final draft 3.0

Construction of a Contact Pressure Sensor University of West Indies Mechanical Engineering Department

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THE UNIVERSITY OF THE WEST INDIES

DEPARTMENT OF MECHANICAL ENGINEERING

MENG 3019: FINAL YEAR PROJECT

TITLE: CONSTRUCTION OF A CONTACT PRESSURE SENSOR

SUPERVISOR: DR. J. BRIDGE

SECOND MARKER: PROF. E.I. EKWUE

THIRD MARKER: PROF. C.A.C. IMBERT

SUBMITTED BY : LOMAS PERSAD

ID# : 806000915

DATE SUBMITTED : 15/04/09


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ACKNOWLEDGEMENTS

Firstly, I would like to thank Prabhu Shri Ram for giving me the strength and determination

throughout the project, from beginning to end.

Secondly I would like to thank my parents and family for their resolute support and

understanding. They played a major role in the success of this project. Special thanks to my dad

Gyandeo Persad, my mom Judy Persad and my brother Artma Persad.

Thirdly, I would like to thank Dr. Bridge for affording me the opportunity of this project. She

played an important role in the successful completion of this project. Her door was always open

for advice and assistance. I sincerely thank her for that.

To my technicians Steve Ramoutar and Mr. Subransingh, I would like to thank for all their

guidance and expertise. Their time, insights and efforts made the completion of the project a

success.

Special mention must be made to Amit from the workshop who fabricated the parts needed for

the project. I thank him for the high quality work he did on the project. Also, to Sadira from

physics department who allowed me the use of their equipment whenever I needed it, I express

my deepest gratitude.

Finally, I would like to thank all my friends for their advice, warm wishes and support that I

needed to persevere through the completion of this project.


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ABSTRACT

The aim of the project was to construct a pressure sensor to measure the contact pressure

between two flanges of a flange joint. The main objective was to determine the variation of

contact pressure when there is and increased pressure in the flange joint. This was done using a

voltage signal from a strain gauge and relating it to a decrease in contact pressure. The nature of

the project was such that it required a knowledge of strain gauges, instrumentation associated

with the strain gauges and a complete understanding of a bolted flange joint.

The project was design to accurately determine the variation of contact pressure of the flange

joint and predict the failure point of the joint under pressure. This was done by performing

physical test as well as modeling the joint using Solidworks, performing a finite element analysis

of the joint in Algor and comparing the results.

The objectives of the project were completed and a relationship between the voltage signal of the

sensor and the decrease in contact pressure was established. The success of this project proves

that the implementation of such a sensor to a flange joint has major benefits in understanding the

behavior of a flange joint when subjected to a buildup of pressure.


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TABLE OF CONTENTS

ACKNOWLEDGEMENTS ........................................................................................... i

ABSTRACT .................................................................................................................. ii

LIST OF FIGURES ...................................................................................................... v

LIST OF GRAPHS ...................................................................................................... vi

LIST OF TABLES ...................................................................................................... vii

Chapter 1

INTRODUCTION ........................................................................................................ 1

1.1 RATIONALE .............................................................................................. 1

1.2 OBJECTIVES ............................................................................................. 2

1.3 SCOPE ........................................................................................................ 2

Chapter 2

LITERATURE REVIEW ............................................................................................. 3

2.1 What is Pressure .......................................................................................... 3

2.2 Measurement Systems ................................................................................ 3

2.3 Different technologies used in making pressure sensors ............................ 5

2.4 Technologies for Tactile Sensing ................................................................ 6

2.5 The Flange Joint .......................................................................................... 9

2.6 Design Factors .......................................................................................... 10

Chapter 3

ALTERNATIVE DESIGNS ....................................................................................... 16

3.1 Alternative 1.............................................................................................. 16

3.2 Alternative 2.............................................................................................. 17

Chapter 4

FINAL DESIGN ......................................................................................................... 18

4.1 Final design ............................................................................................... 18

4.2 Limitations on design ................................................................................ 19

4.3 Alternative due to Limitations .................................................................. 19


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4.4 ANALYSIS OF DESIGNS ....................................................................... 20

Chapter 5

FABRICATION .......................................................................................................... 21

5.1 PROCESS PLAN ...................................................................................... 22

Chapter 6

INSTRUMENTATION USED ................................................................................... 26

6.1 Strain indicator model P-350A ................................................................. 26

6.2 Strain gauges ............................................................................................. 27

6.3 Hounsfield tensometer connected to a computer ...................................... 28

6.4 Plotter or Recorder .................................................................................... 29

Chapter 7

RESULTS ................................................................................................................... 30

Test 1 ............................................................................................................... 30

Test 2 ............................................................................................................... 34

Test 3 ............................................................................................................... 39

Test 4 ............................................................................................................... 41

Test 5 ............................................................................................................... 43

Chapter 8

CALCULATIONS ...................................................................................................... 45

8.1 Bolt stiffness, Kb ....................................................................................... 45

8.2 Joint Stiffness, Kj ...................................................................................... 47

8.3 Preload on bolts, Fp ................................................................................... 48

8.4 Calculation of Load Distribution using Bolt/Joint Stiffness ..................... 48

Contact pressure-Voltage calibration curves .................................................. 51

Chapter 9

FINITE ELEMENT ANALYSIS OF THE FLANGE JOINT .................................... 53

Chapter 10

DISCUSSION ............................................................................................................. 56


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Chapter 11

CONCLUSION ........................................................................................................... 59

REFERENCES ........................................................................................................... 60

Appendix A -Pictures .................................................................................................. 61

Appendix B –Drawings............................................................................................... 67

Appendix C - Results .................................................................................................. 75

Appendix D -Calculations........................................................................................... 87


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LIST OF FIGURES

Figure 1 Instrument model with amplifier, analog to digital converter, and computer output ....... 4

Figure 2 showing a typical Capacitive Sensor (Reprinted from Measurement, Instrumentation

and Sensors handbook) ................................................................................................................... 7

Figure 3 showing a Piezoelectric transducer (Reprinted from Measurement, Instrumentation and

Sensors handbook) .......................................................................................................................... 8

Figure 4 application of strain gauge to flange joint ...................................................................... 10

Figure 5 showing a typical Bonded Foil Strain Gauge ................................................................ 12

Figure 6 showing the Wheatstone Bridge circuit (reprinted from sensors and Transducers) ...... 13

Figure 7 showing the application of a strain gauge with temperature compensation (reprinted

from National Instruments website).............................................................................................. 13

Figure 8 Illustrating Alternative design 1 (created in solidworks) .............................................. 16

Figure 9 Illustrating the alternative design 2 (created in solidworks) .......................................... 17

Figure 10 Illustrating the application of the strain gauge (created in solidworks) ....................... 18

Figure 11 The Strain indicators used ............................................................................................ 26

Figure 12A shows the strain gauge connected to the leads of the indicator Figure 11B shows

the equivalent circuit ..................................................................................................................... 27

Figure 13 shows the strain gauge connected in a quarter bridge configuration ............................ 27

Figure 14 Shows the Hounsfield Tensometer ............................................................................... 28

Figure 15 shows the Plotter used to record the voltage signal ...................................................... 29

Figure 16 Showing the order in which the bolts were tightened .................................................. 34

Figure 17 shows the mesh of the CAD model in Algor ................................................................ 53

Figure 18 location of the fixed boundary condition...................................................................... 53

Figure 19 Location of the externally applied force ....................................................................... 54

Figure 20 shows the preload applied to the bolts .......................................................................... 55

Figure 21 shows the application of rigid boundary conditions to the flanges .............................. 55


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LIST OF GRAPHS

Graph 1 Force vs Extension .......................................................................................................... 31

Graph 2 Force vs Voltage ,V1 ....................................................................................................... 31

Graph 3 Force vs Voltage ,V2 ....................................................................................................... 32

Graph 4 Force vs Extension .......................................................................................................... 32

Graph 5 Force vs Voltage,V1 ........................................................................................................ 33

Graph 6 Force vs Voltage, V2 ....................................................................................................... 33

graph 7 Force vs Extension ........................................................................................................... 34

graph 8 Force vs Voltage, V1 ........................................................................................................ 35

graph 9 Force vs Voltage, V2 ........................................................................................................ 35

graph 10 Force vs Extension ......................................................................................................... 36

graph 11 Force vs Voltage, V1 ...................................................................................................... 36

graph 12 Force vs Voltage, V2 ...................................................................................................... 37

graph 13 Force vs Extension test 3 ............................................................................................... 40

graph 14 Force vs Extension test 3 ............................................................................................... 40

graph 15 Force vs Extension test 4.1 ............................................................................................ 42



graph 18 Force vs Voltage test 5.2................................................................................................ 44

graph 19 Shows the Contact pressure vs Voltage quadratic relationship .................................... 51

graph 20 shows the linear model of the contact pressure-voltage relationship ............................ 52


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LIST OF TABLES

Table 1 showing the calculation for the weighting of each criterion ............................................ 20

Table 2 Illustrating the justification for choosing final design ..................................................... 20

Table 3 showing five main part groups of the design ................................................................... 21

Table 4 Process plan for the flanges ............................................................................................. 23

Table 5 Process Plan for the angle iron ........................................................................................ 24

Table 6 Process Plan for the Sensor Strip ..................................................................................... 25

Table 7 Showing calculated joint stiffness from test 1 and 2 ....................................................... 38

Table 8 Shows the comparison of K values from test 3 and 2 ...................................................... 40

Table 9 shows the voltage reading from test 3 ............................................................................. 41

Table 10 Shows the Voltage result from test 4 ............................................................................. 43


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CHAPTER 1

INTRODUCTION

1.1 RATIONALE

Sensors are used extensively in industries because of the many advantages they offer.

Sensors offer the ability to sense a specified parameter and produce a signal that can be used for

processing in a control system. Pressure sensors are one of the most popular sensors in the

industry. They are used to monitor pressure thereby providing information on when the system

might fail. Because of the high pressures of fluids in an industry, failure can be devastating hence

better sensing systems needs to be implemented.

