A method for characterizing a cutting mode of a micro-milling repair process of a surface defect of a KDP crystal

Abstract

This invention discloses a method for characterizing the cutting mode during the micro-milling repair process of KDP crystal surface defects. It relates to the field of optical component processing technology and addresses the problem that existing methods assume the workpiece material surface is defect-free, lacking a three-dimensional model of the cutting energy specificity for ball-end micro-milling that considers the presence of micro-defects. The method includes the following steps: Step 1, selecting repair process parameters and measuring the depth of crystal surface defects; Step 2, establishing a three-dimensional calculation model of the average cutting area of ​​ball-end micro-milling; Step 3, collecting the cutting force during the surface defect micro-milling repair process; Step 4, constructing a cutting energy specificity model for the ball-end micro-milling repair process; Step 5, analyzing the cutting mode during the micro-milling repair process based on the cutting energy specificity model. This invention provides a reference for improving surface quality, controlling size effects, and optimizing process parameters in actual repair processes, thereby further improving the surface quality of repaired KDP crystal components.

Description

Technical Field

[0001] This invention relates to the field of optical component processing technology, and more specifically, to a method for characterizing the cutting mode of the micromilling repair process for surface defects of KDP crystals. Background Technology

[0002] Laser-driven inertial confinement fusion (ICF) uses lasers as an energy source to implode target pellets, achieving controlled thermonuclear fusion and providing humanity with abundant, economical, and clean energy. KDP crystals, with their high linear photoelectric coefficient and ability to grow into large-size optical components, are irreplaceable functional crystal materials in ICF. Currently, diamond single-point flying cut technology is the most widely used and recognized method for processing large-size KDP crystal components. However, during the flying cut process, various micro-defects, such as scratches and pits, inevitably form on the soft and brittle surface of the KDP crystal. With continuous irradiation by high-power lasers, these defects rapidly expand, causing severe laser damage to the KDP crystal. Therefore, Lawrence Livermore National Laboratory (LLNL) first proposed a repair strategy: using a ball end mill to remove surface defects in the KDP crystal, forming a curved repair profile to mitigate its rapid expansion behavior under laser irradiation. However, KDP crystals exhibit significant anisotropy and are prone to cracking at high cutting temperatures. Therefore, obtaining an ultra-smooth repair surface is a huge challenge in the micro-milling repair process of KDP crystals.

[0003] When the maximum milling thickness exceeds the critical cutting thickness for the transition from the brittle to the ductile domain, brittle cutting occurs during the repair process. Conversely, when the maximum milling thickness is less than the critical cutting thickness for the transition from the ductile to the plowing mode, the undeformed cutting thickness is much smaller than the radius of the ball end mill's cutting edge, preventing chip formation and causing the generated debris to adhere to the machined surface, resulting in severe size effects. When ball end milling repairs defects on the surface of KDP crystals, different milling methods alter the undeformed cutting thickness, leading to brittle, ductile, or plowing cutting modes, resulting in random fluctuations in surface roughness and reduced surface quality. Therefore, characterizing the cutting mode is crucial for obtaining an ultra-smooth repaired surface on KDP crystals during micromilling repair, and cutting specific energy is an important characterization method for studying the cutting mode. Current research on cutting energy models primarily focuses on simplified two-dimensional turning processes. Furthermore, both turning and micro-milling processes employ size effect models that assume a defect-free workpiece surface. However, for KDP crystals with surface defects, a three-dimensional model of cutting energy for ball-end micro-milling, considering the presence of micro-defects, has yet to be established to characterize the cutting mode during the micro-milling repair of KDP crystal surface defects. Therefore, quantitative analysis based on cutting energy is of significant theoretical and engineering application value for studying the material removal mechanism of KDP crystal surfaces during ball-end micro-milling repair. Summary of the Invention

[0004] The technical problem to be solved by this invention is:

[0005] Existing methods assume that the surface of the workpiece material is defect-free, and a three-dimensional model of the cutting energy of ball end micromilling that takes into account the presence of micro-defects has not yet been established to characterize the cutting mode in the micromilling repair process of KDP crystal surface defects.

