Design method for regular polygon slow tool servo tool path

Abstract

The invention discloses a regular polygon slow tool servo tool path design method which is realized on an ultra-precise single-point diamond lathe with linear motion axes X and Z and a turning main shaft C with angle positioning. The projection of the whole tool path on the XOY plane is designed into a regular polygon by utilizing the triangle geometry principle, equal-angle discrete sampling and step length gradual change mode, and the regular polygon is divided into turning areas with the number consistent with that of the edges of the polygon; and in all the turning areas, the cutter does linear motion relative to the machined workpiece, and linear turning is conducted on the to-be-machined workpiece. Compared with an existing Archimedes spiral turning technology, the designed tool path comprehensively considers feeding linkage of the X axis and the Z axis, the machining mode is optimized, and compensation of the arc curvature radius of the tool is convenient.

Description

Technical Field

[0003] The invention relates to ultra-precision turning, and in particular to a three-axis single-point diamond lathe slow-tool servo regular polygon tool path design method, which provides a new technical solution for the processing of optical reflectors containing array structures such as metal polygonal prisms and laser radar rotating mirrors. Background Art

[0005] At present, the processing and manufacturing technology of optical surfaces such as metal multi-faceted prisms or laser radar rotating mirrors usually adopts ultra-precision single-point diamond fly cutter milling, conventional rotary turning and slow tool servo turning technology. Fly cutter milling requires the tool to be placed on a vacuum suction cup, and the reflector to be processed is fixed on a high-precision turntable, and the two cooperate with each other to complete the processing. However, this method is difficult to align the tool at the beginning, and it is difficult to ensure that the feed amount of all surfaces is consistent. At the same time, the accuracy of the turntable limits the angular accuracy of the two adjacent surfaces of the reflector. Although conventional rotary turning technology has high efficiency, such as the patent "A method for processing a metal multi-faceted reflective prism ZL202111194632.2", its main problem is that it requires high-precision bevel fixtures or rotating workpieces to realize the processing of all surfaces, there is a certain amount of repeated positioning error, and the processing size is limited. As a method of optical free-form surface processing, slow tool servo turning technology can also be used for the processing of such optical elements. There is no need for a turntable and a rotating fixture. With the designed tool path, all optical surfaces can be formed at one time, and the angular accuracy between the array surfaces depends entirely on the C-axis accuracy of the lathe itself.

[0006] The projections of the existing slow tool servo tool paths on the XOY plane are all circular spirals. For special optical surfaces with multiple plane arrays, such as prisms and rotating mirrors, the spiral tool paths are prone to tool back angle interference and scratches, which seriously affect the smoothness of the optical surface. In addition, the edge lengths of the adjacent surfaces of the prism are the parts with sudden changes in curvature. Due to the limitations of the corresponding frequencies of the Z and C axes, the turning speed here slows down and the turning is discontinuous, affecting the final accuracy. Summary of the invention

[0008] The purpose of the present invention is to overcome the shortcomings of the prior art and propose a regular polygon slow tool servo tool path design method. The equidistant spiral path is transformed into a regular polygon path, the angle accuracy of the adjacent surface is improved, and the molding is performed in one step, thereby overcoming the difficult processing problem of special optical surfaces caused by the surface shape being a planar array.

[0009] The present invention adopts the following technical solution:

[0010] The regular polygon slow tool servo tool path is a regular polygon 3D linear path composed of the polar diameter ρ, polar angle θ and the sagittal height Z of the surface to be processed. It is implemented on an ultra-precision lathe with linear motion axes X, Z and an angularly positioned turning spindle C. The lathe X-axis, C-axis and Z-axis complete the corresponding feed motion according to the polar diameter ρ, polar angle θ and sagittal height Z values. The design method of the regular polygon 3D linear tool path is as follows:

[0011] The projection path is the path of the 3D tool path projected onto the XOY plane (or ρ-θ plane) perpendicular to the Z axis of the lathe. The projection path consists of the polar radius ρ and the polar angle θ. The polar angle range is 0-2π and is divided into n turning zones by the number of sides of the regular polygon n. In all turning zones, the tool turns the workpiece to be processed and moves linearly relative to the workpiece. In the kth path circle, the polar radius ρ of each tool position point P in the first turning zone is defined as,

[0012] (5)

[0013] (6)

[0014] (7)

[0015] Where θ is the polar angle, L is the apicocenter distance of the regular polygon on the kth path circle, and θ k is the maximum edge polar angle of the first turning area, k=1,2,3.... is the path number, d is the path sampling step, L min and L max They are respectively the size of the tool position point polar diameter ρ when the polar angle of the first turning zone is 0, and this value is determined by the size of the optical surface to be processed; the relationship between the polar diameter ρ and the polar angle θ is calculated by combining the above formula, and then each projected tool position point P in the first turning zone is completely defined; the subsequent 2-n turning zone polar diameters are based on the above method, and in the order of each turning zone, the next cutting zone polar angle is increased to the maximum edge polar angle value θ of the previous turning zone k The sum of the polar angle θ of the turning area, that is, the polar angle of the second turning area θ|2=θ+θ k , the polar angle of the third turning zone θ|3=θ+2θ k Substitute into equation (1) and equation (2) and calculate each polar diameter sequentially;

[0016] The complete 3D tool path expression is {ρ,θ,Z}, where the Z value is calculated by the projection path (ρ,θ) of each turning area combined with the surface height f equation.

