nenl te

mraTehra

Accepted 5 September 2014Available online 16 September 2014

Keywords:Six-componentForcemoment balance

es th

To design the structural parameters of the balance, were used derived equations as well as

wired together as a Wheatstone bridge circuit. The electri-cal signals are proportional to the forces applied on themodel. By considering the relationship between the

nt of force andith the inure separatre two imp

features of its performance [1]. Each of these facinuenced by structural design, fabrication, and ction. At the structural design stage, the balances abilityto measure separate components and the linearity of thebalance depend on the selected dimensions, structuralform, and materials. These parameters are obtained byconsidering the design-related requirements and issues.

http://dx.doi.org/10.1016/j.measurement.2014.09.0110263-2241/ 2014 Elsevier Ltd. All rights reserved.

Corresponding author. Tel.: +98 2177240540x2982; fax: +982177240488.

E-mail address: mnouri@iust.ac.ir (N.M. Nouri).

Measurement 58 (2014) 544555

Contents lists available at ScienceDirect

Measure

journal homepage: www.elseviponents, and the forces exerted on the model cause strainin the exural elements. The strains produced at speciclocations on the elastic components are converted to vari-ation of electrical signals by strain gauges that have been

dently measuring a specic componemoment with minimum interactions wof other components. The ability to measponents and the linearity of the balance auencee com-ortanttors isalibra-Measurement techniques are needed in water tunneltests in order to estimate different operating parametersof hydrodynamic devices. Multi-component, strain-gaugebalances normally are used to measure the hydrodynamicforces and moments in water tunnels. The force balance isa complex, elastic structure with a number of exural com-

the model in the water tunnel can be measured directly.Based on the design of their measuring elements, these

balances can measure from one to six components. Theseparation of components from one another is achievedthrough an appropriate design and wiring scheme of elas-tic elements. Each element should be capable of indepen-Strain gaugeWater tunnelDesign evaluation

1. Introductionthe nite element method in an iterative process. At every step in this process, the dimen-sions obtained from the derived equations were determined by considering the nominalstrain. The nite element method was used to demonstrate the manner in which the strainwas distributed and the reliability of the quantities obtained from the derived equations.To evaluate the designed balance, the strain distribution, linearity, stiffness, and the bal-ances ability to produce separate component outputs were investigated. The results thatwere obtained indicating that the designed structure satised all the design criteria. Arst-order model was used to calibrate the balance. The evaluation of the sensitivity matrixshowed that the error that resulted from the effects of the non-linearity associated with theapplied loads was less than 0.05%.

2014 Elsevier Ltd. All rights reserved.

applied force and the balances output signal and by usingthe calibration models, the forces and moments exerted onReceived 8 April 2014Received in revised form 31 July 2014

component balance. This balance is used to measure the forces and moments in modeltests conducted in the water tunnel at the Iran University of Science & Technology (IUST).Design methodology of a six-compoforces and moments in water tunne

N.M. Nouri , Karim Mostafapour, Maryam KaSchool of Mechanical Engineering, Iran University of Science and Technology,

a r t i c l e i n f o

Article history:

a b s t r a c t

This article describt balance for measuringsts

n, Robab Bohadorin, Narmak, Iran

e methodology used in the design and evaluation of a new, six-

ment

er .com/ locate /measurement

transducers [68].The proper structural design of a balance requires an

N.M. Nouri et al. /Measurement 58 (2014) 544555 545accurate knowledge of the design criteria and adherenceto these criteria. No explanation is presented concerningthe extent to which each of these criteria exerts its inu-ence, because their relative importance depends on thetype of balance and the specic objective for which it willbe used. In addition, these criteria are not independent,and many interactions exist between them. Therefore,the method used for the structural design can affect thecost and accuracy of the design. Different balances havebeen designed specically based on the requirements ofwater [912] and wind [1315] tunnels. This type of thebalance is used in water tunnel where the frequency testis less than 10 Hz. Also, force balances were developed tomeasure aerodynamic forces and moments on hypersonicmodels in ground-based test facilities [16,17]. This mea-surement technique overcome the limitation with shorttime test and can be used for measuring force and momenton the cavitation test model in a water tunnel. The princi-ples that govern the design of these balances were outlinedin [18,19]. However, there has been no mention in existingdocuments of the process of determining the parameters ofthe structural design. There is a lack of information regard-ing the process-performance relationships of transducersdue to highly-competitive market.

This article describes the methodology that was used todesign a new, six-component balance. This balance is usedfor measuring the forces and moments in testing models inthe water tunnel at the Iran University of Science & Tech-nology. The innovative methodology applied for the designand evaluation of a new, six-component balance that it isused for measuring the forces and moments in water tun-nel tests is the novel contribution of this article.

