A method for selecting an optimal cutting direction across a surface of a structural feature of a scale

Abstract

The application discloses a method for selecting an optimal cutting direction of a cross-scale structure feature surface, changes the spectrum component of the cross-section profile of the target cross-scale structure feature surface by changing the nominal cutting direction, thereby changing the error between the machinable cross-scale structure feature surface and the target cross-scale structure feature surface. α Within the selection range of the nominal cutting direction, the nominal cutting direction is changed with an angle resolution of ξ α The average overall relative error between the machinable cross-scale structure feature surface and the target cross-scale structure feature surface under all the nominal cutting directions is calculated, the nominal cutting direction with the minimum average overall relative error is selected as the optimal cutting direction of the cross-scale structure feature surface, thereby the error between the machinable cross-scale structure feature surface and the target cross-scale structure feature surface during cutting machining can be reduced, the error between the finally machined cross-scale structure feature surface and the given cross-scale structure feature surface is further reduced, and the machining precision is improved.

Description

Technical Field

[0001] This invention relates to the field of cutting technology, and specifically to a method for selecting the optimal cutting direction for cross-scale structural feature surfaces. Background Technology

[0002] Structured surfaces exhibit numerous superior properties in altering surface wetting, tribological, and optical characteristics, thus attracting increasing attention and research in fields such as optics, bionics, bioengineering, and advanced manufacturing. Multi-scale structural feature surfaces are also gaining traction due to their ability to achieve different functions through the superposition of structures at different scales. These functional surfaces, composed of subsurfaces with structures at various scales, possess complex curvature, functional structural features, and ultra-high geometric precision and machining requirements, posing significant challenges to current precision manufacturing practices.

[0003] Due to its high processing flexibility, economic efficiency, and suitability for mass production, ultra-precision cutting using diamond tools is widely considered one of the most promising technologies for machining cross-scale structural features. Currently, multi-component coordinated vibration cutting processes can be used to machine cross-scale structural features. These systems consist of three components with different working bandwidths: a three-axis servo platform, a workpiece servo mechanism, and an ultrasonic elliptical vibrating tool. These three components will generate coordinated motion during machining, respectively undertaking the machining of structures at the millimeter, micrometer, and nanometer scales. The multi-component coordinated vibration cutting process generates a three-dimensional shape on the workpiece based on the principle of tool tip trajectory replication and line-by-line machining. During line-by-line machining, firstly, the three components are assigned corresponding motions according to the different scale components in the cross-sectional profile of the cutting plane. Then, the coordinated motion of the three components will give the tool tip a synthetic cutting trajectory. Finally, the bottom of the synthetic cutting trajectory will be replicated onto the workpiece, thus forming the desired cross-sectional profile spanning the millimeter-micrometer-nanometer scale range.

[0004] To machine multi-scale structural feature surfaces using multi-component coordinated vibration cutting technology, it is necessary to extract the target multi-scale cross-sectional profile from the given multi-scale structural feature surface. Then, the components in the target multi-scale cross-sectional profile are divided into millimeter, micrometer, and nanometer scale components according to different spatial frequencies, thus forming three target cross-sectional profiles of different scales. To ensure the motion stability and machining accuracy of the moving parts, the components in these three target cross-sectional profiles that satisfy the working bandwidth of the three components need to be extracted to form a machinable cross-sectional profile, facilitating the planning of the motion trajectories of the three moving parts and the determination of other process parameters. However, in actual machining, because the target cross-sectional profile contains components with spatial frequencies outside the working bandwidth of the three components—that is, unmachinable cross-sectional profile components—there will be errors between the multi-scale structural feature surface formed by the extracted machinable cross-sectional profiles and the target multi-scale structural feature surface, resulting in an error between the final machined multi-scale structural feature surface and the given multi-scale structural feature surface. Summary of the Invention

[0005] In order to overcome the shortcomings of the prior art, the purpose of this invention is to provide a method for selecting the optimal cutting direction of a cross-scale structural feature surface, which can reduce the error between the final machined cross-scale structural feature surface and the given cross-scale structural feature surface, and improve the machining accuracy.

[0006] To solve the above problems, the technical solution adopted by the present invention is as follows: a method for selecting the optimal cutting direction for cross-scale structural feature surfaces, comprising the following steps:

[0007] Step S100: For a given cross-scale structural feature surface, determine the spatial frequency range of the machinable cross-sectional profile and the target cross-sectional profile at the millimeter, micrometer, and nanometer scales, and determine the initial cross-scale structural feature surface with the cutting direction at 0°.

[0008] Step S200, with x α To achieve angular resolution within the 0° to 180° angular range, the nominal cutting direction is changed, and the initial multi-scale structural feature surface is rotated and transformed to obtain the nominal cutting direction. ix α The target cross-sectional profiles at the millimeter, micrometer, and nanometer scales are calculated within the spatial frequency range determined in step S100 based on the target cross-sectional feature surface under this cutting direction.

