Laser cleaning path automatic planning method and laser cleaning device

Abstract

The invention relates to a laser cleaning path automatic planning method and a laser cleaning device. Three-dimensional information of a to-be-cleaned workpiece is obtained, a cleaning path is planned, a partition cleaning strategy of the to-be-cleaned workpiece is obtained, galvanometer adjusting information of laser cleaning equipment is configured, and the to-be-cleaned workpiece is cleaned according to the galvanometer adjusting information. The laser cleaning equipment is controlled to clean the to-be-cleaned workpiece according to the planned partition cleaning strategy, and the galvanometer is adjusted in real time based on the galvanometer adjustment information to adapt to the change of the surface shape of the to-be-cleaned workpiece; the device comprises a base, a position transfer unit realizes position movement of the device except the base, a three-dimensional scanning construction unit is arranged at the output end of the position transfer unit and is used for scanning a to-be-cleaned workpiece and constructing three-dimensional information of the workpiece, and finally a laser cleaning unit is used for performing laser cleaning on the to-be-cleaned workpiece. According to the method, the cleaning efficiency is improved, intelligent selection of cleaning paths and cleaning strategies is completed, redundancy and repetition of the cleaning paths are reduced, loopholes of cleaning work are reduced, and completeness and comprehensiveness of cleaning are ensured.

Description

Technical Field

[0001] The present invention relates to the technical field of calculation, extrapolation or counting, and in particular to a laser cleaning path automatic planning method and a laser cleaning device. Background Art

[0002] Workpiece cleaning is an important part of industrial production. It can remove impurities such as oil, dust, rust, etc. on the surface of the workpiece and improve the quality and performance of the workpiece. Currently, the commonly used workpiece cleaning methods are spray cleaning, immersion cleaning and laser cleaning. Traditional workpiece cleaning methods have the following problems:

[0003] (1) The cleaning parameters such as temperature, pressure, time, etc. cannot be automatically adjusted according to the workpieces of different types, sizes, shapes, and surface cleanliness, resulting in poor cleaning effects or waste of resources;

[0004] (2) The cleaning fluid treatment method cannot be automatically adjusted according to the workpieces of different types, sizes, shapes, and surface cleanliness, resulting in unstable cleaning fluid performance or unsuitability for the workpieces;

[0005] (3) The degree of contamination on the workpiece surface cannot be detected and fed back, resulting in excessive or insufficient cleaning.

[0006] For example, the workpiece cleaning method and cleaning system disclosed in the Chinese patent publication number CN116871231A, the cleaning system realizes the recognition of workpiece features and the setting of cleaning parameters through image processing and fuzzy logic and other technologies; realizes the optimization control of the cleaning liquid circulation module through genetic algorithms and other technologies; realizes the feedback adjustment of the cleaning effect through cleanliness detection and other technologies. This feature uses image acquisition and image processing technologies to obtain the image data of the workpiece through shooting and scanning technologies; processes the image data through preprocessing and feature extraction technologies to obtain the feature data of the workpiece; and analyzes the feature data through classification and other technologies to obtain information such as the type, size, and shape of the workpiece. There is also a workpiece cleaning method disclosed in Chinese Patent Publication No. CN115488107A, which fixes the workpiece to be cleaned and determines the focal length of the laser output beam on the surface of the workpiece to be cleaned, controls the laser to output the laser beam according to different output parameters, performs at least two scanning ablation on the first cleaning surface, flips the workpiece to be cleaned so that the second cleaning surface of the workpiece to be cleaned faces the laser, controls the laser to output the laser beam according to different output parameters, performs at least two scanning ablation on the second cleaning surface, and then flips the workpiece to be cleaned to obtain a cleaned workpiece.

[0007] In the above cleaning, when there are differences between workpieces, manually setting the path is time-consuming and laborious, while the more common convolutional neural network algorithm requires a large amount of data and workpiece information to select the cleaning path, and there are non-standard situations in workpiece processing, so manual participation is still required.

