UPTEC F05 000

Examensarbete 20 pJuni 2007

Full-scale Measurements of a 9.3 MW Hydropower Unit in Porjus A Prestudy of the Instrumentation of the

Runner and the Guide Bearings

Ida Jansson

Teknisk- naturvetenskaplig fakultet UTH-enheten Besöksadress: Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0 Postadress: Box 536 751 21 Uppsala Telefon: 018 – 471 30 03 Telefax: 018 – 471 30 00 Hemsida: http://www.teknat.uu.se/student

Abstract

Full-Scale Measurements on a 9.3 MW HydropowerUnit in Porjus

Ida Jansson

In this diploma thesis two partial studies of the instrumentation of a hydropower unitare conducted. These are carried out within the scope of the JUSPOWER-project.The first part of the thesis deals with the instrumentation of the runner. Theincorporation of sensors in a Kaplan runner blade is tested in a experimental set-upon a laboratory scale without dismantling the runner. A further development of thedesign is suggested that enables damaged sensors to be replaced. The sensors arecalibrated with a system destined to be used on site. The results show that thesensors function properly in the test set-up. Further calibration will though beneeded during the installation on the runner blade and under operational conditions.The suction cup of the calibration system may have to be modified depending on theshape of the runner blade.

The second part is a comparison study concerned with the choice of sensors forradial load measurements at the guide bearings. To measure the load on the bearingsegments, the dowel peg on the bearing segment would either be replaced by a loadcell or modified so strain gages could be bonded onto the peg itself. The performanceof the sensors is evaluated in a loading machine with respect to linearity, hysteresisand sensitivity. Furthermore, the stiffness of the load cell is experimentallydetermined in a load machine. The results show that the strain gages bonded on themodified dowel peg do not have a reliable output signal. However, the installation ofthe tested load cell would alter the stiffness of the dowel peg. The load cell had astiffness that was almost 50 % lower than the dowel peg.

ISSN: 1650-8300, UPTEC ES05 000Examinator: Ulla TengbladÄmnesgranskare: Urban LundinHandledare: Michel Cervantes

Tackord

Jag tar mig friheten att ga over till mitt favoritsprak i tackordet. Detfinns inte rum att namna alla som varit till min hjalp under arbetet. Underarbetets gang har jag lart mig hur vardefullt det ar att kunna fahjalp avandra manniskor och att lyssna till deras erfarenheter. Mitt arbete hade intevarit mojligt utan alla de talmodiga som svarat pa mina fragor. Ett ord franen manniska ar som en hel vecka med huvudet i en bok.

Jag vill borja med att tacka Michel Cervantes, min handledare som hardefinierat min arbetsuppgift och vaglett mig. Utan ditt stod och delaktighethar jag aldrig kunnat utfora mitt arbete. Tack for att du utan forbehall stalltupp och hjalpt till nar jag varit vilsen.

Nasta person som jag vill namna ar Allan Holmgren. Med din arlighetoch oppenhet blev jag val mottagen pa avdelningen. Forutom din om-tanke du visat savill jag dessutom namna dina insatser i projektet. Allanar var uppfinnare och experimentmakare. Han ligger bakom den nya desig-nen pa var testplatta. Allan, du behover inte vanta pa att forskarna skauppfinna. Det ar du som gor det!

Jag vill rikta ett speciellt tack till Jan-Olov Aidanpaa som varit delak-tig i arbetet med instrumenteringen av styrlager. Tack for din hjalpsamhetoch for att du talmodigt besvarat min fragor om rotordynamik. Jag villocksa tacka Mattias Lundstrom for hans mottagande i Alvkarleby. Tackfor att du stallde upp med sakort varsel och for att du ordnade med helaexperimentuppstallningen.

Jag vill sa klart aven tacka Sergej, den tredje mannen i projektet, varlagerexpert. Tack for visningen i labbet och allt du berattat for mig om badelager och Porjus. Snart slar jag dig i innebandy!

Sist sa vill jag tacka mina arbetskamrater pa Stromningslara. Om jaginte haft kaffet att se fram emot sahade jag aldrig fatt dagarna att ga!

1

Sammanfattning

En tilltagande industrialiseringsvag i Sverige foranledde utbyggnaden av vat-tenkraft i Norrbotten under tidigt 1900-tal. Den forsta i raden av de utbyg-gnationer som skedde i Lule Alv var Porjus kraftstation, ett med den tidensmatt gigantiskt projekt som stod klart for drift 1916. Kraftstationen byggdesfor att forse malmbanan mellan Kiruna och Narvik med elkraft.

Idag star vattenkraften infor nya utmaningar. Elektrisk effekt ar momen-tan. Pa det elektriska stamnatet maste balans rada mellan producerad ochkonsumerad effekt. Vattenkraft har relativt goda egenskaper som kalla tillreglerkraft. Vattenreservoarer mojliggor reglering av hur stor effekt fran vat-tnet som omvandlas till elektrisk effekt. Den avreglerade elmarknaden harlett till att vattenkraftmaskiner kors under andra driftsforhallanden an vadde ursprungligen konstruerades for. Idag kan vissa anlaggningar startas fleraganger om dagen vilket innebar okade pafrestningar pa maskineri. Samtidigtborjar livstiden hos flera anlaggningar att narma sig sitt slut. Saledes finnsidag ett fornyelsebehov inom vattenkraftteknik. Fornyelse kraver satsningpa forskning och utveckling inom vattenkraftteknik. I ett projekt pa Luleastekniska universtitet planeras fullskalematningar pa en prototyp i Porjusgamla vattenkraftstation. Prototypen bestar av en generator, turbin ochlager som haller den roterande axeln pa plats. Prototypen tillhor stiftelsenPorjus Hydro Power Center som ags av olika aktorer i kraftbranschen. En-heten ar avsedd att anvandas till forskning och utveckling vilket innebar attmatningar kan utforas under driftsforhallanden som inte kan testas pa enstation avsedd for kommersiell drift. Examensarbetet utgor en del av dettaforskningsprojekt.

Examensarbetet bestar av tva olika forstudier av den planerade in-strumenteringen av prototypen. Syftet med arbetet ar att utvardera ochforbattra foreslagna matsystem. Den forsta delstudien ror dynamiska matningarav tryckfaltet pa ett av lophjulsbladen. Olika satt att montera tryckgivarepa lophjulsbladet har testats med hjalp av en testplatta som har fatt utgoramodell av lophjulsbladet. En preliminar design av bearbetningen av bladetutarbetades som mojliggor att skadade tryckgivarna kan bytas ut. Tryckgi-varna ar installerade i mynt som i sin tur ska monteras pa det bearbetadebladet. Plastror ar foreslaget att anvandas for att skydda kablage mot fyll-ningsmaterialet i de frasta kanalerna pa lophjulet. Kontaktdon till givarnaska positioneras i lophjulskonan. Kablage kommer sedan att ledas genom ax-eln. Digitalisering och tradlos overforing kommer att ske hogst upp i axeln.

Den andra delstudien ror matningar av den radiella lasten pa varje en-skilt lagersegment i de tre olika styrlager som positionerar axeln i radiell led.Tva olika foreslagna matmetoder har utvarderats. I den ena matmetoden

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anvands lagerdubben som sitter pa varje lagersegment for att mata las-ten. Dubben bearbetas och tojningsgivare limmas pa dubben i de re-gioner med stort tojning. I den andra matmetoden byts lagerdubben utmot en fardigkaliberad lastcell med liknande dimensioner som lagerdubben.Aven i lastcellen ar de aktiva elementen tojningsgivare. Utvarderningen avde tva olika metoderna gjordes med avseende pa givarkarakteristik ochmatobjektets styvhet i jamforelse med en obearbetad lagerdubb. Resultatenvisar att kansligheten for signalerna fran tojningsgivare limmade pa lager-dubben var valdigt lag i forhallande till lastcellen. Lagre kanslighet innebarlagre nogrannhet och en signal som ar kansligare for brus. Utvarderingenmed avseende pa matobjektens styvhet visar att lastcellen har nastan 50 %lagre styvhet an den obearbetade lagerdubben vid en last pa 5 ton. Dentotala styvhetsforandringen av lagret uppskattas till 75 %. Skillnaden istyvhet mellan den bearbetade och den oberabetade lagerdubben ligger inomosakerhetsintervallet hos matningen. Slutsatsen av delstudien ar att ingenav de foreslagna matmetoderna kan anvandas for matning av radiell lastpa lagersegment i styrlager. En upphandling av en lastcell har darfor gjortsmed kanslighet och styvhet enligt faststallda krav.

