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Investigation of dynamic stress recovery in elastic gear simulations using different reduction techniques

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Abstract

Stresses in gear contact simulations, performed using elastic multibody systems, are recovered. A single gear pair is used for stress investigations and an impact is chosen as simulation case representing an extremely dynamical situation. The gears are modeled as a reduced elastic multibody system allowing a fast computation of the dynamical problem. Depending on the projection matrix which is used for model order reduction, stresses can sometimes not be recovered accurately throughout the whole gear. Thus, the main focus in this paper lies on the selection of the functions which make up the projection matrix and, therefore, determine the elastic deformations and the quality of recovered stresses. However, the chosen set of modes does not only affect stress calculation, it also strongly affects the computation of the dynamics of the gear system and, thus, the computational effort, and may lead to serious drawbacks. This issue is discussed, too. Upon that, several different mode sets are analyzed trying to minimize the computational effort of the elastic multibody system for the given problem while still being able to recover accurate stress values on distinct geometric areas. The stress values are compared with a finite element reference computation. The novel contribution of this paper is the determination of a minimal set of modes including ones assigned to the nodes of the gear contact surface, which are able to accurately recover stresses but minimize the numerical drawbacks.

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References

  1. DIN 3990-1 (1987) Tragfähigkeitsberechnung von Stirnrädern, Teil 1: Einführung und allgemeine Einflussfaktoren (in German). Beuth Verlag, Berlin

  2. ISO 281 (2010) Rolling bearings: dynamic load ratings and rating life, Deutsches Institut for Normung

  3. Schiehlen W, Eberhard P (2014) Applied dynamics. Springer, Berlin

    Book  MATH  Google Scholar 

  4. Shabana AA (2005) Dynamics of multibody systems. Cambridge University Press, New York

    Book  MATH  Google Scholar 

  5. Wittenburg J (1977) Dynamics of systems of rigid bodies. Teubner, Stuttgart

    Book  MATH  Google Scholar 

  6. Helsen J, Vanhollebeke F, Marrant B, Vandepitte D, Desmet W (2011) Multibody modelling of varying complexity for modal behaviour analysis of wind turbine gearboxes. J Renew Energy 36(11):3098–3113

    Article  Google Scholar 

  7. Walt M, Butterfield S, McNiff B (2007) Improving wind turbine gearbox reliability. In: European wind energy Cconference, Milan, Italy

  8. Simpack. http://www.simpack.com. Accessed on 3 Feb 2017

  9. Zienkiewicz OC, Taylor RL, Zhu JZ (2013) The finite element method: its basis & fundamentals, 7th edn. Butterworth-Heinemann, Oxford

    MATH  Google Scholar 

  10. Cook RD, Malkus DS, Plesha ME, Witt RJ (2002) Concepts and applications of finite element analysis. Wiley, New York

    Google Scholar 

  11. Wriggers P (2002) Computational contact mechanics. Wiley, Chichester

    MATH  Google Scholar 

  12. Chang SH, Huston RL (1983) A finite element stress analysis of spur gears including fillet radii and rim thickness effects. J Mech Transm Autom Des 105(3):327–330

    Article  Google Scholar 

  13. Reddy S, Handschuh R (1995) Contact stress analysis of spiral bevel gears using finite element analysis. J Mech Des 117:235–240

    Article  Google Scholar 

  14. Chen YC, Tsay CB (2002) Stress analysis of a helical gear set with localized bearing contact. Finite Elem Anal Des 38(8):707–723

    Article  MATH  Google Scholar 

  15. Lin T, Ou H, Li R (2007) A finite element method for 3D static and dynamic contact/impact analysis of gear drives. Comput Methods Appl Mech Eng 196(9):1716–1728

    Article  MATH  Google Scholar 

  16. Schwertassek R, Wallrapp O (1999) Dynamik flexibler Mehrkörpersysteme (in German). Vieweg, Braunschweig

    Book  Google Scholar 

  17. Shabana AA (1997) Flexible multibody dynamics: review of past and recent developments. Multibody Syst Dyn 1(2):189–222

    Article  MathSciNet  MATH  Google Scholar 

  18. Tobias C, Eberhard P (2011) Stress recovery with Krylov-subspaces in reduced elastic multibody systems. Multibody Syst Dyn 25(4):377–393

    Article  MathSciNet  MATH  Google Scholar 

  19. Wilde RA (1976) Failure in gears and related machine components. In: Mechanical failure, definition of the problem: proceedings of the 20th meeting of the mechanical failures prevention group, held at the National Bureau of standards, Washington, DC, May 8–10, 1974. No. 423. US Dept. of Commerce, National Bureau of Standards: for sale by the Supt. of Docs., US Govt. Print. Off