2. Design requirements and considerations

The proper structural design of a balance requires accu-rate knowledge of the design criteria and adherence tothese criteria. No explanation is presented concerning theextent to which each of these criteria exerts its inuence,because their relative importance depends on the type ofbalance and the specic objective for which it will be used.In addition, these criteria are not independent, and manyinteractions exist between them. The requirements andconsiderations for the design of the balance are listedbelow:Past research in this area focused on the performance char-acteristics of the elastic components of a force transducerin order to obtain satisfactory performance. Elastic materi-als may exhibit different hysteresis responses, and theselection of the type of material for the elastic componentscauses different hysteresis errors in force transducers[24]. The sensing element of the sensor should bedesigned in such a way as to minimize interference errorsand to provide the proper distribution of strain at variousstrain gauge locations. Some supplementary informationgiven in [5] and the nite element studies were used toanalyze the strain distribution on similar types of force1. In view of the limitations on the size of the model, thediameter of the balance cannot exceed 20 mm.

2. The ranges of forces and moments (nominal capacities)that the balance can measure were dened as follows:

Drag force : FD 0 to 60 N

Lift force : FL 50 to 50 N

Side force : FY 50 to 50 N

Pitching moment : MY 1 to 1 N m

Rolling moment : MX 1 to 1 N m

Yawing moment : MZ 1 to 1 N m3. Large signal strains with an appropriate safety factor

(acceptable sensitivity of the Wheatstone bridge): toraise the sensitivity of the Wheatstone bridge, fouractive strain gauges are used in the circuit. Bending-type strains are produced in the locations where thestrain gauges were installed. The maximum output ofthe Wheatstone bridge was assumed to be about1.5 mV/V 10% [19].

4. High stiffness: As the stiffness of the exural elementsincreases, the interference error decreases.

5. The deection of the balance with respect to its longitu-dinal axis should be minimized because it causes thesolutions to become non-linear.

6. The uniform distribution of strain where it is measured:since the electrical output of each measuring element islimited by the maximum allowable strain at the loca-tion of the strain gauge, this level of strain should existuniformly throughout the entire measurement networkso that the signal is maximized and the performance ofthe balance is improved. To properly distribute thestrain, the maximum difference between the strainsproduced at the measurement locations is consideredto be less than 15% of the maximum strain value [20].

7. Design for the ease of machining and installation ofstrain gauges: one of the most important design consid-erations is the ease of installation of strain gauges andthe ease of the machining operation [21]. If the exuralelements are designed in such a way that the installa-tion of the strain gauges and the machining processare difcult to perform, high costs will be imposed onthe system.

8. High strength and low hysteresis [19]: loading in excessof the dened design specications may cause internalstresses in the force-measuring system. By selecting amaterial with high strength and low hysteresis, therewill be less deviation from the linear state.

3. Structural design of the balance

The structural design of the balance allows it to mea-sure the applied forces and moments along the coordinatesattached to the axes of the model. Flexural elements andstrain gauges were used for the design of the balance,and each force or moment component was proportional

to the strain produced on a specic elastic element. Fourmeasurement sections were designed to measure the sixcomponents of force and moment (Fig. 1). The separationof forces and moments was made possible by the designsof the sections of the balance and by the way the straingauges were positioned. Fig. 1 shows the balance that wedesigned, and the measurement sections included:

The drag-measurement section: Since the balance wasdesigned so that it was positioned along the axesattached to the model, the drag-measurement sectionwas designed in such a way that the strain producedas a result of axial force at the locations of the straingauges was bending strain type. The section containsfour gauges on each of the two sides of the exuremember, as shown in Fig. 1(c). Gauges D1, D2, D3 andD4, were installed on beams at the beginning and endof the section. The four gauges are connected togetherto form one Wheatstone bridges, as shown. Thesebeams were able to withstand the loads of ve othercomponents, but they were relatively exible in thedirection of axial load.

Rolling moment section: The rolling moment section isa cross-shaped surface made up of four rectangularbeams (two horizontal and two vertical). The sectioncontains four gauges on each of the two sides of theexure member, as shown in Fig. 1(b). Gauges R 1, R2,R3 and R4, were installed on each of the four beams atthe end of the section. The four gauges are connected

moment created compressive strain at two of thestrain-gauge locations and tensile strain at the othertwo locations. This cross-shaped section was very sensi-tive to moment changes, but it had relatively high stiff-ness against the other components. For this cross-shaped section, the deformation created by the rollingmoment was directly converted to pure bending inthe beam.

Pitching section: This section consisted of three rectan-gular beams. The lift force and the pitching momentwere measured by this section. The strain gauges wereinstalled on the side beam, and they were symmetricalwith respect to the central beam. The eight gauges areconnected together to form two Wheatstone bridges,as shown Fig. 1(a). The pitching moment was almostcompletely converted to tension or compression in theside beams. By appropriately wiring and arranging thestrain gauges on the section, the lift force and bendingmoment can be separated and measured indepen-dently. The beams were made sufciently thin so theywould have the required sensitivity, and they providedthe stiffness that was required and the minimumamount of deviation from the centerline.