[0006] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0007] This invention provides a method for characterizing the cutting mode during the micromilling repair process of KDP crystal surface defects, comprising the following steps:

[0008] Step 1: Select repair process parameters and measure the depth of defects on the crystal surface;

[0009] Step 2: Establish a three-dimensional calculation model for the average cutting area of ​​ball end micro-milling;

[0010] Step 3: Collect the cutting force during the micro-milling repair of surface defects;

[0011] Step 4: Construct a cutting energy model for the ball end micro-milling repair process;

[0012] Step 5: Based on the cutting energy model, analyze the cutting mode in the micro-milling repair process.

[0013] Furthermore, the repair process parameters mentioned in step one include spindle speed, milling depth, feed rate, and tool tilt angle; a white light interferometer is used to measure the depth of surface defects.

[0014] Furthermore, the average cutting area mentioned in step two is the ratio of the semicircular volume V to the semicircular circumference l; the semicircular volume V is the crystal volume removed by the two cutting edges that participate in the micro-milling repair process within a 360° rotation of the ball end mill; the semicircular circumference l is the length of the arc formed by the intersection of the spherical surface formed after one cutting edge of the ball end mill completes the material removal and the KDP crystal defect surface.

[0015] Furthermore, the method for calculating the circumference l of the semicircle in step two is as follows:

[0016] The actual cutting depth M for KDP crystal surface repair is:

[0017]

[0018] In the formula a p d represents the milling depth of the defect-free surface of a KDP crystal. s For the depth of the defect;

[0019] The radius R1 of the circle formed by the intersection of the ball end mill and the KDP crystal surface is:

[0020]

[0021] In the formula, R is the tool radius.

[0022] The circumference l of the semicircle is considered as the length of the intersection line between the hemisphere and the KDP crystal surface, and is expressed as:

[0023]

[0024] From the above formula, the circumference l of the semicircle can be obtained as:

[0025]

[0026] Furthermore, the formula for the volume V of the semicircle mentioned in step two is:

[0027]

[0028] In the formula, θ1 = arccos(N / R1), where N is the feed per tooth of the ball end mill.

[0029] Furthermore, the cutting specific energy Kc mentioned in step four is the average cutting force. The ratio of the average cutting area to the average cutting area, i.e.

[0030]

[0031] The average cutting force It represents the difference in magnitude between the maximum and minimum cutting force during each tooth cutting cycle.

[0032] Furthermore, in step five, based on the aforementioned cutting energy specificity model, the cutting energy specificity results at different defect depths are obtained, and the cutting energy specificity function equation K is fitted to obtain the result. c =a×x -b +c, where a, b, and c control the amplitude, curvature, and position of the cutting energy fitting function, respectively; further, the different cutting modes in the micro-milling repair process of KDP crystal surface defects are analyzed by the changing trend of the cutting energy function equation.

[0033] Compared with the prior art, the beneficial effects of the present invention are:

[0034] This invention discloses a method for characterizing the cutting modes in the micro-milling repair process of KDP crystal surface defects. First, it calculates the specific cutting energy of the KDP crystal defect surface using a mathematical model, providing a basis for subsequent characterization of the cutting modes. Second, it quantitatively studies the relationship between the specific cutting energy and different cutting modes. Third, this method has a certain degree of universality and can be extended to characterizing the cutting modes in the micro-milling repair process of various KDP crystal surface defects, such as pits and protrusions. Fourth, this invention provides a reference for improving surface quality, controlling size effects, and optimizing process parameters in actual repair processes, thereby further improving the surface quality of repaired KDP crystal components. Attached Figure Description

[0035] Figure 1 This is a flowchart of a method for characterizing the cutting mode of the micro-milling repair process for surface defects of KDP crystals in an embodiment of the present invention;

[0036] Figure 2 This is a schematic diagram of the cutting energy calculation model for the microsphere milling process of KDP crystal scratch defect surface in an embodiment of the present invention.

