Balancing of a linear elastic rotor-bearing system with arbitrarily distributed unbalance using the Numerical Assembly Technique

Georg Quinz*, Marcel Simon Prem, Michael Klanner, Katrin Ellermann

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In this paper, a new application of the Numerical Assembly Technique is presented for the balancing of linear elastic rotor-bearing systems with a stepped shaft and arbitrarily distributed mass unbalance. The method improves existing balancing techniques by combining the advantages of modal balancing with the fast calculation of an efficient numerical method. The rotating stepped circular shaft is modelled according to the Rayleigh beam theory. The Numerical Assembly Technique is used to calculate the steady-state harmonic response, eigenvalues and the associated mode shapes of the rotor. The displacements of a simulation are compared to measured displacements of the rotor-bearing system to calculate the generalized unbalance for each eigenvalue. The generalized unbalances are modified according to modal theory to calculate orthogonal correction masses. In this manner, a rotor-bearing system is balanced using a single measurement of the displacement at one position on the rotor for every critical speed. Three numerical examples are used to show the accuracy and the balancing success of the proposed method.
Original languageEnglish
Article numbere138237
Number of pages7
JournalBulletin of the Polish Academy of Sciences: Technical Sciences
Issue number6
Publication statusPublished - Dec 2021


  • Modal balancing
  • Numerical Assembly Technique
  • Recursive eigenvalue search algorithm
  • Rotor dynamics

ASJC Scopus subject areas

  • Engineering(all)
  • Artificial Intelligence
  • Information Systems
  • Atomic and Molecular Physics, and Optics
  • Computer Networks and Communications

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