Effects of Mounting and Exciter Coupling on Vibrothermographic NDE

Transcription

1 Effects of Mounting and Exciter Coupling on Vibrothermographic NDE Jyani S. Vaddi, Gabriel Murray and Stephen D. Holland Department of Aerospace Engineering and Center for Nondestructive Evaluation, Iowa State University, 1915 Scholl Road, Ames IA, USA Abstract. Vibrothermography, also known as Sonic IR and Thermosonics, is notoriously sensitive to extrinsic parameters such as specimen mounting and transducer coupling. This is a result of the complicated resonances which deliver vibrational energy and allow the crack to heat up. We present an approximate theory which explains how the mechanical mounting and transducer coupling affect the resonances of the specimen, and compare this theory with simulation and experiment. Based on these explanations we suggest guidelines to assist practitioners in minimizing the sensitivity of their vibrothermography tests to specimen mounting and transducer coupling. INTRODUCTION Vibrothermography is a nondestructive evaluation method for detecting cracks and delaminations in materials. When a specimen with crack is vibrated, the crack faces generate heat due to friction between contacting asperities[1, 2]. A broadband piezoelectric transducer generates vibrations in the specimen and a calibrated infrared camera records the heat generated at the crack faces[3]. The amount of heat generated at a crack depends on the vibrational strains in the specimen among several other factors like vibration frequency, crack morphology and crack closure state[4, 5, 6, 7]. Vibrothermography is a three step process: specimen vibration, frictional heat generation at the crack and heat flow to the surface. The goal of our research project is to develop a forward model for vibrothermographic process. This model should be able to predict the surface temperature of a specimen given a particular crack configuration and vibration excitation. We model vibration and heat flow computationally and crack heat generation empirically. Because of the large number of intrinsic crack parameters involved in the heat generation process, a fully computational model of vibrothermography is not feasible and therefore, crack heat modeling has to be empirical. Modeling the vibration generation accurately is the first step in developing an accurate predictive model. In this paper, we discuss the role played by the specimen mounting fixtures and exciter coupling in vibration generation. To develop our vibration model, we selected rectangular bar shaped titanium and inconel alloy materials as our specimens. The advantage with this geometry is that flexural vibration theory for beams is well established (see ref [8, 9]) and makes it possible to validate our computational model and experiments against analytical solutions. We vibrate our specimens at their flexural resonance frequencies in order to maximize the vibrational amplitude and heat generation. The resonance frequency is identified by first vibrating the specimen with a frequency sweep excitation and then selecting the peak in the resulting vibration spectrum of the specimen. The specimen is then vibrated with a tone burst excitation at the resonance frequency. We have observed that the observed resonance frequency is typically higher than the natural resonance of the specimen. Also, the resonance frequency seems to be affected by how and where the specimen is mounted. In order to precisely model the vibration, understanding this dependence of resonance on extrinsic boundary conditions is extremely important. In this paper, we will discuss how specimen mounting and vibration excitation affect vibration generation and the resonance frequency in the specimen. While generating vibrations in the specimens, we use a layer of soft material called a couplant at the contact point between the transducer tip and specimen. Using a couplant material prevents direct metal to metal contact between transducer and specimen and prevents surface damage to the specimen. Using a couplant also makes the specimen motion more repeatable and independent of transducer. Apart from using couplant between transducer and specimen, we also use layers of soft material called isolators at the contact points between specimen and the mounting grips that provide vibration isolation. The function of isolators too is to eliminate the direct metal on metal contact between the specimen and mounts and preventing surface damage and reducing contact nonlinearily. Using soft isolators also minimizes energy dissipation into the rigid mounts. Typical material choices for

