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Robotic Ultrasonic Measurement of Residual Stress in Complex Curved Surface Components

Robotic Ultrasonic Measurement of Residual Stress in Complex Curved Surface Components Hindawi Applied Bionics and Biomechanics Volume 2019, Article ID 2797896, 8 pages https://doi.org/10.1155/2019/2797896 Research Article Robotic Ultrasonic Measurement of Residual Stress in Complex Curved Surface Components 1,2 1,2 1,2 1,2 1,2 Qinxue Pan , Chang Shao , Dingguo Xiao , Ruipeng Pan , Xiaohao Liu , 1,2 and Wei Song School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China Key Laboratory of Fundamental Science for Advanced Machining, Beijing Institute of Technology, Beijing 100081, China Correspondence should be addressed to Qinxue Pan; panqx@bit.edu.cn Received 1 May 2018; Revised 21 November 2018; Accepted 4 December 2018; Published 3 March 2019 Guest Editor: Dongming Gan Copyright © 2019 Qinxue Pan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The automatic measurement, especially for products with complex shapes, has always been one of the most important application areas of robots. Aiming at the challenge of measuring residual stress under curved surface, in this paper, the residual stress ultrasonic measuring robot system with two manipulators is constructed, which is based on combining industrial robot technology with residual stress ultrasonic nondestructive measuring technology. The system is mainly composed of a motion control system, an ultrasonic detection system, and a data processing system. The robotic arm controls the movement of the two ultrasonic transducers along the set scanning path which is based on the geometric model of components and adjusts the transducer’s posture in time according to the shape of the workpiece being measured. The configuration information based on workpiece coordinate system is transformed into a position data that takes into consideration the first critical angle and can be recognized by the robot. Considering the effect of curvature, the principle model of residual stress measuring by the critical refraction longitudinal wave is established. The measured signal including the stress state of the measured region, as well as the actual position and posture information of the transducers, is processed by the computer in real time, which realizes automatic nondestructive measurement of residual stress under curved surface. 1. Introduction propagation of cracks, causing the components to suddenly break under the working load, leading to malfunctions and Currently, complex surface components have been widely even serious safety accidents [2]. Therefore, it is very impor- tant to measure and evaluate the residual stress of complex used in aviation, aerospace, marine, automobile, and molds industry and have played an extremely important role, surface components. such as in engine blades and propellers, which is directly Ultrasonic detection technology based on acoustic elas- related to the reliability and safety of the equipment. The ticity principle is one of the reliable and effective methods manufacturing process of complex surface components is for residual stress nondestructive measuring. Residual stress cumbersome and complex, which will inevitably produce ultrasonic measuring technology is more and more widely residual stress on the surface [1]. Even after a certain process, used in the inspection of residual stress of regular-shaped for example, heat treatment, the residual stress is also dif- members such as rails, pipes, gears, and hubs due to its ficult to eliminate completely. On the other hand, these com- advantages of nondestructivity, harmlessness, reliability, plex surface components will also have residual stresses accuracy, and convenience. Duquennoy et al., of the Univer- due to impact loads, thermal loads, and corrosion during sity of Valensina, France, used Rayleigh waves that excited by long-term service. The existence of this residual stress not laser and received by PZT to measure the residual stress on only seriously affects the shape and mechanical properties the pipe surface [3]. Using the similar method, Wanwan of the components but also promotes the generation and et al. measured the residual stress in a cast iron brake disc 2 Applied Bionics and Biomechanics Reflective the nondestructive detection of the tangential residual stress shear wave state in the propagation direction in the surface layer. Incident As shown in Figure 1, when the longitudinal wave prop- longitudinal wave Reflective agates from a medium with a slower wave velocity to a cr longitudinal wave medium with a faster wave velocity (such as from water to metal material), according to Snell’s theorem, there is an inci- Critical refractive dent angle so that the refracted longitudinal wave has a Medium 1 longitudinal Wave refraction angle of 90 degrees. This refracted longitudinal Medium 2 훽 = 90 wave will propagate along the surface of the second medium. This incident angle is called the first critical angle (θ ), and cr the resulting refracted longitudinal waves are called critical Refractive Shear Wave refraction longitudinal wave (L ). cr The first critical angle can be obtained by Snell’s theorem: Figure 1: Wave conversion. −1 1L θ = sin , 1 cr and compared with that measured by X-ray stress analyser V 2L [4]. In general, the research hotspots of ultrasonic nonde- structive testing of residual stress mainly focus on different where V is the longitudinal wave velocity of medium 1 and 1L application objects and different ways of ultrasonic signal V is the longitudinal wave velocity of medium 2. 