Static Friction in Slip Critical Bolt

Joints

Coefficient of Friction in Steel, Aluminium and ED Coated Steel

Marcus Lång

Faculty of health, science and technology

Degree project of Bachelor of Science in Mechanical Engineering

22,5 ECTS Credits

Supervisor: Anders Wickberg

Examiner: Nils Hallbäck

Date: 05/06 -17

Revision 1

i

Abstract

This project was performed together with ÅF Industry AB in Trollhättan, Sweden. ÅF’s

expertise in Trollhättan is oriented towards the automotive industry. It was conducted within

the section of CAE and safety where they, for instance, dimension bolt joints in the cars. Bolt

joints play an important role in the automotive industry. Slip critical bolt joints are used

widely throughout the vehicles. With lack of good test data, the bolt joints need to be

dimensioned conservatively. This may lead to that bolt joints are over-dimensioned, adding

more mass to the car. On the contrary, the availability of reliable test data enables designers to

optimize joint dimensions to achieve a safe design with minimized mass.

A mechanical testing configuration has been designed as well as a testing procedure for a test

to determine the static friction value between mating surfaces in bolt joints. The testing

configuration has been used to perform tests to find the static friction coefficient in different

materials. The study contains varied combinations of steel, aluminium and ED-Coated steel.

The study resulted in tables with levels of probability, see one example below (see Figure i).

Figure i. Summary of results with the mean value and +/- three standard deviations, 99.730%

probability.

The developed test configuration is robust and relatively simple to use and is recommended

for further use. For improved statistical significance, it was noted that more samples should be

used than was used in this study. The aluminium has a smoother surface finish and that could

be the reason why its coefficient of friction is lower than steel. It is therefore considered

important to also include surface roughness when presenting coefficient of friction results.

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Abbreviations

CAD - Computer Aided Design

CAE - Computer Aided Engineering

ED - Electrophoretic Deposition

ISO - International Organization of Standardization

Nm - Newtonmeter

mV – Millivolt

Ra – Arithmetic mean deviation of assessed profile (Surface roughness)

SFN - Swedish Fastener Network

VDI - Verein Deutscher Ingenieure (The Association of German Engineers)

V – Volt

Symbols (Statistics)

𝐴𝑔 = 𝐴𝑟𝑒𝑎 𝑢𝑛𝑑𝑒𝑟 𝑡ℎ𝑒 𝑔𝑟𝑎𝑝ℎ 𝑤𝑖𝑡ℎ 𝑙𝑖𝑚𝑖𝑡 𝑍1 & 𝑍2

𝑓(𝑥) = 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛

𝑘 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑑𝑒𝑝𝑒𝑛𝑑𝑖𝑛𝑔 𝑜𝑛 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑒𝑠𝑡𝑠

𝑛 = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑒𝑠𝑡𝑠 𝑡𝑜 𝑏𝑒 𝑑𝑜𝑛𝑒

𝑆𝑥 = 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛

𝑋 = 𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛 𝑖𝑛 𝑠𝑎𝑚𝑝𝑙𝑒 (𝑖)

�� = 𝑚𝑒𝑎𝑛 𝑣𝑎𝑙𝑢𝑒

�� = 𝑇𝑟𝑢𝑒 𝑚𝑒𝑎𝑛 𝑣𝑎𝑙𝑢𝑒 𝑤𝑖𝑡ℎ 𝑐𝑒𝑟𝑡𝑎𝑖𝑛 𝑐𝑜𝑛𝑓𝑖𝑑𝑒𝑛𝑐𝑒

𝑍 = 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑛𝑜𝑟𝑚𝑎𝑙 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒

iii

Symbols (Friction & Bolt joints)

𝐴 = 𝐶𝑟𝑜𝑠𝑠 𝑠𝑒𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑎𝑟𝑒𝑎 [𝑚𝑚2]

𝐴𝑠 = 𝑆𝑡𝑟𝑒𝑠𝑠 𝑎𝑟𝑒𝑎 [𝑚𝑚2]

𝑑2 = 𝐵𝑎𝑠𝑖𝑐 𝑝𝑖𝑡𝑐ℎ 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 𝑒𝑥𝑡𝑒𝑟𝑛𝑎𝑙 𝑡ℎ𝑟𝑒𝑎𝑑 [𝑚𝑚]

𝑑3 = 𝑀𝑖𝑛𝑜𝑟 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 𝑒𝑥𝑡𝑒𝑟𝑛𝑎𝑙 𝑡ℎ𝑟𝑒𝑎𝑑 [𝑚𝑚]

𝐹𝑎𝑥 = 𝐴𝑥𝑖𝑎𝑙 𝑏𝑜𝑙𝑡 𝑝𝑟𝑒𝑙𝑜𝑎𝑑 [𝑁]

𝐹𝑓 = 𝐹𝑟𝑖𝑐𝑡𝑖𝑜𝑛 𝐹𝑜𝑟𝑐𝑒 [𝑁]

𝐹𝑚8𝑚𝑎𝑥= 𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝑎𝑥𝑖𝑎𝑙 𝑝𝑟𝑒𝑙𝑜𝑎𝑑 𝑖𝑛 𝑎 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑/ 𝐼𝑆𝑂. . . 𝑀8 𝑏𝑜𝑙𝑡 [𝑁]

𝑁 = 𝑁𝑜𝑟𝑚𝑎𝑙 𝑙𝑜𝑎𝑑 [𝑁] (Reminder, the normal load is always perpendicular to the friction force)

𝑛𝑓 = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛 𝑠𝑢𝑟𝑓𝑎𝑐𝑒𝑠

𝑃 = 𝑃𝑖𝑡𝑐ℎ [𝑚𝑚]

𝑟2 = 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑓𝑟𝑜𝑚 𝑐𝑒𝑛𝑡𝑒𝑟 𝑜𝑓 𝑡ℎ𝑒 𝑏𝑜𝑙𝑡 𝑡𝑜 𝑡ℎ𝑒 𝑚𝑖𝑑𝑑𝑙𝑒 𝑝𝑜𝑖𝑛𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑡ℎ𝑟𝑒𝑎𝑑 𝑟𝑎𝑑𝑖𝑢𝑠 [𝑚]

𝑟𝑓 = 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑓𝑟𝑜𝑚 𝑐𝑒𝑛𝑡𝑒𝑟 𝑜𝑓 𝑡ℎ𝑒 𝑏𝑜𝑙𝑡 𝑡𝑜 𝑡ℎ𝑒 𝑚𝑖𝑑𝑑𝑙𝑒 𝑝𝑜𝑖𝑛𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑏𝑜𝑙𝑡 ℎ𝑒𝑎𝑑 𝑟𝑎𝑑𝑖𝑢𝑠 [𝑚]

