Keywords: Eddy current sensors, Force and stress measurement, and Monitoring of bridge structures.

Transcription

1 A4.3 Force and Stress Measurements with Eddy Current Sensors Ji-Gou Liu ( and Wolf-Jürgen Becker (1 (1 University of Kassel, Department of Electrical Engineering, Wilhelmshöher Allee 71, D-3411 Kassel, Germany . Becker@mt.e-technik.uni-kassel.de ( GeoForschungsZentrum Potsdam, Div. 5 Geomechanics and Geotechnology Telegrafenberg, D Potsdam, Germany jgliu@gfz-potsdam.de Keywords: Eddy current sensors, Force and stress measurement, and Monitoring of bridge structures. 1. Introduction The monitoring of bridge concrete structures is increasingly significant because bridge damages can be early recognized and costs can be reduced in this way. In order to monitor bridge concrete structures fiber stress elements with integrated sensors are developed and applied to some bridge buildings [3]. The fiber sensors, however, are only applicable for monitoring of new built bridges, and their measuring systems are more expensive. The monitoring of old bridges, which are built with steel cables, is still problematic. The use of magneto-elastic sensors for tensile loading detection needs a complex computer controlled measuring system and data bank generated by a lot of calibrations []. In [1] a Micro-Magnetic Measuring Technique (3MA was proposed for the force and stress measurement of pre-stressed steels. This method uses electromagnetic multi-parameters for stress measurement. Complicated calibrations and signal processing are necessary for the stress measurement using the 3MA method, either. Thanks to the financial support of the German Research Association (DFG two structures and measuring conditions of eddy current sensors are optimized for the force and stress measurements with applications to the monitoring of bridge concrete structures. The experimental results show good properties of the optimized eddy current sensors, which are suitable for force and stress measurements [5, 6, 7]. In this paper eddy current sensors are introduced for force and stress measurements. To further improve sensor sensitivity and to reduce hysteresis between loading and unloading the sensors are miniaturized and measuring conditions (exciting current I and testing frequency f are optimized by using experiment results. Examples show potential applications to force and stress measurement of tensioned steel elements and to the monitoring of pre-stressed bridge cables and concrete structures.. Eddy Current Sensors Two sensor structures shown in Fig. 1 are suitable for force and stress measurements in tensile steel elements [5, 6]. To improve the sensor sensitivity and to reduce the hysteresis one uses a special small U- core in sensor 1, and a small E-core in sensor. Such miniaturized sensors have a higher sensitivity, a good linearity, and a smaller hysteresis. As example Table 1 shows a comparison of application parameters of the sensor 1 measured at f=1 khz. The sensitivity and correlation coefficient of the sensor using a small core U5.5/4/ is higher than that using a larger core U/16/11/6, and the hysteresis is vice versa. (a Sensor 1 using a ferrite U-core (b Sensor using a ferrite E-core Fig.1 Two variants of eddy current sensors for force and stress measurement in pre-stressed steel wire Therefore an eddy current sensor should be miniaturized for force and stress measurements. Small cores e.g. U5.5/4/ and E8.8/4/ can better be used for the sensor development.

