Research Article A New Method for Field-Balancing of High-Speed Flexible Rotors without Trial Weights Y. A. Khulief, 1 M. A. Mohiuddin, 2 and M. El-Gebeily 3 1 Department of Mechanical Engineering, King Fahd University of Petroleum & Minerals, KFUPM Box 1767, Dhahran 31261, Saudi Arabia 2 Data & Consulting Services, Schlumberger, Dhahran Tech Valley, Dhahran 31261, Saudi Arabia 3 Department of Mathematics, King Fahd University of Petroleum & Minerals, KFUPM Box 1767, Dhahran 31261, Saudi Arabia Correspondence should be addressed to Y. A. Khulief; khulief@kfupm.edu.sa Received 15 January 2014; Revised 20 April 2014; Accepted 21 May 2014; Published 15 June 2014 Academic Editor: Hyeong Joon Ahn Copyright © 2014 Y. A. Khulief et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Flexible rotor balancing, in general, relies to a great extent on physical insight into the modal nature of the unbalance response. Te objective of this investigation is to develop a hybrid experimental/analytical technique for balancing high-speed fexible rotors. Te developed technique adopts an approach that combines the fnite element modeling, experimental modal analysis, vibration measurements, and mathematical identifcation. Te modal imbalances are identifed and then transformed to the nodal space, in order to determine a set of physical balancing masses at some selected correction planes. Te developed method does not rely on trial runs. In addition, the method does not require operating the supercritical rotor in a high-speed balancing facility, while accounting for the contribution of higher signifcant modes. Te developed scheme is applied to a multidisk, multibearing, high-speed fexible rotor, where the interaction between the rotor-bending operating defections and the forces resulting from the residual unbalance are appreciable. Some new benchmark solutions and observations are reported. Te applicability, reliability, and challenges that may be encountered in feld applications are addressed. 1. Introduction Flexible rotors are of major concern to vibrations and balanc- ing specialists, as they become increasingly integrated into many rotating machines. Generator rotors, in general, are fexible rotors; for example, power plant size generator rotors operate above the frst and second bending modes, while long slender rotors run above the third or higher modes. Most turbine rotors are quasi-fexible, which imply that they operate above the frst bending mode and sometimes the second. Flexible and quasi-fexible rotors exhibit appreciable dynamic response as they run through their critical speeds. According to ISO standards [1–3], fexible rotors are classifed into fve groups with diferent balancing techniques for each, wherein rigid body balancing could be applied to a group of fexible rotors when some special requirements are met; otherwise, high speed balancing must be used. Flexible rotor balancing is signifcantly more complex than rigid rotor balancing. Te fexible rotor continually changes its elastic confguration as more critical speeds are encountered, and additional balance planes may be required. Since it is recognized that rotor-bending operating defections modify the resulting forces from residual unbalance, fexible rotors need to be balanced at high speed. Balancing fexible rotors has attracted the attention of many investigators during the last forty years. A number of pioneering investigations addressed some analytical and experimental aspects of the problem [4–6]. Te infuence coef- ficient and modal balancing techniques are the two principal approaches used for balancing fexible rotors. Modal balanc- ing is not readily computerizable, as it relies on balancing the critical modes one by one and therefore requires high degree of operator insight. Te number of correction planes used for modal balancing may also vary according to the adopted balancing scheme. Te issue of the number of planes required for modal balancing of fexible rotors and whether it should Hindawi Publishing Corporation International Journal of Rotating Machinery Volume 2014, Article ID 603241, 11 pages http://dx.doi.org/10.1155/2014/603241