design and manufacturing of a thrust measurement system ...1228202/fulltext01.pdf · design and...

Design and manufacturing of athrust measurement system fora micro jet engine

Enabling in-flight drag estimation for subscaleaircraft testing

Anna Martinez

Linköpings universitet

Institutionen för ekonomisk och industriell utveckling

Examensarbete 2018|LIU-IEI-TEK-A-18/03161-SE

Linköpings universitet

Institutionen för ekonomisk och industriell utveckling

Ämnesomr̊adet Fluida och Mekatroniska System

Examensarbete 2018|LIU-IEI-TEK-A-18/03161-SE

Design and manufacturing of athrust measurement system fora micro jet engine

Enabling in-flight drag estimation for subscaleaircraft testing

Anna Martinez (annma929)

Academic supervisor: Alejandro SobronExaminer: David Lundström

Linköping universitet

SE-581 83 Linköping, Sverige

013-28 10 00, www.liu.se

Linköping University Electronic Press

Upphovsrätt

Detta dokument hålls tillgängligt på Internet – eller dess framtida ersättare – från

publiceringsdatum under förutsättning att inga extraordinära omständigheter

uppstår.

Tillgång till dokumentet innebär tillstånd för var och en att läsa, ladda ner,

skriva ut enstaka kopior för enskilt bruk och att använda det oförändrat för icke-

kommersiell forskning och för undervisning. Överföring av upphovsrätten vid

en senare tidpunkt kan inte upphäva detta tillstånd. All annan användning av

dokumentet kräver upphovsmannens medgivande. För att garantera äktheten,

säkerheten och tillgängligheten finns lösningar av teknisk och administrativ art.

Upphovsmannens ideella rätt innefattar rätt att bli nämnd som upphovsman i

den omfattning som god sed kräver vid användning av dokumentet på ovan be-

skrivna sätt samt skydd mot att dokumentet ändras eller presenteras i sådan form

eller i sådant sammanhang som är kränkande för upphovsmannens litterära eller

konstnärliga anseende eller egenart.

För ytterligare information om Linköping University Electronic Press se för-

lagets hemsida http://www.ep.liu.se/.

Copyright

The publishers will keep this document online on the Internet – or its possible

replacement – from the date of publication barring exceptional circumstances.

The online availability of the document implies permanent permission for

anyone to read, to download, or to print out single copies for his/her own use

and to use it unchanged for non-commercial research and educational purpose.

Subsequent transfers of copyright cannot revoke this permission. All other uses

of the document are conditional upon the consent of the copyright owner. The

publisher has taken technical and administrative measures to assure authenticity,

security and accessibility.

According to intellectual property law the author has the right to be

mentioned when his/her work is accessed as described above and to be protected

against infringement.

For additional information about the Linköping University Electronic Press

and its procedures for publication and for assurance of document integrity,

please refer to its www home page: http://www.ep.liu.se/.

© Anna Martinez.

http://www.ep.liu.se/http://www.ep.liu.se/

Abstract

Good estimation of aerodynamic coefficients is of fundamental importance in thedesign and development process of an aircraft. Generally, these parameters are ob-tained using analytical, numerical and experimental methods, which are sometimeseither inaccurate or very expensive. The use of subscale aircraft is becoming in-creasingly common in the study and evaluation of new aircraft concepts. Flighttesting results in an efficient solution for obtaining parameters that can define dragcharacteristics. This project presents a solution for achieving the drag aerodynamicmodel from the design and manufacturing of a micro engine thrust measuring sys-tem integrated on subscale aircraft. Strain gauge technology permits to identify thestresses that the engine forces cause to the aircraft internal structure by analysingthe strain of several strategic zones of the engine mounting created for this purpose.Different structural support geometries have been presented and stress-analysed to-gether with the design of the appropriate strain gauge model configuration in orderto select and manufacture a system that represents a good compromise betweenall the requirements while ensuring the quality and accuracy of the data acquired.After calibration, installation and set-up, the system is ready for real in-flight mea-surements.

Acknowledgements

Foremost, I would like to express my sincere gratitude to my supervisor AlejandroSobron for providing support, advice and guidance during the development of thisproject. The regular meetings and his counselling and resolution of doubts havebeen contributed greatly to the successful completion of this research.

I would like to thank David Lundström for the support of this research, encour-agement, insightful comments and for all the advice provided. Also for helping meto choose the right direction in several stages and providing the tools needed whenregarding to manufacturing the mounting and affording the adequate strain gauges.

I would also like to thank the Linköping University Workshop for the efficacy andefficiency when manufacturing of the pieces needed.

Finally, I would like to express my deep appreciation where the most basic sourceof my life energy resides: my family and my friends. Their support has been alwaysunconditional and essential.

Nomenclature

Abbreviations and Acronyms

Abbreviation Meaning

CAD Computer aided designGF Gauge FactorLiU Linköping UniversitySG Strain gaugesSW SolidWorks

Latin Symbols

Symbol Description Units

a Acceleration[ms−1

]CL Lift coefficient [−]CD Drag coefficient [−]D Drag [N ]

DR Ram drag [N ]

FG Gross thrust [N ]

L Lift [N ]

g Gravity[ms−2

]m Aircraft mass [kg]

Tm Thrust measured [N ]

q dynamic pressure [Pa]

R Resistance [Ω]

S Wing surface[m2]

Vout Output voltage [V ]

Vin Input voltage [V ]

W Aircraft gross weight [N ]

Greek Symbols

Symbol Description Units

α Angle of attack [rad]

β Side-slip angle [rad]

� Strain [−]δTy Nozzle deflection around y-body axis [rad]

δTz Nozzle deflection around z-body axis [rad]

σ Axial stress [Pa]

Subscripts and superscripts

Abbreviation Meaning

i running number

b body-axis reference system

w wind-axis reference system

Contents

1 Introduction 1

1.1 Frame of reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Theory 5

2.1 Thrust measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1.1 Strain gauges . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1.2 Wheatstone bridge . . . . . . . . . . . . . . . . . . . . . . . . 8

2.1.3 Signal-conditioning circuitry . . . . . . . . . . . . . . . . . . 11

2.1.4 Measuring structure . . . . . . . . . . . . . . . . . . . . . . . 13

2.2 Aerodynamic model . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3 Method 17

3.1 Design of the measurement structure . . . . . . . . . . . . . . . . . . 18

3.1.1 Relevant criteria for the design . . . . . . . . . . . . . . . . . 18

3.1.2 Stress and strain preliminary analysis . . . . . . . . . . . . . 19

3.1.3 Initial design . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.1.4 Alternative solutions . . . . . . . . . . . . . . . . . . . . . . . 25

3.2 Selection of the preliminary geometric design of the measurement device 31

3.2.1 Selected configuration: C-IX . . . . . . . . . . . . . . . . . . 33

3.3 Detailed design and implementation of the measuring device . . . . . 36

3.3.1 Strain gauge selection . . . . . . . . . . . . . . . . . . . . . . 36

3.3.2 Sizing of the load cell and mounting device . . . . . . . . . . 38

3.3.3 Signal conditioning circuit . . . . . . . . . . . . . . . . . . . . 40

3.3.4 Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.4 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.5 Implementation of the drag model . . . . . . . . . . . . . . . . . . . 42

4 Results and discussion 45

4.1 Outcome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.2 Measurement system manufacturing . . . . . . . . . . . . . . . . . . 46

4.3 Aircraft testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

5 Conclusions 49

6 Future work 51

Appendices 55

A Structural analysis of the designed geometries 55

A.1 Configuration I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

A.1.1 Von Misses stresses . . . . . . . . . . . . . . . . . . . . . . . . 55

A.1.2 Unitary strain in Y direction . . . . . . . . . . . . . . . . . . 57

A.2 Configuration II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58



A.3 Configuration III . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62


A.3.2 Unitary strain in X direction . . . . . . . . . . . . . . . . . . 64

A.4 Configuration IV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65



A.4.3 Unitary strain in Z direction . . . . . . . . . . . . . . . . . . 69

A.5 Configuration V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70



A.6 Configuration VI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74




A.7 Configuration VII . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79



A.8 Configuration VIII . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82




A.9 Configuration IX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87



A.10 Configuration X . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91



A.11 Configuration XI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94



A.12 Configuration XII . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98









A.15 Configuration XV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107



A.16 Configuration XVI . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110



A.17 Configuration C-IVA . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

A.17.1 Unitary strain in Z direction . . . . . . . . . . . . . . . . . . 114A.18 Configuration C-IVB . . . . . . . . . . . . . . . . . . . . . . . . . . . 115


B Amplifier characteristics 119B.1 Amplifier Specifications . . . . . . . . . . . . . . . . . . . . . . . . . 119B.2 Set Up connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

C Final drawings 122

1 Introduction

Knowledge of aerodynamic behaviour under real operating conditions is crucial foroptimizing the performance of an aircraft. The use of measurement methods duringflight is increasing due to the importance of obtaining accurate aerodynamic modelsfor the design and construction of aircraft.

