Coaxiality automatic detection equipment and detection method thereof

Abstract

The invention discloses coaxiality automatic detection equipment and a detection method thereof, and a support used for workpiece coaxiality detection, the coaxiality automatic detection equipment comprises an adjusting fixing frame arranged on the support, and the adjusting fixing frame is provided with two detection stations; the two visual detection systems are used for shooting workpiece images and comprise ICCD (Intensified Charge Coupled Device) cameras, telecentric lenses and light source mechanisms, the ICCD cameras are arranged on the adjusting fixing frame and are in one-to-one correspondence with the detection stations, the telecentric lenses are arranged at the bottoms of the ICCD cameras, and the light source mechanisms are arranged at the bottoms of the telecentric lenses; the ICCD camera is used for detecting the circumference of the small hole; the telecentric lens is used for keeping the image magnification constant when the ICCD camera detects that the object distance changes; the light source mechanism is used for providing a light source for workpiece detection; and the rotating mechanisms are arranged on the adjusting fixing frame, correspond to the detection stations one by one and are used for driving the workpieces to rotate. According to the invention, the mode of combining deep learning with visual detection is realized, manual operation is replaced, and the production efficiency is improved.

Description

Technical Field

[0001] This invention relates to the field of automatic coaxiality detection technology, and in particular to an automatic coaxiality detection device and its detection method. Background Technology

[0002] Coaxiality measurement is a detection method for controlling the coaxiality error between the measured axis and the reference axis of shaft parts. The error is manifested as the offset of the cross-sectional center, bending or tilting of the axis.

[0003] Currently, in the process of coaxiality testing of special components, operators need to hold a special inspection tool and insert a probe into the small hole of the guide ring. The contact between the probe and the guide ring is determined by whether the circuit on the special inspection tool is conductive, thereby determining whether the coaxiality between the small hole on the guide ring and the largest outer circle of the special component is within the acceptable range. However, there are still the following shortcomings: since this component is only used in national special equipment, the radius difference between the largest outer circle and the second largest outer circle is extremely small, and the circumference of the largest outer circle cannot be obtained by visual inspection. Moreover, there is no device on the market that can be directly used to test the coaxiality between the small hole and the largest outer circle. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings mentioned above by providing an automatic coaxiality detection device and method that uses deep learning combined with visual inspection to replace manual operation and improve production efficiency.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution: an automatic coaxiality detection device and its detection method, comprising a support for detecting the coaxiality of a workpiece, including: An adjustable fixing frame is mounted on a support, and the adjustable fixing frame has two testing stations. The vision inspection system consists of two units, used to capture images of the workpiece, including: an ICCD camera mounted on an adjustment frame and corresponding to each inspection station, a telecentric lens mounted at the bottom of the ICCD camera, and a light source mechanism mounted at the bottom of the telecentric lens; The ICCD camera is used to detect the circumference of a pinhole; The telecentric lens is used by the ICCD camera to detect that the image magnification remains constant when the object distance changes; The light source mechanism is used to provide a light source for workpiece inspection; The rotating mechanism is mounted on the adjusting and fixed frame and corresponds to each inspection station to drive the workpiece to rotate. The lifting mechanism is mounted on the support and corresponds to each inspection station to drive the workpiece to the inspection station. The side-pushing mechanism is used to push the workpiece to center and clamp it, including a telescopic component set on the adjusting fixed frame, a fixed block set on the telescopic end of the telescopic component, and bidirectional clamping components symmetrically set on the fixed block.

[0006] Furthermore, the rotating mechanism includes a drive unit mounted on the adjusting frame and a drive gear mounted on the output shaft of the drive unit; It also includes a driven gear ring mounted on the adjustment fixture and facing the testing station, the driven gear ring meshing with the driving gear.

[0007] Furthermore, the bidirectional clamping member includes traction rods symmetrically arranged on the fixed block and slide rods arranged on the adjusting fixed frame; It also includes a sliding sleeve symmetrically arranged on the slide rod and a clamping block arranged on the sliding sleeve for clamping the workpiece, wherein the end of the slide rod is slidably connected to the sliding sleeve.

