Two-plane automatic balancing: a symmetry breaking analysis

David J Rodrigues, Alan R Champneys, Michael I Friswell, R E Wilson

Research output: Contribution to journalArticle (Academic Journal)peer-review

28 Citations (Scopus)
302 Downloads (Pure)


We present an analysis of a two-plane automatic balancing device for rotating machinery. The mechanism consists of a pair of races that contain balancing balls which move to eliminate imbalance due to rotor eccentricity or principal axis misalignment. A model is developed that includes the effect of support anisotropy and rotor acceleration. The symmetry of the imbalance is considered, and techniques from equivariant bifurcation theory are used to derive a necessary condition for the stability of balanced operation. The unfolding of the solution structure is explored and we investigate mechanical systems in which either the supports or the automatic ball balancer is asymmetric. Here it is shown that, provided the imbalance is small, the balanced state is robust to the considered asymmetries.
Translated title of the contributionTwo-plane automatic balancing: a symmetry breaking analysis
Original languageEnglish
Pages (from-to)1139-1154
Number of pages7
JournalInternational Journal of Non-Linear Mechanics
Issue number9
Early online date18 May 2011
Publication statusPublished - Nov 2011


  • Automatic balancing
  • Rotordynamics
  • Bifurcations with symmetry


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