DEVELOPMENT OF A LOAD CELL FOR FORCE MEASUREMENTS SUBJECT TO FLOW INTERFERENCES

by T.K. Woon

A strain-gage load cell of cantilever type has been developed specifically for force measurements for flow interference study in a wind tunnel. In order to mea- sure small loads accurately, the load cell makes use of four active strain gages in a Wheatstone-bridge arrangement to in- crease the load-cell sensitivity and is temperature compen- sated. The load cell is capable of measuring forces on a struc- ture regardless of the point of loading on the model structure. The load cell is designed to ensure that the moment compo- nents, the lift force and the cross-wind force due to flow in- teraction among structural models do not affect the drag force measurements when it is installed in along-wind direction. The calibration process confirms that the effects of force and moment coupling are indeed negligible and can be accounted for. The same is true when the load cell is installed in cross- wind direction for cross-wind force measurements. The load cell exhibits linear characteristics.

INTRODUCTION Due to the complexity of flow interactions in neighboring

structures, flow-interference studies have often followed the ex- perimental approach using load cells and wind tunnels. To mea- sure the force components separately and accurately, the load cell must be capable of eliminating the effects from others as well as from the resulting moments. Otherwise the effects must be ac- counted for quantitatively. It is the objective of the paper to pre- sent the design, fabrication and calibration of a load cell suitable for force measurements in flow interference studies.

LOAD CELL DESIGN AND FABRICATION

follows: The load cell design requirements and specifications are as

-No loading constraint: the force measurements are inde-

-No force component interference: force component inter-

-No moment component interferences: moment component

-High sensitivity: the load cell should be able to measure

-Linearity: output from the load cell should be linearly pro-

The output from a load cell is a function of the force inputs as well as the points of force loading. The force inputs consist of three mutually independent components, i.e., the drag force F , , the cross-wind force F2 and the lift force F3. When the point of reference is selected, the moment about this point can be con- veniently decomposed into three components, i.e., the rolling mo- ment M , , the pitching moment M 2 and the twisting moment M,.

pendent of point of loading.

ferences must be negligible and accountable.

interferences must be negligible and accountable.

small loads in the range of 3N.

portional to the applied loads.

7: K. Woon is Associate Professoz Nanyang Technological University, School of Mechanical and Production Engineering, Singapore.

The systems of force and moment components are shown in Fig. I . From a mathematical stand point, one finds

where Eo = load-cell outputs. The above function can be written in the following Taylor’s series at no-load condition and the sec- ond- and higher-order terms are neglected.

a a + F2 - + F3 - aF2 aF,

Eo = Eo(O, 0, 0, 0, 0, 0) +

Equation (2) forms the basis for load-cell calibration. The partial derivatives reflect the effects of force and moment coupling under no-load condition. Each term in this equation must be determined via calibrations.

Suppose the load cell is placed along-wind direction with no flow interferences. It can then be assumed that F , >> F2;

Wind load

,Model s t r u c t u r e

Fig. I - The systems of force and moment components

Experimental Techniques 25

F , >> F,; M, >> M, and M , >> M,. Equation (1 ) can be simplified to

Eo = w,, RA) (3)

Where the loading force F, is equal to the drag force acting at point A whose location is defined by the position vector RA. The arrangement of the strain gages has to be designed to eliminate the dependence of loading on the load cell.

A rectangular aluminum bar was used to fabricate the load cell. The physical dimensions of the load cell are shown in Fig. 2. Spacers were provided between the model structure and the load cell. This allowed the force transmitted onto the load cell and at the same time eliminated any frictional effects between the two structures due to deflection. Near the load-cell base, two cavities were machined symmetrically with respect to the center axis z. In order to measure small loads in the range of 3N, four active strain gages were used to give high sensitivity as required. Two strain gages were to be mounted in each cavity and were marked in numerical sequence (Fig. 2). The W K-type strain

- -m I! Aluminium bar

I Model s t r u c t u r e 2 . 3 f

I - - -..#

I

I Fig. 2- Load-cell dimensions and strain-gage installations

gages were used with a gage factor of 2. Strain gages 2 and 4 were located directly on top of strain gages 1 and 3 at a con- venient distance L apart. The load cell was of cantilever type with four active strain gages connected to form a constant voltage Wheatstone-bridge circuit as shown in Fig. 3. With this arrange- ment, strain gages 1 and 2 were subject to tension while gages 3 and 4 were under compression and vice versa. At section M- M , the moment experienced by gages 2-4 is ( F I L M ) while at section N-N the moment experienced by gages 1-3 is ( F I L N ) . The sensitivity of strain gages is (Ref. 1)

ARIR = SE

and SE a applied moments

where R = strain-gage resistance, AR = change of gage resis- tance under loads, and S and E are the gage factor and axial strain, respectively.

It follows that,

and

where K is a proportional constant.

lowing relationship can be obtained (Ref. 1). For a constant voltage Wheatstone-bridge in Fig. 3, the fol-

where E, is the voltage supply and the subscripts denote the strain-gage number. Substituting eqs (4) and (5) into eq (6),

(7)

where L = (LN - LM) is the distance between the gages and is a constant. For a given strain-gage type and power supply, it can be seen that the load-cell output does not depend on the point of loading and is only a function of the applied force F,.