[0008] The detection method of the coaxiality automatic detection equipment includes the following steps: S1. The lifting mechanism lifts the workpiece to the inspection position of the adjusting and fixing frame. The telescopic part on the side push mechanism drives the fixing block to move. The traction rod on the fixing block drives the clamping block on the sliding sleeve to clamp the workpiece in the center. The traction rod rotates on the sliding sleeve and the fixing block, and the sliding sleeve slides on the sliding rod to clamp the workpiece, triggering the photo-taking command.

[0009] S2. Start the inspection process. The ICCD camera, telecentric lens and light source mechanism on the vision inspection system take the first image of the workpiece.

[0010] S3. Repeat steps 1 and 2 to take the second, third, and fourth images of the workpiece in sequence.

[0011] S4. A quadruple edge detection strategy is adopted to improve robustness. By using a learning network model and automatic detection, the true center coordinates and radius of the circle are finally determined. S5. After each rotation of the workpiece and before image acquisition, the side push mechanism of the detection station clamps the maximum outer circle of the workpiece on the bidirectional clamping part. Therefore, it is assumed that the rotation center of the entire component, including the guide ring, is the center of the maximum outer circle. Therefore, the algorithm uses the least squares method to refit the four sets of detected hole center data onto a new small circle, and uses the center of this circle as the center of the maximum outer circle of the damper. S6. By using the center position of the workpiece center hole in the four images, the system software model fits the maximum outer circle center of the minimum boundary and calculates the maximum center distance with the center of the four workpiece center holes, thereby determining whether the coaxiality is qualified.

[0012] Furthermore, the process of using a learning network model and automatic detection to obtain the edge region of the small hole includes the following steps: a) Gaussian blur + subtract from original image and then add back to original image + Canny edge detection; b. Bilateral filtering + Canny edge detection; c. Use an edge-enhancing convolution kernel + Canny edge detection; d. Original image + Canny edge detection; e. Obtain 4 sets of edges. Based on the fact that the actual hole is circular and the radius of the edge is a fixed value, select the correct edges from the 4 sets. Based on multiple sets of edges, use the least squares method to fit multiple circle centers and radii. Use the DBSCAN algorithm to cluster and find outliers, and finally determine the true circle center coordinates and radius.

[0013] Furthermore, the least squares formula is as follows: ; Where (x) i y i e represents the coordinates of each point on the edge. i The algebraic error for each point on the edge is not the geometric distance from the point to the center of the circle, but rather the residual produced after linearizing the original equation of the circle. B and C are twice the coordinates of the center a and b, respectively, and D is a constant term containing the center and radius of the circle, D=r. 2 -a 2 -b 2 S is the sum of squared algebraic errors of all points. By finding the minimum sum of squared errors, we can find the best fitting parameters (B, C, D), and then obtain the coordinates of the center (a, b) and the radius r.

[0014] Furthermore, the standard equation of the circle is: ; Where (x) m y n (m, n) represents the coordinates of the outer circle center of the damper opening obtained visually, (m, n) represents the center of the maximum outer circle, and r represents the radius of the maximum outer circle. During the rotation, the center of the outer circle of the damper opening rotates around the center of the maximum outer circle, and the circle it fits is concentric with the maximum outer circle.