[0008] Another example is a workpiece cleaning method disclosed in Chinese patent publication number CN108284107A, which introduces working gas into the plasma generator and extracts the gas in the plasma generator so that the gas pressure in the plasma generator is within a preset range; starts the power supply to discharge the working gas remaining in the plasma generator to generate plasma to clean the workpiece to be cleaned; after a preset time, introduces air into the plasma generator to restore the internal pressure of the plasma generator to normal. The workpiece cleaning method provided by the present invention can avoid the generation of wastewater and reduce environmental pollution.

[0009] The above-mentioned cleaning system is based on water washing, and completes feature extraction from the image data of the workpiece to obtain the type, size and shape of the workpiece. When the workpiece is large or has too many features such as special-shaped surfaces and stepped shafts, there are too many feature extraction results, which increases the possibility of conflicts in cleaning decisions. In addition, when the above-mentioned cleaning system does not select a suitable cleaning path based on the characteristics of the workpiece, the cleaning path can only be set manually, and the control has the problems of high labor costs and inability to be fully standardized. Summary of the invention

[0010] In order to solve the above technical problems, the present invention provides a laser cleaning path automatic planning method and a laser cleaning device.

[0011] The technical solution adopted by the present invention is a method for automatically planning a laser cleaning path, the method comprising the following steps:

[0012] S1 obtains three-dimensional information of the workpiece to be cleaned;

[0013] S2 plans a cleaning path based on the three-dimensional information to obtain a partition cleaning strategy for the workpiece to be cleaned;

[0014] S3 configures the galvanometer adjustment information of the laser cleaning device corresponding to the partition cleaning strategy;

[0015] S4 controls the laser cleaning device to clean the workpiece to be cleaned according to the planned partition cleaning strategy, and adjusts the galvanometer in real time based on the galvanometer adjustment information to adapt to the change of the surface shape of the workpiece to be cleaned.

[0016] Preferably, in S2, the features of each preset size surface in the three-dimensional information of the workpiece to be cleaned are extracted, and a set is established for each surface based on each feature to obtain a corresponding partition.

[0017] Preferably, the features include protrusions, depressions and flatness; a coordinate set is established for each highest point in the partition corresponding to the protruding features, a coordinate set is established for each lowest point in the partition corresponding to the depression features, and a coordinate set is established for each center point in the partition corresponding to the flat features, and the path corresponding to the minimum distance between each two coordinates is extracted as the optimal path for the partition cleaning strategy.

[0018] Preferably, in S3, configuring the galvanometer adjustment information includes the following steps:

[0019] S3.1 sets the neighborhood radius and core radius of each partition set of the workpiece to be cleaned, and presets the adjustment angle range of the galvanometer; during laser cleaning, the laser focus depth has the best cleaning effect within a certain range, so the core radius is set, and the focus depth requirement must be met within the core radius; the neighborhood radius includes the surrounding area of ​​the current cleaning area, and is used to determine which adjacent area the next cleaning will be in in the optimal path judgment method; based on the adjustment angle of the galvanometer, the change range of the normal vector in the partitioned area is determined, and for adjacent faces with the same features, even if they may have certain fluctuations, as long as they belong to the same feature, they will be merged;

[0020] S3.2 calculates the normal vectors of the points in the partition based on the preset parameters as the basis for partition judgment; obviously, the points in the partition of the flat feature do not need to be calculated;

[0021] S3.3 filtering the calculated normal vector according to the preset angle range, deleting the points where the angle between the normal vector and the Z axis is not within the preset adjustment angle range of the galvanometer, where the Z axis is the axis in the vertical direction; the cleaning of the range corresponding to the filtered points can be achieved by secondary cleaning;

[0022] S3.4 combines the partition cleaning strategy to plan the optimal galvanometer motion information.

[0023] A laser cleaning device using the laser cleaning path automatic planning method, the device comprising:

[0024] A base;

[0025] a position transfer unit, disposed on the base, for realizing the position movement of the device except the base;

[0026] A three-dimensional scanning and constructing unit, provided at the output end of the position transfer unit, for scanning the workpiece to be cleaned and constructing three-dimensional information of the workpiece;

[0027] A laser cleaning unit, provided at the output end of the three-dimensional scanning construction unit, for laser cleaning the workpiece to be cleaned;

[0028] A controller is provided in conjunction with the position transfer unit, the three-dimensional scanning construction unit and the laser cleaning unit.

