CN116644609A - Application method of surface fitting technology in small-batch die laser cutting processing - Google Patents
Application method of surface fitting technology in small-batch die laser cutting processing Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23K—SOLDERING OR UNSOLDERING; WELDING; CLADDING OR PLATING BY SOLDERING OR WELDING; CUTTING BY APPLYING HEAT LOCALLY, e.g. FLAME CUTTING; WORKING BY LASER BEAM
- B23K26/00—Working by laser beam, e.g. welding, cutting or boring
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Abstract
The application relates to an application method of a curve fitting technology in small batch die laser cutting processing, which comprises the steps of performing fitting operation through a CATIA fitting module, driving a theoretical product through software, extending on an actual drawn product part, fitting ATOS scanning results of theoretical product data through the CATIA fitting module, and completely driving the theoretical product to the actual product part. The application ensures the relative relation among the holes, trimming outline and appearance of the product, and is formed by one-step processing; avoiding repeated operation, reducing a large number of cost resources such as equipment, manpower, logistics and the like, and greatly improving the production efficiency while ensuring the product quality.
Description
Technical Field
The application belongs to the technical field of stamping, and relates to an application method of a curve fitting technology in small-batch die laser cutting processing.
Background
Along with the continuous deepening of the whole vehicle enterprises on user demands and market positioning grasp, the whole vehicle enterprises put higher and higher demands on stamping dies, the product development period is shortened, the product manufacturing cost is reduced, small batch dies can quickly and accurately manufacture required products, the cost is relatively low, the market demands can be quickly reflected, a traditional manufacturing system is replaced, and a large amount of laser cutting is utilized to replace a traditional trimming process from the stamping process; rebound is a problem that a stamping die inevitably exists, the traditional process is required to be repeated and improved by a large number of rebound, and each round of workpiece is verified on a detection tool after being rectified. Referring to fig. 1, curved surfaces with greater spring back have large deviations from shape boundaries, trim profiles, holes, etc. Because the specific magnitude of the rebound quantity cannot be accurately judged, the rebound quantity is repeatedly corrected in the rectifying and modifying process, and a large amount of equipment resources, human resources and logistics resources are wasted. In addition, each time the bench worker adjusts, the correction is performed completely according to the difference value of the manual detection amount, and the accuracy of the correction cannot be ensured.
Patent document CN102152009B discloses a rapid high-precision manufacturing method of a layered modular automobile panel mold based on a laser combined machining technology. The method takes laser cutting processing as the main part and takes laser surface strengthening and cladding technology as the auxiliary part, and combines with a layered modular mold structure design method, thereby realizing the rapid high-precision manufacture of the automobile covering part mold and providing a rapid and economic technical support means for sample vehicle trial manufacture and covering part mold trial manufacture in the development of new vehicles. The method comprises the process steps of die layered cutting, modularized combined positioning and connection, laser surface strengthening, cladding treatment and the like, and finally forms at a local key position, wherein materials are distributed in a functionally gradient way from the outside to the inside, and each structural layer has different mechanical properties and functions, so that the overall performance requirement of the die can be ensured, the process can be simplified, and the cost can be reduced. The method can provide samples for the trial production of 200 sample vehicles, and can provide fully reliable design data which is proved by experiments for the steel mold for the actual production.
