0
Research Papers

Numerical and Experimental Study of Clearance Nonlinearities Based on Nonlinear Response Reconstruction

[+] Author and Article Information
Jie Liu

State Key Laboratory for
Manufacturing Systems Engineering,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: jieliu2013@stu.xjtu.edu.cn

Bing Li

State Key Laboratory for
Manufacturing Systems Engineering,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: bli@mail.xjtu.edu.cn

Huihui Miao

State Key Laboratory for
Manufacturing Systems Engineering,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: mhh1989@stu.xjtu.edu.cn

Anqi He

State Key Laboratory for
Manufacturing Systems Engineering,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: 15909293029@163.com

Shangkun Zhu

State Key Laboratory for
Manufacturing Systems Engineering,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: zhusk268@163.com

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received February 27, 2017; final manuscript received August 23, 2017; published online November 1, 2017. Assoc. Editor: Mohammad Younis.

J. Comput. Nonlinear Dynam 13(2), 021001 (Nov 01, 2017) (17 pages) Paper No: CND-17-1089; doi: 10.1115/1.4037927 History: Received February 27, 2017; Revised August 23, 2017

With the growing structural complexity and growing demands on structural reliability, nonlinear parameters identification is an efficient approach to provide better understanding of dynamic behaviors of the nonlinear system and contribute significantly to improve system performance. However, the dynamic response at nonlinear location, which cannot always be measured by the sensor, is the basis for most of these identification algorithms, and the clearance nonlinearity, which always exists to degrade the dynamic performance of mechanical structures, is rarely identified in previous studies. In this paper, based on the thought of output feedback which the nonlinear force is viewed as the internal feedback force of the nonlinear system acting on the underlying linear model, a frequency-domain nonlinear response reconstruction method is proposed to reconstruct the dynamic response at the nonlinear location from the arbitrary location where the sensor can be installed. For the clearance nonlinear system, the force graph method which is based on the reconstructed displacement response and nonlinear force is presented to identify the clearance value. The feasibility of the reconstruction method and identification method is verified by simulation data from a cantilever beam model with clearance nonlinearity. A clearance test-bed, which is a continuum structure with adjustable clearance nonlinearity, is designed to verify the effectiveness of proposed methods. The experimental results show that the reconstruction method can precisely reconstruct the displacement response at the clearance location from measured responses at reference locations, and based on the reconstructed response, the force graph method can also precisely identify the clearance parameter.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Sun, D. , 2016, “ Tracking Accuracy Analysis of a Planar Flexible Manipulator With Lubricated Joint and Interval Uncertainty,” ASME J. Comput. Nonlinear Dyn., 11(5), p. 051024. [CrossRef]
Zhang, J. , and Du, X. , 2015, “ Time-Dependent Reliability Analysis for Function Generation Mechanisms With Random Joint Clearances,” Mech. Mach. Theory, 92, pp. 184–199. [CrossRef]
Wang, Z. , Tian, Q. , Hu, H. , and Flores, P. , 2016, “ Nonlinear Dynamics and Chaotic Control of a Flexible Multibody System With Uncertain Joint Clearance,” Nonlinear Dyn., 86(3), pp. 1571–1597. [CrossRef]
Li, P. , Chen, W. , Li, D. , Yu, R. , and Zhang, W. , 2016, “ Wear Analysis of Two Revolute Joints With Clearance in Multibody Systems,” ASME J. Comput. Nonlinear Dyn., 11(1), p. 011009. [CrossRef]
