Initial Investigation

Excessive vibration of an induced draft (I. D.) fan at a coal-fired power plant was causing shaft mounted proximity probes to alarm. The alarm state prevented the fan from be operated at full load, thus reducing the efficiency of the power production. This condition existed for an extended period of time before a thorough study of the problem was conducted.

Vibration signature analysis of the fan and its drive train was performed to determine the cause of the excessive vibration. It was determined that the largest vibration was occurring mainly in the vertical direction at the running speed of the fan (1x) and was most severe at the driven end of the train. Due to the directional nature of the 1x vibration (i.e. predominately vertical), fan unbalance was ruled out as a possible cause of the problem. Additionally, it was noted that there was a perceivable vibration of the concrete deck of the fan mezzanine. It was suspected that resonance of reinforced deck structure may be the cause of the excessive vibration.

Operating Deflection Shape

In order to determine whether resonance was indeed the cause of the problem, an operating deflection shape (ODS) was obtained. The fan could not be shut down to facilitate obtaining a set frequency response functions via modal testing. The ODS was accomplished by taking acceleration data during fan operation in a regularly-spaced grid on the concrete deck of the mezzanine. A multi-channel recorder was used to acquire the data, and a reference channel was used to synchronize the phase of subsequent recordings during data processing. Although some points of the grid were inaccessible, enough points were taken to animate the ODS with Vibrant Technologies ME’Scope software.

One mode of vibration dominated the other motions present in the resulting ODS animation. This mode occurred at 1x. The shape of this mode of vibration resembled that of the first mode of a plate, one antinode near mid-span. Figure 1 below illustrates the maximum positive and negative displacements of deck due to the vibration at 1x. The concrete deck and supporting steel substructure were flexing up and down near the center of the deck’s span with the maximum displacement occurring near the end which supported the fan.

Figure 1 – ODS animation snapshots of the maximum positive and negative displacements of the concrete deck surface. (Note that relative locations of the fan and motor are indicated in figure 2.)

Finite Element Model

An FEA model of the reinforced deck structure was created with beam and plate elements. The mass of the motor and fan were represented as nodal masses at their respective locations. Figure 2 illustrates the FEA model of the steel substructure and the concrete deck.

Figure 2 – FEA model setup

The FEA model was used as a platform for examining proposed redesign configurations. The FEA model was “calibrated” to match the dominate mode of vibration demonstrated in the ODS. This was accomplished by making slight adjustments to the model (i.e. altering the rigidity of the bond between the steel girders and the concrete deck as well as the stiffness of the concrete). The adjustments were necessary as some degradation of the concrete/girder bond was suspected. In fact, this degradation likely led a change in stiffness and the resonant condition at hand. Figure 3 represents the FEA predicted mode shape that matched the observed ODS.

Figure 3 – FEA model results

Redesign Solutions – FEA Predicted Results

Using the validated finite element model, several redesign solutions were considered. These redesign solutions attempted to stiffen the structure enough to avoid resonance at 1x as well as possible the 2x and 3x harmonics of running speed. Other possible solutions such as altering system mass, adding damping, and adding passive or active vibration absorption were deemed either impractical or cost prohibitive.

The redesign solution chosen was to modify the steel substructure by adding two k-braces to the support columns as well as 2 girders along the span between these braces. This span was the zone that was undergoing the most displacement in both the ODS and the FEA model. Figure 4 illustrates the selected redesign configuration.

Figure 4 – Selected redesign configuration

The FEA model predicted that this design change would increase the first critical frequency of the deck structure by approximately 30%. It was estimated that this increase would reduced the response (i.e. magnification factor) of the deck by about 50%. This estimation was based on a worst case damping coefficient extrapolated from field data and the closed form solution of a single degree of freedom system. Although a 50% attenuation of the response was not ideal, the FEA model predicted that major structural modifications would be required in order to obtain a 70% to 80% reduction in response. Additionally, a 50% attenuation would be sufficient to avoid the alarm condition that forcing the operation of the I. D. fan below full load.

Conclusion

The use of model testing techniques and FEA together to solve vibration problems is a powerful technique. In the case presented, the deck structure of an I. D. fan was redesigned in order to avoid an unacceptable resonant condition. An FEA model was validated using an ODS. It was then employed to test various design configurations. A design was selected that the FEA model predicted would succeed and that was feasible from both cost and implementation perspectives.