[0029] Preferably, the position transfer unit includes a planar stroke control mechanism disposed on the base and a longitudinal stroke control mechanism disposed on the planar stroke control mechanism. The output end of the longitudinal stroke control mechanism is cooperatively arranged with the three-dimensional scanning and constructing unit through a first steering knuckle, and the first steering knuckle is cooperatively arranged with the controller.

[0030] Preferably, a second steering knuckle is provided between the three-dimensional scanning and constructing unit and the laser cleaning unit, and the second steering knuckle is cooperatively arranged with the controller.

[0031] Preferably, a long focal depth lens is provided in cooperation with the laser cleaning unit. The focal length f and the beam diameter w0 of the long focal depth lens respectively satisfy f > f0 and w0 < w00, where f0 is a preset reference focal length and w00 is a preset reference spot diameter.

[0032] The present invention relates to a method for automatically planning a laser cleaning path and a laser cleaning device. The three-dimensional information of the workpiece to be cleaned is obtained, the cleaning path is planned and the partition cleaning strategy for the workpiece to be cleaned is obtained, the galvanometer adjustment information of the laser cleaning equipment is configured, the laser cleaning equipment is controlled to clean the workpiece to be cleaned according to the planned partition cleaning strategy, and the galvanometer is adjusted in real time based on the galvanometer adjustment information to adapt to the change of the surface shape of the workpiece to be cleaned; the device includes a base, and the position transfer unit realizes the position movement of the device except the base. Its output end is provided with a three-dimensional scanning and constructing unit for scanning the workpiece to be cleaned and constructing the three-dimensional information of the workpiece, and finally the laser cleaning unit is used to perform laser cleaning on the workpiece to be cleaned.

[0033] The beneficial effects of the present invention are as follows:

[0034] (1) The type, size and shape of the workpiece are quickly obtained by scanning, and based on the obtained three-dimensional solid model, the automatic planning of the cleaning path is automatically completed through interference analysis, the cleaning efficiency is improved, and the intelligent selection of the cleaning path and cleaning strategy is completed;

[0035] (2) Path verification is performed according to the selection result to avoid situations such as cleaning failure or movement interference causing impact on the workpiece;

[0036] (3) By disassembling the three-dimensional solid model, multiple partitions are obtained, the connection paths between each partition on the uncleaned area are established, the coverage paths of all partitions are connected, and the paths of the to-be-cleaned area and the uncleaned area are combined to obtain the entire path planning of the workpiece to be cleaned, reducing the redundancy and repetition of the cleaning path, improving the cleaning efficiency, reducing the loopholes in the cleaning work, and ensuring the integrity and comprehensiveness of the cleaning. Description of the Drawings

[0037] Figure 1 is the flowchart of the method of the present invention;

[0038] Figure 2 It is a schematic diagram of the partition cleaning strategy in the present invention;

[0039] Figure 3 It is a schematic structural diagram of the laser cleaning device of the present invention. DETAILED DESCRIPTION

[0040] The present invention is further described in detail below in conjunction with embodiments, but the protection scope of the present invention is not limited thereto.

[0041] like Figure 1 The present invention relates to a method for automatic planning of a laser cleaning path, the method comprising the following steps:

[0042] S1 obtains three-dimensional information of the workpiece to be cleaned;

[0043] S2 plans a cleaning path based on the three-dimensional information to obtain a partition cleaning strategy for the workpiece to be cleaned;

[0044] S3 configures the galvanometer adjustment information of the laser cleaning device corresponding to the partition cleaning strategy;

[0045] S4 controls the laser cleaning device to clean the workpiece to be cleaned according to the planned partition cleaning strategy, and adjusts the galvanometer in real time based on the galvanometer adjustment information to adapt to the change of the surface shape of the workpiece to be cleaned.