Yawing section: The yawing section resembled thepitching section with the exception that the yawingsection was rotated 90 about the middle axis relativeto the pitching section (Fig. 1(d)).

This balance is used for measuring the hydrodynamic

comp

546 N.M. Nouri et al. /Measurement 58 (2014) 544555together to form one Wheatstone bridges, as shown.The application of load resulting from the rolling

Fig. 1. Six-component balance for the measurement of three forceforces acting on model autonomous underwater vehicles(AUVs) such as, submarines, torpedoes in a water tunnel.

onents and three moment components by means of strain gauges.

The above balance are placed inside the test model.The model shape shown in Fig. 2 is the length to diameter(L/D) ratio of 9.5. The total length and maximum diameterof the model was 0.333 and 0.035 m, respectively. Themodel consists of three anodized aluminum pieces which

balance. The bending stress at the location of the straingauge location is dened as:

r MIC

3

variety of meshing options. Grid independence wasproved by taking a coarse, medium and a ne grid. All

and b

N.M. Nouri et al. /Measurement 58 (2014) 544555 547are connected to each other in the longitudinal direction.At the aft end of the model, some clearance from the stingwas allowed to provide for model deections. Thus, thereis no contact between sting and the model and the end-point of balance is xed to sting.

4. Design methodology

The measurement sections are the regions in the bal-ance where the strains are measured. These sections weredesigned in such a way that the applied loads produced abending type of stress at the locations of the strain gauges.In the given design, the design variables were the locationsat which the strain gauges were installed and the dimen-sions of the exural elements. These dimensions weredetermined from the design considerations, and they werebased on the nominal capacity and the nominal strain. Todesign each of the measuring element, the structuralparameters were extracted using the equations and thenite element method in an iterative process. In this pro-cess, at every step, the optimal dimensions obtained fromthe derived equations were calculated by considering thenominal strain. The nite element method demonstratedthe manner in which the strain was distributed and thereliability of the dimensions obtained from the derivedequations.

4.1. Fundamental equations

The ultimate goal was to fabricate a balance in whichthe selected section was sensitive in the direction of theconsidered component and insensitive in the other direc-tions. This objective can be accomplished through theproper design of the sections and appropriate wiring tech-niques. Four active strain gauges were used to measureeach component of the balance in the Wheatstone bridgecircuit. Eq. (1) shows the relationship between the strainthat was produced and the output of the Wheatstonebridge [19].

VVe

14ke1 e2 e3 e4 1

where V is the output voltage, Ve is the input voltage, k isthe gauge factor, and e1,2,3,4 are the amounts of strainobtained from the gauges. The measured strain is equal to:

e rE

2

where r is the stress measured by the gauge, and E is theYoungs modulus of the material used to construct the

Fig. 2. Test modelfurther analysis was done using the ne structures grid.In order to obtain the distribution of the strain, rst,the measurement sections was simulated by some con-straints. In simulation, the sections were isolated fromthe balance, and their locations of contact are replacedby different constrains. Strain probes were placed at rel-evant locations where strain gauges need to be mounted.Strain distribution was analyzed based on maximumloads throughout this study.

alance assembly.where IC and M are the section modulus and the momentproduced at the location of the gauge, respectively. Consid-ering the design of the balance in which the strains gener-ated at the locations of the strain gauges are equal, theratio of the input signal to output signal for the completebridge can be simplied as follows:

VVe

ke 4

4.2. Finite element method

A nite-element model can be thought of as a system ofsolid springs. When a load is applied to the structure, allelements deform until all forces balance. In this study thenite-element analysis were carried out in order to analyzethe stress and strain distribution on the measurement sec-tions. FEM was used to evaluate the strain values in thearea where the strain gauges were bonded. These valueswere compared with those obtained from the equation.For an analysis of the measurement sections, the followingassumptions were made.

(1) The elastic properties of the measurement sectionswere independent of direction.

(2) The model was assumed to be perfectly elastic. Aperfectly elastic model was obeyed of Hooks law.

(3) There were no body forces on the measurementsections.

(4) The load distributions on locations of contact of themeasurement sections were uniform.

