A computation technique has been developed at Pratt & Whitney Aircraft (P&WA) in which localized dynamic flexibilities in an assembled rotor or case can be rapidly determined from experimental mode shape and frequency data. A dynamic mathematical model of the structure is developed with empirical flexibility terms assigned to mechanical joints such as flanges, splines, couplings, etc. The vibratory response of the structure is measured in laboratory tests and compared with calculated values. Agreement between calculated and experimental mode shapes and frequencies is obtained by a computerized random search technique, which determines the flexibility terms that produce the best match between experimental data and calculated values for all of the vibration modes compared. The technique was developed for rotor critical speed applications, but it may be applied to any simple or complex beam type structure.

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The TF30 P-lll + engine developed a high-pressure spool rotor dynamic instability when it went into production in mid-1986. Vibration rejection rates were as high as 50% until the instability was eliminated with the incorporation of an oil-film damper at the high-pressure turbine (HPT) bearing. This paper focuses on the analytical treatment of the instability and includes a summary of engine testing that was done to help diagnose the problem. Correlation between test and analysis implicates the aerodynamic cross-coupled forces from the HPT system as the destabilizing mechanism. Results from the stability model are presented that show the damper completely suppressing the instability as later confirmed by ground-level tests. This experience points out the subtle characteristic of rotor instability and the need for improved quantification of the destabilizing mechanisms that produce it. The predecessor engine model had been in service for years without the problem, yet it developed a rotor instability with the incorporation of a new HPT that had no obvious impact on engine rotor dynamics. Nomenclatureaverage blade height k = lateral stiffness coefficient M = moment P -pressure S = scale factor s = complex whirl frequency T = stage torque | 8 = thermodynamic efficiency factor gradient d = logarithmic decrement or rotor deflection e = material hysteresis factor X = damping exponent B = rotor slope T = trunnion stiffness coefficient Q = damped whirl frequency Subscripts brg = bearing C = cross-coupled, as in cross-coupled stiffness D = direct, as in direct stiffness gnd = ground HPT = high-pressure turbine RC = rear case rel = relative rot = rotor T = total, as in total pressure x =x direction y =y direction