With advances in technology, it has become easy to apply sensors to a wide array of

applications. In this project, a pressure sensor is being designed for sensing the contact pressure

between two flanges, which can form the key component in a more efficient and better pressure

management system than existing methods. Conventionally, a technician would have to

periodically check the bolts holding the flanges together and ensure that there are no leaks but an

integrated sensor can provide real time information about the variation in pressure between the

flanges. This can provide a more efficient and reliable system to prevent failure, thereby saving

time wasted by the technician on “useless” maintenance checks among other things. The contact

pressure sensor would determine the contact pressure between two flanges using a transducer

which produces a signal. Using this signal a value is then displayed for monitoring.

Furthermore, this signal can also be integrated with other components to form a closed loop

control system which offers another advantage for using a sensor.


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1.2 OBJECTIVES

To investigate existing contact pressure sensors

To design a user friendly sensor system to measure and output the value of the contact

pressure for the flange joint.

To build and the test the workings of the sensor design

1.3 SCOPE

The pressure sensor would measure the contact pressure between two flat face flanges

which are operating in a typical industry. The sensors that would be considered for this

application are tactile sensors which include piezoelectric, piezoresistive and capacitive type

sensors. From these types of sensors, a suitable macro sensor would be chosen and implemented.

Also, the effects of temperature, fatigue or relaxation on the flange joint would not be

considered in this project.


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CHAPTER 2

LITERATURE REVIEW

2.1 What is Pressure

Pressure can be defined as the measure of force per-unit-area, acting perpendicularly to

any surface. The standard SI unit for pressure measurement is the Pascal (Pa) which is equivalent

to one Newton per square meter (N/m2). In the English system however, pressure is usually

expressed in pounds per square inch (psi).

The pressure measured can be divided into three different categories: absolute pressure, gauge

pressure and differential pressure.

Absolute pressure refers to the absolute value of the force per-unit-area exerted on a

surface by a fluid. Gauge pressure is the measurement of the difference between the absolute

pressure and the local atmospheric pressure. So, the gage pressure value is measured with respect

to the atmospheric pressure. Differential pressure is simply the measurement of one unknown

pressure with reference to another unknown pressure. The pressure measured is the difference

between the two unknown pressures.

However, for purpose of this project, the pressure that is being measured would not be

any of these three categories since the pressure being measure is a contact pressure between two

solid bodies and not of a fluid.

2.2 Measurement Systems

Measurements are performed by physical devices called sensors or transducers, which

are capable of converting a physical quantity to a more readily manipulated electrical quantity

(Sinclair, 2001). Sensors, therefore, convert the change of a physical quantity (e.g. strain) to a

corresponding (usually proportional) change in an electrical quantity (e.g., voltage). Often, the

direct output of the sensor requires additional manipulation before the electrical output is

available in a useful form. For instance, there is a change in resistance resulting from a change in

the surface stresses of a material. The quantity measured by the resistance strain gauges must


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first be converted to a change in voltage through a suitable circuit (the Wheatstone bridge) and

then amplified from the millivolt to the volt level. The manipulations needed to produce the

desired end result are referred to as signal conditioning. The wiring of the sensor to the signal

conditioning circuitry requires significant attention to grounding and shielding procedures, to

ensure that the resulting signal is as free from noise and interference as possible. Very often, the

conditioned sensor signal is then converted to digital form and recorded in a computer for

additional manipulation, or is displayed in some form. Figure 1 shows a schematic of the sensing

process.

Figure 1 Instrument model with amplifier, analog to digital converter, and computer output

(Reprinted from Measurement, Instrumentation and Sensors handbook)

A sensor is usually accompanied by a set of specifications that indicate its overall

effectiveness in measuring the desired physical variable. The following definitions will help in

understanding a sensor data sheet:

Accuracy: Conformity of the measurement to the true value, usually in percent of full-scale

reading.

Error: Difference between measurement and true value, usually in percent of full-scale reading

Precision: Number of significant figures of the measurement

Resolution: Smallest measurable increment

Span: Linear operating range

Range: The range of measurable values

Linearity: Conformity to an ideal linear calibration curve, usually in percent of reading or of

full-scale reading


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2.3 Different technologies used in making pressure sensors

Fiber optic sensors

This technology uses the properties of fiber optics to affect light propagating in a fiber

such that it can be used to form sensors. Pressure sensors can be made by constructing

miniaturized fiber optic interferometers to sense nanometer scale displacement of membranes.

Pressure can also be made to induce loss into a fiber to form intensity based sensors.

Mechanical deflection

This technology uses the mechanical properties of a liquid to measure its pressure. Such

as, the effect of pressure on a spring system and the changes of compression of spring can be

used to measure pressure.

Strain gauge

This technology makes use of the changes in resistance that some materials experience

due to change in its stretch or strain. This technology makes use of the change of conductivity of

material when experiencing different pressures, calculates that difference and maps it to the

change of pressure.

Semiconductor piezoresistive

This technology uses the change in conductivity of semiconductors due to the change in

pressure to measure the pressure.

Microelectromechanical systems (MEMS)

This technology combines microelectronics with tiny mechanical systems such as valves,

gears, and any other mechanical systems all on one semiconductor chip using nanotechnology to

measure pressure.

Vibrating elements (silicon resonance, for example)

This technology uses the change in vibration on the molecular level of the different

materials elements due to change in pressure to calculate the pressure.

http://en.wikipedia.org/wiki/Fiber_optics

http://en.wikipedia.org/wiki/Spring_%28device%29

http://en.wikipedia.org/wiki/Strain_gauge

http://en.wikipedia.org/wiki/Electrical_conductivity

http://en.wikipedia.org/wiki/Semiconductors

http://en.wikipedia.org/wiki/Microelectromechanical_systems


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Variable capacitance

This technology uses the change of capacitance due to change of the distance between the

plates of a capacitor because of change in pressure to calculate the pressure.

2.4 Technologies for Tactile Sensing

For the application of a pressure sensor to measure the contact pressure between two

flanges, tactile sensors were found to be the most applicable sensors to use. The type of tactile

sensors to be considered includes;

Piezoresistive

Piezoresistive sensors (also known as strain-gage sensors) are the most common type of

pressure sensors in use today (Webster, 1999). Piezoresistive effect refers to a change in the

electric resistance of a material when stresses or strains are applied. Piezoresistive materials can

be used to make strain gages that, when incorporated into diaphragms, are well suited for sensing

the induced strains as the diaphragm is deflected by an applied pressure. The sensitivity of a

strain gage is expressed by its gage factor, which is defined as the fractional change in resistance,

Gauge Factor =(∆𝑅/𝑅)

𝜀

Capacitive

Tactile sensors within this category are concerned with measuring capacitance or voltage,

which varies under applied load. The capacitance of a parallel-plate capacitor depends on the

separation of the plates and their areas. A sensor using an elastomeric separator between the

plates provides compliance such that the capacitance will vary according to the applied normal

load.

http://en.wikipedia.org/wiki/Capacitance


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Figure 2 showing a typical Capacitive Sensor (Reprinted from Measurement, Instrumentation and Sensors

handbook)

When a load is applied to the transducer, the capacitor is deformed as shown in Figure 2.

The force will cause the distance between the parallel plates of the capacitor to decrease or

increase (according if the force is a compressive or tensile force), causing the capacitance to

change, also changing the voltage across the plates. The force will result in a change in h and the

voltage depends on h so, the voltage across the capacitor or the capacitance can be related to the

force applied.

C= 𝜀𝐴

ℎ E(t) =

−𝑞(𝑡)

𝜀𝐴 V(t) = − 𝐸 𝑡 𝑑ℎ =

𝑞 𝑡 ℎ

𝜀𝐴

ℎ

0

Where, E(t) is the instantaneous electric field

V(t) is the voltage across the plates

ε is the permittivity of the dielectric

Piezoelectric

A material is called piezoelectric, if, when subjected to a stress or deformation, it

produces electricity. Longitudinal piezoelectric effect occurs when the electricity is produced in

the same direction of the stress (Webster, 1999).

In Figure 3, a normal stress, σ ( F/A) is applied along the Direction 3 and the charges are

generated on the surfaces perpendicular to Direction 3. A transversal piezoelectric effect occurs


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when the electricity is produced in the direction perpendicular to the stress. The voltage V

generated across the electrodes by the stress σ is given by:

Figure 3 showing a Piezoelectric transducer (Reprinted from Measurement, Instrumentation and Sensors

handbook)

V= 𝑑 ℎ

𝜀𝜎

Where, d = Piezoelectric constant associated with the longitudinal piezoelectric effect

ε = Permittivity

h = Thickness of the piezoelectric material

σ =a normal stress (F/A)

Since piezoelectric materials are insulators, the transducer shown in Figure 3, can be considered

as a capacitor, from an electrical point of view. Consequently,

V= 𝑄

𝐶=

𝑄

𝜀𝐴ℎ

Where, Q = Charge induced by the stress

C = Capacitance of the parallel capacitor

A = Area of each electrode

h = Thickness of the piezoelectric material.


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2.5 The Flange Joint

When assembled, a flange gasket seal or „joint” is subject to compressive pressure

between the faces of the flanges, usually achieved by bolts under load. The behavior of a flanged

joint in service depends on whether or not the tension created in the fasteners will clamp the joint

components together with a force great enough to resist failure of the seal, but small enough to

avoid damage to the fasteners, joint components, gasket etc. The clamping load on the joint is

created on assembly, as the nuts on the fasteners are tightened. This creates tension in the

fastener (preload). Although there may be some plastic deformation in the threads when a

fastener is tightened normally, especially on the first tightening, most of the joint components

respond elastically as the nuts are tightened. Effectively, the entire system operates as a spring,

with the fasteners being stretched and the other joint components being compressed.

The flange joint may fail due to the following: - Low bolting torques, over-tight bolt

loads, weak bolt materials, inadequate bolt, washer / nut lubrication, poor flange design or

materials, poor gasket cutting or storage, improper installation practices.

For the majority of materials in the flange system (including gaskets, fasteners, nuts, washers),

relaxation sets in after a fairly short time. For soft gasket materials, one of the major factors is

usually the creep relaxation of the gasket. These effects are accentuated at elevated temperatures,

with the net result that the compressive load on the gasket is reduced, or the contact pressure

between the flanges is reduced, thus increasing the possibility of a leak. Hence a system needs to

be implemented to monitor the contact pressure between the flanges. Conventional systems that

check the contact pressure sensor include periodically checking the flange joint and using

ultrasonics to determine the stresses on the fasteners.