The FE meshes consisted of linear tetrahedral ele-ments, the tetrahedral elements can adjust more easilyto the curves and spline surfaces of the model, preservingits proportion form. The solid structure is meshed usingNETGEN [22]. It is a powerful 3D tetrahedral mesh gener-ator that can handle complex geometries and a great

5. Design of the measuring elements

Selecting the types of materials for the balance requireda lot of attention and forethought, because these decisionscan have a signicant effect on the cost and performance ofthe balance. The process of selecting the materials includedthree major categories that had to be considered, i.e. (1)mechanical characteristics, (2) thermal characteristics,and (3) a number of other characteristics that can be gen-erally referred to as fabrication considerations [20]. Twoof the most important and effective factors in the selectionof a material is the amount of stresses it will incur and theaccessible space based on the considerations and require-ments of the design. Considering the said factors and alsothe fact that the balance will be placed inside a water tun-nel, TiAl6V4 was the material of choice. Based on the

mined from the relation (3).

r 3FDL2bh2

5

where r 82:5 MPa and FD 60 N. The initial values ofdimensions L, h, and b were approximated by Eq. (5). Themanner in which the strain of this section could be distrib-uted in the longitudinal direction was investigated byapplying the load of FD 60 N. In order to obtain the distri-bution of the strain, rst, the drag section was simulated bysome constrains. In this simulation, the section was iso-lated from the balance, and their locations of contact arereplaced by different constrains. After the convergence ofthe solution, the uniformity of the strain distribution andthe interference effects were examined and, if necessary,the dimensions were corrected again using Eq. (5). Thisprocedure was continued until the dimensions that wereidentied satised the design criteria. The distribution ofthe strain along the installation line of the strain gauges

ution

548 N.M. Nouri et al. /Measurement 58 (2014) 5445555.1. Drag section

Fig. 3(a) shows the structure of the drag section. In thegure, h is the thickness of the beam, b is the width of thebeam, and L is the distance between the two strain gaugeson the beam. This section was designed in such a way thatit acts like a beam that is xed at both ends in response tothe applied axial load; the amounts of strain produced atthe two locations of the strain gauges due to the axial loadare equal. By considering each beam as a beam with twoxed ends and substituting M FDl2 , l L2, C h2 andI 112 bh

3 into Eq. (3), the amount of bending stress at thelocations of the strain gauges can be obtained as:

Fig. 3. Structure and strain distribdesign considerations, the maximum output of the Wheat-stone bridge for the specied design can be considered tobe about 1.5 mV/V Since the exact value of the gauge factoris not known in the design stage, we assumed that it was 2,i.e. k = 2. Using Eq. (1), the amount of nominal strain at thestrain gauge location was calculated as 750 microstrainmicrostrain 750 106 m=m. By inserting the amountof strain obtained and the Youngs modulus of the selectedmaterial E 110;000 N=mm2 into Eq. (2), the designstress was calculated at the location of the strain gaugebased on the maximum load of 82.5 MPa. Based on thisamount of calculated strain and the design considerations,the dimensions of the measuring sections were deter-for the nalized dimensions is shown in Fig. 3(b). The dif-ference between the values of strain obtained from Eq. (5)and from the nite element method at the locations of thestrain gauges was 5%. Therefore, the results provided bythe FEM were considered to be reasonable consideringthe sensitivity criterion of ea 750 ls 10% for nominalstrain.

5.2. Rolling moment section

Fig. 4(a) shows the structure of the rolling section. Inthis gure, h, b, D and L are the thickness of the beam,the width of the beam, the diameter of balance, the dis-tance of the installed strain gauge from the middle of therolling section, along the axial direction, respectively. Thegoverning equations for the analysis of the rolling sectionare similar to the equations associated with the drag sec-tion. The cross-shaped rolling section converts the rollingmoment to the bending moment in rectangular beams.The designed section acts similar to a beam with two xedends. The amount of stress generated as a result of the roll-ing moment at the locations of the strain gauges isobtained from the following relationship:

r 3FLbh2

: 6

of the drag-measurement section.

distrib

N.M. Nouri et al. /Measurement 58 (2014) 544555 549The force exerted on each beam in the rolling section, F,is equal to:

F TAD b2J

: 7

In the above relationship T, J, and A are the rolling moment,the second moment of area about the longitudinal axis ofbalance, and the beams cross-sectional area, respectively.

By substituting A = bh, J bh b2h23Db23

, T =Mx into

Eq. (7) and substituting Eq. (7) into Eq. (6), the amount ofbending stress at the locations of the strain gauges isobtained as:

r 3MxL23 bh

2 b2h2Db D b

8

where r 82:5 MPa and Mx 1 N m. The procedure forcalculating the values of the dimensions (using Eq. (8)and applying the nite element method) is similar tothe procedure used for the drag section. Fig. 4(b) showsthe distribution of the strain for the rolling section alongthe installation line of strain gauges for the nalizeddimensions. The difference between the values obtainedfrom Eq. (8) and from the nite element method at thelocation of the strain gauge was 5%. Therefore, the resultsprovided by the FEM were reasonable considering the

Fig. 4. Structure and strainsensitivity criterion of ea 750 ls 10% for nominalstrain.

