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Bladevibration Operational blade
Turbi blades are predominantly subjected to periodic nozzle excitation distributed along the blade lengths (Rao and Vyas, 1985; Irretier, 1988; Rieger, 1988). The load on a rotating blade can thus be described as a Fourier-series, the various harmonic coefficients of which are affected by the unevenness of the nozzle spacing as well as partial (i.e.uneven) steam admission. Rao and Vyas (1985) consider three components ofthe forcing function namely in the rotor-axial and tangential directions as well as amoment acting on the blade.
Rotational effects
The most intuitive effect of rotation on a structure is that of rotational stiffening as a result ofcentrifugal forces. From experimentation on a single-blade rotor, Fan et al (1994) note that rotational stiffening causes the blade natural frequencies to increase in a nonlinear way, since the blade centrifugal force is proportional to the square of the rotation speed.
Analytical and numerical study
Cantilever beam theory
It is useful for understanding the characteristics of ELDV to consider a cantilever beam of length l, vibrating under the influence of an arbitrary concentrated load F, while translating at a constant speed c , perpendicular to a stationary LDV (see Figure 2). This is in effect an application of CSLDV with a uniform scanning rate. Torsional, sideways and axial vibrations are not taken into account for this demonstration.
Effect of scanning speed
Since ELDV measurements are dependent on scanning speed, it is necessary to determine the extent of this influence. In this section the cantilever beam considered in Section 2.2.3 is subjected to a half-wave sine pulse of amplitude 10 N with duration of 0.5ms. This choice of excitation was made to simulate an impulse force, allowing the simultaneous excitation of all the natural frequencies considered. The pulse duration was chosen to have an excitation bandwidth that encompassed the relevant natural frequencies. A sampling frequency of 12.8 kHz allowed sufficient measurement bandwidth to detect the beam’s fourth natural frequency in the frequency spectra. In this section, the scanning direction will be from beam tip to root starting from t = 0 s. When the initial displacements and velocities of the beam are set to zero, spectra can be calculated from the EVRs without having to use windowing
Experimental setup
The test rotor depicted in Figure 21 was used to investigate the condition monitoring capabilities of the ELDV measurement technique described in Section 2.4.2. The rotor was driven with a speed-controlled motor and consisted of a solid shaft (supported by two bearings) with a hub and a single flat, straight blade. A Heidenhain ERN 120 shaft encoder provided accurate rotor angular position feedback during testing and the blade was dynamically perturbed during rotation by means of a compressed air-jet. A piezoelectric dynamic pressure sensor installed close to the nozzle, measured the back-pressure at the nozzle arising from the airflow blockage caused by the blade during rotation. Stationary modal testing was performed on the rotor prior to testing for the purpose of FEM updating.
Test setup
The test rotor of Section 3.2 was again employed and installed with five straight, flat blades. The test rotor was driven directly by the speed-controlled motor at speeds of 720, 960, 1200 and 1440 RPM during testing. As previously, a piezoelectric dynamic pressure sensor measured the back-pressure at the nozzle arising from the airflow blockage caused by the blade during rotation. Due to manufacturing tolerances of the blade-clamp interfaces, it was necessary to use epoxy to eliminate gaps between the blade and clamp surfaces prior to clamping. This was found to minimize the variation in the natural frequencies of the blades, arising from differences in the clamping boundary conditions.
Conclusions
This thesis focussed on developing suitable signal processing techniques for ELDV measurements performed on axial-flow turbomachinery blades for the purpose of onlinecondition monitoring and damage detection.
Chapter 1 Introduction and Literature Study
1.1 Introduction
1.2 Blade vibration
1.2.1 Operational blade excitation
1.2.2 Rotational effects
1.2.3 Blade manufacturing tolerances
1.2.3.1 Blade roots
1.2.3.2 Mistuning
1.3 Blade damage and failure modes
1.3.1 Fatigue
1.3.2 Stress-corrosion
1.3.3 Foreign object damage
1.3.4 Flutter
Chapter 2 Eulerian Laser Doppler Vibrometry
2.1 Introduction
2.2 Analytical and numerical study
2.2.1 Cantilever beam theory
2.2.2 ELDV analytical formulation
2.2.3 Numerical simulation of ELDV
2.2.4 Effect of scanning speed
2.2.4.1 Modulation frequency
2.2.4.2 Frequency resolution
Chapter 3 Rotor-axial Eulerian Laser Doppler Vibrometry applied to a single-blade axial-flow test rotor
3.1 Introduction
3.2 Experimental setup
3.2.1 Measurement and control
3.2.2 Laser alignment
3.3 Experimental measurements
3.4 Finite element model
3.5 Phase angle as a damage indicator
Chapter 4 Rotor-axial Eulerian laser Doppler vibrometry applied to a five-blade axial flow test rotor
4.1 Introduction
4.2 Test setup
4.3 Test control and measurement
4.4 FEM
4.4.1 Model updating
4.4.2 TLDV simulation
Chapter 5 Conclusions and further work
5.1 Conclusions
5.2 Further work
References
Appendix A Rotor-Circumferential ELDV
A.1 Introduction
A.2 RC ELDV mathematical definition
A.2.1 Vector-loop equations