Instrumenteringen av prototypen kommer att paborjas under augustimanad 2007. Denna forstudie ger riktlinjer inor det planerade arbetet, menutgor inte nagot fardigt forslag. Den slutgiltiga designen av instrumenterin-gen maste utarbetas pa plats.

Figure 1: A hydropower machine

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Contents

1 Introduction 61.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.2 Scope of the study . . . . . . . . . . . . . . . . . . . . . . . . 7

2 The JUSPOWER-project 82.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2 The Porjus Hydro Power Center . . . . . . . . . . . . . . . . . 82.3 Pressure measurements on the runner . . . . . . . . . . . . . . 92.4 Load measurements on the guide bearings . . . . . . . . . . . 10

3 Measurement Systems 113.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.2 The composition of a measurement system . . . . . . . . . . . 113.3 Sensor characteristics . . . . . . . . . . . . . . . . . . . . . . . 12

3.3.1 Static properties . . . . . . . . . . . . . . . . . . . . . 123.3.2 Dynamic properties . . . . . . . . . . . . . . . . . . . . 13

3.4 Sensing elements . . . . . . . . . . . . . . . . . . . . . . . . . 163.4.1 Metal strain gages . . . . . . . . . . . . . . . . . . . . 163.4.2 Diffused semiconductor strain gages . . . . . . . . . . . 17

3.5 Signal conditioning elements . . . . . . . . . . . . . . . . . . . 183.5.1 The Wheatstone Bridge . . . . . . . . . . . . . . . . . 18

3.6 Signal processing elements . . . . . . . . . . . . . . . . . . . . 19

4 Instrumentation of the runner 204.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4.2.1 Experimental set-up of the montage . . . . . . . . . . . 214.2.2 Experimental set-up of the calibration . . . . . . . . . 24

4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.3.1 The design . . . . . . . . . . . . . . . . . . . . . . . . . 254.3.2 Calibration of the pressure sensors . . . . . . . . . . . 26

4

4.4 Discussion and conclusions . . . . . . . . . . . . . . . . . . . . 29

5 Instrumentation of the Load Measurements on the GuideBearings 315.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315.2 Installation of the sensing elements in the guide bearings . . . 325.3 Tested Measurement Techniques . . . . . . . . . . . . . . . . . 33

5.3.1 Modified dowel peg with strain gages (DP) . . . . . . . 335.3.2 Standard Load Cell (LC) . . . . . . . . . . . . . . . . . 34

5.4 Calibration of the sensors . . . . . . . . . . . . . . . . . . . . 355.4.1 Experimental set-up . . . . . . . . . . . . . . . . . . . 355.4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5.5 Comparison of the stiffness of the sensors . . . . . . . . . . . . 395.5.1 Experimental set-up . . . . . . . . . . . . . . . . . . . 405.5.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5.6 Discussion and conclusions . . . . . . . . . . . . . . . . . . . . 50

6 Discussion and Conclusions 51

5

Chapter 1

Introduction

1.1 Background

The rivers are part of the continuous water cycle on earth. The slope of theriver makes the water flow. While meandering its way through the landscape,the potential energy in the water turns into kinetic energy and heat. Therivers are part of human societies. There is a rich variety of examples of howhumans have utilized the rivers trough history.

Figure 1.1: A Hydropower ma-chine

The invention of Turbomachinery led toa big impact on the human society. For ex-ample, this enabled engineers to constructhydropower plants that converted the hy-draulic power into electrical power. Thisurged for construction of dams so the poten-tial energy of the river could be concentratedand its flow could be regulated. In a hy-dropower plant, the hydraulic energy is har-vested by a turbine and converted to electri-cal energy by a generator. On a global level,the hydroelectric power capacity is about 20% of the total electric power capacity. InSweden, hydroelectricity stands for approxi-mately 50 % of the total electric energy pro-duction.

The deregulation of the electricity market has put new constraints onhydroelectric power generation. Electric power is instant. The grid must bebalanced so the production equals the consumption of power. Hydropowerplants possess good properties as a mean for regulating the production of

6

electric power since the flow through the units can be regulated. Therefore,hydroelectric power is used to balance the grid. However, the machines werebuilt to operate during stable conditions. Transient conditions and operationon partial loads increase the stress levels on the machinery. This calls forfurther investigation of the dynamic properties of hydropower machines. Inthe JUSPOWER-project, full-scale measurements will be performed on theU9-unit, a 10 MW prototype in the Porjus Hydropower Center, a researchand development center located in Lule Alv. The prototype is designatedfor research and development and is equipped with the latest technology. Inthe JUSPOWER-project, more than 200 sensors will be installed on severalparts of the machine, comprising the turbine, the generator and the bearings.Simultaneous dynamic measurements on several parts of the machine willmake it possible to study interactions between each part. Furthermore, staticmeasurements enable a better knowledge of the individual parts.

1.2 Scope of the study

This diploma thesis deals with parts of the planned instrumentation of theU9-unit in the JUSPOWER-project. Since the measurements will be per-formed on a prototype, attention must be put on a suitable choice of mea-surement system. The scope of this study is to evaluate and further improvethe suggested design of the instrumentation of the runner and the guide bear-ings. Two partial studies are conducted. The first work is concerned withthe incorporation of pressure sensors on one of the runner blades on the pres-sure and suction side. The aim is to find an appropriate durable design thatenables damaged sensors to be replaced. The second work is concerned withthe choice of sensors for the radial load measurements on the guide bearings.The performance of two measurement techniques is evaluated as well as howthe installation of the sensors would alter the characteristics of the guidebearings.

7

Chapter 2

The JUSPOWER-project

2.1 Introduction

In the JUSPOWER-project, full-scale measurements will be performed atthe U9-unit in Porjus Hydropower Center. More than 200 sensors will beinstalled on both rotating and static parts of the machine, i.e. the generator,the bearings and the runner. The aim of the JUSPOWER-project is twofold.Simultaneous measurements of each part of the machine will make it possibleto dynamically characterize the machine. Furthermore, the measurementswill also provide a better knowledge of each part of the machine.

2.2 The Porjus Hydro Power Center

Hydropower was introduced in the northern part of Sweden during the begin-ning of the 20th century. The expansion of the mining industry had increasedthe need of energy. A railway was planned for transportation of the ore to theNorwegian cost.The construction of an electrified railway demanded power.This was the main reason behind the decision to construct the Porjus HydroPower Station, the first hydropower station that was built in Lule Alv [1].

Today, the old station is not in commercial use. A new station has beenconstructed comprising two units with a total installed capacity of 465 MW.Apart from being conserved as a museum, the old power station is beingused by the foundation Porjus Hydropower Centre, a training, research anddevelopment centre. The foundation is owned by Vattenfall, Alstom andGE Hydro. Two 10 MW units are installed in the machine hall in the oldPower Station. The U8 unit is used for training. The JUSPOWER-projectis concerned with measurements at the U9 unit dedicated for research anddevelopment.

8

The U9-unit is equipped with a Powerformer Generator and a KaplanTurbine. The Powerformer Generator is high voltage Generator. The KaplanTurbine is an axial flow turbine. The water hits the runner in its axialdirection. The rotational speed of the unit is fairly high, 600 rpm.

2.3 Pressure measurements on the runner

Figure 2.1: Kaplan Turbine at the U9-unit

The runner of the Kaplan Turbineconsists of six dismountable blades.In the JUSPOWER-project, minia-ture piezo-resistive pressure sensorswill be incorporated in one of theblades. Approximately 20 sensorswill be positioned on each of the sideof the blade.

The aim of the pressure measure-ments is twofold. Rotor-fluid inter-actions and purely flow-related is-sues will be investigated. Dynamicmeasurements enable the excitationfrequencies of the turbine to be determined. What more, given the differencein the pressure distribution between the pressure and the suction sides of theblade, the angular resolved and time dependent forces on the runner exertedby the water can be estimated. The measurements are also of interest toflow-related problems, such as validation of numerical simulations of the flowfield in the neigbourhood of the runner and better knowledge about scale-upformulas between the model and the prototype.