[0037] Figure 3 This refers to the micro-milling device for collecting cutting force in an embodiment of the present invention;

[0038] Figure 4 This is a schematic diagram of the average cutting force in an embodiment of the present invention;

[0039] Figure 5 This is a curve of the cutting specific energy function equation obtained by fitting in an embodiment of the present invention;

[0040] Figure 6 This is a curve showing the relationship between surface roughness and scratch defect depth obtained through fitting in an embodiment of the present invention. Detailed Implementation

[0041] In the description of this invention, it should be noted that the terms "first," "second," and "third" mentioned in the embodiments of this invention are for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Therefore, a feature defined with "first," "second," and "third" may explicitly or implicitly include one or more of that feature.

[0042] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0043] Specific implementation method one: as follows Figure 1 As shown, the present invention provides a method for characterizing the cutting mode of the micro-milling repair process for surface defects of KDP crystals, comprising the following steps:

[0044] Step 1: Select repair process parameters and measure the depth of defects on the crystal surface;

[0045] Step 2: Establish a three-dimensional calculation model for the average cutting area of ​​ball end micro-milling;

[0046] Step 3: Collect the cutting force during the micro-milling repair of surface defects;

[0047] Step 4: Construct a cutting energy model for the ball end micro-milling repair process;

[0048] Step 5: Based on the cutting energy model, analyze the cutting mode in the micro-milling repair process.

[0049] The repair process parameters described in Step 1 include spindle speed, depth of cut, feed rate, and tool tilt angle. The specific parameters are: tool tilt angle 30°, spindle speed 50000 r / min, depth of cut 25µm, and feed rate 2mm / s. The measured depths of the scratch defects are 4, 8, 12, 16, 20, and 24µm. A white light interferometer is used to measure the depth of the surface scratch defects.

[0050] The average cutting area mentioned in step two is the ratio of the semicircular volume V to the semicircular circumference l; the semicircular volume V refers to the crystal volume removed by the two cutting edges that participate in the micro-milling repair process within a 360° rotation of the ball end mill; the semicircular circumference l refers to the length of the arc formed by the intersection of the spherical surface formed after one cutting edge of the ball end mill has completed material removal and the KDP crystal defect surface.

[0051] Specifically, such as Figure 2As shown, when the ball end mill rotates 360 degrees, the average cutting area is the ratio of the semicircular volume V (the cutting volume between the (j-1)th tooth and the jth tooth) to the semicircular circumference l (the cutting volume between the (j-1)th tooth and the jth tooth).

[0052] The semicircle V is composed of V1 and V2, that is:

[0053] (1)

[0054] In the (j-1)th tooth of the micro-milling repair process, the vertex of the bottom of the sphere is designated as the origin of the O-XYZ coordinate system, with the X, Y, and Z axes being the reverse feed direction, the transverse feed direction, and the upward direction perpendicular to the XPY plane, respectively.

[0055] When x is between 0 and N, the spherical surface cut by the j-th tooth in the O-XYZ coordinate system is represented as:

[0056] (2)

[0057] In the formula, R is the tool radius, M is the actual cutting depth, and N is the feed per tooth of the ball end mill.

[0058] Meanwhile, the spherical expression for the cutting of the (j-1)th tooth is:

[0059] (3)

[0060] The intersection line between the spherical surface cut by the (j-1)th tooth and the KDP crystal surface in the O-XYZ coordinate system is:

[0061] (4)

[0062] Due to the presence of scratches, the actual cutting depth M of the KDP crystal repair surface is:

[0063] (5)

[0064] In the formula a p d represents the milling depth of the defect-free surface of a KDP crystal. s This refers to the defect depth.