2 Table 1 Comparison of application parameters of sensor 1 using a larger U-core (U16/11/6, l=16mm, h=11mm, d=6mm and a smaller U-core (U5.5/4/, l=5.5mm, h=4mm, d=mm Used U-core of Sensitivity (% MPa -1 Hysteresis (% Correlation coefficient sensor 1 R s L s R s L s R s L s U16/11/ U5.5/4/ The two sensors have a nearly same sensor properties (sensitivity, linearity and hysteresis etc.. A sensor coil, however, can be built more easily on a U-core than on a E-core, so that a coil with more winding number N can be used in the sensor 1. This is useful for improving the sensor sensitivity. The sensitivity, linearity and hysteresis of an eddy current force and stress sensor depend strongly on testing conditions, i.e., exciting current I and testing frequency f. The testing conditions must be optimized to obtain a high sensor sensitivity, a good linearity and a low hysteresis. To find the optimal testing conditions for the force and stress measurements the coil impedance of a sensor fixed on a steel wire (DUT is measured with an impedance measuring instrument HP 484A under exciting of different current with different frequencies. Fig. and Fig. 3 show, for instance, the resistance R s and inductance L s as function of testing frequency and exciting current. 5.5 Resistance /ohm I=1 ma 15 I=3 ma Frequency f/khz Inductance Ls /mh I=1 ma I=3 ma Frequency f /khz Fig. Frequency response of resistance R s and inductance L s of the sensor 1 5. Resistance /ohm Hz 1 khz khz Exciting current I /ma Inductance Ls /mh Hz 1 khz khz Exciting current I /ma Fig. 3 Resistance R s and Inductance L s of the sensor 1 as function of exciting current I The resistance R s of an eddy current sensor increases with the testing frequency f and changes more strongly with the exciting current in the higher frequency range than in the lower frequency range. The Inductance L s is vice versa (Fig.. The testing frequency is normally selected between 1 Hz and 1 khz. In the higher frequency range coil capacitance is not negligible. The resistance R s and inductance L s increase firstly with the exciting current I. After reaching their maximum they decrease with the exciting current. The optimal exciting current is about 3 ma for the resistance. The maximum of the inductance changes with the frequency and exciting current. For frequency from 1 Hz to 1 khz the optimal exciting current changes from 5mA to 5mA. Table shows a summary of testing conditions of eddy current sensors used for the force and stress measurement.

3 Therefore the exciting current of an eddy current sensor used for force and stress measurement is relative high. This is very different from eddy current sensors used for distance measurement. Table Optimal exciting current in frequency range from 1 Hz to 1 khz Sensor Resistance R s Inductance L s Sensor 1 3 ma 5 ma 5 ma Sensor 4 ma 3 ma 6 ma 3. Force and Stress Measurement To investigate the sensitivity, linearity, and hysteresis of the force/stress measurement a sensor is fixed on a steel wire (DUT that is tensed with a special stress apparatus. The maximum value of axial stress of the wire is about 93 MPa. This allows a measurement in the elastic range of the stress-strain diagram. The tensile force/stress is measured with strain gauge used as a reference force sensor. The coil impedance of the eddy current sensor is measured with an impedance measuring instrument HP 484A. Fig. 4 shows the resistance R s and the inductance L s of sensor 1 as function of mechanical stress. The relation between R s and, and L s and is nearly linear in the measuring stress range. Mean correlation coefficient is equal to The hysteresis of the loading and unloading curves is less than 3%. Inductance Ls /mh Loading Unloading Resistance /ohm Loading Unloading Stress /MPa Stress /MPa Fig. 4 Resistance R s and inductance L s of sensor 1 as function of mechanical stress (f= khz 931 The sensitivity, hysteresis and correlation coefficients as function of the testing frequency is shown in Fig. 5 and Fig. 6. Under exciting a current of 3mA the sensitivity (negative increases with the testing frequency, especially the sensitivity of the resistance R s. The hysteresis decreases inversely with the testing frequency. The correlation coefficient of R s is more than.998 in the frequency range from 5Hz to 1 khz, while that of L s decreases from.999 to.993 with the frequency. Therefore the testing frequency should be selected from khz to 1 khz in order to obtain good sensitivity and small hysteresis. 8 Sensitivity in % /MPa Ls Frequency f in khz Hysteresis in % 6 4 Ls Frequency f in khz Fig. 5 Maximal sensitivity and hysteresis of the resistance and inductance of sensor 1 as function of testing frequency (exciting current I=3 ma Table 3 shows the application parameters (sensitivity, hysteresis and correlation coefficient of sensor 1 and sensor at a testing frequency of 1 khz and under exciting a current of 3 ma and 4 ma. To reduce the hysteresis influence a calibration curve should be determined by averaging the loading and unloading curves. In this case the error cased by the hysteresis is a half of the hysteresis value.

