Method for correcting shape error in free-form surface machining

Abstract

The invention discloses a shape error correction method for free-form surface machining, which comprises the following steps of: analyzing the path characteristics of an original cutter through a linearization error theory, establishing a slow cutter servo turning cutter path simulation model, and describing the cutting path of the cutter by adopting an Archimedes spiral. And on the basis, cutter radius compensation is carried out, cutter contact data after compensation are obtained, and the accuracy of a cutting track is ensured. Then, obtaining point clouds of the free-form surface to be processed, and obtaining source point clouds and target point clouds respectively; in order to realize reliable matching between the source point cloud and the target point cloud, point cloud coarse registration is used for coarse registration, and then point cloud fine registration is used for fine registration. And finally, calculating a shape error through a least square method, and applying the shape error to correction so as to obtain a processed free-form surface type.

Description

Technical Field

[0001] This invention relates to a shape error correction method for free-form surface machining, belonging to the field of ultra-precision machining. Background Technology

[0002] With the advancement of optical technology, the application of freeform surfaces is becoming increasingly widespread. However, variations in processing paths, material properties, and the processing environment often lead to large and difficult-to-correct shape errors in the finished product. To address this issue, existing technologies primarily rely on comparing the theoretical surface with the actual processed surface for subsequent correction and adjustment. Traditional correction methods often depend on manual experience, lack a systematic approach, and are ill-suited for complex processed shapes. Therefore, developing an efficient and automated shape error correction method is of great significance for improving the processing accuracy of freeform surfaces. Summary of the Invention

[0003] To address the issues of low efficiency and insufficient accuracy in existing shape error processing methods for freeform surface machining, this invention proposes a method for correcting shape errors in freeform surface machining. This method first analyzes the characteristics of the original toolpath using linearized error theory, establishes a simulation model of the tool trajectory path in slow-tool servo turning, and uses an Archimedean spiral to describe the cutting trajectory. Based on this, tool radius compensation is performed, and the compensated tool contact point data is obtained to ensure the accuracy of the cutting trajectory. Next, the point cloud of the freeform surface to be machined is acquired, resulting in source and target point clouds. To achieve reliable matching between the source and target point clouds, a coarse registration algorithm is used for coarse registration, followed by a fine registration algorithm. Finally, the shape error is calculated using the least squares method and applied for correction, thereby obtaining the machined freeform surface profile.

[0004] As attached Figure 1 As shown, the present invention provides a method for correcting shape errors in freeform surface machining, comprising the following steps: Step 1: Freeform surface shape representation method based on discrete measurement data point cloud. In the absence of a known surface model, the theoretical surface is reconstructed from the discrete measurement data through polynomial fitting or interpolation, and the surface alignment and shape representation are performed. Step 2: Perform slow-speed servo turning on the characterized freeform optical element, determine a suitable turning trajectory to improve the surface accuracy of the freeform optical element, and select reasonable tool parameters, including tool radius, tool radius of curvature, tool rake angle and tool clearance angle, to avoid machining interference. Step 3: The selection of the tool radius wrap angle is related to the cross-sectional curve z=g(x) of the surface to be machined. The tool parameters are optimized by calculating the angle between the normal vector and the X-axis. θ1=arctan(z′) (1) θ2=-arctan(z′) (2) θ≥2max{θ 1max ,θ 2max} (3) R t = -ft / 60 (4) θ t =θt (5) The angle between the normal vector at the cutting point and the X-axis is acute, θ1; the angle between the normal vector at the cutting point and the X-axis is acute, θ2; where R is the workpiece radius. t θ is the distance from the cutting point to the center of the workpiece. t The angle between the cutting point and the X-axis is denoted by f, where f is the radial feed rate of the tool, and t is the cutting time. Step 4: The selection of the tool clearance angle takes into account the slope of all cross-sectional curves on the surface to be machined that intersect with the plane, ensuring that the tool clearance angle is greater than the slope corresponding to the cutting point of all circumferential curves; ρ≥|max(arctan(f'))| (6) Step 5: Establish a tool path simulation model based on the obtained tool parameters, and analyze the characteristics of the original tool path according to the linearization error theory, as shown in the attached figure. Figure 2 A simulation model of the tool trajectory path in slow-speed servo turning is constructed, and the cutting point position is represented as an Archimedean spiral during the surface generation process. x = R t cos(θ t (7) y = R t sin(θ t (8) Where R is the workpiece radius, R t This is the distance from the cutting point to the center of the workpiece. Step Six, as attached Figure 3 Based on the obtained tool position point, tool radius compensation is performed. The compensated cutting point is the tool contact point, and the cutting trajectory is the actual machining trajectory. The surface profile equation of the freeform surface to be processed, z = f(x,y), at any angle α is z = f(r), and the equidistant curve of this curve is z = g(r). Step 7: Calculate the surface profile equation for any angle α of the freeform surface to be processed, and obtain the equidistant curve of the curve; calculate the compensated tool contact point coordinates based on the discrete point data on the profile curve; fit the tool contact point coordinates to the original freeform surface equation to obtain the processed freeform surface shape. Where the discrete points (r) taken on the curve profile q ,f(r q Then the corresponding tool position (r) o ,f(r o )), where r o =r q ; Step 8: Represent the designed surface and the theoretical surface as the target point cloud X, and the point cloud obtained after processing and detection as the source point cloud Y. A two-step matching method is adopted. First, the coarse registration algorithm of the point cloud is used to make the source point cloud and the target point cloud approximate within a small deviation range. Then, the fine registration algorithm of the point cloud is used to achieve accurate matching. The goal is to find an optimal transformation that minimizes the difference between the source point cloud and the target point cloud. R = R z (γ)R y (β)R x (α) (16) T(x)=Rx+t (21) Where R is the rotation matrix, representing the rotation angles (α, β, γ) about each axis, and t is the translation vector, representing the translation amount along each axis (ti). x ,t y ,t z ); Step 9: The downsampling technique is used to reduce the point cloud density and improve processing efficiency. Then, the shape error E of the processed freeform surface is calculated by matching, and the PV and RMS are calculated by the shape error E. E=Z ij -Z' ij (twenty two) PV = max(E) - min(E) (23) Step 10, as attached Figure 4 The target point cloud is superimposed on the obtained shape error E in reverse, which yields a new surface shape for processing. The surface is then processed again and the correction process is repeated to obtain a freeform surface element that meets the processing requirements.

