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January/February 2003 EXPERIMENTAL TECHNIQUES 21
TECHNIQUES
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TECHNIQUES by D.I. Kang, J.H. Kim and Y.K. Park
DEVELOPMENT OF A BINOCULAR TYPESIX-COMPONENT LOAD CELL
This paper presents the development of a binoculartype six-component load cell using experimental de-sign with an orthogonal array. The finite elementanalysis is adopted to obtain the strain distribu-
tions of the sensing element, and the analysis of variance isutilized for determining the main design variables of thesensing element which have a significant effect on the outputstrain. The calibration of the designed six-component loadcell is performed to evaluate the coupling error of each force/moment component. Test results show that the fabricatedsensor with maximum capacities of 196 N in forces and 19.6Nm in moments has a coupling error less than 3% Full Scale(FS).
INTRODUCTIONForces and moments should be measured accurately to guar-antee the stability of the quality of products in industrialfields such as robot, machine tool, automobile and ship. Amulti-component force sensor, which consists of multiplesensing elements, has been widely used to measure forces
Fig. 1: Schematic diagram of binocular-type structure formeasuring six-component force /moment
and moments in these fields.It is not easy, however, to de-sign a multi-component forcesensor due to its complicatedstructure and errors causedby coupling between forceand moment components.
Ono and Hatamura1–2 de-signed a multi-componentforce sensor using a parallelplate structure and a radialplate structure. Kim etal.3 also designed a three-component force sensor witha multiple parallel platestructure for which coupling errors were less than 3%. Ya-buki4 designed a six-component force sensor with parallelplate structures for a robot arm. However, it is not easy tofabricate the sensing element with a parallel plate structuredue to the difficulty of its complex geometry. On the otherhand, it is easy to manufacture the binocular-type structurefor a sensing element. The rated capacity of the momentcomponents over force components was also significantlylarger due to the higher rigidity of the binocular-type struc-ture compared with the parallel plate structure. Addition-ally, it is easy to determine the locations of strain gages foreach force /moment component because of the uniformity ofthe strain distribution. Therefore, this paper presents thedevelopment of a six-component force /moment sensor withbinocular-type sensing elements and shows the design meth-odology using an experimental technique based on the finite
D.I. Kang is Director, J.H. Kim is Senior Researcher, and Y.K. Park is Senior Re-searcher, in the Division of Physical Metrology of KRISS, Korea.
element analysis because of the complexity of the sensor ge-ometry.
DESIGN OF A FORCE/MOMENT SENSOR USINGFEM AND EXPERIMENTAL TECHNIQUEFigure 1 shows a basic binocular-type structure for measur-ing two-component force and moment. The capacity of thesix-component force sensor is 196 N in each force componentand 19.6 Nm in each moment component. Figure 2 showsfinite element meshes of a basic binocular structure and itsdeformed shapes in the case of the vertical force Fy and themoment Mz. The finite element mesh used the ANSYS pro-gram and an 8-node isoparametric plane stress elementsince strain gages are attached to the surface of the sensingelement. The material used is Al 2024-T351, which has anelastic modulus of 68.6 GPa and a Poisson’s ratio of 0.3. Fig-ure 3 shows the geometric factors (a, b, c, d, g and t) of abasic structure for design of the force /moment sensor. Whenthe main variables of the sensing element are as follows: t� 2 mm; a � 4 mm; b � 8 mm; c � 5 mm; d � 10 mm; g �15 mm, Figure 4 shows the axial strain distributions along
the x-axis direction shown inFigure 3 on the upper sur-face of the binocular struc-ture. For the Fy component,the strain distribution wassymmetric about the y-axisat the center of the sensingelement and for Mz compo-nent, the bending point sym-metry was at the center ofthe sensing element. Usingthese strain distributions,the locations of strain gagescan be determined to reducethe coupling effect of eachforce or moment component.
