CHAPTER 3 ADAPTIVE ROBOTIC SYSTEM FOR 3D PROFILE GRINDING/POLISHING XiaoQi Chen*,Zhiming Gong*,Han Huang*,Shuzhi Ge**,Libo Zhou*** *Singapore Institute of Manufacturing Technology, 71 Nanyang Drive,Singapore 638075 **Department of Electrical Computer Engineering.The National University of Singapore,10 Kent Ridge Crescent,Singapore 119260 ***Department of System Engineering,Ibaraki University,Japan 1. Introduction Robotic machining has certain advantages over conventional CNC machining:high flexibility,capability of integration with peripherals such as sensors and external actuators,and lower cost.Attempts have been made to apply robotic machining to advanced material processing.United Technology Research Centre (UTRC)has been developing robotic machining technologies since early 80's [1.A two-axis closed-loop controlled micro-manipulator has been developed for automated chamfering and deburring,but is yet to be further explored for polishing 3D profiles.Berger et al [2]have reported an advanced mechatronic system for turbine blade manufacturing and repair.Their work proposed a high-speed multi-axis milling machine to cut difficult-to-machine materials.A 3D profile measurement sensor system was proposed for compensating the part tolerances.Again the work was confined to a laboratory exploration Most recently,Chen and Hu [3,4]have implemented a robot system for sculpture surface cutting,meant for rapid prototyping.A part model is used to generate robot path and trajectory.The 3D sculpture surface is produced based on robot position control.In [5],a force controlled robotic finishing
CHAPTER 3 ADAPTIVE ROBOTIC SYSTEM FOR 3D PROFILE GRINDING/POLISHING XiaoQi Chen*, Zhiming Gong*, Han Huang*, Shuzhi Ge**, Libo Zhou*** *Singapore Institute of Manufacturing Technology, 71 Nanyang Drive, Singapore 638075 **Department of Electrical & Computer Engineering, The National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260 *** Department of System Engineering, Ibaraki University, Japan 1. Introduction Robotic machining has certain advantages over conventional CNC machining: high flexibility, capability of integration with peripherals such as sensors and external actuators, and lower cost. Attempts have been made to apply robotic machining to advanced material processing. United Technology Research Centre (UTRC) has been developing robotic machining technologies since early 80’s [1]. A two-axis closed-loop controlled micro-manipulator has been developed for automated chamfering and deburring, but is yet to be further explored for polishing 3D profiles. Berger et al [2] have reported an advanced mechatronic system for turbine blade manufacturing and repair. Their work proposed a high-speed multi-axis milling machine to cut difficult-to-machine materials. A 3D profile measurement sensor system was proposed for compensating the part tolerances. Again the work was confined to a laboratory exploration. Most recently, Chen and Hu [3, 4] have implemented a robot system for sculpture surface cutting, meant for rapid prototyping. A part model is used to generate robot path and trajectory. The 3D sculpture surface is produced based on robot position control. In [5], a force controlled robotic finishing
56 X O Chen,Z M Gong,H Huang.S Z Ge,and L B Zhou system is discussed.The idea is that a force-controlled robot can follow the edges or the surfaces of the workpiece using force control functions. Kunida and Nakagawa [6]have developed a curved surface polishing robot system using a magneto-pressed tool and a magnetic force sensor.Desired contact force can be maintained during polishing.In more sophisticated robotic machining applications,dual manipulators may be required. Adaptive neural network control has been attempted for coordinated manipulation in a constrained environment [7].As far as practical applications are concerned,robotic machining has been mostly restricted to simple operations under well-defined conditions,such as deburring, polishing and chamfering of new parts. As compared with manufacturing new parts,one of the major difficulties in overhauling aerospace components is that the part geometry is severely distorted after service in the high-temperature and high-pressure condition.As a result,the intended automation system cannot rely on the teach-and-play or programming-and-cut methods used for conventional robotic or machining applications.Another challenge is to overcome the process dynamics that is very much empirical and largely knowledge- based.Despite extensive research work and laboratory prototyping and implementation by researchers all over the world,automated systems for blending and polishing of 3D distorted profiles,such as refurbishment High-Pressure Turbine (HPT)vanes,do not exist in today's factories.The operation is manually done in almost every overhaul