2L excitation and reception in recent years [5–8]. For complex surface components, in order to excite and The residual stress ultrasonic measuring has a strict receive the critical refracted longitudinal wave at the surface requirement on the incident and receiving angles of the of the component, it must be ensured that the ultrasonic transducer. However, for a complex curved surface compo- transducer is tilted by a certain angle. The angle between nent, the change of curvature will seriously affect the inci- the excitation transducer and the normal of incident point dence, propagation, and reception of the ultrasonic signal, is equal to a positive critical angle, and the receive transducer which poses great challenges to ultrasonic measuring of and the normal of exit point is equal to a negative critical residual stress in complex surface components. The tradi- angle. It must also ensure that the exciting and receiving tional manual measurement not only is difficult to ensure transducers are in the same plane as the refracted longitudi- the necessary position and posture of the ultrasonic trans- nal wave propagation path. The excitation, propagation, ducer but also has disadvantages such as low efficiency, large and reception process of critical refraction longitudinal wave labor intensity, poor detection accuracy, and difficulty in along the surface is shown in Figure 2. quantitative analysis. In order to overcome the diffusion of the ultrasonic The development of high-precision, multi-degrees-of-- beam in the coupling agent and improve the detection sensi- freedom robots has brought a new support to the ultrasonic tivity and resolution of the curved surface workpiece, the measurement for complex surface components [9, 10]. focal transducer is used for detection, which is shown in In this paper, an ultrasonic residual stress measurement Figure 3. The focus position of the transducer in water can method based on robot technology is proposed, which takes obtained by calculation or experiment. full advantage of a robot’s precise control of ultrasonic trans- According to the principle of ultrasound, the focal length ducer position and automatic scanning. It adjusts the posture of the transducer in water is calculated as follows: of the ultrasonic transducer in real time according to the detection position. The actual posture information of the F = , 2 ultrasonic transducers and the ultrasonic signal at this posi- 1 − C /C 2 1 tion is processed by the computer to obtain the residual stress value of the measured area. where F, R, C , and C are the focal length of the transducer 1 2 in water, curvature radius of the acoustic lens, ultrasound speed in the lens, and ultrasound speed in water, respectively. 2. Materials and Methods Based on the theory of acoustic elasticity, the relationship between ultrasonic longitudinal wave velocity and stress can 2.1. Ultrasonic Measuring Principle of Residual Stress in be simplified as follows: Curved Surface Components. The main basis for the ultra- sonic measurement of stress is the acoustic elasticity theory, V = V 1 − K σ , 3 Lσ L0 L that is, the stress state in the elastic solid will affect the prop- agation speed of the ultrasonic wave in a material [11, 12]. where V represents the longitudinal wave velocity when Lσ Theoretical and experimental studies show that the ultra- the stress is σ, V is the longitudinal wave velocity in the L0 sonic longitudinal wave with the propagation direction being absence of stress, and K is the acoustic elastic coefficient of consistent with the stress direction is most sensitive to the longitudinal wave. change of stress. Therefore, it is necessary to generate a lon- Suppose that the propagation path is s, the propagation gitudinal wave propagating along the surface. By measuring time is t and the tangential stress on the path is σ. Because the change of the longitudinal wave speed, we can realize the velocity is difficult to measure directly, the different time Applied Bionics and Biomechanics 3 Receiving Transducer Propagation Exciting path of Lcr cr Transducer 휃 cr Specimen Figure 2: Critical refracted longitudinal waves propagating in a curved surface. component, the computer-aided manufacturing (CAM) numerical simulation software is used to obtain the position and normal vector of the scanning trajectory points in the Cartesian coordinate system. As shown in Figure 4, the robot arm that holds the exciting transducer is defined as the master manipulator and the robot arm that holds the receiving transducer as the slave manipulator. Both the master manipulator and slave manipulator move in the zig-zag scanning mode, and the slave manipula- tor always keeps a certain distance from the master manipu- lator in the stepping direction, which determines the spatial resolution of the detection. Figure 5 shows two different zig-zag scan modes for surface workpiece. Through this two different scanning methods, we can get the stress compo- nents in two directions, and then according to the principle of force synthesis, we can determine the stress vector in the surface direction. 2.3. Coordinate Transformation. Considering the require- ments for transducer position orientation, the pose informa- tion in the Cartesian coordinate system of workpiece cannot be directly recognized and used by the robot controller. We need to convert that into point and the orientation data of the transducer based on the coordinate system of the robot. As shown in Figure 6, taking the master manipulator Figure 3: Spherical focus transducer. motion control as an example, set the reference coordinate system of the robot as W and the tool coordinate system that ultrasound travels the same distance is used to calculate as M . The tool coordinate system translated along the the stress state on the path: z-axis to the focus of the ultrasonic transducer is C , the workpiece coordinate system is A , and the measured s s sK σ discrete coordinate system is B . The origin of the B Δt = − = , coordinate system is specified at the scanning point. The V 1 − K σ V V 1 − K σ L0 L L0 L0 L Z-axis is along the normal direction of the scanning point, the X-axis goes along the incident point to the exit point, Δt ⋅ V L0 σ = 5 and the Y-axis direction is determined according to the K s + Δt ⋅ V L L0 right-hand rule. 