Shanyue GUAN, Xiaokai WANG, Lin HUA, Yixuan LI

Hubei Key Laboratory of Advanced Technology for Automotive Components, Wuhan University of Technology,Wuhan 430070, China

Hubei Collaborative Innovation Center for Automotive Components Technology, Wuhan 430070, China School of Automotive Engineering, Wuhan University of Technology, Wuhan 430070, China

KEYWORDS Aeroengine casing;Acoustic Field Threshold Segmentation (AFTS);Curved surfaces;Total Focusing Method(TFM);Vector Coherence Factor(VCF)

Abstract The aeroengine casing ring forgings have complex cross-section shapes, when the conventional ultrasonic or phased array is applied to detect such curved surfaces,the inspection images always have low resolution and even artifacts due to the distortion of the wave beam.In this article,taking a type of aeroengine casing ring forging as an example, the Total Focusing Method (TFM)algorithms for curved surfaces are investigated. First, the Acoustic Field Threshold Segmentation(AFTS) algorithm is proposed to reduce background noise and data calculation. Furthermore,the Vector Coherence Factor(VCF)is adopted to improve the lateral resolution of the TFM imaging.Finally,a series of 0.8 mm diameter Side-Drilled Holes(SDHs)are machined below convex and concave surfaces of the specimen. The quantitative comparison of the detection images using the conventional TFM, AFTS-TFM, VCF-TFM, and AFTS-VCF-TFM is implemented in terms of data volume, imaging Signal-to-Noise Ratio (SNR), and defect echo width. The results show that compared with conventional TFM,the data volume of AFTS-VCF-TFM algorithm for convex and concave is decreased by 32.39% and 73.40%, respectively. Moreover, the average SNR of the AFTS-VCF-TFM is gained up to 40.0 dB, while the average 6 dB-drop echo width of defects is reduced to 0.74 mm.

1. Introduction

Ring forgings are widely applied in aeroengines, mainly used for the casing, sealing, connection, air intake, compression,and air injection. The working conditions of aeroengine ring forgings are poor, with high temperature, high pressure, high corrosion, and other characteristics.1Aeroengine casing is the key load-bearing component,including intake casing,combustor casing,high-pressure turbine casing,etc.The quality of the ring forgings used for the aeroengine casing is directly related to the performance and service life of the aeroengine.2,3In addition, to reduce the material waste in machining, the shape of the ring forgings is getting closer to the shape of the aeroengine casing,there are more convex and concave surfaces.What’s more,curved structures such as flanges and fillets are usually in a state of stress concentration and huge loads,the defects in curved surfaces are more likely to cause the failure of parts.4The titanium alloy aeroengine intake casing ring forging with curved surfaces is taken as the object. The processes of titanium alloy ring forgings contain smelting,forging,and heat treatment,which are easy to cause small defects such as cracks, inclusions, and folds.5–7Because the current ultrasonic system lacks the capability of complex ring forgings with curved structures, the rectangle cross-section shape of ring forgings is normally inspected in practice. With the development of ultrasonic phased array and Total Focusing Method(TFM) technique, the research of ultrasonic automatic detection of complex curved surface parts has arisen in recent years.Compared with conventional ultrasonic inspection, the ultrasonic phased array has greater advantages in the inspection of the curved parts because of its dynamic focusing and multi-angle scanning. However, due to the influence of curved surfaces, there are still artifacts and noise, complicated calculations of beam ray paths,and low imaging efficiency for ultrasonic phased array imaging.