[0065] The radius R1 of the circular surface formed by the intersection of the ball end mill and the KDP crystal surface, i.e., the radius R1 of the intersection line between the spherical surface cut by the j-th tooth or the (j-1)-th tooth and the KDP crystal surface in the O-XYZ coordinate system, is:

[0066] (6)

[0067] In the O-XYZ coordinate system, the circumference l of the semicircle is regarded as the length of the intersection line between the hemisphere and the KDP crystal surface, which is:

[0068] (7)

[0069] Through homogeneous transformation and triple integral calculation, V1 can be obtained from formulas (2), (4) and (6):

[0070] (8)

[0071] From formulas (3), (4) and (6), V2 can be obtained as:

[0072] (9)

[0073] In the formula, θ1 = arccos(N / R1).

[0074] From equations (5), (8), and (9), the volume V of the semicircle can be obtained as:

[0075] (10)

[0076] From equations (5), (6), and (7), the circumference l of the semicircle can be obtained as:

[0077] (11).

[0078] The cutting specific energy Kc mentioned in step four is the average cutting force. The ratio of the average cutting area to the average cutting area, i.e.

[0079] (12)

[0080] The average cutting force It represents the difference in magnitude between the maximum and minimum cutting force during each tooth cutting cycle.

[0081] Cutting specific energy K c It is an important indicator characterizing the size effect and cutting mode during the cutting process. In turning, the specific cutting energy can be regarded as the ratio of the cutting force to the cross-sectional area of ​​the cutting section (the product of the cutting thickness and the width). However, in ball end milling, the cutting thickness changes continuously in both the radial and axial directions of the tool, so it is defined as the average cutting force (F). P-V The ratio of the average cutting area to the average cutting area.

[0082] like Figure 3As shown, milling experiments on KDP crystals were conducted using a self-developed ultra-precision five-axis machine tool, with a 0.25mm radius ball end mill as the repair tool. Cutting forces were collected using a Kistler 9119A force gauge. Because KDP crystals are hygroscopic, all micro-milling experiments were performed in a dry environment. During data processing, the number of sampling points for cutting force values ​​was increased, and the average value was calculated. (See figure...) Figure 4 As shown, the average cutting force is the difference between the maximum and minimum values ​​of the cutting force within each tooth cutting cycle.

[0083] In step five, based on the cutting energy specificity model, the cutting energy specificity results at different defect depths are obtained, and the cutting energy specificity function equation K is fitted to obtain the result. c =a×x -b +c, where a, b, and c control the amplitude, curvature, and position of the cutting energy fitting function, respectively; further, the different cutting modes in the micro-milling repair process of KDP crystal surface defects are analyzed by the changing trend of the cutting energy function equation.

[0084] like Figure 5 As shown, when the scratch defect depth is 24µm, the cutting energy is the highest, and plowing phenomenon can be observed based on morphological analysis. This is because the consumed energy is not fully used for chip formation, leading to plowing and strong interfacial friction between the tool and the milling surface. When the scratch defect depth is between 8µm and 20µm, the increase in cutting force caused by local brittle fracture is small, and the cutting energy begins to decrease nonlinearly. The cutting mode at this time belongs to the plastic domain. When the scratch defect depth is less than 8µm, the cutting energy gradually tends to stabilize. This is because the cutting force caused by continuous brittle fracture is unstable and varies greatly. The cutting process at this time is in brittle mode cutting, which is very consistent with the brittle fracture of the surface morphology.

[0085] Potential function (K) c =a×x -b +c) can accurately establish the relationship between cutting specific energy and scratch depth during micromilling repair of scratches in KDP crystals. This is because its coefficient of determination (Rc) 2 The value is 0.983, and the constants a, b, and c are 2.478 × 10⁻⁶. -6 4.874, 7.80. Therefore, based on the quantitative analysis of cutting specific energy, as the size of the scratch defect increases, the micromilling repair process of KDP crystal scratch defects will undergo a brittle-plastic transition or even a severe size effect, thereby changing the material removal mode.