Subscale models can represent a good option for estimating such parameters infull-size aircraft, either because of the possibility of studying them in wind tunnelsor due to the lower complexity in the dynamic measurement procedures mentionedabove. When developing the design process of new or improved aircraft, flight testson subscale models are practical resources for increasing the information collectedfrom the full scale aircraft design while providing methodologies that ensure thereduction of costs and time on modifications and tests while maintaining acceptablequality standards. Moreover, they allow for the comparison of testing results withthe predicted theoretical behaviour and detect possible problems.

Several methodologies are currently implemented in order to estimate in-flight dragbehaviour on subscale aircraft. This project presents a drag estimation from thein-flight study of the thrust model and the measurement of certain flight parametersof a subscale aircraft. Thrust model is obtained by the design of a measuring systemfor the micro engine which takes advantage from the structural stresses transfer andthe strain gauge technology.

1.1 Frame of reference

Some studies [1] [2] describe the implementation of drag models during flight per-formance by the acquisition of flight-data (accelerations, angle of attack, slide-slipangle, deflections of the nozzle, etc.) from installed measuring systems and the ob-tention of the thrust model from values of the engine mass flow and net thrust.Last values are usually determined by measuring specific engine parameters such astemperatures, pressures, fuel flow and several engine calibration data.The solution proposed on this projects obtains the thrust model by the mechanicalstudy of the stress and strain that the internal structure suffers due to this force.

Strain gauges sensors are one of the most suitable options when measuring the stressproduced on a structure due to dynamic thrust. The forces produced by the jet en-gine are transmitted as stresses to the structure. Analysing the change of electricalresistance on this kind of sensors in several strategic zones, the strain can be readand, with the adequate implementation of an electrical circuit, transformed into val-ues of force. By modifying and redesigning the structural support that fixes a microengine to the internal structure of the subscale aircraft, the installation of a straingauges circuitry permits direct in-flight measuring of thrust avoiding interferencesof other vertical or lateral forces.

1

1.2 Outline

As described in the Theory section, in the first phases of the project, to understandthe functioning of strain measurements, various theoretical foundations have beenstudied: the strain gauge theory, the operation of the Wheatstone bridge, the ex-perimental design optimization procedures that allow the adequate measurements incommercial load cells, the adequate procedures during strain gauge installation andcalibration and, of course, the fundamentals of elasticity and resistance of materials.

During the investigation phase, a deep research has been developed about the typesof strain gauges according to their constructive characteristics, which include thematerials they are made of, their length, width, grid pattern, among others. Inaddition, their functional characteristics have been studied, which determine thecorrect operation in service, such as non-linearity and gauge factor. All these pa-rameters have been taken into account when selecting the gauges.

Subsequently, a search of the main construction geometries that make up the com-mercial load cells has been made to find inspiration when making the current designs.The electronic instrumentation of sensors used to analyse a certain signal and quan-tify the various errors that occur in the measurement of the same has been alsodone. It began by researching the theoretical foundations that surround the tech-nology used in the design and manufacture of the different types of load cells thatexist in the market. This phase includes the investigation of the main geometries ofthese deformable elements, as well as the mechanical behaviour they exhibit.

Once the research phase has been completed, the computer design of different loadcells has started on the Methodology section. Before designing itself, it has beennecessary to establish the design parameters: the maximum force that the mountingsystem would have to support according to the maximum thrust that the enginecould provide and the maximum values of lateral and vertical accelerations in theaircraft, the material to be used, the maximum weight it could reach, etc. Once thepremises have been established, the design program has been selected.

Later, the design phase has begun, which has been useful to understand the me-chanical stresses that are generated in the deformable elements according to theirgeometry. Thanks to a mixture of ideas taken from commercial designs and knowl-edge acquired in the previous investigations, several own designs have been made inorder to obtain the values of the stress concentrations.

After reasonably obtaining the type of geometry to be optimized, some modificationsand improvements have been performed to obtain the most correct measurementsof the beams, reaching a compromise solution between obtained deformations andother concerning details. After the final design specification, it has been decided tomanufacture the piece in the University workshop in order to perform a calibrationtest and validate the results obtained from the designed model. In addition, the

2

electronic installation and wiring necessary for signal processing has been designedand manufactured.

Regarding the development of the thrust model, the first attempt has been theanalysis of the forces that affect during the performance of a flight. It has beenimperative to identify which parameters are variables and which ones were alreadyknown. For this reason, the measurement systems already installed in the aircrafthave been investigated.After these considerations, a set of equations which define the lift and drag coeffi-cients has been found, only depending on the thrust measurements carried on in thisproject and the already measured values of other variables such as the accelerationsin body axis and the angles of the aircraft with respect to the wind and velocityincidence. This model is really important to know the aerodynamic behaviour ofthe subscale aircraft during flight and will be detailed in the following sections.

3

2 Theory

2.1 Thrust measurement

In order to obtain the values of the dynamic thrust of the model, a measuring sys-tem has been implemented in the mount of the engine, between the mounting clampand the internal structure of the aircraft. The horizontal force implemented by theexhaust gases of the jet turbine is directly transferred to the structure of the aircraft.Measuring this mechanical force, the thrust can be determined.

Several options have been studied in order to implement the mechanism designed tomeasure the transmission of force between the engine and the model. All of themare based on the measurement of the elastic deformation of certain structures usingstrain gauges. This is the operating principle of the load cells. Therefore, the ob-jective is to perform an adequate structure or piece capable to join the model andthe engine and, at the same time, equipped with this type of gauges to determinethe strains. The collected data will enable the computation of the forces applied tothe structure and consequently the thrust of the engine.

2.1.1 Strain gauges

A very interesting way to evaluate the external forces applied to a solid is by studyingthe resistance to this stress, which can be determined by measuring its mechanicaldeformation.

The electrical resistance strain gauges are used, once adhered to the solid, to beable to make a reading of the average deformation under their surface. They con-sist in a conductive or semi-conductive foil layer into a grid pattern mounted on aninsulating backing or carrier (Figure 2). The grid pattern, which is used to increasethe total length of the cable, provides more accuracy when measuring the strain inone direction, increasing the effective length of the wire in the direction of the strainstudied and minimizing the perpendicular one.

Figure 1: Behaviour, stretched cable. [3] Figure 2: SG main elements. [4]

5

When applying a force to a conductor or semiconductor cable, a variation on theelectrical resistance can be appreciated, being increased when the cable is stretchedand being decreased when the cable is compressed. In the Figure 1 it the variationof the cross-section of a cable can be observed, during its stretch or compression.When it is compressed, the cross-sectional area is increased resulting in a highercapability to let the electrons pass through, reducing then the resistance of the ca-ble. However, the overall resistance increases when the cross-sectional area becomessmaller due to the stretching of the material.

Characteristic parameters

The electrical resistance strain gauges have two main characteristic parameters: theiroverall resistance and their gauge factor.The strain gauges resistance values range from 30 to 3000 ohms, being 120 ohmsand 350 ohms the most common values used in stress analysis.The gauge factor (GF) is related to the resistance variation of the gauge with thestrain. Specifically, it is defined dimensionless as the ratio of the fractional changein the resistance to the fractional change in length along the axis of the gauge [5]:

GF =∆R/R

∆L/L=

∆R/R

�(1)

As it can be observed in the equation 1, the lower the value of the GF is, the lesssensitive is the strain gauge. With this factor, which is previously established bythe manufacturer of the strain gauge, the changes of the resistance due to the stresseffects on the structure can be read in terms of strain.

In order to be able to apply this correlation between the strain and the fractionalchange of the resistance, the structure to be measured must be working in the elasticregion of the stress-strain curve of its material. With higher strains, the materialwould reach the plastic region and the gauge wire would get a permanent deforma-tion which would not allow an adequate measurement of future mechanical stresses.The importance of designing a structure capable to work on this elastic conditionsis essential to ensure the success on the required measurements.