𝑇𝑡𝑖 = 𝑇𝑜𝑟𝑞𝑢𝑒 𝑡𝑖𝑔ℎ𝑡𝑒𝑛𝑖𝑛𝑔 𝑡𝑜𝑡𝑎𝑙 [𝑁𝑚]

𝑇𝑡ℎ = 𝑇𝑜𝑟𝑞𝑢𝑒 𝑡ℎ𝑟𝑒𝑎𝑑 𝑡𝑖𝑔ℎ𝑡𝑒𝑛𝑖𝑛𝑔 [𝑁𝑚]

𝑇𝑓 = 𝑇𝑜𝑟𝑞𝑢𝑒 𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑏𝑜𝑙𝑡 𝑎𝑛𝑑 𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 [𝑁𝑚]

𝜇 = 𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛

𝜇𝑠 = 𝑆𝑡𝑎𝑡𝑖𝑐 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛

𝜑 = 𝑇ℎ𝑟𝑒𝑎𝑑 ℎ𝑒𝑙𝑖𝑥 𝑎𝑛𝑔𝑙𝑒 [𝑑𝑒𝑔𝑟𝑒𝑒𝑠]

𝜌 = 𝐹𝑟𝑖𝑐𝑡𝑖𝑜𝑛 𝑎𝑛𝑔𝑙𝑒 𝑖𝑛 𝑡ℎ𝑟𝑒𝑎𝑑 [𝑑𝑒𝑔𝑟𝑒𝑒𝑠]

𝜎 = 𝑇𝑒𝑛𝑠𝑖𝑙𝑒 𝑠𝑡𝑟𝑒𝑠𝑠 [𝑀𝑃𝑎 𝑜𝑟 𝑁

𝑚𝑚2]

𝜇𝑡 = 𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛 𝑖𝑛 𝑡ℎ𝑒 𝑡ℎ𝑟𝑒𝑎𝑑𝑠

𝜂 = 𝐵𝑜𝑙𝑡 𝑡𝑒𝑛𝑠𝑖𝑙𝑒 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ 𝑢𝑡𝑖𝑙𝑖𝑧𝑎𝑡𝑖𝑜𝑛

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TABLE OF CONTENTS

1. INTRODUCTION ..................................................................................................................... 5

1.1 BACKGROUND / PROBLEM DESCRIPTION ............................................................................................ 5

1.2 PURPOSE ...................................................................................................................................... 6

1.3 OBJECTIVE .................................................................................................................................... 7

1.4 DELIMITATIONS ............................................................................................................................. 7

2. THEORY ................................................................................................................................. 8

2.1 DRY FRICTION ............................................................................................................................... 8

2.2 BOLT JOINTS ............................................................................................................................... 10

2.2.1 Slip Critical Bolt Joints...................................................................................................... 11

2.2.2 Bolt Joint Equations ......................................................................................................... 12

2.3 LITERATURE STUDY ...................................................................................................................... 15

2.3.1 Coefficient of friction data............................................................................................... 15

2.3.2 Methods to find the coefficient of friction ...................................................................... 19

3. METHOD ............................................................................................................................. 21

3.1 TEST CONFIGURATION .................................................................................................................. 21

3.1.1 Material Planning ............................................................................................................ 26

3.1.2 Equipment ....................................................................................................................... 29

3.1.3 Data Acquisition .............................................................................................................. 32

3.2 PREPARATORY STATISTICAL CALCULATIONS....................................................................................... 35

4. PROCEDURE ........................................................................................................................ 37

5. RESULTS .............................................................................................................................. 43

6. DISCUSSION ........................................................................................................................ 44

7. CONCLUSION ....................................................................................................................... 51

8. FUTURE WORK .................................................................................................................... 52

ACKNOWLEDGEMENT................................................................................................................. 53

REFERENCES ............................................................................................................................... 54

APPENDIX A: PRETENSION OF THE BOLT...................................................................................... 56

APPENDIX B: DRAWINGS OF SPECIMENS ..................................................................................... 57

APPENDIX C: MATERIAL CALCULATIONS ...................................................................................... 59

APPENDIX D: DETAILED TEST DATA ............................................................................................. 60

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1. INTRODUCTION

This project was performed together with ÅF Industry AB in Trollhättan, Sweden. ÅF’s

expertise in Trollhättan is oriented towards the automotive industry. It was conducted within

the section of CAE and safety. It is a degree project at Karlstad University within the

department of engineering science and physics. The supervisors at ÅF are Christian Näslund

and Görgen Karlsson. Supervisor at Karlstad University is Anders Wickberg.

1.1 Background / Problem description

Bolt joints play an important role in the automotive industry. They are used widely throughout

the whole car. One typical example of automotive bolt joints is the fixing of control arms (see

Figure 1 and Figure 2).

Figure 1. View of the control arm fixed with a bolt joint to the subframe.

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Figure 2. Closer look at the bolt joint connecting the control arm to the subframe.

These bolt joints fix the control arms to the subframe which is fixed to the car body. During

driving the bolt joints are subjected to shear loads in different directions depending on the

driving situation. It is important that slipping does not occur in the bolt joints. Slipping in the

bolt joints would cause noise, deteriorated handling and in the worst-case unscrewing of the

nut or fatigue fracture of the bolt. In analysis and dimensioning of bolt joints it is very

important to have relevant values of static friction between the mating surfaces. In a bolt joint,

the combination of axial preload from the bolt and the friction between the mating surfaces

are dimensioning the capacity to carry external shear load and the function of the connection.

1.2 Purpose

With lack of good test data, the bolt joints need to be dimensioned conservatively. This may

lead to that bolt joints are over-dimensioned, adding more mass to the car. On the contrary,

the availability of reliable test data enables designers to optimize joint dimensions to achieve

a safe design with minimized mass.

Page | 7

1.3 Objective

The project consists of two milestones and one main objective which are:

Milestone:

• Make a study in literature to find the static friction value between different

combinations of steel and aluminium materials used in automotive bolt joints.

Main objectives:

• Design the mechanical testing configuration as well as a testing procedure for a test to

determine the static friction value between mating surfaces in bolt joints.

• Perform tests and set up a table including the static friction value and the different

combinations of steel and aluminium (with a certain surface roughness). The tests will

also include another parameter which is an electrophoretic deposition surface

treatment (known as ED coating).