Ting, K.-L. , Hsu, K.-L. , Yu, Z. , and Wang, J. , 2017, “ Clearance-Induced Output Position Uncertainty of Planar Linkages With Revolute and Prismatic Joints,” Mech. Mach. Theory, 111, pp. 66–75. [CrossRef]
Yaqubi, S. , Dardel, M. , Daniali, H. M. , and Ghasemi, M. H. , 2016, “ Modeling and Control of Crank–Slider Mechanism With Multiple Clearance Joints,” Multibody Syst. Dyn., 36(2), pp. 143–167. [CrossRef]
Sun, D. , Chen, G. , Shi, Y. , Wang, T. , and Sun, R. , 2015, “ Model Reduction of a Flexible Multibody System With Clearance,” Mech. Mach. Theory, 85, pp. 106–115. [CrossRef]
Vörös, J. , 2002, “ Modeling and Parameter Identification of Systems With Multisegment Piecewise-Linear Characteristics,” IEEE Trans. Autom. Control, 47(1), pp. 184–188. [CrossRef]
Koyuncu, A. , Cigeroglu, E. , Yumer, M. , and Özgüven, H. , 2013, “ Localization and Identification of Structural Nonlinearities Using Neural Networks,” Topics in Nonlinear Dynamics, Vol. 1, Springer, New York, pp. 103–112. [CrossRef]
Liu, J. , Li, B. , Jin, W. , Han, L. , and Quan, S. , 2017, “ Experiments on Clearance Identification in Cantilever Beams Reduced From Artillery Mechanism,” Proc. Inst. Mech. Eng., Part C, 231(6), pp. 1010–1032. [CrossRef]
Kerschen, G. , Worden, K. , Vakakis, A. F. , and Golinval, J.-C. , 2006, “ Past, Present and Future of Nonlinear System Identification in Structural Dynamics,” Mech. Syst. Signal Process., 20(3), pp. 505–592. [CrossRef]
Noël, J.-P. , Renson, L. , and Kerschen, G. , 2014, “ Complex Dynamics of a Nonlinear Aerospace Structure: Experimental Identification and Modal Interactions,” J. Sound Vib., 333(12), pp. 2588–2607. [CrossRef]
Renson, L. , Kerschen, G. , and Cochelin, B. , 2016, “ Numerical Computation of Nonlinear Normal Modes in Mechanical Engineering,” J. Sound Vib., 364, pp. 177–206. [CrossRef]
Adams, D. E. , and Allemang, R. J. , 1999, “ A New Derivation of the Frequency Response Function Matrix for Vibrating Non-Linear Systems,” J. Sound Vib., 227(5), pp. 1083–1108. [CrossRef]
Adams, D. , and Allemang, R. , 1999, “ Characterization of Nonlinear Vibrating Systems Using Internal Feedback and Frequency Response Modulation,” ASME J. Sound Vib., 121(4), pp. 495–500. [CrossRef]
Marchesiello, S. , and Garibaldi, L. , 2008, “ Identification of Clearance-Type Nonlinearities,” Mech. Syst. Signal Process., 22(5), pp. 1133–1145. [CrossRef]
Noël, J.-P. , and Kerschen, G. , 2013, “ Frequency-Domain Subspace Identification for Nonlinear Mechanical Systems,” Mech. Syst. Signal Process., 40(2), pp. 701–717. [CrossRef]
Noël, J.-P. , Marchesiello, S. , and Kerschen, G. , 2014, “ Subspace-Based Identification of a Nonlinear Spacecraft in the Time and Frequency Domains,” Mech. Syst. Signal Process., 43(1), pp. 217–236. [CrossRef]
Li, B. , Han, L. , Jin, W. , and Quan, S. , 2015, “ Theoretical and Experimental Identification of Cantilever Beam With Clearances Using Statistical and Subspace-Based Methods,” ASME J. Comput. Nonlinear Dyn., 11(3), p. 031003. [CrossRef]
Vörös, J. , 2007, “ Parameter Identification of Wiener Systems With Multisegment Piecewise-Linear Nonlinearities,” Syst. Control Lett., 56(2), pp. 99–105. [CrossRef]
Özer, M. B. , and Özgüven, H. N. , 2002, “ A New Method for Localization and Identification of Non-Linearities in Structures,” Sixth Biennial Conference on Engineering Systems Design and Analysis (ESDA), Istanbul, Turkey, July 8–11, pp. 8–11.
Özer, M. B. , Özgüven, H. N. , and Royston, T. J. , 2009, “ Identification of Structural Non-Linearities Using Describing Functions and the Sherman–Morrison Method,” Mech. Syst. Signal Process., 23(1), pp. 30–44. [CrossRef]
Arslan, Ö. , Aykan, M. , and Özgüven, H. N. , 2011, “ Parametric Identification of Structural Nonlinearities From Measured Frequency Response Data,” Mech. Syst. Signal Process., 25(4), pp. 1112–1125. [CrossRef]