2.2. Trajectory Planning. According to the principle of ultra- Through the CAM simulation software, we can easily get sonic measurement of residual stress for curved surface com- the position and normal information of the discrete points on ponents, it must be ensured that the exciting and receiving the surface of the workpiece in the workpiece coordinate transducers move along the set path with a specific posture. system. Considering the location parameters of transducer Therefore, it is necessary to perform trajectory planning on installation, scanning path and the requirements of incident the measured surface to obtain the controlled movement or exit direction of ultrasonic wave, the purpose of coordinate point of the manipulator. Based on the CAD model of the transformation is to transform the position and normal 4 Applied Bionics and Biomechanics Master Slave manipulator manipulator Specimen Figure 4: Manipulator distribution. Scanning path of master Incident point Exit point manipulator Propagation path Stepping direction (a) Incident point Exit point Scanning path of master manipulator Stepping direction Propagation path (b) Figure 5: Different zig-zag scan modes for surface workpiece. direction information of discrete points and the deflection in the Cartesian coordinate system of workpiece A .Accord- angle of transducer into the position and posture of trajectory ing to the principle of coordinate transformation, points in the coordinate system of the robots. W W A C For a space vector P, let its position in the coordinate sys- P = T T P, 6 A C A B C tem A , B , C ,and W be expressed as P, P, P,and P, respectively. According to the principle of robot kinemat- A A A B ABA R P R R R P + P A C CORG B C CORG BORG ics, we need to identify the posture of transducers in the coor- T = = 7 0 1 0 0 0 1 dinate system of the robot W based on the pose information Applied Bionics and Biomechanics 5 Master manipulator y O B C C z y W B Specimen A Figure 6: Definition of the coordinate systems in the master manipulator. where propagation path, the measured discrete coordinate system B and transducer coordinate system C should satisfy the following relationship: ξ ξ ξ X Y Z R = , 8 φ φ φ X Y Z 10 0 cos θ 0 −sin θ cr cr ψ ψ ψ X Y Z R = 0 −10 01 0 ξ , ξ , ξ is the direction vector of the X-axis of coordinate X Y Z system B in the coordinate system A ; φ = φ , φ , φ is X Y Z 00 −1 sin θ 0 cos θ cr cr the direction vector of the Y-axis of coordinate system B cos θ 0 sin θ cr cr in the coordinate system A ;and ψ = ψ , ψ , ψ is the X Y Z direction vector of the Z-axis of coordinate system B in = 0 −10 , the coordinate system A . Supposing that the location of the incident point is P and the location of the out point is sin θ 0 −cos θ cr cr P at some time, their positions and normal directions in the coordinate system A can be expressed as A T B P = x , y , z , nx , ny , nz , P =0 12 i i i i i i i CORG A T P = x , y , z , nx , ny , nz , o o o o o o o Bring equations (8), (11), and (12) into equation (7): where x, y, z represents the position information and nx, ny, nz represents the normal vector. ξ ξ ξ cos θ 0 sin θ According to the definition of axes in coordinate system X Y Z cr cr B , R = φ φ φ 0 −10 C X Y Z ψ = ψ , ψ , ψ = nx , ny , nz , X Y Z i i i ψ ψ ψ sin θ 0 −cos θ X Y Z cr cr ψ × x − x , y − y , z − z o i o i o i ξ cθ + ξ sθ −ξ ξ sθ − ξ cθ X cr Z cr Y X cr Z cr φ = φ , φ , φ = , X Y Z ψ × x − x , y − y , z − z o i o i o i = φ cθ + φ sθ −φ φ sθ − φ cθ , X cr Z cr Y X cr Z cr ψ × x − x , y − y , z − z × nx , ny , nz o i o i i i o i i ξ = φ × ψ = ψ × x − x , y − y , z − z ψ cθ + ψ sθ −ψ ψ sθ − ψ cθ o i o i o i Y cr Y cr Y Y cr Y cr A A P = P = In order to ensure that the focal point of the receiving CORG CORG transducer coincides with the measured point and that the acoustic axis deviates from the θ of the incident point nor- cr mal within the plane formed by the incident axis and the 6 Applied Bionics and Biomechanics Water coupling system ultrasonic signal Receiving Exciting Data Acquisition transceiver Pulse transceiver Specimen Card Transducer Transducer system Trigger Geometric module model Holding Holding device device Master Slave manipulator manipulator robotic arm motion system Robot position control module in lower computer Robot controller Robot position control Ultrasonic detection module in upper computer module control and data processing system Industrial control computer Figure 7: Ultrasonic measuring robot system. cos and sin are abbreviated as c and s, respectively. In this case, W W A R = R R C A C ψ = ψ , ψ , ψ = nx , ny , nz , X Y Z o o o ξ cθ + ξ sθ −ξ ξ sθ − ξ cθ X cr Z cr Y X cr Z cr ψ × x − x , y − y , z − z i o i o i o φ = φ , φ , φ = , X Y Z ψ × x − x , y − y , z − z = R φ cθ + φ sθ −φ φ sθ − φ cθ , i o i o i o A X cr Z cr Y X cr Z cr ψ × x − x , y − y , z − z nx , ny , nz i o i o o o i o o ψ cθ + ψ sθ −ψ ψ sθ − ψ cθ ξ = φ × ψ = , Y cr Y cr Y Y cr Y cr ψ × x − x , y − y , z − z i o i o i o ξ ξ ξ cos −θ 0 sin −θ X Y Z cr cr i R = φ φ φ 0 −10 , C X Y Z W W A W W W P = R P + P = R y + P CORG CORG AORG AORG A A i ψ ψ ψ sin −θ 0 −cos −θ X Y Z cr cr A A P = P = CORG BORG Although the workpiece coordinate system A is unknown, its position and posture is fixed in the detection process. Therefore, we can calibrate the coordinate system A by several characteristic points to determine the trans- formation matrix R and T between the workpiece A AORG 3. Results and Discussion coordinate system A and the reference coordinate system W W of the robot W . Bringing the R and T into equa- Ultrasonic measuring robot for residual stress of complex A AORG tions 14 and 15, we can calculate the position and posture surface components includes hardware system and software of the excitation transducer in coordinate W . system. As shown in Figure 7, the hardware system is mainly The pose determination method of the receiving trans- composed of three parts: the robotic arm motion mecha- ducer is similar to that of the