The application of a strain gauge as part of the system would provide a great advantage in

that it would indicate real time changes in the contact pressure, which is vital in monitoring the

flange joint for failure. Figure 4 shows how the strain gauge is to be implemented.


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Nut

Fastener

So, when the flanges move apart, it would result in an elongation in the strip (that is held

using two pieces of angle iron) causing a strain, which the strain gauge would measure.

2.6 Design Factors

The strain gauge sensor was found to be the most suitable sensor for the application. This

was determined because of the fact that stress and strain of a material are easily related. Hence

once the strain of a material is determined, it can be related to a stress or pressure by applying

relevant formulae. In addition to this, a bonded foil strain gage has a number of desirable

characteristics needed to make a good pressure transducer such as;

Small and predictable thermal effects allow accurate operation over a wide temperature

range. Compensation and correction techniques are straightforward.

Strain gages can be creep corrected by the manufacturer to match the requirements of the

transducer designer.

Small size and low mass allows operation over a wide frequency range and minimum

sensitivity to shock effect.

Gasket

Figure 4 application of strain gauge to

flange joint

Flanges

Strip of

metal with

strain

gauge

attached

Washers


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Because the strain gage is fully bonded to the strip of metal, there are no mechanical

connections to compromise ruggedness and dynamic performance.

It is essentially insensitive to supply voltage frequency so it can be used with AC or DC

systems.

The cost of the strain gage is relatively low and readily available in a variety of shapes,

sizes and materials.

Strain gages are very stable and transducers retain their calibration and performance over

extended periods of time.

Strain gages have excellent repeatability and linearity over a wide range of strains.

The use of a capacitive sensor may not be advisable since this type of sensor would require

the plates of the capacitor to be on the face of the flange, with the gasket acting as a dielectric.

This is not ideal since any materials introduced between the flange joint other than a gasket can

greatly affect the integrity of the joint. Also the properties of the gasket material do not lend

themselves to act as a dielectric. Hence the option of a capacitive pressure sensor was not

practical.

Piezoelectric materials are very similar to the capacitive sensor in that due to the

Piezoelectric effect, the material has to be place between the application of the force as with the

Capacitive sensor in order to sense the pressure. So the same problems as mentioned above

would occur.

The Strain Gauge

When an axial force is applied to a material, it results in a change in length of the

material. Strain is defined by this change in length of the material divided by its original length.

Normal stress is found when the force is divided by the area perpendicular to the line of action of

the force. Stress and strain are related by a quantity known as Young‟s modulus of Elasticity (E)

and is given by the ratio of stress over strain.


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E = 𝑆𝑡𝑟𝑒𝑠𝑠

𝑆𝑡𝑟𝑎𝑖𝑛 =

𝜎

𝜀

The metallic strain gauge consists of a very fine wire or, more commonly, metallic foil

arranged in a grid pattern. The grid pattern maximizes the amount of metallic wire or foil subject

to strain in the parallel direction. The cross sectional area of the grid is minimized to reduce the

effect of shear strain and Poisson Strain. The grid is bonded to a thin backing, called the carrier,

which is attached directly to the test specimen. Therefore, the strain experienced by the test

specimen is transferred directly to the strain gauge, which responds with a linear change in

electrical resistance (Sinclair, 2001).

Figure 5 showing a typical Bonded Foil Strain Gauge (reprinted from sensors and Transducers)

The strain gauge would be attached to a strip of metal which fasten to the joint by using

two pieces of angle iron on either side of the flange joint (refer to figure 8) . Therefore when the

flanges move apart the strip would elongate and the strain gauge would detect a strain

measurement. This strain measurement would be very small strain values. Therefore, to measure

the strain requires accurate measurement of very small changes in resistance.

To measure such small changes in resistance, the strain gauge is used in a bridge configuration

with a voltage excitation source. The general Wheatstone bridge, illustrated below in figure 6,

consists of four resistive arms with an excitation voltage, Vin, that is applied across the bridge.


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Figure 6 showing the Wheatstone Bridge circuit (reprinted from sensors and Transducers)

If the bridge output is zero then the bridge is said to be balanced, so when balanced, Vout

= 0V and for this to happen then R1R3=R2R4 must hold true.

Now if R4 is replaced by the strain gauge, then any changes in strain gauge resistance will

unbalance the bridge and produce a nonzero output voltage. This voltage signal is then

conditioned using an appropriate signal conditioning module and the result is displayed.

The Wheatstone bridge can be used to directly cancel the effect of thermal drift. If R1 is a

strain gage bonded to a specimen and R2 is a strain gage held onto a specimen with heat sink

compound (a thermally conductive grease available at any electronics store), then R1 will

respond to strain plus temperature, and R2 will only respond to temperature. Since the bridge

subtracts the output of R1 from that of R2, the temperature effect cancels.

Figure 7 showing the application of a strain gauge with temperature compensation (reprinted from National

Instruments website)

Also, by using two strain gauges in the bridge, the effect of temperature can be further

minimized. For example, Figure 7 illustrates a strain gauge configuration where one gauge is


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active and a second gauge is placed transverse to the applied strain. Therefore, the strain has little

effect on the second gauge, called the dummy gauge. However, any changes in temperature will

affect both gauges in the same way. Because the temperature changes are identical in the two

gauges, the ratio of their resistance does not change, the voltage Vout does not change, and the

effects of the temperature change are minimized.

The Wheatstone bridge offer many advantages. In most cases complete temperature

compensation can be achieved over an extremely wide temperature range. By using the

computational characteristics of the bridge, electrical output can be increased by as much as four

times the output from a single gage. Also, by gage location and grid geometry the Wheatstone

bridge can cancel unwanted components involved in a measurement.

The electrical output signal from the bridge will be:

A millivolt signal directly proportional to the applied voltage. Typically it will be 30

millivolts to a 10-volt excitation when rated pressure is applied to the transducer.

Directly proportional to the sums and differences of the unit changes in resistances of the

four arms of the bridge.

A linear signal with respect to the input pressure

Directly proportional to the product of the applied voltage and the net unit change in the

resistance of all four arms.

Strain gauge measurement involves sensing extremely small changes in resistance.

Therefore, proper selection and use of the bridge, signal conditioning, wiring, and data

acquisition components are required for reliable measurements. To ensure accurate strain

measurements, it is important to consider the following:

Excitation – Strain gauge signal conditioners typically provide a constant voltage source to

power the bridge. While there is no standard voltage level that is recognized industry wide,

excitation voltage levels of around 3 and 10 V are common. While a higher excitation voltage

generates a proportionately higher output voltage, the higher voltage can also cause larger errors

because of self-heating.

Amplification – The output of strain gauges and bridges is relatively small. In practice, most

strain gauge bridges and strain-based transducers will output less than 10 mV/V (10 mV of


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output per volt of excitation voltage). With 10 V excitation, the output signal will be 100 mV.

Therefore, strain gauge signal conditioners usually include amplifiers to boost the signal level to

increase measurement resolution and improve signal-to-noise ratios.

Filtering – Strain gauges are often located in electrically noisy environments. It is therefore

essential to be able to eliminate noise that can couple to strain gauges. Low pass filters, when

used in conjunction with strain gauges, can remove high-frequency noise prevalent in most

environmental settings.

Offset-Nulling Circuit – The second balancing method uses an adjustable resistance, a

potentiometer, to physically adjust the output of the bridge to zero. By varying the resistance of

potentiometer, you can control the level of the bridge output and set the initial output to zero

volts.

Shunt Calibration – The normal procedure to verify the output of a strain gauge measurement

system relative to some predetermined mechanical input or strain is called shunt calibration.

Shunt calibration involves simulating the input of strain by changing the resistance of an arm in

the bridge by some known amount. This is accomplished by shunting, or connecting, a large

resistor of known value across one arm of the bridge, creating a known change in resistance “due

to strain”. The output of the bridge can then be measured and compared to the expected voltage

value. The results are used to correct span errors in the entire measurement path, or to simply

verify general operation to gain confidence in the setup.


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CHAPTER 3

ALTERNATIVE DESIGNS

3.1 Alternative 1

One alternative is to use a capacitive type sensor to measure the contact pressure sensor.

A capacitive sensor measures the capacitance change due to the change in distance between the

two parallel capacitor plates. The application would be to modify the washer of the bolts holding

the flanges together so that it acts as a capacitor. When the bolts are tightened, it would result in

the compression of the washer. So if the bolts lose their tension due to creep or relaxation, the

compressive force acting on the washer would decrease and the two parallel faces of the washer

would move apart changing the voltage and capacitance of the capacitive washer. The voltage

across the washer can then be related to the compressive force or pressure acting on the washer.

Figure 8 Illustrating Alternative design 1 (created in solidworks)

Flanges Washer modified to act as a capacitor


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3.2 Alternative 2

Another alternative is to use a strain gauge however the strain gauge would be on the bolt.

Since the contact pressure between the flanges is directly dependent on the compressive force

exerted by the bolts on the flanges, any strain on the bolt can be related to the contact pressure

between the flanges.

Figure 9 Illustrating the alternative design 2 (created in solidworks)

Strain gauge on body of bolt Flange Face

The problem with this design is that it may be cumbersome to attach the strain gauge to the

body of the bolt as shown when the bolts are in place since there are wires attached to the strain

gauge which carry the voltage signal.


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CHAPTER 4

FINAL DESIGN

4.1 Final design

The strain gauge would be bonded to a strip of metal that is fixed across the flange joint

using two pieces of angle iron as shown below. When the pressure in the pipes build up and

cause the flanges to move apart due to elongation of the bolts, it would result in an elongation of

the strip of metal. The strain gauge would then measure this elongation by outputting a change in

resistance. Using a Wheatstone Bridge circuit, this resistance is converted to a voltage signal.

After the voltage signal is amplified and condition, it is plotted or it can be digitized and the

value outputted to a screen. After calibration and calculation, this value can be related to the

pressure acting between the flanges.

There are two strips of metal attached to the flange around the circumference of the

flanges 180 degrees apart and they are attached to the flanges using the existing bolts for the

flange joint and the angle iron parts. So the angle iron are held in place using the existing bolts

for the flange joint while the strip of metal is bolted onto the two angle iron pieces as shown in

the figure 8. The operation of this pressure sensor design is then tested in the Strengths lab.