[0017] (8)

[0018] The above-mentioned regular polygon slow-tool servo tool path is divided into at least three equally linear turning areas. Two adjacent turning areas are smoothly connected without breakpoints using the above-mentioned method. One tool path can be used to complete the turning of at least three small workpieces, and can also complete the processing of a polyhedron prism or a laser radar rotating mirror.

[0019] The 3D tool path proposed in the present invention belongs to full-area linear path turning, and has the following requirements for the surface features of the workpiece, especially the polyhedron prism angle:

[0020] (9)

[0021] Where β is the angle between the bottom surface of the polyhedral prism and the edge length. In order to avoid the contact interference problem between the back angle of the turning tool and the surface to be machined, the β value is controlled within 45°. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 This is a schematic diagram of the processing of a regular octahedron laser radar rotating mirror workpiece;

[0024] Figure 2 This is a side view of the octahedral laser radar rotating mirror workpiece;

[0025] Figure 3 It is a projection diagram of a regular polygon tool path of the present invention;

[0026] Figure 4 It is a curve diagram of the change of the Z value of the vector height within a rotation period;

[0027] Figure 5 It is a distribution curve of the polar diameter ρ value within a rotation period. DETAILED DESCRIPTION

[0029] The technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0030] Example 1

[0031] See attached Figure 1 and attached Figure 2 The workpiece to be processed in this embodiment is a regular octahedron laser radar rotating mirror workpiece, the bottom length is 30 mm, the rotating mirror surface is flat, the slope angle is 30°, and the height is 6 mm. According to this optical surface, the regular polygon projection tool path designed is shown in the attached Figure 3 , the path is divided into 8 turning zones. In all turning zones, the tool performs linear turning on the workpiece. The angle θ in each zone k If the minimum polar diameter L is 135°, the polar angle range of the first turning area is 0-135°, the polar angle range of the second turning area is 135-270°, and so on until the polar angles of all turning surfaces are defined.min and L max They are 10 mm and 15 mm respectively. With d = 0.1 mm as the sampling step, the total path circle is 50; according to formula (1), formula (2) and formula (3), in the first path circle, the polar radius ρ of each tool position point P in the first turning area is,

[0032] ρ=L·cos(135 / 2) / cos(135 / 2-θ) (0 ≤ θ ≤ 135) (10)

[0033] L=14.9-0.1·(θ / 135) / 8 (10 ≤ L ≤ 15) (11)

[0034] The complete 3D tool path expression is {ρ,θ,Z}, where the Z value is:

[0035] Z=(L max -L)·tanβ (12)

[0036] Where β is the bevel angle 30°.

[0037] Figure 4 This is the variation curve of the Z value of the sagittal height in a rotation cycle of 0-360°. As can be seen from the figure, the overall distribution is linear. At this time, the response of the Z axis of the lathe has no sudden change, which is conducive to the stable operation of the lathe and improves the processing accuracy.

[0038] Figure 5 This is the distribution curve of the polar diameter ρ value in a rotation cycle of 0-360°. It can be seen from the figure that the X-axis has 8 continuous smooth fluctuations, and the difference between the maximum and minimum fluctuations is 0.2 mm. The peak value of the fluctuation change corresponds to the edge of the rotating mirror. The two are smoothly connected, and there is no sudden change on the surface of the connection.

Claims

1. A regular polygon slow tool servo tool path design method, characterized by: The regular polygon slow tool servo tool path is a regular polygon 3D linear path composed of a polar diameter ρ, a polar angle θ and a sagittal height Z of the surface to be processed, which is implemented on an ultra-precision lathe with linear motion axes X, Z and a turning spindle C with angle positioning. The lathe X-axis, C-axis and Z-axis complete the corresponding feed motion according to the polar diameter ρ, polar angle θ and sagittal height Z values ​​respectively; The design method of the regular polygon 3D linear tool path is as follows: The projection path is the path of the 3D tool path projected onto the XOY plane (or ρ-θ plane) perpendicular to the Z axis of the lathe. The projection path is composed of the polar radius ρ and the polar angle θ; the polar angle range of 0-2π is divided into n turning zones by the number of sides of the regular polygon n. In all turning zones, the tool performs linear turning on the workpiece to be processed; in the kth path circle, the polar radius ρ of each tool position point P in the first turning zone is defined as, (1) (2) (3) Where θ is the polar angle, L is the apicocenter distance of the regular polygon on the kth path circle, and θ k is the maximum edge polar angle of the first turning area, k=1,2,3.... is the path number, d is the path sampling step, L min and L max They are respectively the size of the tool position point polar diameter ρ when the polar angle of the first turning zone is 0, and this value is determined by the size of the optical surface to be processed; the relationship between the polar diameter ρ and the polar angle θ is calculated by combining the above formula, and then each projected tool position point P in the first turning zone is completely defined; the subsequent 2-n turning zone polar diameters are based on the above method, and in the order of each turning zone, the next cutting zone polar angle is increased to the maximum edge polar angle value θ of the previous turning zone k The sum of the polar angle θ of the turning area, that is, the polar angle of the second turning area θ|2=θ+θ k , the polar angle of the third turning zone θ|3=θ+2θ k Substitute into equation (1) and equation (2) and calculate each polar diameter sequentially; The complete expression of the 3D tool path is {ρ,θ,Z}, where the Z value is calculated by the projection path (ρ,θ) of each turning area combined with the surface height f equation. (4) The regular polygon slow tool servo tool path is divided into at least three equally linear turning areas. Two adjacent turning areas are smoothly connected without breakpoints using the above method. One tool path can be used to complete the turning of at least three small workpieces, and can also complete the processing of a polyhedron prism or a laser radar rotating mirror.

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