Selection criteria

The adequate selection of the strain gauges that are going to be used to implementthe measuring system is vital to optimizing its performance for the current operatingand environmental conditions. Other goals to achieve are minimizing the cost ofthe acquisition, ensuring an easy installation and providing reliable and accuratestrain measurements. An adequate combination of strain-sensitive alloy, carriermaterial, gauge pattern, dimensions, grid resistance, self-temperature compensationnumber, adhesive and protective coating for the application of design must be chosen.Therefore, the mode to select the correct parameters goes through looking for thecombination of them which best satisfies the installation and operating constraintsor requirements, considering some compromises.

6

• Strain-sensing alloysThis parameter is the most determinant one when designing the operatingcharacteristics of the strain gauge. Main commercial strain gauges are dividedon series, each one fixed and identified by their respective letter designations.This series are mainly related to the materials of the the measurement grid.Most commonly used ones are [6]:

– Constantan in self-temperature-compensated form.Considering the modern alloys, it is the most used one. It has an ade-quate gauge factor, relatively insensitive to temperature or strain level.It is characterized by good large strain measurements capability andgood fatigue life and elongation capability, when temperatures are notabove 65 ◦C. This kind of alloys can be processed for self-temperature-compensation (S-T-C).

– Annealed constantan.It is the most selected grid material for applications when very largestrains need to be measured (50000 µ�). It is very ductile but it is notrecommended for cyclic applications of strain.

– Isoelastic.Their fatigue life is superior than in A alloy, as well as their gauge factor.It is not commonly usable for static strain measurements, since its ther-mal output is so high. It is recommended when purely dynamic strainmeasurements are to be made and when a high output is needed.

– Nickel-chromium alloy with inself-temperature-compensated form.They have an excellent stability and a good fatigue life. It is recom-mended for extended static strain measurements over the temperaturerange from −269 ◦C to −26 ◦C. For short periods, they can be exposedto temperatures as high as 400 ◦C.

• Backing materialsThe backing material is responsible of providing electrical insulation betweenthe tested structure and the alloy, adhering this both elements and providingprotection to the grid pattern. Conventional strain gauges have two main back-ing materials: polyamide and glass-fibre-reinforced epoxy-phenolic. Polyamideis a tough and extremely flexible plastic. It is easy to handle and can workat temperatures from −495 ◦C to 175 ◦C. By the other hand, for applica-tions which demand a widest range of temperatures, the glass-fibre-reinforcedepoxy-phenolic is used [6]. Backing materials also have to match with thematerial chosen for the alloy grid so the most convenient combination must beselected.

• Gage lengthThe strain gauge length is the strain-sensitive length of the grid. As it can beobserved in Figure 3, the area of maximum strain is located in a small region,relative to the total length of the gauge. The indicated strain is computed bythe average of the strain distribution on the grid, so if it is too long, the strainindicated by the gauge will be too small.

7

The solution must find a comprise,since a very small gauge may introduceother problems. When stability un-der static strain, maximum allowableelongation and endurance when sub-jected to alternating cyclic strain aredetermining design factors, gauges withlonger lengths (more than about 3 mm)tend to show better performances. Figure 3: Strain along length [7]

They are easier to handle during installation procedures and provide improvedheat dissipation. Gage lengths can vary from 0.2 to 100 mm.

• Gage patternThe gauge patter defines the number of grids, their orientation and shape. Thestress analysis are done in a point of measurement. When the stress to study isuniaxial and the directions of the principal axes are known, a single-grid gaugeis the best option. In this case, the selection of the pattern depends on thefollowing parameters: the selection of the adequate gauge resistance, the gridwith and the solder tab definition, which has to be compatible in orientationand size with the space available in the gauge installation site.Regarding to the grid resistance, the most common values are about 120 ΩOhms, 350 Ω and 1000 Ω . A higher resistance means a reduction in the heatgeneration rate, an improvement in the signal-to-noise ratio and a decrease insome lead-wire effects.

For the strain gauge selection, despite several parameters involved have been de-tailed, the procedure can be reduced to only a few steps. Commercial gauges followtheir codes and provide different series. The process of selecting a strain gaugebrings compromise.

As it has been previously explained, the choice of parameters that tend to sat-isfy one specific requirement, can work against others. For example, in places withlimited installation space available and extremely high stress gradient, short gaugesseem to be the best option, however, they are characterized by a small maximumelongation, reducing useful life due to fatigue, less stable behaviour and greater dif-ficulty in its installation. It is necessary to reach a global commitment to satisfy anyset of circumstances, and to judge that commitment in the validity and accuracy ofthe data obtained.

2.1.2 Wheatstone bridge

In order to determine the value of the strain gauge resistance, the most commonsolution is the implementation of a Wheatstone bridge. It is an electrical configura-tion build by four resistors (they can be passive or variable) which form a circuit likethe one that is shown in Figure 4. A voltage measurement provides the changes in

8

resistance of one or multiple resistors. An input voltage is given (Vin) to know theoutput one (Vout) and notice its variation. Studying the circuit, the output voltagecan be written as [8]:

Figure 4: Wheatstone bridge

Vout = Vin

[R1

R1 +R2

R3R3 +R4

](2)

When all the resistors have the same value or just the current flowing in the leftbranch is equal to the one in the right branch it can be said that the bridge isbalanced. This means that there is no current flow through the ammeter and thevoltage Vout is zero. Then, and happens when:

R1R4 = R2R3 (3)

When one resistor increases or decreases the resistance, the bridge becomes unbal-anced. Then, a current flow exists through the ammeter and a potential differenceappears on it (Vout). Under this conditions, any variation in the values of one ormore resistors in any branch of the circuit would provide an Vout different to zero.Then, when one or more resistors are changed to strain gauges, it is possible todetermine (by knowing the output voltage of the bridge and considering equation 2)the relative variation of the resistance of the gauge and, consequently, the strain.Depending on the number of passive resistors substituted by gauges, some differentconfigurations of the Wheatstone bridge can be obtained [9].

Quarter bridge configuration

When replacing with a strain gauge one of the resistors, any change experimented init will unbalance the bridge and it will be noticed in the Vout variation. Consideringthat the bridge is initially in equilibrium (all the passive resistors have the same valueof the strain gauge when any stress acts on it), and taking into account equation 1,the equation of the bridge can be rewritten as:

Vout = Vin

[GF �

4 + 2 GF �

](4)

Two noticeable problems with this configurations are the non-lineal result of theoutput voltage and the impossibility to avoid the effects of the thermal changes onthe resistance of the strain gauge. This last issue could be solved using materialsfor the wore which have not huge changes with temperature, but as a reasonablesolution, a half bridge should be employed.

9

Figure 5: Quarter bridge configuration [10] Figure 6: Full bridge configuration [10]

Half bridge configuration

• Employment of a dummy gauge

A second gauge is added, replacing a constant resistor. However, this secondgauge is orientated 90◦ with respect to the first one (and so to the force prin-cipal direction). Then, this second gauge will not be affected by the principalforce and the strain will be on the transversal direction (�t), which is relatedto the main force direction strain (�a), by the Poisson coefficient(µ) of thematerial of the structure by:

�t = −µ�a (5)

The name of this second gauge is dummy gauge and it allows to thermallycompensate the bridge. When the temperature affects both strain gauges, theincrement of the resistance due to this phenomena would be canceled, as bothgauges are located at adjacent branches.The same objective is achieved by suiting the dummy gauge in a part of thestructure which is not affected by the stress but has the same thermal con-ditions as the first gauge. With this configuration, the problem of the non-linearity of the output voltage is not solved.

• Employment of two active gauges

In order to solve the remaining problem of the non-linearity of the outputvoltage signal, two gauges can be located on adjacent branches in order tosubtract the variations on the resistance or located in opposite branches tosum this variations.When both strain gauges are located in adjacent branches, the bridge is ther-mally balanced, but for the case of the gauges located in opposite branches,to avoid the effect of the temperature, two dummy gauges should be addedinstead of the other resistors and the bridge would turn up into a full bridge.For both cases the variation of the output voltage expression would becomelinear:

Vout = Vin

[GF �

2

](6)

10

Full bridge configuration

The full bridge configuration (Figure 8) is the most complete one, which providesmore precision on the measurements. In this case, all four resistors are replaced byactive strain gauges. They have the same nominal resistance, as the bridge shouldbe balanced in a non-stress situation. Then, the variations of the output voltagefollow the expression on equation 7:

Vout = VinGF

4[�1 − �2 + �3 − �4] (7)

When all the strain gauges are located in a configuration which ensures that theywill have the same value of strain in absolute terms, the value of the output voltageturns to:

Vout = VinGF �

4(8)

It can be observed that the output voltage for this case is proportional to the strainon the gauges. It facilitates the computations and the fact of having a higher voltagerange ensures higher precisions.