[0046] The following is a detailed description of each step.

[0047] In S1, a three-dimensional model of the workpiece needs to be established before laser cleaning, which is generally accomplished by setting up a scanning mechanism or similar equipment.

[0048] In this embodiment, several cameras and processors are used, and the cameras are used to collect two-dimensional images of the workpiece to be cleaned from different angles. These images can be color images or depth images, and the processor is used to process the collected two-dimensional images, which specifically includes the following steps:

[0049] S1.1 Confirm the camera's internal parameters, such as focal length, principal point coordinates, etc., and confirm the camera's external parameters, such as the camera's position and orientation. This is usually done through a camera calibration process, which can be done using a specific calibration plate or an object of known size.

[0050] S1.2 extract feature points from each image, including but not limited to corner points, edge points, etc., and try to match these feature points between different images to determine the correspondence between the same spatial points in different images;

[0051] S1.3 Using the matched feature points and camera parameters, three-dimensional point cloud data is calculated by triangulation or other methods to obtain some discrete points on the workpiece surface;

[0052] S1.4 generating a three-dimensional mesh model of the workpiece based on the calculated point cloud data;

[0053] S1.5 further optimizes and processes the generated 3D model, such as removing noise, filling holes, smoothing surfaces, etc., to improve the quality of the model.

[0054] In S1.3, the projection equation of the i-th camera is,

[0055]

[0056] Among them, i is the serial number of the camera, P i is the projection matrix of the i-th camera, K i is the internal parameter matrix of the i-th camera, [P i , t i ] is the external parameter matrix;

[0057] The three-dimensional coordinates of the workpiece feature point are X i =[x,y,z,1] T , then the image coordinates of the projection at the i-th viewing angle are: Available,

[0058]

[0059] Right now,

[0060] x i (p i3 X)-p i1 X=0

[0061] y i (p i3 X)-p i2 X=0

[0062] x i (p i2 X)-y i (p i1 X)=0

[0063] Combining the three equations, we get the matrix equation:

[0064]

[0065] Given X = [x i ,y i , z i , 1] T , the degree of freedom of X is 3. It can be seen that one viewing angle of the projection of point X can provide two constraints. At least two viewing angles are needed to solve the three-dimensional coordinates of X. If the same three-dimensional point X has projection coordinates of images from N viewing angles, the least squares method is used to solve it.

[0066] In S2, the features of each preset size surface in the three-dimensional information of the workpiece to be cleaned are extracted, and each surface is set up based on each feature to obtain the corresponding partition, and the convex set is recorded as T = [t1, t2, ...t n ], and record the concave set as A = [a1, a2, ...a n ], and record the flattened set as P = [p1, p2, ... p n ].

[0067] Features include ridges, valleys, and flatness;

[0068] In the specific implementation process, the method for judging convexity, concavity and flatness is as follows:

[0069] Taking the contact surface between the workpiece and the cleaning device as the reference plane, calculate the angle θ between the normal of each point on the workpiece surface and the normal of the reference plane. When -5°≤θ≤5°, the partition is judged to be flat; when θ>5°, it is judged to be convex; when θ<-5°, it is judged to be concave. In practical applications, the partition generally corresponds to the cleaning range of the laser cleaning head.

[0070] A coordinate set is established for each highest point in the partition set T corresponding to the convex features, a coordinate set is established for each lowest point in the partition set A corresponding to the concave features, and a coordinate set is established for each center point in the partition set P corresponding to the flat features. The path corresponding to the minimum distance between each two coordinates is extracted respectively, that is, the shortest coordinate distance from T to A, T to P, and A to P is calculated as the optimal path for the partition cleaning strategy.

[0071] In the present invention, path verification is also required; in the specific implementation process, the path verification is to import the three-dimensional model, set the laser cleaning focal depth, laser power, laser spot diameter and other parameters in the laser cleaning device through the three-dimensional model, and judge whether the cleaning of each partition is successful based on the maximum movement threshold and actual movement of each point of the given laser cleaning device.