[0005] Beneficial effects: This invention not only optimizes the processing method for freeform surfaces technically, but also provides an operable solution for industry. By accurately assessing and compensating for shape errors, it improves the processing accuracy of freeform surface optical elements, demonstrating significant practical value. Attached Figure Description

[0006] Figure 1 This is a flowchart of a freeform surface correction method; Figure 2 This is a toolpath result diagram. Figure 3 This is a diagram showing the results of tool radius compensation. Figure 4 These are the results before and after surface matching. Detailed Implementation

[0007] Example 1: A method for machining shape errors in freeform surfaces.

[0008] As attached Figure 1 As shown, the present invention provides a method for processing shape errors in freeform surfaces, comprising the following steps: Step 1: Freeform surface shape representation method based on discrete measurement data point cloud. In the absence of a known surface model, the theoretical surface is reconstructed from the discrete measurement data through polynomial fitting or interpolation, and the surface alignment and shape representation are performed. Step 2: Perform slow-speed servo turning on the characterized freeform optical element, determine a suitable turning trajectory to improve the surface accuracy of the freeform optical element, and select reasonable tool parameters, including tool radius, tool radius of curvature, tool rake angle and tool clearance angle, to avoid machining interference. Step 3: The selection of the tool radius wrap angle is related to the cross-sectional curve z=g(x) of the surface to be machined. The tool parameters are optimized by calculating the angle between the normal vector and the X-axis. θ1=arctan(z′) (1) θ2=-arctan(z′) (2) θ≥2max{θ 1max ,θ 2max} (3) R t = -ft / 60 (4) θ t =θt (5) The angle between the normal vector at the cutting point and the X-axis is acute, θ1; the angle between the normal vector at the cutting point and the X-axis is acute, θ2; where R is the workpiece radius. t θ is the distance from the cutting point to the center of the workpiece. t The angle between the cutting point and the X-axis is denoted by f, where f is the radial feed rate of the tool, and t is the cutting time. Step 4: The selection of the tool clearance angle takes into account the slope of all cross-sectional curves on the surface to be machined that intersect with the plane, ensuring that the tool clearance angle is greater than the slope corresponding to the cutting point of all circumferential curves; ρ≥|max(arctan(f'))| (6) Step 5: Establish a tool path simulation model based on the obtained tool parameters, and analyze the characteristics of the original tool path according to the linearization error theory, as shown in the attached figure. Figure 2 A simulation model of the tool trajectory path in slow-speed servo turning is constructed, and the cutting point position is represented as an Archimedean spiral during the surface generation process. x = R t cos(θ t (7) y = R t sin(θ t (8) Where R is the workpiece radius, R t This is the distance from the cutting point to the center of the workpiece. Step Six, as attached Figure 3 Based on the obtained tool position point, tool radius compensation is performed. The compensated cutting point is the tool contact point, and the cutting trajectory is the actual machining trajectory. The surface profile equation of the freeform surface to be processed, z = f(x,y), at any angle α is z = f(r), and the equidistant curve of this curve is z = g(r). Step 7: Calculate the surface profile equation for any angle α of the freeform surface to be processed, and obtain the equidistant curve of the curve; calculate the compensated tool contact point coordinates based on the discrete point data on the profile curve; fit the tool contact point coordinates to the original freeform surface equation to obtain the processed freeform surface shape. Where the discrete points (r) taken on the curve profile q ,f(r q Then the corresponding tool position (r) o ,f(r o )), where r o =r q; Step 8: Represent the designed surface and the theoretical surface as the target point cloud X, and the point cloud obtained after processing and detection as the source point cloud Y. A two-step matching method is adopted. First, the coarse registration algorithm of the point cloud is used to make the source point cloud and the target point cloud approximate within a small deviation range. Then, the fine registration algorithm of the point cloud is used to achieve accurate matching. The goal is to find an optimal transformation that minimizes the difference between the source point cloud and the target point cloud. R = R z (γ)R y (β)R x (α) (16) T(x)=Rx+t (21) Where R is the rotation matrix, representing the rotation angles (α, β, γ) about each axis, and t is the translation vector, representing the translation amount along each axis (ti). x ,t y ,t z ); Step 9: The downsampling technique is used to reduce the point cloud density and improve processing efficiency. Then, the shape error E of the processed freeform surface is calculated by matching, and the PV and RMS are calculated by the shape error E. E=Z ij -Z' ij (twenty two) PV = max(E) - min(E) (23) Step 10, as attached Figure 4 The target point cloud is superimposed on the obtained shape error E in reverse, which yields a new surface shape for processing. The surface is then processed again and the correction process is repeated to obtain a freeform surface element that meets the processing requirements.

