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Substructure coupling approach to parameterization of passive dynamic auxiliary systems

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Abstract

A physical structure might show undesired forced vibrations when excited by a specific force signal. Moreover, if the resulting deflections influence the acting force, undesired self-excited vibrations can result. In such cases a usual approach is to modify the structure by mounting passive tuned mass dampers (TMD). Different strategies are available to design such TMD. The different approaches have in common, that the original structure is approximated as a single degree of freedom (SDOF) system. This approximation limits the applicability of the design strategies. This paper attempts to solve the abovementioned drawback. Based on a frequency domain substructure coupling approach, it is proposed to apply a sequential quadratic programming algorithm to determine effective parameters of TMD. The approach considers the multiple degrees of freedom (MDOF) character of the original structure. The new method is evaluated by means of a simple finite element model of a simplified milling machine assembly. By means of this analytical example, it is shown that both SDOF TMD and MDOF TMD can be parameterized by the new method. The practical applicability is proven by designing a STMD for a linear axis test bench. Finally, limitations of the method and reasonable subsequent research tasks are discussed.

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References

  1. Altintas Y, Weck M (2004) Chatter stability of metal cutting and grinding. CIRP Ann Manuf Technol 53(2):619–642. doi:10.1016/S0007-8506(07)60032-8

    Article  Google Scholar 

  2. Bajpai VK, Garg TK, Gupta MK (2007) Vibration-dampers for smoke stacks. In: 3rd WSEAS international conference on applied and theoretical mechanics, Spain, pp 124–130

  3. Brecher C, Bäumler S, Brockmann B (2013) Hilfsmassendämpfer für Werkzeugmaschinen. Optimierte Auslegung passiver Hilfsmassendämpfer zur Stabilisierung von Bearbeitungsprozessen. Werkstattstech Online 5:395–401

    Google Scholar 

  4. Brecher C, Schmidt S, Fey M (2015) On the integration of tuned multi-mass dampers into a topology optimization method for machine tool structural dynamics. In: 11th world congress on structural and multidisciplinary optimization. Sydney

  5. Brecher C, Fey M, Tenbrock C, Daniels M (2015) Multipoint constraints for modeling of machine tool dynamics. J Manuf Sci Eng. doi:10.1115/1.4031771

    Google Scholar 

  6. Brock JE (1946) A note on the damped vibration absorber. Trans ASME J Appl Mech 13(4):A-284

    Google Scholar 

  7. Conn AR, Gould NIM, Toint PL (2000) Trust-region methods, society for industrial and applied mathematics. Philadelphia. doi:10.1137/1.9780898719857

    Google Scholar 

  8. Ewins DJ (2000) Modal testing: theory, practice and application, 2nd edn. Research Studies Press, Baldock Hertfordshire, England, Philadelphia

    Google Scholar 

  9. Glover F (1998) A template for scatter search and path relinking. In: Hao J, Lutton E, Ronald E, Schoenauer M, Snyers D (eds) Artificial evolution. Springer, Berlin Heidelberg, pp 1–51. doi:10.1007/BFb0026589

    Chapter  Google Scholar 

  10. Han SP (1977) A globally convergent method for nonlinear programming. J Optim Theory Appl 22(3):297–309. doi:10.1007/BF00932858

    Article  MathSciNet  MATH  Google Scholar 

  11. Den Hartog JP (1934) Mechanical vibrations. Dover Publ, New York

    MATH  Google Scholar 

  12. Heirman GHK, Desmet W (2010) Interface reduction of flexible bodies for efficient modeling of body flexibility in multibody dynamics. Multibody Syst Dyn 24(2):219–234. doi:10.1007/s11044-010-9198-7

    Article  MATH  Google Scholar 

  13. Joshi AS, Jangid RS (1997) Optimum parameters of multiple tuned mass dampers for base-excited damped systems. J Sound Vib 202(5):657–667. doi:10.1006/jsvi.1996.0859

    Article  Google Scholar 

  14. Keinänen J, Tammi K, Sainio H (2013) Adjustable tuned mass damper concept for a diesel generator. MTZ Ind 3(2):44–49. doi:10.1007/s40353-013-0098-1