2.1.3 Signal-conditioning circuitry

Selecting the appropriate strain gauge is very important in order to ensure thecorrect functioning of the measurement device, as well as the design of the adequatesignal-conditioning circuit.It essential to get useful results and reliable. It includes an amplifier to get a readableoutput voltage signal from the Wheatstone bridge and a power supply. In additionto the gain stage, the circuit is useful for filtering out of the signal specific noisesources [11].

Figure 7: Diagram of the measuring system [11]

11

Bridge excitation voltage

The designed Wheatstone bridge can be supplied from DC or AC voltage, dependingon the amplifier system to be used. In the case of this design, the options to get thissignal must be studied. The power supply should be one able to offer an stabilizedvoltage signal. Voltage peaks can be responsible of critical errors when reading theoutput signal due to its low values.

The circuit can take advantage of a power source previously installed on the plane orintegrate an extra one. The type of excitation must be decided taking into accountthe amplifier that will be used on the circuit and the maximum permissible electricalloading on the strain gauges selected. The most common working ranges of voltagefor this applications are from 1 to 10 V.

Amplifier

As it has been previously explained, the variations on the resistance of the straingauges are very negligible so the output voltage from the Wheatstone bridge circuitis very small and difficult to interpret. The way to observe this voltage with moreaccuracy is to install an amplifier between the bridge and the signal reader.

Figure 8: Diagram of the amplifier circuitry [3]

An operational amplifier is a DC-coupled high-gain electronic voltage amplifier witha differential input and it is usually a single-ended output. It produces an outputvoltage that is typically millions of times larger than the voltage difference betweenits input terminals. Typically, the very large gain of the operational amplifier is con-trolled by negative feedback, which largely determines the magnitude of its outputvoltage gain in amplifier applications. [12]

Therefore, this kind of amplifier is used to convert and amplify the bridge exci-tation voltage (which its order of magnitude is typically in the millivolt range) intoa larger voltage, suitable for being converted to a digital signal or displayed.

12

Another device to consider is the instrumentation amplifier. The instrumentationamplifier has all the characteristics of the operational amplifier: differential amplifi-cation, high input impedance and low output impedance; but it has other importantcharacteristics: the gain can be modified by a resistance (RG) and it is constant overa wide band of frequencies. They are high-precision devices specifically designed forthe amplification of weak differential voltage signals, thus being suitable for circuitswith the characteristics that this study meets.

When selecting the amplifier, several considerations must be made. For example,the gain of the amplifier must be chosen depending on the output swing of the bridgeand the input of the A/D converter.

2.1.4 Measuring structure

An structure designed to withstand the loads of compression, tension and bendingmust be developed, able to hold the strain gauges that detect the strains that mustbe registered. Many structures that fulfil this requirements have been already de-signed and commercialized. They are called load cells and have several differentconfigurations depending on their function and the type of stress that must be anal-ysed.A load cell is a transducer used to convert a certain force into a measurable electricalsignal. This conversion between the mechanical magnitude of force and the electri-cal magnitude is carried out by the use of strain gauges as deformation sensors. Tobetter understand the function of a load cell, it can be modelled as a spring elementsubjected to a certain deformation by a mechanical force and this offers a resistantforce of equal value that opposes this deformation. This deformation is detected bythe strain gauges, located in strategically points of the load cell.

Load cells must accomplish some structural requirements. As previously mentioned,the structure must work always in the elastic regime, have strains that are in themeasuring range of the strain gauge and withstand fatigue properly.

In order to design the one required for the measurement of the thrust, some ofthe most adequate configurations have been investigated and studied thoroughly.There are countless commercial load cells that can be classified according to thedifferent shapes, ranges of weight measurement, application, different environments,static or dynamic measurements, among others.The principal types of load cells can be divided by its behaviour:

• Bending stress behaviour

• Shear stress behaviour

• Tension and compression behaviour

With the basis of its functioning or an structural combination of more than oneconfiguration, a design that fits the general interests of the project can be devel-oped. The most relevant configurations for the actual requirements of the study arepresented below.

13

Compression configurations

A good way to configure the design is with the incorporation of some elements thatcan be studied as bending beams. Then, one can consider that the point of applica-tion of the load to the structure translates linearity to the loading axis. This is thebest advantage of the multiple bending beams; to reduce ore erase non-linearities.In the following sections some options are presented.

Binocular geometry

With this kind of configuration, the sensitivity of the load cell to off-axis loads isminimized. Figure 9 shows a double beam load cell with a centred application ofa force. In this configuration, each bifurcation must communicate axial loads whilesimultaneously experiencing bending.One interesting attribute of this kind of load cell is that all the strain gauges thatconform the full Wheatstone bridge ideally experience identical axial strain, resultingin a cancellation of axial strain effects in the output of the bridge.

Figure 9: Double beam load cell 1 [13] Figure 10: Double beam load cell 2 [13]

As it can be observed in Figure 10, when a force of compression is applied in thecenter of the load cell, the superior beam shows a compressive strain in the boundersnear the force application and a tensile strain in the outer ones, as it would happenin a simple cantilever beam. When the force is axially applied and the load cell issymmetric, the values of the strain are equal, too. Then, the compensation of thefull Wheatstone bridge is also possible.

Both designs behave in a similar way. The aim of the differences between bothgeometries is to take the maximum advantage of the location of the strain gauges ineach case.

Axial ring geometry

As in the case of the previously explained configuration, this one also providesthe cancellation of axial strain effects in the Wheatstone bridge, as the strain gaugelocations experience identical axial strain. The laterals, where the strain gauges arelocated, compensate the non-interesting efforts. In the outer part of the ring, thereare tensile strains, while the inner part suffers compressive strains.

14

Figure 11: Axial ring load cell [13] Figure 12: Compression load cell [13]

Figure 11 shows the basic geometry of this type of load cells. By the other hand, formore complex applications, other designs are used, as the one on Figure 12, whichincludes the axial ring inside the beam design.

Bending beam configurations

The adventage of this type of load cell is the fact that they are almost insensitive tothe load application point that they produce equal and opposite axial loads withineach of the beams in response to extraneous couples. That happens because straingauges can be located in a way able to cancel the effects of axial loads.However, when high forces are applied, some bending can appear in the beams,producing small non-linearities.

Figure 13: Binocular and S-type load cells [13]

Binocular cantilever beams

Figure 12 shows S-type load cells (left) and binocular load cells (right). Binocularload cells are really popular for low force applications. The maximum strains occurin the strain gauge locations and have the same absolute value, offering the possi-bility of having a linear model of stress with the full Wheatstone bridge.

S-type beams

The S-beam load cells affected by stress generate strain zones in the centred hole.In this kind of geometry, the tensile and compressive stresses can also be symmet-rically compensated. They are normally used for tension stresses but can also bebidirectional.

15

2.2 Aerodynamic model

With the data acquired from the flight testing, a model of dynamic thrust based onstatic measurements has been developed. The aim of this section is to determine amodel able to describe the drag of the aircraft during the flight. The model comesfrom the thrust results obtained in the first section of this project and also from thedata that the measurement systems installed on the aircraft register.

Modelling the flight behaviour of a subscale jet aircraft is important in order tocompare the data obtained with the one predicted or expected, and be able to cre-ate an estimation of the performance of the flight in each condition or flight stage.Predicting the drag polar of the aircraft allows the manufacturer to modify the con-cepts of the design that compromise the efficiency and also to save characteristicperformance data related to the capability of the aircraft.

The lift and drag forces of the aircraft cannot be measured directly, but they can beobtained from some other measurable quantities. For the consideration of drag andthrust, Figure 14 summarizes the relevant forces acting during flight.

Figure 14: Forces acting during flight [1]

Where

FG is the gross thrust produced by the jet engine.

D is the drag of the aircraft.

DR is the ram drag, product of the flight velocity and the engine air mass flowrate [2].

L is the lift of the aircraft.

