Modal Analysis of Exhaust Fan Impeller

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The fan consists of the impeller and the shaft that is supported at its ends by two double-row barrel bearings. The impeller and the shaft are joined each other by 24 bolts on the center wheel disc. Figure 2 gives the basic dimensions of the shaft and the impeller. The fan is powered by motor with power of 1500 kW and maximum 1000 rpm. During steel melting process the fan operates in the interval from 400 to 1000 rpm that corresponded to the rotational frequency range 6.67 ÷ 16.67 Hz. Rotational velocity can be regulated by changing the frequency of the input voltage. The connection of the motor with the shaft is ensured by a sector spring clutch.

Figure 2. Basic dimensions of the impeller and shaft

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3. Operational Analysis of the Fan Vibration

As the first, it was needed to get the estimation of dynamic behavior of the fan during its operation. For that purpose we performed the measurement which main aim was to determine vibration level at different values of the rotational frequency. The responses were measured by three uniaxial accelerometers Bruel&Kjaer 4507B and one triaxial accelerometer Bruel&Kjaer 4506B. The locations of the individual sensors as well as measurement directions are obvious from Figure 3.

Figure 3 .Locations and measurement directions of accelerometers

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During the measurement angular velocities of the fans were increased in the interval from 400 to 1000 rpm. The rotation velocities were regulated by using frequency changer. Its frequency was increased gradually by 1 Hz. The vibration level was assessed on the base of effective vibration velocity. Its value was determined from measurement data in accordance with international standard STN ISO 10816-1(Mechanical vibration - Evaluation of machine vibration by measurements on non-rotating parts) by the equation:

(1)

where to are the acceleration amplitudes that correspond to frequencies to of the frequency spectrum with range 2.5 ÷ 1000 Hz. Graphical charts of the effective vibration velocities for the whole range of the impeller‘s working rotations are shown in Figure 4.

Figure 4 shows that for certain rotational frequencies the vibration intensity of the fan is several-fold higher than in others, especially in horizontal and axial directions. According to STN ISO 10816-1 ^[8], for big power units with the power exceeding 300kW and other big machines with rotating masses that are fixed to solid and heavy foundations which are relatively solid in the direction of the vibration measurement, it is necessary to consider class III for which the band ranges are defined according to Table 1.

Figure 4. Effective vibration velocity as function of rotation frequency

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Table 1. Typical band boundaries of effective vibration velocities of machine in class III [8]

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Tables index

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4. Modal Analysis of the Impeller

The knowledge of impeller’s natural frequencies is necessary for confirmation or exclusion of the assumption that the excessive vibration is caused by resonance. In the first phase, we performed experimental modal analysis of the non-rotating fan. Ten different input DOFs were chosen on the analyzed structure. Nine of which were on the shaft, point 10 was on the central disc of the rotating wheel. Selection of exciting points was limited because of the restricted access to the space of the rotating wheel. Individual locations and impact directions are given in Figure 5.

Figure 5. Locations and directions of excitations

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The structure was excited by impact hammer Bruel&Kjaer 8210. The responses of vibration were measured by using five accelerometers Bruel&Kjaer 4507B. Their locations and measurement directions are given on Figure 6.

Figure 6. Locations and directions of measured responses

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The result of measurement is the set of frequency response functions between the individual input and output DOFs. This set was used to obtain Complex Mode Indicator Function which allows simply estimate the natural frequencies of the impeller. The CMIF plot is shown in Figure 7.

Figure 7. Complex Mode Indicator Function of the analyzed structure

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As obvious from Figure 7, the first natural frequency of the impeller is approximately 25.6 Hz. During operation, its maximal rotational frequency is 16.67 Hz. Since in the course of the experiment it was not possible to choose more locations of excitation, numerical modal analysis of the system shaft - rotating wheel was performed by using finite element method. Finite element mesh consisting of ten node tetrahedrons is shown in Figure 8. A much finer mesh was used for the bolts and contact regions.

Figure 8. Finite element mesh of the numerical model

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Resonance frequencies were determined for five different values of rotational frequencies of the shaft. The results of the numerical simulations are given in Table 2. Mode shapes of the analyzed finite element mode are shown in Figure 9. The results of the numerical solution also confirmed the finding that the first natural frequency of the structure lay outside the working rotational frequencies of the fan.

Figure 9. Mode shapes of the analyzed model at 1000 rpm

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Table 2. Natural frequencies of the impeller obtained by FEM analysis

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