The TFM becomes a research highlight in the Non-Destructive Testing (NDT) field because it has the benefit of higher detection accuracy and resolution.The current research mainly focuses on the Full-Matrix Capture(FMC)data acceleration processing,8,9TFM real-time imaging,10,11and imaging post-processing technology.12,13However, there are few investigations about the influence of curved surfaces on the acoustic field characteristics of TFM imaging. For TFM inspection of components with curved surfaces, one of the main discussions is the measurement of unknown complex geometry.Yang et al.developed the multistep angular spectrum approach to measure irregular surfaces of specimens.14Malkin et al. used TFM to reconstruct the unknown surface and studied the influence of surface measurement error on defect detection accuracy.15However, the aeroengine casing ring forgings are machined precisely according to geometric drawings, so their cross-section profiles are given, that is, the acoustic ray paths can be calculated explicitly for known curved surfaces of ring forgings. Apart from that, some researchers also investigated the modified TFM to simplify the calculation. The virtual source aperture imaging with auto-focusing was given to reduce the processing complexity of time-of-flight calculation.16,17A modified TFM imaging using the phased shift migration was established to detect layered objects with complex geometry.18The radiation path calculation of dualmedium curved surface TFM imaging is more complex, so it is essential to reduce the amount of data computation.

In ultrasonic testing, the signal at the defect has better phase consistency compared with background noise, so the phase coherence technique is commonly used to improve the lateral resolution and reduce sidelobes amplitude.19Camacho et al. proposed Phase Coherence Factor (PCF) and Sign Coherence Factor(SCF)to suppress the side and grating lobes of S-scan images.20The Circular Coherence Factor(CCF)was presented to take into account standard deviation and the consistency of phrases,and the processed images were smoother.21The weighting coefficient of the ultrasonic signal is obtained using a statistical method,and the weighting coefficient matrix corresponds to each pixel in the imaging area, so it can be easily superimposed with other imaging algorithms.22,23The phase coherence technique requires solving the coherence factor of each pixel in the imaging area,so it increases the amount of computation and can not optimize the TFM imaging efficiency.

This paper aims to research the TFM inspection of aeroengine casing ring forging with curved surfaces. To reduce the noise and data calculation of the TFM algorithm, the Acoustic Field Threshold Segmentation (AFTS)-TFM is proposed. Then, the Vector Coherence Factor (VCF) is used to enhance the imaging resolution. The TFM inspecting experiment is performed on the aeroengine casing ring forging specimen with artificial defects. Finally, the imaging results of different TFM algorithms is compared.

2. TFM algorithm of curved surfaces

As shown in Fig. 1, the probe array is taken as the x-axis and the center line of the array as the y-axis to establish a twodimensional coordinate system. In the linear ultrasonic array TFM imaging model, it is assumed that the functional expression of the curved surface is y=f（x ).The imaging area can be regarded as composed of many focal points F（x，y).The corresponding amplitude of the focal point can be obtained by calculating the flight time of the ultrasonic wave from the transmitting element to the receiving element.24For the TFM imaging algorithm, the amplitude of all transmitting and receiving array elements combined at the focal point is superimposed, that is

where IFis the amplitude at the focal point F（x，y); N is the total number of elements of the probe; Sijis the signal transmitted by the i th element and received by the j th element;tij（x，y)is the flight time of the ultrasonic wave.As can be seen from Fig. 1, assume the transmitting element is Mi（x1i，0); the receiving element is Mj（x1j，0）. According to the acoustic ray paths in curved surfaces, the flight time can be calculated as

where L1iand L2iare the transmitting paths;L1jand L2jare the receiving paths;c1and c2are the longitudinal wave velocity in water and metal respectively. According to the curved surface equation y2=f（x2), the coordinates of the curved surface intersection of the transmitting path Qi（x2i，y2i)and the receiving path Qj（x2j，y2j)can be obtained by Fermat’s principle.25In this way,the superposition amplitudes of all focal points in the imaging area are calculated successively, and then the TFM images of curved surfaces are obtained.

Fig. 1 TFM imaging algorithm for curved surfaces.

3. TFM algorithm combining AFTS and VCF

3.1. AFTS-TFM algorithm

Based on the Rayleigh-Sommerfeld integral and multiple line source model,26the acoustic field of each element in convex and concave surfaces can be simulated. Taking the immersion TFM inspection of curved parts as an example,a typical commercial 10 MHz array with 64 elements was selected.The array had an element pitch of 0.30 mm and element width of 0.25 mm.The simulation parameters of the probe were consistent with the experimental setup.From observing the results in Figs. 2 and 3, there were acoustic fields of different elements below convex and concave surfaces (M = 8, 16, 32), M is the serial number of elements. The acoustic pressure in the detection area was gradually increased as the element approached the center. The element in the center of the probe(M = 32 and M = 33) had the strongest acoustic pressure.The farther the element deviated from the center, the weaker the acoustic field energy was. Because the larger the incidence angle, the more serious the reflection and scattering of ultrasonic waves, and the weaker the energy of the acoustic field inside the curved surfaces. Furthermore, the variation of acoustic pressure for the concave surface was more obvious,because the concave surface had a greater effect on the incidence angle of ultrasonic waves.

