Method for cutting fluorite crystals and fluorite crystals

Abstract

The application relates to a calcium fluoride crystal cutting processing method and calcium fluoride crystal, which comprises the following steps: S1, obtaining a first minimum brittle-plastic transition critical cutting depth in ordinary cutting processing; S2, establishing a tool motion trajectory model based on an elliptical vibration ultra-precision cutting processing technology; S3, establishing a three-dimensional cutting thickness model based on the motion trajectory model, and obtaining a maximum instantaneous effective cutting thickness; S4, judging whether the maximum instantaneous effective cutting thickness is smaller than the first minimum brittle-plastic transition critical cutting depth; if yes, executing step S5; if not, executing step S2; S5, obtaining a brittle-plastic transition critical cutting depth model; and S6, processing a workpiece based on the brittle-plastic transition critical cutting depth model, and obtaining a plastic domain removed calcium fluoride crystal. The calcium fluoride crystal cutting processing method and the calcium fluoride crystal meet the high surface quality requirement in a subsequent process, improve processing efficiency, and provide technical support for improving the manufacturing level of calcium fluoride crystal optical parts.

Description

Technical Field

[0001] This invention relates to the field of optical component processing technology, and in particular to a method for machining calcium fluoride crystals and calcium fluoride crystals. Background Technology

[0002] The projection lithography objective system is a core component of an ultraviolet lithography machine, capable of achieving imaging quality close to the diffraction limit. Given that single-crystal calcium fluoride (… It has excellent properties such as high transmittance, low birefringence and high laser damage threshold in the ultraviolet band, and is an essential optical material for manufacturing deep ultraviolet projection lithography objectives.

[0003] Currently, the ultra-smooth optical surface of calcium fluoride crystal projection lithography objectives can be achieved through a process of ultra-precision cutting, diamond micron polishing, silica sol polishing, and ion beam shaping. The final processed surface can achieve sub-nanometer precision across the entire frequency band, including surface shape, waviness, and surface roughness.

[0004] Among these processes, ultra-precision machining is one of the key fundamental techniques for obtaining ultra-smooth optical surfaces in calcium fluoride crystal projection lithography objectives. The ultra-precision machining process for calcium fluoride crystals must meet the high surface quality requirements of subsequent polishing and ion beam shaping, including crack-free and low-subsurface-damage, nanoscale surface roughness, and interferometer-measurable surface accuracy. Plastic domain removal is crucial for meeting these high surface quality requirements; however, as a typical anisotropic soft and brittle material, calcium fluoride crystals are difficult to process efficiently to achieve ultra-smooth optical surfaces with low-subsurface-damage and plastic domain removal.

[0005] In existing technologies, ultra-precision machining of calcium fluoride crystals can achieve the removal of plastic domains on arbitrary crystal planes and orientations under extremely small cutting depths (50 nm), but it suffers from low efficiency. In recent years, elliptical vibration-assisted methods, which have characteristics such as low cutting force, low cutting heat, and high resistance to adhesive wear, have shown the potential to increase the critical cutting depth for the brittle-ductile transition in ultra-precision machining of difficult-to-machine brittle materials such as single-crystal silicon, silicon carbide, and tungsten carbide, thereby improving machining efficiency. However, the influence of material anisotropy and elliptical vibration effects on the removal of plastic domains in calcium fluoride crystals is still unclear, making it difficult to achieve stable and controllable plastic domain cutting and failing to provide a theoretical basis for improving machining efficiency. Summary of the Invention

[0006] Therefore, the technical problem to be solved by the present invention is to overcome the difficulty of achieving efficient and controllable removal of the plastic domain of calcium fluoride crystals in the prior art, and to provide a method for cutting and processing calcium fluoride crystals and calcium fluoride crystals, which can meet the high surface quality requirements of subsequent processes while improving processing efficiency, and provide technical support for improving the manufacturing level of calcium fluoride crystal optical components.