Aykan, M. , and Özgüven, H. N. , 2013, “ Parametric Identification of Nonlinearity in Structural Systems Using Describing Function Inversion,” Mech. Syst. Signal Process., 40(1), pp. 356–376. [CrossRef]
Adams, D. , and Allemang, R. , 2000, “ A Frequency Domain Method for Estimating the Parameters of a Non-Linear Structural Dynamic Model Through Feedback,” Mech. Syst. Signal Process., 14(4), pp. 637–656. [CrossRef]
Spottswood, S. M. , 2006, “ Identification of Nonlinear Parameters From Experimental Data for Reduced Order Models,” Ph.D. dissertation, University of Cincinnati, Cincinnati, OH. https://etd.ohiolink.edu/pg_10?0::NO:10:P10_ACCESSION_NUM:ucin1163016945
Li, J. , and Law, S. , 2011, “ Substructural Response Reconstruction in Wavelet Domain,” ASME J. Appl. Mech., 78(4), p. 041010. [CrossRef]
Brandt, A. , 2011, Noise and Vibration Analysis: Signal Analysis and Experimental Procedures, Wiley, New York. [CrossRef]
Oppenheim, A. V. , Willsky, A. S. , and Nawab, S. H. , 2014, Signals and Systems, Pearson, New York.
Gilardi, G. , and Sharf, I. , 2002, “ Literature Survey of Contact Dynamics Modelling,” Mech. Mach. Theory, 37(10), pp. 1213–1239. [CrossRef]
Ribeiro, A. , Silva, J. , and Maia, N. , 2000, “ On the Generalisation of the Transmissibility Concept,” Mech. Syst. Signal Process., 14(1), pp. 29–35. [CrossRef]
Friswell, M. , and Mottershead, J. E. , 1995, Finite Element Model Updating in Structural Dynamics, Springer Science & Business Media, Dordrecht, The Netherlands. [CrossRef]
Moens, D. , and Vandepitte, D. , 2002, “ Fuzzy Finite Element Method for Frequency Response Function Analysis of Uncertain Structures,” AIAA J., 40(1), pp. 126–136. [CrossRef]
Hughes, T. J. , 2012, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Dover Publications, Mineola, NY.
Canbaloğlu, G. , and Özgüven, H. N. , 2014, “ Model Updating of Nonlinear Structures,” Nonlinear Dynamics, Vol. 2, Springer International Publishing, Cham, Switzerland, pp. 69–81. [CrossRef]
Canbaloğlu, G. , and Özgüven, H. N. , 2016, “ Model Updating of Nonlinear Structures From Measured FRFs,” Mech. Syst. Signal Process., 80, pp. 282–301. [CrossRef]
Canbaloğlu, G. , and Özgüven, H. N. , 2013, “ Obtaining Linear FRFs for Model Updating in Structures With Multiple Nonlinearities Including Friction,” Topics in Nonlinear Dynamics, Vol. 1, Springer, New York, pp. 145–157. [CrossRef]
Flores, P. , Ambrósio, J. , and Claro, J. P. , 2004, “ Dynamic Analysis for Planar Multibody Mechanical Systems With Lubricated Joints,” Multibody Syst. Dyn., 12(1), pp. 47–74. [CrossRef]
Flores, P. , 2010, “ A Parametric Study on the Dynamic Response of Planar Multibody Systems With Multiple Clearance Joints,” Nonlinear Dyn., 61(4), pp. 633–653. [CrossRef]
Liu, J. , and Li, B. , 2016, “ Theoretical and Experimental Identification of Clearance Nonlinearities for a Continuum Structure,” ASME J. Comput. Nonlinear Dyn., 11(4), p. 041019. [CrossRef]
Chopra, A. K. , 1995, Dynamics of Structures, Prentice Hall, Upper Saddle River, NJ.
Zou, K. , and Nagarajaiah, S. , 2015, “ Study of a Piecewise Linear Dynamic System With Negative and Positive Stiffness,” Commun. Nonlinear Sci. Numer. Simul., 22(1), pp. 1084–1101. [CrossRef]
Zou, K. , and Nagarajaiah, S. , 2015, “ The Solution Structure of the Düffing Oscillator's Transient Response and General Solution,” Nonlinear Dyn., 81(1–2), pp. 621–639. [CrossRef]
Haroon, M. , and Adams, D. E. , 2009, “ A Modified H2 Algorithm for Improved Frequency Response Function and Nonlinear Parameter Estimation,” J. Sound Vib., 320(4–5), pp. 822–837. [CrossRef]
Brandt, A. , and Brincker, R. , 2011, “ Impact Excitation Processing for Improved Frequency Response Quality,” Structural Dynamics, Vol. 3, Springer, New York, pp. 89–95.