According to the TFM acoustic field simulation analysis of curved surfaces, the smaller the incident angle of the element and the larger the energy injection,the strong acoustic pressure area of each element is different.It is well known that the weaker the energy of the acoustic field,the smaller the echo amplitude of defects.Because the weak acoustic field area is involved in TFM imaging calculation, on the one hand, more noise artifacts are brought,and on the other hand,the amount of data calculation is increased.In consequence,the AFTS-TFM imaging of curved surfaces is established based on acoustic field threshold segmentation.The acoustic energy distribution area of each element in the curved surfaces can be determined using the acoustic field simulation.By setting a reasonable threshold,the effective imaging area ofeachelementbelowcurvedsurfaces can beselected.Itcan avoid noise interference in the invalid area of each element and improve the efficiency of TFM while ensuring imaging quality.

Fig. 2 Acoustic field of different elements for convex surface.

Fig. 3 Acoustic field of different elements for concave surface.

According to the conventional defect quantitative evaluation method of ultrasonic NDT testing, that is –12 dB drop method, the threshold value of the effective acoustic field is determined.27,28In addition,by comparing the effects of different thresholds on TFM imaging results, the 1/4 of the maximum value of acoustic pressure of each element is taken as the threshold value:

where Pi（x，y)is the acoustic pressure of the i th element at the focal point F（x，y).

The imaging area of each element is divided according to the acoustic field threshold value, and the effective imaging area coefficient matrix is generated. The amplitudes of focal points in the effective area are calculated according to the TFM algorithm, and the amplitude of focal points in the non-imaging area is defined as 0:

where IAFTS-TFMis the amplitude of AFTS-TFM images.

As shown in Figs.2 and 3,the acoustic field of convex and concave surfaces of aeroengine casing ring forging was calculated.The strong acoustic pressure area of the central element was the largest, and its maximum acoustic pressure Pmax=0.392, taking 1/4 of the maximum pressure as the threshold value, that was TH=0.098. Figs. 4 and 5 show the imaging areas and non-imaging areas of each element of convex and concave surfaces respectively. The closer the element was to the central axis, the larger the effective imaging area was. For the edge element, there was a smaller effective imaging area,because it had the larger incidence angle of ultrasonic wave and the acoustic field energy was weaker. Using the AFTS-TFM to filtrate the non-imaging area of each element,which can avoid the redundant calculation in the invalid area,and can also avoid bringing in more noise effectively.

3.2. VCF-TFM algorithm

Phase coherence is proposed to improve the resolution of ultrasonic images, the theory is that if the ultrasonic signals come from the defect reflector at the focus,their instantaneous phase is unified. On the contrary, the phase of the non-defect position is dispersed. The phase coherence factor can be measured by statistical methods such as standard deviation and variance. CCF can represent the continuous circular distribution of the ultrasonic signal phase.29Hilbert transform Saij（t)=Sij（t)+jH[Sij（t)] is used to obtain the phase of ultrasonic signals φ（t)=arctan（H[Sij（t)]/Saij（t)), where Saijis analytical signals, H[Sij(t)] is Hilbert transform for signals Sij(t).Therefore, the circular coherence factor FCCF（x，y) can be calculated as

Fig. 4 Imaging area threshold segmentation of different elements for convex surface.

Fig. 5 Imaging area threshold segmentation of different elements for concave surface.