Figure 10 Illustrating the application of the strain gauge (created in solidworks)

Bolt Angle Iron Strip of metal with strain gauge attached


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4.2 Limitations on design

There existed various external factors that applied constraints on the design and dictated

how the assembly would be designed.

Firstly, to simulate the effect of pressure build up causing the flanges move apart, the

Hounsfield Tensometer was used to pull the flanges apart. So the assembly was designed to fit in

the machine. This meant that the flanges had to be 6 inches in diameter and also a rod being

attached to each of the flanges. The purpose of the rod is used as the connecting member for the

assembly and the Tensometer and would be connected using a pin.Refer to Appendix A Picture 1

Although the flange is 6 inches in diameter, ASME B16[1].5 standards for such a Flange

size were adhered to. Refer to appendix B-drawing 2 for dimensions of the design.

Also, due to the limitation on the size of the assembly, only two strips of metal 180

degrees could be attached to the flange joint where ideally it should have been 3 such strips 120

degrees apart in order to have an accurate account of the variation of contact pressure around the

circumference of the flange joint.

4.3 Alternative due to Limitations

Initially it was thought that to overcome the problem of only 2 strips 180 degrees apart, a

flat was machined across the thickness of the flanges and holes were drilled on the thickness of

the flange to bolt the strip of metal on (refer to appendix A- picture 1), in order to have the ideal

orientation of 3 strips around the circumference. However, this design had many faults such as

the strip was too small for the strain gauge to fit also because of its small length, the tolerance

level for the hole and bolt would have to be very small for it to be sensitive enough.

So the use of the angle iron to fasten the strip of metal across the flange was considered. This

design was acceptable in that it allowed the strain gauge to fit on the strip of metal and could be

used with the existing holes and bolts of the flange joint. So the design offered an acceptable

compromise hence it was used.


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4.4 ANALYSIS OF DESIGNS

PUGH MATRIX

Maintenance Cost Sensitivity Durability

Maintenance 1 0.5 2 3

Cost 2 1 3 2

Sensitivity 0.5 0.33 1 0.5

Durability 0.33 0.5 2 1

Total 3.83 2.33 8 6.5

Overall Total 20.66

Fractions 0.185 0.113 0.387 0.315 Table 1 showing the calculation for the weighting of each criterion

These criteria were chosen after analysis on the vital aspects that would make up the pressure

sensor.

Maintenance implies how easily the sensors can be removed from the flange joint and

replaced if faulty.

Cost takes into consideration all the components of the sensor system.

Sensitivity is the measure of how efficient the sensor would measure the contact

pressure between the flanges.

Durability is a measure of how long the design, once implemented, would last.

SELECTION MATRIX

Table 2 Illustrating the justification for choosing final design

Each design was rated against the four criterions on a scale of one to five, with one

representing a low score and five a high score in the respective criterion. From the result, it is

observed that the final design got the highest score with alternative design 2 having a close but

lower score. The reason why alternative 2 and final design were so closely rated was because

they both employ the use of a strain gauge but in a different application.

Final design Alternative 1 Alternative 2

maintenance (x 0.185) 4 3 1

cost (x 0.113) 3 2 3

sensitivity (x 0.387) 3 3 4

durability ( x 0.315) 4 3 3

Total 3.5 2.89 3.01


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CHAPTER 5

FABRICATION The entire assembly consisted of 5 main part groups (refer to appendix B –Drawing 6) as shown

below.

Part

Group

Number

Part Name Dimensions of Part Material Number of

Parts in the

Assembly

1

Flanges with rod

welded

6 inches outer

diameter for

flanges

Bolt circle

diameter of 5

inches

Bolt hole diameter

of 0.55 inches

0.5 inch thickness

of flange

rod length of 4

inches with an

outer diameter of 1

inch and internal

diameter of 0.6

inches at a depth of

1.2 inches.

Mild steel

2

2

Bolt with washer

and nut for the

flange joint

5/8 inch Hex bolt

2 inch bolt length

11.16 inch Hex nut

5/8 inch flat

washer

Mild steel

A307 bolts

4

3

Angle Iron

0.25 inch thick

angle iron

Width 1 inch

Length 2 inches

Mild Steel

4

4

Metal Strip

4.125 inches

Length

0.125 inch width

Mild Steel

2

5

Bolts with Lock

washers and Nuts

for holding metal

strip

11 mm Bolt, lock

washer and nut

2 inch bolt length

Mild Steel

4

Table 3 showing five main part groups of the design


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The Fabrication process was applicable for part groups 1, 3 and 4 as the others groups required

no type of machining.

5.1 PROCESS PLAN

PART 1: THE FLANGES

Tools and

Machinery

Scriber, dividers, steel rule, odd leg caliper, hammer, punch, file, drill

press, vertical milling machine horizontal band saw.

Materials A half inch thick rectangular block of mild steel, one inch mild steel rod

Description On the Rectangular block two circles of 6.3 inches was marked

off using a scriber.

The hammer and punch were used to outline the two circles

The circular pieces were then cut using a blow torch.

After it was cooled, a hole of diameter 1 inch was drilled in the

center of the two circular plates using the vertical drill press.

Two 1 inch rods were then cut to length 4.125 inches on the

horizontal band saw.

The rod was then inserted into the hole in the circular plates and

was welded to it from the contact surface the circular plate or

flange.

The weld was then grinded down to the surface of the flange.


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The entire flange was then mounted on the lathe and machined to

the required dimensions which included machining the contact

surface of the flange flat.

Emery paper was then used to provide a smooth finish on the

flange contact surfaces.

After this was done, the bolt circle of 5 inches was marked off

including the positions of the four bolt holes.

The guide holes of 12mm were drilled in the flanges using the

vertical milling machine at each of the bolt hole position.

Then the full diameter of 5/8” for the holes was drilled using the

drill press

The flanges were then bolted together at which point, it was

mounted on the lathe and the internal diameter of 0.66” at a depth

of 2 inches was machined on both rods of the flange.

The holes of diameter 5/16” were drilled on the each rod 2” away

from the end of the rod.

Finally, all the sharp edges were filed smooth.

Table 4 Process plan for the flanges

PART 3: THE ANGLE IRON


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Tools and

Machinery

Scriber, steel rule, odd leg caliper, hammer, punch, file, drill press,

vertical band saw.

Materials Mild steel angle iron, 1/4” thick.

Description Four one inch lengths were marked off on the angle iron.

The angle iron was then cut to these lengths on the vertical band

saw.

The hammer and punch were used to mark the center of two

holes on two of the faces at an angle of 90 degrees.

The holes of diameter 0.55 inches were drilled on all four parts

using the drill press.

Then the holes of diameter 0.24 inches were drilled on the other

face of the four parts.

The edges were then made smooth using a file.

Table 5 Process Plan for the angle iron

PART 4: THE METAL STRIP/ SENSOR STRIP

Tools and

Machinery

Scriber, steel rule, odd leg caliper, hammer, punch, file, drill press,

horizontal band saw.

Materials 1/8” thick mild steel bar

Description Two lengths of 4 1/8” were marked off on the steel bar.

The strips of metal were then cut using on the horizontal band

saw.

The center of the holes on each strip were measured and marked


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off using the hammer and punch.

The holes of diameter 0.24” were then drilled on the drill press

2.875” inches apart from each other.

The edges of the strips were made smooth using a file.

The surface of the strip was prepared by removing the scale and

using emery paper to provide a smooth finish.

The strain gauges were then bonded to the strips of metal,

clamped in place and left overnight to dry.

Table 6 Process Plan for the Sensor Strip


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CHAPTER 6

INSTRUMENTATION USED

6.1 Strain indicator model P-350A Manufacturer: VISHAY

Figure 11 The Strain indicators used

This strain indicator is designed primarily for use with the resistance type strain gauges

that are used in this project. The P-350A employs the null-balance principle. That is the operator

must center a null galvanometer prior to reading the output. The instrument uses a 1000 Hz

carrier; bridge excitation, rebalance circuitry and the null amplifier all operate at this carrier

frequency.

While the P-350A by itself will accept only one input (full, half or quarter bridge), it can

be used as the central indicator for a multiple channel static strain gauge data acquisition system.

For the purpose of this project, each strain gauge is connected to a strain indicator in a quarter

bridge configuration.

SPECIFICATIONS/FEATURES

Display: Direct reading inline digital display, including sign to +/- 49,999 με

Gain Factor Control: 0.10 to 10.0

Range: +/- 49,999 με

Power source: Internal battery or 115 volts AC.


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Dimensions: 9” W x 6-1/2” H x 7” D

Weight: 9 pounds

The gain factor was set to 2.1 and the circuit was connected as shown below.

Figure 12A shows the strain gauge connected to the leads of the indicator Figure 11B shows the equivalent circuit

Here E is the excitation voltage and E0 is the voltage reading.

6.2 Strain gauges The property of the strain gauge is as follows.

Material Composition GF Resistivity

(Ohm/mil-ft) Resistance /

Constantan 45% NI, 55%

Cu

2.0 290 120

Figure 13 shows the strain gauge connected in a quarter bridge configuration


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6.3 Hounsfield tensometer connected to a computer

Manufacturer: Tinius Olsen

Figure 14 Shows the Hounsfield Tensometer

This is a horizontal bench top testing machine for determining Tension, Compression,

Shear, Flexure and other mechanical and physical properties of materials. It has a limit of

20,000N and outputs Force-extension values to a computer.


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6.4 Plotter or Recorder

Manufacturer: Kipp & Zonen

Figure 15 shows the Plotter used to record the voltage signal

The recorder has two inputs and is connected to each of the strain indicators. It is used to

plot the voltage signals from each of the quarter bridge circuits. The scale on the x axis was set to

2cm = 10mV while the speed of the movement of the graph paper was set to 0.5mm/s.


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CHAPTER 7

RESULTS

The testing was carried out using the equipment mentioned previously and five tests were

conducted.

The entire flange assembly with the sensors were mounted in the Tensometer and

secured. Then, both strain gauges were then connected to a strain indicator in a quarter bridge

configuration as shown in Figure 11A. The recorder was connected to each of the strain indicator

and the circuit was balanced using the strain indicator.

Each test that was done was repeated for two trials. For the Voltage signal graphs

obtained from the plotter, refer to appendix C.

Test 1 For the first test, the flange joint was tightened by hand without knowing any real

indication of the preloads on the bolts.