On the other hand, it is not easy to evaluate the main geo-metric factors of a binocular structure because of the diffi-culty of its theoretical analysis. Therefore, finite elementanalysis was applied to investigate the effects of geometricfactors of a binocular structure on the sensitivity of eachforce or moment component. Table 1 presents the six mainfactors and two levels. The L16 orthogonal array was usedto exclude the reciprocal factor for not less than three fac-tors.5 Table 2 shows the axial strains of the binocular struc-ture on the L16 array in case of Fy of 196 N or Mz of 19.6Nm. The main factors were arranged on the rows(1, 2, 4, 7,8 and 11) of the L16 array. Table 3 shows the AN-OVA(analysis of variance) summary for the force Fy calcu-lated from Table 2. Here SS, f, V, F and P mean the sum ofsquares, the freedom, the mean square, the variance ratioand the percent contribution, respectively. Table 4 shows theANOVA summary for the moment component Mz. The AN-OVA can be performed simply by5
22 EXPERIMENTAL TECHNIQUES January/February 2003
TECHNIQUES
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BINOCULAR TYPE SIX-COMPONENT LOAD CELL
Fig. 4: Axial strain distributions on the upper surface of thebinocular-type structure
Table 1—Levels of the Main Geometric Factors forthe Binocular Structure
FACTORLEVEL
t(mm)
a(mm)
b(mm)
c(mm)
d(mm)
g(mm)
1 1.5 4 5 5 15 10
2 2.0 5 10 7 20 20
Fig. 2: Finite element mesh of binocular-type structure usedand its deformed shapes in the case of (a) vertical force Fy
and (b) momet Mz
Fig. 3: Geometric main factors of binocular-type structurefor designing the force /moment sensor
f � N � 1, f � k � 1, f � k � 1,T A A B B
f � f � ( f � f � � � �)e T A B
N kA2 2 2T A Ti2SS � y � , SS � � ,� �T i AN n Ni�1 i�1 Ai
kB 2 2B TiSS � � (1)�B n Ni�1 Bi
S � SS � (SS � SS � � � �)e T A B
SS S VA e AV � , V � , F �A e Af f VA e e
(SS � V � f )A e AP � � 100%A SST
where N, kA, T, Ai, nAi, yi and e are the number of experi-ments, the number of level at factor A, the total of results,the sum of factor A at level i, the number of factor A at leveli, the observed value and the error, respectively.
Considering that the F distribution calculated from theFisher test is 5.12 in the case of the 95 % confidence level,it is found that the geometric factors in the order t � d �b � c affect the bending strains of the binocular structureunder the Fy force condition. The factors in the order b � c� t affect the bending strains of the binocular structure un-der the Mz moment condition. However, the contribution rate
January/February 2003 EXPERIMENTAL TECHNIQUES 23
TECHNIQUES
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BINOCULAR TYPE SIX-COMPONENT LOAD CELL
Table 2—Strains Obtained from Finite ElementAnalysis with the Trial of the Geometric Factors ofBinocular Structure on L16 Array
TRIAL
FACTOR (mm)
t a b c d g
STRAIN(�m / m)
Fy Mz
1 1.5 4 5 5 15 10 807 493
2 1.5 4 5 5 20 20 1057 508
3 1.5 4 10 7 15 10 548 194
4 1.5 4 10 7 20 20 712 194
5 1.5 5 5 7 15 20 676 327
6 1.5 5 5 7 20 10 871 293
7 1.5 5 10 5 15 20 631 297
8 1.5 5 10 5 20 10 817 263
9 2.0 4 5 7 15 20 370 247
10 2.0 4 5 7 20 10 476 220
11 2.0 4 10 5 15 20 345 222
12 2.0 4 10 5 20 10 447 190
13 2.0 5 5 5 15 10 433 364
14 2.0 5 5 5 20 20 568 377
15 2.0 5 10 7 15 10 301 146
16 2.0 5 10 7 20 20 391 148
Table 3—ANOVA Summary for the Sensing ElementSubjected to the Force Component Fy
FACTOR SS(�105) f V(�105) F P
t 4.86 1 4.86 183.45 67.9%
a 0.00342 1 0.00342 0.13 �0.3%
b 0.71 1 0.71 26.82 26.82%
c 0.361 1 0.361 13.63 13.63%
d 0.942 1 0.942 35.59 35.59%
g 0.00156 1 0.00156 0.06 0.06%
Error 0.238 9 0.0265
Total 7.115 15
Table 4—ANOVA Summary for the Sensing ElementSubjected to the Moment Component Mz
FACTOR SS(�105) f V(�105) F P
t 0.268 1 0.268 20.32 13.9%
