Modelling of a stator casing’s destructive vibration has allowed its modification on-site. Fabio Parodi, Massimiliano Manarini and Michele Raciti explain why its refit and its optimisation was an operation of short duration and minimum complexity.

When the operation of a 1980s-designed generator led to damage to its components over time, vibration of its frame was determined to be the culprit.

But rather than removing the unit as a whole to allow it to undergo modification to reduce this movement, repairs instead went ahead with the machine in-situ.

Not only did the ensuing changes to the 60 Hz machine extend the life of the stator’s frame but the complexity of the refitting operation and the time taken to complete it were reduced too.

This was because the work was carried out during a major overhaul outage and because the repair was on-site in nature, which in turn was due to optimisation of the necessary generator modifications for such a repair.

A high level of vibration during operation of the steam turbine-driven generator had caused fatigue stress that had resulted in severe damage, such as the fracture of the connecting bolts between the upper and lower parts of the frame of the generator’s stator.

During a test on run up, measurements revealed that substantial vibration of the unit occurred only with the generator in its excited state and at the natural frequency of the frame, close to 123 Hz, or about twice the angular speed of the rotor when it was running at nominal speed.

The frame vibrates in response to the vibration of the stator core, which deforms under the electromagnetic force produced by the rotating magnetic field. Figure 1 shows how the high level of distortion of the frame stresses the bolts that join the two parts of the frame and ultimately causing their rupture.

Figure 1: Vibration in the stator frame deforms it
Figure 1: Vibration in the stator frame deforms it

A 3D finite element model (FEM) of the stator under the action of the electromagnetic force allowed us to determine what modifications should be made to the frame to raise the frequency of its resonance. The modification implemented reduced the vibration by 50 per cent, as calculations predicted.

Five sequential stages characterised the process of repair. First was an initial vibration measurement and reverse engineering of the main components, followed by computer simulation of the dynamic behaviour of the stator. Design of the frame modification and numerical verification of this refit then followed, after which came the on-site repair of the frame. Our activity concluded with a final measurement of the frame’s vibration to ensure the modification had been successful.

Initial measurement

During the first stage, placing vibration probes at three regions of the frame allowed us to investigate the vibration of the stator frame during a run up with the machine excited. Probes inserted through openings at the horizontal centre line allowed the vibration of the core to be recorded. We then determined the ratio between the two types of vibration, horizontally and radially.

At a number of measurement points the frame vibration amplitude increased strongly when the machine was operating at near the nominal speed. A natural frequency of the frame of about 123 Hz was causing dynamic amplification, as Figures 2, 3 & 4 show.

Figure 2: Frame vibration, channel 3 (mm/s rms - rpm)
Figure 2: Frame vibration, channel 3 (mm/s rms – rpm)
Figure 3: Frame vibration, channel 10 (mm/s rms - rpm)
Figure 3: Frame vibration, channel 10 (mm/s rms – rpm)
Figure 4: Radial vibration at the top of the upper frame, channel 7 (mm/s rms - rpm)
Figure 4: Radial vibration at the top of the upper frame, channel 7 (mm/s rms – rpm)

The ratio of frame vibration to core vibration (R) was greater than 2, which confirmed that a natural frequency was causing a strong increase in the amplitude of the vibration.

Simulation tool

We employed multi-purpose 3D FEM software from ANSY to perform the simulation of the stator’s dynamic behaviour. By measuring the dimensions of the frame and core we were able to reverse engineer them and complete the model.

Figure 5 shows the FEM model of the machine with all the structural components affected by the vibration, the lower and upper parts of the stator frame, and the stator core.

Figure 5: The FEM model of the complete stator
Figure 5: The FEM model of the complete stator

Under load conditions

Under load conditions, the generator was under the same conditions as during the vibration measurement: a run up with excitation at no load.

Here two more forces became apparent. One was a tangential load due to the active power torque and bar bouncing load. As the overall effect is a reduction of radial vibration depending on apparent power and power factor, this does not change the nature of the problem.