W is the weight of the aircraft.

α is the total angle of attack.

β is the total side-slip angle.

σ is the engine installation angle.

Lift and drag can be expressed as function of the other parameters that are actuallyknown or previously calculated. In the following sections a study of how each forceacts during flight will be developed. From the equivalence found in diagram forcesand the study of its behaviour both aerodynamic forces will be determined andmathematically described.

16

3 Method

The first objective of this project is the design, construction and implementation ofa system able to determine the thrust of the aircraft engine. All the developmenthas started researching the theoretical foundations that surround the technologyrelated to the design and manufacture of different types of load cells commerciallyavailable. This phase includes the investigation of the most common geometries ofthese deformable elements, their relevant characteristics, construction parameters,the mechanical behaviour they exhibit and the influence of these specifications inthe application they carry out.

Once concluded the preliminary study and background research, the design phasestarts. Several geometrical options have been proposed, in order to identify themechanical stresses that are generated in the deformable elements where the straingauges are going to be located.The different configurations have been implemented from ideas taken from the com-mercial designs and the knowledge that has been acquired during the investigationphase. The software used to extrude the different designs and to determine thevalues of the stress concentrations has been Solidworks, which includes a module todevelop stress structural analysis and simulations.

After considering all the proposed designs, one has been chosen, considering asselection criteria its mechanical behaviour, the impact that its installation on theaircraft would produce, the ability to reduce or eliminate the interference of un-wanted loads, its constructive facility, its operative advantages and the feasibility ofincluding the strain gauges in the deformable parts.Once the type of geometry to be optimized has been determined, several studies andanalysis have been developed in order to obtain the definitive geometrical parame-ters, reaching a compromise solution between the criteria previously stated.

After the manufacturing of the holding structure designed, the strain gauges need tobe installed. The electric system has been also implemented. Then is when the cal-ibrating process starts, ensuring the adequate behaviour of the measuring system.Finally, the data is collected and analysed. It provides an accurate informationabout the thrust experimented by the aircraft during flight, as expected.

The last objective has been the description of a thrust model that provides thedrag from information about the thrust measured and other factors that the air-craft measuring systems already collect. This allows an acceptable reproduction ofthe drag polar, which is essential to know and study the flight and aerodynamiccharacteristics of an aircraft.

17

3.1 Design of the measurement structure

The first decision that must be taken is the type of anchor that the engine will have,which allows to measure the forces that it exerts on the aircraft. In this case, thereare many possible options to consider, from modifying some parts of the existinganchor to replacing the original mounting system with another that fulfils bothfunctions. The degree of change, the difficulty of the new assembly and the addedweight must be taken into account when assessing the possible options.

3.1.1 Relevant criteria for the design

The structural design must always work in the elastic region, enduring fatigue andensuring deformation in measurable strain values. Furthermore, the most importantaspects to be studied for the mounting design are described below, as well as theirinfluence on decision making and the analysis method used to calculate the relevantaspects in each case:

• Weight of the support.The material used to design all the load cells is the aluminium alloy AW5754-H111, very common in similar applications and easy to obtain because ofits extended availability in the university workshop, to be able to make acomparative study of the total resulting mass calculated for each piece.

• Space required.There are numerous space restrictions. It must be checked that all designsmeet the requirements of available space and do not pose a problem for thenormal operation of the aircraft or produce any structural interference.

• Difficulty of implementation and assembly.All the necessary elements must be taken into account for the integration ofthe load cells in order to carry out an optimal design, which must not be verycomplex to fix.

• Interdependence of strains due to horizontal and vertical forces.The operation of the strain gauges allows to know the stress in a region dueto the strain that this region suffers. The forces exerted on the load cell arenot axial or unidirectional.Therefore, a design must be implemented to separate the loads of interest(thrust) from those caused by other reasons, such as loads due to the weight ofthe engine. Accordingly, when the aircraft performs an horizontal flight, thoseforces don’t suppose a problem, since they can be considered and compensatedin the resistance model or in the calibration method.The problem comes with any acceleration in the vertical plane, which provokevariable vertical forces that can cause stresses and strains in the piece thatinterfere with those caused by the thrust, being then difficult to distinguishbetween them. For this reason, the study about how to eliminate or minimizethe consequences of this forces on the strain gauge locations must be done.

18

3.1.2 Stress and strain preliminary analysis

In order to accomplish all the requirements, the proposed geometries must be morethoroughly studied. Solidworks CAD software has been used in order to create theconfigurations, determine the possible reactions to the all the expected forces andobtain an accurate computations of the main characteristics (weight, regime of de-formation, effects of the stresses,etc).To face all the problems described in the previous subsection, once indicated thepreliminary geometry of the piece, some structural analysis of the model must beimplemented. All the analysis consider that the piece is joined by screws to themounting of the motor and embedded by the other end to the frame of the air-craft. In order to simplify the model, the central part of the engine mountingis erased, and the forces are directly applied in the bounders of the mounting.

Figure 15: Engine mounting jointFigure 16: Bounder fixed to main frame

For the conditions of the geometry and the results of the sum of efforts, the studyis made based on the anti-symmetry of the two supports of the engine.

The simplified conditions studied are described below:

1. Maximum engine thrust: An uniform force is applied to the side of the lowermounting of the motor equivalent to half of the maximum thrust of the motor,80 N.

2. Engine weight in engine-off condition: A force is applied to the upper surfaceof the superior mounting simulating half of the weight of the engine (0.7 kg)and a gravity condition is applied to the entire assembly of g.

3. Engine weight in critical vertical acceleration condition: A force is applied tothe upper surface of the superior mounting, simulating half the weight of theengine (0.7 kg) and a gravity condition is applied to the whole assembly of 5 g.

T

Figure 17: Thrust simulation

g

m

Figure 18: Engine vertical forces

19

3.1.3 Initial design

The first consideration for implementing the new mounting system has been thedesign of a support that is incorporated on the top of the existing wooden beamsthat hold the motor (Figure 19).

Figure 19: CAD of the mounting system Figure 20: Real mounting system

This support allows to measure the horizontal force exerted by the thrust calculatingthe displacements suffered by the shear stress, as it can be seen in Figure 21. As ithas been already explained in the theoretical model, by the addition of strain gaugesat some critical points of interest, the thrust can be determined.

Figure 21: First solution proposed

This option has been discarded for several relevant reasons. For the specific case ofstudy, the structure requires an important stiffness to be able to design a sufficientlyrobust attachment. This critically increases the weight of the aircraft. The motormounting has some geometric characteristics that force the load cells to have a toolong length, due to the union by means of vertical screws.This makes it difficult to assemble the load cells to the main frame, because thecell practically fits the available vertical space and the distance between it and thebottom of the fuselage is too small. Consequently, the design of alternative modelsthat facilitate their incorporation to the aircraft and better adjust to the designrequirements must be redefined.

The main line design is intended to offer a solution which includes the strain gaugelocations in the beam that already supports the engine, creating a load cell withadequate geometry conditions to satisfy both objectives.

20

In the theory section, the main configurations of the common load cells have beendescribed. The possible designs that can be considered using the main load cellprinciples are shown up below.

Binocular configurations for tensile forces

First designs take advantages of the benefits of double ended bending beam loadcell principles. Two different geometrical configurations have been tested in orderto know how they would fit inside a structure inspired in the original mounting.

Figure 22: Configuration 1 Figure 23: Configuration 2

Both configurations are a good solution for studying the tensile force on the beamdue to the stresses that the engine mounting transmits. The mounting of the straingauges in both configurations is easy. For configuration I, the location of the straingauges is the same as Figure 10. The placing of the strain gauges in configurationII follow the Figure 9 strategy. In the Y-direction strain analysis for the maximumthrust simulation (Figure 5 and 12 Appendix A) the region of tensile and compres-sive strain can be observed, as expected.

As the joint of the mounting plate with the load cell beam is fixed with verticalscrews, the transmission of the horizontal forces is not uniform neither centred inthe X direction of the beam. This physical condition provides differences between thestresses and strains experimented on the upper region of the double bending beamand the lower one. This problem could be neglected with the posterior calibratingof the system or with the use only of two strain gauges in each beam, providing ahole Wheatstone bridge, taking advantage of the symmetry of the beam. In thatcase, if one of this configurations is chosen, a simulation without extruding the sym-metrical lower part would be implemented, concluding in a simpler geometry withwhich conserves the same applications and characteristics.The main problem for these configurations is the strain variation in the regions ofthe load cells due to the vertical forces that appear when the aircraft is performinga vertical acceleration. For horizontal flights, the vertical force and the strains (inthe direction of the strain gauge alloys) can be calibrated and neglected, as they areknown and correspond to the weight of the engine.