LOAD-CELL CALIBRATION A number of calibration weights are used as applied loads.

The load cell is connected to a strain meter which provides power

Fig. 3- Constant voltage Wheatstone-bridge circuit

26 September/October 1996

supply to the Wheatstone-bridge circuit. The strain meter also amplifies the electrical voltage signal to a higher level in the range of 0-10 volts. This signal is then measured using a digital meter. The points of loading and the magnitudes of the applied load F, are varied in sequence systematically. In addition to the applied load F,, the calibration process is continued with the cross-wind load F, acting simultaneously in the cross-wind di- rection. The points of loading are also varied accordingly. Sim- ilarly, the lift force F3 is also applied. The calibration curves are plotted in Figs. 4 to 9.

With reference to eq (2). the effects of force and moment coupling on the load-cell outputs can be assessed quantitatively by each partial derivative term in the equation. Figure 4 shows the variation of output as a function of applied force F, at various loading points. It can be seen that the points of loading have no effects on the outputs and that a linear relationship exits between the outputs and applied forces. The variations of output as a function of cross-wind force and lift force are given in Figs. 5 and 6, respectively. Both the cross-wind force and lift force play no part on the outputs as a,/a, = 0 and a,/a, = 0. Figure 7 depicts the outputs as a function of the rolling moments at var- ious applied loads. The results indicate that a,/$,,, = 0. Figures 8 and 9 give the outputs as a function of the pitching moments and twisting moments, respectively. It can also be observed that both aEQ/aM2 = 0 and aEo/aM, = 0. As a result, eq (2) reduces to

2 -

0

Eo = Eo(O. 0, 0, 0, 0, 0) + F , - Eo ( a 3

- Fl=0.98N - F1=1.96N - F1=2.94N

' 1 1 1 1 " " " " 1 1 " " ~

8 '1 wo I:

4 c

/

Y O J " " " " " " " ~ 0 1 2 3

Applied force F, N Fig. 4- Load-cell output versus applied force at various loading points

8t

- Fl=0.98N - Fl=l.WN - F1=2.94N

0 0.0 0.5 1 .o 1.5 2.0

Cross-wind force F2 N Fig. 5-Load-cell output versus cross-wind force

"E

Experimental Techniques 27

10

8 gt a - c. B 6: > - lL0 5

4 -

3-

2 -

1 -

8 1 L

I

4 -

2-

0

L

- Fl=0.98N - Fl=1.96N -0- Fl=2.94N

" " ' i " ' l " " l " " l " " ~

12-

10

8 - v) c - - P : Uo 6 -

4 -

2 -

0 t " L ' I ' " ' I ' ' " ' 0.00 0.10 0.20 0.30

Twisting moment M, Nm

Fig. 9- Load-cell output versus twisting moment

EO = 0.4 + 3.36 FI

FI = 0.298(& - 0.4)

(9) or

(10) The units for E, and F , are volts and Newtons respectively.

The calibration exercises show that the effects of the cross- wind forces and lift forces on the drag force measurements are negligible and that these effects reflected in the partial derivatives in eq (2) can be determined quantitatively through calibration. The moment components play no part in the load-cell outputs. Furthermore the points of loading do not affect the load-cell out- puts. These unique features make this load cell a simple and reliable instrument as compared to an expansive multicomponent load cell. The load-cell sensitivity is high enough to measure small forces in the range of 3N. This means that the load cell can be installed in cross-wind direction to measure the cross- wind loads even when the other force components are dominant. The constraints on using this type of load cell are that the flow is unidirectional and its direction is known a priori. The load cell must be placed in along-wind direction so that the actual drag force will be measured.

CONCLUSIONS The load cell meets the design requirements and specifica-

tions. The effects of force and moment coupling are negligible on the load-cell Derformance. The load cell is simple in design

-

- and gives reasoiable sensitivity and a linear output. It can be used for small force measurements and is suitable for flow- o " " ' l " " l " " ~ " " ~

0.0 0.2 0.4 0.6 0.8 interference studies.

Pitching moment M, Nm ACKNOWLEDGMENT The author would like to express his gratitude for the contri-

butions made by Mr. Lee S.L. to this project. Fig. 8-load-cell output versus pitching moment

REFERENCES 1. Dally, J.W., Riley, W E and McConneff. K.G., "Instrumenfation for

2. Thomas. G.B.. and Roy, D.M. . "Mechanical Measurements." Addison

3. Gorlin. S.M.. and Slezinger; 1.1.. "Wind Tunnel and rheir Instruments."

From Fig. 4 and at no-load condition, EdO, 0, 0, 0, 0, 0) = 0.4 and dE,,IdF, = 3.36. (1990).

Engineering Measurements," John Wiley & Sons lnc. (1984).

The following calibration equations are obtained. National Science Foundation (1966).

28 September /October 1996