[0015] The beneficial effects of this invention are reflected in: 1. This invention uses a lifting mechanism to raise the workpiece to the inspection station of the adjusting and fixing frame. The telescopic component on the side-pushing mechanism moves the fixing block, and the traction rod on the fixing block drives the clamping block on the sliding sleeve to center and clamp the workpiece. The traction rod rotates on the sliding sleeve and the fixing block, and the sliding sleeve slides on the traction rod to clamp the workpiece, triggering a photographing command and starting the inspection process. The ICCD camera, telecentric lens, and light source mechanism on the vision inspection system capture the first image of the workpiece. Steps 1 and 2 are repeated to capture the second, third, and fourth images of the workpiece sequentially. A four-fold edge detection strategy is used to improve robustness. A learning network model and automatic detection are used to find the edge region of the small hole. The invention includes the following steps: a) Gaussian blur + subtract from original image and then add back to original image + Canny edge detection; b. Bilateral filtering + Canny edge detection; c. Use an edge-enhancing convolution kernel + Canny edge detection; d. Original image + Canny edge detection; e. Obtain 4 sets of edges. Based on the fact that the actual hole is circular and the radius of the edge is a fixed value, select the correct edges from the 4 sets. Based on multiple sets of edges, use the least squares method to fit multiple circle centers and radii. Cluster according to the DBSCAN algorithm and find outliers. Finally, determine the true circle center coordinates and radius. After each rotation of the workpiece and before image acquisition, the side push mechanism of the detection station clamps the maximum outer circle of the workpiece on the bidirectional clamping part. Therefore, it is considered that the rotation center of the entire component, including the guide ring, is the center of the maximum outer circle. Therefore, the algorithm uses the least squares method to refit the 4 sets of detected small hole center data onto a new small circle. The center of this circle is used as the center of the maximum outer circle of the damper, thereby improving the detection efficiency. The detection cycle is reduced from 15 seconds per piece manually to 8 seconds per piece. A non-contact detection method is adopted to eliminate the risk of clamping or scratching the workpiece.

[0016] 2. In this invention, by using the center position of the copper ring's central hole in four images, the system software model fits the maximum outer circle center of the minimum boundary and calculates the maximum center distance with the center of the four copper ring's central holes, thereby determining whether the coaxiality is qualified.

[0017] 3. This invention, when the maximum outer circle of the smallest boundary cannot be effectively obtained through visual inspection, rotates the workpiece multiple times to actually fit the coordinates of the outer circle center, and then obtains the coaxiality. This avoids the influence of deviations in the outer circle inspection on the inspection results, realizes the automatic detection of the coaxiality between the small hole and the outer circle of the smallest boundary, improves production efficiency, and reduces the labor intensity of personnel. Attached Figure Description

[0018] Figure 1 This is a three-dimensional structural view of the present invention; Figure 2 This is another perspective view of the three-dimensional structure of the present invention; Figure 3 This is a front view of the present invention; Figure 4 This is a three-dimensional structural view of the rotating mechanism and the side-pushing mechanism of the present invention; Figure 5 This is a three-dimensional structural view of the side-pushing mechanism of the present invention; Figure 6 This is a flowchart of the automatic detection process of the present invention; Figure 7 This is a diagram showing the distal position detection of the small hole in this invention; Figure 8 This is a schematic diagram showing the relationship between the center of the small hole and the center of the outer circle of the minimum boundary during the rotation process of the present invention.

[0019] In the picture: 1. ICCD camera; 2. Telecentric lens; 3. Light source mechanism; 4. Rotating mechanism; 41. Drive unit; 42. Driving gear; 43. Driven gear ring; 5. Side pushing mechanism; 51. Telescopic component; 52. Fixing block; 53. Traction rod; 54. Sliding sleeve; 55. Sliding rod; 56. Clamping block; 6. Lifting mechanism; 7. Adjust the fixing bracket. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Unless otherwise specified, the embodiments and features in the embodiments of this application can be combined with each other. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] Please see Figure 1-8 This invention discloses an automatic coaxiality detection device and method, and a bracket for detecting the coaxiality of workpieces, characterized in that it comprises: The adjusting bracket 7 is set on the support and has two testing stations. The adjusting bracket 7 is fixed to the support by bolts. The visual inspection system consists of two units, used to capture images of workpieces. Each unit includes: an ICCD camera 1 mounted on an adjusting frame 7 and corresponding to a specific inspection station; a telecentric lens 2 mounted at the bottom of the ICCD camera 1; and a light source mechanism 3 mounted at the bottom of the telecentric lens 2. The adjusting frame 7 and the ICCD camera 1 are fixedly mounted with bolts. The ICCD camera 1 is connected to the telecentric lens 2. The ICCD camera 1 is an enhanced charge-coupled device camera, a high-sensitivity imaging device combining an image intensifier and a CCD sensor, primarily used for imaging in low light, extremely low light, or fast-moving scenes. The light source mechanism 3 is fixedly mounted to the telecentric lens 2 with bolts. ICCD camera 1 is used for detecting the circumference of a pinhole; The telecentric lens 2 is used by the ICCD camera 1 to detect that the image magnification remains constant when the object distance changes; Light source mechanism 3 is used to provide a light source for workpiece inspection; The rotating mechanism 4 is mounted on the adjusting and fixing frame 7 and corresponds to each inspection station to drive the workpiece to rotate. The lifting mechanism 6 is mounted on the support and corresponds to each inspection station. It is used to drive the workpiece to the inspection station. The lifting mechanism 6 is a lifting rod or an electric push rod. The side-pushing mechanism 5 is used to push the workpiece to center and clamp it. It includes a telescopic member 51 set on the adjusting fixed frame 7, a fixed block 52 set on the telescopic end of the telescopic member 51, and bidirectional clamping members symmetrically set on the fixed block 52. The telescopic member 51 is fixedly installed to the adjusting fixed frame 7 by bolts. The telescopic member 51 is an electric push rod. The fixed block 52 is fixedly installed to the telescopic end of the telescopic member 51 by bolts.