21

However, when the aircraft is climbing or descending, the acceleration changes thestresses transmitted by the engine to the mounting, and they consequently providenew strains that interfere in the measurements of the strain gauges.In both cases, the vertical forces produced when the engine is vertically acceleratingwith 5g (worst case considered), the tensile and compressive strain in the locationsand directions of interests can’t be neglected and suppose a big problem for themeasurements, being the configuration II better, without meeting the necessary re-quirements.

Axial ring configuration

The geometric configurations presented below stand out for their ease of construc-tion and structural simplicity. In both cases, as in the ones described above, theX-direction deformation in the ring can be measured on the upper and lower parts,or only in one of the two bifurcations and use the values of the other mounting beamto complete the Wheatstone bridge. For configurations III and IV, the location ofthe strain gauges is the same as Figure 11. In the X-direction strain analysis forthe maximum thrust simulation (Figure 19 and 26 Appendix A) the region of tensileand compressive strain can be observed, as expected.


Configuration III is more interesting than the previous configurations because it re-duces the problem of interference in strain measurements when there is a verticalacceleration in the model. As it can be seen in Figure 20 from Appendix A, thezones of maximum deformation are located near the embedding of the beam andaffect very little in the positions of the ring where the gauges are placed. This isone of the most remarkable advantages of this design.

The aim of the configuration IV is to try to implement the geometry III in a waythat is limited to the existing volume of the rectangular beam. For that reason,four slots that allow the tensile force to be experienced in the center of the ring arecreated. The result of the stain analysis with the performance of the engine is asexpected and its volume is reduced, to the detriment of the ability to reduce strains

22

due to possible vertical forces. For this consideration, as can be seen in Figure 27,the forces cause deformations that can compromise the measurements taken.

Compression beam configuration

Maintaining the design of load cells capable of measuring axial stresses and compres-sions, two more designs have been made also with the premise of taking advantageof only the space determined for the engine’s support beam. In this case, the be-haviour of the cell with the vertical forces is intended to be improved. By the otherhand, the designs have been thought to avoid the accumulation of tensions in theareas next to the slots, which were critical in case IV.

The locations of the strain gauges correspond to those in Figure 12.


The stresses and strains are distributed in the expected way along the parts and itis possible to reduce a little the stress peaks in areas far from the location of thegauges (Figures 36 and 43 from Appendix A).Anyway, the concerning issue of the strains that are created due to the vertical forcesdoes not disappear, and even gets worse.

The problem with this type of design is that they maintain the section of the supportbeam, but as slots are made in it to get the geometry of the load cell, those lessrobust areas tend to be more affected by the consequences of bending.

Bending beam configuration

It has been found interesting to study the behaviour of a bending beam load cellgeometry. Configurations VII and VIII have been designed with the objective ofintegrating that technology to the beams that fix the mounting plate of the engine.First one includes the load cell in the original shape of the beam. Since some prob-lems with this kind of designs have been reported in the previous two configurations,VIII tries to provide more robustness to fight against the bending strains.Load cells are positioned as the explained designs form figure 13.

23


Structural analysis from Configuration VII show the previous problems of bending-provoked strains on the location of the gauges. The increase of material in config-uration VIII eliminates this concerning issue, in the detriment of the sensibility ofthe strain in the gauges region. The stresses are not enough to be able to computethe tensile force applied to the whole beam.

One solution, after these studies, should be the implementation of a beam witha bigger slot in the center than the one in the second option, but also reinforcing thestructure to prevent the bending effects that presents the first design on the straingauge zone.

Other configurations

After the attempt to include all the studied load cell commercial types in the mount-ing design, an other interesting configuration has been implemented.

Configurations IX and X are designed with the intention of provoking a stress dis-tribution in the transverse fragment (considering the main direction of the beam)that causes a tensile strain in its rear part and a compressive one in the front part.


24

From the first proposed geometry, the minimum affectation of the possible verticalforces must be highlighted. All buckling is concentrated in the longitudinal thinbeams (Figure 70 from Appendix A). It is an interesting design to analyse morethoroughly to optimize its results.

In the second design tries to increase the section of the longitudinal parts whilereducing these from the transversal part to observe the consequences.The sensitivity of that region increases (Figure 77 from Appendix A) but some in-fluence of vertical forces also appears, although this is not as worrisome as in otherdesigns.

3.1.4 Alternative solutions

After acquiring a greater knowledge about the behaviour of the assembly structurewhen the load cell function is incorporated, the most concerning problems provokedby the previous configurations have been.Possible new ways to fulfil the requirements have been presented, preventing themfrom compromising or affecting measures. The most relevant concerns are relatedto the interference of vertical forces in the measurements of horizontal ones.The following solutions have been studied:

• Implementation of a bending beam on the fixed bounder.

Figure 32: Configuration XI Figure 33: Configuration XII

Both configurations locate the strain gauges at the same places than config-uration VII. With these geometrical variations, the shear stress on the loadcell produces the expected strain values as a response to the horizontal forcedue to the thrust. The main difference is that in these cases, when a verti-cal force appears, it affects almost in the same way and values the strains inthe region of the semi-beam (Figures 85 and 92 from Appendix A) where thestrain gauges are located. Then, the interference can be reduced by calibrating.

However, it is not possible to avoid all the strain due to the vertical forces.Configuration XI has a better response to this problem than configuration XII.

25

• Reinforcement of measurement sections to prevent bending.The main idea to try to minimize the strain due to the bending caused by thevertical forces transmitted by the mounting plate. Consequently, some pre-vious configurations have been mixed and reinforced in the places where thestrain gauge should be located in a way that ensures that the transversal forcesand stresses don’t affect in a critical manner the strain with same directionthat the strain gauges alloys.In order to avoid bending caused by the eccentricity of the horizontal forcesfrom the axis of inertia of the beam, it has been slotted to contain the mount-ing in its middle. All the following designs have incorporated this technique.

Figure 34: Configuration XIII Figure 35: Configuration XIV

Configuration XIII shows a geometry similar to a half-ring configuration. Thetransversal part added to the beam has been extruded to be more sensible totensile strains while the rest of the beam maintains a considerable slendernesswith the objective of grouping the stresses due to the bending effect provokedby the application of vertical forces.Observing the stress analysis (Figures 97, 98, 99 and 100 from Appendix A),the σx and �x are concentrated in the circular zone. When a critical verticalforce is applied, the most stressed and strained zone is the bending beam be-fore the extrusion made. Some strains affect the region of interest, but theyhave been reduced drastically compared to ones in previous similar designs.

Configuration XIV has been thought to reduce non-axial force effects on thebending load cell located in the bounder of previous XI and XII beams. Ithas been reinforced with a symmetric load cell in the lower part, to reduce thebending moment.As it can be observed in Figures 104 and 105 from Appendix A, the y−strainon gauge locations is reduced, but exists anyway. The problem with this kindof solution is that, since the load cell is located in the boundary which is fixedwith the aircraft main frame, the bending moment there is bigger than in partslocated more closer to the application of the vertical force (other boundary ofthe beam). However, increasing the roundness in the critical corners of thestructure, this strains could even be reduced to almost avoid interferences.

26

• Reduction of the unpleasant strains on gauge locations by slots.Another strategy is to design geometrical regions (far away from strain gaugeregions) easy to become critical when bending moments appear. It dependson the moments of inertia of cross-sections.

Figure 36: Configuration XV Figure 37: Configuration XVI

Configuration XV tries to highlight the tensile stress effects in the studiedparts. It is a mix between configuration I and III where the transversal beamssuffer shear stresses when the structure is under an axial tensile force. Theload cell region has been located near the point of application of the forces inorder to reduce as much as able the bending moment. Strain gauges locationfollows the same pattern than configuration I.Figures 109 and 110 from Appendix A show a significant improvement in forceinterference avoidance. When a critical vertical force is applied, the regionsof the strain gauges are practically non-affected. The behaviour of this zoneswhen horizontal forces are acting is the expected one, with tensile strains nearthe beam and a compression ones in the ends.

