16 3 rd International Conference on Mechanical, Industrial, and Manufacturing Engineering (MIME 16) ISBN: 978-1-6595-313-7 Automatic Ultrasonic Testing for Components with Complex Surfaces Dayong Guo, Guojun Jiang, Yue Wu, Jiayi Cheng Department of Mechanical Engineering, Tsinghua Uniersity, Beijing, P.R. China ABSTRACT: This paper deals with an automatic ultrasonic testing system for cured surface parts without CAD models in aerospace field, such as blades. The applied technology is mainly about automatic surface reconstruction algorithm and scan path planning algorithm. The automatic surface reconstruction algorithm is automatically sampling interpolating points on the component surface and then reconstructing the surface S(u,) passing through the points with B-spline. The scan path planning algorithm is based on the surface S(u,), which consists of feeding the scan lines with constant arc increment in direction and subdiiding the scan lines with constant arc increment. These algorithms were integrated into the fie-axis water immersion ultrasonic testing system. In some experiments, the surface reconstruction algorithm can be proed to reconstruct the component surface model precisely and the scan path planning algorithm can be proed to scan the component surface uniformly and contribute to get uniform C-scan image. 1 INSTRUCTIONS In fields of aerospace, naigation, energy and so on, blades and impellers with complex surface are extremely difficult to be inspected nondestructiely. Therefore, manual testing are still being adopted uniersally. But it is of low efficiency and high loss detecting rate. Recently, ultrasonic testing (UT) technologies are gradually adopted for the components with complex surfaces. C-scan images or 3D models obtained by UT can reduce the loss detecting rate and increase efficiency (Feng, 1) (Wu & Zhou, 6). Some research has been already conducted for cured surface parts by UT (Wu & Zhou, 6) (Mineo, et al., 1). These papers introduced the process of UT for components with complex surfaces, as shown in Figure 1. The surface reconstruction algorithm introduced in the paper (Wu & Zhou, 6) is about constructing a rough surface on the interpolating points sampled manually and then constructing a precise surface again based on the rough surface, which is of low efficiency. The path planning algorithm introduced in the paper (Wu & Zhou, 6) is about generating nearly arc-length interal inspection points, which may reduce the number of scan points but would bring complex scan paths that could reduce the efficiency. A UT system based on an industrial robot was deeloped in the paper (Mineo, et al., 1), which can proide additional flexibility and autonomy to automatic NDT. 7 Ultrasonic beam should be along with the normal ector of the point in the surface, when the component is inspected by the ultrasonic longitudinal testing probe. Therefore, the CAD model of the component should be obtained and the probe scan path should be planned before UT. Y cured surface parts Is CAD model known? Match the part s coordinate with CAD model Preprocess the surface CAD model Scan path planning N Obtain key points on the surface Surface reconstruction with the key points Control the probe test the part along the scan path C-scan imaging Result analysis Figure 1. Flow chart of UT for components with complex surface.
_ This paper relies on a fie-axis water immersion UT system which has been deeloped. And this paper shall focus on the components without CAD models, such as STL, STEP files. Firstly, the interpolating points in the cured surface should be sampled, and then the B-spline surface CAD model could be reconstructed passing through the interpolating points. Secondly, the scan path can be planned based on the reconstructed B-spline surface model, and then the probe can be moed along the scan paths and inspect the component. Lastly, the C- scan image can be obtained after the scan. AUTOMATIC SURFACE RECONSTRUCTION The automatic surface reconstruction method is based on ultrasonic distance measurement theory without other deices, such as three coordinate measuring machines, which contributes to reduce the complexity and improe the integration of the UT system. In the water immersion UT system, the probe can transmit the ultrasonic beam and receie the surface echo. Therefore, the water path can be measured according to Equation 1 below: c t D = (1) water path where c = sound speed in water; t = flying time of sound. The automatic surface reconstruction algorithm is actually sampling (m+1) (n+1) interpolating points on the component surface and constructing a surface passing through these interpolation with B-spline surface interpolation method. In the fie-axis water immersion UT system, the interpolating points coordinates could be easily calculated according to the fie axis parameters and the water paths..1 B-Spline cure and surface interpolation B-splines hae so many useful properties that they hae been one of the most popular and successful methods for modeling cures and surfaces in CAD field. The B-spline cure and surface can be defined below (Choong-Gyoo & Lim, 1999) (Les & Wayne, 1)..1.1 B-spline cure definition Gien an ordered list of control points P i, i n, and the basis function N i,p (u) is defined on a knot ector U={,,,u p+1,,u m-p-1,1,,1}. Then the B-spline cure of order p can be defined by Equation below. C n ( u) = N ( u P, u 1 () i = ) i, p i.1. B-spline surface definition Gien (m+1) (n+1) control points P i, j, and the basis function N i,p (u) of order p in the u direction and the basis function M j,q () of order q in the