Balancing of High-Speed Machinery

1 Introduction.- 2 Theoretical Background.- Basic Vibration Theory.- Undamped Free Vibration Model.- Damped Free Vibration Model.- Undamped Forced Vibration Model.- Damped Forced Vibration Model.- Basic Theory of Lateral Rotor Vibrations.- Conical Jeffcott Analysis.- Combined Jeffcott Analysis.- Synchronous Rotor Response Notation.- Elliptical Orbit Response.- 3 Review of Literature on Rotor Balancing.- General and Rigid Rotor Balancing Literature.- Modal Balancing Literature.- Influence Coefficient Balancing Literature.- Literature on Combined Modal/Influence Coefficient Balancing Methods and Comparative Studies.- 4 Rotor Balancing Methods and Instrumentation.- Rigid Rotor Balancing.- Flexible Rotor Balancing.- Vibration Measurement for Rotor Balancing.- 5 Modal Balancing.- Analytical Development.- Application to Balancing.- N and (N+2) Plane Modal Balancing.- Advantages and Limitations of Modal Balancing.- 6 Influence Coefficient Balancing.- Analytical Development.- Calculation of Correction Masses.- Calculation of Influence Coefficients.- Procedure for Influence Coefficient Balancing.- Advantages and Limitations of Influence Coefficient Balancing.- Elimination of Non-independent Balancing Planes.- Analytical Development of the Orthogonalization Procedure.- Constraining the Non-independent Planes.- Numerical Examples.- 7 The Unified Balancing Approach.- Analytical Development.- Calculation of Modal Trial Mass Sets.- Calculation of Modal Correction Mass Sets.- Calculation of Influence Coefficients.- Procedure for Application of the Unified Balancing Approach.- 8 Experimental Comparisons of the Various Methods.- Test Rotor System.- Influence Coefficient Balancing Tests.- Balancing at the First Critical Speed.- Balancing at the Third Critical Speed.- Balancing at the Fourth Critical Speed.- Enhanced Modal Balancing Tests.- Balancing the First Mode.- Balancing the Third Mode.- Balancing the Fourth Mode.- Unified Balancing Approach Tests.- Balancing at the First Critical Speed.- Balancing at the Third Critical Speed.- Balancing at the Fourth Critical Speed.- 9 Application of the Principle of Reciprocity to Flexible Rotor Balancing.- Principle of Reciprocity.- Numerical Verification of Reciprocity.- Experimental Verification of Reciprocity.- Supercritical Shaft Verification.- Demo Rig Measurements.- Using Reciprocity in Flexible Rotor Balancing.- Glossary of Terms for High-Speed Rotor Balancing.- References.