5.3. Pitching moment section

Fig. 5(a) shows the structure of the pitching section. Inthis gure, h is the thickness of the beam, b is the widthof the beam, d is the distance between the balances twoside beams, and L is the distance between the two straingauges used to measure lift force along the axial direction.The design of the pitching section allowed it separate thepitching moment from the lift force. This section consistedof three rectangular beams. To design the pitching section,the dimensions L, h, and b were calculated by applyingpure force and not accounting for the pure effects of thepitching moment. In response to pure force FL, each ofthe beams acts as a beam with two xed ends. The bendingstress at the locations of the strain gauges was obtainedfrom:

r 3FLbh2

: 9

Based on Fig. 5(a) F FL3 and the following values wereused to determine the values of the dimensions, i.e.r 82:5 MPa and FL 50 N. The procedure for the calcula-tion of the dimensions (using Eq. (9) and applying the niteelement method) was similar to the procedure used for thedrag section. Taking into account the design considerationsfor the manner of strain distribution and the application ofthe combined load (lift force and pitching moment), thedistance between the two side beams (d) were determined.The effects of the combined load emerged in the form ofcompressive stress and pure tension in the two side beams.The stress due to the combined load at the locations of thestrain gauges, which was used for the measurement of thepitching moment, is equal to:

r MY FL Sdhb

: 10

In the above relationship, S denotes the distancebetween the point of application of the load and the loca-tion of the strain gauge for the measurement of themoment. To calculate d using Eq. (10), the following valueswere used: MY 1 N m, FL 50 N, r 82:5 MPa and

ution of the rolling section.S 36 mm. The values of h and b have already been calcu-lated. For the pitching section, the distribution of the strainalong the installation line of the strain gauges, which wasobtained through the nite element method for the naldimensions by applying the pure and combined loads, isshown in Fig. 5(b) and (c), respectively. The maximum dif-ference between the values of strain obtained from Eqs. (9)and (10) and from the nite element method at the loca-tions of the strain gauges was 1.5%. Therefore, the resultsprovided by the FEM were reasonable, considering the sen-sitivity criterion of ea 750 ls 10% for nominal strain.

5.4. Yawing moment section

Fig. 6(a) shows the structure of the yawing section. Inthis gure, h is the thickness of the beam, b is the widthof the beam, d is the distance between the balances two

550 N.M. Nouri et al. /Measurement 58 (2014) 544555side beams, and L is the distance between the two straingauges used to measure the side force along the axialdirection. The governing equations for the analysis andthe procedures for calculating the dimensions of the yaw-ing section are similar to those used in pitching section. Todetermine the values of the dimensions, the following rela-tionships were used: Mz 1 N m, Fs 50 N, r 82:5 MPaand S 150 mm. For the yawing section, the distributionof strain along the installation line of the strain gauges,which was obtained using the nite element method forthe nal dimensions by applying the pure and combinedloads, is shown in Fig. 6(b) and (c), respectively. The max-imum difference between the strain values obtained fromEqs. (9) and (10) and from the nite element method atthe locations of the strain gauges was 2%. Therefore, theresults provided by the FEM were reasonable consideringthe sensitivity criterion of ea 750 ls 10% for nominalstrain.

6. Strain analysis

The electrical output of each measuring sectiondepends on the strain produced at the locations of thestrain gauges; therefore, the manner of strain distributionwhere the strain gauges were installed would be effective

Fig. 5. Structure and strain distribuin improving the balances performance. Following the cal-culation of the main dimensions of the balance, strain dis-tribution was analyzed based on maximum loads. Theanalysis of the strain distribution was performed by FEM,and 3D tetrahedral mesh was applied on the model. Forthe simulation of the balance, 991,764 mesh elementswere generated. Four types of loads were used to evaluatethe distribution of the strain, and this distribution for theapplication of each load is shown in Fig. 7.

The rst load that was applied was the force of drag.The strain distribution resulting from the drag force wasshown along the installation locations of the strain gauges.Fig. 7(a) shows that the difference between the maximumand minimum strains at the locations of the strain gauges,considering a gauge length of 1 mm, was less than 14% ofthe maximum strain. Also, the difference between maxi-mum values of sensitivity obtained from the derived equa-tions and from the FE analysis (using Eq. (1) at the straingauges installation locations in the drag section) was 4%.

The second applied load was the rolling moment aboutthe x-axis. Fig. 7(b) shows the distribution of strain thatwas produced as a result of the rolling moment. Fig. 7(b)shows that the difference between the maximum and min-imum strains at the strain gauges installation locations,considering a gauge length of 1 mm, was less than 15%of the maximum strain. Also the difference between the

tion of the pitching section.

Fig. 6. Structure and strain distribution of the yawing section.

Fig. 7. Strain distribution for four types of loadings.

N.M. Nouri et al. /Measurement 58 (2014) 544555 551

neously on the balance tip. The type of mesh conguration

tress

552 N.M. Nouri et al. /Measurement 58 (2014) 544555maximum values of sensitivity obtained from the derivedequations and from the FE analysis (using Eq. (1) at thestrain gauges installation locations in the rolling section)was 4%.

