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Development of a 3-component load cell for structural impact testing

A. G. HANSSEN1,2,*, T. AUESTAD1, M. LANGSETH1 and T. TRYLAND3

1Structural Impact Laboratory (SIMLab), Department of Structural Engineering, Norwegian University of Science and

Technology (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 test

specimen is mounted directly on the load cell, which measures the axial force as well as two orthogonal bending

moments. 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 strain

gauge is sampled separately. Afterwards, this data is used to compute the axial force and the bending moments. The load

cell was originally developed for testing of automotive components.

Key words: load cell, impact, energy absorption, crash testing, ls-dyna

1. Introduction

The objective of this study was to develop a cost-eective load cell, which could be applied for

high-speed oset testing of bumper systems. A description of the test set-up using the load cell is

given by Hanssen et al. (2003). The nal load cell design is shown in Figure 1. The load cell is

machined 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 and

with a wall thickness and outer diameter of 7 mm and 100 mm, respectively. Both ends of the

central shaft are connected to thick anges (80 mm). Such a thickness is necessary in order to

realise 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 ange

thickness was determined by use of numerical simulations, see Section 2.2. The load cell has 5

spherical 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 ve

holes, see illustration in Figure 3. This yields sucient information to fully calibrate the load

cell statically, Section 3. The rear ange has a hollow, circular cross section and incorporates six

threaded M16 holes for fastening to an external surface. The frontal ange has a square cross

section and is tted with four 11 mm holes, one in each corner, to accommodate the test

specimens. The requirements for the load-cell were as follows: (1) Capacity of 200 kN at a load

eccentricity 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-z

2. Load cell design

2.1. CAPACITY FOR ECCENTRIC LOADING

The 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) is

given by

N

N0 11 2

ed

12 hd hd

2 1

where d is the outer diameter and h is the wall thickness. N0 is the capacity for pure-axial loading

given by N0 =r0 A where r0 is the yield stress and A is the cross sectional area.

195

115

160 x 160

80

0

11

R22

.2

80

19

5

80

35

16

0

50

55

13

0

160

100

86

40

4

M16

65

11

65

160

50

50

50

55

Rear view

Front view

Side view

Section view

Strain-gauge location

Front

Rear

Figure 1. Load-cell design.

16 A.G. Hanssen et al.

2.2. LINEAR STRAIN DISTRIBUTION

The inuence of the ange thickness on the strain distribution over the cross section of the load

cell can be seen from Figure 2(a). These results are based on numerical simulations by use of the

non-linear, nite element code LS-DYNA (Hallquist, 1998). The loading was applied through a

sphere, located 50 mm from the symmetry axis of the load cell. In Figure 2(a), the stress

distribution 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 the

volume elements located on the perimeter of the load cell. As can be seen, the stress distribution

is 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 four

strain 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 average

value 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 now

rSz 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 central

loading. 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, the

occurrence 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

-1

0

1

2

3

4

5

B = 20 mm40 mm

100 mm

B

z

z

/x d-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

-1

0

1

2

3

4

z

z

/x d

e = 0

e = 50 mm

90z

0z

180z

270z

0z +

90z +

180z +

270z +

y

xN

Straingauge

Cross 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) Strain

distribution of nal load cell design (ange thickness B=80 mm.)

Development of a 3-component load cell 17

forces or bending moments. In the same manner as described above, the load cell was subjected

to a pure shear force at the top ange. The maximum axial force recorded for strain-gauge

locations 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 the

central shaft of the load cell is no longer linear. Finally, the load cell was subjected to a pure

twisting moment. For twisting moments of 10, 20, 30 and 40 kNm the recorded maximum axial

force measure was 0.2, 0.6, 1.2 and 1.8 kN, respectively. Again, this is insignicant.

2.3. DYNAMIC BEHAVIOUR

The dynamic behaviour of the load cell was studied numerically by use of LS-DYNA. First, an

eigenvalue analysis was carried out using the same nite element model as described above. The

frequency response in terms of the ve lowest eigenfrequencies was: 1.53, 1.53, 1.63, 3.025 and

3.025 kHz. The two lowest eigenmodes correspond to bending of the central shaft around

orthogonal axes. A similar behaviour is also observed for modes four and ve. The third

eigenmode is axial twisting. The range of applicability (loading rate) of the load cell will be

governed 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 the

characteristic period Ts is given by the loading velocity v0 and the half-plastic lobe length of

deformation 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 v0

normal force can be decomposed into an axial force and two orthogonal bending moments

around the x an