[0007] This invention provides a method for machining calcium fluoride crystals, comprising the following steps:

[0008] S1. Obtain the first minimum critical depth of cut for brittle-plastic transition during normal cutting.

[0009] S2. Based on the ultra-precision cutting process of elliptical vibration, establish a motion trajectory model of the tool when cutting the workpiece;

[0010] S3. Based on the motion trajectory model, establish a three-dimensional cutting thickness model when the tool cuts the workpiece, and obtain the maximum instantaneous effective cutting thickness during elliptical vibration ultra-precision cutting.

[0011] S4. Determine whether the maximum instantaneous effective cutting thickness is less than the first minimum brittle-plastic transition critical cutting depth; if yes, proceed to step S5; if no, proceed to step S2.

[0012] S5. Obtain the critical cutting depth model for brittle-plastic transition during elliptical vibration ultra-precision cutting.

[0013] S6. Based on the critical cutting depth model of the brittle-plastic transition, the workpiece is machined to obtain calcium fluoride crystals removed from the plastic domain by elliptical vibration ultra-precision cutting.

[0014] In one embodiment of the present invention, the motion trajectory model includes a first motion trajectory model along the cutting motion direction of the tool; step S2 includes:

[0015] S21. Obtain the first motion trajectory model;

[0016] The origin is the center of the elliptical vibration trajectory of the cutting tool tip. Establish coordinate system The shaft is parallel to the cutting direction of the tool. shaft and the The axis is perpendicular;

[0017] The first motion trajectory model is:

[0018]

[0019]

[0020] in, For the cutting tool in Displacement in the direction, For the cutting tool in Displacement in the direction, The amplitude is the direction of the cutting motion. The amplitude is in the depth of cut. The vibration frequency, For cutting speed, For phase difference, For time.

[0021] In one embodiment of the present invention, the three-dimensional cutting thickness model includes a first cutting thickness model along the cutting motion direction of the tool; step S3 includes:

[0022] S31. Based on the first motion trajectory model, obtain the first cutting thickness model;

[0023] Let the starting time of the first tool movement be... The starting time for the second cut is The trajectory of the first tool movement is then:

[0024]

[0025]

[0026] The trajectory of the second tool movement is as follows:

[0027]

[0028]

[0029] The distance between the first and second tool paths, i.e., the first instantaneous effective cutting thickness between the first and second tool paths; within one cycle arrive Time discretization The values ​​are respectively The distance between two consecutive toolpaths is... ;

[0030] The first cutting thickness model is:

[0031]

[0032] S32, Based on the first cutting thickness model The first maximum instantaneous effective cutting thickness along the cutting motion direction of the tool is obtained. .

[0033] In one embodiment of the present invention, step S4 includes:

[0034] S41. Determine the first maximum instantaneous effective cutting thickness. Is it less than the first minimum critical depth of cut for brittle-plastic transition? If yes, proceed to step S51; if no, proceed to step S21.

[0035] The critical depth of cut model for brittle-plastic transition includes a first critical depth of cut model for brittle-plastic transition along the cutting motion direction of the tool;

[0036] Step S5 includes:

[0037] S51, Record the first maximum instantaneous effective cutting thickness The corresponding mathematical model is the first critical cutting depth model for brittle-plastic transition; proceed to step S6.

[0038] In one embodiment of the present invention, the motion trajectory model includes a second motion trajectory model along the feed motion direction of the tool; step S2 includes:

[0039] S22. Obtain the second motion trajectory model;

[0040] The second motion trajectory model includes multiple tool path interface contour curves, each of which is formed by one pass of the tool during the feed process; any tool path interface contour curve is selected and denoted as the first tool path interface contour curve.