Configuration XVI comes from the geometry of configuration VII. It tries toreinforce the parts where the load cell is defined by increasing the height ofthe beam and promote bending strains in the other parts, including a big slotwhich facilitates bending.Stress analysis show that the structure acts similar that XII when horizontalforces are applied, but it reduces the affectation of the strain gauge areas whenvertical forces appear. The strain gauges have to be located in the middle ofthe inner section of the load shell in order to reduce better this affectation.The result of both designs is promising, especially the first one.

• Use of biaxial strain-gaugesStrain gauge allows are only able to measure the strain in its longitudinal di-rection. Advantage from this characteristic can be taken in order to neglectthe strains of bending caused by vertical forces. An investigation on theory ofstructures regarding to beams with tensile and bending forces has been made.

27

When this kind of biaxial forces are applied in a cantilever beam, the stress inthe longitudinal direction of the beam σx can be computed by superposition.Figure 38 shows the case of a beam exposed to bending and tensile stressesdue forces Fx and Fy:

Figure 38: Superposition of tensile stress and bending moment [14]

Then, the strain in the direction of the strain gauge measurements is theresult of summing the strain due to the tensile stress and the bending momentprovoked by the vertical force:

σx = σx(FX) + σx(FV ) =FHA

+FV x y

Iz(9)

Where:

– A is the section of the beam.

– x is the distance between FV and the studied cross-section.

– y is the distance from the beam’s neutral axis to the point of interestalong the height of the cross section.

When the horizontal force is applied with some eccentricity, as in the case ofstudy, the neutral longitudinal plane does not coincide with the xz plane ofinertia of the beam. It has the same effects than an axial horizontal forcesuperposed to a bending moment, as it can be observed in Figure 39.

28

Figure 39: Eccentric axial force [15]

And the axial strain results:

σx = σx(N) + σx(Mz) =FHA

+FH e y

Iz(10)

A combination between these two situations can be computed. Then, whenan eccentric axial force acts on a beam while a vertical force provides bending,the axial strain results:

σx = σx(N) + σx(Mz) + σx(FV ) =FHA

+FH e y

Iz+FV x y

Iz(11)

Starting from the previous premises, a way to implement the Wheatstonebridge avoiding axial stresses generated by the vertical force can be imple-mented.Two strain gauges are mounted in the direction of axial strain with one onthe upper side of the beam and the other on the lower side. The other twoact together as a Poisson gage and are mounted perpendicular to the principalaxis of strain with one on the upper side of the strain specimen and the otheron the lower side.

Looking at the upper and lower surfaces of the beam, the axial strain is com-pensated. Therefore, when the gauges are located like in figure 40, the bendingstresses are neglected.

Figure 40: Strain gauge proposed location [16]

Where the Wheatstone bridge has a full configuration. Two strain gauges canbe located in each beam or the whole of them in one.

29

Figure 41: Full bridge [17]

− R1 and R3 are the active strain gauge el-ements measuring compressive Poisson effect(−ν�).− R2 and R4 are the active strain gauge ele-ments measuring tensile strain (+�).− VEX , RL and VCH are the excitation voltage,lead resistance and the measured voltage.

This kind of configuration has some interesting advantages: having four activestrain gauge elements provides more accuracy to the measurements. Moreover,as a full bridge configuration, it provides temperature compensation, as wellas ensuring the rejection of bending strains. It also compensates for lead re-sistance and for the aggregate effect on the principle strain measurement dueto the Poisson’s ratio of the material.

The cross-section must not be too slender or some buckling will appear due toaxial forces.

Figure 42: Configuration XVII Figure 43: Configuration XVIII

In order to ensure that the eccentric situation of the axial force applicationdoes not compromise the results of the axial strain, the best way to locate thestrain gauges is using the top surfaces of both mounting beams to avoid thedifferences that can appear between the upper and lower surfaces.

Moreover, the eccentricity provokes bending in the slimmer region. For com-pletely avoiding this issue, a slot to fit the mounting plate of the engine insidethe beam can be designed, as in some previous configurations.

Both configurations XVII and XVIII are solutions for this kind of bidirectionalstrain gauge positioning. Configuration XVII has the thinner part located nearthe point of force application. It increases critical strain in this location, tosuit there the gauges. Configuration XVIII has a cross−sectional area with agood performing in cases of bending.

30

3.2 Selection of the preliminary geometric de-

sign of the measurement device

In order to select the most suitable geometrical configuration, a list of relevant cri-teria which determine its functionality, utility and effectiveness has been developedbelow.Each parameter to fulfil has a different relevance in the decision taking. Therefore,different punctuations which show their priority have been given and all the designsare evaluated following the detailed criteria.

[ A ] Interference of horizontal forces.All the designs consider that the measurements on both structural beams canbe considered as equals because of its symmetry. Actually, the measurementsof the two parts of the mounting structure are not necessarily equal. Duringsome manoeuvres, as row moments, the weight of the aircraft can affect bothvertical and horizontal axis of the aircraft.Also gyroscope effects compromise the equality of measurements. The propul-sion engine has parts which rotate at high speed possessing considerable an-gular momentum. Whenever aircraft changes its course (for example a yawmoment), gyroscopic forces are introduced; these may be of considerable mag-nitude if the rate of turn is large. Since an aircraft moves in three dimensions,rotation about all three axes may occur simultaneously during a manoeuvre,and this adds to the complication. These forces, though not large in magni-tude, introduce variations in the strain measurements of the gauges and needto be considered and neglected.When the measurements are done in both beams separately, it is ensured.However, when only one Wheatstone bridge is used, some considerations mustbe done in order to avoid this issue.

[ B ] Interference of vertical forces.As previously commented, it is important to avoid the interference of thevertical forces when measuring the strain of the beams. Vertical forces producesome bending effects which create non-wanted strains.When the strain gauges are located on the neutral axis of the bending, theyare not affected by the strains due to variations of the weight of the enginedue to vertical accelerations or forces that appear when some manoeuvres aredone. Also, biaxial strain gauges can be connected in a way in order to reducethe effect of this elements on the thrust measurement.

[ C ] Weight of the design.As all the mounting structures designed are made from the same material (analuminium alloy), the sizing of the geometry of the pieces is the most relevantparameter of this criteria. The weight is important for the actual balance ofthe aircraft. The new mounting system should not overpass a weight of morethan 1 kg. This criteria is concerning when the weight is too high, but notmuch decisive when the difference is low and doesn’t affect the change of theCG position of the aircraft in a critical way.

31

[ D ] Geometry and sizing.An important precept when choosing the design is its inclusion within thestructural system of the aircraft. A support that fits inside without compro-mising any essential part of the structure and that minimizes the necessarychanges for its incorporation is needed.Beams which incorporate the load cell design inside its original geometry willbe better appreciated and also those which don’t need huge changes in thedistribution of the existing elements for their installation.

[ E ] Sturdiness of the subjection system.The fact of working in elastic regime is essential for the well-behaviour of themeasuring system. All the pieces have been designed to accomplish this state-ment. However, other structural parameters must be considered, as well. Thesturdiness of the design is important, as vibrations of the engine mountingdue to its configuration should be reduced as much as possible. By the otherhand, a notable bending of the beams because of the vertical and horizontalforces must also be avoided. For this reason, sturdy designs will be betterappreciated, as the engine needs to be correctly fixed inside the aircraft.Designs which can suit an extra diagonal support between the measuring sys-tem and the fixing on the aircraft frame will have a better response in orderto avoid bending effects.

[ F ] Simplicity of the manufacturing.An easy manufacturing of the load cell structure should be ensured in order toobtain the piece in a reasonable time and as similar as possible to the originaldrawings, ensuring boulders and simply geometries.

[ G ] Ease of strain gauges installation.The surfaces where the strain gauges need to be located should be enoughbig to ensure that they can fit there without also covering non-wanted extrasurfaces. Moreover, this places should allow the easy installation of the gauges.This criteria depends on the operative length and width of the strain gauges.Most common ones are commercialized from 3 mm to 6 mm so the locationplaces must ensure measurable dimensions of this proportions.

[ H ] Budget of the whole designSince most of the structures have been thought to be made of an aluminiumalloy, the price depending on the size and geometry of them is not a concerningparameter due to the small variations that the changes produce in the man-ufacturing of the piece. Regarding to relevant changes on the budget, theymust be focused on the number of strain gauges in use, as well as the possibleusing of more than one amplifier or maybe the need of adding a junction box.The junction box is needed when more than one Wheatstone bridges are used,in order to obtain one single value of voltage or strain. Two Wheatstonebridges also imply more strain gauges to complete the design, which meanincreasing the cost too. To obtain the wanted temperature compensation, aminimum of four strain gauges (one full bridge configuration) are needed, andregarding to cost criteria, it becomes the most convenient design.

