Enriching balancing information using the unbalance covariance matrix

Abstract

Traditionally, rotor balancing is performed based only on vibration readings from either a balancing machine or from a machine in which the rotor is being balanced in-situ. These readings cannot reflect the complete state of unbalance in the rotor. The reason for this is that higher frequency modes do not make a significant contribution to response in any one operating condition. The resolution of measuring instrumentation is always limited and, as demands grow for ever-improved balance quality, this instrumentation struggles more and more with reducing signal-to-noise ratios. When balance corrections are made to a rotor based only on these vibration readings, the components of unbalance that tend to excite only the higher modes of the original configuration can make a significant contribution to response if the properties of the stator change.

This article presents a novel approach to robust balancing. It relies on the use of additional information in the form of a rotor unbalance covariance matrix. In theory, this covariance matrix could be obtained if a large sample from the population of all rotors of this type could be tested in a very high-quality (and high-speed) balancing machine. This suggestion is impracticable in all real situations. However, it is entirely conceivable that modelling of the manufacturing processes used to create the rotor could deliver this covariance matrix. This article begins by illustrating how such a covariance matrix might be obtained from modelling and then goes on to explain how the information within the covariance matrix can be combined with a set of measurements from a specific rotor to provide an improved estimate of the actual state of unbalance on that rotor. Examples are included to demonstrate the proposed robust balancing method.

Keywords

covariance covariance matrix unbalance balancing robust balancing

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