[0041] Along the feed direction, take the point on the first tool path interface contour curve that is furthest from its lowest point. One of the points with half the feed rate Establish with the origin as the starting point. coordinate system The shaft is parallel to the feed direction of the tool. shaft and the The axis is perpendicular;

[0042] The first tool path interface contour curve is:

[0043]

[0044] The second tool path profile curve is defined as the one feed rate curve that differs from the first tool path profile curve. The second tool path profile curve is as follows:

[0045]

[0046] in, It is a positive integer. For the cutting tool in Displacement in the direction, For the cutting tool in Displacement in the direction, For feed rate, Let be the radius of the arc of the cutting tool.

[0047] In one embodiment of the present invention, the three-dimensional cutting thickness model includes a second cutting thickness model along the feed direction of the tool; step S3 includes:

[0048] S33. Based on the second motion trajectory model, obtain the second cutting thickness model;

[0049] The second cutting thickness model is:

[0050]

[0051] Where D is the depth of cut;

[0052]

[0053]

[0054]

[0055] S34, Based on the second cutting thickness model The second maximum instantaneous effective cutting thickness along the feed direction of the tool is obtained. .

[0056] In one embodiment of the present invention, step S4 includes:

[0057] S42. Determine the second maximum instantaneous effective cutting thickness. Is it less than the first minimum critical depth of cut for brittle-plastic transition? If yes, proceed to step S52; if no, proceed to step S22.

[0058] The critical depth of cut model for the brittle-plastic transition includes a second critical depth of cut model for the brittle-plastic transition along the feed direction of the tool.

[0059] Step S5 includes:

[0060] S52, Record the second maximum instantaneous effective cutting thickness The corresponding mathematical model is the second critical cutting depth model for brittle-plastic transition; proceed to step S6.

[0061] In one embodiment of the present invention, step S1 includes:

[0062] S11. Take the same workpiece and perform a variable cutting and deep scratching experiment to obtain a control workpiece;

[0063] S12. Observe and analyze the brittle-plastic deformation characteristics of the groove surface of the control workpiece to obtain the first minimum critical cutting depth for brittle-plastic transition.

[0064] In one embodiment of the present invention, step S11 includes:

[0065] Take the same workpiece and perform a variable cutting depth scratch test every 30° angle on the (100), (110) and (111) crystal planes of the workpiece; repeat the variable cutting depth scratch test in each direction three times to obtain a control workpiece.

[0066] The present invention also provides a calcium fluoride crystal, which is obtained by processing based on the calcium fluoride crystal cutting method described in any one of the above-mentioned methods.

[0067] The technical solution of the present invention has the following advantages over the prior art:

[0068] The calcium fluoride crystal machining method of this invention, based on the critical depth-of-cut model for the brittle-plastic transition and elliptical vibration ultra-precision machining process, enables efficient, stable, and controllable removal of the plastic domain from workpieces with arbitrary crystal planes and orientations under different cutting parameters, providing technical support for improving the manufacturing level of calcium fluoride crystal optical components. Machining workpieces using the calcium fluoride crystal machining method of this invention not only meets the high surface quality requirements of subsequent processes but also increases the critical depth-of-cut for the brittle-plastic transition, thereby improving machining efficiency. Attached Figure Description

[0069] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings, wherein...

[0070] Figure 1 This is a flowchart of the calcium fluoride crystal cutting process in a preferred embodiment of the present invention;

[0071] Figure 2 This is a three-dimensional structural diagram of the cutting process in a preferred embodiment of the present invention;

[0072] Figure 3 This is a schematic diagram of the cutting process along the tool feed direction in a preferred embodiment of the present invention;

[0073] Figure 4 This is a schematic diagram of the cutting process along the cutting direction of the tool in a preferred embodiment of the present invention;

[0074] Figure 5 This is a cross-sectional view of the corresponding point along the tool feed direction in a preferred embodiment of the present invention.

