International Symposium on Computerized Tomography for
Industrial Applications and Image Processing in Radiology
March, 15 - 17, 1999 Berlin, Germany Proceedings BB 67-CD
published by DGZfP

TABLE OF CONTENTS

Abstract Introduction and experimental setup Physical model and data acquisition Image reconstruction Results and discussion Acknowledgment References

Abstract

The first row of turbine blades used in power generating gas turbines has to withstand high temperatures and stress. Failure of the blades during operation can lead to very high costs for repair and loss of power-production. To investigate those blades three-dimensional (3D) x-ray tomography is used for non-destructive evaluation (NDE). The tomografic system was designed in house and consists of a microfocus x-ray tube, a precise manipulator and a high-resolution detection system based on an image intensifier coupled to a CCD camera. The system enables cone-beam data acquisition. This paper describes the methods used and discusses some results of NDE of different turbine blades.

Introduction and Experimental setup

X-ray computerised tomography (CT) is widely used for non-destructive evaluation (NDE) in many important industrial applications. In the present paper, NDE of turbine blades used in power generation is considered. Turbine blades, especially the ones in the first and second row, have to withstand high temperatures and stress. Beside the structural integrity, the cooling of those blades is crucial for normal operation. Failure of the blades during operation, may cause excessive repair costs and additionally costs will be added for the loss of power-production. To investigate blades non-destructively during maintenance a special x-ray system was built at KEMA. The system consists of three main parts (see Figure 1) [1]:

• a microfocus x-ray tube as a source for irradiation of the objects. The tube has a focus size in the range of 3-10 µm and is operated at voltages of 45-200 kV.
• a precise manipulation mechanism enabling translation and rotation of the objects with a maximum weight of 5 kg;
• a high resolution detection system, comprised of an image intensifier to convert x-rays into visible light which in turn is registered by a cooled 12-bit CCD camera with a spatial resolution of 1350×1035 pixels. The image intensifier is a standard device with an optimised performance; it has an output screen with a diameter of 20 mm and a resolution of 48 lp/mm, which provides an optimal match with the resolution of the camera. The sensitive CCD chip is shielded from the radiation by means of a lead screen. Besides, the camera is set out of the beam by using a periscope system with a mirror.

The whole system is controlled by a PC, steering the manipulation mechanism through a stepper motor controller with a controllable step size of about 1 µm. The detection system is connected through an interface that can control the camera settings and can read out the CCD chip. The system is mechanically supported by a rail system permitting the geometrical magnification to be varied. The field of view of the system is a sphere with a diameter of 24 cm.

Fig 1: Diagram of the experimental set-up.

Physical model and Data acquisition

The linear attenuation coefficient f(x,y,z) is the physical quantity which can be imaged by our system. Neglecting the dependence of f on the energy and taking into account the continuity of the medium, the next relation can be written


(1)

between the line integrals of f, which are often called "projections", and the incident I⁰ and detected I x-ray beam intensities. Changing orientation of the beam, as many line integrals as necessary to reconstruct function f from equation (1) may be acquired. Subsequently, function f can be visualised as a three-dimensional image. In our system, data acquisition is carried out by rotating the manipulation table over the vertical axis z. By varying the angle of rotation from 0 to 2 and acquiring the CCD image I(u,v) for each angle, a complete set of cone-beam tomographic data is collected. The image I(u,v) is a function of the co-ordinates in the detection plane which, as seen from figure 2, is parallel to the detector front side and crosses the origin of the (x,y,z) co-ordinates system.


Fig 2: Geometry for cone-beam scanning.

Notice, that two assumptions have been made implicitly: (a) the x-ray beam is mono-energetic; (b) the geometry is precisely known. In practice, both assumptions are violated. Firstly, our tube produces a polychromatic beam, which results, after attenuation, in beam hardening. In this case, the low energy photons are preferentially absorbed, so that the remaining beam has a higher average energy. To reduce this effect, a Cu filter is applied. Secondly, because of mechanical instability and limited precision of the mechanical alignment, the actual positions of the source, the rotation axis and the detection plane will always be displaced from the positions assumed. While longitudinal displacements can be tolerated, lateral misalignment cannot be disregarded, since it causes mismatching of the rotation axis for different angles, which may lead to large reconstruction errors. To find out the parameters of misalignment, two 180-degree-opposed radiographs of a circular aperture drilled in a steel plate are measured. By computing the difference between positions of the centre-of-mass in the opposed scans of the aperture, the parameters of the aligned co-ordinates (uN,vN) in the detection plane are obtained, which is used to compute the aligned data I(uN,vN) by applying rotation-translation transform to I(u,v) (see [2] for details of the method).

Image reconstruction

The image reconstruction process is an inversion problem. The inversion of cone-beam projections
g_q (u,v)=ln(I⁰ / I_q(u,v)) can be written as


(2)

where g' _q (u,v) = g_q (u,v)´ R(R²+u²+v² )^-1/2, R is the distance of the detection plane from the source (see figure 2) and h(u,v) is the impulse function of a reconstruction filter. Values of u_q ,v_q and f are determined by geometry as uq=f (x,y,q )´ (xcosq - ysinq ), vq =f (x,y,q )´ z and f (x,y,q )=R/(R+xsinq - ycosq ). The use of the impulse function h(u,v)=I | w | W(w )exp(iw u)dw independent of v gives us the Feldkamp filter with the apodisation window W. There are different forms of the apodisation window. For instance, good results can be obtained if W is implemented as a wavelet-based filter bank [3].