1.4 Delimitations

The study only concerns tests of steel and aluminium. It is the friction between the mating

surfaces that is considered. The study will not include the friction in the thread nor in the

mating surface of the bolt head and washer. The tests only include dry friction, thus there are

no lubrication or dirty surfaces. The tests will be done with the same test geometry and bolt

joint geometry. Testing is limited to the double shear type of bolt joint.

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2. THEORY

2.1 Dry Friction

Dry friction force is the force that occurs when an object is being pulled across a clean surface

without any kind of lubricant. The friction force is caused by the objects mass and the surface

roughness between the materials which makes it hard to pull it away since it must overcome

many small humps (see Figure 3).[1]

Figure 3. A block of mass being pulled and a zoomed in view of the material interference.

There are two laws of friction [2]:

First law of friction – The friction force is proportional to the normal load.

Second law of friction – The friction force is independent of the apparent area of contact.

As stated in the first law there is a proportional relationship between friction force and the

normal load. Thus, the friction force can be expressed as equation (1):

𝐹𝑓 = 𝜇𝑁 (1)

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The maximum friction force that is achievable is the one right before the slipping point (see

Figure 4). The friction and pull force is proportional until it starts to slip. After that the friction

is slightly lowered, but constant, and the object will start to accelerate.[1]

Figure 4. Graph with friction force on y-axis and pull force on x-axis.

If the static coefficient of friction is unknown, it is possible to calculate it by rewrite equation

(1) as equation (2):

𝜇 =𝐹𝑓

𝑁 (2)

Therefore, it is necessary to know the friction force and the normal load. These values could

be measured in an experiment (which could look like Figure 3) where a force is applied until

the block slips and the mass or normal load is known. With those values, it is possible to

calculate the static coefficient of friction in that specific case that was analysed.

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2.2 Bolt Joints

In this chapter, there is essential information, expressions and equations that will be used

throughout this study.

A bolt joint is a joint where two or more parts are mated with a bolt (see Figure 5). It could be

attached through the parts and locked with a nut on the other side, or there could be internal

threads in the material which the bolt is screwed in to. There are many different types of bolt

joints which are used for different purposes such as tensile stress, shear load, sealing joints,

slip critical joints etc.

Figure 5. Two parts connected with a bolt joint.

To make sure it is possible to mount the bolt in a hole, a certain level of clearance is necessary

(see Figure 6). The clearance fit in the hole is also necessary to make the mounting of the bolt

quick and easy [3]. The hole is also larger than the bolt to make sure the hole-edges do not

damage the bolt thread when mounting.

Figure 6. Drawing of a bolt joint, showing the clearance.

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2.2.1 Slip Critical Bolt Joints

A slip critical bolt joint is a fastening connection where no slipping is allowed. It is a bolt

joint where the bolt does not get exposed to shear loads. Instead, shear forces are transferred

as friction forces between the mating surfaces without causing any relative movement within

the joint (see Figure 7). As mentioned in the problem description it is very important that

slipping does not occur. In a car suspension-bolt joint slipping would cause noise, deteriorated

handling and in the worst-case unscrewing of the nut or fatigue fracture of the bolt which can

be life threatening in several applications [4]. If the slip critical bolt joint is used to adjust the

wheel settings, it could be very dangerous as well. Slipping in such joint would cause the car

to wobble and turn without the driver’s knowledge, before it is too late.

Figure 7. Bolt joint with a shear load and the reacting friction forces.

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2.2.2 Bolt Joint Equations

Relevant equations regarding bolt joints and slip critical bolt joints follows.

Tightening torque equation (3):

𝑇𝑡𝑖 = 𝑇𝑡ℎ + 𝑇𝑓 (3)

The tightening torque is divided into two torques, which is a torque to exceed thread friction

equation (4) and a torque exceed friction between bolt head and material equation (6).

𝑇𝑡ℎ = 𝑟2𝐹𝑎𝑥tan (𝜑 + 𝜌) (4)

Where 𝜌 is the angle of the pitch normal to the friction in the threads:

𝜌 = arctan (1.155𝜇𝑡) (5)

𝑇𝑓 = 𝑟𝑓𝐹𝑎𝑥𝜇 (6)

Equation (4) & (6) in (3) gives total tightening torque to a bolt joint accordingly equation (7):

𝑇𝑡𝑖 = 𝐹𝑎𝑥[𝑟2tan (𝜑 + 𝜌) + 𝑟𝑓𝜇] (7)

Another relevant equation that is necessary to calculate the tension of the bolt [5] follows:

Page | 13

𝜎 =

η𝜎𝑠

√1 + 3 [4

1 +𝑑3

𝑑2

(𝑃

𝜋𝑑2+ 1.155𝜇𝑡)]

2

(8)

Equation (8) accounts for both tensile and torsional stress. That means it is possible to figure

out the maximum achievable preload if the bolt is utilized up to its yield strength. Rewrite

equation (8) as:

𝐹𝑎𝑥 =η𝜎𝑠𝐴𝑠

√1 + 3 [4

1 +𝑑3

𝑑2

(𝑃

𝜋𝑑2+ 1.155𝜇𝑡)]

2

(9)

If the bolt joint looks like the one below (see Figure 8), it is necessary to make an update to

equation (1) since there are two friction surfaces and consequently two friction forces. It is

also relevant to change the normal load to the axial preload since it is equal in a vertical

equilibrium. A general friction force equation (10) including the number of friction surfaces

in a bolt joint is shown below:

𝐹𝑓 = 𝜇𝑠𝐹𝑎𝑥𝑛𝑓 (10)

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Figure 8. Forces acting in a slip critical joint.

By using equation (7) and (9) it is possible to calculate the axial preload and by using the

axial preload it is possible to calculate the friction force. It is also possible to calculate the

other way around if the coefficient of friction is desired. Then the values of the axial preload

and the friction force needs to be calculated or known. Rewrite equation (10) as:

𝜇𝑠 =𝐹𝑓

𝐹𝑎𝑥𝑛𝑓 (11)

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2.3 Literature Study

This literature study was made to find relevant coefficient of friction values and experimental

methods to find it.

2.3.1 Coefficient of friction data

Swedish Fasteners Network

There is a Swedish fasteners network which is called SFN. It is an association consisting of

several well-known automotive companies, mainly in Sweden, who share valuable

information regarding bolt joints with each other and the public. They have made an online

manual which is used by design engineers, processors and fitters, mainly within the

automotive industry [6]. They present data regarding the coefficient of friction between steel

and aluminium as well as steel with surface treatment. The values of static friction as reported

by SFN can be found in Table 1.