9

2.4 Load measurements on the guide bear-

ings

Figure 2.2: Bearing positions

The shaft of the U9-unit is re-strained by three guide bearings sup-ported by one thrust bearing. Theguide bearings maintain the shaftin its radial position. In this re-port, the load measurements on theguide bearings are considered. Thelower and the upper generator guidebearings (GBLG and GBUB in Fig-ure 2.2) must balance the attrac-tion force of the generator on therotor. The hydraulic radial load isbalanced by the guide bearing of theturbine (GBT) that is positioned ontop of the turbine. The thrust bear-ing (TB) supports the weight of themachine and the hydraulic thrust[2].

In turbo machinery the axis isnormally mounted horizontally. The static load on the guide bearings couldthen be approximated as the weight of the machine. This determines theworking point of the machine. In hydropower units the static load on theguide bearings is not well defined since the shaft is usually mounted vertically.

The measurements will be carried out at various operational points andduring steady-state and transient conditions. The aim of the load measure-ments of the guide bearings is threefold:

• Determine the static load on each bearing segment

• Determine the dynamic load on each bearing segment

• Determine the damping and the stiffness of the guide bearings

The static load is an average value of the force acting on each bearing seg-ment. The dynamic load is defined as the time dependent forces acting onthe bearing segments. If the dynamic load is coupled with displacementmeasurements, the stiffness and the damping of the guide bearings can bequantified.

The dynamic load demands a high sampling frequency whereas the staticload could be sampled with a low frequency (0.5 Hz).

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Chapter 3

Measurement Systems

3.1 Introduction

Several constraints are put on the instrumentation of a prototype comparedto the set-up of model test-rigs. Not only the installation of the sensing ele-ments could be a delicate problem but also the acquisition of the signals willimpose certain difficulties. In this chapter, a brief introduction will be givento what parts a measurement system is composed of and what the essentialcharacteristics of sensing elements are. Thereafter, a more detailed descrip-tion follows of the sensing elements and the signal conditioning elementsconsidered in this report.

3.2 The composition of a measurement sys-

tem

What is a measurement system? In Principles of Measurement Systems,Bentley[3] identifies the three following types of element in a measurementsystem:

• Sensing elements

• Signal conditioning elements

• Signal processing elements

Let us look at the measurement system of the pressure on the runner bladeto exemplify each part. The sensing element transforms the physical mea-sured property into another property. On the runner blade, semi-conductor

11

strain-gages will be incorporated that converts pressure to a change in resis-tance. This is the sensing element of the system. The signal conditioningelement converts the output of the sensing element to a more suitable form.Each pressure transducer consists of four sensing elements connected in abridge circuit. The bridge circuit produces an output signal in dc voltage.This is the signal conditioning element in our system. The signal processingelement involves the digitalization of the output signal. The output signalsof the bridge circuits will be transferred in cables through the shaft of theprototype to the top where the conversion from analogue to digital signalswill take place. The signal then will be transferred by a wireless system andacquired by a computer. This is our signal processing element.

According to Bentley[3] the word ”transducer” is commonly used to sig-nify a package that may incorporate several elements. For example, a Swisscompany will supply piezo-resistive pressure transducers (PRT) that will bemounted on the runner blade. The PRT’s comprise both the sensing andthe signal conditioning element in our system. In Handbook of Modern Sen-sors [4] Fraden distinguishes between sensors and transducers by definingsensor as a device that responds to a stimulus by delivering an output sig-nal. He defines a transducer as a single energy converter. A sensor maythen consist of several transducers. Even though Fraden’s definition also iswhat is found in dictionaries, the common practice in the measuring indus-try is to use transducers as defined by Bentley. Among the scientists in theJUSPOWER-project, the word sensor is used in the sense as transducers re-ferred to by Bentley. In this report, the word sensor will be used in a widersense than transducer; this could be a sensing element or a whole measure-ment system that delivers a conditioned output signal. A transducer will bereferred to according to Bentley’s definition; it will say a delivered packageby the industry that has a conditioned output signal.

3.3 Sensor characteristics

3.3.1 Static properties

The static behaviour of a sensor is characterized by its transfer function fdefined as

O = f(I) (3.1)

I is the input and O is the output of the the sensor. The sensors consideredin this report are linear. It will say, the transfer function is of the form

O = f(I) = KI + a (3.2)

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The following static characteristics of linear sensors will be referred to inthis report

Full-scale output The full-scale output is the span of the output. This isabbreviated FSO.

FSO = Omax −Omin

Sensitivity The slope of the line 3.2, K gives us the sensitivity of the sensor.

Linearity The linearity of a sensor is defined as the maximum deviation ofthe output from the ideal value given by 3.2. This is normalized interms of percentage of FSO.

Hysteresis Hysteresis means lag of effect or delay before an action. Thehysteresis of a sensor is defined as the difference of the output for afixed measured value under increasing or decreasing input. This isnormalized in terms of percentage of FSO.

3.3.2 Dynamic properties

In the JUSPOWER-project, the dynamic behaviour of a hydropower-unitwill be investigated. Time dependent variables will be measured. The sensorsmust respond to a time varying input. Therefore, the dynamic properties ofthe sensors must be known.

To examplify the dynamic properties of a sensor, let us again considerthe sensing element in the pressure measurement system on the runner. Thesensing element is a single-crystal silicone diaphragm that is strained underan applied load.1 Let us make a simplified one-dimensional model of thesilicone diaphragm as a spring with a certain mass, stiffness and dampingconstant.2 The strain of the diaphragm, ε, will then be equal to the displace-ment of the spring, x, normalized by its initial length l0 as

ε =x

l0(3.3)

What happens if the spring is given an initial displacement from its equi-librium position? The forces acting on the system is the spring force and adamping force proportional to the velocity of the displacement. The differen-tial equation of motion that governs the behaviour of the silicone diaphragmis then given by

x +c

mx +

k

mx = 0 (3.4)

1See for example [5]2For further information about vibrations see [6] or any textbook in fundamental vi-

bration theory

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If the damping is zero, the solution will be given by a sinusoidal motion

with the angular frequency ωn =√

km

. It will say, our silicone diaphragmstarts to vibrate. However, if the system is damped, a transient solution isobtained. No vibrations will occur or the amplitude of the vibrations willdecay dependent on the variables c,m and k.

We are interested in how our model will behave if the spring is excited by atime dependent force. This will model the output of our sensing element givenan input with a certain frequency. The excitation force can be representedby the complex vector fe(t) = Foe

iωet. The equation of motion of the springis then given by

x +c

mx +

k

mx = fe(t) (3.5)

The output of our sensing element is the strain of the string which isproportional to the displacement according to 3.3. The complete solution of3.5 is the homogeneous solution (solution of 3.4of and the particular solutionof 3.5. Let us assume a solution of the displacement x(t) with the samefrequency as the excitation force and the phase shift , φ, given by

x(t) = Xe−iφeiωet = Xeiωet (3.6)

How is then the magnitude of fe(t) and xe(t) related to each other andwhat is the phase shift φ? This can be represented by the complex frequencyresponse, H(ωe), of the system. It is given by

X = H(ωe)F0/k (3.7)

The properties of H(ωe) depend on the damping ratio and the relation be-tween the natural frequency, ωn, of the system and the excitation frequency,ωe. In Figure 3.1 the amplitude of the complex transfer function is plotted asfunction of the frequency ratio for different damping ratios. The amplitudeof H(ωe) is given by

|H(ωe)| = 1√(1− ωn

ωe)2 + (2ζ ωn

ωe)2

(3.8)

It can be seen that for ωe << ωn the amplitude is equal to unity. With thisin mind, consider the static transfer function 3.2. If we want our diaphragmto behave like 3.2, the frequency of the pressure should be smaller than thenatural frequency of the diaphragm. We also want a small damping ratioto avoid a time shift of the measured variable. The dynamic properties ofsilicon diaphragms make them very suitable as sensing elements for dynamicmeasurements. Their natural frequency is very high and the damping ratiois low. The vibrations that occur due to their natural frequency is inherentnoise of the sensor that could be removed by a low-pass filter.

