A Calibration Technique for Bi-axial Shake Tables with Stepper Motor

Abstract

Shaking tables are frequently used to determine the dynamic behavior of structures in the laboratory environment. In order to obtain realistic results in experimental studies, table response and performance should be consistent with the desired motion. In this multidisciplinary study, an application of a new method for determining and calibrating the mechanical response of a developed bi-axial displacement controlled shake table according to the desired motion data is presented. The bi-axial shake table's electro-mechanical components consist of stepper motors, ball screw sets, linear ball bearings, and linear potentiometers positioned on both axes for displacement measurements. For the control and data acquisition (DAQ) unit of the shake table, an open-source electronic prototyping platform Arduino was used. From several experimental results, it was seen that, with the presented calibration method, harmonic and earthquake simulations could be achieved with a relative root mean square error (relative RMS error) of less than 5% for desired displacement-time histories.

Keywords

• Shaking table
• calibration
• Arduino
• stepper motor
• ball screw set
• linear ball bearing
• linear potentiometer

References

1. O. Ozcelik, J.E. Luco, J.P. Conte, Identification of the mechanical subsystem of the NEES-UCSD shake table by a least-squares approach, Journal of Engineering Mechanics, 134(2008)23–34. https://doi.org/10.1061/(ASCE)0733-9399(2008)134:1(23)
2. S.E. Kim, D.H. Lee, C. Ngo-Huu, Shaking table tests of a two story unbraced steel frame. Journal of Constructional Steel Research, 63 (2007) 412–421. https://doi.org/10.1016/j.jcsr.2006.04.009
3. J. Kuehn, D. Epp, W. N. Patten, High-fidelity control of a seismic shake table, Earthquake Engineering and Structural Dynamics, 28 (1999) 1235–1254. https://doi.org/10.1002/(SICI)1096-9845(199911)28:11<1235::AID-EQE864>3.0.CO;2-H
4. N. Nakata, Acceleration trajectory tracking control for earthquake simulators, Engineering Structures, 32 (2010) 2229–2236. https://doi.org/10.1016/j.engstruct. 2010.03.025
5. J. E. Luco, O. Ozcelik, J. P. Conte, Acceleration Tracking Performance of the UCSD-NEES Shake Table. Journal of Structural Engineering, 136 (2010) 481–490. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000137
6. T. Y. Yang, K. Li, J. Y. Lin, Y. Li, D. P. Tung, Development of high-performance shake tables using the hierarchical control strategy and nonlinear control techniques, Earthquake Engineering & Structural Dynamics, 44 (2015) 1717–1728. https://doi.org/10.1002/eqe.2551
7. M. Saranik, D. Lenoir, L. Jézéquel, Shaking table test and numerical damage behaviour analysis of a steel portal frame with bolted connections, Computers and Structures, 112–113 (2012) 327–341. https://doi.org/10.1016/j.compstruc.2012.07.009
8. R. Zhang, P. V. Lauenstein, B. M. Phillips, Real-time hybrid simulation of a shear building with a uni-axial shake table, Engineering Structures, 119 (2016) 217–229. https://doi.org/10.1016/j.engstruct.2016.04.022.

9. A. C. Altunisik, A. Yetisken, V. Kahya, Experimental study on control performance of tuned liquid column dampers considering different excitation directions, Mechanical Systems and Signal Processing, 102 (2018) 59–71. https://doi.org/10.1016/j.ymssp. 2017.09.021
10. Z. Fırat Alemdar, Betonarme Köprü Kolonlarında Plastik Mafsal Bölgelerinin Modellenmesi, İMO Teknik Dergi, 444 (2015) 7279-7286.
11. A. Ashasi-Sorkhabi, H. Malekghasemi, O. Mercan, Implementation and verification of real-time hybrid simulation (RTHS) using a shake table for research and education, Journal of Vibration and Control, 21(8) (2015) 1459–1472. DOI: 10.1177/1077546313498616
12. A. Najafi, B. F. Spencer Jr, Modified model-based control of shake tables for online acceleration tracking, Earthquake Engng Struct Dyn., (2020) 1–17. DOI: 10.1002/eqe.3326
13. E. Damcı, Ç. Şekerci, Development of a Low-Cost Single-Axis Shake Table Based on Arduino. Experimental Techniques, 43 (2019) 179-198. https://doi.org/10.1007/s40799-018-0287-5
14. MATLAB version R2017b, 2017, computer program, The MathWorks Inc., Natick, Massachusetts.
15. PEER Ground Motion Database - PEER Center. http://ngawest2.berkeley.edu/ (Accessed, 15th November 2018).