Table 1. Static friction values in different steel and aluminium combinations.[7] (Own translation)

Verein Deutscher Ingenieure

There is a German association of engineers called VDI (Verein Deutscher Ingenieure). They

have collected a lot of reliable and important information about bolt joints in a document

called “VDI 2230”. It contains approximate values of static friction between many different

Page | 16

materials. The values can be found in Table 2. Thus, VDI recommend that the coefficient of

friction should be checked by tests in each case to verify the design.

Table 2. Approximate values of static friction as stated in VDI 2230.[8]

Bolted Joint Engineering

A book called ‘Bolted joint engineering’ covers information regarding bolt joint

fundamentals. It contains information about both bolt joint design, calculations and examples.

It also contains appendices with information about different coefficients, for instance

coefficient of static friction. It is a table covering coefficient of friction between different

materials (steel, aluminium and cast iron) with altered surface treatments and with/without

lubrication (see Table 3). All surfaces have been lathed to a surface roughness around 1.6 to

6.3 Ra.

Page | 17

Table 3. Friction coefficients of contact surfaces stated in ‘Bolted joint engineering’ .[4]

Grondin, Jin and Josi

Grondin, Jin and Josi did a review of former tests that were conducted to find the coefficient

of friction. They collected all data from each experiment in tables and calculated the mean

value of the slip coefficient (see Table 4). They looked at coefficient of friction for steel with a

clean mill scale surface.

Table 4. Measured slip coefficients (Clean Mill Scale).[9]

Page | 18

European Standard

There is also a European standard called EN 1090-2:2008 which contains information about

technical requirements for the execution of steel structures. Thus, it includes a table with the

coefficient of friction in steel with altered surface treatments, note that it is not applicable for

stainless steel (see Table 5).

Table 5. Classifications that may be assumed for friction surfaces stated by EN 1090-2:2008.[10]

Page | 19

2.3.2 Methods to find the coefficient of friction

Tensile testing machine

There is a European standard with guidelines about how to determine the slip coefficient. The

specimens shall be exposed to shear load in a tension testing machine. There is a standard

dimension of the specimen that should be used. The preload in each bolt shall be measured,

but it does not say how it shall be measured. They have a guideline formula to decide the

number of tests to be made, it depends on the standard deviation and a factor. It will be

calculated in the study but not used entirely since all materials must be ordered in

advance.[10]

Study with a tensile testing machine

Heistermann made a study where tests were made to find the static coefficient of friction. Her

method consisted of a tensile testing machine pulling steel plates, with two or more bolt

joints, apart (see Figure 9). The preload was measured with help of strain gauges which were

inserted into each bolt.

Figure 9. Test configuration Heistermann used during the friction experiment.[11]

Page | 20

By using this method, it is only necessary to attach load cells since a tensile testing machine

already has force and displacement sensors built-in.

Load Table

Another study regarding bolt joints was made by Frank and Yura. They came up with an

alternative solution to test the coefficient of friction compared to the ISO standard and

Heistermann (see Figure 10).

Figure 10. Another test setup to measure forces to calculate the friction. [12]

In this setup, there is a hydraulic cylinder which creates a force to the drilled nut which is in

contact to the specimens. The setup is placed on a load cell which is used to measure the

applied shear load. To measure the slipping point, two electrical deflection gauges were used.

They do not explain how to apply the shear load but only that load should be applied.

Page | 21

3. METHOD

The literature study and the development of the test method were done parallel because the

delivery time on materials and sensors is long. Which means the test method equipment and

the material had to be ordered early in the project. The testing phase was done in ÅF’s

workshop in Trollhättan, since they wanted to be a part of the test and have the possibility to

repeat the test with other material combinations, surface treatments or surface profiles.

3.1 Test Configuration

The main objective with the test method is to get as accurate coefficient of frictions values as

possible. Hence it is necessary to make the tests as realistic as possible and to minimize all

probable errors. The intention is to keep all parameters constant between the tests except the

ones that are studied.

The test method was decided together with knowledgeable people from ÅF. ÅF wanted to

purchase equipment that they could use for this project as well as other purposes and projects.

They would also like to use the equipment that they already have in house as much as

possible. ÅF has a hydraulic cylinder with a pump which could be used to apply shear load

and they also have a sensor to measure position. Since this equipment was available it was

decided to use them both.

The following principles for the testing were decided upon:

• Use a fork connection to get two friction surfaces instead of one. This is due to the

possible differences in the surface finish which could cause diverging test results. If

two surfaces are used that means the probable test error is halved. A fork joint also

gives less bending moment in the bolt joint compared to a single shear joint.

• Apply the shear load with a pull force. This is to make sure the test remains as straight

as possible throughout the whole movement.

Page | 22

• The preload should be measured with a cylindrical load cell beneath the bolt head or

beneath the nut. The load cell should have thick washers above and below to reduce

the contact pressure and protect the cell.

• It is very important slipping occurs in the tested bolt joint and not in the fixture bolt

joints because otherwise the test will obviously fail since the measuring is done to a

specific bolt. It must be assured that no slipping occurs in the fixture bolt joints.

• Conduct the tests with an ISO M8 bolt. Perform calculations to ensure that this bolt

size is suitable for the existing equipment.

• The tests are supposed to be conducted in the workshop. The condition in the work

shop is room temperature.

To find the maximum achievable preload when the bolt is utilized up to its yield strength the

following calculations were made by using equation (9) (see appendix A ‘Pretension of the

bolt’ for additional information regarding these calculations):

𝐹𝑎𝑥 =η𝜎𝑠𝐴𝑠

√1+3[4

1+𝑑3𝑑2

(𝑃

𝜋𝑑2+1.155𝜇𝑡)]

2= 19503 𝑁

Calibration tests were made to find a good preload value, which ended up at 18 kN. That

means, that in each test the bolt was tightened until the preload transducer showed 18 kN.

This method was found to give the most consistent preload values. Tightening the bolt to a

specific torque or torque and angle was seen to give a considerable spread of measured

preloads.

Page | 23

The hydraulic cylinder can produce shear load up to 40kN. If 70% of the load is applied,

which is a safety and probable error limit since it is never good to use the equipment up to its

maximum rating. By using the shear load of the hydraulic cylinder and the maximum preload,

the coefficient of friction could be calculated with use of equation (11):

𝜇𝑠 =𝐹𝑓

𝐹𝑎𝑥∗𝑛𝑓= 0.71

The conclusion from these values is that the M8 bolt is a good choice of bolt for the testing.

With the maximum bolt preload and using 70% of cylinder capacity the pulling force can

cause slipping with friction coefficients up to 0.71. This kind of values are not expected to be

achieved during the testing of these material combinations.