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0 0.5 1 1.5 2 2.5 30

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

← ζ =0.1

← ζ =0.25

← ζ =0.5

← ζ =0.75 ← ζ =1

Xk F0

ωn

ω

Figure 3.1: Amplitude of H(ωe) for different damping ratios,ζ

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3.4 Sensing elements

The sensing elements considered in this report are strain gages. A straingage is a resistor connected in a conditioning circuit. The input of a straingage is a displacement which is normalized by its original length as strain.The output of a strain gage is an electrical resistance. The gages consideredin this report are made of metal or silicon.

3.4.1 Metal strain gages

Figure 3.2: Metal strain gages

Metal strain gages are widely usedfor experimental stress analysis.They consist of a grid of wires or foilbonded to a insulating backing. Thegage could then be bonded on a testobject to measure its strain.

Bonded foil metal strain gageswere tested in this study as sens-ing objects for the instrumentationof the guide bearings. Both thetested techniques use bonded foilmetal gages as the sensing elements.

What is the relation between theinput and the output of a metalstrain gage? Our input is the strainof the test object, ε. The resistanceof the wire is

R = ρl

A(3.9)

By differentiating 3.9 and by nor-malizing with the initial resistanceR0 we have

dR

R=

dl

l− dA

A+

dρ

ρ(3.10)

The ratio between the longitudinal strain and the radial strain is givenby Poisson’s ratio, εl = −νε. Commonly, the change in resistivity can bedisregarded. Thereby, we have an expression for our transfer function as

4R

R= (1 + 2ν)ε +

dρ

ρ(3.11)

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The sensitivity of the sensor will then be given by K = (1 + 2ν). A typicalvalue of K for metal strain gages is 2.

Strain gages are sensitive to temperature change. Hoffmann distinguishesbetween three temperature dependent parameters that will contribute to theoutput of the sensor [7]:

• Thermal strain of the test object, εo(T )

• Thermal strain of the measurement grid εg(T )

• Increase of the resistance of the measurement grid εr(T )/K

The additional thermal input of the gage is then given by

εT = (εt − εt + εr/K)4T (3.12)

There exist several techniques for compensating for this thermal influenceon the strain gage. This will be further discussed in 3.5.1

3.4.2 Diffused semiconductor strain gages

Figure 3.3: Strain gage diffused on sil-icon

Semiconductor strain gages are thesensing elements in the piezo-resistive transducers that will be in-corporated in the runner blade. Thesensing element in a PRT is a sili-con diaphragm. In this case, no gageis bonded to the strained material.By diffusing impurities in the sili-con, regions with low resistivity arecreated[5]. These regions form stripsthat function as resistors when con-nected in a circuit. The strips are leaded directly on the silicon. The straingage will then itself be a part of the material that experience the strain.

Semiconductor strain gages are sensitive to strain in both the longitudinaland the transverse direction. Its sensitivity is given by the piezo-resistivecoefficients as 4R

R= πlσl + πtσt (3.13)

The stress pattern could be approximated as two dimensional since thesilicon wafer’s height is much smaller than its length and with.

The piezo-resistive coefficients depend on the material type, orientationof the resistors and the temperature. This means that the sensitivity will

17

vary with temperature. Furthermore, a temperature shift may occur due toan additional thermal stress component of the material that will result in anoffset of the signal.

3.5 Signal conditioning elements

3.5.1 The Wheatstone Bridge

Figure 3.4: A Wheatstonebridge

The output of a sensing element normallyneeds some kind of conditioning. For exam-ple, the output of a strain gage, a changein resistance is transformed by the Wheat-stone bridge circuit to a useful signal thatcan be acquired. Apart from conditioningthe output, the bridge can also be used tocompensate for the thermal output of a sen-sor.

Consider the circuit in Figure 3.4. Thecircuit is excited by a voltage, Vs. The cur-rent in each arm will then be I1 = Vs/(R1 +R2) and I2 = Vs/(R3 + R4). We writethe general expression for the output signalVo = Vo+ − Vo− in terms of the magnitude of the resistors as

Vo+ − Vo− = I1(R1)− I2(R4) = VR1(R3 + R4)−R4(R1 + R2)

(R1 + R2)(R3 + R4)(3.14)

If one of the gages is a sensing element, what will the output of our bridgecircuit be? The resistors, R1, ..R4 have all the same magnitude, R. If the gageis unloaded, the potential difference, Vo+−Vo− will be zero. The same amountof current will flow through the two arms. But what happens if R1 = R+4R?If we assume that 4R << R The term 4R in the denominator in 3.14 canbe neglected and the output signal is

Vo =V

4

4R

R(3.15)

This expression can be generalized to

Vo

V=

1

4(4R1

R1

− 4R2

R2

+4R3

R3

− 4R4

R4

) (3.16)

for all the resistors as sensing elements.Strain gauges connected in Wheatstone bridges can be divided into quar-

ter, half and full-bridges according to the number of sensing elements.

18

3.6 Signal processing elements

The data of the measurements need to be acquired in some way. If han-dling large amount of data, computers are valuable tool. Digitalization of ananalogue signal will also make the signal unsensitive to noise. An analoguesignal is a continuous signal. A digital signal is a discrete signal. During theconversion from an analogue to a digital signal, the A/D conversion, a snap-shot of the analogue signal is taken at an instant of time. The time intervalbetween each snapshot determines the sampling frequency of the signal. Thesampling frequency determines the time resolution of the signal. It must beat least twice the expected frequency of the measured property according tothe Nyquist theorem.

The digital signal is a binary number as opposed to the analogue valuethat has an infinite precision. The resolution of the digital signal is deter-mined by the number of bits, N , that is used by the A/D-converter. Thenumber of quantized values are given by 2N . The measurement range of theanalogue signal of the PRT is 240 mV and the A/D-converter that will beused has 16 bits which give a precision according to

240

216= 0.0037 mV (3.17)

The sensitivity of the PRT is approximately 12 mV/bar which gives a preci-sion of 30.4 Pa. The precision should also be compared to the amplitude ofthe noise present in the analogue signal.

19

Chapter 4

Instrumentation of the runner

4.1 Introduction

This chapter deals with the instrumentation of the runner. One of the bladesof the Kaplan-runner will be dismantled and miniature piezo-resistive pres-sure sensors will be incorporated in the blade on the pressure and the suctionside. Miniature piezo-resistive pressure sensors have previously been used intests on a model of a Francis runner performed by EPFL in Lausanne [8].In Figure 4.1, the milling of the Francis runner blade can be seen. However,the instrumentation of a prototype imposes new difficulties.

The dismantling of the blade is a very costly process. Therefore, since itis unclear how the sensors will behave during operating conditions, damagedsensors must be replaceable without dismantling the runner. What is more,the sensors need to be mounted on the blade without changing the shape andthe durability of the blade. A calibration system is also needed to calibratethe sensors incorporated in the blade before its reinstallation on the runner.

Figure 4.1: A Francis runnermodel blade

The scope of this partial study is to developa design of the incorporation of sensors ina Kaplan runner. This is tested on a lab-oratory scale. An experimental set-up isused that consists of a test plate that sim-ulates the runner blade. Furthermore, themounted sensors are calibrated with a sys-tem that is conceived to be used on the U9Kaplan blade.

20

4.2 Methods

4.2.1 Experimental set-up of the montage

Since the sensors cannot be directly incorporated in the Kaplan-runner atthe U9-unit, the sensors are mounted in housings on circular metal coins.The test plate is therefore milled with housings for the metal coins and railsfor the cables. The metal coins are attached in the housings by screws. Resinis used to fill the rails and the irregularities of the screw-heads. Variations ofthis design are tested and the results are evaluated according to the statedrequirements.

Experimental equipment

The test plate

(a) T1

(b) T2

Figure 4.2: Milling of the test plate

The test plate is a piece of stainlesssteel with the dimension 20× 15× 2cm. Both of the sides (T1 andT2) were milled with housings to fitmetal coins with encapsulated sen-sors (see figure 1). Open channelsfor the sensor cables were milled foreach housing. The principal differ-ence between the two sides is thehousings at T2 is separated from theopen channels by an enclosed chan-nel. The purpose of the enclosedchannel is to obtain a better sealingof the coin.

The metal coins

Three kinds of metal coins withscrews were tested. The varied pa-rameters were its height, type andnumber of screws. Two of the metalcoins were manufactured and sent toSwitzerland for incorporation of thePRT’s (see Figure 5.3.1). In Table4.1 the data of each coin is listed.

