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Development of a 3-component load cell for structural impact testingA. G. HANSSEN1,2,*, T. AUESTAD1, M. LANGSETH1 and T. TRYLAND31Structural Impact Laboratory (SIMLab), Department of Structural Engineering, Norwegian University of Science andTechnology (NTNU), N-7491, Trondheim, Norway; 2SINTEF Materials Technology, Rich Birkelandsvei 2B, N-7465,Trondheim, Norway; 3Hydro Automotive Structures, N-2831, Raufoss, Norway*Author for correspondence (E-mail: arve.hanssen@bygg.ntnu.no)Abstract. This paper describes the development of a 3-component load cell for structural impact testing. The testspecimen is mounted directly on the load cell, which measures the axial force as well as two orthogonal bendingmoments. Basically, the load cell is a stocky cylinder with thick end anges machined in one piece of high-strength steel.The load measurement system is based upon four strain gauges glued to the central shaft. The signal from each straingauge is sampled separately. Afterwards, this data is used to compute the axial force and the bending moments. The loadcell was originally developed for testing of automotive components.Key words: load cell, impact, energy absorption, crash testing, ls-dyna1. IntroductionThe objective of this study was to develop a cost-eective load cell, which could be applied forhigh-speed oset testing of bumper systems. A description of the test set-up using the load cell isgiven by Hanssen et al. (2003). The nal load cell design is shown in Figure 1. The load cell ismachined from one piece of high-strength steel with a minimum yield stress of r0=600 MPa(proportionality limit). Four strain gauges are evenly distributed on the perimeter in the middle-plane of the central shaft. The shaft is a stocky, hollow cylinder of circular cross-section andwith a wall thickness and outer diameter of 7 mm and 100 mm, respectively. Both ends of thecentral shaft are connected to thick anges (80 mm). Such a thickness is necessary in order torealise a linear strain distribution (Euler-Bernoulli) over the cross section in the central shaft,which forms the basis for the calibration formulas given below, Section 3. The required angethickness was determined by use of numerical simulations, see Section 2.2. The load cell has 5spherical indents machined into the front ange, which are for calibration purposes. Here,compressive load is applied to the load cell through a steel ball successively located in all veholes, see illustration in Figure 3. This yields sucient information to fully calibrate the loadcell statically, Section 3. The rear ange has a hollow, circular cross section and incorporates sixthreaded M16 holes for fastening to an external surface. The frontal ange has a square crosssection and is tted with four 11 mm holes, one in each corner, to accommodate the testspecimens. The requirements for the load-cell were as follows: (1) Capacity of 200 kN at a loadeccentricity of 100 mm, (2) Natural frequency of system should be above 400 Hz and (3)Accuracy in average force level within 5%.International Journal of Mechanics and Materials in Design (2005) 2: 1522 Springer 2006DOI 10.1007/s10999-005-0513-z2. Load cell design2.1. CAPACITY FOR ECCENTRIC LOADINGThe capacity N of a hollow, circular cylinder as function of the load eccentricity e, Figure 3,(assuming a linear strain distribution over the cross section and neglecting transversal shear) isgiven byNN0 11 2ed12 hd hd 2 1where d is the outer diameter and h is the wall thickness. N0 is the capacity for pure-axial loadinggiven by N0 =r0 A where r0 is the yield stress and A is the cross sectional area.195115160 x 16080011R22.2801958035160505513016010086404M1665116516050505055Rear viewFront viewSide viewSection viewStrain-gauge locationFrontRearFigure 1. Load-cell design.16 A.G. Hanssen et al.2.2. LINEAR STRAIN DISTRIBUTIONThe inuence of the ange thickness on the strain distribution over the cross section of the loadcell can be seen from Figure 2(a). These results are based on numerical simulations by use of thenon-linear, nite element code LS-DYNA (Hallquist, 1998). The loading was applied through asphere, located 50 mm from the symmetry axis of the load cell. In Figure 2(a), the stressdistribution is given for three dierent values of the ange thickness, B=20, 