[0022] In use, the lifting mechanism 6 lifts the workpiece to the inspection position of the adjusting and fixing frame 7. The rotating mechanism 4 drives the workpiece to rotate. Then, the telescopic part 51 on the side pushing mechanism 5 drives the fixing block 52 to slide on the adjusting and fixing frame 7. The fixing block 52 drives the bidirectional clamping part to clamp the workpiece. Then, the ICCD camera 1, the telecentric lens 2 and the light source mechanism 3 inspect the workpiece.

[0023] In a specific embodiment, the rotating mechanism 4 includes a drive unit 41 disposed on the adjusting fixed frame 7 and a drive gear 42 disposed on the output shaft of the drive unit 41. The drive unit 41 is a servo motor. The drive unit 41 and the drive gear 42 are fixedly installed by bolts and flanges. The drive unit 41 is used to drive the drive gear 42 to rotate. It also includes a driven gear ring 43 set on the adjustment fixture 7 and facing the inspection station. The driven gear ring 43 meshes with the driving gear 42 and is rotatably connected to the adjustment fixture 7. The driving gear 42 is used to drive the driven gear ring 43 to rotate. The inner side of the driven gear ring 43 is used to install the workpiece, and the driven gear ring 43 is used to drive the workpiece to rotate.

[0024] In one embodiment, the bidirectional clamping member includes a traction rod 53 symmetrically arranged on the fixing block 52 and a slide rod 55 arranged on the adjusting fixing frame 7. The fixing block 52 is rotatably connected to the traction rod 53, and the adjusting fixing frame 7 is fixedly installed to the slide rod 55 by bolts. It also includes sliding sleeves 54 symmetrically arranged on the sliding rod 55 and clamping blocks 56 arranged on the sliding sleeves 54 for clamping the workpiece. The end of the sliding rod 55 is slidably connected to the sliding sleeve 54. There are two sliding sleeves 54.

[0025] The detection method of the coaxiality automatic detection equipment includes the following steps: S1. The lifting mechanism 6 lifts the workpiece to the inspection position of the adjusting and fixing frame 7. The telescopic part 51 on the side pushing mechanism 5 drives the fixing block 52 to move. The traction rod 53 on the fixing block 52 drives the clamping block 56 on the sliding sleeve 54 to clamp the workpiece in the center. The traction rod 53 rotates on the sliding sleeve 53 and the fixing block 52. The sliding sleeve 53 slides on the sliding rod 55 to clamp the workpiece and trigger the photo taking command.

[0026] S2. Start the inspection process. The ICCD camera 1, telecentric lens 2 and light source mechanism 3 on the vision inspection system take the first image of the workpiece.

[0027] S3. Repeat steps 1 and 2 to take the second, third, and fourth images of the workpiece in sequence.

[0028] S4. A quadruple edge detection strategy is adopted to improve robustness. By using a learning network model and automatic detection, the true center coordinates and radius of the circle are finally determined. S5. After each rotation of the workpiece and before image acquisition, the side-pushing mechanism 5 of the detection station clamps the maximum outer circle of the workpiece on the bidirectional clamping part. Therefore, it is assumed that the rotation center of the entire component, including the guide ring, is the center of the maximum outer circle. Thus, the algorithm uses the least squares method to refit the four sets of detected hole center data onto a new small circle, and uses the center of this circle as the center of the maximum outer circle of the damper. S6. By using the center position of the workpiece center hole in the four images, the system software model fits the maximum outer circle center of the minimum boundary and calculates the maximum center distance with the center of the four workpiece center holes, thereby determining whether the coaxiality is qualified.