Patent document CN101474722a discloses a laser cutting positioning method for a stamping part and a device for laser cutting positioning for the stamping part, in order to select a plurality of positioning references for positioning when the stamping part is cut, determine the shape of positioning templates for positioning at each positioning reference, arrange each positioning template at the corresponding positioning reference, place the stamping part on the positioning template, it is realized by arranging the positioning templates on a workbench, each positioning template is respectively provided with a positioning surface, the workbench surface is provided with a positioning reference line, and each positioning template is respectively arranged on the positioning reference line. The application can rapidly, accurately and efficiently position the stamping parts during laser cutting, realizes that different stamping parts adopt the same standardized tool and have higher clamping accuracy and precision, simultaneously provides a convenient, rapid and economic method for producing large-batch stamping parts by using die samples and not adopting trimming dies, and is particularly suitable for die manufacturing enterprises and stamping part production enterprises
Patent document CN109961517a discloses a triangle mesh re-parameterization method for parametric surface fitting. The method comprises the following steps: acquiring an initial parameterized triangular grid and generating a parameter curved surface; calculating a re-parameterized correction vector of the vertex according to the projection of the error vector of the vertex on the curved surface; initializing a correction coefficient of each triangular mesh vertex; putting all triangles in the triangular mesh into an inspection queue, checking whether the triangle re-parameterization result meets the limiting condition, removing the triangles from the inspection queue if the triangle re-parameterization result meets the limiting condition, and gradually adjusting correction coefficients of the triangle vertexes if the triangle re-parameterization result does not meet the limiting condition until the triangle re-parameterization result meets the limiting condition; and finally updating the parameter space coordinates of the vertex according to the correction vector and the correction coefficient to obtain a new parameterized result. The application can efficiently optimize the parameterized result and simultaneously ensure that the defects of overlapping of the triangular meshes of the parameter space and the like are not introduced, and the re-parameterized result can be used for fitting the parameter curved surface and obtaining a fitting result with higher precision.
The above patent has low relevance to the present application.
Disclosure of Invention
The application aims to solve the technical problems in the prior art and provides an application method of a curve fitting technology in small-batch die laser cutting processing.
After the curved surface deformation technology is used, the theoretical product is completely ensured to extend on the actual workpiece, the position of each shape is ensured, the deviation of the workpiece shape caused by rebound is eliminated, the repeated rectifying work is reduced, the labor intensity of a bench worker is reduced, the workpiece is molded once in the laser cutting production, the error is reduced, and the workpiece productivity is improved. The method is accurately verified through the production of small batch moulds of a certain high-end custom-made vehicle model, and the method is accurate and efficient, and can be greatly carried out in actual production; the application is an effective method by combining the application of the curved surface deformation technology with the laser cutting processing strategy.
It is noted that relational terms such as first and second, and the like are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Moreover, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus.
In order to solve the technical problems, the application is realized by adopting the following technical scheme:
the application method of the curve fitting technology in the laser cutting processing of the small batch of dies is characterized in that:
and carrying out fitting operation through a CATIA fitting module, driving a theoretical product through software, extending on an actual drawing product part, fitting an ATOS scanning result (STL format file) of theoretical product data through the CATIA fitting module, and completely driving the theoretical product to the actual product part.
Noun interpretation:
actual drawing piece: drawing piece with normal and actual mould state
ATOS scans STL mesh data: the actual drawing is scanned by ATOS (i.e., the driven data) to produce grid data in STL format.
Fitting data: and carrying out data calculation fitting between the theoretical product and the actual product by a CATIA fitting module, and finally generating data which can be used for laser cutting processing.
The application method of the curve fitting technology in the laser cutting processing of the small batch of dies specifically comprises the following steps:
defining a driven data source;
obtaining the top point of the driven curved surface, and calculating the curvature of the driven curved surface;
determining the distance between the obtained dotted lines, namely the actual distance between the actual drawing piece at the same position and the theoretical product data space;
calculating the combination of distances between the dotted lines and generating a grid result by using the nature of the curved surface fitting;
fitting the fitting data and optimizing.
Further, the definition is driven data source, specifically: in the drawing process, the actual receiving line is consistent with the theoretical receiving line, the error is within 5 percent, and the coloring of the pressing surface and the coloring of the female die reach the acceptance criterion; drawing the stabilized part, completing ATOS scanning photographing, and retaining stable driven data.
Further, the vertex on the driven curved surface is obtained, and the curvature of the driven curved surface is calculated; the method specifically comprises the following steps:
in the ATOS scanning process, when the coordinates of the dotted line and the projection values are selected, the two parameters closest to the scanning parameters, namely the two closest parts after numerical comparison in the drawing parts scanned in the same batch, are selected.
Further, the determining the distance between the resulting dotted lines: at the same location, the actual distance of the actual drawing member from the theoretical product data space.
Further, the specific calculation method for calculating the combination of the distances between the dotted lines comprises the following steps: and under the CATIA software fitting module, carrying out data collection and calculation by comparing ATOS scanning data of the actual drawing pieces in the same batch to obtain the most stable drawing data result, and finally generating a grid data result for actual processing, namely driven data.