[0075] Explanation of reference numerals in the accompanying drawings: 10. Tool; 11. Rake face; 12. Flank face; 13. Tool tip; D1. Direction of cutting motion; D2. Direction of feed motion; 20. Workpiece; 31. Trajectory of the first tool pass; 32. Trajectory of the second tool pass; 33. Contour curve of the first tool pass interface; 34. Contour curve of the second tool pass interface. Detailed Implementation

[0076] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0077] Reference Figure 1 The present invention discloses a method for machining calcium fluoride crystals, comprising the following steps:

[0078] S1. Obtain the first minimum critical depth of cut for brittle-plastic transition during normal cutting.

[0079] S2. Based on the ultra-precision cutting process of elliptical vibration, establish a motion trajectory model of tool 10 cutting workpiece 20;

[0080] S3. Based on the motion trajectory model, establish a three-dimensional cutting thickness model when the tool 10 cuts the workpiece 20, and obtain the maximum instantaneous effective cutting thickness during elliptical vibration ultra-precision cutting.

[0081] S4. Determine whether the maximum instantaneous effective cutting thickness is less than the first minimum brittle-plastic transition critical cutting depth; if yes, proceed to step S5; if no, proceed to step S2.

[0082] S5. Obtain the critical cutting depth model for brittle-plastic transition during elliptical vibration ultra-precision cutting.

[0083] S6. Based on the critical cutting depth model of the brittle-plastic transition, the workpiece 20 is machined to obtain calcium fluoride crystals removed from the plastic domain by ultra-precision cutting using elliptical vibration.

[0084] In existing technologies, calcium fluoride crystals require cutting under plasticity conditions to ensure a crack-free machined surface. However, the critical depth of cut for the brittle-plastic transition of calcium fluoride crystals during conventional cutting is very small, allowing only a very thin layer of material to be cut at a time. Elliptical vibration ultra-precision cutting can increase the critical depth of cut for the brittle-plastic transition of calcium fluoride crystals, allowing for a thicker layer to be cut at a time, thus improving machining efficiency compared to conventional cutting. However, the influence of material anisotropy and elliptical vibration effects on the removal of the plasticity domain in calcium fluoride crystals remains unclear. To ensure stability, the cutting depth is usually set to a small value, much smaller than the actual critical depth of cut for the brittle-plastic transition, making it difficult to achieve efficient, stable, and controllable plasticity domain cutting.

[0085] The calcium fluoride crystal machining method of this invention, based on the critical depth-of-cut model for the brittle-plastic transition and elliptical vibration ultra-precision machining process, can efficiently, stably, and controllably remove the plastic domain of workpiece 20 with arbitrary crystal planes and orientations under different cutting parameters, providing technical support for improving the manufacturing level of calcium fluoride crystal optical components. Machining workpiece 20 using the calcium fluoride crystal machining method of this invention not only meets the high surface quality requirements of subsequent processes but also increases the critical depth-of-cut for the brittle-plastic transition, thereby improving machining efficiency.

[0086] Elliptical vibration ultra-precision cutting process is an existing technology, referring to Figure 2 As shown, during the machining process, the workpiece 20 is fixed, while the cutting tool 10 moves relative to the workpiece 20. Preferably, a circular arc-shaped diamond cutting tool 10 is selected to ensure machining efficiency and quality. The cutting tool 10 includes a rake face 11, a flank face 12, and a cutting tip 13. The relative motion of the cutting tool 10 can be divided into motion along the feed direction D2 and motion along the cutting direction D1. After completing one machining operation along the cutting direction D1, the cutting tool 10 feeds one feed amount along the feed direction D2. Then proceed with the next cut.

[0087] I. Obtaining the first minimum critical depth of cut for the brittle-plastic transition during ordinary cutting:

[0088] S11. Take the same workpiece 20 and conduct a variable cutting and deep scratching experiment to obtain a control workpiece.

[0089] Specifically, variable depth scoring experiments were performed on the (100), (110), and (111) crystal planes of workpiece 20 at 30° angles. The variable depth scoring experiment in each direction was repeated three times to obtain a control workpiece. The definitions of each crystal plane are common knowledge to those skilled in the art and will not be elaborated further.