[0029] In one embodiment, the edge region of the small hole is obtained by using a learned network model and automatic detection, including the following steps: a) Gaussian blur + subtract from original image and then add back to original image + Canny edge detection; b. Bilateral filtering + Canny edge detection; c. Use an edge-enhancing convolution kernel + Canny edge detection; d. Original image + Canny edge detection; e. Obtain 4 sets of edges. Based on the fact that the actual hole is circular and the radius of the edge is a fixed value, select the correct edges from the 4 sets. Based on multiple sets of edges, use the least squares method to fit multiple circle centers and radii. Cluster according to the DBSCAN algorithm and find outliers. Finally, determine the true circle center coordinates and radius. The DBSCAN algorithm is a density-based clustering algorithm.

[0030] In a specific embodiment, the least squares formula is: ; Where (x) i y i e represents the coordinates of each point on the edge. i The algebraic error of each point on the edge is not the geometric distance from the point to the center of the circle, but the residual generated after linearizing the original equation of the circle. B and C are twice the coordinates of the center a and b, respectively. D is a constant term including the center and radius of the circle, D = r² - a² - b². S is the sum of squared algebraic errors of all points. By finding the minimum sum of squared errors, the best fitting parameters (B, C, D) can be found, and then the coordinates of the center (a, b) and the radius r can be obtained.

[0031] In one embodiment, the standard equation of a circle is: ; Where (x) m y n (m, n) represents the coordinates of the outer circle center of the damper opening obtained visually, (m, n) represents the center of the maximum outer circle, and r represents the radius of the maximum outer circle. During the rotation, the center of the outer circle of the damper opening rotates around the center of the maximum outer circle, and the circle it fits is concentric with the maximum outer circle.

[0032] It should be noted that if the embodiments of the present invention involve directional indicators (such as up, down, left, right, front, back, etc.), the directional indicators are only used to explain the relative positional relationship and movement of the components in a certain specific posture (as shown in the figure). If the specific posture changes, the directional indicators will also change accordingly.

[0033] Furthermore, if the embodiments of this invention involve descriptions such as "first" or "second," these descriptions are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined with "first" or "second" may explicitly or implicitly include at least one of those features. Additionally, the technical solutions of the various embodiments can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. If the combination of technical solutions is contradictory or impossible to implement, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by this invention.

[0034] Additionally, "multiple" refers to two or more.

[0035] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An automatic coaxiality detection device, comprising a support for detecting the coaxiality of a workpiece, characterized in that, include: An adjustment fixing frame (7) is set on a support, and two testing stations are provided on the adjustment fixing frame (7); The visual inspection system consists of two units, used to capture images of the workpiece, including: an ICCD camera (1) set on the adjustment fixture (7) and corresponding to the inspection station, a telecentric lens (2) set at the bottom of the ICCD camera (1), and a light source mechanism (3) set at the bottom of the telecentric lens (2). The ICCD camera (1) is used to detect the circumference of the pinhole; The telecentric lens (2) is used by the ICCD camera (1) to detect that the image magnification remains constant when the object distance changes; The light source mechanism (3) is used to provide a light source for workpiece inspection; The rotating mechanism (4) is set on the adjusting fixed frame (7) and corresponds to the detection station one by one, and is used to drive the workpiece to rotate; The lifting mechanism (6) is set on the support and corresponds to the inspection station one by one, and is used to drive the workpiece to move to the inspection station; The side-pushing mechanism (5) is used to push the workpiece to center and clamp it, including a telescopic member (51) set on the adjusting fixed frame (7), a fixed block (52) set on the telescopic end of the telescopic member (51), and a bidirectional clamping member symmetrically set on the fixed block (52).

