CN-121995845-A - Method for correcting shape error by free-form surface machining

Abstract

The invention discloses a method for correcting shape errors by free-form surface machining, which is characterized in that the characteristics of an original cutter path are analyzed through linearization error theory, a slow cutter servo turning cutter path simulation model is established, and an Archimedes spiral line is adopted to describe the cutting path of a cutter. On the basis, the radius compensation of the cutter is carried out, the compensated cutter contact point data is obtained, and the accuracy of the cutting track is ensured. And then, acquiring point clouds of the free curved surface to be processed, and respectively obtaining a source point cloud and a target point cloud. In order to achieve reliable matching between the source point cloud and the target point cloud, coarse registration is performed by adopting point cloud coarse registration, and then fine registration is performed by utilizing point cloud fine registration. Finally, the shape error is calculated by a least square method and is applied to correction, so that the machined free-form surface type is obtained.

Inventors

• XUE CHANGXI
• YU BOXIN

Assignees

• 长春理工大学

Dates

Publication Date

20260508

Application Date

20241104

Claims (1)

1. 1. The invention provides a method for correcting shape errors by free-form surface machining, which is characterized by comprising the following steps: Step one, reconstructing a theoretical curved surface from discrete measurement data through polynomial fitting or interpolation under the condition of lacking a known curved surface model based on a free curved surface shape representation method of a discrete measurement data point cloud, and carrying out surface alignment and shape representation; Step two, performing slow-tool servo turning on the represented free-form surface optical element, determining a proper turning track to improve the surface type precision of the free-form surface optical element, and selecting reasonable tool parameters including a tool radius, a tool arc wrap angle, a tool front angle and a tool rear angle to avoid machining interference phenomenon; step three, selecting a cutter arc wrap angle and correlating with a section curve z=g (X) of a curved surface to be processed, and optimizing cutter parameters by calculating an included angle between a vector and an X axis; θ 1 =arctan(z′) (1) θ 2 =-arctan(z′) (2) θ≥2max{θ 1max ,θ 2max } (3) R t =-ft/60 (4) θ t =θt (5) When the included angle between the normal vector at the cutting point and the X axis is an acute angle, the included angle between the normal vector at the cutting point and the X axis is theta 1 , and when the included angle between the normal vector at the cutting point and the X axis is an acute angle, theta 2 , wherein R is the radius of the workpiece, R t is the distance from the cutting point to the center of the workpiece, theta t is the included angle between the cutting point and the X axis, f is the radial feeding speed of the cutter, and t is the cutting time; step four, selecting a cutter relief angle, wherein the slope of all section curves intersecting with a plane on a curved surface to be processed is considered, so that the cutter relief angle is ensured to be larger than the slope corresponding to all circumferential curve cutting points; ρ≥|max(arctan(f'))| (6) fifthly, establishing a tool path simulation model according to the obtained tool parameters, analyzing the characteristics of an original tool path according to a linearization error theory, as shown in fig. 2, constructing a simulation model of a slow-tool servo turning tool path, and expressing a cutting point as an Archimedes spiral line in the curved surface generation process; x=R t cos(θ t ) (7) y=R t sin(θ t ) (8) Wherein R is the radius of the workpiece, and R t is the distance from the cutting point to the center of the workpiece; step six, according to the obtained cutter position points, carrying out cutter radius compensation according to the figure 3, wherein the compensated cutting points are cutter contact points, and the cutting track is an actual processing track; wherein the curve profile equation of the free-form surface equation z=f (x, y) to be processed at any angle α is z=f (r), and the equidistant curve of the curve is z=g (r); Step seven, calculating a curved surface outline equation of any angle alpha of the free-form surface to be processed to obtain an equidistant curve of the curve, calculating compensated cutter contact point data coordinates according to discrete point data on the outline curve, fitting the cutter contact point coordinates through an original free-form surface equation to obtain a processed free-form surface; Wherein when a discrete point (r q ,f(r q ) is taken on the curve profile), then the corresponding knife location point (r o ,f(r o )), wherein r o ＝r q ; Step eight, representing a design curved surface and a theoretical curved surface as a target point cloud X, taking a point cloud obtained through detection after processing as a source point cloud Y, adopting a two-step matching method, firstly approximating the source point cloud and the target point cloud within a small deviation range by utilizing a point cloud coarse registration algorithm, and then realizing accurate matching by a point cloud fine registration algorithm; R=R z (γ)R y (β)R x (α) (16) T(x)=Rx+t (21) Where R is a rotation matrix representing the rotation angles (α, β, γ) about each axis, and t is a translation vector representing the amount of translation along each axis (t x ,t y ,t z ); step nine, reducing the point cloud density by utilizing a downsampling technology, improving the processing efficiency, calculating the shape error E of the processed free-form surface by matching, and calculating PV and RMS by the shape error E; E=Z ij -Z' ij (22) PV=max(E)-min(E) (23) and step ten, reversely superposing the target point cloud and the obtained shape error E as shown in fig. 4, thus obtaining a new processing surface type, and carrying out processing again to carry out a correction flow again to obtain the free-form surface element meeting the processing requirements.