40 and 100 mm.The axial stress on the outer-wall in the middle-plane of the central shaft is denoted by rz. Thecorresponding average value of the axial stress for all x/d ratios is denoted by rz. The stressdistribution rz=rz is given as a function of x/d, where x is the coordinate as dened in Fig-ure 2(b). The data points of Figure 2 are based on the axial stress at the integration point of thevolume elements located on the perimeter of the load cell. As can be seen, the stress distributionis highly non-linear for ange thicknesses of 20 and 40 mm. For B=100 mm, the stress dis-tribution is practically linear. The nal load cell was made with a ange thickness of 80 mm.Figure 2(b) shows the stress distribution for this case. Assume that the signal from the fourstrain gauges (rz0, rz90, rz180, rz270) relates to the axial stress of four brick elements located onthe perimeter of the load cell, see illustration of Figure 2(b). Let the corresponding averagevalue be denoted by rSz rz0 rz90 rz180 rz270 =4. In order for the strain gauges to give agood representation of the true axial force then rSz rz. For Figure 2b one nds thatrSz =rz 1:0057. On can also imagine that the set of four strain gauges is rotated an angle hrelative to the axis of loading, Figure 2(b). The average strain-gauge signal is nowrSz rz0h rz90h rz180h rz270h =4. By varying h from 0 to 90 degrees it was found thatthe error margins are 0:9949 < rSz =rz < 1:0057. Hence the error appears to be well within 1%for a load eccentricity of 50 mm. Figure 2(b) also shows the strain distribution for centralloading. For this case the distribution is practically linear. The load cells instrumentation is notable to capture transversal shear forces or any axial twisting moments. On the other hand, theoccurrence of such reactions should not cause the instrumentation to record any signicant axial-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1-1012345B = 20 mm40 mm100 mmBzz/x d-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1-101234zz/x de = 0e = 50 mm90z 0z 180z 270z 0z +90z +180z +270z +yxNStraingaugeCross section of load cell (central part)0z 90z 180z 270z e(b)(a)Figure 2. (a) Cross-section strain distribution for various ange thicknesses, eccentric loading (e=50 mm). (b) Straindistribution of nal load cell design (ange thickness B=80 mm.)Development of a 3-component load cell 17forces or bending moments. In the same manner as described above, the load cell was subjectedto a pure shear force at the top ange. The maximum axial force recorded for strain-gaugelocations 0 < h < 90 were 0.69, 9.68 and 36.6 kN for shear force levels of 100, 200 and300 kN, respectively. For shear force levels higher than 250 kN the strain distribution in thecentral shaft of the load cell is no longer linear. Finally, the load cell was subjected to a puretwisting moment. For twisting moments of 10, 20, 30 and 40 kNm the recorded maximum axialforce measure was 0.2, 0.6, 1.2 and 1.8 kN, respectively. Again, this is insignicant.2.3. DYNAMIC BEHAVIOURThe dynamic behaviour of the load cell was studied numerically by use of LS-DYNA. First, aneigenvalue analysis was carried out using the same nite element model as described above. Thefrequency response in terms of the ve lowest eigenfrequencies was: 1.53, 1.53, 1.63, 3.025 and3.025 kHz. The two lowest eigenmodes correspond to bending of the central shaft aroundorthogonal axes. A similar behaviour is also observed for modes four and ve. The thirdeigenmode is axial twisting. The range of applicability (loading rate) of the load cell will begoverned by the cells lowest eigenfrequency fe. Assume that the loading takes place at a velocityv0 and that the impacted structure shows an oscillating force vs. time response with a charac-teristic period Ts. This is typical for an axially loaded extrusion. For such a structure thecharacteristic period Ts is given by the loading velocity v0 and the half-plastic lobe length ofdeformation L, i.e. Ts=2L/v0. For a hollow, square extrusion L bh=b1=3 (Jones, 1989) givingTs 2bh=b1=3=v0. Here b and h are the width and thickness of the extrusion respectively.Assume that loading is to take place at frequency ratios feTs1 < 0:2 to keep the amount ofdynamic magnication below 5% (SDOF-system, no damping (Clough and Penzien, 1975)),then v0 < 0:4febh=b1=3. Using