The third applied load was a combination of the liftforce and the pitching moment. Fig. 7(c) shows the distri-bution of strain produced by the application of the com-bined load. Fig. 7(c) shows that the difference betweenthe maximum and minimum strains at the strain gaugeslocations, considering a gauge length of 1 mm, was lessthan 13% of the maximum strain. And the differencebetween the maximum values of sensitivity obtained fromthe derived equations and from the FE analysis (using Eq.(1) at the strain gauges installation locations at this sec-tion on) was 5%.

The fourth applied load was a combination of the sideforce and the yawing moment. Fig. 7(d) shows the strainanalysis along the installation locations of the straingauges. This gure also illustrates the distribution of thestrain produced as a result of the combined load.Fig. 7(d) shows that the difference between the maximumand minimum strains at the strain gauges installationlocations, considering a gauge length of 1 mm, was lessthan 10% of the maximum strain. Also, the differencebetween the maximum values of sensitivity obtained fromderived equations and from the FE analysis (using Eq. (1) atthe strain gauges installation locations at this section) was5%.

Fig. 8. Von Mises sBy comparing the strains obtained at the locations ofthe strain gauges using the nite element method andthe derived equations for four types of loadings and con-sidering the sensitivity criterion 1:5 mV=V 10% , itwas concluded that the analyses that were performed pro-duced acceptable results. Considering the analysis of strainperformed for four types of loadings, the differencebetween the maximum and minimum strains at straingauges installation locations, considering a gauge lengthof 1 mm, was less than 15%, which is acceptable withregards to the design criterion for strain distribution.

7. Stress analysis

A six-component balance is a complex structure withmany different dimensions. In IUSTs water tunnel tests,was similar to that in the strain distribution analysis,which could also be valid for stress analysis consideringthe results obtained, as compared to the values determinedfrom the derived equations. Fig. 8 shows the Von Misesstress for the applied loads. In view of the illustrated distri-bution, the maximum stress occurred at the side section.The maximum stress value was 583 MPa, which, in com-parison with the allowed stress of 1000 MPa, provided anacceptable safety margin.

8. Review of interactions and interference effects

To minimize interference effects, it is necessary toinstall the strain gauges at the proper locations. The posi-tions of the installed strain gauges used for the detectionof forces are shown in Fig. 1. For the installation and wiringof the strain gauges bridges, the following considerationswere envisioned:combined loads are normally applied on the experimentalmodels. Such combined loads induce more complicatedstresses in the balance and therefore require special atten-tion. In these conditions, the stress analysis of the balanceis a concern. For the analysis of stress, the real-case com-bined loads were evaluated by different models, and thecritical loading cases were selected. In this loading, sixcomponents with nominal values were applied simulta-

for critical loading. For measuring each component, four active straingauges in the form of a Wheatstone bridge wereinstalled next to each other.

The installations location and arrangement of the straingauges as a Wheatstone bridge were planned in such away that the strain gauge had maximum sensitivity inthe direction of the considered component and the low-est reaction to other components.

In order to evaluate the sensitivity and interferenceeffects, after determining the installation locations of thestrain gauges, the ratio of output voltage to input voltageof each channel was calculated using the values of strainobtained from the nite element method and formula(1). The VOUTVIN ratio of each bridge versus the applied loadis shown in Fig. 9 for the six types of loadings. VOUT and

N.M. Nouri et al. /Measurement 58 (2014) 544555 553VIN are the output and input voltages of each channel,respectively. The range of loading for the balance was fromzero to the nominal capacity of each component, which isindicated in the plotted diagrams. The diagrams demon-strate the linear performance of the balance against theapplied loads. By choosing suitable installation locationsfor the strain gauges and wiring them properly as a Wheat-stone bridge, it was possible for this balance to measurethe forces and moments separately. In response to the loadof the corresponding plane, every measuring section pro-vided the desired sensitivity and the required stiffnessagainst the other components. Fig. 9 shows that the maxi-mum sensitivity of the Wheatstone bridge for the fourmeasuring sections, considering the nominal load, was inthe range of 1.361.63 mV/V, which constitutes an

Fig. 9. Voltage ratio versus applied load for sixacceptable sensitivity range for the balance if we considerthe design sensitivity criterion of VOUTVIN 1:5mV=V 10%

.