transmitting transducer. The nism, the ultrasonic signal transceiver system, and the con- only differences between them are the establishment of coor- trol and data processing system. Two six-DOF industrial dinate system B and the deflection direction of transducer. robots are used to implement the gripping, position, and Applied Bionics and Biomechanics 7 Lcr Wave −512 −1024 −512 −1536 −2048 −1024 0 10 20 30 40 26.5 27.0 27.5 28.0 Time/us Time/us Ultrasonic signal original sampling data . . fourier interpolation by 10 times Figure 8: Ultrasonic signal. Figure 9: Ultrasonic signals before and after interpolation in different stress states. posture control of the ultrasonic transducers and automatic scanning; the ultrasonic signal transceiver system mainly includes a pulse transceiver, a high-frequency data acquisi- tion card, two ultrasonic transducers, and a water coupling system. The role of this system is to excite and receive ultra- sonic signals at the detection location. The control and pro- cessing system is the “brain” of the entire measuring robot, realizing the core tasks of motion control and ultrasonic 0.5 signal processing. The software system consists of the upper computer soft- ware subsystem and the lower computer software subsystem. The two subsystems cooperate with each other to jointly per- −1 −0.5 −0.059 0.5 1 Time/us form functions such as communication and control of the ultrasonic signal transceiver system and the manipulator movement system. The upper computer software is imple- −0.5 mented in the industrial control computer to complete the trajectory planning and coordinate transforming. Another core task of the upper computer software is to process the −1.0 ultrasonic transducer posture data and ultrasonic signals to obtain residual stress results. The ultrasonic signal is shown Figure 10: Cross-correlation of ultrasonic signals under two in Figure 8. The lower computer software refers to the soft- different stress states. ware system implemented in the controller of the robot and is mainly responsible for robot motion control, external trig- gering ultrasonic pulse transceiver, and reading and transfer- ring the robot position information. the nondestructive automatic detection of the residual stress in the surface of a complex curved surface component by According to equation 5, the time difference directly using critical refracted longitudinal wave. determines the accuracy of the results. For acoustic time method of measuring residual stress, we are only interested (1) Deduced an ultrasonic measuring principle and cal- in the effect of stress on the ultrasonic signal in the time culation formula of residual stress in curved surface domain. Hence, as shown in Figures 9 and 10, we combine components interpolation and time-delayed autocorrelation theory to improve the accuracy of time measurement and calculate (2) Proposed a trajectory planning strategy for the robot the delay of two sets of signals. with two manipulators (3) Established a coordinate transformation formula 4. Conclusions between the workpiece coordinate system and the In this paper, a new ultrasonic measuring robot system robot coordinate system in consideration of the first critical angle with two manipulators was designed, which can realize Signal amplitude/mV Signal amplitude/mV Corr 8 Applied Bionics and Biomechanics [9] T. Chunlei, Research on Several Detection Problems of Multi-- (4) A system architecture of ultrasonic measuring robot Degree-of-Freedom Ultrasonic Automatic Detection System, for residual stress in complex curved surface compo- Zhejiang University, 2011. nents was proposed [10] Y. Xiuchao, 3D Reconstruction Technology for Flaw Detection of Aero-Engine Blades, Lanzhou University of Technology, Data Availability [11] D. S. Hughes and J. L. Kelly, “Second-order elastic deformation The data used to support the findings of this study are of solids,” Physics Review, vol. 92, no. 5, pp. 1145–1149, 1953. available from the corresponding author upon request. [12] J. L. Rose, Ultrasound in Solids, Science Press, 2004. Disclosure The authors declare that this funding does not lead to any conflict of interests regarding the publication of this manuscript. Conflicts of Interest The authors declare that there is no conflict of interest regarding the publication of this paper and there is no any other possible conflict of interests in the manuscript. Acknowledgments This research and publication is supported by the project of Basic Technology Research which is funded by Technology and Quality Division of the Ministry of Industry and Information Technology (grant no. JSZL2017602B002). References [1] Z. Hong, H. Xiao, C. Yanyan, W. Yangzhong, and W. Linfeng, “Finite Element analysis of milling surface residual stresses,” Machine and Hydraulics, vol. 5, pp. 49–52, 2013. [2] X. Juan, “Aeroengine blade processing deformation analysis and control measures,” China's New Technology and New Products, vol. 17, pp. 60-61, 2018. [3] M. Duquennoy, M. Ouaftouh, M. L. Qian, F. Jenot, and M. Ourak, “Ultrasonic characterization of residual stresses in steel rods using a laser line source and piezoelectric transduc- ers,” NDT & E International, vol. 34, no. 5, pp. 355–362, 2001. [4] F. Wanwan, Y. Pan, R. Dongheng, W. Hao, and Y. Yuanfeng, “Residual stress in cast iron brake disc measured by laser-generated surface wave technique,” Materials for Mechanical Engineering, vol. 9, pp. 78–82, 2018. [5] J. Wong, Laser Ultrasonic Nondestructive Testing of Metal Surface Defects and Rail Tread Residual Stress, Beijing Jiao- tong University, 2016. [6] R. Murayama and H. Nishino, “A pipe inspection using a cir- cumferential SH-mode plate wave generated in a pipe by an electromagnetic acoustic transducer (EMAT),” World Journal of Engineering and Technology, vol. 6, no. 3, pp. 671–683, 2018. [7] N. Nakamura, K. Ashida, T. Takishita, H. Ogi, and M. Hirao, “Inspection of stress corrosion cracking in welded stainless steel pipe using point-focusing electromagnetic-acoustic trans- ducer,” NDT & E International, vol. 83, pp. 88–93, 2016. [8] C. Xu, W. Junfeng, S. Jianfeng, T. Haibing, L. Lianpo, and R. Xin, “Ultrasonic nondestructive testing and in situ regula- tion technology of residual stress for oil and gas pipelines,” Petroleum Science Bulletin, vol. 1, no. 3, pp. 442–449, 2016. 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Robotic Ultrasonic Measurement of Residual Stress in Complex Curved Surface Components

