Skip to main content

Advertisement

SpringerLink
Log in

Optimization of an inerter-based vibration isolation system and helical spring fatigue life assessment

  • SPECIAL
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

This paper presents an analytical analysis and optimization of vibration-induced fatigue in a generalized, linear two-degree-of-freedom inerter-based vibration isolation system. The system consists of a source body and a receiving body, coupled through an isolator. The isolator consists of a spring, a damper, and an inerter. A broadband frequency force excitation of the source body is assumed throughout the investigation. Optimized system, in which the kinetic energy of the receiving body is minimized, is compared with sub-optimal systems by contrasting the fatigue life of a receiving body helical spring with several alternative isolator setup cases. The optimization is based on minimizing specific kinetic energy, but it also increases the number of cycles to fatigue failure of the considered helical spring. A significant portion of this improvement is due to the inclusion of an optimally tuned inerter in the isolator. Various helical spring deflection and stress correction factors from referent literature are discussed. Most convenient spring stress and deflection correction factors are adopted and employed in conjunction with pure shear governed proportional stress in the context of high-cycle fatigue.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Rao, S.S.: Mechanical Vibrations, 5th edn. Prentice Hall, New York (2010)

    Google Scholar 

  2. Smith, M.C.: Synthesis of mechanical networks: the inerter. IEEE Trans. Autom. Control 47(10), 1648–1662 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  3. Steinberg, D.S.: Vibration Analysis for Electronic Equipment, Third edn. Wiley, New York (2000)

    Google Scholar 

  4. Bishop, N.W.M., Sherratt, F.: Finite Element Based Fatigue Calculations. NAFEMS, Farnham (2000)

    Google Scholar 

  5. Lee, Y., Barkey, M.E., Kang, H.: Metal Fatigue Analysis Handbook. Practical Problem-Solving Techniques for Computer-Aided Engineering. Elsevier, Waltham (2012)

    Google Scholar 

  6. Wahl, A.M.: Helical compression and tension springs. ASME paper A-38. J. Appl. Mech. 2(1), A-35–A-37 (1935)

    Google Scholar 

  7. Wahl, A.M.: Mechanical Springs, 1st edn. Penton, Cleveland (1944)

    Google Scholar 

  8. DIN EN 2089-1-1963-01 (1963) Helical Springs Made From Round Wire and Rod—Calculation and Design of Compression Springs

  9. DIN EN 2089-1-1963-02 (1963) Helical Springs Made From Round Wire and Rod—Calculation and Design of Tension Springs

  10. Din EN 13906-1: Cylindrical Helical Springs Made From Round Wire and Bar—Calculation and Design—Part 1: Compression Springs. BeuthVerlag, Berlin (2002)

    Google Scholar 

  11. Din EN 13906-2: Cylindrical Helical Springs Made From Round Wire and Bar—Calculation and Design—Part 2: Extension Springs. BeuthVerlag, Berlin (2002)

    Google Scholar 

  12. Ancker Jr., C.J., Goodier, J.N.: Pitch and curvature correction for helical springs. ASME J. Appl. Mech. 25(4), 466–470 (1958)

    MATH  Google Scholar 

  13. Dym, C.L.: Consistent derivations of spring rates for helical springs. ASME J. Mech. Des. 131(7), 1–5 (2009)

    Article  Google Scholar 

  14. Research Committee on the Analysis of Helical Spring: Report of research committee on the analysis of helical spring. Trans. Jpn. Soc. Spring Eng. 2004(49), 35–75 (2004)

    Article  Google Scholar 

  15. Society of Automotive Engineers (SAE): Spring Design Manual. Ae Series. Society of Automotive Engineers Inc., Warrendale (1990)

    Google Scholar 

  16. Hearn, E.J.: Mechanics of Materials, Volume 1, An Introduction to the Mechanics of Elastic and Plastic Deformation of Solids and Structural Materials, 3rd edn. Butterworth-Heinemann, Oxford (1997)

    Google Scholar 

  17. Meissner, M., Schorcht, H.-J., Kletzin, U.: Metallfedern: Grundlagen, Werkstoffe, Berechnung, Gestaltung und Rechnereinsatz, 3rd edn. Springer, Berlin (2015)

    Book  Google Scholar 

  18. Shimoseki, M., Hamano, T., Imaizumi, T.: FEM for Springs. Springer, Berlin (2003)

    Book  Google Scholar 

  19. Timoshenko, S.P.: Strength of Materials, Part I, Elementary Theory and Problems, 2nd edn. D. Van Nostrand, New York (1940)

    MATH  Google Scholar 

  20. Timoshenko, S.P.: Strength of Materials, Part II, Advanced Theory and Problems, 2nd edn. D. Van Nostrand, New York (1940)

    MATH  Google Scholar 

  21. Timoshenko, S.P., Goodier, J.N.: Theory of Elasticity, 2nd edn. McGraw-Hill, New York (1951)

    MATH  Google Scholar 

  22. Budynas, R.G., Nisbett, J.K.: Shigley’s Mechanical Engineering Design, 10th edn. McGraw-Hill, New York (2015)

    Google Scholar 

  23. Ugural, A.C.: Mechanical Design of Machine Components, 2nd edn. CRC Press, Boca Raton (2015)

    Google Scholar 

  24. Stephens, R.I., Fatemi, A., Stephens, R.R., Fuchs, H.O.: Metal Fatigue in Engineering, 2nd edn. Wiley, New York (2005)