9. Error analysis result

For error analysis, the designed balance must be cali-brated. Generally, there are different models for the cali-bration of the balance, i.e. different orders of equations(rst, second, or third order) can be used depending onthe types of equations selected for data processing andthe desired degree of precision. In this article, after com-paring various calibration models and considering differ-ent parameters with respect to the requirements of thewater tunnel tests under investigation and the balancesdesign, the [R] = [C][H] model was used [23]. In this model,

force and moment measuring channels.

vide a pattern for the design of similar, multi-component

gnitust-ord

.0082

.4939

.0001

.0044

.0056

.8756

554 N.M. Nouri et al. /Measurement 58 (2014) 544555the output voltage (R) is a function of calibration coef-cients (C) and applied loads on the balance (H). To obtainthe calibration coefcients, the loading of the balancewas conducted by taking the real conditions of tests intoaccount. The loads were applied according to Fig. 9. Theelectrical output of each measuring section depends onthe strain produced installation locations of the straingauges. Therefore, the strain at the locations of the straingauges (according to Fig. 7) was calculated using the niteelement method. After determining the strain at installa-tion locations of the strain gauges, the VOUTVIN ratio of eachbridge was calculated by substituting the values of strainobtained from the nite element method into the formula(1). The rst-order coefcients were determined from thedata of discrete loads applied on the balance and the ratioof the output voltage to the input voltage using the leastsquares regression method proposed by Ramaswamyet al. [24]. In this method, the calibration coefcients aredetermined based on the assumption that the sum of thedifferences of the squares between the measured voltageratio and the voltage ratio obtained from calibration coef-cients is a minimum value.

For the six-component balance, calibration is alwaysrepresented by six different equations; but the number ofterms in each equation can vary depending on the orderof the equation. In the designed balance, the range of stres-ses, in comparison with the yield strength TiAl6V4, isrelatively low, so the second-order interactions were disre-garded against the rst-order interactions.

The sensitivity matrix is the inverse form of matrix [C],with the following array values:

C1

0:6756 0:0048 0:0453 0:0012 0:0234 0:00040:0090 0:7240 0:0011 0:0017 0:0008 0:01760:0005 0:0000 0:6365 0:0003 0:0001 0:00570:0001 0:0002 0:0001 0:6235 0:0003 0:00010:0374 0:0003 0:0453 0:0001 0:6930 0:00160:0000 0:0305 0:0405 0:0001 0:0007 0:5982

2666666664

3777777775:

Table 1Errors for each component for a sample loading case.

Type ofappliedload

Magnitude ofapplied load

Magnitude of load calculated fromsensitivities ([H] = [C1][R])

Mar

Lift 19 19.5128 19Pitch 0.4940 0.4822 0Roll 0.2 0.1917 0Drag 26 26.0286 26Side 14 14.1313 14Yaw 0.8760 0.8894 0The coefcients that were obtained indicate the sensi-tivities and interactions without considering the effectsof fabrication, assembly, and wiring. The percentage erroris dened as:

Percentage errorApplied loadComputed loadApplied load

100:11

Table 1 shows the data obtained from the calibrationequations and also the percentage of error for a sampleloading case. The interference errors were determinedbalances.

References

[1] A. Bray, G. Barbato, R. Levi, Theory and Practice of ForceMeasurement, Academic Press, London, 1990. pp. 42168.

[2] T. Allgeier, W.T. Evans, Mechanical hysteresis in force transducersmanufactured from precipitation-hardened stainless steel, J. Mech.Eng. Sci. 209 (1995) 125132. Part C.

[3] P.S. Alexopoulos, C.W. Cho, C.P. Hu, Li Che-Yu, Determination of theanelastic modulus for several metals, Acta Metall. (1981) 549577.from the sensitivities. The maximum error that resultedfrom the interference effects of the applied loads was lessthan 3%. Non-linear interaction terms omitted in this cali-bration and the process of tting curves to obtain the cal-ibration constants introduce non-linear errors in thecalculated forces and moments. The results show that thesix-component balance developed in this study has goodperformance, with the errors of non-linearity and repeat-ability less than 0.05%.

10. Conclusions

The innovative methodology was applied to the designand evaluation of a new, six-component balance that it isused for measuring the forces and moments in water tun-nel tests. The use of derived equations as well as the niteelement method for determination of structural parame-ters of the designed balance resulted in the reduction ofthe time required for the design and increased the reliabil-ity of the solutions. The six-component balance developedin this study has good performance, with the errors of non-linearity and repeatability less than 0.05%, and interferenceeffects less than 3%. The results of our evaluations indi-cated that the dimensions obtained in an iterative processusing analytical and numerical methods satised all thedesign criteria. Therefore, the design and evaluation pro-cess used for the new, six-component balance could pro-

de of load calculated from theer coefcients ([H] = [C1][R])

Interferenceerrorpercentage

Nonlinearerrorpercentage

2.70 0.0432.39 0.0201.00 00.11 0.0170.94 0.041.53 0.046[4] D.R. Chichili, K.T. Ramesh, K.J. Hemker, The high-strain-rate responseof alpha titanium: experiments, deformation mechanisms andmodeling, Acta Mater. (1998) 461025.