The optimal corresponding result is searched and calculated and selected by a fitting module (Digitized Shape Editor module) of CATIA software on the curved surface by combining the point line and the inter-plane distance, and the point coordinates and the projection values are extracted from the original data to serve as scanning and fitting standards; the drawing piece is subjected to data partition cutting in software, and the purpose of the drawing piece is to independently fit a region with larger rebound, so that the deformation of the currently processed product region is minimum, and the drawing piece is more accurate in data fitting; after the point cloud of the ATOS scanning drawing piece is imported, the partitioning clipping is used for fitting, and if the whole set can lead to serious deformation of a product, data distortion and inaccuracy are caused. The cut point cloud data is converted to generate actual rebound distance between the point cloud and a theoretical product, the distance is marked, in the data conversion process, the tolerance of Accumacy (precision tolerance in data fitting) is selected to be 0.01-0.05 mm, the option of visual analysis (the type displayed in fitting) is used as a point, if the effect after fitting is not ideal or a larger deviation is expected, the value of Threshold (the starting point position) is adjusted, the default value is usually 2, the adjustment is usually carried out within 1-5, and the calculation is carried out through adjustment until the required result is reached. After the processing, fitting data with color code prompt results are obtained. In the data processing process, the problem that the direction of the theoretical curved surface is opposite to the fitting direction is encountered, the result is the problem of the sequence of selection, and the problem can be corrected by visual inspection
Further, the fitting data is fit, specifically: when the boundary is extracted, the deformed data are discontinuous, and the discontinuous features are fitted by utilizing curves, so that the original shape features of the product are ensured; when the shape of the product is reconstructed, the maximum limit of the curved surface and ATOS scanning white light is ensured to be close, and no angle exists between the two curved surfaces;
and the fitting module of CATIA software is used for driving theoretical data to ATOS scanning STL grid data through calculation to finally obtain fitting data, and the fitting data is used for carrying out laser cutting programming and carrying out actual laser cutting.
Further, the fitting data are optimized, specifically: the boundary contour is the contour of the rebound product, which is different from the theoretical product by a rebound value, the rebound of the product is compensated manually, and the product reaches a qualified position on the gauge.
Further, the driven data is driven data in STL format.
Further, the tolerance of the accurate tolerance in the data fitting is selected to be between 0.01mm and 0.05mm, the type of the selection displayed in the fitting is selected as a point, if the effect after the fitting is not ideal or if the deviation is larger than expected, the value of the starting point position is adjusted, the default value is usually 2, the adjustment is usually carried out within 1-5, and the calculation is carried out through adjustment until the required result is reached
Compared with the prior art, the application has the beneficial effects that:
the application relates to an application method of a curved surface deformation technology in laser cutting of four-door inner plates of a small-batch die, which comprises the steps of driving a theoretical product through software by the curved surface deformation technology, extending on an actual drawn product part, and completely driving the phase position relation of theoretical product data to the actual product part; the traditional correction is to repeatedly measure and obtain actual deviation on the gauge through a fitter, manually change the deviation for a laser cutting programmer, debug the workpiece through a press after the deviation is changed, repeatedly verify, and consume a large amount of equipment resources, manpower resources, logistics resources and the like. Long period, high labor intensity, poor accuracy and the like. After the method is implemented, the processing error of the workpiece caused by rebound can be ensured, the laser cutting times are reduced to the maximum extent, and the error is reduced; the main advantages are:
1. through software fitting, the relative relation among the product hole, the trimming outline and the appearance is ensured, and the product is formed by one-step processing;
2. the traditional processing technology has the advantage that the finished piece has rebound after being drawn during processing. Laser cutting is to use theoretical trimming contour, hole, shape and other information on the rebound product. After the rebound is recovered on the clamp, the data such as trimming, holes, shapes and the like after laser cutting have shape displacement deviation with the actual inspection, so that the trimming outline is long or short, and the detection requirement is not met. After the CATIA software fitting module (Digitized Shape Editor module performs data driving), the situation can be effectively avoided, repeated operation is avoided, a large number of cost resources such as equipment, manpower and logistics are reduced, the product quality is ensured, and meanwhile, the production efficiency is greatly improved.