Image segmentation serves to select certain objects in the image f for the final display. A segmentation algorithm using thresholding of f is used, assuming that two grey levels representing the air and the material of a component have to be distinguished. This is done by assigning all image values which are below the threshold to 0, while setting all values which are higher than or equal to the threshold to 1. Also, unwanted structures from the display can be removed by cutting a half-space in (x,y,z) away, using a plane defined in the standard form by parameters a,b,c,d. In this way, it is possible to remove, for instance, a wall of the turbine blade from the display. A binary image model results


(3)

where t_min, t_max are the minimum and maximum thresholds. In the visualisation step, (x,y,z)=₀M(x,y,z) is used as the density of the medium, while M serves as the co-efficient of emission of the light. Then the intensity of the light reaching the eye at point p from direction d is


(4)

By increasing the density constant ₀, the volume can be made less transparent. In this way, surfaces of the model M can be visualised. Our volume rendering algorithm is based on evaluation of integral (4) by Euler integration stepping through the volume.

Fig 3: The x-y cross-section of 3D reconstruction's of a turbine blade.(a) the reconstruction without corrections for beam hardening and misalignment (b) the reconstruction with compensation for lateral misalignment of the system(c) the reconstruction of data measured with a Cu filter and corrected for lateral misalignment of the system.

Results and discussion

This paragraph describes some results of the application of our system. In the first experiment, two turbine blades were investigated, one of which was in good condition, while the other one had a defect of the internal surface, which was seen beforehand in optical investigation. In a complete circular scan, 180 cone-beam projections at a resolution of 512 × 512 pixels were measured. The 3D images were reconstructed using a grid of 512³ voxels, where the side of each voxel was 0.1 mm. Figure 3 shows the (x,y) cross-section of three different reconstruction's of the first blade. The image in figure 3(a) was reconstructed directly by formula (2) using no additional corrections, therefore, large artefacts are visible. Using results of a calibration measurement, the data were corrected for a displacement of 1.9 mm and a tilt of 0.6 degrees. This improved the spatial structure of the reconstruction (Figure 3 (b)), but not the density reconstruction, which is strongly deteriorated by beam hardening artefacts. To reduce them, a Cu filter was applied.

The reconstruction of the data measured with the Cu filter and corrected for misalignment (Figure 3(c)) has the best quality, compared to the other two reconstruction's. However, quantitative reconstruction of the concave wall of the blade proves to be difficult even in the case of applying all corrections mentioned. For the 3D visualisations, algorithm (3) was applied using t_min=0.2 f_max and t_max= f_max, where f_max was the maximum value of the image. Two cutting planes were used. The first was oriented in such a way that one wall of the blade was removed from the display, opening a view into the blade. The second plane cuts off the upper part of the blade. Figure 4 (a) shows the results of applying the volume rendering algorithm (4). Here the internal area of the blade can be seen. This area contains ribs which form the cooling channel and generate the turbulence, enabling the cooling of the blade during operation. No defects are visible in this image. Fig. 4 (b) depicts the reconstruction of the other blade. By comparing Figure 4 (a) and (b) a relatively small defect of the internal surface of the blade is revealed in figure 4(b). These results can be used to draw conclusions about the condition of the blades.


Fig 4: Cut-away views of 3D reconstruction's of turbine blades: (a) a view of the internal area of a blade without defects; (b) a damaged blade, with the defect on the internal surface (in the middle of the top) and the defect of the wall of the cooling channel (on the right side, below)

To visualise relatively small defects, region-of-interest (ROI) tomography can be used. An example is given in Figure 5 (a), where a ROI image of a turbine blade containing a crack is presented. A remark has to be made that the quality of the ROI reconstruction is usually lower than that of reconstruction with a complete data set. For instance, characteristic fuzzy structures of the surface can be observed in the ROI image (Figure 5 (a)). Nevertheless, the crack is clearly visible and its position can be accurately determined. Another example is presented in figure 5 (b) where an image of a turbine blade with a complicated internal structure is shown. All edges of the structure are reconstructed quite accurately. This permits us to use this image for assessing the geometrical structure of the inside of the blade.

Fig 5: The region-of-interest 3D tomography of turbine blades: (a) a view across a crack in a turbine blade; (b) a view of an internal structure of a blade.)

Acknowledgement

The research described in this paper was performed by KEMA Nederland B.V. and was supported by the power production sector of the Dutch electricity companies under a corporate R&D contract.

References

1. A.V. Bronnikov and D.Killian, "Cone-beam tomography system used for non-destructive evaluation of critical components in power generation, Nuclear Instr. and Meth. In Physics Research A, vol. 422, 1-3, pp. 909-913, 1999.
2. A.V. Bronnikov, "Virtual alignment of x-ray tomography system using two calibration aperture measurements," Optical Engineering, vol. 38, 2, pp. 381-386, 1999.
3. A.V. Bronnikov and G. Duifhuis, "Wavelet-based image enhancement in x-ray imaging and tomography," Appl. Optics, vol. 37, 20, pp. 4437-4448, 1998.