Claims

1. This invention provides a method for correcting shape errors in freeform surface machining, characterized in that, Includes the following steps: Step 1: Freeform surface shape representation method based on discrete measurement data point cloud. In the absence of a known surface model, the theoretical surface is reconstructed from the discrete measurement data through polynomial fitting or interpolation, and the surface alignment and shape representation are performed. Step 2: Perform slow-speed servo turning on the characterized freeform optical element, determine a suitable turning trajectory to improve the surface accuracy of the freeform optical element, and select reasonable tool parameters, including tool radius, tool radius of curvature, tool rake angle and tool clearance angle, to avoid machining interference. Step 3: The selection of the tool radius wrap angle is related to the cross-sectional curve z=g(x) of the surface to be machined. The tool parameters are optimized by calculating the angle between the normal vector and the X-axis. θ1=arctan(z′) (1) θ2=-arctan(z′) (2) θ≥2max{θ 1max ,i 2max } (3) R t =-ft / 60 (4) i t =θt (5) The angle between the normal vector at the cutting point and the X-axis is acute, θ1; the angle between the normal vector at the cutting point and the X-axis is acute, θ2; where R is the workpiece radius. t θ is the distance from the cutting point to the center of the workpiece. t The angle between the cutting point and the X-axis is denoted by f, where f is the radial feed rate of the tool, and t is the cutting time. Step 4: The selection of the tool clearance angle takes into account the slope of all cross-sectional curves on the surface to be machined that intersect with the plane, ensuring that the tool clearance angle is greater than the slope corresponding to the cutting point of all circumferential curves; ρ≥|max(arctan(f'))| (6) Step 5: Establish a tool path simulation model based on the obtained tool parameters, analyze the characteristics of the original tool path according to the linearization error theory, and construct a simulation model of the slow tool servo turning tool path as shown in Figure 2. In the process of surface generation, the cutting point position is represented as an Archimedean spiral. x=R t cos(θ t ) (7) y=R t sin(θ t ) (8) Where R is the workpiece radius, R t This is the distance from the cutting point to the center of the workpiece; Step 6: As shown in Figure 3, perform tool radius compensation based on the obtained tool position point. The compensated cutting point is the tool contact point, and the cutting trajectory is the actual machining trajectory. The surface profile equation of the freeform surface to be processed, z = f(x,y), at any angle α is z = f(r), and the equidistant curve of this curve is z = g(r). Step 7: Calculate the surface profile equation for any angle α of the freeform surface to be processed, and obtain the equidistant curve of the curve; calculate the compensated tool contact point coordinates based on the discrete point data on the profile curve; fit the tool contact point coordinates to the original freeform surface equation to obtain the processed freeform surface shape. Where the discrete points (r) taken on the curve profile q ,f(r q Then the corresponding tool position (r) o ,f(r o )), where r o =r q ; Step 8: Represent the designed surface and the theoretical surface as the target point cloud X, and the point cloud obtained after processing and detection as the source point cloud Y. A two-step matching method is adopted. First, the coarse registration algorithm of the point cloud is used to make the source point cloud and the target point cloud approximate within a small deviation range. Then, the fine registration algorithm of the point cloud is used to achieve accurate matching. The goal is to find an optimal transformation that minimizes the difference between the source point cloud and the target point cloud. R=R z (c)R y (b)R x (a) (16) T(x)=Rx+t (21) Where R is the rotation matrix, representing the rotation angles (α, β, γ) about each axis, and t is the translation vector, representing the translation amount along each axis (ti). x ,t y ,t z ); Step 9: The downsampling technique is used to reduce the point cloud density and improve processing efficiency. Then, the shape error E of the processed freeform surface is calculated by matching, and the PV and RMS are calculated by the shape error E. E=Z ij -Z' ij (22) PV = max(E) - min(E) (23) Step 10: As shown in Figure 4, the target point cloud and the obtained shape error E are superimposed in reverse to obtain a new processing surface. The process is repeated through processing to obtain a freeform surface element that meets the processing requirements.

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