[0009] Step S300: In the nominal cutting direction ix αNext, within the spatial frequency range determined in step S100, the machinable cross-sectional profiles at the millimeter, micrometer, and nanometer scales under this cutting direction are calculated.

[0010] Step S400, in the nominal cutting direction ix α Next, based on the target cross-sectional profile in step S200 and the machinable cross-sectional profile in step S300, the overall relative error between the machinable multi-scale structural feature surface and the target multi-scale structural feature surface is calculated.

[0011] Step S500: Within the nominal cutting direction selection range, repeat steps S200 to S400 until the overall relative error between the machinable multi-scale structural feature surface and the target multi-scale structural feature surface under all nominal cutting directions is calculated, wherein... i =0~ I ,and I Satisfy the following formula (1):

[0012] (1);

[0013] in, i When =0, the target multi-scale structural feature surface is the initial multi-scale structural feature surface, and the nominal cutting direction is the X direction of the initial multi-scale structural feature surface;

[0014] Step S600: Select the nominal cutting direction with the smallest average overall relative error as the optimal cutting direction for the cross-scale structural feature surface.

[0015] Compared to existing technologies, the advantages of this invention are as follows: This method alters the spectral composition of the cross-sectional profile of the target multi-scale structural feature surface by changing the nominal cutting direction, thereby changing the relative error between the machinable multi-scale structural feature surface and the target multi-scale structural feature surface. Within the range of nominal cutting direction selection, with... x α The nominal cutting direction is changed to adjust the angular resolution, and the average overall relative error between the machinable cross-scale structural feature surface and the target cross-scale structural feature surface under all nominal cutting directions is calculated. The nominal cutting direction with the smallest average overall relative error is selected as the optimal cutting direction for the cross-scale structural feature surface. This reduces the error between the machinable cross-scale structural feature surface and the target cross-scale structural feature surface during machining, thereby reducing the error between the final machined cross-scale structural feature surface and the given cross-scale structural feature surface and improving machining accuracy.

[0016] The method for selecting the optimal cutting direction for the multi-scale structural feature surface described above includes the following steps in step S100:

[0017] Step S110: Determine the operating frequency of the ultrasonic elliptical vibrating tool. f e Maximum operating frequency of the workpiece servo mechanism Maximum operating frequency of the three-axis servo platform and maximum nominal cutting speed ;

[0018] Step S120: Based on the working frequency of the ultrasonic elliptical vibration tool f e and maximum nominal cutting speed Maximum spatial wavelength of machinable nanostructures with defined cross-sectional profiles Based on the maximum operating frequency of the workpiece servo mechanism and maximum nominal cutting speed Minimum spatial wavelength for determining the profile of a machinable micron structure Based on the maximum operating frequency of the three-axis servo platform and maximum nominal cutting speed Minimum spatial wavelength for determining the cross-sectional profile of a machinable millimeter structure ;

[0019] Step S130: Based on the maximum spatial wavelength of the processable nanostructure in step S120. The minimum spatial wavelength that can be processed into micron-sized structures and the minimum spatial wavelength for machining millimeter structures Sure:

[0020] The spatial frequency range of the machinable cross-sectional profile at the millimeter scale is 0~ ;

[0021] The spatial frequency range of machinable cross-sectional profiles at the micrometer scale is: ;

[0022] The spatial frequency range of the machinable cross-sectional profile at the nanoscale is: ~+∞;

[0023] The spatial frequency range of the target cross-sectional profile at the millimeter scale is 0~ ;

[0024] The spatial frequency range of the target cross-sectional profile at the micrometer scale is ;

[0025] The spatial frequency range of the target cross-sectional profile at the nanoscale is ~+∞.

[0026] In the above-described method for selecting the optimal cutting direction for a multi-scale structural feature surface, in step S100, the morphology function of the initial multi-scale structural feature surface with the cutting direction at 0° is:

[0027] (2);

[0028] In step S200, in the nominal cutting direction is ix α The topography function of the target multi-scale structural feature surface is as follows:

[0029] (3)

[0030] The method for selecting the optimal cutting direction for the multi-scale structural feature surface described above includes the following steps in step S200:

[0031] Step S210: In the nominal cutting direction ix α Below, taking the nominal cutting direction as the X-axis and the feed direction as the Y-axis, along the X and Y directions respectively... x x and x y To achieve spatial resolution, the shape function of the target cross-sectional profile is sampled, and the target multi-scale structural surface is meshed onto a series of grid points;

[0032] Step S220: Using Fast Fourier Transform (FFT) FFT ) obtained the i Spatial spectrum of a cross-sectional profile S i ,and

[0033] (4);

[0034] The spectral components of the target cross-sectional profile at the millimeter, micrometer, and nanometer scales are as follows:

[0035] (5)

[0036] Step S230: Utilize the inverse fast Fourier transform (FFT) IFFT The target cross-sectional profiles at the millimeter, micrometer, and nanometer scales were obtained as follows:

[0037] (6)

[0038] Step S240, repeat steps S220 to S230 until all target cross-sectional profiles in the Y direction are obtained. Then, all millimeter, micrometer, and nanometer-scale target cross-sectional profiles in the Y direction will respectively constitute the target millimeter-scale subsurface. Target micron-scale subsurface and target nanoscale subsurface .