The force -extension readings were taken from the machine by starting and stopping the

machine at approximately equal intervals. As a result of the starting and stopping, the graph of

voltage from each strain gauge that was plotted from the recorder was a step graph (see appendix

C). Where each step represented when the tensometer was stopped so the voltage reading at the

step corresponded to the value of the force recorded at that time. Hence from this data, a

relationship between the applied force from the machine and the voltage reading from the strain

gauge can be found. This test was repeated for two trials.

From the results that were obtained shown in appendix C, graphs of force vs. extension

and force vs. voltage for each strain gauge were plotted as shown below.


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Trial 1

Graph 1 Force vs Extension

Graph 2 Force vs Voltage ,V1

y = 11347x

y = 10983x

0

5000

10000

15000

20000

25000

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Forc

e/

N

Extension, e / mm

Force vs Extension

Loading

unloading

y = 253.87x + 1321.7

y = 258.59x + 1463.7

0

5000

10000

15000

20000

25000

0 10 20 30 40 50 60 70 80

Forc

e/

N

Voltage/ mV

Force vs Voltage, V1

F vs V loading

F vs V unloading


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Graph 3 Force vs Voltage ,V2

Trial 2

Graph 4 Force vs Extension

y = 897.58x + 1502.2

y = 1007x + 3182.6

0

5000

10000

15000

20000

25000

0 5 10 15 20 25

Forc

e/N

Voltage/ mV


Loading

Unloading

y = 11592x

y = 11447x

0

5000

10000

15000

20000

25000

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Forc

e/N

Extension, e/ mm

Force vs Extension

Loading

Unloading


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Graph 5 Force vs Voltage,V1

Graph 6 Force vs Voltage, V2

y = 250.85x + 1866.7

y = 252.27x + 1851.9

0

5000

10000

15000

20000

25000

0 10 20 30 40 50 60 70 80

Forc

e/N

Voltage/mV


F vs V1 loading

F vs V1 unloading

y = 989.19x + 1662.8

y = 994.07x + 3498

0

5000

10000

15000

20000

25000

0 5 10 15 20 25

Forc

e/N

Voltage/mV


Loading

Unloading


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Test 2 This test was performed the same as test 1. The only difference was that the bolts were

tightened using a torque wrench. The value of the torque applied to each of the bolts was 70

Pound-force foot (lbf-ft) which is equal to 94.42 Nm. When using the torque wrench, the head of

the bolt was fixed and the torque wrench was used to tighten the nut.

Figure 16 Showing the order in which the bolts were tightened

Trial 1

graph 7 Force vs Extension

y = 11936x

y = 12067x

0

5000

10000

15000

20000

25000

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Forc

e/N

Extension, e/mm

Force vs Extension

loading

unloading


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graph 8 Force vs Voltage, V1


y = 319.3x + 4403.3

y = 314.24x + 3633.6

0

5000

10000

15000

20000

25000

0 10 20 30 40 50 60

Forc

e/N

Voltage/mV


Loading

Unloading

y = 365.62x + 3502.2

y = 345.89x + 5158.6

0

5000

10000

15000

20000

25000

0 10 20 30 40 50 60

Forc

e/N

Voltage/mV


Loading

Unloading


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Trial 2

graph 10 Force vs Extension


y = 12027x

y = 12058x

0

5000

10000

15000

20000

25000

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Forc

e/N

Extension, e/mm

Force vs Extension

Loading

Unloading

y = 312.24x + 4607

y = 289.98x + 5410.7

0

5000

10000

15000

20000

25000

0 10 20 30 40 50 60

Forc

e/N

Voltage/mV


Loading

Unloading


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Analysis of the graphs showed that a linear relationship between force and extension, and

a linear expression best modeled the Force-Voltage relationship. These relationships are showed

below. Test 1

F- e relationship

trial 1 trial2

Loading y = 11347x y = 11592x

Unloading y = 10983x y = 11447x

F- V1 relationship

trial 1 trial2

Loading y = 253.87x + 1321.7 y = 250.85x + 1866.7

Unloading y = 258.59x + 1463.7 y = 252.27x + 1851.9

F- V2 relationship

trial 1 trial2

Loading y = 1007x + 3182.6 y = 994.07x + 3498

Unloading y = 897.58x + 1502.2 y = 989.19x + 1662.8

y = 388.44x + 2909.7

y = 348.15x + 5063.1

0

5000

10000

15000

20000

25000

0 5 10 15 20 25 30 35 40 45 50

Forc

e/N

Voltage/mV


Loading

Unloading


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Test 2

F- e relationship

trial 1 trial2

Loading y = 11936x y = 12027x

Unloading y = 12067x y = 12058x

F- V1 relationship

trial 1 trial2

Loading y = 319.3x + 4403.3 y = 312.24x + 4607

Unloading y = 314.24x + 3633.6 y = 289.98x + 5410.7

F- V2 relationship

trial 1 trial2

Loading y = 345.89x + 5158.6 y = 348.15x + 5063.1

Unloading y = 365.62x + 3502.2

y = 388.44x + 2909.7

From test 2 the average Force-voltage relationships were found as the following

For V1 y= 308x +4515.65

For V2 y =362.02x + 4158.4

The relationship between force and extension was a very linear one which showed that hooke‟s

law was obeyed. So, F=k e

Therefore the stiffness ,K of the joint is given by the gradient of the F-e graph. This

overall joint stiffness included the resistance of the four bolts and that of the two strips of metal

across the flange.

An average value k for loading and

unloading for both trials in test 1 was found.

The same K values were calculated for test 2 for

both trials.

K ave. loading = (11347 + 11592)/2 = 11469.5

N/mm

K ave. unloading = (10983 + 11447)/2 = 11215

N/mm

K ave. loading = (11936 + 12027)/2 = 11981.5

N/mm

K ave. unloading = (12067 +12058)/2 = 12062.5

N/mm

Table 7 Showing calculated joint stiffness from test 1 and 2


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Voltage signal graphs for test 1 and test 2 (refer to appendix C)

From the relationship established for force vs. voltage, it is noticed that this relationship

was different both strain gauges in test 1 this meant that when tensile force was applied to the

flange joint, it resulted in uneven strain in the senor strips. This is due to the fact that since the

bolts were not tightened evenly, it resulted in an uneven preload on each of the bolt. Therefore

the contact pressure of the flange joint would vary throughout the entire joint, so the strain

gauges gave different readings.

In test 2 however, the Force-voltage relationship for each strain gauge was fairly similar

which showed that when each of the bolts were tightened using a 70 lbf-ft torque, it resulted in

an evenly distributed contact pressure between the flanges. So when a tensile force is applied to

the flanges, the strain on each strip would be similar.

All the tests subsequent to test 1 and 2 were conducted using the Hounsfield Tensometer

connected to a desktop computer which automatically recorded the force-extension values and

the preload of 70 Pound-force foot (lbf-ft) on the four bolts were maintained . Since it was a

continuous process of loading and unloading the flanges, the graph of the strain voltage are

continuous curves in this case.

Also, due to the fact that the tensometer gave over 500 force-extension readings, only the

F-e graphs would be included in the results.

Test 3 Test 3 was conducted in the same manner as test 2 except that instead of manually

recording the F-e values, the values were outputted from the Tensometer straight to a computer.

As the force-voltage relationship has already been established, this test was used to determine the

stiffness of the joint and compare the value to that obtained in test 2 when the force-extension

values were recorded manually.


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Trial 1

graph 13 Force vs Extension test 3

Trial 2

graph 14 Force vs Extension test 3

Values from test 3

Values from test 2

K ave. loading = (12426 +11921)= 12173.5 N/mm

K ave. loading = 11981.5 N/mm

K ave. unloading = (12694+12085)= 12389.5 N/mm

K ave. unloading = 12062.5 N/mm

Table 8 Shows the comparison of K values from test 3 and 2

So it can be concluded that with a high level of accuracy that the joint stiffness , k 12000

N/mm.

y = 12426x

y = 12694x

-5000

0

5000

10000

15000

20000

25000

0 0.5 1 1.5 2

Forc

e/N

Extension, e/mm

Force vs Extension

loading

unloading

y = 11921x

y = 12085x

0

5000

10000

15000

20000

25000

0 0.5 1 1.5 2

Forc

e/N

Extension, e/mm

Force vs Extension

loading

unloading


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Voltage signal graph for test 3 (refer to appendix C)

It should be noted that on the voltage graphs obtained from test 3, there was a large

difference in the magnitude of the signal for both strain gauges. This is was due to an error when

using the recorder. The scale for the red signal was set to 20mV per cm instead of 10mV per cm

as was used throughout, so both strain gauges gave approximately the same strain reading.

Also at the end of loading, it was observed that graph became vertical or flat. The

explanation for this is that after loading, there was a pause before unloading as the F-e results

were sent from the tensometer to the computer. So since there was no additional force to cause a

strain, both the signals had a constant voltage reading during the pause.

Trial 1

Trial 2

The force at the end of loading = 20100 N

The force at the end of loading = 19953.33 N

Voltage reading at the end of loading for blue

signal = 47mV


signal = 45mV

Voltage at the end of loading for red signal

= 52mV

Voltage at the end of loading for red signal

= 50mV

Table 9 shows the voltage reading from test 3

The results show that both strain gauge recorded the same level of strain. The reason for

the small difference is due to the different sensitivity setting on each strain indicator since it

could not be determined accurately if the sensitivity were the same. So for bolts 180 apart, the

behavior is symmetric.

Test 4 In this test, one of the sensor strips was removed. The reason for doing this was to inspect

the level stiffness the two sensor strips added to the flange joint.


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Trial 1

graph 15 Force vs Extension test 4.1

Trial 2


So,

K ave. loading = (11723+12404)= 12063.5 N/mm

K ave. unloading = (11803+12509)= 12156 N/mm

y = 11723x

y = 11830x

0

5000

10000

15000

20000

25000

0 0.5 1 1.5 2

Forc

e/N

Extension, e/mm

Force vs Extension

loading

unloading

y = 12404x

y = 12509x

0

5000

10000

15000

20000

25000

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Forc

e/N

Extension ,e/mm

Force vs Extension

loading

unloading


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Voltage signal graph for test 4 (refer to appendix C)

Since there was only one strain gauge connected, there would only be one signal. Also it

should be noted that the error of setting the scale to 20mV per cm instead of 10mV per cm was

corrected.