The test configuration below is the one that is set to be used (see Figure 11). This whole fixture

is placed on an I-beam on the opposite side of the hydraulic cylinder.

Figure 11. Layout of the test configuration.

Page | 24

To make sure that slipping occurs in the middle specimen, the other bolt joints will be pulled

into contact with the plates so that they get exposed to shear load. This is since the slipping

occur long before the bolts fail due to shear load or plate bearing failure. The measured bolt

will have some slipping distance until it gets exposed to the shear load to make sure it does

slip.

The linear position transducer was fixed to the fixture part of the test configuration and

measured, by wire, to the part that exerts the shear load (see Figure 12). This is since it is

important that the position transducer itself never moves but only the rod. A force transducer

was used to measure the shear load (static friction force). It was placed between the hydraulic

cylinder and the pin that exerts the shear load (Figure 12). The load cell which is used to

measure the preload is placed below the specimen to avoid interference with the position wire.

Figure 12. Test configuration and placement of the gauge instruments.

Page | 25

For weak materials, it is important to exert the shear load with surface pressure in two holes to

avoid tear out. A fork joint could be used as an extension of the existing testing configuration

(see Figure 13). This was found out during the testing since the aluminium was plasticized

when applying shear load with surface pressure in one hole.

Figure 13. Double fork connections of the test configuration.

Page | 26

3.1.1 Material Planning

The specification of the specimen materials was set to steel, S355, and aluminium, 6082. To

determine the exact shape of the specimen geometry a CAD model (in CATIA V5) of the test

method was created (see Figure 14) from the sketch above (see Figure 11).

Figure 14. CAD model of the test configuration.

Because of the symmetry potential and to facilitate the manufacturing of the specimens (1, 2

and 3) have the same geometry (see Figure 15, and appendix B ‘Drawings of the Specimen’ for

complete drawing). Part 4 is different, but only one of part 4 is necessary since it can be

reused in all the tests (see appendix B ‘Drawing of the specimens’ for complete drawing).

This means that only one kind of specimen is necessary, though in different materials and

surface treatments.

Page | 27

Figure 15. Geometry of the specimen in millimeters with a thickness of 5[mm].

With help of the CAD model it is easy to change dimensions to make sure each bolt does not

get too close to each other. The design of the specimen follows the ISO standards regarding

the clearance in holes. To make it easy to see when slipping occurs a coarse hole diameter is

selected [13]. The thickness of the specimen is set to 5mm to make sure the clamping length

is enough and to make the specimen realistic. ISO 2768-m is added as a general tolerance on

the drawing to make sure that geometrical deviations are minimised.

To get a feel of the surface finishes that were used see the specimens below (see Figure 16).

The steel has an average surface roughness of approximately 1.8 μm while the aluminium has

an approximately average surface roughness of 0.15 μm.

Figure 16. Surfaces of the material used before the tests.

Page | 28

An excel sheet including parameters like number of tests done, length of specimen, material

combinations etc (See Appendix C ‘Material Calculations’) was built. The sheet is used to

make changes easier since all calculation are automatic. This way it is possible to change e.g.

number of tests and achieve correct information to the specimen supplier before ordering.

This information could be for example; number of specimen parts, total length or total amount

of weight depending on what they need to return an offer.

It is important the specimen stays as equal as possible throughout all tests. Hence, all

specimen will be washed and cleaned with cleaning alcohol. It is also necessary to use a new

specimen with an “unused” surface each time a new test is done, since the surface pressure

and slipping have an impact on the surface finish/roughness. It is decided to replicate each

material combination five times each. This is a decent number of replications since the

accuracy versus number of test curve starts to level off at that point [14]. It is also planned for

three extra tests setups for each kind to ensure the study can be completed in case problems

occur. Additionally, it is planned for extra specimens to try out the test configuration, make

calibration tests and to verify that everything works as it should.

All bolts, nuts and washers follows the same ISO standard that is usually used in the

automotive industry. All fasteners are bright zinc plated, the dimensions and ISO standards

that will be used are:

M8x80 (8.8) ISO 4017 – Main bolt where the preload will be measured.

M8x30 (8.8) ISO 4017 – Used to mount the specimen onto the fixture part.

Nut M8 ISO 4032 – Beneath the load cell and the thick washer.

Thick washer 8,4x24x2 ISO 7093 – Placed on either side of the load cell.

Standard washer 8,4x16x1,6 ISO 7089 – Placed beneath the bolt head.

Page | 29

3.1.2 Equipment

Hydraulic Cylinder

Hydraulic cylinder with a pump to produce the force (see Figure 17). It has a maximum load of

4 tonnes (~40kN). It was used to apply shear load.

Figure 17. The hydraulic cylinder which is used to apply shear load.

Position Transducer

Novotechnik T25 position transducer (see Figure 18). Movement up to 150mm. Linearity up to

± 0.2%. Repeatability to ± 0.002mm. Used to measure movement (slipping point).

Figure 18. This is the kind of position transducer that was used.

Page | 30

M10 Bolt with groove

The bolt itself is mounted onto the specimen that is supposed to slip. A wire was connected

from the position transducer into the groove. It was used together with the position transducer

to measure the slip.

Figure 19. M10 bolt with a groove.

Force Transducer

A force transducer was used to measure shear load (see Figure 20). It has a maximum usage

limit at 30 000 N and is linear to that point as well.

Figure 20. The force transducer that was used to measure shear load.

Page | 31

Load Cell

A load cell was used to measure preload (see Figure 21). It is accurate and linear for loads

between 10 000 N up to 38 000 N. It is designed to fit M8 bolts and the contact surface has

the same diameter (Ø24mm) as the thick washer that is used to even out the pressure.

Figure 21. Load cell used to measure preload.

Torque Wrench

Holex electronic torque wrench (see Figure 22). ± 2% accuracy. Usage up to 30 Nm.

Figure 22. Electronic torque wrench.

Page | 32

3.1.3 Data Acquisition

IPEmotion was used as the software to collect and analyse all the data from each test. All the

instruments were brought to ÅF calibrated, together with a calibration certificate. The values

from the calibration certificate of each instrument are inserted into the configuration file in

IPEmotion. It was changed to show newton N as the output values instead of volt V or

millivolt mV since it was set to hit a specific preload value in newton. The sampling rate

was set to 500 Hz for each instrument.

The setup of the analyse step only needs to be done one time. Four charts are inserted and the

signals are applied into one chart each. The preload is applied to two charts to see both the

preload increase and to see what happened to the preload during the slip. When each test file

is uploaded into to analyse tab these graphs should appear (see Figure 23). The graphs show;

1 – Position vs time

2 – Shear load vs time

3 – Preload vs time

4 – Preload vs time (measured during tightening)

Where time is represented vertical in Figure 23.