service factory.To this end,a concerted effort has been made to implement a robotic system for 3D profile grinding and polishing for production use. Following the discussion on the perspective and approach of 3D profile grinding and polishing in Chapter 2,this chapter focuses on the development of core technological modules and full implementation of a working prototype.Section 2 discusses the selected finishing robot,Self- Aligned End-Effector(SAE),and control interface.Section 3 explains the In-Situ Profile Measurement (IPM)and coordinate transformation necessary to construct the part geometry.Template-based Optimal Profile Fitting (OPF)requirements,algorithm,and software development are detailed in Section 4.It is followed by the discussion on Adaptive Robotic Path Planning (ARP)in Section 5.Section 6 highlights the working prototype "SMART 3D Grinding/Polishing System",the first-of-its-kind for blending distorted 3D profiles.Section 7 presents the results of benchmarking tests conducted on the SMART system for JT9D High-
56 X Q Chen, Z M Gong, H Huang, S Z Ge, and L B Zhou system is discussed. The idea is that a force-controlled robot can follow the edges or the surfaces of the workpiece using force control functions. Kunida and Nakagawa [6] have developed a curved surface polishing robot system using a magneto-pressed tool and a magnetic force sensor. Desired contact force can be maintained during polishing. In more sophisticated robotic machining applications, dual manipulators may be required. Adaptive neural network control has been attempted for coordinated manipulation in a constrained environment [7]. As far as practical applications are concerned, robotic machining has been mostly restricted to simple operations under well-defined conditions, such as deburring, polishing and chamfering of new parts. As compared with manufacturing new parts, one of the major difficulties in overhauling aerospace components is that the part geometry is severely distorted after service in the high-temperature and high-pressure condition. As a result, the intended automation system cannot rely on the teach-and-play or programming-and-cut methods used for conventional robotic or machining applications. Another challenge is to overcome the process dynamics that is very much empirical and largely knowledgebased. Despite extensive research work and laboratory prototyping and implementation by researchers all over the world, automated systems for blending and polishing of 3D distorted profiles, such as refurbishment High-Pressure Turbine (HPT) vanes, do not exist in today’s factories. The operation is manually done in almost every overhaul service factory. To this end, a concerted effort has been made to implement a robotic system for 3D profile grinding and polishing for production use. Following the discussion on the perspective and approach of 3D profile grinding and polishing in Chapter 2, this chapter focuses on the development of core technological modules and full implementation of a working prototype. Section 2 discusses the selected finishing robot, SelfAligned End-Effector (SAE), and control interface. Section 3 explains the In-Situ Profile Measurement (IPM) and coordinate transformation necessary to construct the part geometry. Template-based Optimal Profile Fitting (OPF) requirements, algorithm, and software development are detailed in Section 4. It is followed by the discussion on Adaptive Robotic Path Planning (ARP) in Section 5. Section 6 highlights the working prototype “SMART 3D Grinding/Polishing System”, the first-of-its-kind for blending distorted 3D profiles. Section 7 presents the results of benchmarking tests conducted on the SMART system for JT9D High-
Adaptive Robotic System for 3D Profile Grinding/Polishing 57 Pressure Turbine (HPT)vanes.Finally,the chapter is concluded with some remarks on the technological breakthrough and its implications. 2. Finishing Robot and Control Interface 2.1 Finishing Robot In order for a line tool (contact area between the contact wheel and the workpiece can be approximated to a line)to follow a 3D surface profile,the finishing robot must have a greater dexterity as compared with a dedicated 5-axis CNC machine tool.It is quite natural that the operator uses two hands to manipulate the part to obtain desired contact force and compliance between the part and the tool.In principle,two robot arms could imitate the operator's two arms to achieve the required dexterity and rigidity. However,it poses tremendous difficulties in controlling the two mechanical arms to accomplish contact tasks.Instead,a 6-axis robot arm is preferred for its ease of motion control. A robot for 3D blending operations has to overcome extreme reactive forces as compared to conventional industrial robots for welding,pick-and- place,glue dispensing and