[0039] The method for selecting the optimal cutting direction for the multi-scale structural feature surface described above includes the following steps in step S300:

[0040] Step S310: Determine the lateral feed distance c f ,and c f for x y Multiples of:

[0041] (7)

[0042] Step S320: Along the nominal cutting direction ix α Multiscale structural features surface k Each cross-sectional profile will share the same spatial cutting trajectory, and the first... i The shared cross-sectional profile is as follows:

[0043] (8);

[0044] Step S330: Using Fast Fourier Transform (FFT) FFT ) obtained the i Spectral components of a shared cross-sectional profile:

[0045] (9)

[0046] The spectral components of the machinable cross-sectional profiles at the millimeter, micrometer, and nanometer scales are as follows:

[0047] (10)

[0048] Step S340: Utilize the inverse fast Fourier transform (FFT) IFFT The machinable cross-sectional profiles at the millimeter, micrometer, and nanometer scales are obtained as follows:

[0049] 11;

[0050] Step S350, repeat steps S320 to S340 until all machinable cross-sectional profiles in the Y direction are obtained. Then, all millimeter, micrometer, and nanometer-scale machinable cross-sectional profiles in the Y direction will respectively constitute machinable millimeter-scale subsurfaces. Micron-scale subsurfaces can be processed and machinable nanoscale subsurfaces .

[0051] The method for selecting the optimal cutting direction for the multi-scale structural feature surface described above includes the following steps in step S400:

[0052] Step S410: Define the relative error matrix between the machinable subsurface and the target subsurface at the millimeter, micrometer, and nanometer scales as follows:

[0053] 12;

[0054] Step S420: Define the overall relative error matrix between the machinable multi-scale structural surface and the target multi-scale structural surface as follows:

[0055] 13.

[0056] The above-described method for selecting the optimal cutting direction for cross-scale structural feature surfaces involves, in step S600, searching for the cutting direction with the minimum average overall relative error using the following equation and selecting it as the optimal cutting direction:

[0057] 14;

[0058] in, ME ( ix α ) is in the nominal cutting direction ix α The average overall relative error between the machinable multi-scale structural surface and the target multi-scale structural surface. N i In the nominal cutting direction ix α The number of sampling points on the target multi-scale structural surface.

[0059] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments. Attached Figure Description

[0060] Figure 1 This is a flowchart illustrating the steps of Embodiment 1 of the present invention;

[0061] Figure 2 This is a schematic diagram of the spectrum division at different scales in Embodiment 2 of the present invention;

[0062] Figure 3 This is a schematic diagram of the cutting direction selection range in Embodiment 2 of the present invention;

[0063] Figure 4 This is a surface diagram of the cross-millimeter-micrometer-nanoscale structure designed in Embodiment 3 of the present invention;

[0064] Figure 5 This is a schematic diagram of the average overall relative error value under different cutting directions in Embodiment 3 of the present invention;

[0065] Figure 6 This is a schematic diagram of the machinable multi-scale structural surface and the overall relative error matrix in the 0° cutting direction of Embodiment 3 of the present invention;

[0066] Figure 7 This is a schematic diagram of the machinable multi-scale structural surface and the overall relative error matrix under the 136° cutting direction in Embodiment 3 of the present invention;

[0067] Figure 8 This is a comparison diagram of the machined surface and the target surface under the 0° cutting direction and the 136° cutting direction in Embodiment 3 of the present invention;

[0068] Figure 9 This is a comparison diagram of the target cross-sectional profile and the machined cross-sectional profile in the 0° cutting direction according to Embodiment 3 of the present invention;

[0069] Figure 10 This is a comparison diagram of the target cross-sectional profile and the machined cross-sectional profile in the 136° cutting direction of Embodiment 3 of the present invention. Detailed Implementation

[0070] The embodiments of the present invention are described in detail below:

[0071] Example 1

[0072] Reference Figure 1 Embodiment 1 of the present invention provides a method for selecting the optimal cutting direction for a cross-scale structural feature surface, comprising the following steps:

[0073] Step S100: For a given cross-scale structural feature surface, determine the spatial frequency range of the machinable cross-sectional profile and the target cross-sectional profile at the millimeter, micrometer, and nanometer scales, and determine the initial cross-scale structural feature surface with the cutting direction at 0°.

[0074] Step S200, with x α To achieve angular resolution within the 0° to 180° angular range, the nominal cutting direction is changed, and the initial multi-scale structural feature surface is rotated and transformed to obtain the nominal cutting direction. ix α The target cross-sectional profiles at the millimeter, micrometer, and nanometer scales are calculated within the spatial frequency range determined in step S100 based on the target cross-sectional feature surface under this cutting direction.