The timelines are linked to make it easy to see position (slipping point) and shear load at the

same time without having them in the same graph window. Same goes for graph three, it has

the same linked timeline as graph one and two. Graph four has a different timeline and is used

to see that nothing odd happened during the tightening process.

Page | 33

Figure 23. Analyse setup of the graphs.

Page | 34

A sheet with prefix and comments has been done in advance (see Table 6). It contains the order

that the test should be performed in as well as the name of each test file. There was a column

where it was possible to write notes about the test, e.g. “Combined slip and alignment” or

whatever happed during the test that was odd. There were also columns with space to write

date and tim e to make it easier to track files in case any file disappears.

Table 6. Prefix and comments, example of a test.

Page | 35

3.2 Preparatory statistical calculations

The following formulas were used to calculate the statistical values such as normal

distribution, the confidence intervals and the number of tests to be done.

Normal distribution Curve:

𝑓(𝑥) =1

√2𝜋𝑆𝑥2

𝑒−

12(

𝑥−��𝑆𝑥

)2

(12)

The area under the normal distribution curve is equal to the probability. Integration of (12)

gives the probability of a certain interval. A new variable Z is set to make the integration

easier:

𝑍 =𝑋 − ��

𝑆𝑥 (13)

Equation (13) used in (12) gives:

𝑓(𝑧) =1

√2𝜋𝑆𝑥2

𝑒−12

(𝑍2)

(14)

The area under the graph with Z1 & Z2 limits:

𝐴𝑔 = ∫1

√2𝜋𝑆𝑥2

𝑒−12

(𝑍2)𝑑𝑧

𝑍2

𝑍1

(15)

Page | 36

The standard probability interval six standard deviations or four standard deviations could be

used instead of equation (15). But if any other interval or percentage is desired, that equation

does the work.

Equation (16) states the true mean value with a 95% or 99% confidence interval, where the k

value depends on number of samples which can be found in a table [15]:

�� = �� ± 𝑘𝑆𝑥 (16)

EN 1090-2:2008 contains a formula (see equation (17)) for calculating the required number of

tests in a static friction test [10]. Thus, it is more accurate above 10 tests but could be used as

a guideline.

𝑛 > [

𝑆𝑥

��∗ 100

3,5]

2

(17)

With the usage of these formulas in excel only two input values from each test are necessary,

which is shear load and preload. This will make all the statistical values appear as well as the

graph.

Page | 37

4. PROCEDURE

These procedure steps make sure the testing procedure is as equal as possible in each test.

The following steps are only necessary to do one time, in preparation of the iterative

procedure:

i. Fasten the fixed part into the fixture and ensure it is bearing to the hole edge together

with the position transducer fixture. This step only needs to be done one time since it

won’t be moved or replaced during all the tests. Make sure the fixed part and the

position transducer fixture gets exposed to shear loads and will not slip (see Figure 24).

ii. Also, mount the force transducer onto the hydraulic cylinder.

iii. Wash and clean the specimens with cleaning alcohol.

iv. Start IPEmotion, open the configuration file and detect the measuring devices. Press

display to make sure IPEmotion detect the signals. Under the “View” tab, insert three

charts and add one signal to each chart to be able to track the values of all signals.

Figure 24. Fasten the fixed part together with the position transducer.

Page | 38

The following steps are necessary to do each new test:

First off it is important to do each test with new specimens with unused surfaces.

1. Mount the bolt with the groove in the hole (see Figure 25).

Figure 25. Mount the bolt with the groove.

.

2. Connect the specimen to the hydraulic cylinder with a pin bolt (see Figure 26).

Figure 26. Specimen connected to the hydraulic cylinder.

3. Mount the outer specimens with two bolts, the M8x30 bolts (see Figure 27). Tighten the

bolts with 21 Nm. Use a standard washer below the head and lock it up with a M8 nut.

The M8x30 bolt, the standard washer and the nut can be reused in all tests. It is

important the specimens are aligned with the fixture part and exposed to shear load

Page | 39

(since it should not slip). Exert the shear load on the specimen with help of the

hydraulic cylinder while tightening.

Figure 27. Mount the other specimens.

4. Place the load cell in position with the tested bolt, the M8x80 bolt (see Figure 28). Place

one standard washer beneath the bolt head. Place one thick washer on either side of

the load cell and a nut at the bottom to lock it up. Do not tighten the bolt with full

torque yet. Make sure the parts are aligned, a clamp could be used here as well. Also,

make sure the bolt does not get exposed to shear load since it is supposed to slip. It is

important to use a completely new M8x80 bolt, M8 nut, standard washer and the thick

washer on the bottom of the load cell each new test.

Figure 28.Mount the load cell together with the bolt.

Page | 40

5. Add a prefix for preload, press display to make sure all signals are live and press

record in IPEmotion.

6. Tighten the bolt with the load cell until 18 kN can be read from the force reading of

the load cell, with as constant speed as possible. After the tightening is done, it is

important to wait roughly the same time every test. This is because of the adhesion

and relaxation for instance.

7. Stop the recording.

8. Add a new prefix for position and shear load.

9. Mount the position wire (see Figure 29).

Figure 29. Mount the position wire.

10. Mark the outer edge of the fork connection to make it easy to see that slipping occurs

in the tested bolt joint (see Figure 30).

Page | 41

Figure 30. Mark the material to see if slipping occurred at the tested bolt joint afterwards.

This is what the test configuration should look like before starting the test (see Figure

31). Keep track during the testing and be ready to write notifications if something

happens. E.g. if there is a slight rotation at the same time as slipping due to not fully

aligned parts or if the preload deviate too much etc.

Figure 31. Test configuration ready and good to go.

11. Press display to make sure all signals are live, press record in IPEmotion and apply

shear load with the hydraulic cylinder until slipping occurs. Stop the recording, check

the marks so that slipping occurred in the right place (see Figure 32). If so, the middle

part’s mark should not be aligned with the upper and lower specimen marks.

Page | 42

Figure 32. Make sure slipping occurred at the right place.

12. Save the specimens and mark them with their test number. If something looks odd

while analysing the data, it is good to know what specimens it was, to be able to

analyse the surface as well. Notify if any deviations happened during the test, as well

as the date and time.