Trial 1

Trial 2

The force at the end of loading = 19867.33 N

The force at the end of loading = 19930.67N


signal = 41 mV


signal = 41 mV

Table 10 Shows the Voltage result from test 4

Test 5 The remaining sensor strip was removed and the flange joint alone was tested.


y = 9188.2x

y = 9178.2x

0

5000

10000

15000

20000

25000

0 0.5 1 1.5 2 2.5

Forc

e/N

Extension, e/mm

Force vs Extension

loading

unloading


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graph 18 Force vs Voltage test 5.2 From the results obtained from test 4 and test 5, it can be concluded that the effect of the

two sensor strips on the entire joint stiffness can be considered as negligible since the stiffness

value did not change from the average value of 12,000 N/mm.

y = 12245x

y = 12560x

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Forc

e/N

Extension, e/mm

Force vs Extension

loading

unloading


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CHAPTER 8

CALCULATIONS

For the test conducted, it was noticed that separation of the flanges did not occur so it can

be concluded that the maximum force applied to the flange joint was less than the initial

clamping force of the joint.

The purpose of the bolt is to clamp the two flanges together. Twisting the nut stretches

the bolt to produce the clamping force. This clamping force is called the pretension or bolt

preload. Since the members are being clamped together, the clamping force that produces

tension in the bolt induces compression in the members.

8.1 Bolt stiffness, Kb The stiffness of the portion of a bolt or screw within the clamped zone will generally

consist of two parts, that of the unthreaded shank portion and that of the threaded portion. Thus

the stiffness constant of the bolt is equivalent to the stiffnesses of two springs in series.

For two springs in series, the spring rates of the threaded and unthreaded portions of the bolt in

the clamped zone are, respectively,

where At = tensile-stress area

lt = length of threaded portion of grip

Ad = major-diameter area of fastener

ld = length of unthreaded portion in grip


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There were four bolts used to hold the flanges together. Each bolt size was 3/8 inch with

two being 1.5 inches in length and the other two of length 2.25 inches. The difference in length

was due to the fact that two bolts were used to hold the angle iron in place so they needed to be

longer.

For a 3/8 inch bolt

At = 0.0775 in2 = 5.0 x10

-5 m

2

E= 200 x 109N/m

2

Ad = (π (0.375/2)2) = 0.1104 in

2 = 7.12 x 10

-5 m

2

Threaded length, LT = 2d + 0.25 inches

= 2(0.375) +0.25

= 1 inch =0.0254 m

So for shorter bolts, lt= 0.0254 m and ld = (0.0381- 0.0254) = 0.0127 m

For longer bolts, lt= 0.0254 m and ld = (0.05715 - 0.0254) = 0.03175 m

For bolt 1 of 1.5 inch length

kt = (5.0 x10-5

x 200 x 109)/ 0.0254 = 393.7 x 10

6 N/m

kd = (7.12 x 10-5

x 200 x 109)/ (0.0127) = 1121.3 x 10

6 N/m

So total stiffness for this bolt is

Kb1 = ([1/393.7 x 106] + [1/1121.3 x 10

6])

-1

= 291.4 x 106 N/m

For the bolt 2 of length 2.25 inches

kt = (5.0 x10-5

x 200 x 109)/ 0.0254 = 393.7 x 10

6 N/m

kd = (7.12 x 10-5

x 200 x 109)/ (0.03175) = 448.5 x 10

6 N/m

So total stiffness for this bolt is

Kb2 = ([1/393.7 x 106] + [1/ 448.5 x 10

6])

-1

= 209.7 x 106 N/m


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8.2 Joint Stiffness, Kj

The relationship E = stress /strain = σ /e is used to determine the stiffness of a section.

Where Area, A = area of the flange – area of the bolt holes = (π32) – (π0.275

2)

= 28.04 in2 = 1.81x 10

-2 m

2

Young‟s modulus, E = 207 x 109 N/m

2

L= 0.5 in = 1.27 x 10-2

m.

So, k1 = (1.81x 10-2

x 207 x 109)/ 1.27 x 10

-2

= 2.95 x 1011

N/m

And k1 =k2

So Kj= [(1/2.95 x 1011

) + (1/ 2.95 x 1011

)]-1

= 1.47 x1011

N/m.


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8.3 Preload on bolts, Fp Fp = T / kd

Where, T = torque = 94.9 Nm

d= size of bolt shank = 9.52 x 10-3

m

k = torque coefficient = 0.2 for zinc plated bolts.

So preload Fp = 94.9 / (0.2 x 9.52 x 10-3

) = 48,842.4 N

However this value does not represent the actual preload on the bolt since in using a

torque wrench to apply a preload on the bolts, there are inherent errors. So, the measured torque

can be attributed to losses and not the preload. These losses include under head friction of the

bolt and thread deformation. In fact in some cases, 85% of the measure torques can be attributed

to losses.

For this reason, since it is know that the joint did not separate during testing after a

maximum force of 20,000N was applied which showed that the preload must have been greater

than this value, the preload was estimated to be around 24,000N.

Also, assuming the flanges to be rigid, the preload value represents the initial contact

force and the value needed to separate the flange joint.

So initial contact pressure = F/A = 24000/1.81x 10-2

= 1.325 x 106 N/m

2.

8.4 Calculation of Load Distribution using Bolt/Joint Stiffness

For the joint preloaded with a force Fp which is then subject to an externally applied load

Fe which tends to separate the join, the resulting deflection of the joint and bolt are the same

providing that Fe is less than the separation force.

Where, Fbe =force on bolts

Fje= force on joint

Fe= total externally applied force


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Fbe = (Kb/Kj)x Fje

But Fje = Fe - Fbe

So,

Fbe = (Kb/ Kj) x (Fe - Fbe)

Making Fbe the subject we get

Fbe = [Kb / (Kj + Kb)] x Fe

Similarly, Fje = [Kj / (Kj + Kb)] x Fe

And,

Combined bolt stiffness, Kb = (2 Kb1 + 2 Kb2)

= 1002.2 x 106 N/m.

And joint stiffness, Kj = 1.47 x1011

N/m.

Therefore,

Fbe = 0.00677Fe & Fje = 0.993Fe

These values show that majority of the external load is taken by the joint while the bolts “feels”

very little of this load. It should be noted that this is so only when the Fp > Fe.

Following the application of the external force,

Total force on the bolt, Fbt = Fp + Fbe

Total force on the joint, Fjt = Fp – Fje

= Fp – 0.993Fe

So the change in contact pressure = (Fp – 0.993Fe ) / A

= (Fp – 0.993Fe ) / 1.81 x 10-2

= (Fp/1.81 x 10-2

) – (0.993Fe / 1.81 x 10-2

)

= (24000/1.81 x 10-2

) - (0.993Fe / 1.81 x 10-2

)

= 1.325 x 106 – (0.993Fe / 1.81 x 10

-2)……………….[1]

= initial contact pressure – change in contact pressure due to Fe


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Although the Force-voltage relationship was modeled as being linear, calculations were

performed using a quadratic force-voltage relationship and a linear force-voltage

relationship.

To see the quadratic relationship, refer to appendix C.

For Quadratic relationship

From the results for test 2,

An average relationship between force, F and Voltage was found.

So for V1, y = -2.51x2 +435.59x + 3666.15……………….[2]

for V2, y = -4.2x2 +552.12x + 2992.83…………………[3]

where, y = Force Fe in N, and x = voltage in mV

For V1

Substituting equation 2 into equation 1

Contact pressure = 1.325 x 106 – [0.993{-2.51x

2 +435.59x + 3666.15} / 1.81 x 10

-2]

= 1.325 x 106– [-137.6x

2 + 23897.2x + 201104.9]

Let y = 1.325 x 106– [-137.6x

2 + 23897.2x + 201104.9]………………..[4]

Where y = contact pressure in N/m2, x = to the voltage in mV

For V2

Substituting equation 3 into equation 1

Contact pressure = 1.325 x 106 – [0.993{-4.15x

2 +544.9x + 2953.92} / 1.81 x 10

-2]

= 1.325 x 106– [-227.67x

2 + 29895x + 162057.46]

Let y = 1.325 x 106– [-227.67x

2 + 29895x + 162057.46]………………..[5]


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Where y = contact pressure in N/m2, x = to the voltage in mV

Graphs for equations 4 and 5 were then plotted.

Contact pressure-Voltage calibration curves

graph 19 Shows the Contact pressure vs Voltage quadratic relationship

The problem with this model was that it only catered for the contact pressure behavior in

only the operating Voltage range when the tests were conducted. That is values up to around 50

mV. So it could not predict the behavior of the contact pressure of the joint above this voltage

level for this. This is illustrated when the curves are extrapolated, the contact pressure begins to

increase after a certain value of voltage which is not expected to happen since as the voltage

increases, the contact pressure should gradually decrease to zero at which point the external force

is equal the clamp load and the joint is about to separate.

y = 137.57x2 - 23897x + 1E+06

y = 227.67x2 - 29895x + 1E+06

0

200000

400000

600000

800000

1000000

1200000

1400000

0 10 20 30 40 50 60 70 80

Co

nta

ct p

ress

ure

, N/m

2

Voltage, V1 /mV

Contact Pressure vs Voltage, V1

V1

V2


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So this model was rejected and a linear model was investigated. The same calculations were

performed for the linear relationship and a similar graph was plotted.

graph 20 shows the linear model of the contact pressure-voltage relationship

This model shows that around 60-68mV the joint would separate. That is where the graph

cuts the x axis where the contact pressure is zero.

Using the average force-voltage relationship

For V1 as y= 308x +4515.65 and for V2 as y =362.02x + 4158.4

The forces were found that corresponded to a voltage range of 60 to 68mV

The corresponding forces were 25459.56N when V1 = 68mV

And 25879.6 N when V2 = 60 mV.

y = -16922x + 1E+06

y = -19861x + 1E+06

-400000

-200000

0

200000

400000

600000

800000

1000000

1200000

0 10 20 30 40 50 60 70 80

con

tact

pre

ssu

re, N

/m2

Voltage, mV

Contact pressure vs Voltage

V1

V2


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CHAPTER 9

FINITE ELEMENT ANALYSIS OF THE FLANGE JOINT (Refer to appendix E for the entire FEA report)

After the model was created in Solidworks, it was imported into Algor where a finite element

analysis of the model was performed. Brick elements were used to mesh the parts. Figure 14 shows the

model after meshing.

