Dynamic characterization of hysteresis elements in mechanical systems. I. Theoretical analysis

Chaos

Volumn 15, Issue 1, 2005, Pages

  Al Bender, F ^a   Symens, W ^b  

^a UNIVERSITY OF LEUVEN   (Belgium)

^b Flanders' MECHATRONICS Technology Centre   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 17744390629     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1844991     Document Type: Article

References (38)

1. R. Arnell, P. Davies, J. Halling, and T. Whomes, Tribology (Macmillan Education, London, 1991).
2. B. Armstrong-Hélouvry, Control of Machines with Friction (Kluwer Academic, Dordrecht, 1991).
3. T. Prajogo, Ph.D. thesis, Katholieke Universiteit Leuven, Division of Production Engineering, Machine Design and Automation (1998).
4. F. Al-Bender, V. Lampaert, and J. Swevers, Chaos 14, 446 (2004).
5. U. Parlitz, A. Hornstein, D. Engster, F. Al-Bender, V. Lampaert, T. Tjahjawidodo, S. Fassois, D. Rizos, C. Wong, and K. Worden, Chaos 14, 420 (2004).
6. M. Goldfarb and N. Celanovic, ASME J. Dyn. Syst., Meas., Control 119, 478 (1997).
7. J. Swevers, F. Al-Bender, C. Ganseman, and T. Prajogo, IEEE Trans. Autom. Control 45, 675 (2000).
8. V. Lampaert, J. Swevers, and F. Al-Bender, IEEE Trans. Autom. Control 47, 683 (2002).
9. A. Smyth, S. Masri, E. Kosmatopoulos, A. Chassiakos, and T. Caughey, Int. J. Non-Linear Mech. 37, 1435 (2002).
10. S. Seelecke, Int. J. Non-Linear Mech. 37, 1363 (2002).
11. D. Capecchi and F. Vestroni, J. Eng. Mech. 111, 1515 (1985).
12. W. Iwan, ASME J. Appl. Mech. 33, 893 (1966).
13. W. Iwan, ASME J. Appl. Mech. 34, 612 (1967).
14. R. Masiani, D. Capecchi, and F. Vestroni, Int. J. Non-Linear Mech. 37, 1421 (2002).
15. F. Altpeter, Ph.D. thesis, École Polytechnique Féderale de Lausanne (1999).
16. C. Ganseman, Ph.D. thesis, Katholieke Universiteit Leuven, Division of Production Engineering, Machine Design and Automation (1998).
17. F. Vestroni and M. Noori, Int. J. Non-Linear Mech. 37, 1261 (2002), Special Issue on Hysteresis.
18. I. Mayergoyz, Mathematical Models of Hysteresis (Springer-Verlag, New York, 1991).
19. G. Masing, 2nd International Congress for Applied Mechanics (Zurich, 1926), pp. 332-335 (in German).
20. K. Smith, P. Watson, and T. Topper, J. Mater. 5, 767 (1970).
21. S. Futami, A. Furutani, and S. Yoshida, Nanotechnology 1, 31 (1990).
22. Damping of Vibrations, edited by Z. Osuiski (A.A. Balkema, Rotterdam, 1998).
23. B. Lazan, Damping of Materials and Members in Structural Mechanics (Pergamon, London, 1968).
24. i).
25. Since the values for most parameters in this Part I of the paper are not based on physical measurements and only qualitative differences between the different results are examined, no units are assigned to the numerical values of the different variables.
26. B. Armstrong and B. Amin, Automatica 32, 679 (1996).
27. R. H. Macmillan, Non-Linear Control System Analysis (Pergamon, London, 1962).
28. G. J. Taylor and R. G. Brown, Analysis and Design of Feedback Control Systems, 2nd ed. (McGraw-Hill, New York, 1960).
29. Note that in this formulation of the friction force, the dependency of f on the sign of the velocity is made explicit.
30. This choice makes calculations somewhat easier.
31. Absolute frequency response functions show the frequency content of the respective output signals without dividing them by the amplitude of the input signal, only the phase information of the input signal is used. This way the phase shift between the input frequency and the fundamental frequency of the output signal can be plotted. The reason for using the AFRF in this Part I of the paper instead of the commonly used frequency response functions (FRF), where the output is divided by the input, is that the AFRFs give more clear figures for the analysis considered here.
32. The excitation amplitudes for all Case A AFRFs considered in this Part I of the paper are: 0.4; 0.6; 0.8; 0.9; 0.99; 0.8x4π; 1.2 and 1.4.
33. This well-known behavior in nonlinear analysis is called "folding."
34. The excitation amplitudes for all Case B AFRFs considered in this Part I of the paper are: 0.05; 0.1; 0.5; 2 and 10.
35. The excitation amplitudes are: 0.9; 1.1; 1.2; 1.5 and 1.8 for a virgin curve with a saturation force of 1.
36. W. Symens, F. Al-Bender, J. Swevers, and H. Van Brussel, in Proceedings of the Modelling, Identification and Control Conference (IASTED, 2002), pp. 380-385.
37. V. Lampaert, J. Swevers, and F. Al-Bender, in Proceedings of the International Seminar on Modal Analysis (2000).
38. J. Schoukens and R. Pintelon, System Identification: A Frequency Domain Approach (IEEE, Piscataway, NJ, 2001).