21

Figure 4.3: Drawing of coin

Table 4.1: Coin dataCoin Height Number of screws Type of screws Incorporated sensorC1 2.5 mm 4 M2 S1C2 5 mm 4 M2 S2C3 2.5 mm 2 M2.5 -

22

The pressure transducers

Figure 4.4: Coin with sensor

The selected sensors are miniature piezo-resisitve pressure transducers (PRT) man-ufactured by a Swiss company. The func-tioning of PRT is further described in 4.Theactive die of the sensor consists of a sili-cone wafer with the dimensions 1 × 1 × 0.6mm. Four active gages are connected in afull bridge. The maximum excitation volt-age of the bridge is 12 VDC. According tothe specifications, the approximate calibra-tion factor is 20mV/V.

The two metal coins C1 and C2 were sentto the Swiss company to incorporate the sen-sors in their housing. The sensors are cov-

ered by a filling of silicone on the top and on the bottom. The sensors weredelivered calibrated with a sensitivity according to Table 4.2.

Table 4.2: Sensor DataSensor Measurement range Sensitivity (mV/bar)S1 3.5 bar 14.05S2 7 bar 24.9

Cable protection and filling material

The rails of the test plate is filled with resin. The tested resins are a 2-component epoxy and a steel-reinforced epoxy. The cables must be protectedfrom the filling material so a damaged sensors can be replaceable. A plasticline is used to protect the cables from the resin.

23

4.2.2 Experimental set-up of the calibration

Figure 4.5: Suction cup on to-gether with the test plate

The performance of the pressure transduc-ers are tested with a calibration system thatconsists of a pressure calibrator and a suc-tion cup. The calibration system is con-ceived to be used on site during the instal-lation of the sensors on the runner blade.Therefore, the purpose of the calibration istwofold. The mounting of the sensors on theblade should not affect their performance.The sensors thus need to be calibrated afterthe montage. Furthermore, the calibrationsystem needs to be tested to see if it can beused on site.

The suction cup connects the pressurecalibrator to the pressure sensor mounted on the test plate. The cup ispositioned with its center over the pressure sensor and a suction pressureholds it to the plate. A vacuum pump ensures a sufficient level of the suctionpressure. The central region of the cup is isolated from the suction pressureby o-rings and connected to a pressure calibrator. The portable pressurecalibrator has a measurement range of 0 to 10 bar. Its permissible deviation is±0.0025 bar. The pressure medium is air. The applied pressure is controlledmanually by a pump.

In the set-up of the calibration, the sensors are excited by a voltage of 5VDC. The output signal is acquired by the pressure calibrator which allowsus to log the calibration pressure simultaneously. The logging is controlledmanually.

The ambient room temperature is also measured. The sensor S1 is onlybe calibrated in the range 0-1 bar because no sealing could be obtained forhigher pressure levels.

The temperature dependence of the calibration factor is tested by heatingthe test plate with a hot air gun.

24

4.3 Results

4.3.1 The design

The results are evaluated according to the following criteria:

• Minimum intervention on the blade

• The sensors must be replaceable

• Sealing

• Durability

The best results were obtained with the following test equipment:

• Milling of the test plate T2

• Coin C3

• Thread Sealing LOCTITE

• Sensor S2

• Steel-reinforced resin

• Plastic line to protect the cables

Figure 4.6: Final montage

The plastic line protects the ca-bles. This ensures that the coincan be demounted without damagethe cables. Thereby, damage sen-sors are replaceable. The plasticline demands a good sealing betweenthe coin and the blade. This iswhy the milling of the test plateT2 was chosen. This will ensurea waterproof montage together withthe thread sealing LOCTITE on thescrews and between the coin and thetest plate. The design of the coinC3 was chosen since two screws weresufficient.The steel-reinforced resin

gave a smoother surface than the 2-component epoxy. However, the durabil-ity may be lower. The sensor S2 was chosen since it had a larger measurementrange and will thus be more resistable.

25

4.3.2 Calibration of the pressure sensors

Calibration of S1 and S2

The sensor S1 with the measurement range 0-3.5 bar was only calibrated oncebefore it was damaged. The calibration was performed at suction pressure.18 points were logged with increasing and decreasing pressure. The datawas fitted to a polynomial of degree 1. The following transfer function wasobtained:

O = KI + a = 25.6I + 11.4 (4.1)

where O is the output signal i mV and I is the input in bar. The linearity is0.0514 %FSO. It is calculated as the maximum deviation of the data points.The sensitivity of the sensor, K = 25.6 mV/bar can be compared to thesensitivity K = 24.9 mV/bar specified on the datasheet of the sensor. Eq4.1 also tells us that the sensor had a zero shift of 11.4 mV (with vacuum asthe reference point).

15 20 25 30 35 400

0.2

0.4

0.6

0.8

1

1.2

Output signal (mV)

Ref

eren

ce p

ress

ure

(bar

)

Calibration of sensor S1

Data pointsFitted polynomial

Figure 4.7: Calibration S1

The temperature dependence of the calibration factor was tested by heat-ing the test plate with a hot air gun. Calibration at increased temperatureshowed a decreased sensitivity. The results are given in Table 4.3

26

2 4 6 8 10 12 140.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

Output signal (mV)

Ref

eren

ce p

ress

ure

(bar

)Temperature dependence of the sensitivity

Increased temperatureAmbient temperature

Figure 4.8: Calibration S1

Table 4.3: Transfer function at different temperaturesTemperature Sensitivity K Zero shift aAmbient 14.6 mV/bar -1.1Increased 13.8 mV/bar -0.1

A zero shift of 0.7 mV was obtained at atmospheric pressure with a tem-perature variation of 0 to 20 degrees C.

Evaluation of the calibration system

Figure 4.9: Suction cup

A few problems with the calibration systemwere encountered. The suction cup did notfunction if the calibration pressure exceeded4 bar. It suction pressure could not holdon the cup to the plate. The cup ”jumped”and a chock wave hit the sensor with theconsequence that one of the semi-conductorstrain gages was damaged.

27

The suction pressure must be sufficiently low to balance the force appliedby the pressure on the central area. Equilibrium of the forces gives Fp = Fs.Given the dimensions of the suction cup, the maximum suction pressure thatmust be applied to hold on the cup to the plate at maximum calibrationpressure could be calculated as

ps = ppR2

c −R2s

R2s

(4.2)

where pp is the maximum calibration pressure, Rc the radius of the suctioncup and Rs the radius of the central region where the calibration pressureis applied. Calculating ps for pp = 7 bar, the maximum suction pressureis 3 bar. The available vacuum pump should be able to apply this suctionpressure. However, the suction cup will not function if the o-rings are not incontact with the surface of the plate so sealing will be obtained.

Moreover, there is a risk of leakage in the housing of the coin. Thisis the second encountered problem with the calibration system. If air getsthrough into the housing, the pressure will sink and no static calibration canbe performed since the plastic line that is used to protect the cables is incontact with the atmospheric pressure.

28

4.4 Discussion and conclusions

The results of this partial study are guidelines of how the sensors shouldbe incorporated in the runner blade. A preliminary design is suggested forthe milling of the blade according to Figure 4.10. The runnner blade will bedismantled in August 2007. Before the milling of the blade, the emplacementof the sensors will be determined by using a numerical simulation of thevelocity field in the neigbourhood of the runner blade.

A few remarks could be done regarding the instrumentation of the runner.First of all, we must be critical towards our results concerning the design ofthe incorporation of the sensors. The results can only serve as guidelines. Thework was conducted on a laboratory scale without a detailed picture of therunner blade. Our design seemed to be a good choice after the experimentsconducted with the test plate, but we do not know what problems that mayoccur during the milling of the runner blade.

Several issues were considered during this work that could not be re-solved. For example, the runner do not only experience the hydraulic load,it is also strained by the centripetal force due to the rotation. The ro-tational speed of the runner, 10 Hz, is fairly high compared to other hy-dropowermachines. The sensing element in the transducers, a silicone di-aphragm, responds to load applied perpendicular to its surface. If it isstrained in another direction the characteristics of the sensor may be al-tered. How do we calibrate the sensors while they experience the centripetalforce? Maybe the test plate could be put in a loading machine and strained.