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Abstract

Hindawi Applied Bionics and Biomechanics Volume 2019, Article ID 2797896, 8 pages https://doi.org/10.1155/2019/2797896 Research Article Robotic Ultrasonic Measurement of Residual Stress in Complex Curved Surface Components 1,2 1,2 1,2 1,2 1,2 Qinxue Pan , Chang Shao , Dingguo Xiao , Ruipeng Pan , Xiaohao Liu , 1,2 and Wei Song School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China Key Laboratory of Fundamental Science for Advanced Machining, Beijing Institute of Technology, Beijing 100081, China Correspondence should be addressed to Qinxue Pan; panqx@bit.edu.cn Received 1 May 2018; Revised 21 November 2018; Accepted 4 December 2018; Published 3 March 2019 Guest Editor: Dongming Gan Copyright © 2019 Qinxue Pan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The automatic measurement, especially for products with complex shapes, has always been one of the most important application areas of robots. Aiming at the challenge of measuring residual stress under curved surface, in this paper, the residual stress ultrasonic measuring robot system with two manipulators is constructed, which is based on combining industrial robot technology with residual stress ultrasonic nondestructive measuring technology. The system is mainly composed of a motion control system, an ultrasonic detection system, and a data processing system. The robotic arm controls the movement of the two ultrasonic transducers along the set scanning path which is based on the geometric model of components and adjusts the transducer’s posture in time according to the shape of the workpiece being measured. The configuration information based on workpiece coordinate system is transformed into a position data that takes into consideration the first critical angle and can be recognized by the robot. Considering the effect of curvature, the principle model of residual stress measuring by the critical refraction longitudinal wave is established. The measured signal including the stress state of the measured region, as well as the actual position and posture information of the transducers, is processed by the computer in real time, which realizes automatic nondestructive measurement of residual stress under curved surface. 1. Introduction propagation of cracks, causing the components to suddenly break under the working load, leading to malfunctions and Currently, complex surface components have been widely even serious safety accidents [2]. Therefore, it is very impor- tant to measure and evaluate the residual stress of complex used in aviation, aerospace, marine, automobile, and molds industry and have played an extremely important role, surface components. such as in engine blades and propellers, which is directly Ultrasonic detection technology based on acoustic elas- related to the reliability and safety of the equipment. The ticity principle is one of the reliable and effective methods manufacturing process of complex surface components is for residual stress nondestructive measuring. Residual stress cumbersome and complex, which will inevitably produce ultrasonic measuring technology is more and more widely residual stress on the surface [1]. Even after a certain process, used in the inspection of residual stress of regular-shaped for example, heat treatment, the residual stress is also dif- members such as rails, pipes, gears, and hubs due to its ficult to eliminate completely. On the other hand, these com- advantages of nondestructivity, harmlessness, reliability, plex surface components will also have residual stresses accuracy, and convenience. Duquennoy et al., of the Univer- due to impact loads, thermal loads, and corrosion during sity of Valensina, France, used Rayleigh waves that excited by long-term service. The existence of this residual stress not laser and received by PZT to measure the residual stress on only seriously affects the shape and mechanical properties the pipe surface [3]. Using the similar method, Wanwan of the components but also promotes the generation and et al. measured the residual stress in a cast iron brake disc 2 Applied Bionics and Biomechanics Reflective the nondestructive detection of the tangential residual stress shear wave state in the propagation direction in the surface layer. Incident As shown in Figure 1, when the longitudinal wave prop- longitudinal wave Reflective agates from a medium with a slower wave velocity to a cr longitudinal wave medium with a faster wave velocity (such as from water to metal material), according to Snell’s theorem, there is an inci- Critical refractive dent angle so that the refracted longitudinal wave has a Medium 1 longitudinal Wave refraction angle of 90 degrees. This refracted longitudinal Medium 2 훽 = 90 wave will propagate along the surface of the second medium. This incident angle is called the first critical angle (θ ), and cr the resulting refracted longitudinal waves are called critical Refractive Shear Wave refraction longitudinal wave (L ). cr The first critical angle can be obtained by Snell’s theorem: Figure 1: Wave conversion. −1 1L θ = sin , 1 cr and compared with that measured by X-ray stress analyser V 2L [4]. In general, the research hotspots of ultrasonic nonde- structive testing of residual stress mainly focus on different where V is the longitudinal wave velocity of medium 1 and 1L application objects and different ways of ultrasonic signal V is the longitudinal wave velocity of medium 2. 