2. The coaxiality automatic detection device according to claim 1, characterized in that: The rotating mechanism (4) includes a drive unit (41) mounted on the adjusting frame (7) and a drive gear (42) mounted on the output shaft of the drive unit (41). It also includes a driven gear ring (43) mounted on the adjustment fixture (7) and facing the testing station, the driven gear ring (43) meshing with the driving gear (42).

3. The coaxiality automatic detection device according to claim 1, characterized in that: The bidirectional clamping component includes a traction rod (53) symmetrically arranged on the fixed block (52) and a slide rod (55) arranged on the adjusting fixed frame (7). It also includes a sliding sleeve (54) symmetrically arranged on the sliding rod (55) and a clamping block (56) arranged on the sliding sleeve (54) for clamping the workpiece, wherein the end of the sliding rod (55) is slidably connected to the sliding sleeve (54).

4. The detection method of the coaxiality automatic detection device according to any one of claims 1-3, characterized in that: Includes the following steps: S1. The lifting mechanism (6) drives the workpiece to the inspection position of the adjusting fixed frame (7). The telescopic part (51) on the side push mechanism (5) drives the fixed block (52) to move. The traction rod (53) on the fixed block (52) drives the clamping block (56) on the sliding sleeve (54) to clamp the workpiece in the center. The traction rod (53) rotates on the sliding sleeve (53) and the fixed block (52). The sliding sleeve (53) slides on the sliding rod (55) to clamp the workpiece and trigger the photo taking command. S2. Start the inspection process. The ICCD camera (1), telecentric lens (2) and light source mechanism (3) on the vision inspection system take the first image of the workpiece. S3. Repeat steps 1 and 2 to take the second, third, and fourth images of the workpiece in sequence. S4. A quadruple edge detection strategy is adopted to improve robustness. By using a learning network model and automatic detection, the true center coordinates and radius of the circle are finally determined. S5. After each rotation of the workpiece, before image acquisition, the side push mechanism (5) of the detection station clamps the maximum outer circle of the workpiece on the bidirectional clamping part. Therefore, it is considered that the rotation center of the entire component including the guide ring is the center of the maximum outer circle. Therefore, the algorithm uses the least squares method to refit the four sets of detected hole center data onto a new small circle, and uses the center of this circle as the center of the maximum outer circle of the damper. S6. By using the center position of the workpiece center hole in the four images, the system software model fits the maximum outer circle center of the minimum boundary and calculates the maximum center distance with the center of the four workpiece center holes, thereby determining whether the coaxiality is qualified.

5. The detection method of the coaxiality automatic detection device according to claim 4, characterized in that, The method of using a learning network model and automatic detection to obtain the edge region of the small hole includes the following steps: a) Gaussian blur + subtract from original image and then add back to original image + Canny edge detection; b. Bilateral filtering + Canny edge detection; c. Use an edge-enhancing convolution kernel + Canny edge detection; d. Original image + Canny edge detection; e. Obtain 4 sets of edges. Based on the fact that the actual hole is circular and the radius of the edge is a fixed value, select the correct edges from the 4 sets. Based on multiple sets of edges, use the least squares method to fit multiple circle centers and radii. Use the DBSCAN algorithm to cluster and find outliers, and finally determine the true circle center coordinates and radius.

6. The detection method of the coaxiality automatic detection device according to claim 5, characterized in that: The least squares formula is: ; Where (x) i y i e represents the coordinates of each point on the edge. i The algebraic error of each point on the edge is not the geometric distance from the point to the center of the circle, but the residual generated after linearizing the original equation of the circle. B and C are twice the coordinates of the center a and b, respectively. D is a constant term including the center and radius of the circle, D = r² - a² - b². S is the sum of squared algebraic errors of all points. By finding the minimum sum of squared errors, the best fitting parameters (B, C, D) can be found, and then the coordinates of the center (a, b) and the radius r can be obtained.

7. The detection method of the coaxiality automatic detection device according to claim 6, characterized in that: The standard equation of the circle is: ; Where (x) m y n (m, n) represents the coordinates of the outer circle center of the damper opening obtained visually, (m, n) represents the center of the maximum outer circle, and r represents the radius of the maximum outer circle. During the rotation, the center of the outer circle of the damper opening rotates around the center of the maximum outer circle, and the circle it fits is concentric with the maximum outer circle.

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