[0090] Preferably, a variable depth-of-cut ordinary scribing experiment is conducted using an ultra-precision lathe, a single-crystal diamond tool 10 with an arc-shaped cutting edge, and a calcium fluoride crystal workpiece that has undergone ultra-precision polishing pretreatment. This can efficiently obtain the corresponding minimum critical depth of cut for the brittle-plastic transition.

[0091] S12. Observe and analyze the brittle-plastic deformation characteristics of the groove surface of the control workpiece to obtain the first minimum critical cutting depth for brittle-plastic transition. Preferably, a scanning electron microscope (SEM) and a white light interferometer are used to observe and analyze the brittle-plastic deformation characteristics of the groove surface of the control workpiece, resulting in accurate results. How to observe and analyze the brittle-plastic deformation characteristics is common knowledge and will not be elaborated further.

[0092] II. Based on the ultra-precision cutting process using elliptical vibration, a motion trajectory model is established for tool 10 cutting workpiece 20:

[0093] Analysis of the relative motion process between the tool 10 and the workpiece 20 during the machining process.

[0094] S21. Obtain the first motion trajectory model.

[0095] Reference Figure 2 and Figure 3 As shown, the motion trajectory model includes a first motion trajectory model along the cutting motion direction D1 of the tool 10.

[0096] Along the cutting motion direction D1, the tool 10 undergoes elliptical vibration motion. The origin is the center of the elliptical vibration trajectory of the tool tip 13. Establish Coordinate system, where, The shaft is parallel to the cutting motion direction D1 of the tool 10. shaft and The axis is perpendicular. In the figure, the shaded area represents the cross-sectional area of ​​the cutting layer.

[0097] The first motion trajectory model is:

[0098] (1)

[0099] (2)

[0100] in, For the cutting tool 10 in Displacement in the direction, For the cutting tool 10 in Displacement in the direction, Let D1 be the amplitude of the cutting motion direction. The amplitude is in the depth of cut. The vibration frequency, For cutting speed, For phase difference, For time. Based on formulas (1) and (2), the first motion trajectory model of the tool 10 along the cutting motion direction D1 can be accurately expressed.

[0101] S22. Obtain the second motion trajectory model.

[0102] Reference Figure 2 and Figure 4 As shown, the motion trajectory model also includes a second motion trajectory model along the feed motion direction D2 of the tool 10.

[0103] The second motion trajectory model includes multiple tool path interface contour curves. Each tool path interface contour curve is formed by one pass of the tool 10 during the feed process, and each tool path interface contour curve is an arc-shaped curve. One arbitrary tool path interface contour curve is denoted as the first tool path interface contour curve 33.

[0104] Along the feed direction D2, take the distance from the lowest point on the first tool path interface contour curve 33. One of the points with half the feed rate Establish with the origin as the starting point. Coordinate system, where, The shaft is parallel to the feed direction D2 of the tool 10. shaft and The axis is perpendicular. It should be noted that the lowest point on the first toolpath interface contour curve 33... This indicates that the point is at The value corresponding to the axis is the smallest.

[0105] The first toolpath interface contour curve 33 is:

[0106] (3)

[0107] Let the second feed interface profile curve 34 be the one feed rate difference between the first feed interface profile curve 33 and the second feed interface profile curve 34. The second feed interface profile curve 34 is as follows:

[0108] (4)

[0109] in, It is a positive integer. For the cutting tool 10 in Displacement in the direction, For the cutting tool 10 in Displacement in the direction, For feed rate, Let be the radius of the arc of tool 10. Based on formulas (3) and (4), the second motion trajectory model of tool 10 along the feed motion direction D2 can be accurately expressed.