2 FIGURE 1. Experiment set up of a vibrothermography test specimen with mount isolators and transducer couplant in place. The arrows on the left point towards mount isolators and the arrow on the right points towards the transducer couplant. couplant and isolators are paper, plastic, leather etc. We use layers of cardstock material as couplant and isolators. Figure 1 shows an image of a specimen mounted with isolators and couplant in place. We hypothesize that isolators and couplant act like lossy nonlinear springs in parallel with the specimen and increase the effective specimen stiffness and hence affect the resonance frequency. Therefore, isolators, in effect change the otherwise indeterminate boundary conditions at the mounting points into spring boundary conditions. Based on our assumptions, the following three observations can be made: 1. As the number of isolator layers increase, isolators become more compliant and the resonance frequency decreases. 2. As the static load on the mounts increases, isolators become more stiff and hence the resonance frequency increases. 3. As the mounting location position changes from node to antinode of a flexural mode, the observed resonance frequency increases. We tested these hypotheses with a series of experiments and measured the resonance frequency of the specimen at several isolator and couplant configurations. Apart from the experiments, we also performed simulations to calculate the resonance frequency of the specimen. It is to be noted that despite our assumption that the isolators are lossy springs, the damping introduced by the isolators is out of scope of this article and will not be considered in our analysis in the rest of the paper. THEORY AND HYPOTHESIS When the transducer is directly in contact with the specimen without a couplant in place, the observed resonance frequency in the specimen depends on the transducer used and is influenced by the contact nonlinearity between the transducer and specimen. The resonances observed in this case arise from the interaction between the transducer and specimen and therefore are called system resonances. These system resonances are highly nonrepeatable and depend on exactly how the transducer is in contact with the specimen and what transducer is used. However, if a couplant is placed between the transducer tip and specimen, the contact nonlinearity of the transducer-specimen system is eliminated and the observed resonances become independent of the transducer used. To explain this behavior, we used mobility theory to model the transducer-couplant-specimen system and solve for specimen velocities in terms of mobilities[10]. According to the mobility theory, a mechanical system can be represented as an analogous electrical circuit with each component represented by its electrical analog. Well established circuit principles can then be used to solve for the velocities and forces in terms of mobilities of individual components[11].

3 FIGURE 2. (left) Equivalent cirucit representation of transducer, couplant and specimen. V oc represents the open circuit velocity of the transducer, M t, M s and M c represent the mobilities of transducer, specimen and couplant respectively. (right) Illustration of isolators as spring foundations and couplant as intermediate spring between transducer and specimen. Figure 2 shows the simplified circuit representation of the specimen, transducer and couplant in terms of individual mobilities. The right half of figure 2 shows the illustration of isolators and couplant as springs attached to the specimen. By solving the electrical circuit, the expression for specimen velocity, v s is given by equation 1[12] v s = M s M s + M c + M t v oc (1) where M s, M c and M t are the mobilities of the specimen, couplant and transducer respectively and v oc is the open circuit velocity of the transducer, i.e., the velocity of the tip of the transducer when no specimen is attached to it. We have previously shown in ref. [12] that if the couplant is more compliant than the specimen and transducer combined, the complicated system resonances can be eliminated and the specimen resonances become more repeatable. Isolators behave in many ways identical to a couplant in that they reduce the nonlinearity at the specimen and mount contact and also prevent damage to the specimen surface. In addition, since isolators are typically lot less stiff than the rigid mounts, they convert the otherwise indeterminate boundary conditions at the mounting points into spring foundation boundary conditions. The spring foundation boundary condition is valid as long as the specimen motion is with in the same order of magnitude as that of the isolators. The resonance frequencies of a beam on elastic foundation depend on the stiffness of the foundation along with the flexural rigidity of the beam [8, 13]. Therefore, as the stiffness of isolators increases, the observed resonance frequency is exptected to increase as well. Also, since isolators are placed between the specimen and rigid mounts, the deformation in an isolator depends on the specimen deformation at that mount location. Since, the specimen deformation is minimum at vibrational nodes and is maximum at antinodes, the overall effect of isolators is minimum when the specimen is mounted at vibrational nodes and is maximum when the specimen is mounted at vibrational antinodes. Following this argument, we hypothesize that the shift in observed resonance from the specimen s natural resonance is minimum when mounted at node and is maximum when mounted at antinode. EXPERIMENT AND RESULTS To test our hypotheses above, we performed vibration experiments on a rectangular bar shaped titanium alloy specimen by varying the mounting locations along the specimen length, the static load on the mounts and the number of cardstock layers that act as isolators. In each case, we measured and recorded the 9th resonance frequency of the bar. To first identify the nominal resonance frequency, we used scanning laser vibrometry to measure the mode shapes corresponding to several resonance frequencies of the specimen. By comparing the measured mode shape to the known mode shape of 9th fexural resonance, we identified the desired resonance frequency. Then for each vibraton test, we excited the specimen with a frequency sweep excitation centered about the nominal resonance frequency and measured the vibration spectrum of the specimen. The exact resonance frequency for that test corresponds to the peak in vibration spectrum so obtained. We mounted the specimen at six uniformly spaced locations between a node and an antinode of the 9th resonance mode. We varied the static load between -500N and -3000N on each mount and tested with one, three and five layers