[0075] Step S300: In the nominal cutting direction ix α Next, within the spatial frequency range determined in step S100, the machinable cross-sectional profiles at the millimeter, micrometer, and nanometer scales under this cutting direction are calculated.

[0076] Step S400, in the nominal cutting direction ix α Next, based on the target cross-sectional profile in step S200 and the machinable cross-sectional profile in step S300, the overall relative error between the machinable multi-scale structural feature surface and the target multi-scale structural feature surface is calculated.

[0077] Step S500: Within the nominal cutting direction selection range, repeat steps S200 to S400 until the overall relative error between the machinable multi-scale structural feature surface and the target multi-scale structural feature surface under all nominal cutting directions is calculated, wherein... i =0~ I ,and I Satisfy the following formula (1):

[0078] (1);

[0079] in, i When =0, the target multi-scale structural feature surface is the initial multi-scale structural feature surface, and the nominal cutting direction is the X direction of the initial multi-scale structural feature surface;

[0080] Step S600: Select the nominal cutting direction with the smallest average overall relative error as the optimal cutting direction for the cross-scale structural feature surface.

[0081] This method alters the spectral composition of the cross-sectional profile of the target multi-scale structural feature surface by changing the nominal cutting direction, thereby changing the relative error between the machinable multi-scale structural feature surface and the target multi-scale structural feature surface. Within the range of nominal cutting direction selection, using... x α To adjust the nominal cutting direction for angular resolution, the average overall relative error between the machinable multi-scale structural feature surface and the target multi-scale structural feature surface under all nominal cutting directions is calculated. The nominal cutting direction with the smallest average overall relative error is selected as the optimal cutting direction for the multi-scale structural feature surface. This reduces the error between the machinable and target multi-scale structural feature surfaces during machining, thereby reducing the error between the final machined multi-scale structural feature surface and the given multi-scale structural feature surface, and improving machining accuracy. It should be noted that the cross-sectional profile mentioned in this invention refers to the cross-sectional profile along the XOZ plane, where the X direction is the cutting direction, the Y direction is the feed direction, and the Z direction is the depth of cut direction.

[0082] Example 2

[0083] Embodiment 2 of the present invention provides a method for selecting the optimal cutting direction for a cross-scale structural feature surface, comprising the following steps:

[0084] Step S100: For a given multi-scale structural feature surface, determine the spatial frequency range of the machinable cross-sectional profile and the target cross-sectional profile at the millimeter, micrometer, and nanometer scales, and determine the initial multi-scale structural feature surface with the cutting direction at 0°. The morphology function of the initial multi-scale structural feature surface with the cutting direction at 0° is:

[0085] (2)

[0086] Since the generation of contours at all scales will share the same nominal cutting speed, the moving part with the highest operating frequency will undertake the machining of nanoscale structures to improve overall machining efficiency. When machining nanostructures using ultrasonic elliptical vibration texture, the vibration frequency of the ultrasonic ellipse is fixed, and the machining requirements of nanostructures with different spatial wavelengths can be accurately met by controlling the nominal cutting speed. Therefore, the spatial frequency ranges of three different scale components are determined through the following steps:

[0087] Step S110: Maximum spatial wavelength of the machinable nanostructure with cross-sectional profile From the maximum nominal cutting speed and the working frequency of ultrasonic elliptical vibrating cutter f e Therefore, the operating frequency of the ultrasonic elliptical vibrating cutter should be determined first. f e Maximum operating frequency of the workpiece servo mechanism Maximum operating frequency of the three-axis servo platform and maximum nominal cutting speed ;

[0088] Step S120: Under a given nominal cutting speed profile, the minimum achievable spatial wavelengths of the micrometer-scale and millimeter-scale components of the cross-sectional profile are constrained by the working bandwidths of the workpiece servo mechanism and the three-axis servo platform, respectively. Therefore, based on the working frequency of the ultrasonic elliptical vibration tool... f e and maximum nominal cutting speed Maximum spatial wavelength of machinable nanostructures with defined cross-sectional profiles Based on the maximum operating frequency of the workpiece servo mechanism and maximum nominal cutting speed Minimum spatial wavelength for determining the profile of a machinable micron structure Based on the maximum operating frequency of the three-axis servo platform and maximum nominal cutting speed Minimum spatial wavelength for determining the cross-sectional profile of a machinable millimeter structure Among them, the maximum spatial wavelength that can be processed into nanostructures The minimum spatial wavelength that can be processed into micron-sized structures and the minimum spatial wavelength for machining millimeter structures The determination is made by the following formulas (15), (16) and (17), respectively:

[0089] 12;

[0090] 13;

[0091] 14;

[0092] Step S130: Based on the maximum spatial wavelength of the processable nanostructure in step S120. The minimum spatial wavelength that can be processed into micron-sized structures and the minimum spatial wavelength for machining millimeter structures Sure:

[0093] The spatial frequency range of the machinable cross-sectional profile at the millimeter scale is 0~ ;

[0094] The spatial frequency range of machinable cross-sectional profiles at the micrometer scale is: ;

[0095] The spatial frequency range of the machinable cross-sectional profile at the nanoscale is: ~+∞;

[0096] The spatial frequency range of the target cross-sectional profile at the millimeter scale is 0~ ;

[0097] The spatial frequency range of the target cross-sectional profile at the micrometer scale is ;

[0098] The spatial frequency range of the target cross-sectional profile at the nanoscale is ~+∞.