4 Correlation coefficient Ls Frequency f in khz Relative error in % Loading Unloading Stress in MPa Fig. 6 Correlation coefficient of L s and R s of sensor 1 Fig 7 Relative error of predicted stress using the as function of testing frequency (I=3 ma measured value of R s and L s shown in Fig. 5 Table 3 Application sensor parameters in a measuring range of =931 Mpa (f=1 khz and I=3mA, 4mA Sensor Sensitivity in % MPa -1 Hysteresis in % Correlation coefficient Sensor Sensor Table 4 Comparison between eddy current sensor and micro-magnetic measuring technique (3MA [3]. Method Systematic Repeatability error in % in % Eddy current sensor MA method Based on their good linearity the sensor parameters R s and L s can be modeled with a polynomial of. order instead of a linear model [5,8]: R s so k1 R kr, Ls Lso k1l kl (1 From these equations one predicts the force/stress acted on the device under test: k1l k1l 4kL( Lso Ls k1r k1r 4kR so s ( Ls, ( ( k L k R To improve the repeatability of the measurement one uses the weighted mean value of (L s and (R s : L, R w ( L w ( R (3 ( s s L s R s where w L and w R are weight factors of the values (L s and (R s, respectively. The weight factor w L and w R can be selected from to 1 according to the sensitivity and the correlation coefficient of the measurands L s und R s. Fig. 7 shows relative error of predicted stress using the measured value of R s and L s shown in Fig. 5. The relative error is less than 1.% with reference to 931 MPa for a single measurement. Repeat measurements are carried out to determine the repeatability of eddy current sensors. The repeatability is also less than 1.% with reference to 931 MPa for measurement of force and stress change [6]. The measuring accuracy of the eddy current sensors is compared with that of a micro-magnetic measuring technique (3MA [1]. The result is shown in Table 4. The uncertainty of the eddy current sensors is less than that of the 3MA method. 4. Potential Application to Bridge Monitoring The eddy current sensors can be applied to bridge monitoring. Fig. 8 shows on principle sensors arrangement on a tensed steel braid in pre-stressed concrete. Multi-sensors are fixed at different key positions on the steel braid to measure the stress acted on the device under test. The impedance of the multi-sensors can be measured with an impedance measuring device with the help of a multiplexer and a microprocessor.

5 Sensor Steel braid Pre-stressed Concrete Pre-stressed concrete Sensor Steel braid Fig. 8 Sensor arrangement for monitoring pre-stressed concrete using eddy current sensors The sensor output depends on the stress w acted on an external wire where the sensor is fixed (Fig. 9. The stress acted on the braid b in the braid axis direction can be derived from the stress w : b k w k1 cos( (4 w where k 1 is a conversion factor, which is better determined by experiments. The external wires are braided each other and have a different geometry with that of the middle wire used for the sensor calibration (Fig. 1. The relation between the measuring value k on the middle wire used for calibration and the measuring value D on an external wire can be written by w k k (5 where the conversion factor k can be determined with measurements on a middle wire and an external wire in case of without external force F=. R External wire I - I L Sensors I R Middle wire F b F w I F b Fig. 9 Pre-stressed braid composed of seven wires and sensor arrangement DUT: Pre-stressed steel braid bx wx F r wx MUX Sensor Z Measuring system R swx R wx bx Reference element: Braid middle wire F r Force measuring device Reference stress: k1 k k3 Calibration R R sk R Fig. 1 Calibration for force/stress measurement of pre-stressed steel braid using eddy current sensor In order to realize the force/stress measurement of a pre-stressed steel braid and to reduce measuring errors the measuring system have to be calibrated using reference elements and reference force measuring device. Fig. 1 shows the calibration according to calibration method proposed in [1]. For the calibration a

