Method for establishing aerospace engine process ring coordinate system

Abstract

The application provides a method for establishing a process ring coordinate system of a space engine, and specifically comprises the following steps: installing a quadrant measuring tool in a quadrant hole of the process ring; sticking mark points around an engine structure, and establishing an engine coordinate system through the mark points; moving a robot to a measuring position, and starting a measuring scan; rotating the engine, and generating a point cloud file of the process ring and the quadrant tool in the engine coordinate system; ending the measuring scan, and returning the robot to an initial position; and fitting the process ring coordinate system through the point cloud file of the process ring and the quadrant tool. The application reduces the use of measuring personnel, reduces the process rhythm, and improves the efficiency.

Description

Technical Field

[0001] This invention belongs to the field of automated inspection, specifically a detection method applicable to the establishment of a process ring coordinate system for large structural components of aerospace engines. Background Technology

[0002] As domestic aerospace companies increasingly emphasize improving product testing efficiency and quality, the automated measurement and coordinate system construction methods for large structural components of aerospace engines have gradually become a hot research topic. The establishment of the coordinate system directly affects the benchmark and accuracy of the measurement of each structural component.

[0003] Appendix Figure 1 The model shown is a simplified version of a large structural component in a certain type of aerospace engine. One task involved establishing a coordinate system was to first measure the top process ring and fit its center position as the origin O of the coordinate system. Then, the quadrant holes a and b on the upper surface of the process ring were measured and their centers fitted as A and B. Next, OA was defined as the x-direction of the coordinate system, OB as the y′-direction, and the direction perpendicular to the x and y′ directions as the z-direction. Finally, the y-direction of coordinate system O was determined using the x and z directions, as shown in the attached diagram. Figure 2 As shown.

[0004] Traditional measurement methods utilize laser trackers. Each inspection requires an operator to use the laser tracker's target ball attachment to track and measure the characteristic positions on the process ring end face at the top of the structural component. Because the structural component is located at the top of the engine and is relatively large, at least one operator needs to climb the lifting platform to collect data on the upper part of the process ring each time. Furthermore, fitting the coordinate system center requires collecting the positions of measurement points around the entire circumference of the upper surface of the process ring, necessitating an operator to drive the lifting platform around the engine. Additionally, another operator on the ground is required to observe the target ball's tracking status and record data. The entire process involves a large amount of manual labor, demands high operator skills, and is inherently dangerous due to the height and operation of the lifting platform. It is also time-consuming and inefficient. Therefore, automated inspection methods are needed to improve measurement efficiency. Summary of the Invention

[0005] To improve the efficiency of establishing the process ring coordinate system for the above-mentioned large structural components, this invention proposes an automated method for establishing the coordinate system of large structural components for aerospace engines.

[0006] The technical solution adopted by this invention to achieve the above objectives is: a method for establishing a coordinate system for aerospace engine process rings, comprising the following steps:

[0007] Install quadrant measuring fixtures in the quadrant holes of the process ring;

[0008] Marker points were affixed around the engine structural components, and the engine coordinate system W was established using a tracking device;

[0009] The robot is controlled to move the scanning head to the measurement position of the engine structural component;

[0010] In the engine coordinate system W, the scanning head is started to scan the process ring on the top of the engine structural component. The upper surface of the process ring passes through the measurement position of the scanning head, generating a point cloud file of the process ring and quadrant measurement fixture.

[0011] The process ring coordinate system O was fitted based on the point cloud file.

[0012] The installation of the quadrant measuring fixture in the quadrant hole of the process ring is specifically as follows:

[0013] Before the process ring is installed on the top of the engine structural component, two quadrant measuring fixtures are inserted into process holes a and b of the process ring, respectively.

[0014] The process hole a and process hole b are located at any position on the upper surface of the process ring;

[0015] The quadrant measurement fixture is in the shape of a stepped shaft. The cross-sectional radius F of the lower cylinder D is the same as the radius of the process hole, and the cross-sectional radius E of the upper cylinder C is greater than the cross-sectional radius F.

[0016] The upper cylindrical sections of the two quadrant measuring fixtures have different radii, and the difference Δ should satisfy: 10mm≥Δ≥5mm.

[0017] The process of attaching markers around the engine structural components specifically involves:

[0018] Multiple markers are attached around the engine structural components, so that the tracking device can observe more than four markers even when the engine structural components are rotated to any angle.