painting.The finishing robot not only has to hold the turbine vane in position,but also to press the airfoil surface against the grinding wheel in the normal direction and with controlled contact force,in order to achieve the desired material removal.Thus a finishing robot must have a high loading capacity,stiffness,rigidity and desired dynamic performance when used for airfoil blending operation.After an in- depth evaluation,the six-degree-of-freedom Yamaha Z-II6 robot was chosen for the blending application,shown in Figure 1.Its R and Z axes determine the position of the Tool-Centre-Point (TCP),i.e.,(X,Y,Z) coordinates,while the a B,and yaxes,which form a Roll-Pitch-Roll wrist configuration,determine the orientation of the tool frame.The robot can carry a payload as high as 40 Kg and has a repeatability of 0.1 mm in the worst case.The robot,driven by AC servomotors with absolute position sensing,is dust-proof by applying a positive internal pressure,which is advantageous in the dusty blending environment. 2.2 Self-Aligned End Effector In order to cater to both concave and convex airfoils,a servo-driven Self- Aligned End-Effector(SAE)has been developed,as shown in Figure 2.It
Adaptive Robotic System for 3D Profile Grinding/Polishing 57 Pressure Turbine (HPT) vanes. Finally, the chapter is concluded with some remarks on the technological breakthrough and its implications. 2. Finishing Robot and Control Interface 2.1 Finishing Robot In order for a line tool (contact area between the contact wheel and the workpiece can be approximated to a line) to follow a 3D surface profile, the finishing robot must have a greater dexterity as compared with a dedicated 5-axis CNC machine tool. It is quite natural that the operator uses two hands to manipulate the part to obtain desired contact force and compliance between the part and the tool. In principle, two robot arms could imitate the operator’s two arms to achieve the required dexterity and rigidity. However, it poses tremendous difficulties in controlling the two mechanical arms to accomplish contact tasks. Instead, a 6-axis robot arm is preferred for its ease of motion control. A robot for 3D blending operations has to overcome extreme reactive forces as compared to conventional industrial robots for welding, pick-andplace, glue dispensing and painting. The finishing robot not only has to hold the turbine vane in position, but also to press the airfoil surface against the grinding wheel in the normal direction and with controlled contact force, in order to achieve the desired material removal. Thus a finishing robot must have a high loading capacity, stiffness, rigidity and desired dynamic performance when used for airfoil blending operation. After an indepth evaluation, the six-degree-of-freedom Yamaha Z-II6 robot was chosen for the blending application, shown in Figure 1. Its θ, R and Z axes determine the position of the Tool-Centre-Point (TCP), i.e., (X, Y, Z) coordinates, while the α, β, and γ axes, which form a Roll-Pitch-Roll wrist configuration, determine the orientation of the tool frame. The robot can carry a payload as high as 40 Kg and has a repeatability of 0.1 mm in the worst case. The robot, driven by AC servomotors with absolute position sensing, is dust-proof by applying a positive internal pressure, which is advantageous in the dusty blending environment. 2.2 Self-Aligned End Effector In order to cater to both concave and convex airfoils, a servo-driven SelfAligned End-Effector (SAE) has been developed, as shown in Figure 2. It
58 X Q Chen,Z M Gong.H Huang.S Z Ge,and L B Zhou has an active servo drive mechanism at one end (left)and a passive follower at the other end (right).The active end is mechanically coupled to the robot end-axis y which has a driving torque about 35 Nem.The servo- driven SAE can rotate 360 degrees so that both concave and convex airfoils can contact the grinding wheel of the belt polishing machine in normal directions. 50 axigroke 240 Figure 1 Yamaha six-axis finishing robot Z-I6. Figure 2 Servo-driven self-aligned end-effector
58 X Q Chen, Z M Gong, H Huang, S Z Ge, and L B Zhou has an active servo drive mechanism at one end (left) and a passive follower at the other end (right). The active end is mechanically coupled to the robot end-axis γ which has a driving torque about 35 N•m. The servodriven SAE can rotate 360 degrees so that both concave and convex airfoils can contact the grinding wheel of the belt polishing machine in normal directions. Figure 1 Yamaha six-axis finishing robot Z-II6. Figure 2 Servo-driven self-aligned end-effector