[0086] To confirm the relationship between cutting specific energy and different cutting modes, the surface roughness of the microgrooves on the surface of the KDP crystal scratch defect was measured using a white light interferometer. The results are as follows: Figure 6As shown, the surface roughness gradually decreases with increasing scratch depth, consistent with the trend from the brittle to the ductile domain. For example, under the same repair process parameters, when the defect-free surface of the KDP crystal undergoes brittle fracture, the surface roughness of the microgroove reaches 91 nm. However, when the scratch depth is 16 µm, the milled microgroove has a smooth morphology, and the surface roughness can be reduced to 66 nm. Furthermore, when the scratch depth increases to 24 µm, adhering chips appear at the bottom of the milled microgroove surface, indicating that a severe size effect leads to the plowing phenomenon. Based on the above findings and discussion, it can be inferred that the scratch depth alters the cutting mode during the KDP crystal material removal process, which can be well characterized by the cutting specific energy.

[0087] The above steps utilize the method of the present invention for characterizing the cutting mode during the micro-milling repair process of KDP crystal surface defects. This method enables accurate characterization of the cutting mode and prediction of the surface quality during the micro-milling repair process of KDP crystal surface defects. Furthermore, it quantitatively studies the relationship between the change in specific cutting energy and different cutting modes, demonstrating that this method can provide an important approach and means for predicting the surface quality and characterizing the cutting mode during micro-milling repair of this type of crystal.

[0088] While the present invention has been disclosed above, its scope of protection is not limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present invention, and all such changes and modifications will fall within the scope of protection of the present invention.

Claims

1. A method for characterizing the cutting mode during the micromilling repair process of surface defects in KDP crystals, characterized in that, Includes the following steps: Step 1: Select repair process parameters and measure the depth of defects on the crystal surface; Step 2: Establish a three-dimensional calculation model for the average cutting area of ​​ball end micro-milling; Step 3: Collect the cutting force during the micro-milling repair of surface defects; Step 4: Construct a cutting energy model for the ball end micro-milling repair process; Step 5: Based on the cutting energy ratio model, analyze the cutting mode in the micro-milling repair process; The average cutting area mentioned in step two is the ratio of the volume V of the semicircle to the circumference l of the semicircle; The semicircular volume V is the volume of crystal removed by the two cutting edges that participate in the micro-milling repair process within a 360° rotation of the ball end mill; the semicircular circumference l is the length of the arc formed by the intersection of the spherical surface and the KDP crystal defect surface after one cutting edge of the ball end mill has completed material removal. The method for calculating the circumference l of the semicircle in step two is as follows: The actual cutting depth M for KDP crystal surface repair is: ； In the formula a p d represents the milling depth of the defect-free surface of a KDP crystal. s For the depth of the defect; The radius R1 of the circle formed by the intersection of the ball end mill and the KDP crystal surface is: ； In the formula, R is the tool radius; The circumference l of the semicircle is considered as the length of the intersection line between the hemisphere and the KDP crystal surface, and is expressed as: ； From the above formula, the circumference l of the semicircle can be obtained as: ； The formula for the volume V of the semicircle mentioned in step two is: ； In the formula, θ1 = arccos(N / R1), where N is the feed per tooth of the ball end mill; The cutting specific energy Kc mentioned in step four is the average cutting force. The ratio to the average cutting area, i.e.: ； The average cutting force This represents the difference in magnitude between the maximum and minimum cutting forces during each tooth cutting cycle. In step five, based on the cutting energy specificity model, the cutting energy specificity results at different defect depths are obtained, and the cutting energy specificity function equation K is fitted to obtain the result. c =a×x -b +c, where a, b, and c control the amplitude, curvature, and position of the cutting energy fitting function, respectively; further, the different cutting modes in the micro-milling repair process of KDP crystal surface defects are analyzed by the changing trend of the cutting energy function equation.

2. The method for characterizing the cutting mode of the micro-milling repair process for surface defects of KDP crystals according to claim 1, characterized in that, The repair process parameters mentioned in step one include spindle speed, milling depth, feed rate, and tool tilt angle; a white light interferometer is used to measure the depth of surface defects.

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