    Google Scholar 

  25. Roessle, M.L., Fatemi, A.: Strain-controlled fatigue properties of steels and some simple approximations. Int. J. Fatigue 22(6), 495–511 (2000)

    Article  Google Scholar 

  26. Bannantine, J.A., Comer, J.J., Handrock, J.L.: Fundamentals of Metal Fatigue Analysis. Prentice Hall, Englewood Cliffs (1990)

    Google Scholar 

  27. Romanowicz, P.: Numerical assessment of fatigue load capacity of cylindrical crane wheel using multiaxial high-cycle fatigue criteria. Arch. Appl. Mech. 87, 1707–1726 (2017)

    Article  Google Scholar 

  28. Berger, C., Kaiser, B.: Result of very high cycle fatigue tests on helical compression springs. Int. J. Fatigue 28, 1658–1663 (2006)

    Article  MATH  Google Scholar 

  29. Kaiser, B., Berger, C.: Fatigue behaviour of technical springs. Mater. Werkst. 36(11), 685–696 (2005)

    Article  Google Scholar 

  30. Del Llano-Vizcaya, L., Rubio-González, C., Mesmacque, G., Cervantes-Hernandez, T.: Multiaxial fatigue and failure analysis of helical compression springs. Eng. Fail. Anal. 13(8), 1303–1313 (2006)

    Article  Google Scholar 

  31. Pyttel, B., Ray, K.K., Brunner, I., Tiwari, A., Kaoua, S.A.: Investigation of probable failure position in helical compression springs used in fuel injection system of diesel engines. IOSR J. Mech. Civil Eng. 2(3), 24–29 (2012)

    Article  Google Scholar 

  32. Rivera, R., Chiminelli, A., Gómez, C., Núñez, J.L.: Fatigue failure analysis of a spring for elevator doors. Eng. Fail. Anal. 17(4), 731–738 (2010)

    Article  Google Scholar 

  33. Ružička, M., Doubrava, K.: Loading regimes and designing helical coiled springs for safe fatigue life. Res. Agr. Eng. 51(2), 50–55 (2005)

    Google Scholar 

  34. Kamal, M., Rahman, M.M.: Finite element-based fatigue behaviour of springs in automobile suspension. Int. J. Autom. Mech. Eng. 10, 1910–1919 (2014)

    Article  Google Scholar 

  35. Kuznetsov, A., Mammadov, M., Sultan, I., Hajilarov, E.: Optimization of improved suspension system with inerter device of the quarter-car model in vibration analysis. Arch. Appl. Mech. 81, 1427–1437 (2011)

    Article  Google Scholar 

  36. Cowper, G.R.: The shear coefficients in Timoshenko’s beam theory. ASME J. Appl. Mech. 33(2), 335–340 (1966)

    Article  MATH  Google Scholar 

  37. Mlikota, M., Schmauder, S., Božić, Ž., Hummel, M.: Modelling of overload effects on fatigue crack initiation in case of carbon steel. Fatigue Fract. Eng. Mater. Struct., Special Issue: 16th International Conference on New Trends in Fatigue and Fracture (NT2F16) 40(8):1182–1190 (2017)

  38. Alujević, N., Čakmak, D., Wolf, H., Jokić, M.: Passive and active vibration isolation systems using inerter. J. Sound Vib. 418, 163–183 (2018)

    Article  Google Scholar 

  39. Alujević, N., Wolf, H., Gardonio, P., Tomac, I.: Stability and performance limits for active vibration isolation using blended velocity feedback. J. Sound Vib. 330, 4981–4997 (2011)

    Article  Google Scholar 

  40. Alujević, N., Gardonio, P., Frampton, K.D.: Smart double panel for the sound radiation control: blended velocity feedback. AIAA J. 49(6), 1123–1134 (2011)

    Article  Google Scholar 

  41. Caiazzo, A., Alujević, N., Pluymers, B., Desmet, W.: Active control of turbulent boundary layer-induced sound transmission through the cavity-backed double panels. J. Sound Vib. 422, 161–188 (2018)

    Article  Google Scholar 

  42. James, H.M., Nichols, N.B., Phillips, R.S.: Theory of Servomechanisms. MIT Radiation Laboratory Series, vol. 25, First edn. McGraw-Hill, New York (1947)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, I. Lučića 5, 10000, Zagreb, Croatia

    D. Čakmak, H. Wolf, Ž. Božić & M. Jokić

Authors
  1. D. Čakmak
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. Wolf
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ž. Božić
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. Jokić
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to D. Čakmak.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Čakmak, D., Wolf, H., Božić, Ž. et al. Optimization of an inerter-based vibration isolation system and helical spring fatigue life assessment. Arch Appl Mech 89, 859–872 (2019). https://doi.org/10.1007/s00419-018-1447-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-018-1447-x

Keywords

Search

Navigation