3.3. AFTS-VCF-TFM algorithm

As shown in Fig. 6, combining AFTS with VCF to get the AFTS-VCF-TFM algorithm proposed. First, the effective imaging area coefficient matrix εi（x，y )of each element is determined according to AFTS.Then,the Hilbert transform is used to obtain the phase information of the ultrasonic signals. The weighting factor of AFTS-VCF W-AFTS-VCFis calculated by the VCF method in the effective imaging area,where is required to satisfy the εi（x，y )=1. In addition, the amplitude IAFTS-TFMis superimposed in the effective imaging area. Finally, the weighting factor W-AFTS-VCFis applied to process the TFM amplitude IAFTS-TFMto acquire the new amplitude of TFMAFTS-VCF images ITFM-AFTS-VCF. It can be written as

Fig. 6 Flow chart of AFTS-VCF-TFM algorithm.

4. Aeroengine casing ring forging and experimental setup

The service environment of aeroengine casing is harsh, under enormous pressure and high temperature, so small defects may cause the potential safety hazard of aeroengine. There are strict ultrasonic inspection standards for aeroengine casing ring forgings.33TC2 titanium alloy aeroengine intake casing ring forging was selected as the research object.The longitudinal wave velocity of titanium alloy TC2 was 6163 m/s,and the density was 4.55 g/cm3.The water immersion ultrasonic TFM was utilized to inspect the aeroengine intake casing ring forging with curved surfaces.Fig.7 shows the experimental scheme of ultrasonic TFM inspection of aeroengine casing ring. The rotation platform can derive the ring forging to rotate, and the ultrasonic phased array probe can rotate and scan along with the cross-sectional profile of the ring forging. It meant that the probe only needed to scan the cross-section of ring forgings,and full coverage inspection can be achieved by rotating ring forging.The PANTER ultrasonic phased array industrial controller provided by M2M, France, was used. A linear array probe was selected, the parameters of the phased array probe are shown in Table 1. Computer software sent instructions to excite the phased array probe and received the ultrasonic signals, and the FMC data were collected.

Fig. 7 Schematic illustration of inspecting aeroengine casing ring forging and experimental setup.

Table 1 Specification of phased array probe used in experiment.

As shown in Fig. 8(a), to process the Side-Drilled Holes(SDHs) under the curved surfaces, a specimen was cut from the aeroengine intake casing ring forging. The used specimen had a convex surface of radius R = 15 mm and a concave surface of radius R = 20 mm, the same as in the acoustic simulations. The SDHs were designed according to the aviation ultrasonic testing standard AMS 2631B. Fig. 8(b) and(c) depict the detailed positions of SDHs, they are distributed at different central angles. All SDHs had the same diameter (0.8 mm). On the convex side, there were two SDHs (No. 1 and No. 2) on the concentric arc with a radius of R = 10 mm. On the concave side, the three SDHs (No.3, No. 4, and No. 5) were on the concentric arc with a radius of R = 25 mm.

The cross-section profile of aeroengine casing ring forgings existed convex and concave surfaces. Using the above experimental setup, the water immersion TFM inspection of aeroengine casing ring forging was performed. Fig. 9(a)illustrates the TFM experimental scheme of the aeroengine casing ring forging specimen. The water layer thickness between the probe and the central axis of the curved surfaces was h=10 mm. The experimental setup provided freedom of rotation of the probe,allowing full control of the relative position between the specimen and the probe,see Fig.9(b).During the experiment,the accuracy of the probe position was guaranteed by the consistency between the surface echoes and the curved surfaces of the specimen. By rotating the ultrasonic phased array probe,the FMC data of convex and concave surfaces at different angles were obtained.

Fig. 8 Aeroengine casing ring forging specimen and side-drilled holes positions.

Fig. 9 TFM experiment of aeroengine casing ring forging specimen with curved surfaces.

5. Results and discussion

The conventional TFM images of aeroengine casing ring forging of convex and concave curved surfaces at different angles are shown in Fig. 10. The FMC data were collected at central angles of 0°and 3°for the convex surface,and central angles of 0°and 5°for the concave surface.For defects of the same size,the amplitude was strongest at the central position,and the larger the central angle, the weaker the amplitude was. We can observe from the TFM images that the structure noise caused by curved surfaces was serious,especially the concave surface,the noise artifact was heavy. Therefore, it was significant to study the artifact reduction of curved surface TFM images.