[0072] In S3, configuring the galvanometer adjustment information includes the following steps:

[0073] S3.1 sets the neighborhood radius and core radius of each partition set of the workpiece to be cleaned, and presets the adjustment angle range of the galvanometer; here, the neighborhood radius is used to determine the range of points involved in the normal vector calculation, and the core radius is used to define the core area in the calculation process. Within this area, the laser head does not change its position during cleaning, and cleaning can be achieved by rotating within the core radius; in actual applications, the neighborhood radius is consistent with the step size;

[0074] S3.2 calculates the normal vector of the points in the partition based on the preset parameters as the basis for partition judgment;

[0075] S3.3 filtering the calculated normal vector according to a preset angle range, and deleting points where the angle between the normal vector and the Z axis is not within the preset adjustment angle range of the galvanometer;

[0076] S3.4 combines the partition cleaning strategy to plan the optimal galvanometer motion information.

[0077] like Figure 2 As shown, an embodiment is given;

[0078] a shows the core radius, b and c correspond to its neighborhood radius;

[0079] When partitioning, define area A in the figure as concave, area B as flat, and area C as convex;

[0080] For partitions such as A, the paths on the concave, convex, and flat feature surfaces can be cleaned in sequence (such as S-shaped). For path processing across regions, as shown in points 1 and 2 in the figure, the horizontal movement displacement and vertical lifting height are considered, and the path with the shortest movement is selected.

[0081] In the present invention, a high-power laser has a smaller spot, and a larger spot can effectively cover more areas. Therefore, the angle adjustment range of the galvanometer must meet the requirements of precise focal length adjustment. Specifically, the angle range of the galvanometer is between ±10° and ±20°.

[0082] Furthermore, the present invention also tends to select a long-focus depth lens as part of the laser cleaning device, which has a larger focal depth to adapt to workpieces with different surface heights. During the laser cleaning process, the focal length and beam diameter of the long-focus depth lens are adjusted to maintain the focusing effect between different surface heights to avoid uneven surface treatment or defocusing due to too small focal depth.

[0083] like Figure 3 As shown, the present invention also relates to a laser cleaning device using the above-mentioned laser cleaning path automatic planning method, the device comprising:

[0084] 500 for a base;

[0085] a position transfer unit, provided on the base 500, for realizing the position movement of the device other than the base 500;

[0086] A three-dimensional scanning and constructing unit 100, provided at the output end of the position transfer unit, for scanning the workpiece to be cleaned and constructing three-dimensional information of the workpiece;

[0087] A laser cleaning unit 400, provided at the output end of the three-dimensional scanning construction unit 100, for laser cleaning the workpiece to be cleaned;

[0088] A controller is provided in cooperation with the position transfer unit, the three-dimensional scanning and construction unit 100, and the laser cleaning unit 400.

[0089] Specifically, the position transfer unit includes a planar travel control mechanism 200 provided on a base 500 and a longitudinal travel control mechanism 300 provided on the planar travel control mechanism 200. The output end of the longitudinal travel control mechanism 300 is cooperatively arranged with the three-dimensional scanning and construction unit 100 through a first steering knuckle, and the first steering knuckle is cooperatively arranged with the controller; a second steering knuckle is provided between the three-dimensional scanning and construction unit 100 and the laser cleaning unit 400, and the second steering knuckle is cooperatively arranged with the controller; in the specific implementation process of this device, the cooperative arrangement between the planar travel control mechanism 200 and the longitudinal travel control mechanism 300 and the base 500, and the settings of the first steering knuckle and the second steering knuckle are easily understood by those skilled in the art, and those skilled in the art can set them according to requirements.

[0090] A long focal depth lens is provided in cooperation with the laser cleaning unit 400. The focal length f and the beam diameter w0 of the long focal depth lens respectively satisfy f > f0 and w0 < w00, where f0 is a preset reference focal length and w00 is a preset reference spot diameter; in practical applications, generally, f0 = 150 mm and w0 = 5 mm are set.