[0019] The establishment of the engine coordinate system W using the tracking device is as follows:

[0020] First, start the tracker to enter the marker recognition mode. Then, rotate the engine structural component one full turn so that more than four markers can enter the tracker's field of view and be observed. Establish a coordinate system W by recognizing the markers fixed around the engine structural component.

[0021] The control robot moves the scanning head to the measurement position of the engine structural component, specifically as follows:

[0022] The robot control system manipulates the robot to move the scanning head to the measurement position and records the position of that point;

[0023] The measurement position ensures that the scanning head does not interfere with the process ring and quadrant measurement fixture during the rotation process, and the distance between the scanning head and the process ring is sufficient to scan the point cloud of the process ring and its quadrant measurement fixture.

[0024] The scanning head measures the position of the upper surface of the process ring around the entire circle. Specifically, the engine structural component is rotated clockwise around the entire circle so that the upper surface of the engine structural component's process ring and the installed quadrant measuring fixture both pass the measurement position of the tracking instrument.

[0025] The process ring coordinate system O, which is fitted based on point cloud files, includes the following steps:

[0026] First, import the point cloud file into the Polyworks software;

[0027] Then, the center position of the process ring is fitted and set as the origin O of the coordinate system. The centers of quadrant holes a and b on the upper surface of the process ring are fitted as A and B, respectively.

[0028] Next, let OA be the x-direction of the coordinate system, OB be the y′-direction of the coordinate system, and let the directions perpendicular to x and y′ be the z-directions of the coordinate system. Finally, determine the y-direction of coordinate system O through the x and z directions.

[0029] The process ring coordinate system O, which is fitted based on point cloud files, includes the following steps:

[0030] (1) Import the theoretical models of the process loop and quadrant tooling into Polyworks software;

[0031] (2) Import the point cloud file into Polyworks software;

[0032] (3) In the theoretical model, firstly, the center position of the process ring is set as the origin O′ of the model process ring coordinate system. Then, the centers of the quadrant holes a′ and b′ on the upper end face of the process ring are set as A′ and B′. Next, OA′ is set as the x direction of the coordinate system and OB′ is set as the y′ direction of the coordinate system. The direction perpendicular to x and y′ is set as the z direction of the coordinate system. Finally, the y direction of the coordinate system O′ is determined by the x and z directions.

[0033] (4) Complete the best matching between the point cloud of the process loop and quadrant tooling and the features of the theoretical model, and achieve the alignment of the point cloud and the theoretical model through the best matching;

[0034] (5) Based on the origin and quadrant hole rules of the theoretical model, fit the origin and quadrant hole features of the actual point cloud: By using the coordinate system setting rules of the theoretical model in step (3), fit the origin O and quadrant hole center A and B of the point cloud process ring coordinate system respectively. Let OA be the x direction of the coordinate system and OB be the y′ direction of the coordinate system respectively. Let the direction perpendicular to x and y′ be the z direction of the coordinate system. Finally, determine the y direction of the coordinate system O through the x and z directions.

[0035] A system for establishing a process ring coordinate system for aerospace engines, including...

[0036] The robot is used to drive the Scan head to execute the measurement trajectory;

[0037] Robot base, used to fix the robot and raise its operating trajectory height;

[0038] The 3D measurement system includes a measuring head and a tracker.

[0039] The measuring head, a scanning head for 3D measurement, is fixed to the end of the robot to scan and generate point cloud files of the process loop and quadrant measurement fixtures;

[0040] The tracker is a binocular vision tracker for 3D measurement, used to identify markers pasted around engine structural components and establish the engine coordinate system W;

[0041] Quadrant measuring fixture, used to measure the position of quadrant holes in the process ring;

[0042] A tray for holding and rotating engine structural components circumferentially;

[0043] The host computer is used to generate the process ring coordinate system O of the feature positions by importing the point cloud files of the process ring and quadrant measurement fixture, and at the same time communicate with the 3D measurement system and the robot control system to complete the interaction of automated measurement data.

[0044] The present invention has the following beneficial effects and advantages:

[0045] 1. The application of this invention can reduce the workload of operators in the process of establishing the coordinate system of a certain type of aerospace engine, reduce the use of measurement personnel, and avoid dangerous factors in the high-altitude measurement process.