[0110] III. Based on the motion trajectory model, a three-dimensional cutting thickness model is established when tool 10 cuts workpiece 20, and the maximum instantaneous effective cutting thickness during elliptical vibration ultra-precision cutting is obtained:

[0111] By analyzing the mapping relationship between cutting parameters, tool 10 geometric parameters, elliptical vibration parameters, and instantaneous effective cutting thickness during actual cutting, a three-dimensional cutting thickness model that takes into account the influence of tool 10 feed and reflects the three-dimensional state during ultra-precision cutting of elliptical vibration is established, thereby obtaining the maximum instantaneous effective cutting thickness.

[0112] S31. Based on the first motion trajectory model, obtain the first cutting thickness model.

[0113] The three-dimensional cutting thickness model includes a first cutting thickness model along the cutting motion direction D1 of the tool 10.

[0114] Let the starting time of the first tool movement be... The starting time for the second cut is The trajectory 31 for the first cut is:

[0115] (5)

[0116] (6)

[0117] The second tool path 32 is as follows:

[0118] (7)

[0119] (8)

[0120] The distance between the first tool path 31 and the second tool path 32 is the first instantaneous effective cutting thickness between the first tool path 31 and the second tool path 32.

[0121] Within a period arrive Time discretization The values ​​are respectively The distance between two consecutive toolpaths is... .

[0122] The first cutting thickness model is:

[0123] (9)

[0124] By substituting the parameters into formulas (5) to (8) for calculation, and then substituting the results into formula (9), the corresponding first instantaneous effective cutting thickness can be obtained.

[0125] S32, Based on the first cutting thickness model The first maximum instantaneous effective cutting thickness along the cutting motion direction D1 of the tool 10 is obtained. .

[0126] By comparing the magnitudes of the effective cutting thicknesses at each first instant, the first maximum effective cutting thickness can be obtained. .

[0127] S33. Based on the second motion trajectory model, obtain the second cutting thickness model.

[0128] The three-dimensional cutting thickness model includes a second cutting thickness model along the feed motion direction D2 of the tool 10.

[0129] The second cutting thickness model is:

[0130] (10)

[0131] in, This refers to the depth of cut.

[0132] (11)

[0133] (12)

[0134] (13)

[0135] By substituting the parameters into formulas (3) and (4) for calculation, and then substituting the results into formula (10), the corresponding second instantaneous effective cutting thickness can be obtained.

[0136] S34, Based on the second cutting thickness model The second maximum instantaneous effective cutting thickness along the feed motion direction D2 of the tool 10 is obtained. .

[0137] By comparing the magnitudes of each second instantaneous effective cutting thickness, the second maximum instantaneous effective cutting thickness can be obtained. .

[0138] The following is about The analysis is limited by the scope.

[0139] Reference Figure 4 and Figure 5 As shown, arc The effective arc segment in contact between the cutting edge of tool 10 and workpiece 20, along the arc The effective cutting thickness at the second instant will change continuously.

[0140] Among them, point The distance from the lowest point on the first tool path interface contour curve 33 The point with half the feed rate. This is the point of contact between the cutting edge of tool 10 and the surface to be machined on workpiece 20 at the end of the second pass.

[0141] Yu Hu Take four points above, which are points... ,point ,point and points Midpoint It is the lowest point on the contour curve 34 of the second tool path interface.

[0142] Therefore, it can be concluded that, in the feed motion direction D2, point With point The distance between them is half the feed rate, that is And point With point The distance between them is one feed amount, i.e. The corresponding formulas are (11) and (13).

[0143] point and points For point and points Any two points between them. The point of contact between the cutting edge of tool 10 and the surface to be machined on workpiece 20 at the end of the first pass is called the point of contact. For the point Constructing perpendicular lines, perpendicular lines and arcs The intersection point corresponds to formula (12).

[0144] It can be known that in the arc Up, point The second effective cutting thickness is greatest at point [location], while it is greatest at point [location]. The second effective cutting thickness corresponding to the points on both sides gradually decreases to 0.