2L excitation and reception in recent years [5–8]. For complex surface components, in order to excite and The residual stress ultrasonic measuring has a strict receive the critical refracted longitudinal wave at the surface requirement on the incident and receiving angles of the of the component, it must be ensured that the ultrasonic transducer. However, for a complex curved surface compo- transducer is tilted by a certain angle. The angle between nent, the change of curvature will seriously affect the inci- the excitation transducer and the normal of incident point dence, propagation, and reception of the ultrasonic signal, is equal to a positive critical angle, and the receive transducer which poses great challenges to ultrasonic measuring of and the normal of exit point is equal to a negative critical residual stress in complex surface components. The tradi- angle. It must also ensure that the exciting and receiving tional manual measurement not only is difficult to ensure transducers are in the same plane as the refracted longitudi- the necessary position and posture of the ultrasonic trans- nal wave propagation path. The excitation, propagation, ducer but also has disadvantages such as low efficiency, large and reception process of critical refraction longitudinal wave labor intensity, poor detection accuracy, and difficulty in along the surface is shown in Figure 2. quantitative analysis. In order to overcome the diffusion of the ultrasonic The development of high-precision, multi-degrees-of-- beam in the coupling agent and improve the detection sensi- freedom robots has brought a new support to the ultrasonic tivity and resolution of the curved surface workpiece, the measurement for complex surface components [9, 10]. focal transducer is used for detection, which is shown in In this paper, an ultrasonic residual stress measurement Figure 3. The focus position of the transducer in water can method based on robot technology is proposed, which takes obtained by calculation or experiment. full advantage of a robot’s precise control of ultrasonic trans- According to the principle of ultrasound, the focal length ducer position and automatic scanning. It adjusts the posture of the transducer in water is calculated as follows: of the ultrasonic transducer in real time according to the detection position. The actual posture information of the F = , 2 ultrasonic transducers and the ultrasonic signal at this posi- 1 − C /C 2 1 tion is processed by the computer to obtain the residual stress value of the measured area. where F, R, C , and C are the focal length of the transducer 1 2 in water, curvature radius of the acoustic lens, ultrasound speed in the lens, and ultrasound speed in water, respectively. 2. Materials and Methods Based on the theory of acoustic elasticity, the relationship between ultrasonic longitudinal wave velocity and stress can 2.1. Ultrasonic Measuring Principle of Residual Stress in be simplified as follows: Curved Surface Components. The main basis for the ultra- sonic measurement of stress is the acoustic elasticity theory, V = V 1 − K σ , 3 Lσ L0 L that is, the stress state in the elastic solid will affect the prop- agation speed of the ultrasonic wave in a material [11, 12]. where V represents the longitudinal wave velocity when Lσ Theoretical and experimental studies show that the ultra- the stress is σ, V is the longitudinal wave velocity in the L0 sonic longitudinal wave with the propagation direction being absence of stress, and K is the acoustic elastic coefficient of consistent with the stress direction is most sensitive to the longitudinal wave. change of stress. Therefore, it is necessary to generate a lon- Suppose that the propagation path is s, the propagation gitudinal wave propagating along the surface. By measuring time is t and the tangential stress on the path is σ. Because the change of the longitudinal wave speed, we can realize the velocity is difficult to measure directly, the different time Applied Bionics and Biomechanics 3 Receiving Transducer Propagation Exciting path of Lcr cr Transducer 휃 cr Specimen Figure 2: Critical refracted longitudinal waves propagating in a curved surface. component, the computer-aided manufacturing (CAM) numerical simulation software is used to obtain the position and normal vector of the scanning trajectory points in the Cartesian coordinate system. As shown in Figure 4, the robot arm that holds the exciting transducer is defined as the master manipulator and the robot arm that holds the receiving transducer as the slave manipulator. Both the master manipulator and slave manipulator move in the zig-zag scanning mode, and the slave manipula- tor always keeps a certain distance from the master manipu- lator in the stepping direction, which determines the spatial resolution of the detection. Figure 5 shows two different zig-zag scan modes for surface workpiece. Through this two different scanning methods, we can get the stress compo- nents in two directions, and then according to the principle of force synthesis, we can determine the stress vector in the surface direction. 