fe=1.53 kHz, b=80 mm, h=2 mm yields v0normal force can be decomposed into an axial force and two orthogonal bending momentsaround the x and y-axis, Figure 3. It is evident from this gure that four strain gauges will besucient in order to capture the information from such a loading condition. The average axialstrain is taken as e 1=4 e1 e2 e3 e4 , which in turn denes the resultant axial force asN KNe 1=4 KN e1 e2 e3 e4 1=4 KN k1v1 k2v2 k3v3 k4v4 . However, the pure-axial calibration has determined the constants Ki KNki; i 1:4 and the expression for theaxial force is written asN 14K1v1 K2v2 K3v3 K4v4 23.2. CALIBRATION STEP 2: BENDING MOMENTAssume a state of eccentric loading so thatMy=0 andMx=Ne, Figure 3. The bending momentMx is proportional to the curvature jx of the cross-section, Mx KMjx. The curvature is againproportional to the dierence in axial strains in the following manner, jx kx e4 e2 and onecan writeMx KMkx e4 e2 KMkx k4v4 k2v2 KMKNkx KNk4v4 KNk2v2 Kx K4v4 K2v2 :3TensionCompression4 2 =+1 3, Nev2 v4yxv1v3v2v4StraingaugeCross section of load cell (central part)xM N e= 0yM =N .Figure 3. Strain distribution for development of calibration formulas.Development of a 3-component load cell 190 200 400 600 8000100200300400500N (kN) 0 200 400 600 8000100200300400500Axialloading N (kN) 0 200 400 600 80001002003004005000 200 400 600 8000100200300400500Axialloading N (kN) Gauge 2(mV) K2 = 0.730 kN/mVGauge 3(mV) K3 = 0.836 kN/mV(b) (c) Axialloading Gauge 4(mV) K4 = 0.761 kN/mV-15 -10 -5 0 5 10 15-15-10-50510150xK0xM= 0.0078 -15 -10 -5 0 5 10 15-15-10-5051015= 0.0018 0yK0y-1000 0 1000-15-10-50510150 50 100 150 200 250050100150200250Eccentric loading 0 50 100 150 200 250050100150200250Applied force (kN)Model (kN) Check of axial force. Pos. 2 Applied force (kN)Model (kN) Check of axial force. Pos. 3 Eccentric loading 0 50 100 150 200 250050100150200250Applied force (kN)Model (kN) Check of axial force. Pos. 4 My (kNm) (kN) Nm) Nm) Ky = 0.0100 m ( )1 1 3 3K v K v(a) Eccentric loading Axialloading (i) (e) (k( )4 4 2 2xK K v K v(kNm) (k( )1 1 3 3yK K v K v(kNm) K1 = 0.821 kN/mVN (kN) (mV) Gauge 10 50 100 150 200 250050100150200250Eccentric loading Check of axial force. Pos. 1 Model (kN) Applied force (kN)-10----00 0 1000-15-10-5051015Kx = 0.0109 m (kN) ( )4 4 2 2K v K vMx (kNm) (f ) (j) (g ) (k) (d) (h) (l) Figure 4. Results from calibration procedure.20 A.G. Hanssen et al.Hence, Mx Kx K4v4 K2v2 where the constants K2 and K4 have already been determined bythe pure-axial loading condition in Section 3.1. Eccentric loading around the x-axis will providedata for determination of Kx. The same consideration can be used for eccentric loading aroundthe y-axis and one arrives at My Ky K1v1 K3v3 . The results for the current load cell aregiven in Section 4, Figure 4(ij).If the strain gauges are not correctly positioned, a moment around the x-axis will inducestrains in the strain gauges used for calculation of moment around the y-axis and vice versa.However, this coupling eect can also be taken into consideration by the calibration formulas.Assume that the load cell has been subjected to an axial force and moment only around the x-axis. The computed bending moment around the x-axis is then Mx Kx K4v4 K2v2 . Thecalculated moment around the y-axis is M0y Ky K1v1 K3v3 , where the superindex is used toindicate that this is a residual moment. This error can be related to the computed bendingmoment Mx in the following manner M0y K0yMx K0y Kx K4v4 K2v2 , which easily deter-mines Ky0. The residual moment My0 has to be subtracted from the original expressionMy Ky K1v1 K3v3 . In this way, the complete formulas for the bending moment around thex- and y-axis readMx Kx K4v4 K2v2 K0x Ky K1v1 K3v3 4andMy Ky K1v1 K3v3 K0y Kx K4v4 K2v2 : 54. Load-cell performanceThe load cells manufactured were calibrated in a Dartec 500 kN static testing machine using theapproach described above. The compressive load was applied cyclically at a frequency of 5 Hz.The force level from the Dartec testing machine and the signal from the four strain gauges weresampled digitally. All relevant data for one selected load cells is given in Figure 4. Figure 4(ad)give the relation between force level and signal from each strain gauge for pure-axial loading.The relation is clearly linear although some