Bifurcation analysis of an automatic dynamic balancing mechanism for eccentric rotors

In many industrial applications imbalance is a major cause for unwanted vibrations. One way to compensate for an unknown imbalance is the implementation of an automatic ball balancer. Oil-lubricated automatic ball balancers are applied in hand-held tools and washers. However, in applications such as optical drives fluid lubrication is highly undesirable since it may destroy the optical system upon leakage. Therefore, in this paper, the balancing performance of an automatic ball balancer without fluid lubrication is investigated. The absence of fluid lubrication gives rise to dry friction phenomena which cause the existence of equilibrium sets of the balls in the automatic ball balancer. A model of the system with dry friction, modeled by a set-valued force law, is built based on dedicated experiments. The resulting equilibrium sets and their dependency on system parameters are studied and the consequences for the balancing performance is assessed. Based on these results, it can be concluded that in parts of such equilibrium sets the balancing performance deteriorates when compared to the system without automatic ball balancer; in other words, the balancing performance is endangered by the presence of dry friction. This conclusion is supported by both numerical and experimental results.

http://www.dct.tue.nl/New/Wouw/IJBC2005.pdf

Performance of an automatic ball balancer with dry friction

Analysis of the transient response of an automatic dynamic balancer for eccentric rotors

Three-dimensional modelling and dynamic analysis of an automatic ball balancer in an optical disk drive

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 with those from an experimental rig. Close qualitative and quantitative match is found between the theory and the 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 are proposed.

/pdf/investigation-of-a-multi-ball-automatic-dynamic-balancing-1kqi45bche.pdf

J. R. Kang

Papers

The application of ball-type balancers for radial vibration reduction of high-speed optic disk drives