[0091] Those skilled in the art should understand that the embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0092] The present invention is described with reference to the flowcharts and / or block diagrams of methods, apparatuses (systems), and computer program products according to the embodiments of the present invention. It should be understood that each flow and / or block in the flowchart and / or block diagram, and the combination of flows and / or blocks in the flowchart and / or block diagram can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices generate means for implementing the functions specified in one Figure 1 one process or multiple processes and / or blocks Figure 1 one block or multiple blocks.

[0093] These computer program instructions may also be stored in a computer readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture including an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0094] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0095] Although the preferred embodiments of the present invention have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0096] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A method for automatic planning of a laser cleaning path, characterized in that: The method comprises the following steps: S1 obtains three-dimensional information of the workpiece to be cleaned; S2 plans a cleaning path based on the three-dimensional information to obtain a partition cleaning strategy for the workpiece to be cleaned; S3 configures the galvanometer adjustment information of the laser cleaning device corresponding to the partition cleaning strategy; S4: Controlling the laser cleaning device to clean the workpiece to be cleaned according to the planned partition cleaning strategy, and adjusting the galvanometer in real time based on the galvanometer adjustment information to adapt to the change of the surface shape of the workpiece to be cleaned.

2. The method for automatic planning of a laser cleaning path according to claim 1, characterized in that: In S2, the features of each preset size surface in the three-dimensional information of the workpiece to be cleaned are extracted, and a set is established for each surface based on each feature to obtain a corresponding partition.

3. The method for automatic planning of a laser cleaning path according to claim 2, characterized in that: The features include convexities, concavities and flatness; a coordinate set is established for each highest point in the partition corresponding to the convex features, a coordinate set is established for each lowest point in the partition corresponding to the concave features, and a coordinate set is established for each center point in the partition corresponding to the flat features. The path corresponding to the minimum distance between each two coordinates is extracted as the optimal path for the partition cleaning strategy.

4. The method for automatic planning of a laser cleaning path according to claim 1, characterized in that: In S3, configuring the galvanometer adjustment information includes the following steps: S3.1 sets the neighborhood radius and core radius of each partition set of the workpiece to be cleaned, and presets the adjustment angle range of the galvanometer; S3.2 calculates the normal vector of the points in the partition based on the preset parameters as the basis for partition judgment; S3.3 filtering the calculated normal vector according to a preset angle range, and deleting points where the angle between the normal vector and the Z axis is not within the preset adjustment angle range of the galvanometer; S3.4 combines the partition cleaning strategy to plan the optimal galvanometer motion information.

5. A laser cleaning device using the laser cleaning path automatic planning method according to any one of claims 1 to 4, characterized in that: The device comprises: A base; a position transfer unit, disposed on the base, for realizing the position movement of the device except the base; A three-dimensional scanning and constructing unit, provided at the output end of the position transfer unit, for scanning the workpiece to be cleaned and constructing three-dimensional information of the workpiece; A laser cleaning unit, provided at the output end of the three-dimensional scanning construction unit, for laser cleaning the workpiece to be cleaned; A controller is provided in conjunction with the position transfer unit, the three-dimensional scanning construction unit and the laser cleaning unit.

6. The laser cleaning device according to claim 5, characterized in that: The position transfer unit includes a planar stroke control mechanism arranged on the base and a longitudinal stroke control mechanism arranged on the planar stroke control mechanism. The output end of the longitudinal stroke control mechanism is arranged in cooperation with the three-dimensional scanning construction unit through a first steering knuckle, and the first steering knuckle is arranged in cooperation with the controller.

7. The laser cleaning device according to claim 6, characterized in that: A second steering knuckle is provided between the three-dimensional scanning construction unit and the laser cleaning unit, and the second steering knuckle is arranged in cooperation with the controller.

8. The laser cleaning device according to claim 5, characterized in that: The laser cleaning unit is provided with a telephoto depth lens, the focal length of which is f and beam diameter w 0 respectively satisfies f > f 0. w 0< w 00, where f 0 is the preset base focal length. w 00 is the preset reference spot diameter.

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