Figure 4.10: Preliminarydrawing

Connectors need to be put in the runnercone. Otherwise will the sensors not be re-placeable. In our design, a plastic line en-ables the cable to be disconnected. Thismust be done in the runner cone, a humidenvironment. Previously, in experimentsconducted at the U9, the runner cone wasused for switches. The switches were put ina box sealed with silicone. Another solutionis to use sealed connectors. This issue needssome further investigation.

29

Another issue is the amplification. The maximum excitation voltage willbe chosen to get the highest full-scale output which is 240 mV. Even thoughsemi-conductor strain gages have larger output than ordinary metal straingages, the pressure sensors still have a quite weak signal that risk to beaffected by noise. A high digital resolution is then useless. We want todigitalize the output from the sensors and not the noise. Digital anti-aliasingfilters could be used, but for example noise of 50 Hz from the electric gridlies in the frequency domain of the excitation forces from the hydraulic loadand can not be filtered. This needs to be taken under consideration.

To conclude, the installation work on site should be carried out carefully.The sensors must be calibrated on site to exclude any possible sources ofnoise or malfunctioning.

30

Chapter 5

Instrumentation of the LoadMeasurements on the GuideBearings

5.1 Introduction

Figure 5.1: The dowelpeg

This partial study is concerned with the choice ofsensors for the load measurements on the guidebearings. Two different measurement techniqueshave been evaluated. Their performances have beentested in a loading machine in collaboration withVattenfall R&D in Alvkarleby. To make sure thatthe installation of the sensors does not alter thecharacteristics of the bearings the stiffness of theload cells and the original dowel peg has been deter-mined in a loading machine with three displacementsensors by a laboratory in LTU.

In this chapter, the installation of the sensorsin the guide bearings will be explained and the twoproposed measurement techniques will be described.Thereafter, the methods and the results of the eval-uation work will be presented. In conclusion, thechoice of sensor will be discussed.

31

5.2 Installation of the sensing elements in the

guide bearings

Figure 5.2: One bearing segment withits dowel peg and wedge

Each guide bearing consists of hy-drodynamically lubricated bearingsegments that are equally positionedaround the shaft. The load is carriedby the lubrication film between thesegments and the shaft. The thick-ness of the fluid film is regulated bya wedge in contact with a dowel pegon the bearing segment. The dowelpeg consists of a cylinder that has atop surface with a spherical radius of500 mm. This surface is in noncon-formal contact with the wedge sincethe contact surface of the wedge isplane [9].

In the JUSPOWER-project, theload on each bearing segment will bemeasured. Two different measure-ment techniques are suggested. Thedowel peg between the bearing seg-ment and the wedge experience thesame load as the bearing segment.The dowel peg would either be re-placed by a load cell or modified by

bonding strain gages onto the parts of the peg that experience the moststrain. The latter alternative would conserve the characteristics of the bear-ings, but more attention must be put on the composition of the measurementsystem.

A load cell is a package that consists of conditioned sensing elements.It fulfills some given standards according to its specifications. The sensorcharacteristics of the load cell are given in a calibration sheet. To bondstrain gages directly onto the dowel peg demands calibration. Regions onthe dowel peg must be found with sufficient strain levels and the strain gagesalso need to connected in a bridge circuit.

32

5.3 Tested Measurement Techniques

5.3.1 Modified dowel peg with strain gages (DP)

Figure 5.3: Modified peg

The strength of the signal of a straingage depends on the strain of thetest object according to A strongsignal is desirable. Therefore, theshape of the dowel peg was modifiedso regions would be obtained withincreased strain.

The emplacement of the straingages was determined with a FEM-analysis of the modified dowel peg.A first version was developed and

tested during the autumn 2006. Due to problems with hysteresis a secondversion was developed with a modified shape.

Strain caused by bending moments are preferable to stain due to com-pression of an object, since bending moments give more strain. To obtain abending moment in the bottom, a circular hole is milled in the peg. In thesecond version the diameter of the hole is enlarged to increase the bendingmoment. The hole has a depth of 1 mm and a diameter of 40 mm (see figurex). Two strain gages are bonded in the center of the hole where the higheststrain is obtained. These gages both provide a positive signal and must beconnected in adjacent arms in the Wheatstone bridge. This half-bridge doesnot cancel the strain caused by the thermal expansion since both of the sig-nals are positive. Two holes are drilled that lead through the wires from thebottom to the curved wall of the dowel peg.

On the curved wall of the peg two plane surfaces are cut on oppositesides. On these surfaces gages in half-bridges are bonde nearest the bot-tom of the peg where the highest strain levels are obtained according to theFEM-analysis. The gages respond to the axial compression and the tangen-tial elongation of the peg and give output signals with opposite signs. Byconnecting the two half-bridges together, the strain due to the thermal ex-pansion of the object is cancelled and the output signal is amplified with afactor 2.

Apart from the dowel peg described above, another mounting of a straingage on a dowel peg with larger dimensions is tested. This dowel peg has adrilled hole through its axis where a strain gage is mounted.

33

5.3.2 Standard Load Cell (LC)

Figure 5.4: Standard load cell

The standard load cell is orderedfrom an American company. It isa bonded foil strain gage transducerthat consists of a casing in stainlesssteel and a spherical load button (seeFigure 5.3.2). The dimensions of thestandard load cell were slightly mod-ified to fit in the bearing. The heightof the load button (L) was chosenso the total height of the load cell(H) would be equal to the height ofthe dowel peg. The surface of theload button was modified to have thesame spherical radius as the originalpeg.

One of the major differences be-tween the dowel peg and the LC isthat the load button has a smaller

area than the spherical top surface of the dowel peg. The contacting surfaceof the load cell is then smaller if the contacting surface of the original pegexceeds the area of the top surface of the load cell. Furthermore, the casingof the LC has a smaller diameter than the dowel peg. This will lower thestiffness of the dowel peg.

The load cell is delivered with a calibration sheet. Its calibration factorwas verified in experiments in LTU. It is temperature compensated between15− 70 ◦C.

34

5.4 Calibration of the sensors

5.4.1 Experimental set-up

Figure 5.5: Experimental set-up

The calibration of the sensors was pre-formed in collaboration with VattenfallR&D in Alvkarleby together with MattiasLundstrom.This experimental work dealsmainly with the calibration of the straingages bonded on the modified dowel peg,since the LC is delivered calibrated. TheLC is included in the tests since this will al-low us to compare the signals. If the errordue to the experimental set-up is constantbetween the test objects, the observed vari-ations will be caused by a difference intheir performance.

The loading

The load cell and the dowel pegs were applied by a load in a loading machinewith the measurement range 0-100 kN according to the experimental set-upin Figure 5.4.1. The applied load was regulated manually. The measurementrange was 1 - 50 kN. The output signals were digitalized and sampled with 50Hz. The reference load could only be read manually on the loading machine.The test objects were loaded and unloaded. 25 points were selected wherethe load and the signals were measured.

Tested output signals

Three output signals were tested with active gages mounted on the dowelpeg. The signals 2 and 3 both hade active gages mounted on the same dowelpeg. The data of the signals are shown in Table 5.1. The active gages wereconnected in bridge circuits according to Figure 5.6.

35

Table 5.1: Tested signalsSignal Active gages Emplacement Gage resistance1 4 Load cell 350 ohm2 2 Bottom DP 350 ohm3 4 Curved wall DP 350 ohm4 1 Drilled hole DP 120 ohm

(a) 4 (b) 2

(c) 3

Figure 5.6: Bridge connections of the signals 4,2 and 3

36

Table 5.2: Amplification dataAmplifier Amplified signal VA Excitation voltage VExc Gain1 (1172) 2.88 VDC 8.36 VDC 6892 (1173) 9.62 VDC 8.37 VDC 23003 (1174) 9.62 VDC 8.41 VDC 2290

Amplification

Each signal was amplified with amplifiers built by Vattenfall R&D (see Figure5.7). Each amplifier was supplied by an excitation voltage of 12 VDC. Thegain of the amplifiers was regulated by connecting a shunt resistor accordingto Figure 5.7 where R1, .., R4 = 120 ohm and Rp = 59.9 kohm. The shuntresistor unbalances the bridge. The calibration factor Vo

Vsis given by

Vo

Vs

=1

4(

Rp

R + Rp

− 1) (5.1)

The shunt resistor simulates a strain of 500 µ/m for a quarter bridge witha gage factor K = 2.0.[7] If this corresponds to the full scale output of thesignal, the gain should be regulated so the output signal has a magnitudeof 10 VDC. The measured values and the gain of the amplifiers are listed inTable 5.2.