4 FIGURE 3. Resonance frequency variation with number of isolator layers as measured experimentally (left) and using COMSOL multiphysics simulation(right). As the number of isolator layers increase, the overall stifness of isolators decreases and therefore the observed resonance frequency decreases. FIGURE 4. Resonance frequency variation with static load on the mount as measured experimentally (left) and using COMSOL multiphysics simulation (right). As the static load on the mounts increases, the isolators stiffen and the resonance frequency increases. of cardstock as isolators at all mounts. All the combinations were randomized to eliminate any bias in the observed trends. We also perfomed simulations in COMSOL multiphysics software with representative values for isolator and couplant properties and measured the specimen resonance for all the combinations that we tested experimentally. Figures 3, 4 and 5 show how the observed resonance frequency changes with the number of isolator layers, static load on the mount and the relative mounting position from a node as measured using experiment and COMSOL multiphysics simulation respectively. Since we used representative values for the properties of isolator and couplant material, all our simulation results are qualitative. A more rigorous analysis is in progress to measure the actual values for isolator properties so that the simulation results match better with our experiment. The experiment and simulation results correlate very well qualitatively. As predicted, the resonance frequency decreases with increasing number of isolator layers, increases with increasing static load and increases as the mounting moves from node to antinode. Therefore, all our hypotheses are indeed valid and the isolator does behave like a spring in parallel with the specimen. CONCLUSION Understanding the effects of isolator and couplant on specimen vibration is crucial in developing a predictive vibration model for vibrothermography. Isolators and couplant are used at the contact points between specimen, tranducer and mounting grips to enhance repeatability and reduce the contact nonlinearity. In our vibration model, we hypothesize that the isolators and couplant used for vibration isolation behave like springs and therefore affect the observed resonances of the specimens. We tested our hypotheses with a series of experiments and simulations using commercially available finite element software. Representative results from the simulations seem to correlate well with our hypothesis. A more rigorous quantitative analysis to estimate the exact values of isolator and couplant properties is

5 FIGURE 5. Resonance frequency variation with varying mount location as measured experimentally (left) and using COMSOL multiphysics simulation (right). As the mounting location moves from node to antinode, the resonance frequency first increases and as the mounting moves from antinode to a noe, the resonance frequency decreases. Since specimen deformation is maximum at antinode, the effect of isolator is maximum when mounted at antinode and is minimum when mounted at a node, where the specimen deformation is minimum. in progress. We believe that with appropriate values for isolator properties, quantitative agreement between simulation and experiment can be achieved. ACKNOWLEDGMENTS This material is based on work supported by the Air Force Research Laboratory under Contract #FA D- 5210, Task Order #023 and performed at Iowa State University. REFERENCES 1. K. Reifsnider, E. Henneke, and W. Stinchcomb, Mechanics of nondestructive testing pp (1980). 2. L. Favro, X. Han, Z. Ouyang, G. Sun, H. Sui, and R. Thomas, Review of scientific instruments 71, (2000). 3. S. Holland, First measurements from a new broadband vibrothermography measurement system, in AIP Conference Proceedings, 2007, vol. 894, p J. Renshaw, S. Holland, R. Thompson, and C. Uhl, The effect of crack closure on heat generation in vibrothermography, in American Institute of Physics Conference Series, 2009, vol. 1096, pp W. Zhang, Frequency and load mode dependence of Vibrothermography, Master s thesis, Iowa State University (2010). 6. S. Holland, C. Uhl, and J. Renshaw, Vibrothermographic crack heating: A function of vibration and crack size, in AIP Conference Proceedings, 2009, vol. 1096, p G. Bolu, A. Gachagan, G. Pierce, and G. Harvey, Reliable crack detection in turbine blades using thermosonics: An empirical study, in AIP Conference Proceedings, 2010, vol. 1211, p K. F. Graff, Wave motion in elastic solids, Courier Dover Publications, W. Weaver Jr, S. P. Timoshenko, and D. H. Young, Vibration problems in engineering, John Wiley & Sons, L. L. Beranek, Acoustics, Acoustical Society of America, L. P. Huelsman, Basic circuit theory, Prentice-Hall, J. Vaddi, R. Reusser, and S. Holland, Characterization of Piezoelectric Stack Actuators for Vibrothermography, in AIP Conference Proceedings, 2011, vol. 1335, p D. Thambiratnam, and Y. Zhuge, Computers & structures 60, (1996).