[0046] 2. The application of this invention reduces the cycle time of the process and improves efficiency. Attached Figure Description

[0047] Figure 1 A simplified schematic diagram of the coordinate system for the engine's major structural components and process ring.

[0048] Figure 2 A top-view diagram showing the establishment of the coordinate system for the process ring.

[0049] Figure 3 Schematic diagram of process loop quadrant measurement fixture.

[0050] Figure 4 A diagram showing the location of the hardware platform.

[0051] Figure 5 A schematic diagram of data interaction between the host computer system and the host computer system. Detailed Implementation

[0052] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0053] The present invention includes an industrial robot, a base for fixing the robot, a 3D measurement system, a tray for placing and rotating the engine, two tooling fixtures for measuring quadrant holes, a Polyworks software for fitting spatial position features, a host computer for data interaction, and several marker points that can be pasted onto the surface of the engine structural components.

[0054] Industrial robots are used to drive the Scan head to execute measurement trajectories;

[0055] Robot base, used to fix the robot and raise its operating trajectory height;

[0056] The 3D measurement system includes a scanning head and a visual tracking track.

[0057] Scan is a 3D measurement scanning head that is fixed to the end of a robot to scan and generate point cloud files of process loops and quadrant tooling.

[0058] Track is a binocular vision tracker for 3D measurement, used to identify markers pasted around structural components and establish the engine coordinate system;

[0059] Quadrant measurement fixture, as attached Figure 3 As shown, this is used to measure the position of the quadrant hole in the process ring;

[0060] A tray for holding and rotating the engine around its circumference;

[0061] Marker points are affixed around the engine structural components to establish the engine coordinate system;

[0062] Polyworks software generates a process ring coordinate system for feature locations by importing point cloud files of process rings and quadrant tooling.

[0063] The host computer, as attached Figure 5 As shown, the Polyworks software is running and can communicate with both the 3D measurement system and the robot control system simultaneously to complete the exchange of automated measurement data.

[0064] A method applicable to establishing a coordinate system for aerospace engine process rings includes the following steps:

[0065] 1) Install quadrant measuring fixtures in the quadrant holes of the process ring;

[0066] 2) Affix markers around the engine structural components;

[0067] 3) Establish the engine coordinate system W using Track;

[0068] 4) Move the robot to the measurement location;

[0069] 5) Start Scan to begin scanning;

[0070] 6) Allow the upper surface of the engine process ring to pass through the Scan position;

[0071] 7) Generate point cloud files for the process loop and quadrant tooling;

[0072] 8) The robot returns to its initial position;

[0073] 9) Fit the process loop coordinate system O using Polyworks.

[0074] In step 1, the quadrant measuring fixture is installed on the process ring. Specifically, before the process ring is installed on top of the engine's main structural component (the process ring and its support are on the ground), the following... Figure 3 The tooling in the two quadrants is inserted as shown in the attached figure. Figure 2 In quadrant holes a and b of the process ring shown;

[0075] In step 1, in order to make the attached Figure 3 Quadrant tooling can be installed on the attached Figure 2 In the quadrant hole of the process ring, the cross-sectional radius F of the lower half of the cylindrical part D of the quadrant tooling should be the same as the radius of the process hole.

[0076] In step 2, mark points around the engine structural components, as shown in the attached diagram. Figure 4 Markers are placed around the engine position shown, so that when the engine is rotated to any angle, the Track can observe more than 4 markers.

[0077] In step 3, before establishing the engine coordinate system W, adjust the position and height of the Track so that its field of view allows observation of both the tooling in the top quadrant of the process ring and all the markers pasted around the engine in step 2, as shown in the attached diagram. Figure 4 As shown;

[0078] In step 3, the specific method for establishing the engine coordinate system W through Track is as follows: First, start Track to enter the marker point recognition mode, and then slowly rotate the engine one revolution so that all the marker points pasted in step 2 can enter the Track's field of view and be observed by it. The coordinate system W is established by recognizing and recording the marker points fixed around the engine.

[0079] In step 4, the robot is moved to the measurement position. Specifically, the robot control system moves the scanning head (Scan) to the measurement position (as shown in the attached diagram). Figure 4 (As shown), and record the location of that point in the system;

[0080] In step 4, when the robot measures the position, it should be confirmed that the Scan head does not interfere with the process ring and quadrant tooling of the engine during rotation, and that the distance between the Scan and the process ring can scan the point cloud of the process ring and its quadrant tooling.