[0099] Among them, such as Figure 2 As shown, the spatial frequency range is When processing the contour components, the operating frequency of the corresponding parts may not be within the operating bandwidth of the three moving parts, and therefore they are defined as unprocessable components.

[0100] Step S200, as follows Figure 3 As shown, with x α To achieve angular resolution within the 0° to 180° angular range, the nominal cutting direction is changed, and the initial multi-scale structural feature surface is rotated and transformed to obtain the nominal cutting direction. ixα The target cross-sectional profiles at the millimeter, micrometer, and nanometer scales are calculated based on the target cross-sectional profiles at the millimeter, micrometer, and nanometer scales within the spatial frequency range determined in step S100, according to the target cross-sectional profiles at the millimeter, micrometer, and nanometer scales under this cutting direction.

[0101] After rotational transformation, in the nominal cutting direction is ix α The topography function of the target multi-scale structural feature surface is as follows:

[0102] (3);

[0103] By decoupling the target's multi-scale structural features row by row, the target subsurfaces and machinable subsurfaces at the millimeter, micrometer, and nanometer scales can be reconstructed. The target subsurfaces are reconstructed through the following steps:

[0104] Step S210: In the nominal cutting direction ix α Below, taking the nominal cutting direction as the X-axis and the feed direction as the Y-axis, along the X and Y directions respectively... x x and x y To achieve spatial resolution, the shape function of the target cross-sectional profile is sampled, and the target multi-scale structural surface is meshed onto a series of grid points;

[0105] Step S220: Using Fast Fourier Transform (FFT) FFT ) obtained the i Spatial spectrum of a cross-sectional profile S i ,and

[0106] (4);

[0107] The spectral components of the target cross-sectional profile at the millimeter, micrometer, and nanometer scales are as follows:

[0108] (5)

[0109] Step S230: Utilize the inverse fast Fourier transform (FFT) IFFT The target cross-sectional profiles at the millimeter, micrometer, and nanometer scales were obtained as follows:

[0110] (6)

[0111] Step S240, repeat steps S220 to S230 until all target cross-sectional profiles in the Y direction are obtained. Then, all millimeter, micrometer, and nanometer-scale target cross-sectional profiles in the Y direction will respectively constitute the target millimeter-scale subsurface. Target micron-scale subsurface and target nanoscale subsurface .

[0112] Step S300: In the nominal cutting direction ix α Next, within the spatial frequency range determined in step S100, the machinable cross-sectional profiles at the millimeter, micrometer, and nanometer scales under this cutting direction are calculated. Specifically, the machinable cross-sectional profiles and machinable subsurfaces at the millimeter, micrometer, and nanometer scales under this cutting direction are calculated through the following steps:

[0113] Step S310: Determine the lateral feed distance c f ,and c f for x y Multiples of:

[0114] (7)

[0115] Step S320: Along the nominal cutting direction ix α Multiscale structural features surface k Each cross-sectional profile will share the same spatial cutting trajectory, and the first... i The shared cross-sectional profile is as follows:

[0116] (8);

[0117] Step S330: Using Fast Fourier Transform (FFT) FFT ) obtained the i Spectral components of a shared cross-sectional profile:

[0118] (9)

[0119] The spectral components of the machinable cross-sectional profiles at the millimeter, micrometer, and nanometer scales are as follows:

[0120] (10)

[0121] Step S340: Utilize the inverse fast Fourier transform (FFT) IFFT The machinable cross-sectional profiles at the millimeter, micrometer, and nanometer scales are obtained as follows:

[0122] 11;

[0123] Step S350, repeat steps S320 to S340 until all machinable cross-sectional profiles in the Y direction are obtained. Then, all millimeter, micrometer, and nanometer-scale machinable cross-sectional profiles in the Y direction will respectively constitute machinable millimeter-scale subsurfaces. Micron-scale subsurfaces can be processed and machinable nanoscale subsurfaces .

