Two-Plane Automatic Balancing: A Symmetry Breaking Analysis
DJ Rodrigues, AR Champneys (University of Bristol), MI Friswell (Swansea University) & RE Wilson (University of Bristol)
International Journal of Non-Linear Mechanics, Vol. 46, No. 9, November 2011, pp. 1139-1154
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.
This material has been published in the International Journal of Non-Linear Mechanics, Vol. 46, No. 9, November 2011, pp. 1139-1154, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by the Elsevier.
Link to paper using doi: 10.1016/j.ijnonlinmec.2011.04.033
International Journal of Non-Linear Mechanics