direction are defined on the knot ectors separately below: U={,,,u p+1,,u r-p-1,1,,1} V={,,,u q+1,,u s-p-1,1,,1} Then the B-spline surface can be defined by Equation 3 below: S n m ( u, ) = N ( u) M ( P, u, 1 (3) i = j = ) i, p j, q i, j.1.3 B-spline cure or surface interpolation method This method could be stated as the problem of constructing a B-spline cure or surface passing through the interpolating points, which needs to back-calculate the knot ectors and control points. In motion control field, cubic B-spline (C 3 ) cure or surface is smooth enough, because its acceleration is continuous (Lee & Shih, 4). So this paper would adopt cubic B-spline (C 3 ) cure and surface model.. Automatic surface reconstruction The automatic surface reconstruction algorithm in this paper is extrapolating the next pre-scan line by the former two scan lines, as shown in Equation 4, and each line has (m+1) points. Then while the probe is moed along the pre-scan line and transmits the ultrasonic beam to measure the water path, a third new precise scan line on the component surface could be calculated by the water path and fie axis parameters. This process should be repeated until the component surface is completely coered. Then (n+1) precise scan lines could be captured, which hae (m+1) (n+1) interpolating points. And finally, the surface model can be reconstructed by the B- spline surface interpolation method passing through the interpolating points. The extrapolation method can be stated as following. Gien the former two scan line {P 1, i }, {P, j }, i,j m, the next pre-scan line can be extrapolated by Equation 4 below. P P =, i m (4) P P, i, i P l + P 3, i, i, i, i where l is the extrapolation length between the second line and the pre-scan line. And the first two scan lines should be sampled manually as shown in Figure. After extrapolating the pre-scan line, a B-spline surface S(u,) passing through the (m+1) 3 points can be constructed. And then the probe is moed along the cure S(u,1) and transmits ultrasonic beam to measure the water paths so that the next scan line 8
can be calculated precisely by the fie axis parameters and the water paths. Figure shows the first two scan lines obtained manually and the third pre-scan line extrapolated by the former two scan lines. Figure 3 demonstrates the process of the algorithm. z (m m ) 4 15 1 5 u 5 pre-scan line 1 first two scan lines Figure. Get the first two scan lines manually and extrapolate( * dots: the first two scan lines; o dots: the pre-scan line; red lines: normal ectors of the points in the pre-scan line). z (m m ) 4 15 1 5 u 5 pre-scan line 1 15 15 former two scan lines Figure 3. Process of extrapolating the next pre-scan line( * dots: the scan lines already obtained; o dots: the pre-scan line extrapolated by former two scan lines; red lines: normal ectors of the points in the pre-scan line). in Figure 4, where we can find out that the arc length between the neighboring scan lines is not uniform. In iso-planar method, a scan line can be generated by the surface and the cutting plane, and the scan lines may also distribute nonuniformly so that cutting planes should depend on the worst situation to guarantee the scan lines coer all the surface, which may be of low efficiency. Using these for reference, this paper designed a new path planning algorithm based on B-spline surface S(u,) for ultrasonic testing. The algorithm is feeding the scan line with constant arc increment in parameter direction and subdiiding the scan lines with constant arc increment. z(mm) 4 15 1 5 5 1 15 Figure 4. The effect of iso-parametric feed method. 3.1 Constant feed in direction Constant feed means that there is constant arc length between the neighboring scan lines, which contributes to get uniform C-scan image in feeding direction. Howeer, some cures of distortion are likely to appear for the constant feed strategy, as shown in Figure 5. Considering the shortage of constant feed strategy, this paper improes the method into the constant feed in direction for parametric B-spline surfaces. This method is especially suitable for the cured surfaces of small curature like blades. 3 SCAN PATH PLANNING The effect of C-scan image depends on the scan paths. The more uniform the scan path is, the better the C-scan image is. Ultrasonic testing is like the end milling, because the both tools hae circular testing area or milling area. Therefore, the ultrasonic testing scan path planning strategies can turn to end milling path planning strategies. The milling tool path planning strategies for parametric surfaces include isoparametric method, iso-planar method, and constant scallop-height method (Zhou, 15). The distribution of the scan lines depends on the distribution of parameters in iso-parametric method, which could bring nonuniform scan lines, as shown 9 z(mm) 6 4 15 1 5 1 15 5 Figure 5. Cure distorts in the constant feed strategy. In a scan line, some key data points {Q i }= {(x(u i, i ), y(u i, i ), z(u i, i ))} are known, and then we shall feed the data points {Q i } with constant