The rotor produces a rotating electromagnetic force at 120 Hz, which is twice the network frequency. The stator core vibrates under the action of this force and transmits movement to the frame through the fixing points, the core supporting rings.

The amplitude of the vibration of the frame is a function of the vibration of the core and of the natural frequency of the frame, so to reduce vibration of the generator frame it had to be modified in a way that changed its natural frequency because the vibration of the stator core during operation is unavoidable, i.e. its vibration is inherent in the nature of the electromagnetic machine.

The rotation of the excited rotor produces a magnetic field with an elliptical and synchronous load distribution on the stator core. The rotating load can be thought of as the sum of two components: one constant and one alternating. The first has no effect on the stator frame. It simply squeezes and shrinks the core. The second component, however, excites a mode shape with four nodes at twice the rotor frequency.

Consequently the numerical simulation of the physical phenomenon becomes a harmonic analysis under the action of the alternating component of the magnetic field. Simulation of a rotor run up from 0 Hz to 75 Hz requires the calculation of harmonic response from 0 Hz to 150 Hz because the excitation of the magnetic field is at twice the network frequency.

Design and verification

Considering that the natural frequency is above 120 Hz, the most rational modification would be a stiffening of the frame to shift the resonance and consequently reduce the amplitude of vibration when the machine operates at at nominal speed.

Thus, the designed modification comprised eight stiffening ribs welded to the internal walls. Figure 6 shows the FEM stiffened model with all structural components, the lower part, the upper part, the stator core and the stiffeners.

Figure 6: The FEM stiffened model of the stator frame
Figure 6: The FEM stiffened model of the stator frame

The design of the dimensions of the stiffening ribs aimed to achieve a shift in the natural frequency of 10 Hz and consequently a reduction of 50 per cent in the amplitude of vibration. The calculated R of the displacement of the stator frame to that of the stator core decreased from 2.2 to 1.0, confirming the positive effect of the design (Figures 7 & 8).

Figure 7: Harmonic response of orginal model, according to measures points: R = 0.04/0.018 = 2.2
Figure 7: Harmonic response of orginal model, according to measures points: R = 0.04/0.018 = 2.2
Figure 8: Harmonic response of stiffened model, according to measures points: R = 0.018/0.018 = 1
Figure 8: Harmonic response of stiffened model, according to measures points: R = 0.018/0.018 = 1

The design of the ribs also allowed them to be welded onto the frame while it was in the power plant and to allow the future opening of the upper part of the cover during a major overall. Figure 9 shows the modification made to the actual generator. There are eight semicircular and transversal ribs attached to the internal walls.

Figure 9: The stiffening ribs welded in place on the actual generator
Figure 9: The stiffening ribs welded in place on the actual generator

Five stages characterised the repair: vibration measurement, computer simulation, design of the frame modification and numerical verification, on-site repair and measurement of the vibration of the frame

Final measurements

Vibration of the case after the application of the stiffening ribs is lower than before the modifications. The measured value of R now ranges from 0.6 to 1.1. According to Ansaldo Energia’s experience, that is the correct range of values for a generator with this core support.

The corrective action on the generator has cut the level of vibration by 50 per cent. This reduction is due to the on-site vibration measurements, the analysis of the root cause (which was based on collected vibration pattern data), the FEM software and the knowledge of and experience in the mechanical design of the generator.

The use of 3D FEM analysis has allowed measurements to be made on site and confirmed the result of the root cause analysis. It also allowed us to validate and tailor the solution step by step, to consider different possibilities, which reduced outage time and the complexity of the intervention.

Fabio Parodian is an engineer, Massimiliano Manarini is Generator Balancing Test Room manager and Michele Raciti is a mechanical engineer, all at Ansaldo Energia, Italy. For more information, visit www.ansaldoenergia.it.

This article is based on a Best Paper Awards winner at this year’s POWER-GEN Europe in Vienna.

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