  20. Balmforth N, Watson HJ (1964) A practical look at gear-tooth damage. In: Proceedings of the institution of mechanical engineers, conference proceedings, vol 179, no. 4, Paper 16, SAGE Publications, London

  21. Ku PM (1976) Gear failure modes—importance of lubrication and mechanics. ASLE Trans 19(3):239–249

    Article  Google Scholar 

  22. Amzallag C, Gerey J, Robert J, Bahaud J (1994) Standardization of the rainflow counting method for fatigue analysis. Int J Fatigue 16(4):287–293

    Article  Google Scholar 

  23. Tobias C (2012) Schädigungsberechnung in elastischen Mehrkörpersystemen (in German). Dissertation, Schriften aus dem Institut für Technische und Numerische Mechanik der Universität Stuttgart, vol 24, Shaker, Aachen

  24. Ziegler P, Eberhard P (2009) An elastic multibody model for the simulation of impacts on gear wheels. In: Arczewski K, Fraczek J, Wojtyra M (eds) Proceedings multibody dynamics 2009—ECCOMAS thematic conferences, Warsaw

  25. Guyan RJ (1965) Reduction of stiffness and mass matrices. AIAA J 3(2):380

    Article  Google Scholar 

  26. Craig R (2000) Coupling of substructures for dynamic analyses: an overview. In: Proceedings of the AIAA dynamics specialists conference, Atlanta

  27. Maia N, Silva J (1997) Theoretical and experimental modal analysis. Research Studies Press, Baldock

    Google Scholar 

  28. Ericson TM, Parker RG (2013) Planetary gear modal vibration experiments and correlation against lumped-parameter and finite element models. J Sound Vib 332(9):2350–2375

    Article  Google Scholar 

  29. Kahraman A, Singh R (1990) Non-linear dynamics of a spur gear pair. J Sound Vib 142(1):49–75

    Article  Google Scholar 

  30. Fehr J (2011) Automated and error-controlled model reduction in elastic multibody systems. Dissertation, Schriften aus dem Institut für Technische und Numerische Mechanik der Universität Stuttgart, vol 21, Shaker, Aachen

  31. Bathe K-J (1996) Finite element procedures. Prentice-Hall, Upper Saddle River

    MATH  Google Scholar 

  32. ANSYS INC (2014) Documentation for Ansys, Release 15. Canonsburg

  33. SIMULIA (2013) Abaqus Theory Manual. Abaqus, Inc

  34. Ziegler P (2012) Dynamische Simulation von Zahnradkontakten mit elastischen Modellen (in German). Dissertation, Schriften aus dem Institut für Technische und Numerische Mechanik der Universität Stuttgart, Band 23, Shaker Verlag, Aachen

  35. Dietz S, Knothe K (1997) Reduktion der Anzahl der Freiheitsgrade in Finite-Elemente-Substrukturen (in German), ILR Mitteilung 315. Institut für Luft- und Raumfahrt, Technische Universität, Berlin

    Google Scholar 

  36. Dietz S (1999) Vibration and fatigue analysis of vehicle systems using component modes. Dissertation, VDI Fortschritt-Berichte, Reihe 12, Nr. 401, VDI-Verlag, Düsseldorf

  37. Rubin S (1975) Improved component-mode representation for structural dynamic analysis. AIAA J 13(8):995–1006

    Article  MATH  Google Scholar 

  38. Craig R, Bampton M (1968) Coupling of substructures for dynamic analyses. AIAA J 6(7):1313–1319

  39. Allgöwer F (2000) Robuste Regelung—Teil 1 (in German). In: Lecture notes, University of Stuttgart

  40. Salimbahrami SB (2005) Structure preserving order reduction of large scale second order models. Dissertation, Technische Universität München

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Authors and Affiliations

  1. Institute of Engineering and Computational Mechanics, University of Stuttgart, Pfaffenwaldring 9, 70569, Stuttgart, Germany

    Dennis Schurr, Philip Holzwarth & Peter Eberhard

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  1. Dennis Schurr
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  2. Philip Holzwarth
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  3. Peter Eberhard
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Correspondence to Peter Eberhard.

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Schurr, D., Holzwarth, P. & Eberhard, P. Investigation of dynamic stress recovery in elastic gear simulations using different reduction techniques. Comput Mech 62, 439–456 (2018). https://doi.org/10.1007/s00466-017-1507-z

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  • DOI: https://doi.org/10.1007/s00466-017-1507-z

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