolts for testing nuts
– Uncoated and degreased bolts ISO 4014, ISO 4017, ISO 4762, ISO 8765, ISO 15071, ISO 15072
– Zinc plated bolts A1J acc. to ISO 4042 and degreased

17. 17
Standards and specs of coefficient of friction
ISO 16047 Ford WZ100 Ford WZ101 VOLVO STD
5511,72
BMW GS90003-1
GS90003-2
µtot -- N/A 0,14 0,03 0,12 – 0,18 0,09 – 0,15
F 75% Fp 75% Fp 75% Fp 75% Fp See tables on
GS9003-2
Temperature 10ºC a 35ºC RT RT 10 – 35ºC 10ºC a 35ºC
Rpm 10 a 40 rpm M<16 <30 rpm 30 10 rpm < M16 10 – 25 rpm 10 – 25 RPM
Uncertainty 2% F, T, 3% F, 2% T 2% F, T 2% F, T 2% F, T
Bearing surface 200 – 300HV (HL)
50 – 60 HRC (HH)
Steel
500 – 600HV
Steel
200 – 250HV
≤ 8.8 200-250 HV
10.9 = 300 – 400 HV
12.9 = 350 – 450 HV
Type HH 50 – 60 HRC
Roughness Ra 1,6 ≤ 3 mm; Ra
3,2 3 < h ≤ 6 mm
N4-N5 ISO 1302 Ra 1,2 a 1,6 µm Ra 1,6 max Ra 1,6 max (≤ h 3 mm)
Ra 3,2 max (> h 3 mm
Tolerance flatness See ISO 4759-3
class A
// 4% // 4% // 4% See ISO 4759-3
class A
Dimensions Acc. to standard Acc. to standard Acc. to standard Acc. to standard Acc. to standard
Reference nuts ISO 4032, 8673, 4033,
8674 6H
Thread ISO 965/1 6H ISO 4032 6H ISO 4032 6H ISO 4032, 8673, 4033,
8674 6H
Nut surface Uncoated, oil free S309
zinc plated passiv. lubr.
Uncoated, oil free Uncoated oil free Uncoated, oil free
Reference bolt ISO 965/1 6g ISO 4014 6g ISO 965-2 6g ISO 965-2 6G
Bolt surface Uncoated, oil free S309
zinc plated passiv. lubr.
Uncoated, oil free Uncoated, oil free Uncoated

18. 18
Requirements of coefficient of friction
0,07 0,08 0,09 0,10 0,11 0,12 0,13
VDA 235-101
VW 011 29
Ford WZ 101
GMW 3359, GMW 3044
Renault 01-50-005C
PSA C10 00 54
0,06 0,14 0,15 0,16 0,17 0,18
µth, µb
Low Friction µtot
Normal Friction µtot
µth, µb
µtot (*) µtot (*)µtot
µtot
µtot
µtot
(*)Interval enlarged to include uncertainty of measurement of coefficient of friction
µtot
Volvo STD 5511,72 µtot
BMW GS 90003-1 µtotµth, µb µth, µb

19. 19
International basic vocabulary
Spanish English French German Italian
Coeficiente de fricción Coefficient of friction Coefficient de frottement Reibungszahl Coefficiente d’attrito
Par de apriete, momento de
apriete
Tightening torque Couple de sérrage Anziehdrehmoment Coppia di serraggio,
momento di serraggio
Carga, tensión Clamp force Tension Vorspannkraft Precarico, tensione
Carga de prueba Proof load Tension d’épreuve Prüfkraft Carico di prova
Carga de rotura Ultimate clamp force Tension de rupture Bruchkraft Carico di rottura
Límite elástico Yield point Limite d’élasticité Streckgrenze Limite d’esnervamento
Ángulo de giro Rotating angle Angle de rotation Drehwinkel Angulo di giro
Tornillo Bolt, screw Vis, boulon Schraube Vite, bullone
Tuerca Nut Écrou Mutter Dado
Arandela Washer Rondelle Scheibe Rosetta
Espárrago Stud Goujon Stiftschraube Prigioniero
Rosca Screw thread Filetage Gewinde Filetto, filettatura
Superficie de apoyo Bearing surface Surface d’appui Auflagefläche Superficie sottotesta
Agujero de paso Clearance hole Taraudage Durchgangsloch Foro de passo
Paso de rosca Pitch Pas Steigung Passo

20. 20
THE END
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Thanks for your attention!
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