[0145] IV. Determine whether the maximum instantaneous effective cutting thickness is less than the first minimum critical cutting depth for brittle-plastic transition:

[0146] Controlling the maximum instantaneous effective cutting thickness during elliptical vibration ultra-precision cutting to be less than the first minimum critical cutting depth for brittle-plastic transition during ordinary cutting is one of the key points for efficiently machining to obtain a low-subsurface-damage, ultra-smooth optical surface with plastic domain removal.

[0147] S41. Determine the first maximum instantaneous effective cutting thickness. Is the depth of cut less than the first minimum critical depth for brittle-plastic transition? If yes, proceed to step S51; otherwise, proceed to step S21.

[0148] S42. Determine the second maximum instantaneous effective cutting thickness. Is the depth of cut less than the first minimum brittle-plastic transition critical depth? If yes, proceed to step S52; otherwise, proceed to step S22.

[0149] V. Obtaining the critical depth-of-cut model for the brittle-plastic transition during elliptical vibration ultra-precision machining:

[0150] The critical depth of cut model for brittle-plastic transition includes a first critical depth of cut model for brittle-plastic transition along the cutting motion direction D1 of the tool 10, and a second critical depth of cut model for brittle-plastic transition along the feed motion direction D2 of the tool 10.

[0151] S51, Record the first maximum instantaneous effective cutting thickness The corresponding mathematical model is the critical cutting depth model for the first brittle-plastic transition.

[0152] S52, Record the second maximum instantaneous effective cutting thickness The corresponding mathematical model is the critical cutting depth model for the second brittle-plastic transition.

[0153] VI. Based on the critical depth of cut model for the brittle-plastic transition, workpiece 20 was machined to obtain calcium fluoride crystals removed from the plastic domain by ultra-precision cutting using elliptical vibration:

[0154] Specifically, workpiece 20 is machined based on the first critical cutting depth model of brittle-plastic transition and the second critical cutting depth model of brittle-plastic transition to obtain calcium fluoride crystals removed from the plastic domain by elliptical vibration ultra-precision cutting.

[0155] The present invention also discloses a calcium fluoride crystal, which is obtained by processing the calcium fluoride crystal cutting method described in any of the above embodiments.

[0156] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A method of cutting fluorite crystals, characterized by, Includes the following steps: S1. Obtain the first minimum critical depth of cut for brittle-plastic transition during normal cutting. S2. Based on the elliptical vibration ultra-precision cutting process, establish a motion trajectory model of the tool cutting the workpiece. The motion trajectory model includes a first motion trajectory model along the cutting motion direction of the tool and a second motion trajectory model along the feed motion direction of the tool. This includes S21, obtaining the first motion trajectory model and S22, obtaining the second motion trajectory model. S3. Based on the motion trajectory model, establish a three-dimensional cutting thickness model when the tool cuts the workpiece to obtain the maximum instantaneous effective cutting thickness during elliptical vibration ultra-precision cutting; the maximum instantaneous effective cutting thickness includes a first maximum instantaneous effective cutting thickness along the cutting motion direction of the tool and a second maximum instantaneous effective cutting thickness along the feed motion direction of the tool. S4. Determine whether the maximum instantaneous effective cutting thickness is less than the first minimum brittle-plastic transition critical cutting depth, including S41. Determine the first maximum instantaneous effective cutting thickness. Is it less than the first minimum critical depth of cut for brittle-plastic transition? If yes, proceed to step S51; if no, proceed to step S21. And, S42, determine the second maximum instantaneous effective cutting thickness. Is the depth of cut less than the first minimum brittle-plastic transition critical depth? If yes, proceed to step S52; if no, proceed to step S22. S5. Obtain the critical depth of cut model for brittle-plastic transition during elliptical vibration ultra-precision cutting. The critical depth of cut model for brittle-plastic transition includes a first critical depth of cut model for brittle-plastic transition along the cutting motion direction of the tool and a second critical depth of cut model for brittle-plastic transition along the feed motion direction of the tool. This includes S51, denoted by the first maximum instantaneous effective cutting thickness. The corresponding mathematical model is the first critical cutting depth model for the brittle-plastic transition; and, S52, denoted as the second maximum instantaneous effective cutting thickness. The corresponding mathematical model is the second critical cutting depth model for the brittle-plastic transition; S6. Based on the critical cutting depth model of the brittle-plastic transition, the workpiece is machined to obtain calcium fluoride crystals removed from the plastic domain by ultra-precision cutting using elliptical vibration.