[0081] In step 4, when the robot measures its position, it should also confirm that Scan is within the field of view observed by Track;

[0082] In step 4, the robot should be fixed on the base to raise its running trajectory height so that the measuring head Scan can scan the process ring and its quadrant tooling at the top of the engine structural component.

[0083] In step 5, Scan is started to begin scanning. Specifically, under the engine coordinate system W established in step 3, the 3D measurement system start signal is triggered, so that the laser beam of Scan is projected onto the upper surface of the process ring.

[0084] In step 6, the upper surface of the process ring passes through the Scan position. The specific method is to slowly rotate the engine one revolution clockwise so that the upper surface of the engine process ring and the quadrant tooling installed in step 1 pass through the Scan position.

[0085] In step 7, point cloud files of the process ring and quadrant tooling are generated. The specific method is as follows: stop the rotating engine, trigger the stop signal of the 3D measurement system, generate the point cloud of the scanning process ring and quadrant tooling, and save it as a file.

[0086] In step 8, the robot returns to its initial position. Specifically, the robot control system controls the robot to move the scanning head Scan to the initial position.

[0087] In step 9, the process ring coordinate system O is fitted using Polyworks. The specific method is as follows: First, import the point cloud file generated in step 7 into Polyworks software. Then, fit the center position of the process ring and set it as the origin O of the coordinate system. Next, fit the centers of quadrant holes a and b on the upper surface of the process ring as A and B respectively. Then, set OA as the x-direction of the coordinate system, OB as the y′-direction of the coordinate system, and the direction perpendicular to the x and y′ directions as the z-direction of the coordinate system. Finally, determine the y-direction of coordinate system O using the x and z directions, as shown in the attached figure. Figure 2 As shown.

[0088] In step 9, to distinguish the x and y directions of the coordinate system O, the two quadrant fixtures installed in step 1 (as shown in the attached diagram) are used. Figure 3 The diameter E of the upper cylindrical section C (as shown) should be different, and the difference Δ should satisfy: 10mm ≥ Δ ≥ 5mm

[0089] A method for establishing a coordinate system for aerospace engine manufacturing processes, employing a hardware platform such as... Figure 4 As shown. The robot is fixed to its base. A 3D measurement system's scanning head (Scan) is attached to the robot's end effector. The large structural component of the engine is placed on a rotatable tray. Quadrant inspection fixtures are inserted into the two quadrant holes of the engine structural component's process ring. Several markers that can be recognized by the measurement system are affixed around the large engine structure, ensuring that the vision tracker (Track) can observe at least four markers at any position the engine rotates to. Before starting the measurement, the robot moves the scanning head (Scan) to the measurement position. The positioning of the vision tracker (Track) should be such that it can observe the scanning head (Scan) at the measurement position within its field of view, and also observe the markers on the engine structural component.

[0090] Includes the following steps:

[0091] 1) Install quadrant measuring fixtures in the quadrant holes of the process ring. Specifically, before the process ring is installed to the top of the engine's major structural components, insert the quadrant fixtures into the quadrant holes a and b at the upper end of the process ring.

[0092] 2) Attach markers around the engine structural components. Specifically, attach a certain number of markers at corresponding positions around the engine so that when the engine is rotated to any angle, more than 4 markers can be observed within the field of view of the track.

[0093] 3) The method for establishing the engine coordinate system W using Track is as follows:

[0094] (1) Switch the 3D measurement system to marker recognition mode.

[0095] (2) Slowly rotate the engine one revolution so that Track can recognize and record all the markers pasted on the structural components.

[0096] (3) In the measurement system, the engine coordinate system W is established through these recorded marker points.

[0097] 4) The process of the mobile robot moving to the measurement position is as follows:

[0098] (1) The robot is controlled by the teach pendant to move the Scan head to a position close to the process ring.

[0099] (2) Slowly rotate the engine one revolution to confirm that the Scan head does not interfere with the process ring and quadrant tooling of the engine during the rotation process; otherwise, adjust the robot's pose.