Description

Method for correcting shape error by free-form surface machining Technical Field The invention relates to a shape error correction method for free-form surface machining, and belongs to the field of ultra-precise machining. Background With the advancement of optical technology, free-form surfaces are increasingly used. Variations in the processing path, material properties, and processing environment during processing often result in large errors in the shape of the finished product and are difficult to correct. In order to solve the problem, the prior art mainly carries out subsequent correction and adjustment by comparing the difference between the theoretical curved surface and the actual processed curved surface. Conventional correction methods often rely on manual experience, lack systemicity, and are difficult to accommodate complex tooling shapes. Therefore, developing a highly efficient and automatic shape error correction method is of great importance for improving the machining accuracy of free-form surfaces. Disclosure of Invention Aiming at the problems of low efficiency and insufficient precision of the existing shape error processing method in free-form surface processing, the invention provides a method for correcting shape errors in free-form surface processing. According to the method, the characteristics of an original tool path are analyzed through a linearization error theory, a slow-tool servo turning tool path simulation model is established, and an Archimedes spiral line is adopted to describe the cutting path of the tool. On the basis, the radius compensation of the cutter is carried out, the compensated cutter contact point data is obtained, and the accuracy of the cutting track is ensured. And then, acquiring point clouds of the free curved surface to be processed, and respectively obtaining a source point cloud and a target point cloud. In order to realize reliable matching between the source point cloud and the target point cloud, a point cloud matching rough registration algorithm is adopted for rough registration, and then a point cloud fine registration algorithm is adopted for fine registration. Finally, the shape error is calculated by a least square method and is applied to correction, so that the machined free-form surface type is obtained. As shown in fig. 1, the present invention provides a method for correcting shape errors by free-form surface processing, comprising the following steps: Step one, reconstructing a theoretical curved surface from discrete measurement data through polynomial fitting or interpolation under the condition of lacking a known curved surface model based on a free curved surface shape representation method of a discrete measurement data point cloud, and carrying out surface alignment and shape representation; Step two, performing slow-tool servo turning on the represented free-form surface optical element, determining a proper turning track to improve the surface type precision of the free-form surface optical element, and selecting reasonable tool parameters including a tool radius, a tool arc wrap angle, a tool front angle and a tool rear angle to avoid machining interference phenomenon; step three, selecting a cutter arc wrap angle and correlating with a section curve z=g (X) of a curved surface to be processed, and optimizing cutter parameters by calculating an included angle between a vector and an X axis; θ1=arctan(z′) (1) θ2=-arctan(z′) (2) θ≥2max{θ1max,θ2max} (3) Rt=-ft/60 (4) θt=θt (5) When the included angle between the normal vector at the cutting point and the X axis is an acute angle, the included angle between the normal vector at the cutting point and the X axis is theta 1, and when the included angle between the normal vector at the cutting point and the X axis is an acute angle, theta 2, wherein R is the radius of the workpiece, R t is the distance from the cutting point to the center of the workpiece, theta t is the included angle between the cutting point and the X axis, f is the radial feeding speed of the cutter, and t is the cutting time; step four, selecting a cutter relief angle, wherein the slope of all section curves intersecting with a plane on a curved surface to be processed is considered, so that the cutter relief angle is ensured to be larger than the slope corresponding to all circumferential curve cutting points; ρ≥|max(arctan(f'))| (6) fifthly, establishing a tool path simulation model according to the obtained tool parameters, analyzing the characteristics of an original tool path according to a linearization error theory, as shown in fig. 2, constructing a simulation model of a slow-tool servo turning tool path, and expressing a cutting point as an Archimedes spiral line in the curved surface generation process; x=Rtcos(θt) (7) y=Rtsin(θt) (8) Wherein R is the radius of the workpiece, and R t is the distance from the cutting point to the center of the workpiece; step six, according to the obtained cutter posit