The amplifiers were also used to balance the output signals 1-3. Theoutput signal 4 was connected to amplifier 3 but it was not balanced at zeroload. This was done in Matlab during the data analysis.

Figure 5.7: Amplifier and shunt resistor

37

5.4.2 Results

The output signals are presented with their non-amplified values. The per-formance of the signals is evaluated with respect to their sensitivity, linearityand hysteresis. The values are expressed as percent of the full-scale outputthat was chosen to 50 kN. The parameters are listed in Table 5.3. All thesignals are plotted in Diagram 5.4.2.

−2 0 2 4 6 8 10 120

10

20

30

40

50

60Comparison of the output signals

Output signal (mV)

App

lied

load

(kN

)

1234

Figure 5.8: Calibration curves

Table 5.3: Characteristics of the output signalsOutput signal Linearity Hysteresis Sensitivity (mV/kN)1 0.27 -0.26 0.222 6.55 -7.58 0.0563 2.46 -3.23 0.0524 1.21 0.59 0.034

The signal 1 had the best performance of the tested signals. The signalsof the strain gages had a very low sensitivity compared to the standard loadcell. The 4 had the best performance between the signals of the strain gages.

38

It showed practically no hysteresis. Further measurements should though bedone to confirm the repeatability of the signal. Comparing the signals of theload cell made by the dowel peg of the U9, the signal 3, showed less hysteresisthan the 2.

5.5 Comparison of the stiffness of the sensors

Even though the load cell exhibit good sensor characteristics, it can not re-place the dowel peg in the guide bearing unless it do not alter the dynamicproperties of the bearing. Therefore the stiffness of the load cell is experimen-tally determined at LTU. Apart from the load cell, the stiffness of the originaldowel peg (DP1) and the modified dowel peg (DP2) were also determined.

Figure 5.9: Experimental set-up

39

5.5.1 Experimental set-up

Figure 5.10: Emplacement of the sensors

The test objects were putbetween two cylinders andloaded in an automatic load-ing machine with a mea-surement range of 0-50kN(see Figure 5.5). Three me-chanical displacement sen-sors were mounted betweenthe cylinders according tothe figure. The sensors wereequally positioned on theouter circles of the cylinders.

The displacement sensors had an accuracy of ±0.1µm. The test objects wereloaded and unloaded automatically by the loading machine with a loadingrate of 0.4 kN/s. All the signals were simultaneously recorded with a sam-pling rate of 10 Hz. The data was filtered by a digital low-pass filter with aband-with of 1 Hz. Each measurement was repeated five times. The sampledsignals were

1. Displacement sensor 1 (mm)

2. Displacement sensor 2 (mm)

3. Displacement sensor 3 (mm)

4. Applied load (kN)

40

The relation between the displacement of an object, x and the appliedforce, F could be expressed according to

F = f(x) (5.2)

The stiffness is equal to the partial derivate of Eq (5.3) with respect to x.

k = (∂f

∂x)i (5.3)

The acquired data is a set of points (Fi, xi). To approximate the stiffnessin each point i, the following finite two-sided difference formula can be used(refkanske)

k(i) =f(i + 1)− f(i− 1)

x(i + 1)− x(i− 1)(5.4)

To be able to apply this formula the acquired data was reduced and fil-tered in Matlab with the function resample() The function reduces the datapoints and filters the signal by an anti-aliasing filter. The time interval be-tween the data points was changed from 0.1 s to 2.5 which gave us 100 samplesof each acquired signal per loading. This interval could also be expressed interms of the difference in the applied load which would be more accurately.This formula was only applied to data points in the load range between 1-45kN. The results The numerical scheme (5.3) did not give a stable resultoutside this range, that was probably due to loading machine. Although theloading rate should be constant this was not the case in the end points of theinterval. It is a pi-regulator that controls the loading rate.

The analysis of the obtained data showed that for each test object, thefirst measurement series differs from the four following measurements. Thedisplacement sensors do not return to zero at no load, which must be dueto the experimental set-up since it could only be observed in the first mea-surement series. These measurement series were therefore excluded from thedata analysis.

To see if the performance of the three displacement sensors varied, therepeatability and the hysteresis of each sensor was calculated. (see section3.3) The repeatability could roughly be approximated as the precision of thesensors. However, this do not tell us about how close we are to the real valueof the displacement. We may measure the displacement of the cylinders orthe sensors may be badly positioned so they measure the displacement inanother direction.

If did sensors have an hysteresis, this should be due to the experimen-tal set-up. We do not expect any hysteresis from the tested objects sincemeasurements are performed in the elastic region of the material. Perhaps,

41

the measurement direction vary depending on if the load is increased or de-creased. If we compare the hysteresis of the sensors, this is similar to acomparison of the accuracy of the sensors.

Three vectors of data points for each displacement sensor, l = 1, 2, 3, existfor each of the four loadings, j = 1, ..4. The displacement vector could berepresented by xl,j and the force vector by F j.

Which sets of data points (F, x) should be used to calculate the stiffness?To take into account the variation between the sensors for each loading, thestiffness vector, jl,j was calculated for each of the set of data points

(F j, xl,j) (5.5)

The formula (5.4) was applied to these sets of data points. This gives usi× j vectors of the stiffness with l elements. Each element refers to a specificapplied load if we assume the loading rate was constant during the fourloadings and that the initial value was the same.

The final result of the stiffness was calculated as a mean value for eachof the elements, l.

ki =1

N

j=4∑

j=1

l=3∑

l=1

((ki)l,j) (5.6)

where N = 12, the total number of vectors. The mean value of the obtainedstiffness was also calculated for each sensor, l = 1, .., 3 as

˜(ki)l =1

N

j=4∑

j=1

((ki)l,j) (5.7)

where N = 4, the total number of loadings. The standard deviation of thesethree elements from ˜(kl) is

˜(ki)l =1

3

√√√√[l=3∑

l=1

((ki)l − ˜(ki))2] (5.8)

The maximum value of the standard deviation (5.8) for all of the elementsi is taken as an approximation of the uncertainty of the final result of thestiffness.

42

5.5.2 Results

Displacement

In Figure 5.11 and 5.12 the displacement for the three different positions isplotted as a function of the applied load. The displacement at each positionis a mean value of the measurement series. The variation between the threesensors is probably due to the experimental set-up since this was not changedbetween each repeated measurements. The repeatability has the same orderof magnitude for the three sensors. The precision of the result is thereforehigh. However, if the sensors are evaluated with respect to the hysteresis,the sensor 1 has a different behaviour than the rest. This is probably dueto the experimental set-up of sensor 1. We are inclined to believe that theaccuracy of sensor 1 is less than the rest. It should also be noted that noneof the sensors show any hysteresis at zero load.

Table 5.4: Repeatability Sensors (% FSO) FSO=0.1 mmTest object Sensor 1 Sensor 2 Sensor 3 Mean valueDP1 1.94 0.22 0.04 0.11LC 1.12 0.24 0.01 0.41DP2 1.15 0.06 0.055 0.13Mean value 1.4 0.17 0.029 -

Table 5.5: Hysteresis Sensors (% FSO) FSO=0.1 mmTest object Sensor 1 Sensor 2 Sensor 3 Mean valueDP1 0.38 0.39 0.133 0.19LC 0.48 0.27 0.06 0.17DP2 0.26 0.92 0.24 0.12Mean value 0.22 0.17 0.10 -

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0 0.01 0.02 0.03 0.04 0.05 0.06 0.070

5

10

15

20

25

30

35

40

45

50

Displacement (mm)

App

lied

load

(kN

)Displacement measurements on the dowel peg

Sensor 1Sensor 2Sensor 3

(a) DP1

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.090

5

10

15

20

25

30

35

40

45

50

Displacement (mm)

App

lied

load

(kN

)

Displacement measurements on the load cell

Sensor 1Sensor 2Sensor 3

(b) LC

Figure 5.11: Displacement measurements

44

0 0.01 0.02 0.03 0.04 0.05 0.06 0.070

5

10

15

20

25

30

35

40

45

50

Displacement (mm)