[5] F.R. Ewald, Multi-component force balances for conventional andcryogenic wind tunnels, Meas. Sci. Technol. 11 (2000) R81R94. 20thConference, Albuquerque, NM, June 1518.

[6] M.C. Lindell, Finite element analysis of a NASA national transonicfacility wind tunnel balance, in: Proceedings of the 1st InternationalSymposium on Strain Gauge Balances, NASA CP1999-20901,Hampton, USA, 1999, pp. 595606.

[7] R. Karkehabadi, R.D. Rhew, Linear and nonlinear analysis of a wind-tunnel balance, in: Proceedings of the 4th International Symposiumon Strain Gauge Balances, San Diego, USA, 2004.

[8] V.I. Lagutin, V.I. Lapygin, S.I. Devyatkin, S.S. Trusov, Finite elementanalysis of a combined type strain-gauge balance, in: Proceedings of

the 6th International Symposium on Strain Gauge Balances, Zwolle,the Netherlands, 2008.

[9] D.C. Johnson, A Coning Motion Apparatus for Hydrodynamic ModelTesting in Non-Planar Cross-Flow, Department of Ocean Engineering,MIT, 1982.

[10] C.J. Surez, G.N. Malcolm, B.R. Kramer, B.C. Smith, B.F. Ayers,Development of a multicomponent force and moment balance forwater tunnel applications, NASA Contractor Report 4642, vols. I andII, 1994.

[11] C.S. Lee, N.L. Wong, S. Srigrarom, N.T. Nguyen, Development of 3-component forcemoment balance for low speed water tunnel,World Sci. Publ. Company Mod. Phys. Lett. B 19 (2005) 15751578.

[12] L.P Erm, Development of a Two-Component Strain-Gauge-BalanceLoad Measurement System for the DSTO Water Tunnel, DefenceScience and Technology Organisation, Melbourne, Australia, 2006.DSTO-TR-1835.

[13] M. Samardzic, Z. Anastasijevic, D. Marinkovski, J. Isakovic, L.J. Tancic,Measurement of pitch- and roll-damping derivatives usingsemiconductor ve-component strain gauge balance, Proc. IMechE.Part G: J. Aerospace Eng. 226 (2012) 14011411.

[14] M. Samardzic, Dj. Vukovic, D. Marinkovski, Experiments in VTI withsemiconductor strain gauges on monoblock wind tunnel balances,in: Proceedings of the 8th International Symposium on Strain-GaugeBalances, RUAG, Lucerne, Switzerland, 2012. pp. 18.

[15] M. Samardzic, j. Vukovic, D. Marinkovski, Apparatus formeasurement of pitch and yaw damping derivatives in high

Reynolds number blowdown wind tunnel, Measurement 46 (2013)24572466.

[16] A.L. Smith, D.J. Mee, W.J.T. Daniel, T. Shimoda, Design, modelling andanalysis of a six component force balance for hypervelocity windtunnel testing, Comput. Struct. 79 (11) (2001) 10771088.

[17] S. Trivedi, V. Menezes, Measurement of yaw, pitch and side-force ona lifting model in a hypersonic shock tunnel, Measurement 45(2012) 17551764.

[18] R.D. Rhew, NASA Larc Strain Gage Balance Design Concepts, NASALangley Research Center, Hampton, Virginia, 1998.

[19] Tropea, A.L. Yarin, J.F. Foss, Springer Handbook of ExperimentalFluid Mechanics, 2007.

[20] Technical Note, Strain Gage Installation Procedures for Transducers,Measurement Group Inc., USA, 1978.

[21] Technical Note, Strain Gage Based Transducers, their Design andConstruction, Measurement Group Inc., USA, 1988.

[22] J. Schberl, J. Kepler, NETGEN. An Automatic Three-DimensionalTetrahedral Mesh Generator, University, Linz Austria, 2004.

[23] S.Y.F. Leung, Y.Y. Link, Comparison and Analysis of Strain GaugeBalance Calibration Matrix Mathematical Models, Aeronautical andMaritime Research Laboratory, Defence Science and TechnologyOrganisation, Melbourne, Australia, 1999. DSTO-TR-0857.

[24] M.A. Ramaswamy, T. Srinivas, V.S. Holla, A simple method for windtunnel balance calibration including non-linear interaction terms,in: Proceedings of the ICIASF 87 RECORD, 1987.

N.M. Nouri et al. /Measurement 58 (2014) 544555 555

Design methodology of a six-component balance for measuring forces and moments in water tunnel tests1 Introduction2 Design requirements and considerations3 Structural design of the balance4 Design methodology4.1 Fundamental equations4.2 Finite element method

5 Design of the measuring elements5.1 Drag section5.2 Rolling moment section5.3 Pitching moment section5.4 Yawing moment section

6 Strain analysis7 Stress analysis8 Review of interactions and interference effects9 Error analysis result10 ConclusionsReferences