increment dl in direction, dl can be calculated by Equation 5 below: x x y y z z dl = du+ d + du+ d + du+ d (5) u u u Because the parameter u is constant, so the formula can be simplified like Equation 6 below: x y z dl = d + + (6) According to the formula, we can calculate eery d and get all the key data points in the next scan line {Qnext i }= {(x(u i, i +d i ), y(u i, i +d i ), z(u i, i +d i ))}. This is the process of constant feed method in direction. The Figure 6 shows the effect of constant feed method in direction, where we can find out that the arc length between the neighboring scan lines is constant in parameter direction, which contributes to get uniform C-scan image in the feeding direction. z (m m ) 5 15 1 5 5 1 Figure 6. Constant feed method in direction. 3. Constant arc increment interpolation 15 Constant arc increment interpolation in scan lines makes sure that the scan speed of probe is constant, which contributes to get eenly distributed A-scan data in the scan lines and get uniform C-scan image in the. Figure 7 shows the constant arc increment interpolation (blue * points) and isoparametric increment interpolation (black * points), where we can see that the interpolation points distribute uniformly in the blue line. 7 6 5 4 3 1-1 iso-parametric increment constant arc increment - 4 6 8 1 1 Figure 7. Constant arc increment interpolation and isoparametric increment interpolation. As we know, some key data points are known in a scan line {Q i }={(x(u i, i ), y(u i, i ), z(u i, i ))}, which can be stated by points {UV i }={(u i, i )} and surface model S(u,). So we construct a B-spline cure passing through the points {UV i } and the new cure can be expressed by Equation 7 below. ( t ) ( u, ) = ( u( t ) ( t ) = (7) UV, Therefore, the arc increment formula in the scan line is Equation 8 below. dl = dt x u u x y u y z u z + + + + + t t u t t u t t (8) According to the Equation 8, gien the arc increment dl, we can calculate eery dt and get the interpolation points {(x,y,z)} with constant arc increment. 3.3 Scan path planning The scan path planning algorithm integrates the constant feed method in direction and the constant arc increment interpolation method. The effect of the scan path planning algorithm is shown in Figure 8, where we can find out that the scan lines distribute uniformly and the interpolation points( * ) distribute with constant arc length in the scan lines. z(m m ) 6 4 1 15 1 5 5 1 15 Figure 8. The effect of scan path planning algorithm( redline: normal ectors; * : interpolation points with constant arc increment).
4 RESULT AND DISCUSSION The automatic surface reconstruction algorithm and scan path planning algorithm were integrated into the fie-axis water immersion UT system. And the fie-axis system consists of x, y, z axis and a, b axis, which is flexible enough like an industrial robot. And one blade in the blisk (as shown in Figure 9) was inspected successfully in this paper. The Figure 1 shows the reconstructed surface based on the automatic surface reconstruction algorithm. 6 5 interpolating points were sampled automatically on the cured surface. The Figure 1 shows the errors between designed water path (8mm) and the actual water path of all A-scan data points. The errors are between -.69mm and 1.6mm, and the aerage error is.45mm, and the aerage relatie error is.5%, which is small enough to meet the requirements of the UT. Besides, it declares indirectly that the automatic surface reconstruction algorithm is reliable. The Figure 11 is the C-scan image of the blade, where a small defect (about 1mm.5mm) could be found out. There were some dark zones and bright zones in the C-scan image, because the blade was made using 3D printing technology and it could be of poor uniformity. Figure 11. C-scan image of the blade. Figure 9. Aero-engine blisk. Figure 1. The error between designed water path and the real water path( X axis: the serial number of data point; Y axis: the error between designed water path and the actual one). 5 CONCLUSION Figure 1. The reconstructed cubic B-spline surface model of one blade( * dots: the interpolation points obtained by the automatic surface reconstruction algorithm). This paper deeloped the automatic surface reconstruction algorithm and scan path planning algorithm for the cured surface parts without CAD models, and integrated them into the fie-axis water immersion UT system. The experiment results on a blade demonstrated that the B-spline surface reconstructed by the automatic surface reconstruction algorithm met the accuracy requirements of UT, and the C-scan image captured by the probe moed along the scan paths generated by the second algorithm was uniform, and a small defect was detected successfully. Therefore, the fie-axis automatic UT system for components with complex surfaces was proed to be competent in aerospace field. The future goal of our work is to generate the 3D models of the UT results. The C-scan image is a D 11
image, which can t show depths of defects. But 3D models can show positions and sizes of defects clearly, which contributes to ealuate the quality of workpieces. Howeer, 3D models could bring billions of data, which would be one of the most difficult problems. REFERENCES [1] Choong-Gyoo & Lim, 1999. Uniersal parametrization in B-spline cure and surface interpolation. Computer Aided Geometric Design, 6, pp. 47-4. [] Feng, R., 1. Ultrasonic Handbook. Nanjing: Nanjing Uniersity Press. [3] Lee, W.-Y. & Shih, C.-L., 4. Three-cubic spline methods for generating on-line motion control trajectories. International Journal of Electrical Engineering,, pp. 43-5. [4] Les, P. & Wayne, T., 1. The Nurbs Book(Second Edition). Beijing: Tsinghua Uniersity Press. [5] Mineo, C., Herbert, D. & Morozo, M., 1. Robotic nondestructie inspection. 51st Annual Conference of the British Institute of Non-Destructie Testing 1, NDT, 13 9, pp. 345-35. [6] Wu, S. & Zhou, X., 6. Research of surface reconstruction and path generation by ultrasonic inspection. Journal of Zhejiang Uniersity (Engineering Science), 5, pp. 763-767. [7] Zhou, J., 15. High Efficiency and Accyracy Machning of Complex Surfaces. Hangzhou: Zhejiang Uniersity Press. 1