    Google Scholar 

  15. de Klerk D, Rixen DJ, Voormeeren SN (2008) General framework for dynamic substructuring: history, review and classification of techniques. AIAA J 46(5):1169–1181. doi:10.2514/1.33274

    Article  Google Scholar 

  16. Li H-N, Ni X-L (2007) Optimization of non-uniformly distributed multiple tuned mass damper. J Sound Vib 308(1–2):80–97. doi:10.1016/j.jsv.2007.07.014

    Article  Google Scholar 

  17. Liu GR, Quek SS (2003) The finite element method: a practical course. Butterworth-Heinemann, Oxford, Boston

    MATH  Google Scholar 

  18. MathWorks (2015) Optimization toolbox: user’s guide. R2015b. http://www.mathworks.com/help/pdf_doc/optim/optim_tb.pdf. Accessed 08 Feb 2016

  19. MathWorks (2015) Global optimization toolbox: user’s guide. R2015b. http://www.mathworks.com/help/pdf_doc/gads/gads_tb.pdf. Accessed 08 Feb 2016

  20. Nocedal J, Wright SJ (1999) Numerical optimization. Springer, New York

    Book  MATH  Google Scholar 

  21. Powell MJD (1978) A fast algorithm for nonlinearly constrained optimization calculations. In: Watson GA (ed) Numerical analysis. Springer, Berlin Heidelberg, pp 144–157. doi:10.1007/BFb0067703

    Chapter  Google Scholar 

  22. Sims ND (2007) Vibration absorbers for chatter suppression: a new analytical tuning methodology. J Sound Vib 301(3–4):592–607. doi:10.1016/j.jsv.2006.10.020

    Article  Google Scholar 

  23. Ugray Z, Lasdon L, Plummer J, Glover F, Kelly J, Martí R (2007) Scatter search and local NLP solvers: a multistart framework for global optimization. INFORMS J Comput 19(3):328–340. doi:10.1287/ijoc.1060.0175

    Article  MathSciNet  MATH  Google Scholar 

  24. Wagner H, Ramamurti V, Sastry R, Hartmann K (1973) Dynamics of stockbridge dampers. J Sound Vib 30(2):207–220. doi:10.1016/S0022-460X(73)80114-2

    Article  Google Scholar 

  25. Webster AC, Vaicaitis R (1992) Application of tuned mass dampers to control vibrations of composite floor system. Eng J Am Inst Steel Constr 29(3):116–124

    Google Scholar 

  26. Weck M, Brecher C (2006) Werkzeugmaschinen Konstruktion und Berechnung. Springer, Berlin

    Google Scholar 

  27. Wilson RB (1963) A simplicial algorithm for concave programming, Ph.D. Thesis, Harvard University, Cambridge

  28. Yang Y, Muñoa J, Altintas Y (2010) Optimization of multiple tuned mass dampers to suppress machine tool chatter. Int J Mach Tools Manuf 50(9):834–842. doi:10.1016/j.ijmachtools.2010.04.011

    Article  Google Scholar 

  29. Zuo L, Nayfeh SA (2003) Optimization of the individual stiffness and damping parameters in multiple-tuned-mass-damper systems. Smart Struct Mater Proc SPIE 5052:217–229. doi:10.1117/12.483798

    Google Scholar 

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Acknowledgments

The authors would like to thank the German Research Foundation DFG for the financial support in the project BR2905/55-1. The results presented in this paper have been worked out in this project.

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Authors and Affiliations

  1. Chair of Machine Tools, Laboratory for Machine Tools and Production Engineering, RWTH Aachen University, Steinbachstr. 19, 52074, Aachen, Germany

    C. Brecher, M. Fey & M. Daniels

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  1. C. Brecher
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  2. M. Fey
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  3. M. Daniels
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Correspondence to M. Daniels.

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Brecher, C., Fey, M. & Daniels, M. Substructure coupling approach to parameterization of passive dynamic auxiliary systems. Prod. Eng. Res. Devel. 10, 351–360 (2016). https://doi.org/10.1007/s11740-016-0669-4

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