hysteresis is evident from Gauge 2 and 3. Thehysteresis, or reversibility error, is the dierence between the load cells output when a force hasbeen applied by monotonic increase from zero, and its output at the same force following amonotonic decrease from its rated load (Robinson, 1997). Robinson (1997) gives four hysteresismechanisms for load cells. These are (1) metallurgical hysteresis, (2) local yielding eects,(3) hysteresis in strain-gauge backing and adhesive layer and nally (4) slip at the interfacebetween load cell and support. Given the axissymmetry of the current load cell and supportconditions, hysteresis in the strain-gauge backing and adhesive layer could be a plausibleexplanation for the hysteresis observed for Gauge 2 and 3 only. Four eccentric loading con-ditions were applied to the load cell, namely loading by a steel ball through the four eccentricallyplaced holes in the top ange, Figure 1. First, this load condition can be used to check theperformance of the calibration formula for the total axial force given by Eq. 2 and dened bythe constants Ki, i=1.4 of Figure 4(ad). The results can be seen in Figure 4(eh). The formulasappear to give good results, although the force levels are somewhat underestimated by thecalibration formula for loading in Position 3 (which is the hole directly above Gauge 3). TheDevelopment of a 3-component load cell 21calibration results relating to the two bending moments Mx and My are shown in Figure 4(ij).The corresponding correction for the coupling error between the two bending moments is givenin Figure 4(kl) and is less than 1% for both cases. The two load cells produced within thisproject were calibrated and applied for impact testing of a bumper system. The dynamic resultsfollowed by a discussion are reported by Hanssen et al. (2003).5. ConclusionsA 3-component load cell for measurement of axial force and two orthogonal bending momentshas been developed for structural impact testing. The shape of the load cell was optimised by useof nite element simulations. Finite element simulations were also carried out in order to studythe behaviour of the load cell for dynamic loading conditions. A simple set of calibrationformulas for the axial force and the bending moments was developed based on the assumptionof a linear and elastic strain distribution. Calibration of the load cell showed reasonable line-arity. The load cell was subjected to eccentric loading conditions and the calibrated formula forthe axial force showed good consistency with the applied force levels.ReferencesClough, R.W. and Penzien, J. (1975). Dynamics of Structures, McGraw Hill Company, Singapore, ISBN 0 07 085089 4.Hallquist, J.O. (1998). Theoretical Manual, Livermore Software Technology Corporation, compiled by J.O. Hallquist.Hanssen, A.G., Auestad, T., Tryland, T. and Langseth, M. (2003). The kicking machine: A device for impact testing ofstructural components, International Journal of Crashworthiness 8(4), 385392.Jones, N. (1989). Structural Impact, Cambridge University Press. ISBN 0 521 30180 7.Robinson, G.M. (1997). Finite element modeling of load cell hysteresis, Measurement 20(2), 103107.22 A.G. Hanssen et al. /ColorImageDict > /JPEG2000ColorACSImageDict > /JPEG2000ColorImageDict > /AntiAliasGrayImages false /DownsampleGrayImages true /GrayImageDownsampleType /Bicubic /GrayImageResolution 150 /GrayImageDepth -1 /GrayImageDownsampleThreshold 1.50000 /EncodeGrayImages true /GrayImageFilter /DCTEncode /AutoFilterGrayImages true /GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict > /GrayImageDict > /JPEG2000GrayACSImageDict > /JPEG2000GrayImageDict > /AntiAliasMonoImages false /DownsampleMonoImages true /MonoImageDownsampleType /Bicubic /MonoImageResolution 600 /MonoImageDepth -1 /MonoImageDownsampleThreshold 1.50000 /EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode /MonoImageDict > /AllowPSXObjects false /PDFX1aCheck false /PDFX3Check false /PDFXCompliantPDFOnly false /PDFXNoTrimBoxError true /PDFXTrimBoxToMediaBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXSetBleedBoxToMediaBox true /PDFXBleedBoxToTrimBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXOutputIntentProfile (None) /PDFXOutputCondition () /PDFXRegistryName (http://www.color.org?) /PDFXTrapped /False /Description >>> setdistillerparams> setpagedevice