Active Condition Monitoring of a Marine Gas Turbine through Rotor Shaft Vibration Analysis

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Figure 2. P-V diagram of Brayton Cycle (Ogbonnaya, 2004b)

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Figure 3. T-S diagram of Brayton Cycle (Ogbonnaya, 2004b)

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thus;

(6)

But , thus,

and

Substituting into equation (6) and simplifying gives,

(7)

where r_pis the pressure ratio and ᵞ is the specific heat ratio (Ḉengel and Boles, 1998).

2.2. Vibration of Rotor Shafts

Vibration could be rectilinear or torsional. Torsional vibration is of more consequence to a rotating system. It is a kind of periodic angular motion of elastic shafts with circular rotors rigidly attached to them. This type of vibration is peculiar to GT rotors. The compressors and the turbines of the GT plant are periodically affected by the action of vibration (Maynard et al, 2001). In this work, consideration was given to a spring-mass system constrained to move in the vertical direction and excited by a rotating machine that is unbalanced, as shown in Figure 4. The unbalance is represented by an eccentric mass, m with changing eccentricity, e, which is rotating with angular velocity, ω. By letting x be the displacement of the non-rotating mass (M - m) from the static equilibrium position, the displacement of m is:

(8)

Thus the equation of motion then becomes

(9)

The vibration displacement amplitude is

(10)

Figure 4. Harmonic disturbing force resulting from rotating unbalance (Source: Katsuhiko, 2005)

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Figure 5. Flowchart to compute GT thermodynamics analysis using temperatures

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Figure 6. Flowchart for computing vibration displacement amplitude on bearings 1-4

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Two flowcharts shown in Figure 5 and Figure 6 were drawn from equations 5 and 10 to represent the respective contributions of the thermodynamic and vibration analyses to the active/ dynamic condition monitoring of the GT system. The double-loop flowchart in Figure 5 helped to compute the operating temperatures in the system in order to maintain the required thermal efficiency. The multi-loop flowchart in Figure 6 helps to keep a check on the vibration displacement amplitude of the various bearings to make sure that set and safe operational values are not exceeded during the running of the engine. The java program from this flowchart also ascertains that alarm messages are generated/ displayed if the plant should be distressed and suddenly stopped.

3. Results and Discussion

Various graphs were plotted to provide for proactive condition monitoring of GTs through thermodynamics and rotor shafts vibration analysis. Different computer models were also developed for the analysis. The GT thermodynamic analysis obtained from the compressor, combustor and turbine temperature and pressure values shown in Appendix A were first analysed to determine the efficiency of the GT holistically.

Frequency and amplitude calculations were also computed using turbine speed, eccentricity and active load of the engine. The GT thermodynamic simulation models are shown in Figure 5 and Figure 6. They were used to generate the compressor work, turbine work, combustor heat supplied, network done and the efficiency necessary to determine the capacity of the turbine plant.

3.1. Vibration Analysis

The vibration analysis conducted was done by employing different computer models. The first model was developed for calculating the critical torsional frequency. With the assumption of the value of, the process was initiated by assuming unit amplitudes of vibration for the first or free mass. Based on this, the amplitude and inertia force of the remaining masses were then calculated. The oscillating frequency at varying load was obtained using the rotating speed of the turbine. It was not allowed to exceed or equal the natural frequency above to avoid system resonance.

The second computer model was used to calculate the natural frequency, damping ratio, maximum amplitude at steady state for the unbalance. Both models are shown in Figure 7 and Figure 8 respectively. The generated result is shown in Appendix B.

By inputting the turbine speed for the engine and the various eccentricities relative to the bearing position from the reference point, the corresponding active load, frequencies and vibration displacement amplitudes on the respective bearings were generated. The data in Appendix B were used to plot different graphs. The vibration amplitude on the four bearings was plotted against the turbine speed. The graph is shown in Figure 9, and it was observed that the vibration amplitudes at different bearings were almost constant while the speed of the turbine increased. These high vibration amplitudes at the bearing housings are danger signs that should be monitored in proactive condition monitoring as they can be responsible for the failure of GT shafts causing misalignment and other fatal accidents.

A graph of the active load against turbine speed was also plotted as shown in Figure 10. In a normal situation, a plot of active load against turbine speed should or is expected to produce a seemingly linear graph, but as was observed, there were fluctuations along the line. This shows that the engine load fluctuates with speed due to vibration. It is also clear that vibration reduces the active load, thus reducing useful energy.

Figure 7. Input evaluation interface for computer model

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Figure 8. GT efficiency analysis interfacce of the computer mode

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Figure 9. Program to calculate frequency and amplitude

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Figure 10. Computer model used for rotating unbalance analysis

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Figure 11. Vibration amplitude against turbine speed

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Figure 12. Active load against turbine speed

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