2. The method for machining calcium fluoride crystals according to claim 1, characterized in that, Step S21, obtaining the first motion trajectory model includes: The origin is the center of the elliptical vibration trajectory of the cutting tool tip. Establish coordinate system The shaft is parallel to the cutting direction of the tool. shaft and the The axis is perpendicular; The first motion trajectory model is: ， ， in, For the cutting tool in Displacement in the direction, For the cutting tool in Displacement in the direction, The amplitude is the direction of the cutting motion. The amplitude is in the depth of cut. The vibration frequency, For cutting speed, For phase difference, For time.

3. The method for machining calcium fluoride crystals according to claim 2, characterized in that, The three-dimensional cutting thickness model includes a first cutting thickness model along the cutting motion direction of the tool; step S3 includes: S31. Based on the first motion trajectory model, obtain the first cutting thickness model; Let the starting time of the first tool movement be... The starting time for the second cut is The trajectory of the first tool movement is then: ， ， The trajectory of the second tool movement is as follows: ， ， The distance between the first and second tool paths, i.e., the first instantaneous effective cutting thickness between the first and second tool paths; within one cycle arrive Time discretization The values ​​are respectively The distance between two consecutive toolpaths is... ; The first cutting thickness model is: ， S32, Based on the first cutting thickness model The first maximum instantaneous effective cutting thickness along the cutting motion direction of the tool is obtained. .

4. The method for machining calcium fluoride crystals according to any one of claims 1-3, characterized in that, Step S22, obtaining the second motion trajectory model includes: The second motion trajectory model includes multiple tool path interface contour curves, each of which is formed by one pass of the tool during the feed process; any one of the tool path interface contour curves is selected and denoted as the first tool path interface contour curve. Along the feed direction, take the point on the first tool path interface contour curve that is furthest from its lowest point. One of the points with half the feed rate Establish with the origin as the starting point. coordinate system The shaft is parallel to the feed direction of the tool. shaft and the The axis is perpendicular; The first tool path interface contour curve is: ， The second tool path profile curve is defined as the one feed rate curve that differs from the first tool path profile curve. The second tool path profile curve is as follows: ， in, It is a positive integer. For the cutting tool in Displacement in the direction, For the cutting tool in Displacement in the direction, For feed rate, Let be the radius of the arc of the cutting tool.

5. The method for machining calcium fluoride crystals according to claim 4, characterized in that, The three-dimensional cutting thickness model includes a second cutting thickness model along the feed direction of the tool; step S3 includes: S33. Based on the second motion trajectory model, obtain the second cutting thickness model; The second cutting thickness model is: ， Where D is the depth of cut; ， ， ， S34, Based on the second cutting thickness model The second maximum instantaneous effective cutting thickness along the feed direction of the tool is obtained. .

6. The method for machining calcium fluoride crystals according to claim 1, characterized in that, Step S1 includes: S11. Take the same workpiece and perform a variable cutting and deep scratching experiment to obtain a control workpiece; S12. Observe and analyze the brittle-plastic deformation characteristics of the groove surface of the control workpiece to obtain the first minimum critical cutting depth for brittle-plastic transition.

7. The method for machining calcium fluoride crystals according to claim 6, characterized in that, Step S11 includes: taking the same workpiece and performing a variable cutting deep scratch test every 30° angle on the (100), (110) and (111) crystal planes of the workpiece; repeating the variable cutting deep scratch test in each direction three times to obtain a control workpiece.

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