2.3. Coordinate Transformation. Considering the require- ments for transducer position orientation, the pose informa- tion in the Cartesian coordinate system of workpiece cannot be directly recognized and used by the robot controller. We need to convert that into point and the orientation data of the transducer based on the coordinate system of the robot. As shown in Figure 6, taking the master manipulator Figure 3: Spherical focus transducer. motion control as an example, set the reference coordinate system of the robot as W and the tool coordinate system that ultrasound travels the same distance is used to calculate as M . The tool coordinate system translated along the the stress state on the path: z-axis to the focus of the ultrasonic transducer is C , the workpiece coordinate system is A , and the measured s s sK σ discrete coordinate system is B . The origin of the B Δt = − = , coordinate system is specified at the scanning point. The V 1 − K σ V V 1 − K σ L0 L L0 L0 L Z-axis is along the normal direction of the scanning point, the X-axis goes along the incident point to the exit point, Δt ⋅ V L0 σ = 5 and the Y-axis direction is determined according to the K s + Δt ⋅ V L L0 right-hand rule. 2.2. Trajectory Planning. According to the principle of ultra- Through the CAM simulation software, we can easily get sonic measurement of residual stress for curved surface com- the position and normal information of the discrete points on ponents, it must be ensured that the exciting and receiving the surface of the workpiece in the workpiece coordinate transducers move along the set path with a specific posture. system. Considering the location parameters of transducer Therefore, it is necessary to perform trajectory planning on installation, scanning path and the requirements of incident the measured surface to obtain the controlled movement or exit direction of ultrasonic wave, the purpose of coordinate point of the manipulator. Based on the CAD model of the transformation is to transform the position and normal 4 Applied Bionics and Biomechanics Master Slave manipulator manipulator Specimen Figure 4: Manipulator distribution. Scanning path of master Incident point Exit point manipulator Propagation path Stepping direction (a) Incident point Exit point Scanning path of master manipulator Stepping direction Propagation path (b) Figure 5: Different zig-zag scan modes for surface workpiece. direction information of discrete points and the deflection in the Cartesian coordinate system of workpiece A .Accord- angle of transducer into the position and posture of trajectory ing to the principle of coordinate transformation, points in the coordinate system of the robots. W W A C For a space vector P, let its position in the coordinate sys- P = T T P, 6 A C A B C tem A , B , C ,and W be expressed as P, P, P,and P, respectively. According to the principle of robot kinemat- A A A B ABA R P R R R P + P A C CORG B C CORG BORG ics, we need to identify the posture of transducers in the coor- T = = 7 0 1 0 0 0 1 dinate system of the robot W based on the pose information Applied Bionics and Biomechanics 5 Master manipulator y O B C C z y W B Specimen A Figure 6: Definition of the coordinate systems in the master manipulator. where propagation path, the measured discrete coordinate system B and transducer coordinate system C should satisfy the following relationship: ξ ξ ξ X Y Z R = , 8 φ φ φ X Y Z 10 0 cos θ 0 −sin θ cr cr ψ ψ ψ X Y Z R = 0 −10 01 0 ξ , ξ , ξ is the direction vector of the X-axis of coordinate X Y Z system B in the coordinate system A ; φ = φ , φ , φ is X Y Z 00 −1 sin θ 0 cos θ cr cr the direction vector of the Y-axis of coordinate system B cos θ 0 sin θ cr cr in the coordinate system A ;and ψ = ψ , ψ , ψ is the X Y Z direction vector of the Z-axis of coordinate system B in = 0 −10 , the coordinate system A . Supposing that the location of the incident point is P and the location of the out point is sin θ 0 −cos θ cr cr P at some time, their positions and normal directions in the coordinate system A can be expressed as A T B P = x , y , z , nx , ny , nz , P =0 12 i i i i i i i CORG A T P = x , y , z , nx , ny , nz , o o o o o o o Bring equations (8), (11), and (12) into equation (7): where x, y, z represents the position information and nx, ny, nz represents the normal vector. ξ ξ ξ cos θ 0 sin θ According to the definition of axes in coordinate system X Y Z cr cr B , R = φ φ φ 0 −10 C X Y Z ψ = ψ , ψ , ψ = nx , ny , nz , X Y Z i i i ψ ψ ψ sin θ 0 −cos θ X Y Z cr cr ψ × x − x , y − y , z − z o i o i o i ξ cθ + ξ sθ −ξ ξ sθ − ξ cθ X cr Z cr Y X cr Z cr φ = φ , φ , φ = , X Y Z ψ × x − x , y − y , z − z o i o i o i = φ cθ + φ sθ −φ φ sθ − φ cθ , X cr Z cr Y X cr Z cr ψ × x − x , y − y , z − z × nx , ny , nz o i o i i i o i i ξ = φ × ψ = ψ × x − x , y − y , z − z ψ cθ + ψ sθ −ψ ψ sθ − ψ cθ o i o i o i Y cr Y cr Y Y cr Y cr A A P = P = In order to ensure that the focal point of the receiving CORG CORG transducer coincides with the measured point and that the acoustic axis deviates from the θ of the incident point nor- cr mal within the plane formed by the incident axis and the 6 Applied Bionics and Biomechanics Water coupling system ultrasonic signal Receiving Exciting Data Acquisition transceiver Pulse transceiver Specimen Card Transducer Transducer system Trigger Geometric module model Holding Holding device device Master Slave manipulator manipulator robotic arm motion system Robot position control module in lower computer Robot controller Robot position control Ultrasonic detection module in upper computer module control and data processing system Industrial control computer Figure 7: Ultrasonic measuring robot system. cos and sin are abbreviated as c and s, respectively. In this case, W W A R = R R C A C ψ = ψ , ψ , ψ = nx , ny , nz , X Y Z o o o ξ cθ + ξ sθ −ξ ξ sθ − ξ cθ X cr Z cr Y X cr Z cr ψ × x − x , y − y , z − z i o i o i o φ = φ , φ , φ = , X Y Z ψ × x − x , y − y , z − z = R φ cθ + φ sθ −φ φ sθ − φ cθ , i o i o i o A X cr Z cr Y X cr Z cr ψ × x − x , y − y , z − z nx , ny , nz i o i o o o i o o ψ cθ + ψ sθ −ψ ψ sθ − ψ cθ ξ = φ × ψ = , Y cr Y cr Y Y cr Y cr ψ × x − x , y − y , z − z i o i o i o ξ ξ ξ cos −θ 0 sin −θ X Y Z cr cr i R = φ φ φ 0 −10 , C X Y Z W W A W W W P = R P + P = R y + P CORG CORG AORG AORG A A i ψ ψ ψ sin −θ 0 −cos −θ X Y Z cr cr A A P = P = CORG BORG Although the workpiece coordinate system A is unknown, its position and posture is fixed in the detection process. Therefore, we can calibrate the coordinate system A by several characteristic points to determine the trans- formation matrix R and T between the workpiece A AORG 3. Results and Discussion coordinate system A and the reference coordinate system W W of the robot W . Bringing the R and T into equa- Ultrasonic measuring robot for residual stress of complex A AORG tions 14 and 15, we can calculate the position