Drawings
The application is further described below with reference to the accompanying drawings:
FIG. 1 is a schematic diagram of a common stamping process scheme for a small batch die;
FIG. 2 is a schematic diagram of theoretical product and actual drawing conditions;
FIG. 3 is a schematic diagram of the complete data after fitting;
FIG. 4 is a schematic diagram of a theoretical product projected entirely onto ATOS scan grid data by fitting an internal shape;
FIG. 5 is a schematic diagram of the virtual actual location of the fitted data on the software;
FIG. 6 is a logic block diagram of a method for applying the surface fitting technique of the present application to laser cutting of small batch dies.
In fig. 5:
1. the solid line is the virtual actual position of the fitted data on the software;
2. the dashed line is theoretical data, and the two virtually represent actual rebound displacement through software fitting.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application become more apparent, the technical solutions in the embodiments of the present application will be described in more detail below with reference to the accompanying drawings in the embodiments of the present application. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are some, but not all, embodiments of the application. The embodiments described below by referring to the drawings are illustrative and intended to explain the present application and should not be construed as limiting the application. All other embodiments, which can be made by those skilled in the art based on the embodiments of the application without making any inventive effort, are intended to be within the scope of the application. Embodiments of the present application will be described in detail below with reference to the accompanying drawings.
In the description of the present application, it should be understood that the terms "center," "longitudinal," "lateral," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, merely to facilitate describing the present application and simplify the description, and do not indicate or imply that the devices or elements being referred to must have a specific orientation, be configured and operated in a specific orientation, and therefore should not be construed as limiting the scope of the present application.
The application is described in detail below with reference to the attached drawing figures:
referring to fig. 6, the application relates to an application method of a curved surface deformation technology in laser cutting of four inner plates of a small-batch die, and the application method is characterized in that theoretical products are driven by software through the curved surface deformation technology, are extended on actual drawn product parts, and the relative position relation of theoretical product data is completely driven to the actual product parts. The small batch of dies are started in the early process stage, and laser cutting is used for replacing the traditional formal tool dies.
The dashed lines in fig. 2 represent theoretical products and the solid lines represent actual drawing members with rebound.
And defining a driven data source, ensuring that an actual receiving line and a theoretical receiving line are consistent in the drawing process, ensuring that the error is within 5%, and ensuring that the coloring of a pressing surface and the coloring of a female die meet the acceptance standard of customers. And ensures that the finished piece has no technical problem after the finished piece is discharged. Ensure the drawing to stabilize the piece. ATOS photography was completed, with stable data retained.
And obtaining the top point on the driven curved surface, calculating the curvature of the driven curved surface, and selecting two parameters closest to the scanning parameters as much as possible when selecting the coordinates of the dotted line and the projection value in the ATOS scanning process.
The distance between the resulting dotted lines is determined. At the same location, the actual distance of the actual drawing member from the theoretical product data space.
