Identificación de parámetros en soportes de maquinaria rotativa

1. ASME paper GT2004-54160 July 22, 2004 Identificación de parámetros en soportes de maquinaria rotativa Luis San Andrés Turbomachinery Laboratory Texas A&M University Oscar De Santiago Dresser-Rand Co. IX Ecuadorian Congress on Mathematics Quito, Ecuador

2. Justification: Increasingly stringent vibration limits imposed by industry standards (API 617, 7th Edition, for example) require predictionandvalidation of Critical Speeds and Amplification Factors during shop testing of commissioned turbo machinery. Parameter identification in the field is also promising for condition monitoring and troubleshooting, and in the near future for self-adapting rotor-bearing control systems. • OBJECTIVES: • Based on previously developed methods, this work intends to • Extend the identification method to flexible rotor-bearing systems • Validate these methods for in-situ estimation of bearing force coefficients

3. Identification of Force Coefficients in Flexible Rotor-Bearing Systems Rotor FE Model: Timoshenko-beam General EOMs:

4. Identification of Force Coefficients in Flexible Rotor-Bearing Systems Imbalance loading: Leads to algebraic set: Imbalance distribution (m, u, )a=1..k determines support displacements With harmonic (i.e. synchronous) components cos( t) and sin(t)

5. Identification of Force Coefficients in Flexible Rotor-Bearing Systems Rotor dynamic stiffness matrix Bearing impedance matrices Partition HR Reorder EOMs as:

6. Identification of Force Coefficients in Flexible Rotor-Bearing Systems Identification equations are: Simplification for identical bearing supports Note: still needed two imbalance runs

7. Identification of Force Coefficients in Flexible Rotor-Bearing Systems Free-free modes 196 Hz 384 Hz

8. Measurements for increasing imbalances Identification of Force Coefficients in Flexible Rotor-Bearing Systems u 10.5 gram 7.25 gram CX, CY X2, Y2 X1, Y1 X1 at drive end bearing Linearity of rotor response? Divide amplitude for two largest imbalances by amplitude of lowest imbalance (should overlap the curves) CX at rotor mid span

9. Stiffness Coefficients 3.8 gram 7.25 gram XX, XY YY, YX 10.5 gram Left: Direct Right: Cross-coupled

10. Damping Coefficients 3.8 gram 7.25 gram 10.5 gram Left: Direct Right: Cross-coupled XX, XY YY, YX

11. Force Coefficients: Comparison to earlier results K XX, XY YY, YX Current model includes sensor location away from bearing mid plane ~ 15% change in identified coefficients C Lines : original identification method Symbols: current - enhanced procedure Left: Direct Right: Cross-coupled 10.5 gram

12. Identification of Force Coefficients in Flexible Rotor-Bearing Systems Conclusions: Robust method to identify bearing support force coefficients in flexible rotor-bearing systems Enhanced for practical use: sensors not at mid plane of bearings. Procedure sensitive to numerical conditioning of test data. In particular at critical speeds in systems with little damping. Imbalance must be large enough to reduce NSR Procedure NOT very sensitive to noise (up to 10%)