Adaptive Robotic System for 3D Profile Grinding/Polishing 59 The passive follower ensures that the vane is held in place firmly,and in the meantime secures the axial alignment of the vane.In addition,there are three locators in the SAE to align the vane in a fixed direction.The innovative design minimises the gripping inaccuracies that would otherwise compound the airfoil distortions.The SAE has incorporated pneumatic sensors to detect any part jamming in SAE.An external laser through-beam sensor is integrated to the feeding table to check improper gripping. 2.3 Control Interface As discussed in Chapter 2,there are two sub control systems,namely the Knowledge-Based Process Controller (KBPC)and the Data-Driven Supervisory Controller.The former,controlling all actuators and sensors,is implemented into the industrial robot controller with a powerful robot programming language dedicated to the blending operation.The latter is implemented into the host computer running the Windows NT operating system.Figure 3 shows the system communication and interface between the robot controller,interface PC.and host PC Z-1l6 Robot 少 Profile Robot Controller Measurement Sensor and RS232C Instrument Digital VO Interface Computer 24VDC Running 16 Inputs Prg:Tbmain.exe 16 Outputs OS:MS-DOS T Ethernet Host Computer Running Prg: AutoBlending.exe OS:Windows NT Digital l/O Board Figure 3 System communication and interface. The host computer is interfaced to the robot controller through digital I/Os for handshaking,but the data transactions between the two controllers become difficult.The chief reason is that the robot controller can only communicate with an interface computer,running the manufacturer's program "Tbmain.exe"in MS-DOS,through a RS-232 serial line in the
Adaptive Robotic System for 3D Profile Grinding/Polishing 59 The passive follower ensures that the vane is held in place firmly, and in the meantime secures the axial alignment of the vane. In addition, there are three locators in the SAE to align the vane in a fixed direction. The innovative design minimises the gripping inaccuracies that would otherwise compound the airfoil distortions. The SAE has incorporated pneumatic sensors to detect any part jamming in SAE. An external laser through-beam sensor is integrated to the feeding table to check improper gripping. 2.3 Control Interface As discussed in Chapter 2, there are two sub control systems, namely the Knowledge-Based Process Controller (KBPC) and the Data-Driven Supervisory Controller. The former, controlling all actuators and sensors, is implemented into the industrial robot controller with a powerful robot programming language dedicated to the blending operation. The latter is implemented into the host computer running the Windows NT operating system. Figure 3 shows the system communication and interface between the robot controller, interface PC, and host PC. Z-II6 Robot Robot Controller Profile Measurement Sensor and Instrument Interface Computer Running Prg:Tbmain.exe OS: MS-DOS Host Computer Running Prg: AutoBlending.exe OS: Windows NT Digital I/O Board Ethernet RS232C Digital I/O 24VDC 16 Inputs 16 Outputs Figure 3 System communication and interface. The host computer is interfaced to the robot controller through digital I/Os for handshaking, but the data transactions between the two controllers become difficult. The chief reason is that the robot controller can only communicate with an interface computer, running the manufacturer’s program “Tbmain.exe” in MS-DOS, through a RS-232 serial line in the
60 X O Chen,Z M Gong,H Huang.S Z Ge,and L B Zhou manufacturer's proprietary protocol.To bypass the problem,the host computer is connected to the interface PC via an Ethernet LAN.Data transactions between robot controller and host controller are relayed by the interface PC.The host computer runs the specially developed main program“AutoBlending.exe”. Via the interface computer,measurement data are sent from the robot controller to the host computer in the form of text files through a RS232C interface and an Ethernet network.The computed blending paths are sent back from the host computer to the robot controller by the same route.The executions of the robot programs and the host computer programs are synchronised by the digital inputs/outputs between them. 3. In-Situ Profile Measurement 3.1 Off-Line versus In-Situ Approach The turbine airfoils to be repaired have severe distortions and twists after operations in the high-temperature and high-pressure environment.A teach- and-play robot cannot cope with the distorted profile,nor can a commercial off-line programming system which generates a robot path according to the design data.Due to severe part distortions and part-to-part variations of the turbine vanes for repair,the design (nominal)profile cannot be used directly in a robotic surface finishing process.It is absolutely critical and necessary to have a profile sampling and distortion compensation system in this specific application to deal with part-to-part variations.Before any distortion compensation,the actual profile has to be sampled.Individual robot paths can then be generated for each workpiece from its distorted airfoil profile,which can only be obtained through measurement and profile fitting. Two approaches of profile measurement have been evaluated:Off-line Profile Measurement (OPM)and In-Situ Profile Measurement (IPM).The former utilises an external instrument to measure the profile on a separate fixture.Then the workpiece is released from the fixture,and transferred to the robotic blending system.In the meantime,the measurement data are transmitted to the Supervisory Controller for further processing.The advantages of OPM are: Accurate measurement can be obtained