Referring to fig. 3 and fig. 4, by utilizing the nature of curve fitting, calculating the combination of the distances between the dotted lines and generating a grid result, searching and calculating the combination between the dotted lines and the surfaces on the curved surface to select the optimal corresponding result, and extracting the coordinates and the projection values of the points from the original data as the scanning and fitting standard; the drawing piece is subjected to data partition cutting in software, and the purpose of the drawing piece is to independently fit a region with larger rebound, so that the deformation of the currently processed product region is minimum, and the drawing piece is more accurate in data fitting; after the point cloud of the ATOS scanning drawing piece is imported, the partitioning clipping is used for fitting, and if the whole set can lead to serious deformation of a product, data distortion and inaccuracy are caused. The cut point cloud data is converted to generate actual rebound distance between the point cloud and a theoretical product, the distance is marked, in the data conversion process, the tolerance of Accumacy is selected to be 0.01-0.05 mm, the option of visual analysis is taken as a point, if the fitted effect is not ideal or a larger deviation is expected, the Threshold value is adjusted, the default value is usually 2, the adjustment is usually carried out within 1-5, and the calculation is carried out through adjustment until the required result is reached. After the processing, fitting data with color code prompt results are obtained. In the data processing process, the problem that the direction of the theoretical curved surface is opposite to the fitting direction is encountered, the result is the problem of the sequence of selection, and the problem can be corrected by visual inspection
Referring to fig. 5, the fitting data is optimized, and after fitting, there is a quality problem of the data, that is, the deformed data is discontinuous when the boundary is extracted. The discontinuous features are fitted by curves, so that the original shape features of the product are ensured, otherwise, the data can generate saw tooth shapes when the laser cutting programming is carried out. The processing quality of the product is affected. When the shape of the product is reconstructed, the maximum limit of the curved surface and ATOS scanning white light is guaranteed to be close to each other, no angles are guaranteed to the two curved surfaces, the center is the origin of a machine tool when laser cutting programming is performed, and the deviation is larger in the actual machining process due to the fact that angles are generated when the distance is relatively far, so that the meaning of rebound compensation is lost. Through the above treatment; the boundary contour is the contour of the finished piece after rebound, only one rebound value is different from the theoretical product, after the rebound of the finished piece is compensated manually, the finished piece of the product reaches an ideal state position on the gauge, and repeated debugging, grinding, measuring and other works of a bench worker are reduced.
The curved surface refers to most of the curved surface of the driven data in a limited driving range.
Because of the rebound of the workpiece, the actual workpiece has rebound, the two curved surfaces are not coincident, a range is locally limited, and most of theoretical and actual curved surfaces are coincident through fitting as much as possible;
"without angle" means: through the calculation after limiting the range, the theoretical curved surface is overlapped with the actual curved surface as much as possible, and the angle generated by large rebound is avoided.
The actual part has rebound and has a small angle with the theoretical product data by defining a local range. The angle is reduced as much as possible, and the two curved surfaces are overlapped as much as possible.
During the optimization process, fitting results can be changed according to different limiting ranges of engineer data, and engineers select a best fitting data result by comparing the fitting results through limiting different areas.
Before actual machining, engineers artificially compensate the rebound value of the workpiece into actual machining data through a fitting technology, and a laser cutting programmer can directly machine the workpiece by using the fitted data to show the rebound value of the workpiece on the actual workpiece after laser cutting machining.
And cutting and processing the drawing piece by using a laser cutting device through a simple bracket.
Influence of curved surface deformation on process route: before the curved surface deformation of the workpiece is not carried out, when the workpiece is cut by laser, according to the traditional processing route, the local area of the product part is required to be processed by a clamping fixture and laser equipment for multiple times due to the fact that the working procedures such as trimming and flanging are not completed, the workpiece is repeatedly processed by a press machine, and meanwhile, the workpiece is required to be positioned and tested very high, positioning errors are easy to generate due to repeated processing of the equipment for multiple times, and the final deviation is generated on a detection tool. The method for deforming the curved surface can finish the boundary contour without shaping and flanging in the follow-up process at one time because the shape of the product is finished in the drawing process, avoid errors caused by repeated loading and unloading, reduce the clamping times of the workpiece on a clamping fixture and equipment, reduce the accumulation of deviation caused by clamping, position once, position the workpiece without flanging and shaping in the follow-up process completely once, finish all the boundary contour contents once, greatly improve the working efficiency, reduce complicated process routes, shorten the manufacturing period of the workpiece and greatly improve the precision of the product. The curved surface deformation offset fitting is utilized, so that the product precision is greatly improved compared with the traditional processing route, the work of repeated adjustment and repair of a fitter is transferred to the earlier programming processing stage, the efficiency is improved, and the accumulated error in the process is greatly reduced.
The application method of the curved surface deformation technology in the laser cutting of the four-door inner plate of the small-batch die solves the problem that the actual workpiece has rebound at one time, so that the detection tool is out of tolerance, the detection standard is not met, and a large amount of resources such as manpower, equipment, logistics and the like are solved. The repeated modification caused by the rebound of the workpiece is reduced, a great amount of detection time of a fitter is saved, and the workpiece discharging verification process is performed by repeatedly feeding the workpiece to the press. The above problems can be solved at one time by the curved surface deformation driving technology.
