Advanced experimental techniques for turbine blades dynamic characterization

Transcription

1 Advanced experimental techniques for turbine blades dynamic characterization Authors: Nicola Mitaritonna (Ge Oil&Gas Testing Laboratory) Stefano Cioncolini (Ge Oil&Gas Testing Laboratory) Francesco Piraccini (Ge Oil&Gas Steam Turbines Product development) Lorenzo Cosi (Ge Oil&Gas Steam Turbines Product development) Carlo Cortese (Ge Oil&Gas Steam Turbines Product development) Contact: Abstract The scope of this paper is to show the results of an experimental campaign processed with the aid of an advanced technique - developed at GE-OIL&GAS Test laboratory - Nuovo Pignone Firenze - capable to describe the dynamics of a turbine stage with remarkable accuracy. The technique allows the characterization of the stage in terms of natural frequencies, normalized response intensity and stage modal shape (nodal configuration). In the next chapters, the basics of the experimental technique applied to the validation of a low-pressure steam turbine stage (last stage) are illustrated. Introduction The design of the last stages blades of axial turbines is one of the most challenging aspects in new turbines development. Usually design and experimental validation of these components are the most time-consuming and costly part of new turbine section development programs. For this reason axial turbines OEM s are striving to improve the analytical and experimental methodologies involved in blades development. Figure : Steam Turbine last stage blades with axial entry fir tree and V-shape cover (right), fork root and pin damping system (left) Demand for high-energy conversion efficiency and high power density leads to the design of blades characterized by: High An, which implies high average and local static stress Low eigen-frequencies compared with the frequency of the excitations generated by the machine which are associated with potential vibratory stresses The combination of these two factors makes High Cycles Fatigue design very tough. For what concerns the determination of the static stresses the current capability of commercial Finite Element codes (i.e. Ansys ) to model material and contact non linearity coupled with the use of advanced D geometry modelling codes (i.e. UG ), allows to optimise the blade design in a limited amount of time even in presence of complex architecture features like mid-span, dampers or shrouds. The validation level of these tools is considered proven therefore experimental testing is not needed.

2 Frequency determination is more challenging because commercial FE codes cannot model nonlinearity and accuracy in blade eigen-frequencies prediction resides in the ability to set appropriate boundary conditions at the contact regions. Turbines OEM companies have standard design practices based on test data which establish for any type of contact features the process to determine the right boundary conditions end expected frequency accuracy, therefore testing is usually required just if a very tight accuracy is needed or if the blade has a new architecture.the most challenging task is still the prediction of the blade forced response and thus of the vibration stresses. The number of papers, which are being written each year on this subject, is a good measure of its importance and technical complexity. The research on this subject is moving on two parallel tracks: estimation of the excitation force acting on the blade (analytical and experimental) [Garcia et al. Riaz et al.], and estimation of the response of the blade under a known excitation [Swedowicz and al.]. In this paper a detailed methodology to characterize and compare the response of blades based on Wheel Box testing with oil jet excitation is presented with special focus on the excitation force modelization. A methodology to assess the mode shape of coupled modes it is also discussed and some practical example are presented. Test bed layout The main objective of a Wheel Box test is to determine the experimental Campbell diagram of a turbine stage. The main features of such a test are: Test was performed inside a vacuum over-speed bunker. The blades were excited with N oil-fed nozzles (f excitation = N x Rev and multiples). The rig speed was changed from to 5% to catch all the modes in the operative range. Sprays mass flow was regulated by adjusting inlet pressure and nozzles diameter. The excitation force intensity was analytically modeled. Overspeed Bunker (MFG) Nozzles Motor Gear Fluidrive HS Shaft Figure : test rig layout (top), oil spray (top-right), test rotor assembly in the vacuum bunker (left) The position of the strain gages was chosen with the use of a FE model in order to detect all the modes of interest with an adequate sensitivity and all sensors were eventually routed to a telemetry transmission box placed at the shaft end. The telemetry system used for this test was a Frequency Modulation type by Datatel, which allowed the entire measurement chain to perform with a noise level below. µstrain throughout the whole frequency domain. This lead to high quality measurements, which permitted to appreciate all the vibratory modes, also out of resonance. The data acquisition system collected both slow-variable (static) parameters (jet system oil pressure, temperatures) and dynamic parameters (strain gages signals).

3 Control Room Static Acquisition System TC Telemetry 44 Strain Gages ( x ) Dynamic Acquisition System Figure : wheel box test telemetry and acquisition system layout HP4 A Board 4 BN Keyphasor RC Server&Monitoring Static GPIB Board Sony SIR i PXI Boards 44 Board E Ethernet HUB Workstation Server DDAS Monitoring Static/ Dynamic NP Net The static system was mainly a Datalogger Agilent 4 connected via GPIB to a PC, and the acquired data was shared with the dynamic system by means of a custom software routine. The system was able to backup data on AIT tape with a Khz bandwidth, and to acquire in real time in the frequency domain an FFT every ms for each channel. For FFT the following settings were used: Data block size = 4 pt, Sampling Rate =. Ksa/s, which means 5 KHz bandwidth with a Hz resolution. If higher resolution was required, it was always possible to resample the data from AIT tapes with different settings. All channels were synchronized both in real time and in playback; the phase lag between channels was less than degree. FFT were then stored and processed via software to Campbell diagrams. Excitation models and Response Analysis The main output of the Wheel box test is the Campbell diagram of the blade row. Figure 5 shows the L blade (last stage) Campbell. Blade mode frequencies are detected where response peaks occur. At the crossing with engine orders ( XRev ), where the excitation due to the oil jet passing frequency (and harmonics) matches the blade coupled modes frequency, resonance takes place. This level of analysis normally allows to determine the Campbell of the blade but in order to assess the damping of the blade row further elaborations of the data are required. Since in a Wheel Box test the intensity of the excitation (oil sprays) increases as a function of the rotating speed (for given oil mass flow), the resonant response at higher speed is expected to show higher values. However, the increase in speed also causes an increase in the contact forces between covers (and at the dovetails), thus a reduction of the friction damping, which might represent a further cause of response increase. Therefore, in order to correctly evaluate which part of the increased response is actually due to the lower damping, rather than to the simple increase of the excitation, and to compare the response of the blade at different speeds and conditions it is important to gain some insight on the excitation force and its frequency content. In the past the oil jet was simply modeled as a square impulse function. In this case, an attempt to describe on more physics basis the shape of the excitation was made by the implementation of two models: one based on the Eulerian approach and the other based on the Lagrangian approach. The models, which main features are briefly summarized in Figure 4, were used to determine the frequency content of the excitation for given test conditions (mass flow, rotating speed, nozzle type and stage geometry).

4 πb The total time for possible impacts T is p + Rext T = VB Where p is the blade pitch while R ext is the spray impression dimension on the plane π The time t is randomly chosen in the interval [,T] for each droplet b The time t represent the time elapsed form the instant when the droplet enters the area of possible impacts (D=D) and the impact itself. VD is the velocity of the droplet FORCE Vs TIME [N] The total time for each droplet under consideration to impact the blade is then: t = t' + t' ' Collecting the number of impacts in an histogram as function of the time of impact The force transferred to the blade, from conservation of momentum is then simply: N md Vimp, i i= F( t) = dt V = V V imp D B n t ' = ( D P VBt' ) n ( V V ) D ' B Trailing edge blade α Leading edge V b d max c β β spray nozzle l p Assumptions: - blade represented as an inclined plane - spray modeled as a cone (either full or hollow) - average density in the spray volume * ( t + τ ) * t Ft t = dm V dt * ( ) b m= ρ A() t V sinα dt eff b mt ρeff = Vol() t Ft At V () = ρeff () b sin α A d h Figure 4: spray model main features Lagrangian (top), Eulerian (bottom)

5 The diagram reported in figure Figure shows the measured response of 5 different blades at different crossing (i.e. at different speed). Because of mistuning effects there is a certain blade to blade response variability but the increase in response amplitude is quite evident and the ratio between the average response at 5XRev and the average response at X Rev is around 4. Using this representation of the experimental data it is not possible to distinguish which part of the response increase is due to the excitation variation and which is due to the decrease of damping, which is expected at higher speed. When the same set of data is normalized through the excitation harmonic component, the effect of damping reduction is isolated (see figure Figure ). The normalized data show a smoother trend, the ratio between normalized average response at 5XRev and normalized average response at XRev is reduced from approximately 4 to.. Figure 5: L Blade experimental Campbell diagram Strain Gauge Response Response/Forcing FFT με 4 5/rev /rev /rev /rev /rev με / (FFT comp.) 4 5/rev /rev /rev /rev /rev rpm 4 5 rpm Figure : L Blade first mode crossings response Figure : L Blade first mode crossings normalized response This methodology has also been applied to compare the response of different blade under a normalized excitation. In particular the response of a new steam turbine last stage blade has been compared with the response of an existing and proven one. 4 Phase analysis Coupled cyclic symmetry systems, like shrouded turbine blades, tend to behave like a single vibrating structure and thus to show cyclic symmetric modal solutions which can be seen as a coupled mode, this is well documented in [Singh, Safe diagram ]. These cyclic symmetric modal solutions are usually called nodal diameter solutions because they are characterized by the presence of N diameters symmetrically positioned (ND) at which the modal displacement is approximately zero.

6 Figure : L Blade experimental Campbell diagram. In the box the crossings with the 4 th, 5 th and th (from right to left) engine order are displayed In experimental tests (like Wheel Box, or test vehicle), the identification of the ND solutions is a more complex task for the following reasons: The traditional output monitored during turbines blades testing is the strain gages signal spectrum in terms of amplitude and frequency. Therefore it is not straightforward to assess if the measured response peaks are relevant to single blade or coupled mode shapes The spatial shape of the excitation has to be consistent with the mode shape of the ND solution to transfer energy to the mode and make the response detectable. Therefore just some ND modes are expected to be observed during the test. The blades and shaft system has a mistuned behavior due to the small geometrical differences introduced by the manufacturing process (see Kielb et al.). This mistuning is usually causing the presence of double peaks which make the data analysis more complex. In this study the phase of the strain gage response was used to verify if a detected vibration amplitude peak could be associated to a coupled mode and in case of positive answer to determine the number of nodal diameters of the detected mode. The basic assumption behind this methodology is that in a coupled mode, all the blades vibrate in phase. In this test for L row (last stage) just blades out of 4 were instrumented therefore this methodology was expected to give a sufficient demonstration of the number of ND just for the solutions up to nodal diameters. The acquisition system used, has the capability to track the amplitude and the phase of the response on every engine order ( XRev ). In this case, by setting one of the strain gauges as a reference it is possible to read the evolution of the relative phase of the others throughout the whole rpm range. In Figure Figure the responses of the strain gauges (left) are reported along with their phase (right). The plots are extracted along the th engine order of the Campbell shown in Figure. Phases are calculated using the first blade as a reference (top right plot). Response and phase of blade no. are shown in the two top plots, the next two refer to blade no. and so on. The plots are focused on a narrow band of RPM and are extracted for a specific XRev ( th in this case) of the Campbell diagram. Referring to figure Figure, when a peak in amplitude clearly appears in all the left-side plots (resonance), a coherent phase behavior can be noticed in the plots on the right side (phases have to be read during the coherence window, because after the amplitude s peak the phase returns random, as it was before the appearance of the peak.)

7 The existence of a coherent phase is proving that the observed resonance is relevant to a coupled mode. Since the mode is crossing a XRev excitation the most responding ND solution is expected to be the ND. To support this hypothesis the recorded phase angles are plotted on a polar plot and compared with the theoretical phase of a ND modal solution according to the following procedure: Figure : order plot on the th Xrev. Micro-strain Vs rpm (left), degree Vs rpm (right) ) Plot the theoretical blades disposition for the ND being considered (purple squares in Figure ). In order to do that, calculate first the theoretical phase of each blade using eq.(.) * ND φt ( n) = ( n ) (.) Nb where: φ t : theoretical phase, ND : number of nodal diameters, A t : theoretical amplitude, N b : number of blades, n : nth blade. Then the theoretical blades displacement can be plotted as: d ( n) = cos( φt n ) (.) t This allows to visualize what the theoretical ND disposition should look like (purple squares in Figure ). ) Plot the displacement of the measured blades on the same polar plot according to the measured phase (φ), i.e. using φ measured instead of φ t in eq.(.); see red diamonds in Figure. Figure shows the result of this procedure with the numbers of the example in Figure (resonance along the th XRev). The matching with ND= looks very good. It must be observed that the theoretical displacements calculated in this way are not specifically linked to any vibratory mode shape (axial, tangential or torsional) but only to the nodal configuration. The d t (n) calculated through eq.(.) simply show how the blades are displaced in the range +/- according to the ND specified in eq.(.). The same analysis has been successfully repeated on the 4XRev crossing with first mode. The relevant polar diagram (Figure ), confirms that as expected a 4ND solution is found. ( )

8 Figure : measured (diamonds) and theoretical (lines and squares) phase. ND configuration Figure : measured (diamonds) and theoretical (lines and squares) phase. 4ND configuration A classical example of mistuning effect is observed at 5XRev crossing, (Figure ). In the amplitude plots can be noted how some blades (, 4 and 5) show multiple peaks. Performing the same analysis described earlier on reveals that a coherent 5ND configuration occurs only at approximately rpm. The following peaks, respectively at and 55 rpm, do not show a complete match with the theoretical 5DN, in fact in both cases blades and 5 look off-phase by about. The presence of additional peaks can be often interpreted as a single blade mode that because of the effect of manufacturing variability in the cover contact is suppressed in some blades and visible in others. However, passing through and 5 rpm the stage shows again a coherent response, matching respectively the theoretical ND and ND configurations (Figure ) Figure : order plot on the 5 th Xrev. Micro-strain Vs rpm (left), degree Vs rpm (right). The lines mark the peaks position:,, 55, and 5 rpm.

9 Figure : nodal configuration on the 5 th XRev. Weak 5ND coherence at rpm (left plot), good match with ND at rpm (center) and with ND at 5 rpm (right). 5 Conclusions This paper describes the application of an advanced technique for the characterization of turbine blades. The data acquired during a Wheel Box test have been processed to obtain the blades Campbell diagrams. Further data analysis allowed to extract information on blades response and made possible to compare the resonance magnitude at different crossings, for different modes and also between different blades. The blades characterization was completed with a detailed phase analysis that provided valuable information on nodal configurations behaviour at each crossing. References [] Garcia, J.C., Kubiak, J., Sierra, F., Gonzales, G., Urquiza, G. Numerical analysis of unstable flow in last stage blades of steam turbines, ASME Joint U.S. European Fluids Engineering Summer Meeting [] Riaz, M., Barb, K., Engeda, H. A novel technique for steam turbine exhaust pressure limitation using dynamic pressure sensors, Proceedings of the Institution of Mechanical Engineers, Part C (Journal of Mechanical Engineering Science) PUBLICATION DATE- Sept. 5 [] Szwedowicz, J., Sextro, W., Visser, R., Masserey, P. A., On Forced Vibration of Shrouded Turbine Blades, Proceedings of ASME Turbo Expo