a 0.00176 1 0.00176 0.13 �0.6%
b 0.863 1 0.863 65.39 46.4%
c 0.558 1 0.558 42.29 29.8%
d 0.588 1 0.588 0.45 �0.4%
g 0.0154 1 0.00154 1.17 0.1%
Error 0.119 9 0.0132
Total 1.831 15
Table 5—Design Process for Determining theDimensions of the Binocular-type Structure
CASE
DIMENSION (mm)
t a b c d g
STRAIN (�m / m)
FORCE MOMENT
1 2 4 5 5 15 15 435 382
2 2 4 10 5 15 15 343 217
3 2 4 8 5 15 15 375 268
4 2 4 8 7 15 15 325 182
5 1.5 4 8 5 15 15 692 361
6 1.9 4 8 5 15 15 418 283
7 1.9 4 8 5 10 15 291 299
per difference between level 1 and level 2 should be com-pared. It is finally found that the factors affect the bendingstrains in the order t � d � c � b under the Fy force con-dition and t � c � b under the Mz moment condition. Thethickness of the binocular hole, t, had the most significanteffect on the bending strains under force condition Fy or mo-ment condition Mz. The distance between binocular holes, d,did not affect the bending strains under force condition Fy,but had an effect on the bending strains under moment con-dition Mz. The effects of a and g on the bending strains underboth conditions were negligible. Thus, after the t, b and cvalues were first determined to adjust the designed sensitiv-
ity of the sensing element for the moment component, thefactor d for the force component was finally decided. In thecase of arranging a full bridge circuit (Wheatstone bridgecircuit) with four strain gages, each strain range was de-signed as 280 � 300 �m/m to obtain the rated output 0.5mV/V. Table 5 shows the design process for determining thedimensions of the binocular structure. Therefore, the dimen-sions, t, a, b, c, d and g for the force /moment sensor werefinally determined as 1.9, 4, 8, 5, 10 and 15, respectively.
FABRICATION OF A FORCE/MOMENT SENSORAND ITS CALIBRATIONFigure 5 shows the configuration of the binocular-type, sixcomponents, force /moment sensor.6 The sensor was fabri-cated with Al 2024-T351. The sensing element has upperand lower rings, which individually have two diametricallyopposite connectors, locking holes and accurate thick parts.The sensing unit also has a cross beam, which has horizontaland vertical parts crossing at right angles. In the crossbeam, vertical and transverse binocular openings wereformed on the horizontal and vertical parts. The horizontaland vertical parts of the cross beam were spaced apart fromthe lower and upper rings by a gap respectively. However,the cross beam was connected to the upper and lower ringsthrough the connectors.
24 EXPERIMENTAL TECHNIQUES January/February 2003
TECHNIQUES
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BINOCULAR TYPE SIX-COMPONENT LOAD CELL
Fig. 5: Configuration of the binocular-type sensor formeasuring six-component force /moment
Fig. 6: Positions of strain gages and Wheatstone bridgecircuit with 24 strain gages for sensing six-component force /moment
Table 6—The Calibrated Strain Output of Six-component Force/Moment Sensor Obtained fromWheatstone Bridge Circuit Shown in Figure 6(unit: �m/m FS)
LOADSENSITIVITY Fx Fy Fz Mx My Mz
SFx 1109 4 1 �5 21 �9
SFy 5 1116 �3 21 1 28
SFz �12 6 887 �15 9 3
SMx �3 5 �2 1677 �1 �8
SMy �18 0 �1 �14 1644 10
SMz 10 11 �16 13 �1 1171
The strain gages as shown in Figure 6 were attached to po-sitions of the cross beam to give both maximum strain andoffset coupling strain when the binocular structure is sub-jected to a force or moment component. In case of the Fz, Mxand My components, the strain gages were located at theinner part of the sensor and for the Fx, Fy, Mz components,the outer part of the sensor. The total number of strain gagesshown in Figure 6 was 24 to comprise the six Wheatstonebridge circuits for the force /moment components. The straingages were manufactured by Micro-Measurement Co. (modelMM-N2A-13-T001N350).
