Obtaining Influence Coefficients in Different Formats With Reduced Number of Trial Runs on Two-Plane Balancing

A rotor such as that on a steam turbine or generator is often supported by two bearings with two balance planes available at both ends. Vibrations are monitored by a pair of proximity probes at each bearing. When balancing is performed with the influence coefficient method, there are two approaches to reduce 1X vibration due to unbalance. The first approach is to treat it as a multiple-plane balancing problem involving 2x2 matrix of complex influence coefficients. The second approach is to treat it as two single-plane balance problems using static (in-phase) and couple (180 degree out-of-phase) components, respectively. Conversion equations of influence coefficients between these two approaches have been established previously [1], and used effectively in dealing with two-plane rotor balancing problems [2]-[4].

Sometimes one may have influence coefficients due to weight from one end only, not both ends for the first approach, plus those due to weight from static or couple only, not both, for the second approach. It has been found now that obtaining or knowing half of influence coefficients from the first approach, plus half of those from the second approach, can yield the other half of influence coefficients for the both approaches. In the other words, all influence coefficients in different formats can be obtained without further trial runs once one has half of influence coefficients from the two approaches.        

The above findings and conversion equations are obtained analytically, and verified by experimental results. A real application example is presented to demonstrate its efficiency in dealing with balancing jobs. The corresponding spreadsheets that can easily convert influence coefficients between different formats are presented in the current paper as well. Up to this point, all possible conversion equations between the two approaches have been successfully discovered with influence coefficients in different formats.

[1] Yu, J. J., 2009, Relationship of Influence Coefficients Between Static-Couple and Multiplane Methods on Two-Plane Balancing, ASME Journal of Engineering for Gas Turbines and Power, Vol.131, 012508.

[2] Yu, J. J., 2012, On Two-Plane Balancing of Symmetric Rotors, ASME Paper GT2012-68061, International Gas Turbine & Aeroengine Congress & Exhibition, Copenhagen, Denmark.

[3] Yu, J. J., 2014, The Necessity of a Third Balance Plane for Generator Rotor Field Balancing, ASME Paper GT2014-25706, International Gas Turbine & Aeroengine Congress & Exhibition, Dusseldorf, Germany.

[4] Yu, J. J., Ashar S., 2015, Effect of Higher-Than-Rated-Speed Rotordynamic Modes on Rotor Balancing, ASME Paper GT2015-43405, International Gas Turbine & Aeroengine Congress & Exhibition, Montreal, Canada.