Figure 17 shows the mesh of the CAD model in Algor

The boundary conditions were defined in the following way.

Firstly one the flanges were fixed at the same location were the pin would secure the flange to

the tensometer. Figure 15 shows this location.

Figure 18 location of the fixed boundary condition


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Then, the force pulling the flanges apart is added on the other flange. Figure 16 shows the application of

this force

Figure 19 Location of the externally applied force

The bolt preload was then added by applying a force of 24,000N to each of the major nuts of the

assembly as well as fixing the head of each of the four bolts. Figure 17 shows the application of the

preload.

Figure 20 shows the preload applied to the bolts


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Finally, rigid boundary conditions were applied to the flange surface as shown in figure 18.

Figure 21 shows the application of rigid boundary conditions to the flanges

Using these boundary conditions, the model was evaluated for different magnitudes of an

externally applied load and using the formula below, the strain at the sensor strips were

converted to a voltage and a force-voltage relationship was determined and compared with the

one obtained from the experiments.

For a quarter bridge configuration,

Vout =(G.F x ε x Vin)/4 (for derivation of this formula refer to appendix D.)

Where G.F = gauge factor =2.1,

ε= strain

Vin = excitation voltage


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CHAPTER 10

DISCUSSION

The purpose of the bolts are to clamp the two flanges together. When the bolts are

tightened, they behave like a spring element, that is they elongate when they are tightened so

they exhibit a certain stiffness value. So as they elongate and there is an internal axial force

created within the bolts. This force is known as the preload of the bolt and is a tensile force. The

more the bolt is tightened, the higher the preload value is. The resulting internal tensile force on

the bolts will cause a compressive force on the flange joint so, an axial preload imposes an

internal force on the bolt that imparts a compressive load on the bolted joint. This compressive

force is known as the clamping load. When there are no externally applied forces on the joint, the

preload on the bolts are equal to the clamping load. So preload is what causes the clamping load,

which is used to hold the flange joint together.

Figure 22 Shows a joint diagram

Figure 22 shows the joint diagram which illustrated the point that when preload is applied

to the bolts, it results in a clamping load on the joint as well as an elongation of the bolt and

compression of the joint. Where the red and green lines meet represents the point where the

preload is equal to the clamping load. When an external force is applied to the joint represented

by the blue line in figure 22, part of this external force is dealt with by the bolts while the

majority of it is dealt with by the clamping load, hence reducing the clamping load.

From the results of test 1 it is evident that the contact pressure is dependent on the

preload on the bolts. In this test, the bolts were tightened by hand so it is safe to assume that the


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preload on each of the bolts would be different. This is reflected in the results where each strain

gauge gave very different voltage readings for the same applied force (refer to graph 1 & 2-

appendix C). So this behavior was expected. Also, the Force-voltage relationships obtained from

this test were very different for both strain gauges which were concurrent with what was

expected.

In the subsequent test, a torque wrench was used to control the amount of preload on the

bolts. The reason for using the torque wrench was to accurately determine the initial contact

pressure of the flange joint by knowing the preload on the bolts. However, the use of a torque

wrench has with it a great deal of inaccuracy. Studies have shown that there are large loses when

using the torque wrench, in fact up to 85% of the measured torque can be attributed to losses

which are mostly frictional losses. Also as the torque in the bolt increase so does these frictional

forces hence the errors the error increases also at higher torque values. For this reason the

calculated preload on the bolt, due to the 94.9 Nm torque, of 48,842.4 N was not used as the

actual value of the preload. The true preload could never be accurately known because of the

inherent errors of the torque wrench. So, approximately half this value was used in the

calculation. It should be noted however that the correct value of the preload is of no major

consequence since the sensor would be measuring the decrease in the contact pressure. So the

final equations that were obtained to relate contact pressure to the voltage can be manipulated to

cater for different initial contact pressures. Also the value of the preload used was assumed to be

the average force exerted between the flanges therefore, from this force, the average contact

pressure was found.

From the calculations, it was noticed that the stiffness of the joint was far greater than

that of the combined stiffness of the bolts. In fact Fbe = 0.00677Fe & Fje = 0.993Fe. This meant

that when an external force Fe is applied to the joint, 99.3 % of this force is taken up by the joint

while the remainder is taken up by the bolts.

For test conducted, the joint did not separate. This meant that the clamping load of the

joint was greater than 20,000N limit of the tensometer. Hence calculations were performed under

this condition.


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After the quadratic contact pressure-voltage model was disproved, the linear contact

pressure-voltage model was analyzed. The forces that were calculated which corresponded to the

separation voltages of 60mV and 68mV were 25879.6N and 25459.56N respectively. This meant

that when the externally applied force Fe is near these values, the contact pressure would be zero.

Also the values that were calculated are within the range of the initial preload that was

assumed. This showed that only when the externally applied force is greater than the preload,

only then would the joint separate. The reason why these forces that were calculated were higher

than 24,000N preload was due to the fact that not all the externally applied force was taken up by

the joint. A small percentage (approximately 0.7%) of Fe was taken up by the bolts. So a larger

value than 24,000N would have to be applied to cause the joint to fail.

These results show that when the externally applied load is in the region of the clamp

load, the flange joint is on the brink of failure.

Test 4 and 5 was conducted to assess the level of stiffness or resistance that the strips

added to the joint. The results show that they were negligible when compared to the actual

stiffness of the joint. So the effect of their stiffnesses were neglected in the analysis if the flange

joint.

Some notes on the sensor design

Accuracy: the accuracy of the sensor could not be reliable determined since this required the use

of other techniques to determine the variation of contact pressure and compare the findings from

both experiments. The sensor can be assumed to be fairly accurate since a tensometer was used

control the force applied which produced a strain in the sensor strips. So the use of a precision

instrument such as the tensometer, in calibrating the sensor greatly contributed to the accuracy.

Error: there existed many errors while the tests were performed. Firstly, it was noticed that only

after the applied force surpassed 3,000N that the sensors began display readings. This meant that

the decrease in contact pressure when forces less than 3,000N could not be accounted for. This

error could be reduced by using a softer metal as the sensor strip. Another error was that

sensitivity of both strain indicators could not be accurately set since there calibration to govern


59 | P a g e

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the level of sensitivity on each indicator. This meant that the two strain gauge result would not

be exactly equal to each other. And this was reflected in the results.

Sensitivity: the sensitivity of the sensor was dependent on the instrumentation used. By

increasing the sensitivity, small changes in strain could be accounted for however there is a down

side to this in that as the sensitivity was increased, it limited the highest value of the force that

could be applied since the voltage graph would go beyond the scale of the graph paper. So a

compromise was found after some trials and it was used. As mentioned previously, the

sensitivity could not be quantified.

Precision: the precision estimate for the sensor was found to be 1 significant figure. This was

dictated by the plotter as 1cm on the graph paper represented 5mV. So the smallest graduation on

the graph was 0.5 mV

Resolution: The smallest measureable value of voltage was 0.5mV. This corresponded to a

strain of 793 µε.

Linearity: from the results shown, the final relationship between contact-pressure and voltage

was a linear one. Where the relationship was found to be

y = -16922x +1e6

y= -19861x + 1e6 for V1 and V2 respectively.

Also from the results of voltage signal graphs for all the test, it showed that the graphs were

approximately the same for both trials which showed the repeatability and the linearity of the

sensors.


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CHAPTER 11

CONCLUSION

The contact pressure-voltage relationship was found to be,

y = -16922x +1e6

y= -19861x + 1e6 for V1 and V2 respectively.

Where y represents the decrease in contact pressure in N/m2

and x represents the voltage reading

in mV.

The relationship was best represented as linear. As shown in graph 20.

Also, it was found that as the applied force reduces the clamp force existing within the joint an

additional strain is felt by the bolt which increases the force it sustains. The amount of the

additional force the bolt sustains is smaller than the applied force to the joint. The actual amount

of force the bolt sustains depends upon the ratio of stiffnesses of the bolt to the joint material.

The joint will only fail when the externally applied force overcomes the clamping load in the

joint.

Improvements and scope for future work

The use of a pressure sensitive film instead of a torque wrench to accurately determine

the initial contact pressure

The use of digital strain instrumentation that would afford the user more control of the

specifications of the sensor such as precision and sensitivity.

To investigation of what dimensions and material type that would act as the ideal sensor

strip.

To determine the practicality and use of such sensors in a control system for monitoring a

flange joint.


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REFERENCES

European Sealing Association (ESA), 1992. Guidelines for safe seal usage Flanges and

Gaskets.

Aztec Bolting Services, Inc. Pipe Flange Bolting Guide

Sinclair, Ian R. 2001. Sensor and Transducers, 3rd

ed. Jorden hill, Oxford: Reed

Educational and Professional Publications Ltd.

Webster, John G, Gene Fatton, Dennis Swyt., Peter H. Sydenham, Carsten Thomsen

Ramón Pallás-Areny, James E. Lenz ,Jacob Fraden. 1999. Measurement, instrumentation

and (ASME B16.5a, 1998) sensors handbook, CRC Press.

Measuring Strain with strain gauges. http://zone.ni.com/devzone/cda/tut/p/id/3642

(8/11/08).

Wheatstone bridge circuit. http://www.engineersedge.com/instrumentation (12/03/09).

Algor tutorials.

http://www.algor.com/service_support/tutorials/online_tutorials/FEMPRO_Online_Tutor

ials.htm (20/02/09)

ASME B16.5a. (1998). New York, NY 10016: ASME.

Budynas−Nisbett. (2006). Shigley’s Mechanical Engineering Design. McGraw−Hill.

(2004). Embedment Strain Gauge. Slope Indicator Company.

Walsh, R. A. (2000). ELECTROMECHANICAL DESIGN HANDBOOK. McGRAW-

HILL.

http://zone.ni.com/devzone/cda/tut/p/id/3642

http://www.engineersedge.com/instrumentation

http://www.algor.com/service_support/tutorials/online_tutorials/FEMPRO_Online_Tutorials.htm

http://www.algor.com/service_support/tutorials/online_tutorials/FEMPRO_Online_Tutorials.htm


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Appendix A -Pictures

Picture 1 Shows the Flange joint mounted on the Tensometer

Pin used to connect the flanges to the

Tensometer

Flat Machined across the Flange joint


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Picture 2 Shows the strain gauge


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Picture 3 Flange joint during testing


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Picture 4 shows the size of the flange joint relative to the tensometer


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Picture 5 shows all the equipment used in testing

Plotter Strain indicator Hounsfield tensometer

Computer


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Picture 6 shows the steps involved in Fabrication of the Flange joint


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Appendix B –Drawings

All the models were created using solidworks.