The calibration of the six-component force /moment sensorwas performed by a six-component force /moment standardmachine, which was designed and constructed at theKRISS.7 Table 6 shows the results of the calibration test,which are the expected outputs obtained from the Wheat-sone bridge circuits shown in Figure 6. Here SFX is the out-put of the strain measured from the full bridge circuit for Fxwhen each force /moment component is applied to the sensor.Thus the diagonal terms show the rated outputs of the fullbridge circuit for each force /moment component when thesensor is subjected to the rated capacity, 196 N in the forceor 19.6 Nm in the moment. The other terms mean the out-puts caused by the unwanted coupling effect of each com-ponent. The expected outputs of the components, Fx, Fy andMz, were 1100 �m/m to 1200 �m/m. On the other hand, theother terms, Fz, Mx and My were less than or more than theexpected output. The difference of the rated outputs wascaused by the finite element analysis using a 2-D elementand the location of the binocular-type part in the sensingelement. Table 7 presents the coupling error of the six-component sensor obtained from Table 6. Here each termmeans the ratio of the output of the each full bridge circuitover the diagonal term shown in Table 6. The maximum cou-pling error was 2.51 % in the output of the full bridge circuit,Fy, when the sensing element is subjected to the Mz compo-nent. Thus it is found that from the standpoint of the rigidityand coupling error, the six-component force /moment sensorof the binocular-type structure showed a good performance
compared with the force /moment sensor using some parallelplate structures.
January/February 2003 EXPERIMENTAL TECHNIQUES 25
TECHNIQUES
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BINOCULAR TYPE SIX-COMPONENT LOAD CELL
Table 7—The Coupling Errors of Six-componentForce/moment Sensor (Unit: % FS/FS)
LOADSENSITIVITY Fx Fy Fz Mx My Mz
SFx — 0.36 0.09 0.45 1.89 0.81
SFy 0.45 — 0.27 1.88 0.09 2.51
SFz 1.35 0.68 — 1.69 1.01 0.34
SMx 0.18 0.32 0.12 — 0.06 0.48
SMy 1.08 0.00 0.06 0.85 — 0.61
SMz 0.85 0.94 1.37 1.11 0.08 —
CONCLUSIONSThis paper describes the development of the six-componentforce /moment load cell using multiple binocular-type struc-tures. The experimental technique using the L16 orthogonalarray was applied to determine the dimensions of the maingeometric factors of the binocular structure. The locations ofthe strain gages were determined from the strain distribu-tion using finite element analysis. The load cell consists ofsix Wheatstone full bridge circuits to increase sensitivity andcompensate for ambient temperature. The calibration of thedesigned six-component load cell showed that the fabricatedsensor with the maximum capacities of 196 N in forces and19.6 Nm in moments has a coupling error less than 3 % FS.
ACKNOWLEDGMENTSThis work has been supported by the National ResearchLaboratory for the Force Measurement & Evaluation (Pro-ject No. 2000-N-NL-01-C-141).
References
1. Ono, K., and Hatamura, Y., ‘‘A New Design for 6-componentForce /Torque Sensors,’’ Proceedings of the 11th International Con-ference on Measurement of Force and Mass, Amsterdam, The Neth-erlands, 39–48 (1986).
2. Hatamura, Y., ‘‘Multi-axis Load Sensor,’’ United States PatentNumber; 4, 712, 431(1987)
3. Kim, G.S., Kang, D.I., Jeoung, S.Y., and Joo, J.W., ‘‘Design ofSensing Element for 3-component Load Cell Using Parallel PlateStructure,’’ J. of KSME 21(11), 1871–1884 (1997).
4. Yabuki, A., ‘‘Six-axis Force /Torque Sensor for Assembly Ro-bots,’’ FUJITSU Sci. Tech. J., 26(1), 41–47 (1990).
5. Ross, P.J., ‘‘Taguchi Techniques for Quality Engineering,’’ Mc-Graw- Hill, (1989).
6. Kang, D.I., Kim, G.S., Jeoung, S.Y., and Joo, J.W., ‘‘Design andEvaluation of Binocular Type Six-component Load Cell by UsingExperimental Technique,’’ J. of KSME 21(11), 1921–1930 (1987).
7. Kim, G.S., ‘‘The Development of a Six-component Force /Mo-ment Sensor Testing Machine and its Evaluation of Uncertainty,’’Meas. Sci. Technol. 11, 1377–1382 (2000). �
