MEASUREMENT BY THERMOELASTICITY ON PLASTIC FAN BLADE A. Di Renzo, M. Marsili, M. Moretti, G.L. Rossi Dipartimento di Ingegneria Industriale Università degli Studi di Perugia Via Duranti, 1 06125 Perugia, Italia gianluca@unipg.it antoniomp777@hotmail.it Abstract The problem, here analysed is the possible way to predict fan blades failure due to fatigue stresses. Their lifetimes are, as well known, due to the load amplitude and frequency, that are applied in working conditions. For this reason it is well known the blade resonance frequencies, analysing the possible excitation sources and the resulting stress amplitudes on the blade. In our laboratory was developed a test bench to study resonances, by classical techniques. The test bench was developed to apply also an innovative non contact measurement techniques thermoelastic stress analysis, in resonance conditions. If a prototype for testing is available, thermoelasticity measurement technique allows to identify the most critic points, where stress amplitudes reach maximum value, and therefore to optimize easily the component design. In the paper we illustrate the measurement and testing methodology developed, the results obtained and how is possible to perform a quick component design optimization by using thermoelasticity. Introduction The aim of the fan blade design, is to realize a component able to properly work under specified loading conditions, in given life time. The blade loading is static and dynamic; loads are due to centrifugal forces, aerodynamic forces, and forced vibrations. The blade failure is due, to fatigue stresses phenomenon, caused by the above mentioned loads. It is important to know the blade vibration modes, and the possible resonance frequencies, because resonance conditions amplify the stress on the blade and mode shape give information about stress concentration. Vibrations in resonance conditions of the blade could be influenced by: blade material properties forced vibration induced by others components interaction between the blade and the flow (aeroelastic phenomena) A wrong distribution of the blade inertial mass, due to mistakes in the design or production phase, causes vibrations too. The interaction between the blade and the flow could generate static [1] or dynamic instability (flutter) [1-2], that starts autoexcited vibrations. Another important phenomenon that generates the blade failure is flutter; this happens when the fan rotational speed is elevate. This phenomenon is studied using experimental test and numerical simulations.
In literature [3-4] it was developed many software, able to study aeroelasticity; those software have got three modules, the first is used to model the structure based on finite element method (FEM), the second to study the fluidodynamic called CFD (computational fluid dynamic) and finally the third, that match previous equations. There are some kind of methodologies to approach aeroelastic analysis because they use different model, and different method to match structural and fluidodynamic The first purpose of these numerical models is to know, when the fan works in flutter condition [4-5-6-7]. The experimental analysis on flutter has got two goal: the first is to understand physical phenomenon, the second is used to validate numerical results. In literature [10] there are two methods to start flutter on the, the first is called autoexcited activation and the second controlled activation. The first technique is used to know the blade flutter speed, and the second shows where the blades work in stability and instability regions. The common defect of these two methods, is the centrifugal force absence during the test, that modify flutter natural frequency, so this limitation must be considered in designing phase of the blade. In this article we show how thermoelasticity is used to know stress maps of the blade, when they are working in resonance conditions. 1. Thermoelastic stress analysis (theory) We know that in gases temperature will increase, if it is compressed, and we have the opposite effect when it expands. This phenomenon is present in solids too, and it is called thermoelastic effect. In solids temperature fluctuations is correlated with stress first invariant as we can see in the following equation (1): T T α = ( σ + σ ) C P 1 ρ 2 (1) α = thermal expansion coefficient T = component temperature (K) ρ = density C P = specific heat at costant pressure σ 1, σ 2 = principal stresses This effect in solid generates a very small temperature variation, for this reason only in the last few decades it was developed measurement techniques able to detect that fluctuation (fig. 1). The instrument used in these tests is DeltaTherm 1560, developed by StressPhotonics. The main element is an infrared thermocamera, that detects the small thermal variation on the surface of the target. In order to acquire temperature fluctuations on the scan area in phase with the load applied on the component, DeltaTherm 1560 uses lock-in acquisition technique.
fig. 1: thermoelastic measurment chain 2. Test bench design A test bench was developed, in order to study blade resonances, and to obtain stress maps of the blade when stressed in resonance conditions. In order to generate vibration on the blade an electrodynamical shaker V650, with an amplifier 1000PA developed by LDS was used. The maximum load amplitude possible are: sinusoidal force (amplitude) 1620 N random force1090 N It was design and realized, a support (fig. 2) that have to: rigidly joint the fan to the shaker; to guarantee an optical access to the blade surface; fig. 2: the fan analyzed and the flange.
