SpringerLink
Log in

Computation of dynamic transmission error for gear transmission systems using modal decomposition and Fourier series

Berechnung des dynamischen Übertragungsfehlers bei Zahnradübertragungssystemen mit Hilfe von Modalzerlegung und Fourier-Reihen

  • Originalarbeiten/Originals
  • Published:
Forschung im Ingenieurwesen Aims and scope Submit manuscript

Abstract

In this paper, a method for computing the dynamics of a geared system excited by its static transmission error is proposed. The method is based on the iterative spectral method (ISM) and on the harmonic balance method (HBM). It is shown that the dynamic transmission error (DTE) can be obtained in the frequency domain by solving a linear system of equations, which in turn allows the computation of the modal and physical coordinates of the system.

Zusammenfassung

In diesem Beitrag wird eine Methode vorgestellt, die die Dynamik eines durch dessen statischen Übertragungsfehler angeregten Getriebesystems ausgearbeitet. Die Methode basiert auf der iterativen Spektralmethode (ISM) und der harmonischen Gleichgewichtsmethode (HBM). Es wird gezeigt, dass der dynamische Übertragungsfehler (DTE) im Frequenzbereich durch Lösen eines linearen Gleichungssystems ermittelt werden kann, was wiederum die Berechnung der modalen und physikalischen Koordinaten des Systems ermöglicht.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Similar content being viewed by others

Notes

  1. NLTE: No Load Transmission Error.

  2. It is important to note that in 3D, the geometric vector \(R\) is formed by 12 non null elements which represents the degrees of freedom. In 2D, taking into account that there are only two translations and one rotation, it will be made of the 2 center nodes.

  3. One should note that the DTE values were calculated for an idealized system whereby the shafts have been reduced to simple springs. The primary purpose is to demonstrate the exactitude of the calculation method in a basic example.

References

  1. Harris S (1958) Dynamic loads on the teeth of spur gears. Proc Inst Mech Eng 172:87–112

    Article  Google Scholar 

  2. Velex P, Ajami M (2006) On the modelling of excitations in geared systems by transmission errors. J Sound Vib 290:882–909

    Article  Google Scholar 

  3. Garambois P, Donnard G, Rigaud E, Perret-Liaudet J (2017) Multiphysics coupling between periodic gear mesh excitation and input/output fluctuating torques: Application to a roots vacuum pump. J Sound Vib 405:158–174

    Article  Google Scholar 

  4. Perret-Liaudet J, Sabot J (1991) Dynamics of gears. A method for computation of vibration spectra. Proc.8th world congress IFTOMM on the theory of machines and mechanisms. vol 1

    Google Scholar 

  5. Perret-Liaudet J (1992) Etude des mécanismes de transfert entre l’erreur de transmission et la réponse dynamique des boites de vitesses d’automobile. PhD thesis, Ecully. Ecole centrale de Lyon,

    Google Scholar 

  6. Sainte-Marie N (2016) A transmission-error-based gear dynamic model: Applications to single- and multi-mesh transmissions. PhD Thesis. INSA, Lyon

    Google Scholar 

  7. García-Saldaña JD, Gasull A (2013) A theoretical basis for the harmonics balance method. J Differ Equ 254(1):67–80

    Article  MathSciNet  MATH  Google Scholar 

  8. Masta SMT www.smartmt.com/masta. Accessed 10.02.

Download references

Author information

Authors and Affiliations

  1. Arts et Metiers Institute of Technology, LISPEN, HESAM University, F-59000, Lille, France

    Eddy Abboud, Aurélien Grolet & Olivier Thomas

  2. Valeo Transmissions, Centre d’Étude des Produits Nouveaux Espace Industriel Nord, Route de Poulainville, 80009, Amiens Cedex 1, France

    Eddy Abboud & Hervé Mahé

Authors
  1. Eddy Abboud
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Aurélien Grolet
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hervé Mahé
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Olivier Thomas
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Eddy Abboud.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Abboud, E., Grolet, A., Mahé, H. et al. Computation of dynamic transmission error for gear transmission systems using modal decomposition and Fourier series. Forsch Ingenieurwes 86, 751–755 (2022). https://doi.org/10.1007/s10010-021-00571-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10010-021-00571-x

Search

Navigation