Page | 43

5. RESULTS

The resulting static coefficients of friction between the studied materials are presented in the

two tables below with different probability levels (see Table 7 and Table 8). It is presented with

the mean value (��) and a standard deviation interval within the parentheses afterwards. The

specifications of the materials were; steel S355 and aluminium 6082. The preload was 15-18

kN during all the tests. The tests were conducted in room temperature. See appendix D for

more detailed test data and statistical calculations.

Table 7. Summary of results with the mean value and +/- three standard deviations, 99.730%

probability.

Table 8. Summary of results with the mean value and +/- two standard deviations, 95.450%

probability.

Page | 44

6. DISCUSSION

Literature Study

The friction values in the literature study differed much. They do not include any probability,

which means it is not safe to use to the lowest value for dimensioning in case it could be even

lower. Also, most of them do not have any information regarding the background, the test

method or about how they got the values. It was clear that it is hard to know what values to

use and therefore, the conservative values must be used when dimensioning.

By comparing the achieved values in this study to the values in the literature it is possible to

see connections between the variation of surface profiles and the coefficient of friction (see

Table 9).

Table 9. Comparing achieved results with the literature values.

The aluminium values in this study are lower than in the literature study and so are the surface

roughness. The same goes for steel but the other way around, its coefficient of friction is

higher and so are the surface roughness. That could be the reason the coefficient of friction is

lower in the aluminium to aluminium than steel to steel. It was not expected that the surface

roughness would have that much of an impact, even though it was predictable that the surface

would influence the coefficient of friction slightly. Both the steel and the aluminium were

ordered with a specific surface roughness of 1.6 μm. It was visually noted that aluminium and

Page | 45

steel specimens differ in surface roughness although ordered to the same surface roughness

specification. Thus, the surfaces were measured to the following Ra-values;

Steel - 1.8 μm

Aluminium - 0.15 μm

Other differences in the results compared to the literature study could depend on numerous

factors. It is believed some factors could be the type of steel/aluminium, the area of contact,

temperature and adhesion (since all alloys vary if they are not from the same batch). Other

things that could make the values deviate could be the error sources in this study, more about

them later. This study also has larger intervals then the literature and that could be because my

tables are presented after certain probability levels.

Page | 46

Literature Study Theory vs Test Graphs

In most of the material combinations the graphs from the testing looks almost exactly like the

graph in the theory chapter (see Figure 4) where the friction increase until slipping point (see

Figure 33).

Figure 33. Displacement (y-axis, upper graph), friction force (y-axis, lower graph) and time on x-

axis during one of the steel to steel tests.

There were some tests with the ED coating where the graph looks a little bit different. Right

after the slipping point the shear load get lowered. But only for a moment and then the force

increases again during the slip movement (see Figure 34). That could be caused by the coating

Page | 47

which tears off and increase the friction. It could also be because the coating tears off and the

steel beneath the coating gets in contact which has a higher coefficient of friction, or it could

be an effect from both at the same time. It does not matter when calculating the static friction

value, but it was interesting and important to have in mind when picking the friction force at

the slip points.

Figure 34. Displacement (y-axis, upper graph), friction force (y-axis, lower graph) and time on x-

axis during one of the Aluminium to ED coating tests.

Page | 48

Test Configuration

It was noticed during the testing phase that many unforeseen things can be detected and taken

care of during the calibration. The extension joint of the test configuration for the aluminium

should not affect the results. It is important to allocate many specimens of all kinds of

materials to the calibration of the test configuration, this way it is possible to see problems

before the testing phase begins.

The test configurations worked out well otherwise. The test configuration and procedure gave

reliable output. It was good to measure the slip through a position transducer that is directly

connected from a fixed part to the slipping part. By using built-in measuring devices in e.g.

force transducers it is a probable error because slipping could occur within the device in

bearings etc.

It was necessary to use new specimen with an unused surface each test as intended. The

surface of the specimens was worn after slip (see Figure 35).

Figure 35. Surfaces were worn after slip (From left to right: Steel, Aluminium, ED Coated Steel).

Page | 49

Changed the preload

Initial calibration tests were made with a different preload. The primary idea was to torque the

bolt to its yield limit. Calibration tests were made to find the right tightening specification, 15

Nm and 90 degrees (that gives the correct elongation of this bolt, measured from tests). With

every test the preload deviated much, and therefore it was decided to torque the bolt to a

specific preload (read directly from the load cell measurement) instead to get more even

results. This is the same reason the load cell is used instead of equation (7) and (9), since the

true values deviate much due to the thread friction.

All the tests did not reach 18 kN because of different reasons. The aluminium had problems

with the surface pressure from the small washer which plasticized the material. Further tests

still aimed for 18 kN but most of them ended up slightly lower. I would rather finish all the

test equal since I started with that kind of washer, than change something in between. Even

the bolt was plasticized in some tests with other combinations and therefore, it did not reach

the specific preload that was desired.

Results & Error Sources

The statistical significance of the results depends on the number of tests. In this study, it was

however necessary to limit the number of tests based on economy and time limits. According

to the statistics and the calculations from the ISO recommendations more tests should have

been done on all combinations but Steel to Aluminium and Steel to ED Coating. The ISO

could be misleading on small numbers of test and it changes each time new test values are

applied. It could change from e.g. 13 to 8 tests after applying values from one more test than

before. That means all combinations might not need as many as they say, it is more of a basic

guideline and works better with more than 10 tests. It would always be great to do more tests

but something had to be decided in advance due to the delivery time. Five to eight tests were a

decent number given the statistics and the timeframe since ÅF wanted to test a couple of

different combinations.

The results also depend on the probable error sources as mentioned before. There were a

handful probable error sources throughout this test:

Page | 50

• All the instruments have a level of noise. The noise level of the load cell differs from

0-200 [N] which is approximately 1-1.5% of the true preload. The force transducer

differs 50 [N] which is an error of 0.4-2.5%.

• Stepwise increase instead of linear increase of the shear load. The steps could cause a

peak each time a new step gets initiated. That could make the test slip at a different

shear load than it should due to an impact. This was a known probable problem and

therefore, many practice tests were done to make sure no or as little impact as possible

occur.

• The bolt pretension is lowered by time because of relaxation as mentioned in the

procedure. It is also lowered around the slipping point. The preload was measured all

the way until the slipping occurred, but it was some thoughts about what value to use

in the calculation. Since the preload was lowered right after the slipping point it was

hard to know exactly what values to use. The maximum error did not make much of a

change, less than 1%.

• Friction surfaces not cleaned enough or minor scratches in the surface.

• Test not aligned. It was seen in the tests that the values deviated when a combination

of slip and slight rotation were noted. Those tests were removed when it was

noticeable.

Page | 51

7. CONCLUSION

The study resulted in a table of coefficient of friction between desired material combinations.