The foregoing is merely illustrative of specific embodiments of the present application, and the scope of the application is not limited thereto, but any modifications, equivalents, improvements and alternatives falling within the spirit and principles of the present application will be apparent to those skilled in the art within the scope of the present application. And all that is not described in detail in this specification is well known to those skilled in the art.
Claims (10)
1. The application method of the curve fitting technology in the laser cutting processing of the small batch of dies is characterized in that:
and carrying out fitting operation through a CATIA fitting module, driving a theoretical product through software, extending on an actual drawing product, fitting ATOS scanning results of theoretical product data through the CATIA fitting module, and completely driving the theoretical product to the actual product.
2. The method for applying the surface fitting technology to the laser cutting processing of the small-batch die according to claim 1, which is characterized by comprising the following steps:
defining a driven data source;
obtaining the top point of the driven curved surface, and calculating the curvature of the driven curved surface;
determining the distance between the obtained dotted lines;
calculating the combination of distances between the dotted lines and generating a grid result by using the nature of the curved surface fitting;
fitting the fitting data and optimizing.
3. The method for applying the curve fitting technology to small-batch die laser cutting processing according to claim 2, wherein the method comprises the following steps:
the definition is driven by data sources, specifically: in the drawing process, the actual receiving line is consistent with the theoretical receiving line, the error is within 5 percent, and the coloring of the pressing surface and the coloring of the female die reach the acceptance criterion; drawing the stabilized part, completing ATOS scanning photographing, and retaining stable driven data.
4. A method for applying a surface fitting technique to laser cutting of small batch dies according to claim 3, wherein:
the vertex on the driven curved surface is obtained, and the curvature of the driven curved surface is calculated; the method specifically comprises the following steps:
in the ATOS scanning process, when the coordinates of the dotted line and the projection values are selected, the two parameters closest to the scanning parameters, namely the two closest parts after numerical comparison in the drawing parts scanned in the same batch, are selected.
5. The method for applying the surface fitting technology to small-batch die laser cutting processing according to claim 4, wherein the method comprises the following steps:
the distance between the obtained dotted lines is determined: at the same location, the actual distance of the actual drawing member from the theoretical product data space.
6. The method for applying the surface fitting technique to small-batch die laser cutting processing according to claim 5, wherein the method comprises the following steps:
the specific calculation method for calculating the combination of the distances between the dotted lines comprises the following steps: and under the CATIA software fitting module, carrying out data collection and calculation by comparing ATOS scanning data of the actual drawing pieces in the same batch to obtain the most stable drawing data result, and finally generating a grid data result for actual processing, namely driven data.
7. The method for applying the surface fitting technology to small-batch die laser cutting processing according to claim 6, wherein the method comprises the following steps:
fitting the fitting data specifically means that: when the boundary is extracted, the deformed data are discontinuous, and the discontinuous features are fitted by utilizing curves, so that the original shape features of the product are ensured; when the shape of the product is reconstructed, the maximum limit of the curved surface and ATOS scanning white light is ensured to be close, and no angle exists between the two curved surfaces;
and the fitting module of CATIA software is used for driving theoretical data to ATOS scanning STL grid data through calculation to finally obtain fitting data, and the fitting data is used for carrying out laser cutting programming and carrying out actual laser cutting.
8. The method for applying the surface fitting technique to small-batch die laser cutting processing according to claim 7, wherein the method comprises the following steps:
optimizing fitting data, specifically: the boundary contour is the contour of the rebound product, which is different from the theoretical product by a rebound value, the rebound of the product is compensated manually, and the product reaches a qualified position on the gauge.
9. A method for applying a surface fitting technique to laser cutting of small batch dies according to claim 3, wherein:
the driven data is STL format driven data.
10. The method for applying the surface fitting technique to small-batch die laser cutting processing according to claim 7, wherein the method comprises the following steps:
the tolerance of the accurate tolerance in data fitting is selected to be between 0.01mm and 0.05mm, the type of selection displayed in fitting is a point, if the effect after fitting is not ideal or a large deviation is expected, the value of the starting point position is adjusted, usually the default value is 2, usually the adjustment is carried out within 1-5, and the calculation is carried out through adjustment until the required result is achieved.
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