60 X Q Chen, Z M Gong, H Huang, S Z Ge, and L B Zhou manufacturer’s proprietary protocol. To bypass the problem, the host computer is connected to the interface PC via an Ethernet LAN. Data transactions between robot controller and host controller are relayed by the interface PC. The host computer runs the specially developed main program “AutoBlending.exe”. Via the interface computer, measurement data are sent from the robot controller to the host computer in the form of text files through a RS232C interface and an Ethernet network. The computed blending paths are sent back from the host computer to the robot controller by the same route. The executions of the robot programs and the host computer programs are synchronised by the digital inputs/outputs between them. 3. In-Situ Profile Measurement 3.1 Off-Line versus In-Situ Approach The turbine airfoils to be repaired have severe distortions and twists after operations in the high-temperature and high-pressure environment. A teachand-play robot cannot cope with the distorted profile, nor can a commercial off-line programming system which generates a robot path according to the design data. Due to severe part distortions and part-to-part variations of the turbine vanes for repair, the design (nominal) profile cannot be used directly in a robotic surface finishing process. It is absolutely critical and necessary to have a profile sampling and distortion compensation system in this specific application to deal with part-to-part variations. Before any distortion compensation, the actual profile has to be sampled. Individual robot paths can then be generated for each workpiece from its distorted airfoil profile, which can only be obtained through measurement and profile fitting. Two approaches of profile measurement have been evaluated: Off-line Profile Measurement (OPM) and In-Situ Profile Measurement (IPM). The former utilises an external instrument to measure the profile on a separate fixture. Then the workpiece is released from the fixture, and transferred to the robotic blending system. In the meantime, the measurement data are transmitted to the Supervisory Controller for further processing. The advantages of OPM are: • Accurate measurement can be obtained
Adaptive Robotic System for 3D Profile Grinding/Polishing 61 The measurement can be carried out in parallel with robotic blending operation,hence shortening the cycle time. However,the Off-line Profile Measurement approach suffers some setbacks. .A separate measurement station incurs extra costs.As a minimum configuration,there should be a XYZ table carrying the probe (a commercial CMM for example),and one-axis rotary table to rotate the workpiece. Changing fixturing from the measurement station (held by a rotary table)to the blending system (held by the robot end-effector) introduces datum errors that erode the seemingly accurate measurements obtained. On the other hand,the In-Situ Profile Measurement (IPM)method utilises the robot itself as the measurement instrument together with a range or displacement sensor.Although the robot accuracy (0.1 mm)is much worse than a CMM (about 5 microns),the same end-effector for both profile measurement and the blending operation ensures a common datum, hence minimising fixture errors.Furthermore,the sensor head can be placed in an area where the robot has a better repeatability of less than 50 microns. 3.2 Sensor Techniques Profile measurement sensors fall into two broad categories:contact and non-contact sensors.In the latter,an optical sensor can be used to measure 3D profile.The range sensing principle is based on triangulation.This approach has been evaluated with a 3-axis XYZ table carrying a laser range sensor,as shown in Figure 4.The vane is mounted to a fixture which is driven by a DC servo motor so that both concave and convex airfoil can be measured.The measurement points on the airfoil surface can be calculated from four-axis coordinates and the sensor output.In order to obtain reliable readings from the laser sensor,the XYZ table and the fixture motor should be controlled in such a manner that the laser beam is normal to the surface. By averaging many measurements at the same point,a very good measurement repeatability of about 5 microns can be observed.Since there is no contact between the sensor and workpiece,the measurement process