Fig. 10 Conventional TFM images of aeroengine casing ring forging with curved surfaces.

Table 2 Positioning error of defects for TFM imaging results.

All TFM algorithms were calculated using the same FMC data,the different TFM imaging algorithms would not change the position of the defects. Therefore, taking the conventional TFM images as an example, the positioning error of defects was analyzed by calculating the coordinates of the defect in the TFM images.The pixel point with the maximum amplitude of the defect was defined as the position of the defect in the TFM images.Table 2 displays the angle and depth coordinates of the defects in aeroengine casing ring forging. Compared with the actual position of the SDHs, the defect positioning error of TFM images was calculated. The error was inferior to 0.12° for angle positioning, and inferior to 0.20 mm for depth positioning. It illustrated that the TFM imaging algorithm yielded a satisfactory estimate of the actual position of the defects. And, it was efficient and reliable to inspect aeroengine casing ring forgings with curved surfaces using the immersion TFM imaging algorithm.

The acoustic field of convex and concave surfaces of aeroengine casing ring forging was calculated in Section 3.1,the 1/4 of the maximum pressure was TH=0.098. According to the acoustic field threshold (0.098), the AFTS-TFM images of convex and concave surfaces of aeroengine casing ring forging were obtained, as shown in Fig. 11. It can be seen that the noise level of AFTS-TFM images decreased significantly without changing the amplitude of the defect.Fig.12 compares the data volume of focus points calculation between the conventional TFM and AFTS-TFM algorithms. The focal points data volume of the AFTS-TFM was greatly reduced,in which the focal points data volume of convex surface was reduced by 32.39% and that of the concave surface by 73.40%. Since the TFM algorithm performs 64×64 operations of amplitude calculation at each focal point, reducing the number of focal points can greatly decrease the amount of computation. By comparing the data volume of the TFM and AFTS-TFM algorithms, the difference in imaging time and efficiency can be represented indirectly. In summary, the AFTS-TFM can greatly improve the quality of TFM images and decrease calculation time.

Fig. 13 CCF-TFM images of aeroengine casing ring forging with curved surfaces.

Fig. 14 VCF-TFM images of aeroengine casing ring forging with curved surfaces.

Figs. 13–15 show the resulting images of convex and concave surfaces with CCF-TFM, VCF-TFM, and AFTS-VCFTFM processing. The reflection of ultrasonic waves on the concave surface was more complex, so TFM images of the concave surface had stronger noise than that of the convex surface. As the phase coherence factor amplifies the contribution of phase information,the amplitude of the noise was obviously suppressed. Compared with the conventional TFM image,the noise of CCF-TFM and VCF-TFM algorithms was reduced to varying degrees. Figs. 16 and 17 compare the lateral profile of the arc line at the defect position for different TFM images.In comparison with conventional TFM images, both CCF-TFM and VCF-TFM reduced the width of defect echo. As the VCF considered the effects of signal amplitude and phase on W-VCFweighting factor, the VCF-TFM algorithm had better resolution compared with the CCF-TFM algorithm. The AFTS-VCF-TFM algorithm was the superposition of the AFTS and W-VCFweighting factor processing. Firstly, the AFTS was used to determine the effective imaging area of each array element. Then, the amplitude of ITFM-AFTSwas weighted by W-AFTS-VCFfactors, the new amplitude matrix IAFTS-VCF-TFMcould be acquired. The noise of the original TFM images was reduced by AFTS, and the lateral resolution was further enhanced by W-AFTS-VCF, so the imaging quality of the AFTSVCF-TFM was better than AFTS-TFM, CCF-TFM and VCF-TFM.

For a quantitative assessment of the noise reduction effect of the different TFM algorithms, the Signal-to-Noise Ratio(SNR) is used to represent the noise level of the images.34,35The higher SNR is, the lower the noise level of the image is.The SNR calculation formula of defect image is defined as.

where Imaxis the maximum amplitude value of the defect location;Iaverageis the average amplitude value of background noise in the area of 0.5 mm × 0.5 mm.