[0124] Step S400, in the nominal cutting direction ix α Next, based on the target cross-sectional profile in step S200 and the machinable cross-sectional profile in step S300, calculate the relative error between the machinable multi-scale structural feature surface and the target multi-scale structural feature surface:

[0125] Step S410: Define the relative error matrix between the machinable subsurface and the target subsurface at the millimeter, micrometer, and nanometer scales as follows:

[0126] 12

[0127] Step S420: Define the overall relative error matrix between the machinable multi-scale structural surface and the target multi-scale structural surface as follows:

[0128] 13

[0129] Step S500: Within the nominal cutting direction selection range, repeat steps S200 to S400 until the relative error matrix between the machinable multi-scale structural feature surface and the target multi-scale structural feature surface under all nominal cutting directions is calculated, where... i =0~ I ,and I Satisfy the following formula (1):

[0130] (1);

[0131] in, i When = 0, the target multi-scale structural feature surface is the initial multi-scale structural feature surface, and the nominal cutting direction is the X-direction of the initial multi-scale structural feature surface. For example... x α At 60 degrees, I =3, therefore, the choice of the nominal cutting direction is 0. x α =0°、1 x α =60°、2 x α =120°, 3 x αSince there are four types of nominal cutting directions (180° and 180°), steps S200 to S400 need to be repeated four times to traverse all nominal cutting directions. In other words, the number of traversals is [number missing]. I +1 time.

[0132] Step S600: Select the nominal cutting direction with the smallest average overall relative error as the optimal cutting direction for the cross-scale structural feature surface. Specifically, the optimal cutting direction is selected through the following steps:

[0133] Step S610: Search for the cutting direction with the minimum average overall relative error using the following equation and take it as the optimal cutting direction:

[0134] 14

[0135] in, ME ( ix α ) is in the nominal cutting direction ix α The average overall relative error between the machinable multi-scale structural surface and the target multi-scale structural surface. N i In the nominal cutting direction ix α The number of sampling points on the target multi-scale structural surface.

[0136] Example 3

[0137] Embodiment 3 of the present invention uses an exemplary target multi-scale structural surface for design and processing to verify the superiority of the cutting method with optimal cutting direction selection of the present invention:

[0138] Figure 4 The designed structural surface spanning millimeter-micrometer-nanometer scales consists of freeform surfaces at the millimeter scale. z 1) Cosine surfaces at the micrometer scale ( z 2) and periodic cosine grating nanostructures with fixed height ( z 3) Composed of three parts. The millimeter-scale freeform surface, the micrometer-scale cosine surface, and the periodic cosine grating nanostructure can be mathematically represented as:

[0139] 18

[0140] 16

[0141] 20

[0142] in, It is the curvature of the base surface. This is the cone shape constant. All relevant parameters of the above-mentioned multi-scale structure function surface are shown in Table 1:

[0143]

[0144] Table 1

[0145] The target multi-scale structural surface for this design is: z = z 1+ z 2+ z 3. In this embodiment, the following parameters are set: maximum nominal cutting speed The maximum operating frequency of the workpiece servo mechanism is 40 mm / s. The maximum operating frequency of the three-axis platform is 200 Hz. The operating frequency of the ultrasonic elliptical vibrating cutter is 10 Hz. f e It is 40 kHz.

[0146] The following parameters can be determined by using the steps in Embodiment 2 above:

[0147] Maximum spatial wavelength of processable nanostructures It is 1 μm;

[0148] Minimum spatial wavelength of machinable profiles at the micrometer scale It is 250 μm;

[0149] Minimum spatial wavelength of machinable profile at the millimeter scale It is 5 mm.

[0150] Set spatial sampling resolution x x and x y All are 0.1 μm, the transverse feed distance is fixed at 10 μm, and the current X direction is defined as the 0° nominal cutting direction.

[0151] Using the optimal cutting direction selection method in Embodiment 2 above, at a resolution x α Under the condition of 1°, the cutting direction of the multi-scale structural feature surface of the above design was optimized. The average overall relative error values ​​of the machinable multi-scale structural surface and the target multi-scale structural surface under different cutting directions are as follows: Figure 5 As shown, by Figure 5 It can be determined that the optimal cutting direction is 136°. The average overall relative error under the nominal cutting direction of 136° is approximately 1.08%, which is much smaller than the result of 20.36% under the nominal cutting direction of 0°. Figure 6The diagrams of the machinable multi-scale structural surfaces and the overall relative error matrix under the 0° nominal cutting direction are given. Figure 6 Part a represents the machinable multi-scale structural surface, and part b represents the overall relative error matrix. Figure 7 The diagrams of the machinable multi-scale structural surfaces and the overall relative error matrix under the nominal cutting direction of 136° are presented. Figure 7 Part a represents the machinable multi-scale structural surface, and part b represents the overall relative error matrix.

[0152] After selecting the optimal cutting direction, the target multi-scale structural surface was machined under both the 0° nominal cutting direction and the 136° nominal cutting direction to verify the results.

[0153] Based on the designed machinable multi-scale structural surface under the 0° and 136° nominal cutting directions, the motion trajectories of the three-axis servo platform and the workpiece servo mechanism, as well as the vibration parameters of the ultrasonic elliptical vibrating tool, are planned. During the machining process, a natural single-crystal diamond tool with a tip radius of 0.1 mm, a rake angle of 0°, and a clearance angle of 25° is selected.