Adaptive Robotic System for 3D Profile Grinding/Polishing 61 • The measurement can be carried out in parallel with robotic blending operation, hence shortening the cycle time. However, the Off-line Profile Measurement approach suffers some setbacks. • A separate measurement station incurs extra costs. As a minimum configuration, there should be a XYZ table carrying the probe (a commercial CMM for example), and one-axis rotary table to rotate the workpiece. • Changing fixturing from the measurement station (held by a rotary table) to the blending system (held by the robot end-effector) introduces datum errors that erode the seemingly accurate measurements obtained. On the other hand, the In-Situ Profile Measurement (IPM) method utilises the robot itself as the measurement instrument together with a range or displacement sensor. Although the robot accuracy (0.1 mm) is much worse than a CMM (about 5 microns), the same end-effector for both profile measurement and the blending operation ensures a common datum, hence minimising fixture errors. Furthermore, the sensor head can be placed in an area where the robot has a better repeatability of less than 50 microns. 3.2 Sensor Techniques Profile measurement sensors fall into two broad categories: contact and non-contact sensors. In the latter, an optical sensor can be used to measure 3D profile. The range sensing principle is based on triangulation. This approach has been evaluated with a 3-axis XYZ table carrying a laser range sensor, as shown in Figure 4. The vane is mounted to a fixture which is driven by a DC servo motor so that both concave and convex airfoil can be measured. The measurement points on the airfoil surface can be calculated from four-axis coordinates and the sensor output. In order to obtain reliable readings from the laser sensor, the XYZ table and the fixture motor should be controlled in such a manner that the laser beam is normal to the surface. By averaging many measurements at the same point, a very good measurement repeatability of about 5 microns can be observed. Since there is no contact between the sensor and workpiece, the measurement process
62 X O Chen,Z M Gong,H Huang,S Z Ge,and L B Zhou is continuous,hence very fast.However,the brazed airfoil has very rough surface with shining spots,and the laser sensor does not always produce reliable readings. Laser sensor Part Motorised fixture Figure 4 Profile measurement using laser range sensor LVDT probe Figure 5 In-situ profile measurement using LVDT. The alternative approach is to use a contact probe commonly deployed for a Coordinate Measurement Machine (CMM)or a machining centre. Such a measurement system is slow,but the physical contact between the probe and workpiece ensures the reliability of the measurement.A Linear Variable Differential Transducer (LVDT)has been integrated into the robotic system to carry out the profile measurement.The sensor outputs differential square wave signals,90 degrees phase different.These signals are connected to a linear gauge counter,which outputs Binary-Coded
62 X Q Chen, Z M Gong, H Huang, S Z Ge, and L B Zhou is continuous, hence very fast. However, the brazed airfoil has very rough surface with shining spots, and the laser sensor does not always produce reliable readings. Figure 4 Profile measurement using laser range sensor. Figure 5 In-situ profile measurement using LVDT. The alternative approach is to use a contact probe commonly deployed for a Coordinate Measurement Machine (CMM) or a machining centre. Such a measurement system is slow, but the physical contact between the probe and workpiece ensures the reliability of the measurement. A Linear Variable Differential Transducer (LVDT) has been integrated into the robotic system to carry out the profile measurement. The sensor outputs differential square wave signals, 90 degrees phase different. These signals are connected to a linear gauge counter, which outputs Binary-Coded Laser sensor Part Motorised fixture LVDT probe