Drawing 1 The Flanges


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Drawing 2 Shows the Dimensions of the Flange


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Drawing 3 Shows the Dimensions of the Angle iron


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Drawing 4 Shows the Dimensions of the Sensor Strip


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Drawing 5 the Flange joint Assembly


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Drawing 6 an exploded view of the Assembly showing the 5 main part groups


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Drawing 7 an exploded view of the assembly


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Drawing 8 shows a section view of the assembly


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Appendix C - Results

TEST 1

Trial 1

Loading

Force, F/ N e/mm V1/mV V2/mV

684 0.088 1 0

1286 0.161 3.5 1

2228 0.259 7 2

3600.7 0.388 10 2.5

4624.7 0.478 12 3.5

5618 0.562 15 4.5

6591.3 0.642 18 5.5

7762 0.739 23 6

8730 0.816 26.5 7

9688 0.894 30.5 8

10790.3 0.981 35.5 10

12102 1.084 41 11

12971.7 1.152 45 12

14034 1.233 50 13

14998.9 1.308 54 15

16160 1.398 59 17

17534 1.503 65 20

18701 1.591 70

19992 1.689 76

unloading

Force,F/

N e/mm V1/mV V2/mV

18728.7 1.566 70 17.5

17474 1.482 64 15

16466 1.415 59.5 13

15340 1.338 54 11

13896 1.239 47.5 9.5

12437.3 1.137 41.5 8.5

11614.7 1.08 38 7.5

10488.7 0.999 32.5 6.5

9660.7 0.939 29 5.5

8468.1 0.85 24 4.5

7335.7 0.762 19.5 4

6419.3 0.686 16 3

5297.3 0.599 12 2.5

4196.3 0.506 9.5 1.5

2864.7 0.387 6 1

2009.3 0.302 4 0.5

1488.9 0.245 3.5

996.3 0.184 2

586.3 0.126 1

64.3 0.041


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Trial 2

loading


598 0.067 0 0

1086 0.119 0.5 0.5

1518.3 0.165 1.5 0.5

2100.3 0.225 3 1

2632.7 0.276 4.5 1.5

3071.3 0.317 5.5 2

3706.7 0.375 7 2.5

4268.1 0.425 8.5 2.5

4936.3 0.483 10.5 3

5543.1 0.534 12.5 3.5

6167.3 0.585 14.5 4

7010 0.655 17.5 5

8414 0.769 23.5 6

8989 0.815 26 6.5

10002 0.895 30 7.5

11160.7 0.986 35 8.5

12196 1.066 40 10

13320 1.153 45 11

14174 1.221 48.5 12

15448 1.32 54 14

16644 1.41 59.5 15

17362 1.465 62.5 16

18372 1.543 67 17.5

19160 1.602 71 18.5

20152 1.677 75.5 20

unloading


20124 1.677 75.5 19

19620 1.603 73 17

18574 1.534 68 16

17592 1.468 63 14

16496 1.395 58 12

15328 1.315 53 11

14333 1.247 48 10

13164 1.166 43.5 8

11505 1.05 36 7

10360.7 0.968 31 5.5

9153.3 0.88 26 5

8086 0.8 21.5 4

7039 0.718 17 3

6064 0.641 14 2

5013.2 0.556 10.5 1.5

3994.3 0.47 7.5 1

2859.3 0.367 4.5 0.5

1896.7 0.272 2.5 0.5

1447 0.218 1.5 0

996.7 0.164 1

603.3 0.108 0.5

349.3 0.069


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Test 2

Trial 1

Loading


620 0.135

1176 0.192 0.5

1746 0.242 0.5

2382 0.293 0.5 1

3196 0.357 1 2

4081 0.424 2 3.5

5126 0.504 3 5.5

5684 0.545 4 6.5

6338 0.593 5.5 8

6958 0.639 7.5 9

7760 0.698 8 10.5

8492 0.752 10.5 12

9162 0.802 12 13.5

10142 0.875 15 15.5

10832 0.926 17 17.5

11786 0.996 20 20

12706 1.064 23.5 23.5

13652 1.134 27.5 26.5

14820.2 1.221 32 30.5

15706.1 1.287 35.5 33

16680.3 1.358 39 37

17910.3 1.447 44 40.5

19226 1.544 48.5 45

20264 1.62 52.5 48

Unloading


20236 1.62 52.5 46.5

19730 1.544 51 44.5

18552 1.466 49.5 40

17428 1.392 46 36

16562 1.333 42 32.5

15584 1.267 38.5 29

14550 1.196 35 25.5

13398.7 1.116 31 21

12429.3 1.048 26.5 18

11500 0.983 23 15

10662 0.925 19.5 13

9710 0.858 16.5 11

8747 0.789 13.5 9

7518 0.699 11 6.5

6408 0.617 8 4.5

5378 0.54 6 3

4428 0.469 3.5 1.5

3516 0.398 2 0.5

2438 0.31 1.5

1138 0.195

578 0.139

50.3 0.058


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Trial 2

Loading


610 0.133 0

1700 0.283 1

2654 0.314 0.5 1.5

3500 0.38 1 2.5

4510.7 0.456 2 4.5

5710 0.545 4 6.5

6658 0.616 5.5 8.5

7736 0.696 8 10.5

8880 0.782 11 12.5

9960 0.86 14 15

10574 0.906 15.5 16

11476 0.972 19 19

12374 1.034 22 22

13436 1.119 26.5 25.5

14540.2 1.201 31 29

15532 1.274 35 32.5

16652 1.356 39 36

17452 1.415 42 38.5

18621 1.501 46.5 42

19290 1.55 49 44

20052 1.606 51.5 47

Unloading


20030 1.606 51.5 45.5

19365 1.521 49.5 43

18504 1.464 46 39.5

17450 1.393 42 35.5

16502 1.329 38 32

15094.7 1.233 32.5 27

13524.7 1.125 25.5 21.5

11513 0.985 18 15

9780 0.864 13 10

8375.7 0.764 9 8

7500.7 0.7 7 6.5

6632 0.636 5.5 5

5704 0.566 2.5 3

4512 0.476 0.5 1

3468 0.394 0.5

2512 0.317

1495 0.23

964.7 0.18

276 0.104

6 0.051


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Voltage signal Graphs

For these graphs, the 90 mark indicates the starting point. Hence the voltage there is zero. Also

each increment of 10 away from this point on the x-axis represents an increase of 10mV.

Test 1

graph 1 voltage signal graph trial 1

graph 2 Voltage signal graph trial 2


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Test 2



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Test 3

graph 5 Voltage signal graph test 3


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Test 4

graph 6 Voltage signal graph test 4


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Equations for the quadratic force- voltage relationship from test 2

graph 7 shows the quadratic relationship for force-voltage


y = -3.1411x2 + 473.05x + 3432.9

y = -1.7812x2 + 409.1x + 2910.5

0

5000

10000

15000

20000

25000

0 10 20 30 40 50 60

Forc

e/N

Voltage/mV


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Unloading

y = -3.4883x2 + 529.28x + 2350.2

y = -4.3252x2 + 542.54x + 3906.7

0

5000

10000

15000

20000

25000

0 10 20 30 40 50 60

Forc

e/N

Voltage/mV


Loading

Unloading


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y = -3.0439x2 + 463.98x + 3616.6

y = -2.0548x2 + 396.21x + 4704.6

0

5000

10000

15000

20000

25000

0 10 20 30 40 50 60

Forc

e/N

Voltage/mV


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Unloading

y = -4.588x2 + 593.98x + 1691.5

y = -4.3937x2 + 542.69x + 4022.9

0

5000

10000

15000

20000

25000

0 5 10 15 20 25 30 35 40 45 50

Forc

e/N

Voltage/mV


Loading

Unloading


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Summary of results

F- V1 relationship

trial 1 trial2

Loading

y = -3.1411x2 + 473.05x +

3432.9

y = -3.0439x2 + 463.98x +

3616.6

Unloading

y = -1.7812x2 + 409.1x +

2910.5

y = -2.0548x2 + 396.21x +

4704.6

F- V2 relationship

trial 1 trial2

Loading

y = -4.3252x2 + 542.54x +

3906.7

y = -4.3937x2 + 542.69x +

4022.9

Unloading

y = -3.4883x2 + 529.28x +

2350.2

y = -4.588x2 + 593.98x + 1691.5


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Appendix D -Calculations

Strain gauge

As mentioned previously, each strain gauge was connected to a strain indicator in a quarter

bridge configuration.

Figure 1 show this quarter bridge arrangement.

Figure 1 Quarter bridge

For a given voltage input Vin, the currents flowing through ABC and ADC depend on the

resistances, i.e

Vin = VABC = VADC

And, VABC = IABC (Rg+R3)

VADC = IADC (R1+R2)

So,

IABC = VABC

Rg+R3 =

Vin

Rg+R3

IADC = VADC

R1+R2 =

Vin

R1+R2

Also, the voltage drops from A to B and from A to D are given by,

VAB = IABC .Rg = Vin

Rg+R3 Rg VAD = IADC .R1 =

Vin

R1+R2 R1

The voltage gage reading Vout can then be obtained from,

A

D A

B

C


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Vout = VAB - VAD = Rg

Rg+R3 Vin −

R1

R1+R2 Vin

So, Vout = Rg

Rg+R3 −

R1

R1+R2 Vin ……………….[1]

Figure 2 Quarter bridge arrangement with balancing

For a strain gauge connected in a quarter bridge configuration all the resistances are the same

except for that of the strain gauge. So when balanced, equation 1 becomes

Vout = ∆𝑅

4𝑅 Vin

However gauge factor, G.F = (ΔR/R)/( ΔL/L)

= (ΔR/R)/ε

So, ΔR/R = G.F x ε

Therefore Vout = (G.F x ε x Vin)/4.

B

final draft 3.0

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