32

A table which summarizes the punctuation of all the designed configurations foreach selection criteria is presented below:

A B C D E F G H Σ

C-I 18 /20 8 /20 3 /5 10 /15 15 /15 4 /5 10 /10 10 /10 78

C-II 8 /20 8 /20 3 /5 10 /15 15 /15 4 /5 4 /10 8 /10 60

C-III 18 /20 8 /20 4 /5 12 /15 15 /15 5 /5 10 /10 5 /10 77

C-IV 18 /20 16 /20 5 /5 15 /15 15 /15 5 /5 10 /10 10 /10 94

C-V 18 /20 16 /20 5 /5 15 /15 15 /15 4 /5 4 /10 10 /10 87

C-VI 18 /20 16 /20 5 /5 15 /15 15 /15 3 /5 0 /10 10 /10 82

C-VII 18 /20 16 /20 5 /5 15 /15 15 /15 4 /5 2 /10 5 /10 80

C-VIII 18 /20 12 /20 4 /5 10 /15 15 /15 4 /5 0 /10 5 /10 68

C-IX 8 /20 12 /20 5 /5 15 /15 15 /15 4 /5 2 /10 8 /10 69

C-X 8 /20 12 /20 5 /5 15 /15 15 /15 4 /5 2 /10 8 /10 69

C-XI 18 /20 8 /20 3 /5 5 /15 5 /15 4 /5 10 /10 10 /10 63

C-XII 18 /20 8 /20 3 /5 5 /15 5 /15 4 /5 10 /10 10 /10 63

C-XIII 8 /20 8 /20 5 /5 10 /15 15 /15 4 /5 8 /10 8 /10 66

C-XIV 18 /20 8 /20 3 /5 3 /15 5 /15 3 /5 10 /10 5 /10 55

C-XV 18 /20 8 /20 4 /5 10 /15 15 /15 5 /5 10 /10 10 /10 80

C-XVI 4 /20 12 /20 4 /5 10 /15 2 /15 2 /5 2 /10 5 /10 41

C-XVII 18 /20 15 /20 5 /5 15 /15 15 /15 5 /5 10 /10 7 /10 90

C-XVIII 18 /20 15 /20 4 /5 15 /15 5 /15 3 /5 10 /10 7 /10 77

Table 5: Punctuation of each designed configuration

The Table 1 shows that the most suitable configuration is C-IV. The combinationof the characteristics and advantages of this design make it the best compromisesolution. The technology of using biaxial strain gauges (Configuration XVII) alsohas acceptable results.

3.2.1 Selected configuration: C-IX

In this paragraph the verification of the accomplishment of each requirement for thechosen configuration have been detailed.

The most concerning issue that the mounting has to ensure is the abolition of theinterference of other forces acting while measuring the thrust. The selected designshow a good behaviour when facing this problems and is able to measure thrustwithout mistakes provoked by the other existing forces.

Regarding to the forces related to the weight of the engine and the vertical ac-celerations which the aircraft can experience, if the strain gauges are located in thex-z neutral plain of the geometry, then there is no compression or tension due tothe resultant bending affecting the strain measured. When placing there the straingauges, as shows Figure 44, half of the wire notices the compression and the otherhalf the tensile strain, globally compensating these deformations.

33

Figure 44: Strain gauges locations

Focusing on the interferences due to gyroscopic effects and horizontal accelerations,the way to solve this errors on thrust measuring is to configure the Wheatstonebridge electrical circuit in a way that ensures the correct compensation. When thethrust is higher in one of the two symmetrical mountings, the thrust in the otherone is reduced in a equal absolute value. Therefore, the branches of the bridge mustbe connected taking advantage of this situation, as shown in Figure 45.

Figure 45: Wheatstone bridge configuration

In order to obtain a compensated VCD, the branch AB must be balanced, as well asthe branch CD. An increase of the thrust in the beam A comes with a decrease ofthe same value in beam B.Consequently, the increase of tensile strain measured in beam A (affecting on VAC)will compensate the decrease of compressive strain measured in beam B (affectingon VCB). Also, the increase in compressive strain measured in beam A (affectingon VAD) will be compensated by the decrease in tensile strain measured in beam B(affecting on VDB).This way of connecting the electrical resistive circuit ensures the compensation ofdisequilibriums and obtains the medium thrust which affects the whole structure.

Regarding to the size of the beam, this design respects the dimensions of the originalmounting, having only some slots which define the load cell behaviour. For this rea-son, no extra space is needed inside the structure of the aircraft and configurationIV contemplates the best scenario.

34

Consequently, this configuration is pointed as one of the lighter designs. Not addingtoo much weight in the aircraft helps in maintaining the centre of gravity in thedesired area.

This geometrical design allows some internal changes that ensure a great stiffness toface all the loads that the engine transmits to the structure of the aircraft. Locat-ing the load cell design more proximate to the engine mounting attachment is onerestraint in order to reduce the bending moment in the studied section and also pro-vide enough non-measuring space to install an auxiliary diagonal support to betterdistribute loads and avoid bending in the rear part of the mounting beam, after theengine fixing plate and the load cell configuration.

Fixed to themain frame

Enginelocation

Auxiliarmountings

Modified enginemounting plate

Modified enginemounting plate

Figure 46: Design modifications

The chosen design is characterized by its ease of manufacturing and its geometricsimplicity. These are advantages that save production time and avoid possible de-sign errors. Also, if a change or improvement is needed, it can be achieved in areasonable amount of time without increasing the costs in a worrying way.

The geometry ensures enough wide surfaces to locate the strain gauges, with rea-sonable spaces that facilitate the manipulation and installation of this measuringelements. The locations of the strain gauges have been specified in Figure 45. Thosewhich measure the regions that experience compressive strain have are attached toa curved surface which could modify the measurements. Later, the way to considerthis curvature and how to compute the effects on strain measurements will be de-tailed.

The most remarkable issue of the budget is the number of strain gauges that aregoing to be used. In order to maintain the accuracy of the measurements, the fullbridge configuration is the Wheatstone bridge connection chosen. Therefore, thepossibilities vary between using 4 or 8 strain gauges. Ensuring that the thrust canbe adequately measured with only one Wheatstone bridge is the best way to reducethe costs of the project. Also, the use of uni-axial strain gauges instead of bi-axialones reduces more the costs. The proposed design satisfies both considerations.Only four strain gauges, connected in a full Wheatstone bridge circuit, compute thestrain in four strategical positions to obtain concrete results of the dynamic thrust.

35

3.3 Detailed design and implementation of the

measuring device

Once the geometrical configuration and load cell measurement methodology whichbetter present a solution for getting thrust data have been chosen, the sizing andfurther detailed description has been developed. The aim is to obtain the final designwhich will be manufactured and installed into the aircraft.

3.3.1 Strain gauge selection

Strain gauges have been purchased in HBM [18]. Four SG with the same charac-teristics are needed. First decision depends on the type of strain which needs tobe measured during the stress analysis. In the case of study, since the strain isuni-directional and in the principal stress direction, linear strain gauges with onemeasuring grid are needed.

In general, the length of the gauge is limited by the dimensions of the specimenor the area to be measured. It also depends on the material: if it is inhomogeneous,larger strain gauges are needed. When a local strain needs to be analysed, smallergauges work better. For the case of study, lengths between 3 and 6 mm represent agood solution.

HBM SG are categorized by some of their functional parameters, and ranged infour different series, depending on their applications.The Y SG series are the universal strain gauges for stress analysis and simple trans-ducers. They are easy to handle, robust, flexible, with many geometries and withnominal (rated) resistances available. The C SG series are used for measurementsat extreme temperatures, when they can reach values from -200◦C up to +250◦C.For the manufacturing of transducers the G SG series are widely used. They haverated resistences of 120 or 350 Ω. Finally, V SG series are encasulated strain gaugesfor experimental stress analysis. The strain gauges selected for the design are fromthe Y series, with a measuring grid made of constantan and a measuring grid carrierof polyamide [18].

The selection of the resistance of the strain gauge dep

design and manufacturing of a thrust measurement system ...1228202/fulltext01.pdf · design and...

Documents