and posture surface components includes hardware system and software of the excitation transducer in coordinate W . system. As shown in Figure 7, the hardware system is mainly The pose determination method of the receiving trans- composed of three parts: the robotic arm motion mecha- ducer is similar to that of the transmitting transducer. The nism, the ultrasonic signal transceiver system, and the con- only differences between them are the establishment of coor- trol and data processing system. Two six-DOF industrial dinate system B and the deflection direction of transducer. robots are used to implement the gripping, position, and Applied Bionics and Biomechanics 7 Lcr Wave −512 −1024 −512 −1536 −2048 −1024 0 10 20 30 40 26.5 27.0 27.5 28.0 Time/us Time/us Ultrasonic signal original sampling data . . fourier interpolation by 10 times Figure 8: Ultrasonic signal. Figure 9: Ultrasonic signals before and after interpolation in different stress states. posture control of the ultrasonic transducers and automatic scanning; the ultrasonic signal transceiver system mainly includes a pulse transceiver, a high-frequency data acquisi- tion card, two ultrasonic transducers, and a water coupling system. The role of this system is to excite and receive ultra- sonic signals at the detection location. The control and pro- cessing system is the “brain” of the entire measuring robot, realizing the core tasks of motion control and ultrasonic 0.5 signal processing. The software system consists of the upper computer soft- ware subsystem and the lower computer software subsystem. The two subsystems cooperate with each other to jointly per- −1 −0.5 −0.059 0.5 1 Time/us form functions such as communication and control of the ultrasonic signal transceiver system and the manipulator movement system. The upper computer software is imple- −0.5 mented in the industrial control computer to complete the trajectory planning and coordinate transforming. Another core task of the upper computer software is to process the −1.0 ultrasonic transducer posture data and ultrasonic signals to obtain residual stress results. The ultrasonic signal is shown Figure 10: Cross-correlation of ultrasonic signals under two in Figure 8. The lower computer software refers to the soft- different stress states. ware system implemented in the controller of the robot and is mainly responsible for robot motion control, external trig- gering ultrasonic pulse transceiver, and reading and transfer- ring the robot position information. the nondestructive automatic detection of the residual stress in the surface of a complex curved surface component by According to equation 5, the time difference directly using critical refracted longitudinal wave. determines the accuracy of the results. For acoustic time method of measuring residual stress, we are only interested (1) Deduced an ultrasonic measuring principle and cal- in the effect of stress on the ultrasonic signal in the time culation formula of residual stress in curved surface domain. Hence, as shown in Figures 9 and 10, we combine components interpolation and time-delayed autocorrelation theory to improve the accuracy of time measurement and calculate (2) Proposed a trajectory planning strategy for the robot the delay of two sets of signals. with two manipulators (3) Established a coordinate transformation formula 4. Conclusions between the workpiece coordinate system and the In this paper, a new ultrasonic measuring robot system robot coordinate system in consideration of the first critical angle with two manipulators was designed, which can realize Signal amplitude/mV Signal amplitude/mV Corr 8 Applied Bionics and Biomechanics [9] T. Chunlei, Research on Several Detection Problems of Multi-- (4) A system architecture of ultrasonic measuring robot Degree-of-Freedom Ultrasonic Automatic Detection System, for residual stress in complex curved surface compo- Zhejiang University, 2011. nents was proposed [10] Y. Xiuchao, 3D Reconstruction Technology for Flaw Detection of Aero-Engine Blades, Lanzhou University of Technology, Data Availability [11] D. S. Hughes and J. L. Kelly, “Second-order elastic deformation The data used to support the findings of this study are of solids,” Physics Review, vol. 92, no. 5, pp. 1145–1149, 1953. available from the corresponding author upon request. [12] J. L. Rose, Ultrasound in Solids, Science Press, 2004. Disclosure The authors declare that this funding does not lead to any conflict of interests regarding the publication of this manuscript. Conflicts of Interest The authors declare that there is no conflict of interest regarding the publication of this paper and there is no any other possible conflict of interests in the manuscript. Acknowledgments This research and publication is supported by the project of Basic Technology Research which is funded by Technology and Quality Division of the Ministry of Industry and Information Technology (grant no. JSZL2017602B002). References [1] Z. Hong, H. Xiao, C. Yanyan, W. Yangzhong, and W. Linfeng, “Finite Element analysis of milling surface residual stresses,” Machine and Hydraulics, vol. 5, pp. 49–52, 2013. [2] X. Juan, “Aeroengine blade processing deformation analysis and control measures,” China's New Technology and New Products, vol. 17, pp. 60-61, 2018. [3] M. Duquennoy, M. Ouaftouh, M. L. Qian, F. Jenot, and M. Ourak, “Ultrasonic characterization of residual stresses in steel rods using a laser line source and piezoelectric transduc- ers,” NDT & E International, vol. 34, no. 5, pp. 355–362, 2001. [4] F. Wanwan, Y. Pan, R. Dongheng, W. Hao, and Y. Yuanfeng, “Residual stress in cast iron brake disc measured by laser-generated surface wave technique,” Materials for Mechanical Engineering, vol. 9, pp. 78–82, 2018. [5] J. Wong, Laser Ultrasonic Nondestructive Testing of Metal Surface Defects and Rail Tread Residual Stress, Beijing Jiao- tong University, 2016. [6] R. Murayama and H. 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