9.3.3 Case study: Turbine-generator frequency response

For the turbine-generator specified in Fig. 7.5 and Table 7.2, develop a frequency response chart and make conclusions based on the results. The sinusoidal stimulus torque is to be applied at node 11 (the generator rotor). The response torque amplitude and phase in shaft 10-11 are to be plotted as a function of the applied torque frequency in the range of 0 to 60 Hz. Phase angle in this context means the phase angle of the shaft response torque relative to the applied torque. The modal damping ( ?) in all the subsynchronous modes is assumed to equal 0.001 for this study.

1. Why don t response resonance peaks appear for each of the subsyn-chronous flexible torsional modes, and specifically for modes 3 and 7 having natural frequencies of 21.64 and 53.66 Hz?

2. Why aren t the total phase angle changes equal to 180 as each natural frequency is traversed?

Solution to Case Study 9.3.3. The natural frequencies of the turbine-generator are given in Table 7.3. There are six flexible torsional modes less than 60 Hz (modes 2 to 7). The first mode is a rigid-body mode at zero frequency for which, by definition, there are no shaft-twisting deformations.

The frequency response chart is produced by performing steady-state sinusoidal forced response calculations (using the equations developed in Sec. 8.1) at a number of applied torque frequency steps between 0 and 60 Hz. There needs to be a concentration of...