6 reference middle wire tensed by a special stress apparatus is used as reference element. Under applying three reference forces/stresses ( k1, k, k3 to the middle wire the sensor impedance is measured with the measuring system. One obtains three reference measuring values (R, R sk, R or (L, L sk, L after the calibration. The impedance Z wx of sensor fixed on an external wire of the braid (DUT is measured with the same measuring system. An equivalent resistance R or inductance L can be determined analog (5 (R = R swx /k using the measuring value R swx or L swx of the stress wx. The stress wx can be determined by a quadratic interpolation [1]: wx sk sk sk sk k k k1 k3 sk sk k k (6 The calibration can directly be realized using a reference braid in laboratory or test field, either. In this case combining sensors distributed on the external wires of a steel braid are used for the calibration. 5. Conclusions The investigations of eddy current sensors have shown that sensor structure should be miniaturized and the testing conditions have to be optimized for the measurements of force/stress in pre-stressed steel cables and elements. The sensor sensitivity and linearity can remarkably be improved by miniaturizing the sensor structure and optimizing the testing conditions. The hysteresis can be reasonably reduced in this way, either. The eddy current sensors can be used for force and stress measurement of tensile steel elements, for the monitoring of pre-stressed bridge cables and concrete structures. Further research works will be focused on their applications to bridge structures monitoring and to measurement of residual stress in steel elements. 6. Acknowledgement This work has been supported by the German Research Association (DFG. The authors would like to thank the DFG for the financial support. They thank also Dr. R. Kern, Dr. W. A. Theiner and Dr. G. Dobmann, Fraunhofer-Institute of Non-Destructive Testing Techniques, Saarbrücken/Germany, for their helps at the comparison measurements with the 3MA measuring method, and Mr. T. Gerhold and Dr. W. Ricken, University of Kassel, for their helps at the implementation of the DFG project. References [1] G. Dobmann: Messung der Vorspannung mit mikromagnetischen Methoden, Symposium Zerstörungsfreie Prüfung im Bauwesen in Berlin, Berichtsband 1 der Deutschen Gesellschaft für Zerstörungsfreie Prüfung, S [] H. Falkner, M. Laube, H. Wichmann: Stress Measurement by means of the magneto-elastic method, International Symposium Non-Destructive Testing in Civil Engineering (NDT-CE, Berlin, 1995, Berichtband 48. DGZfP, S [3] S.Wiese, J.Wichern, W.Kowalsky and W.Grahn, Fiberoptical Sesnors in Concrete, XVI IMEKO World Congress, Sept. 5-8,, Vienna, Austria [4] L. Mehnen, E.Kaniusas, E.Leiss and H. Pfützner, Magnetostrictive Force and Displacement Sensor, XVI IMEKO World Congress, Sept. 5-8,, Vienna, Austria [5] J.-G. Liu, T. Gerhold, W. Ricken, W.-J. Becker, E. Fehling, Einfluß der magnetischen Kopplung bei der Vorspannungsmessung an Spannstahl, DACH-Jahrestagung DGZfP, Mai, Innsbruck, Austria, in press [6] J.-G. Liu; W.-J. Becker; T. Gerhold; W. Ricken, E. Fehling, Messung der Vorspannungs-änderung an Spannstahl mittels Wirbelstromsensoren, DGZfP-Workshop zur Material-charakterisierung, 1. Mai, Düsseldorf [7] W. Ricken, J.-G. Liu and W.-J. Becker, GMR- and Eddy Current Sensor in Use of Stress Measurement, EMSA Third European Conference on Magnetic Sensors and Actuators, July, Dresden, Germany, in press [8] W.-J. Becker and J.-G. Liu, Eddy Current Sensors and Applications to Force and Stress Measurements, Tunisia- German-Conference, 7-3 March 1, Hammamet, Tunisia,, in press [9] J.-G. Liu; W.-J. Becker; T. Gerhold; W. Ricken: Parametertrennung in Meßsystemen und Sensoren durch Signalverarbeitung, Technisches Messen, tm 11/, pp [1] J.-G. Liu and U. Frühauf, Self-Calibration Measuring Methods and Application to Measurements of Electrical Quantities, Measurement, vol. 6, no., August 1999, pp