Moderate statistical spread of the results was observed.

For improved statistical significance, it was noted that more samples should be used than was

used in this study.

Measurements for aluminium - aluminium resulted in lower friction coefficients than steel –

steel which differs from what is presented in literature. It was noted that aluminium and steel

specimens differ in surface roughness although ordered to the same surface roughness

specification. It is therefore considered important to also include surface roughness

measurement results when presenting coefficient of friction results.

The developed test procedure is robust and relatively simple to use and is recommended for

further use.

In order to study coefficient of friction for a specific level of bolt preload it was found that the

best method is to tighten the bolt based on measuring the preload from a load cell.

When designing a test procedure and performing tests it is important to dedicate sufficient

time to calibrating and getting to know equipment as well as to perform a good number of

preliminary tests with all kind of specimen materials.

Page | 52

8. FUTURE WORK

The study could proceed by doing more tests with steel, aluminium and ED coating for

improved statistical significance.

The test configuration and the procedure could be used to find the coefficient of friction in

different material combinations than the ones I studied. It could also be used to e.g. test the

influence of lubrication or different surface profiles than the ones that were used in this study.

Since the preload was lowered after slip, that could be something to consider in a further

analysis or study. It could be interesting in bolt joints which are only supposed to slip one

time during its lifetime.

The coefficient of friction was calculated in both preload cases (15Nm+90deg and 18kN) and

it was slightly different. Results indicate that the coefficient of friction increases together with

the surface pressure. It could be just a coincident but it was interesting and could be a track

that is worth considering in a further study.

Page | 53

ACKNOWLEDGEMENT

I would like to acknowledge ÅF Industry who gave me the chance to cooperate and do my

bachelor project together with them. I would specifically like to thank my supervisors at ÅF,

Christian Näslund and Görgen Karlsson, as well as my supervisor at Karlstad University,

Anders Wickberg, for their support and guidance during the whole project. Many thanks to

Lars Sundblad, Anton Risgaard and Mats Berggren for sharing their experience about bolt

joints and testing. It was useful when deciding the test configuration and when conducting the

tests. I would also like to thank Rami Karjalainen and Leif Jensen who helped me with the

software and the practical setup of the test configuration in the workshop.

Page | 54

REFERENCES

[1] Meriam J, Kraige L. Engineering Mechanics Statics. 7th ed. Singapore: Wiley;

2013.

[2] Mate C. Tribology on the small scale. 1st ed. Oxford: Oxford University Press;

2008.

[3] Groover M. Automation, production systems, and computer-integrated

manufacturing, Global Edition. 4th ed. Boston, Mass: Pearson; 2015.

[4] Sakai T. Bolted joint engineering. 1st ed. Berlin [etc]: Beuth; DIN Deutsches

Institut fur Normung; 2008.

[5] SFN - Svenska Nätverket för Skruvförband - Handbok [Internet]. Extra.ivf.se.

2017 [cited 11 April 2017]. Available from:

http://extra.ivf.se/sfn_handbok/template.asp?lank=168

[6] SFN - Svenska Nätverket för Skruvförband - Handbok [Internet]. Extra.ivf.se.

2017 [cited 11 April 2017]. Available from:

http://extra.ivf.se/sfn_handbok/template.asp?lank=69

[7] SFN - Svenska Nätverket för Skruvförband - Handbok [Internet]. Extra.ivf.se.

2017 [cited 11 April 2017]. Available from:

http://extra.ivf.se/sfn_handbok/template.asp?lank=185

[8] Verein Deutscher Ingenieure. Systematic calculation of high duty bolted joints.

Joints with one cylindrical bolt. VDI 2230 Part 1. Berlin: Beuth Verlag GmbH;

2003.

[9] Grondin G, Jin M, Josi G. Slip critical bolted connections - A reliability analysis

for design at the ultimate limit state. Edmonton: University of Alberta; 2007.

Page | 55

[10] British Standards. Execution of steel structures and aluminium structures: Part2:

Technical requirements for the execution of steel structures. BS EN 1090-2:2008.

London: BSI; 2008.

[11] Heistermann C. Behaviour of Pretensioned Bolts in Friction Connections

[Internet]. Luleå; 2011. [cited 11 April 2017]. Available from:

https://www.engineersedge.com/engineering-forum/uploads/behaviour-pretension-

bolts-in-friction.pdf

[12] Frank K, Yura J. An experimental study of bolted shear connections [Internet].

Springfield, Virginia: The National Technical Information Service; 1981. [cited 11

April 2017]. Available from:

http://personal.stevens.edu/~shassiot/SteelDesign/AISC-

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[13] International Organization for Standardization. ISO 237:1979 Fasteners-

Clearance holes for bolts and screws. 1st ed. Geneva: 1979.

[14] Bergman B, Klefsjo B. Kvalitet fran behov till anvandning. 5:5 ed. Lund:

Studentlitteratur; 2012.

[15] Rade L, Westergren B. Mathematics handbook for science and engineering. 5:16

ed. Lund: Studentlitteratur; 2004.

Page | 56

APPENDIX A: PRETENSION OF THE BOLT

Calculation of the pretension in the bolt tightened to yield limit and the coefficient of friction

with a certain shear load (see figure A).

Figure A. Pretension of the bolt and the coefficient of friction.

Page | 57

APPENDIX B: DRAWINGS OF SPECIMENS

Drawings of the specimen and the fixture plate that is used in the fixture (see figure B1 and

B2).

Figure B1. Drawing of the Specimen.

Page | 58

Figure B2. Drawing of the f ixture part.

Page | 59

APPENDIX C: MATERIAL CALCULATIONS

Material calculations to figure out how many specimens to order including extra parts etc.

(see figure C).

Figure C. Excel sheet used to calculate the needed material.

Page | 60

APPENDIX D: DETAILED TEST DATA

Detailed test data and the statistical calculations of each material combination (see figure D1,

D2, D3, D4, D5, D6).

Page | 61

Steel – Steel

Figure D1. Detailed test data, Steel – Steel.

Page | 62

Steel - Aluminium

Figure D2. Detailed test data, Steel – Aluminium.

Page | 63

Steel – ED Coated Steel

Figure D3. Detailed test data, Steel – ED Coating.

Page | 64

Aluminium - Aluminium

Figure D4. Detailed test data, Aluminium - Aluminium.

Page | 65

Aluminium – ED Coated Steel

Figure D5. Detailed test data, Aluminium – ED Coating.

Page | 66

ED Coated Steel – ED Coated Steel

Figure D6. Detailed test data, ED Coating – ED Coating.