[0154] After processing, the machinable multi-scale structural surfaces in the two directions were characterized as millimeter-micrometer structural surfaces using a white light interferometer. The local nanostructures of the three processed surfaces were characterized using an atomic force microscope. The comparison between the measured morphology of the processed surfaces and the designed multi-scale structural surfaces is shown below. Figure 8 , Figure 9 and Figure 10 As shown. Among them, Figure 8 In the diagram, part a represents the target surface, part b represents the machined surface at 0° cutting direction, and part c represents the machined surface at 136° cutting direction. Figure 8 It can be seen that the surface morphology of the machined surface under the 136° cutting direction is richer in detail than that under the 0° cutting direction, and is also closer to the designed multi-scale structural surface. Figure 9 This is a comparison diagram of the target cross-sectional profile and the machined cross-sectional profile in the 0° cutting direction. Figure 10 This is a comparison diagram of the target section profile and the machined section profile under a 136° cutting direction. Figure 9 and Figure 10It can be seen that the error between the cross-sectional profile machined in the 136° cutting direction and the target cross-sectional profile is significantly smaller than the error between the cross-sectional profile machined in the 0° cutting direction and the target cross-sectional profile. This proves that the optimization of the nominal cutting direction can significantly improve the manufacturing accuracy of the cutting process, demonstrating the excellence and effectiveness of this optimal cutting direction selection method. By selecting the optimal cutting direction, the error between the machineable multi-scale structural feature surface and the target multi-scale structural feature surface during cutting can be reduced, thereby reducing the error between the final machined multi-scale structural feature surface and the given multi-scale structural feature surface, and improving the machining accuracy.

[0155] It should be noted that in the description of this invention, any descriptions of orientation, such as up, down, front, back, left, right, etc., indicating orientation or positional relationships, are based on the orientation or positional relationships shown in the accompanying drawings. They are only for the purpose of facilitating the description of this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed or operated in a specific orientation, and should not be construed as a limitation of this invention.

[0156] In the description of this invention, "several" means one or more, "more than" means two or more, "greater than," "less than," "exceeding," etc. are understood to exclude the stated number, while "above," "below," "within," etc. are understood to include the stated number. If "first" or "second" is mentioned, it is only for the purpose of distinguishing technical features and should not be construed as indicating or implying relative importance, or implicitly indicating the number of indicated technical features, or implicitly indicating the order of the indicated technical features.

[0157] In the description of this invention, unless otherwise explicitly defined, terms such as "set up," "install," and "connect" should be interpreted broadly, and those skilled in the art can reasonably determine the specific meaning of the above terms in this invention in conjunction with the specific content of the technical solution.

[0158] The above embodiments are merely preferred embodiments of the present invention and should not be construed as limiting the scope of protection of the present invention. Any non-substantial changes and substitutions made by those skilled in the art based on the present invention shall fall within the scope of protection claimed by the present invention.

Claims

1. A method for selecting the optimal cutting direction for a cross-scale structural feature surface, characterized in that, Includes the following steps: Step S100: For a given cross-scale structural feature surface, determine the spatial frequency range of the machinable cross-sectional profile and the target cross-sectional profile at the millimeter, micrometer, and nanometer scales, and determine the initial cross-scale structural feature surface with the cutting direction at 0°. Step S200, with ξ α To change the nominal cutting direction within the angular resolution range of 0° to 180°, and to obtain the nominal cutting direction iξ by rotating and transforming the initial multi-scale structural feature surface, α The target cross-sectional profiles at the millimeter, micrometer, and nanometer scales are calculated within the spatial frequency range determined in step S100 based on the target cross-sectional feature surface under this cutting direction. Step S300, in the nominal cutting direction iξ α Next, within the spatial frequency range determined in step S100, the machinable cross-sectional profiles at the millimeter, micrometer, and nanometer scales under this cutting direction are calculated. Step S400, in the nominal cutting direction iξ α Next, based on the target cross-sectional profile in step S200 and the machinable cross-sectional profile in step S300, the overall relative error between the machinable multi-scale structural feature surface and the target multi-scale structural feature surface is calculated. Step S500: Within the nominal cutting direction selection range, repeat steps S200 to S400 until the overall relative error between the machinable cross-scale structural feature surface and the target cross-scale structural feature surface under all nominal cutting directions is calculated, where i = 0 ~ I, and I satisfies the following formula (1): I=round(180 / ξ α )⑴; Where i = 0, the target cross-scale structural feature surface is the initial cross-scale structural feature surface, and the nominal cutting direction is the X direction of the initial cross-scale structural feature surface; Step S600: Select the nominal cutting direction with the smallest average overall relative error as the optimal cutting direction for the cross-scale structural feature surface.