[0100] (3) Switch the measurement system to the marker recognition mode and observe whether the scanning head Scan is within its field of view through Track. Otherwise, adjust the robot's pose.

[0101] (4) Trigger the measurement system start signal and check whether the laser beam of Scan is fully projected onto the upper surface of the process ring; otherwise, adjust the robot's pose.

[0102] (5) Record the robot pose at the final adjusted measurement position in the robot system.

[0103] 5) The process of starting Scan is as follows:

[0104] (1) Switch the measurement system to scanning measurement mode.

[0105] (2) Import the established engine coordinate system W into the measurement system.

[0106] (3) Trigger the start signal of the measurement system.

[0107] 6) The upper surface of the process ring passes through the Scan scanning position. Specifically, the engine is slowly rotated clockwise for one revolution so that the upper surface of the engine process ring and the quadrant tooling pass through the position projected by the Scan laser beam.

[0108] 7) The process of generating the point cloud files for the process loop and quadrant tooling is as follows:

[0109] (1) Check the point cloud effect formed by the measurement system in step 6.

[0110] (2) If the point cloud on the upper surface of the process ring is missing, repeat step 6.

[0111] (3) If the point cloud on the surface of the quadrant tool is missing, repeat step 6.

[0112] (4) Trigger the stop signal of the measurement system and save the point cloud files of the measurement process loop and quadrant tooling.

[0113] 8) The robot returns to its initial position by using a robot teach pendant to control the robot and move the Scan head to the initial position.

[0114] 9) The specific process of fitting the process loop coordinate system using Polyworks is as follows:

[0115] (1) Import the theoretical models of the process loop and quadrant tooling into Polyworks software.

[0116] (2) Import the point cloud file generated in step 7 into the Polyworks software.

[0117] (3) In the theoretical model, firstly, the center position of the process ring is set as the origin O′ of the model process ring coordinate system. Then, the centers of the quadrant holes a′ and b′ on the upper end face of the process ring are set as A′ and B′, respectively. Next, OA′ is set as the x direction of the coordinate system and OB′ is set as the y′ direction of the coordinate system. The direction perpendicular to x and y′ is set as the z direction of the coordinate system. Finally, the y direction of the coordinate system O′ is determined by the x and z directions.

[0118] (4) Complete the best matching between the point cloud of the process loop and quadrant tooling and the features of the theoretical model, and achieve the alignment of the point cloud and the theoretical model through the best matching.

[0119] (5) Based on the origin and quadrant hole rules of the theoretical model, fit the origin and quadrant hole features of the actual point cloud: by setting the coordinate system of the theoretical model in step (3), fit the origin O and quadrant hole center A and B of the point cloud process ring coordinate system respectively, then determine the x direction and y′ direction of the coordinate system, then determine the z direction of the coordinate system O, and finally determine the y direction of the coordinate system O.

Claims

1. A method for establishing a coordinate system for aerospace engine process rings, characterized in that, Includes the following steps: Install quadrant measuring fixtures in the quadrant holes of the process ring; Marking points were affixed around the engine structural components, and the engine coordinate system W was established using a tracking device; The robot is controlled to move the scanning head to the measurement position of the engine structural component; In the engine coordinate system W, the scanning head is started to scan the process ring on the top of the engine structural component. The upper surface of the process ring passes through the measurement position of the scanning head, generating a point cloud file of the process ring and quadrant measurement fixture. The process ring coordinate system O was fitted based on the point cloud file.

2. The method for establishing a coordinate system for aerospace engine process rings according to claim 1, characterized in that, The installation of the quadrant measuring fixture in the quadrant hole of the process ring is specifically as follows: Before the process ring is installed on the top of the engine structural component, two quadrant measuring fixtures are inserted into process holes a and b of the process ring, respectively. The process hole a and process hole b are located at any position on the upper surface of the process ring; The quadrant measurement fixture is in the shape of a stepped shaft. The cross-sectional radius F of the lower cylinder D is the same as the radius of the process hole, and the cross-sectional radius E of the upper cylinder C is greater than the cross-sectional radius F. The upper cylindrical sections of the two quadrant measuring fixtures have different radii, and the difference Δ should satisfy: 10mm≥Δ≥5mm.

3. The method for establishing a coordinate system for aerospace engine process rings according to claim 1, characterized in that, The process of attaching markers around the engine structural components specifically involves: Multiple markers are attached around the engine structural components, so that the tracking device can observe more than four markers even when the engine structural components are rotated to any angle.