App

lied

load

(kN

)Displacement measurements of the modified dowel peg

Sensor 1Sensor 2Sensor 3

(a) DP2

Figure 5.12: Displacement measurements

45

0 5 10 15 20 25 30 35 40 45200

400

600

800

1000

1200

1400

1600

Applied Load (kN)

Stif

fnes

s (k

N/m

m)

Comparison of the stiffness

DPLCSG

Figure 5.13: Comparison of the stiffness

Stiffness

A comparison between the tested objects shows that the stiffness of the LCis almost 50 % lower than the DP at 45 kN load. This can be concluded fromDiagram 5.13. The stiffness of the load cell is of the same order of magnitudeas the stiffness of the oil film. How would this affect the total stiffness of thebearing? The total stiffness, kt is given by

kt =1

Σ1/ki

(5.9)

where ki is the stiffness of each part connected in series. Let us write thetotal stiffness of the guide bearing as

kt =1

1/ko + 1/kp

(5.10)

ko is the stiffness of the oil film and kp is the stiffness of the dowel peg. Weneglige The stiffness of the other parts. The original stiffness is then givenby

kt =1

1/ko + 1/2ko

= 2ko/3 (5.11)

46

0 5 10 15 20 25 30 35 40 45200

400

600

800

1000

1200

1400

1600

Applied Load (kN)

Stif

fnes

s (k

N/m

m)

The Stiffness of the modified dowel peg

(a) DP2

Figure 5.14: Obtained stiffness within its uncertainty domain

If the dowel peg is replaced by the load cell we have

kt =1

1/ko + 1/ko

= ko/2 (5.12)

By comparing Eq (5.11) with Eq (5.12) we have

ko/2

2ko/3=

3

4(5.13)

It will say that the new total stiffness is 75 % of the original stiffness.In Diagram 5.14 and 5.15 the obtained stiffness of each of the test objects

is plotted together with the uncertainty domain, ±σ.

47

0 5 10 15 20 25 30 35 40 45200

400

600

800

1000

1200

1400

1600

1800

2000

Applied Load (kN)

Stif

fnes

s (k

N/m

m)

The Stiffness of the dowel peg

(a) DP1

0 5 10 15 20 25 30 35 40 45200

300

400

500

600

700

800

900

Applied Load (kN)

Stif

fnes

s (k

N/m

m)

The Stiffness of the Load Cell

(b) LC

Figure 5.15: Obtained stiffness within its uncertainty domain

48

Table 5.6: Maximum standard deviation stiffness (% FSO) FSO=0.1 mmTest object Max standard deviationDP1 38LC 8.9DP2 15

The uncertainty, ±σ, was calculated as the standard deviation of theresult from each of the three sensors. The obtained difference of the stiffnessbetween the DP1 and the DP2 lies in the uncertainty domain and could notbe validated.

The repeatability was also calculated for the result of the stiffness. In thiscase, the sensor 1 differs again. It is peculiar that the repeatability of thestiffness does not follow the same pattern as the repeatability of displacement(compare with Table 5.4). It could be noted that the uncertainty of the resultof the stiffness of DP1 is very high, 38%FSO. This is due to a differing resultof the displacement of sensor 1. (see Figure 5.12)

Table 5.7: Repeatability Stiffness (% FSO) FSO=0.1 mmTest object Sensor 1 Sensor 2 Sensor 3DP1 0.10 0.015 0.0.026LC 0.023 0.004 0.06DP2 0.056 0.014 0.015Mean value 0.06 0.011 0.016

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5.6 Discussion and conclusions

The purpose of this study was to compare the performance of two kinds ofsensing elements. The output signals of strain gages bonded on a part of theguide bearings were compared with the output signal of a standard load cell.

The strain gages bonded on a dowel peg The results show that the straingages bonded on a dowel peg from guide bearings on the U9-unit do notexhibit sufficiently good properties as sensing elements. The output signalshad a very low sensitivity compared to the standard load cell. A lower sensi-tivity means a lower resolution. This also implies that the output signals aremore sensitive to noise, which should not be neglected since several sources ofnoise may be present in a hydropower station. Two of the three output sig-nals of the strain gages showed a hysteresis that lies without our permissiblerange. Although the strain gage incorporated into the axis of the dowel pegdid not show any hysteresis, it is not preferable to use only one active gagein a bridge circuit, since no amplification is obtained. However, this outputsignal showed the best performance between the tested strain gages. Sincethe temperature of the oil film varies between 20 and 80 ◦C in the guidebearings, the sensors must be temperature compensated. To compensate forthe additional thermal output of a strain gage (see Chapter 5.1, a dummystrain gage can be bonded on an unloaded part of the dowel peg. Accordingto the FEM-analysis the upper parts of the curved wall of the peg are notstrained by the applied load and could be used to position a dummy straingage.

The load cell had the best properties as a sensor. But the load cell as asensor in the guide bearing cannot only be evaluated in a loading machine.We need to know how the load cell responds to load when it is installed in theguide bearing. What is more, the characteristics of the guide bearings may bealtered if the dowel peg is replaced by the load cell. This is why the stiffnessof the load cell was experimentally determined in this study. The results showthat the load cell has a stiffness that is almost 50 % lower than the orginaldowel peg at the maximum applied load 50 kN. The new total stiffness of thebearing is approximately 75 % of the original stiffness. This would alter thethe dynamic characteristics of the guide bearings. Therefore, the tested loadcell can not be used as sensor. The conclusions are that further investigationwill then be needed to find a sensor that fulfills our demands. Even thoughmore work could be put on fabricating our own sensor of the dowel peg, thiswould be too time demanding and since the senors must be installed as soonas possible a tender invitation was done for a load cell the same stiffness asour dowel peg.

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Chapter 6

Discussion and Conclusions

This diploma thesis is concerned with planned full-scale measurements onthe U9-unit in the Porjus Hydropower Center. Two partial studies are con-ducted that deal with the instrumentation of the runner and the guide bear-ings. The results of the first partial study are guidelines of how the pressuremeasurement system on the runner should be set-up. The second work is acomparison study of two methods to measure the radial load at the guidebearings. The results show that none of the tested sensors could be used inthe guide bearings. In parallel with the comparison study, the requirementsof the load sensor were developed. A tender of invitation of a sensor wasdone with these requirements.

This study was conducted in LTU. The tests were carried out in a lab-oratory environment. However, the planned full-scale measurements willbe performed in the Porjus Hydropower Center. The lack of experience ofthe operation of a hydropower plant has limited the outcome of this study.Textbooks cannot give any working experience. The instrumentation of theU9-unit will start in August 2007. Certainly, problems that are not foreseenin this study will show up. The design of the pressure measurement systemis preliminary. But even though the design must be changed, this studywill serve as a good starting point. The preparation work of a full-scalemeasurements should not be understated.

In this study, not much attention was put on the dynamic characteris-tics of the hydropower machine and flow-related issues. The focus of thestudy was mainly the functioning of measurement systems. In future work,more attention must be given to the investigated problems of the full-scalemeasurements. An experimental study of a hydropower machine will requireboth a theoretical understanding of the investigated problems, measurementsystems and experience of the operation of a hydropower plant.

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Bibliography

[1] S. Hansson, Porjus: en vision fr industriell utveckling i ovre Norrland,PhD thesis, Tekniska hogskolan i Lulea, 1994.

[2] M. Cervantes, J.-O. Aidanpaa, S. Glavatskih, and T. Karlsson, Interdis-ciplinary research in full-scale hydropower machines at porjus, jokkmokk,sweden, 2006.

[3] J. P. Bentley, Principles of measurement systems (Harlow:Pearson Pren-tice Hall, 2005).

[4] J. Fraden, Handbook of modern sensors : physics, designs and applica-tions (New York:AIP, 2004).

[5] P. L. D. Tufte, O.N.; Chapman, Journal of Applied Physics 33, 3322(1962).

[6] W. T. Thomson, Theory of vibration : with applications (Lon-don:Chapman, 1993).

[7] K. Hoffmann, An Introduction to Measurements using Strain Gages(Darmstadt:HBM, 1989).

[8] M. Farhat et al., Onboard Measurements of Pressure and Strain Fluctu-ations in a Model of low Head Francis Turbine. part 1 : Instrumentation,in Proceedings of the 21st IAHR Symposium on Hydraulic Machinery andSystems, pp. 865–872, 2002, Using Smart Source Parsing 9-12 Septemberpp 3.

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