2. The method for selecting the optimal cutting direction for a multi-scale structural feature surface according to claim 1, characterized in that, Step S100 includes the following steps: Step S110: Determine the working frequency f of the ultrasonic elliptical vibrating tool. e Maximum operating frequency of the workpiece servo mechanism Maximum operating frequency of the three-axis servo platform and the maximum nominal cutting speed v max ; Step S120: Based on the working frequency f of the ultrasonic elliptical vibrating tool e and the maximum nominal cutting speed v max Maximum spatial wavelength of machinable nanostructures with defined cross-sectional profiles Based on the maximum operating frequency of the workpiece servo mechanism and the maximum nominal cutting speed v max Minimum spatial wavelength for determining the profile of a machinable micron structure Based on the maximum operating frequency of the three-axis servo platform and the maximum nominal cutting speed v max Minimum spatial wavelength for determining the cross-sectional profile of a machinable millimeter structure Step S130: Based on the maximum spatial wavelength of the processable nanostructure in step S120. Minimum spatial wavelength for fabricating micron-sized structures and the minimum spatial wavelength for machining millimeter structures Sure: The spatial frequency range of the machinable cross-sectional profile at the millimeter scale is The spatial frequency range of machinable cross-sectional profiles at the micrometer scale is: The spatial frequency range of the machinable cross-sectional profile at the nanoscale is: The spatial frequency range of the target cross-sectional profile at the millimeter scale is The spatial frequency range of the target cross-sectional profile at the micrometer scale is The spatial frequency range of the target cross-sectional profile at the nanoscale is 3. The method for selecting the optimal cutting direction for cross-scale structural feature surfaces according to claim 2, characterized in that, In step S100, the morphology function of the initial multi-scale structural feature surface with the cutting direction at 0° is: z = Z(x,y)⑵; In step S200, in the nominal cutting direction iξ α The topography function of the target multi-scale structural feature surface is as follows:

4. The method for selecting the optimal cutting direction for cross-scale structural feature surfaces according to claim 3, characterized in that, Step S200 includes the following steps: Step S210, in the nominal cutting direction iξ α Below, taking the nominal cutting direction as the X-axis and the feed direction as the Y-axis, along the X and Y directions respectively with ξ x and ξ y To achieve spatial resolution, the shape function of the target cross-sectional profile is sampled, and the target multi-scale structural surface is meshed onto a series of grid points; Step S220: Obtain the spatial spectrum S of the i-th cross-sectional profile using Fast Fourier Transform (FFT). i ,and The spectral components of the target cross-sectional profile at the millimeter, micrometer, and nanometer scales are as follows: Step S230: Obtain the target cross-sectional profiles at the millimeter, micrometer, and nanometer scales using Inverse Fast Fourier Transform (IFFT): Step S240, repeat steps S220 to S230 until all target cross-sectional profiles in the Y direction are obtained. Then, all millimeter, micrometer, and nanometer-scale target cross-sectional profiles in the Y direction will respectively constitute the target millimeter-scale subsurface. iξα Z mm (x,y), target micron-scale subsurface iξα Z μm (x,y) and target nanoscale subsurface iξα Z nm (x,y).

5. The method for selecting the optimal cutting direction for a multi-scale structural feature surface according to claim 4, characterized in that, Step S300 includes the following steps: Step S310: Determine the lateral feed distance c f And c f For ξ y Multiples of: c f =kξ y ⑺; Step S320, along the nominal cutting direction iξ α The cross-sectional profiles of the multi-scale structural feature surface share the same spatial cutting trajectory, and the i-th shared cross-sectional profile is: Step S330: Obtain the spectral components of the i-th shared cross-sectional profile using Fast Fourier Transform (FFT): The spectral components of the machinable cross-sectional profiles at the millimeter, micrometer, and nanometer scales are as follows: Step S340: Obtain the machinable cross-sectional profiles at the millimeter, micrometer, and nanometer scales using Inverse Fast Fourier Transform (IFFT): Step S350, repeat steps S320 to S340 until all machinable cross-sectional profiles in the Y direction are obtained. Then, all millimeter, micrometer, and nanometer-scale machinable cross-sectional profiles in the Y direction will respectively constitute machinable millimeter-scale subsurfaces. Micrometer-scale subsurfaces can be processed and machinable nanoscale subsurfaces 6. The method for selecting the optimal cutting direction for a multi-scale structural feature surface according to claim 5, characterized in that, Step S400 includes the following steps: Step S410: Define the relative error matrix between the machinable subsurface and the target subsurface at the millimeter, micrometer, and nanometer scales as follows: Step S420: Define the overall relative error matrix between the machinable multi-scale structural surface and the target multi-scale structural surface as follows: E(iξ α )=E mm (in α )+E μm (in α )+E nm (in α )⒀。 7. The method for selecting the optimal cutting direction for a multi-scale structural feature surface according to claim 6, characterized in that, In step S600, the cutting direction that minimizes the average overall relative error is searched using the following equation and taken as the optimal cutting direction: Among them, ME(iξ α ) is in the nominal cutting direction iξ α The average overall relative error between the machinable multi-scale structural surface and the target multi-scale structural surface, N i For the nominal cutting direction iξ α The number of sampling points on the target multi-scale structural surface.

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