Adaptive Robotic System for 3D Profile Grinding/Polishing 63 Decimal (BCD)to a data acquisition board resident in the robot controller. The BCD reading is proportional to the profile sensor displacement.The sensor has a measurement range of 10 mm,resolution of 5 um,and measurement accuracy of 20 um. After gripping the part,the robot approaches the measurement probe,as shown in Figure 5.The sensor measures a number of points in specific cross sections that will be used by the Optimal Profile Fitting(OPF)later. In our development,three sections are selected,as shown in Figure 6. Buttress (a) (b) Figure 6(a)Front view of a turbine vane,(b)Side views of Section C-C. E-E and G-G of the vane airfoil. For each sectional profile,five measurement points are taken from the concave side and five from the convex side.When the measurement points fall into the brazed area,an approximation is made to offset the measured points to the prior-to-braze airfoil surface.The desired height of the airfoil leading edge is determined by probing the buttress of the workpiece. To obtain reliable measurement data,the workpiece is positioned to have a normal contact with the sensor probe during each measurement.The sensory displacement readings only give the displacements in the Z axis.In order to obtain the actual coordinates (X,Y,Z)of the measured points, corresponding robot coordinates have to be used for computation in conjunction with displacement readings
Adaptive Robotic System for 3D Profile Grinding/Polishing 63 Decimal (BCD) to a data acquisition board resident in the robot controller. The BCD reading is proportional to the profile sensor displacement. The sensor has a measurement range of 10 mm, resolution of 5 µm, and measurement accuracy of 20 µm. After gripping the part, the robot approaches the measurement probe, as shown in Figure 5. The sensor measures a number of points in specific cross sections that will be used by the Optimal Profile Fitting (OPF) later. In our development, three sections are selected, as shown in Figure 6. Buttress Airfoil (a) (b) Figure 6 (a) Front view of a turbine vane, (b) Side views of Section C-C, E-E and G-G of the vane airfoil. For each sectional profile, five measurement points are taken from the concave side and five from the convex side. When the measurement points fall into the brazed area, an approximation is made to offset the measured points to the prior-to-braze airfoil surface. The desired height of the airfoil leading edge is determined by probing the buttress of the workpiece. To obtain reliable measurement data, the workpiece is positioned to have a normal contact with the sensor probe during each measurement. The sensory displacement readings only give the displacements in the Z axis. In order to obtain the actual coordinates (X, Y, Z) of the measured points, corresponding robot coordinates have to be used for computation in conjunction with displacement readings
64 X O Chen,Z M Gong,H Huang.S Z Ge,and L B Zhou Since the measurement unit is stationary,the profile measurement data is directly given in the global coordinate system,with the Z coordinate being offset by the sensor displacement.For ease of implementation,the profile measurement data have to be transformed from the global coordinate system into the robot hand coordinate system. 3.3 Coordinate Transform Assume that the robot global coordinate system is A:XYZ,and the gripper (local)coordinate system is B:X'Y'Z'.The former is attached to the base of the robot,while the latter is attached to the robot end-effector.The transformations between the global and local coordinate system,as shown in Figure 7,can be readily derived [16]. ·P Z 0 Local Coordinate System B 0 Point O'in A is (x0.y0.z0) Global Coordinate SystemA Point P in A is (x.y.z) in B is (x'y'.z") Figure 7 Coordinate system transformation. Let the coordinates of the point P be (x,y,z)in the global coordinate system,and (x',y',)in the local coordinate system.The origin O'of the local coordinate system B is (xo.yo,zo)in the global coordinate system. Then the coordinate transformation from the global coordinate system to the local coordinate system is: x-x0 =T y-yo (1) z-Z0
64 X Q Chen, Z M Gong, H Huang, S Z Ge, and L B Zhou Since the measurement unit is stationary, the profile measurement data is directly given in the global coordinate system, with the Z coordinate being offset by the sensor displacement. For ease of implementation, the profile measurement data have to be transformed from the global coordinate system into the robot hand coordinate system. 3.3 Coordinate Transform Assume that the robot global coordinate system is A: XYZ, and the gripper (local) coordinate system is B: X’Y’Z’. The former is attached to the base of the robot, while the latter is attached to the robot end-effector. The transformations between the global and local coordinate system, as shown in Figure 7, can be readily derived [16]. O Z X Y O’ X’ Z’ Y’ P Global Coordinate System A Local Coordinate System B Point O’ in A is (x0,y0, z0) Point P in A is (x, y, z) in B is (x’,y’, z’) Figure 7 Coordinate system transformation. Let the coordinates of the point P be (x, y, z) in the global coordinate system, and (x’, y’, z’) in the local coordinate system. The origin O’ of the local coordinate system B is (x0, y0, z0) in the global coordinate system. Then the coordinate transformation from the global coordinate system to the local coordinate system is: − − − = 0 0 0 ' ' ' z z y y x x T z y x (1)