4. The method for establishing a coordinate system for aerospace engine process rings according to claim 1, characterized in that, The establishment of the engine coordinate system W using the tracking device is as follows: First, start the tracker to enter the marker recognition mode. Then, rotate the engine structural component one full turn so that more than four markers can enter the tracker's field of view and be observed. Establish a coordinate system W by recognizing the markers fixed around the engine structural component.

5. The method for establishing a coordinate system for aerospace engine process rings according to claim 1, characterized in that, The control robot moves the scanning head to the measurement position of the engine structural component, specifically as follows: The robot control system manipulates the robot to move the scanning head to the measurement position and records the position of that point; The measurement position ensures that the scanning head does not interfere with the process ring and quadrant measurement fixture during the rotation process, and the distance between the scanning head and the process ring is sufficient to scan the point cloud of the process ring and its quadrant measurement fixture.

6. The method for establishing a coordinate system for aerospace engine process rings according to claim 1, characterized in that, The scanning head measures the position of the upper surface of the process ring around the entire circle. Specifically, the engine structural component is rotated clockwise around the entire circle so that the upper surface of the engine structural component's process ring and the installed quadrant measuring fixture both pass the measurement position of the tracking instrument.

7. The method for establishing a coordinate system for aerospace engine process rings according to claim 1, characterized in that, The process ring coordinate system O, which is fitted based on point cloud files, includes the following steps: First, import the point cloud file into the Polyworks software; Then, the center position of the process ring is fitted and set as the origin O of the coordinate system. The centers of quadrant holes a and b on the upper surface of the process ring are fitted as A and B, respectively. Next, let OA be the x-direction of the coordinate system, OB be the y′-direction of the coordinate system, and let the directions perpendicular to x and y′ be the z-directions of the coordinate system. Finally, determine the y-direction of coordinate system O through the x and z directions.

8. A method for establishing a coordinate system for aerospace engine process rings according to claim 1 or 7, characterized in that, The process ring coordinate system O, which is fitted based on point cloud files, includes the following steps: (1) Import the theoretical models of the process loop and quadrant tooling into Polyworks software; (2) Import the point cloud file into Polyworks software; (3) In the theoretical model, firstly, the center position of the process ring is set as the origin O′ of the model process ring coordinate system. Then, the centers of the quadrant holes a′ and b′ on the upper end face of the process ring are set as A′ and B′. Next, OA′ is set as the x direction of the coordinate system and OB′ is set as the y′ direction of the coordinate system. The direction perpendicular to x and y′ is set as the z direction of the coordinate system. Finally, the y direction of the coordinate system O′ is determined by the x and z directions. (4) Complete the best matching between the point cloud of the process loop and quadrant tooling and the features of the theoretical model, and achieve the alignment of the point cloud and the theoretical model through the best matching; (5) Based on the origin and quadrant hole rules of the theoretical model, fit the origin and quadrant hole features of the actual point cloud: By using the coordinate system setting rules of the theoretical model in step (3), fit the origin O and quadrant hole center A and B of the point cloud process ring coordinate system respectively. Let OA be the x direction of the coordinate system and OB be the y′ direction of the coordinate system respectively. Let the direction perpendicular to x and y′ be the z direction of the coordinate system. Finally, determine the y direction of the coordinate system O through the x and z directions.

9. A system for establishing a coordinate system for aerospace engine process rings, characterized in that, include The robot is used to drive the Scan head to execute the measurement trajectory; Robot base, used to fix the robot and raise its operating trajectory height; The 3D measurement system includes a measuring head and a tracker. The measuring head, a scanning head for 3D measurement, is fixed to the end of the robot to scan and generate point cloud files of the process loop and quadrant measurement fixtures; The tracker is a binocular vision tracker for 3D measurement, used to identify markers pasted around engine structural components and establish the engine coordinate system W; Quadrant measuring fixture, used to measure the position of quadrant holes in the process ring; A tray for holding and rotating engine structural components circumferentially; The host computer is used to generate the process ring coordinate system O of the feature positions by importing the point cloud files of the process ring and quadrant measurement fixture, and at the same time communicate with the 3D measurement system and the robot control system to complete the interaction of automated measurement data.

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