|Pages||705 - 728|
|Number of pages||24|
|Journal||Philosophical Transactions of the Royal Society A|
|Journal publication date||Mar 2008|
This paper concerns an analytical and experimental investigation into the dynamics
of an automatic dynamic balancer (ADB) designed to quench vibration in eccentric rotors. This fundamentally nonlinear device incorporates several balancing masses that are free to rotate in a circumferentially mounted ball race. An earlier study into the steady state and transient response of the device with two balls is extended to the case of an arbitrary number of balls. Using bifurcation analysis allied to numerical simulation of a fully nonlinear model, the question is addressed of whether increasing the number of balls is advantageous. It is found that it is never possible to perfectly balance the device at rotation speeds comparable with or below the first natural, bending frequency of the rotor. When considering practical implementation of the device, a modification is suggested where individual balls are contained in separate arcs of the ball race, with rigid partitions separating each arc. Simulation results for a partitioned ADB are compared to those from an experimental rig. Close qualitative and quantitative match is found between the theory and experiment, confirming that for sub-resonant rotation speeds, the ADB at best makes no difference to the imbalance, and can make things substantially worse.
Further related configurations worthy of experimental and numerical investigation
Additional information: Article submitted to Royal Society
Sponsorship: The authors would like to thank Jorge Galan Vioque for helpful discussions, Clive Rendall and Tony Griffith for continued technical support while designing, building and running the experimental rig, and Marian Wiercigroch for his comments on an earlier draft. KG was funded by the EPSRC grant GR/535684/01. MIF gratefully acknowledges the support of the Royal Society through a Royal Society-Wolfson Research Merit Award. The visit of AMM to Bristol was made possible through the EU Socrates/Erasmus scheme.
- Jeffcott rotor, autobalancer, vibro-impact, imbalance, multistability, bifurcation