2.1 Blade resonance frequency The measurement chain is illustrated in fig. 1. signal conditioner accelerometer fan blade shaker spectrum analyzer fig. 3: measurement chain amplifier The main components are: electrodynamic shaker LDS 650 and amplifier1000 PA spectrum analyzer Ono Sokki CF940 signal conditioner B&K 2635 piezoeletric accelerometer B&K 4375 The fan was excited using a white noise in the interval between 0 and 500 Hz. The blade frequency response function was measured on the three points illustred in fig. 4 using an accelerometer. fig. 4: measurement points. A typical FRF graph is in fig. 5, and the resonances frequencies founded are illustrated in tab. 1. A Number of frequency resonance Frequency resonance value I 63,75 Hz II 113,75 Hz III 170 Hz IV -
B C I 62,50 Hz II 113,75 Hz III 173,75 Hz IV - I 62,50 Hz II 113,75 Hz III 171,25 Hz IV - tab. 1: frequency resonance value FRF 0-10 -20 0 100 200 300 400 500 600 700 800 Db -30-40 -50-60 Frequenza Hz fig. 5: frequency resonance function graph. Observing the previous table, we can make the following consideration: the first frequency resonance is comprised in the range 61,25 Hz 62,50 Hz. the second frequency resonance is comprised in the range 100 Hz 102 Hz. The FRF measured on the central point (B), has not peak in correspondence of the second frequency, so for this reason we can assert that this is a torsional mode. The third resonance frequency is comprised in the range 147,5 Hz 148,75 Hz. 2.2 Measurement methodology and test by means of thermoelasticity The fan was stressed at the first frequency resonance, using four different amplitude acceleration, measured by accelerometer on the flange (fig. 2): 3g (g = 9,81 m/s^2) 6g 9g 12g In order to identify the area where stresses are maximum, we acquired differential images corresponding to the four value of acceleration. As we can see in fig. 6, the maximum stress zone is found near the cone tip.
fig. 6: the maximum stress zone In order to calibrate the maps of stress in MPa, we have to calculate relation (2). This relation, called calibration factor, is defined as follow: σ x + σ y K = (2) S avg σ y, σ x are stresses in two orthogonal directions, and S avg is the average emission value, calculated in the area where we measure σ y, σ x. To obtain σ y + σ x we put 90 degree strain gauge on a uniform stress pattern zone on the component, and using the relation between stress and strain we have (3): fig. 7: on the left we can see the blade thermoelastic map without strain gauge; on the right the map obtained at the same stresses condition, where we put strain gauge. The circle shows that zone. E( ε x + ε y ) K = (3) S (1 ν ) where E is the Young modulus, ν is the Poisson ratio, ε is the strain. avg
In the following figure we can see the stress maps, obtained for the four different acceleration value. fig. 8: thermoelastic stress pattern of the zone near the cone tip; stress profile is calculated along the arrow. fig. 9: thermoelastic stress pattern of the zone near the cone tip; stress profile is calculated along the arrow. Analyzing to all thermoelastic maps, we can see an high stress concentration near the cone tip. In fig. 10, we can see the trend of the maximum stress in function of the acceleration (g = 9,8 m/s^2):
MPa 25 20 15 10 Series1 5 0 0 5 10 15 a (g) fig. 10: the course of the maximum stress in function of the acceleration to which the fan is subjected. The trend illustrated of the stress is almost linear until acceleration level up to 9g; above these level, material near the cone tip probably exceed the elastic limit. Fatigue test A fatigue test, was carried out at the first frequency resonance (62 Hz), with an acceleration value of 12g. The previewed duration of the test is 25 million cycles (112 hours). This component has been checked every 12 hours, and after 36 hours (8035200 cycles) every blade of the fan started a crack near the cone tip (fig. 11). fig. 11: the arrow indicates the zone where there is the crack. The zone of the maximum tension, that reaches the value of 21,15 MPa, as it can be seen from the tsa, corresponds perfectly with the area where the crack started during the fatigue test (fig. 12).
fig. 12: comparison between thermoelastic maps, and the photo area where the blade have got failure. Conclusions In this article it is point out a measurement methodology and a test bench, to analyze the stress distribution of the blade in resonance conditions. These results are necessary to correctly design this component, to improve reliability. Using tsa, it can be possible to individuate the maximum stress zone, then the area where the component will have got failure. This is a remarkable advantage from the economic point of view, and an important saving of time in phase design.
Bibliografia 1. G.Bindolino, P. Mantegazza, P. Masarati Dispense di aeroelasticità applicata Dipartimento di Ingegneria Aerospaziale, Politecnico di Milano cap.i (pag.11-18), (pag. 137-143), (pag. 144-148), pag(481-490). 2. M.S. Campobasso Effects of flow instability on the linear harmonic analysis of unsteady flow in turbomachinery St Hugs College, Thesis submitted for the degree of Doctor of Philosophy at the University of Oxford (pag.1-11). 3. Vitaly Gnesin, Romuald Rzadkowski,I Luba Kolodyazhnaya A coupled Fluid-Structure Analysis for 3D Flutter in Turbomachines Proceedings of ASME TURBO EXPO 2000 May,8-11,2000,Munich,Germany (pag.1-6). 4. Vitaly Gnesin, Romuald Rzadkowski 3D unsteady forces of the transonic flow though a turbine stage whit vibrating blades Proceedings of ASME TURBOEXPO 2002:Land,Sea and Air, June 3-6,2002 Amsterdam, Netherlands (pag.1-5). 5. K.E. Willcox, J.D. Paduano,J. Peraire, K.C. Hall Low order aerodynamic model for aeroelastic control of turbomachines AIAA Paper 99-1467 (pag.1-7). 6. R. Srivastava, M.A. Bakhle, T.G. Keith, G.L. Stefko Flutter analysis of transonic fan NASA/TM-2002-211818 (pag.1-2). 7. D. M. Vogt, T.H. Fransson A new turbine cascade for aeromechanical testing The 16 th Symposium on Measuring Techniques in Transonic and Supersonic Flow in Cascades and Turbomachines, Cambridge, UK, September 2002 (pag.1-8).