Figures

Grahic Jump Location
Fig. 1

A feedback model of the localized nonlinear system

Grahic Jump Location
Fig. 2

Second derivative plot of the PDF

Grahic Jump Location
Fig. 3

Characteristic curve of the clearance nonlinearity

Grahic Jump Location
Fig. 4

Cantilever beam with single clearance

Grahic Jump Location
Fig. 5

Displacement FRF of the underlying linear model between the exciting location and nonlinear location H12

Grahic Jump Location
Fig. 6

Displacement response at the clearance location: (a) comparison between the reconstructed displacement response and theoretical value, (b) local zoom of the contrast graph, and (c) relative error of the reconstructed response

Grahic Jump Location
Fig. 7

Displacement response at the clearance location: (a) comparison between the reconstructed displacement response and theoretical value and (b) local zoom of the contrast graph

Grahic Jump Location
Fig. 8

Second derivative plot of PDF at the clearance location

Grahic Jump Location
Fig. 9

Sorting nonlinear force–displacement curve

Grahic Jump Location
Fig. 10

Mechanical model of the cantilever with two clearances

Grahic Jump Location
Fig. 11

FRFs of the underlying linear model: (a) H14 and (b) H15

Grahic Jump Location
Fig. 12

Displacement response at clearance 1 location: (a) comparison between the reconstructed displacement response and the theoretical value and (b) relative error of the reconstructed response

Grahic Jump Location
Fig. 13

Displacement response at clearance 2 location: (a) comparison between the reconstructed displacement response and theoretical value and (b) relative error of the reconstructed response

Grahic Jump Location
Fig. 14

Nonlinear force–displacement curves: (a) clearance 1 and (b) clearance 2

Grahic Jump Location
Fig. 15

Mechanical model of the cantilever with two kinds of nonlinearities

Grahic Jump Location
Fig. 16

Characteristic curve of the subsectional linear spring nonlinearity

Grahic Jump Location
Fig. 17

(a) Comparison between the reconstructed displacement response at clearance location and the theoretical value and (b) nonlinear force–displacement curve at the clearance location

Grahic Jump Location
Fig. 18

(a) Comparison between the reconstructed displacement response at nonlinear location and the theoretical value and (b) nonlinear force–displacement curve at the subsectional spring location

Grahic Jump Location
Fig. 19

(a) Comparison between the reconstructed displacement response at nonlinear location and the theoretical value and (b) nonlinear force–displacement curve

Grahic Jump Location
Fig. 20

Clearance test-bed

Grahic Jump Location
Fig. 21

Local zoom of the clearance-adjustment setup

Grahic Jump Location
Fig. 22

The complete test system

Grahic Jump Location
Fig. 23

Schematic diagram of measuring the displacement response at the clearance location

Grahic Jump Location
Fig. 24

Schematic diagram of the experimental scheme: (a) single clearance case and (b) two clearances case

Grahic Jump Location
Fig. 25

FRF between the exciting location and nonlinear location

Grahic Jump Location
Fig. 26

Displacement response at the clearance location: (a) comparison between the reconstructed displacement response and the measured response, (b) local zoom of the contrast graph, and (c) relative error of the reconstructed response

Grahic Jump Location
Fig. 27

Second derivative plot of PDF at the clearance location

Grahic Jump Location
Fig. 28

Nonlinear force–displacement curve

Grahic Jump Location
Fig. 29

Displacement response at clearance 1 location: (a) comparison between the reconstructed displacement response and the measured response, (b) local zoom of the contrast graph, and (c) relative error of the reconstructed response

Grahic Jump Location
Fig. 30

Displacement response at clearance 2 location: (a) comparison between the reconstructed displacement response and the measured response, (b) local zoom of the contrast graph, and (c) relative error of the reconstructed response

Grahic Jump Location
Fig. 31

Nonlinear force–displacement curve: (a) clearance 1 and (b) clearance 2

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In