Fig. 15 AFTS-VCF-TFM images of aeroengine casing ring forging with curved surfaces.

Fig. 16 Lateral profile of convex surface at defect arc line position.

Fig. 17 Lateral profile of concave surface at defect arc line position.

Table 3 SNR of defects with different TFM algorithms.

The SNR of defects in various TFM images is provided in Table 3.As can be seen from Table 3 that the order of imaging SNR from high to low is AFTS-VCF-TFM, AFTS-TFM,VCF-TFM, CCF-TFM, and conventional TFM. With the increase of the central angle of defect, the SNR of the defect images gradually decreased, it illustrated that there was more noise at a larger central angle of the concave surface.By comparing the conventional TFM and AFTS-VCF-TFM,the SNR of convex defect No.1 increased from 33.621 dB to 42.904 dB,increasing by 27.6%. Moreover, the SNR of concave defect No. 3 increased from 26.486 dB to 39.201 dB, increasing by 48.0%. The method of 6 dB-drop (or half amplitude drop) is proposed for sizing defect echo width. Table 4 shows the 6 dB-drop defect echo width of different TFM images of aeroengine casing ring forging with curved surfaces. Under the same gain condition, the narrower the defect echo width was, the higher the lateral resolution was. From Table 4, it can be seen that the VCF and CCF greatly reduced the 6 dB-drop echo width of defects,and the VCF-TFM algorithm had better performance than the CCF-TFM. On the basis of AFTS, the AFTS-VCF-TFM method can be superimposed to further improve the resolution.Compared with the conventional TFM, the 6 dB-drop echo width of convex defects for AFTS-VCF-TFM decreased by 48.39%, and that of concave defects was reduced by 42.8%. As shown in Fig. 18, the average SNR and 6 dB-drop echo width of defects with different TFM algorithms are calculated. The average SNR of theAFTS-VCF-TFM gained up to 40.0 dB, about 39.4% higher than that of conventional TFM, while the average 6 dB-drop echo width of defects reduced to 0.74 mm (by 41.7%). Moreover, the VCF had smaller defect echo width than the CCF and AFTS algorithm, it had a significant enhancement on the lateral resolution. Therefore, the combination of AFTS and VCF was selected to obtain higher SNR and lateral resolution of TFM imaging.

Table 4 6 dB-drop echo width of defects with different TFM algorithms.

Fig.18 Comparison of average SNR and 6 dB-drop echo width of defects with different TFM algorithms.

6. Conclusions

Using a linear array probe to inspect the area below the curved surfaces, there are serious noise and artifacts, and lower resolution. For TFM inspection of aeroengine casing ring forging with curved surfaces, this paper proposes the AFTS-VCFTFM algorithm to improve the imaging quality and reduce the data volume.The acoustic field characteristics of array elements were analyzed, the different elements had different strong acoustic pressure areas below curved surfaces. The AFTS algorithm utilized the acoustic field threshold of each element to divide the imaging area and non-imaging area, it can reduce noise artifacts and redundant data calculation.The immersion TFM experiments of aeroengine casing ring forging with curved surfaces were carried out. The performance of the conventional TFM, AFTS-TFM, CCF-TFM,VCF-TFM,and AFTS-VCF-TFM was compared.The results illustrated that compared with conventional TFM, the data volume of the AFTS-TFM algorithm for curved surfaces can be greatly reduced, especially the data volume of the concave surface decreased by 73.40%. Furthermore, the combination of AFTS and VCF had the highest SNR and lateral resolution compared to other TFM algorithms. The average SNR of the AFTS-VCF-TFM was increased by 39.4%, while the 6 dBdrop echo width of defects was reduced by 41.7%.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This study was supported by the National Key Research and Development Program of China (No. 2019YFB170 4500), the National Natural Science Foundation of China(No.51875428),the Key Research and Development Program of Hubei Province, China (No. 2020BAB144), the Excellent Youth Foundation of Hubei Province, China (No.2019CFA041), the Innovative Research Team Development Program of Ministry of Education of China(No.IRT-17R83)and the 111 Project of China (No. B17034).