A method for processing a structural color pattern on a cylindrical surface

Abstract

The application discloses a method for processing a structural color pattern on a cylindrical surface, which comprises the following steps: first, rasterizing a pixel grid of a to-be-processed pattern to obtain a plurality of pixel grids; then, extracting a hue value h row vector from the pixel grid; and finally, sequentially calculating and converting the hue value h row vector, a light wavelength lambda row vector, a grating spacing d row vector and a theoretical rotating speed omega row vector corresponding to each pixel grid to obtain a theoretical rotating speed curve corresponding to the to-be-processed pattern. The ultrasonic elliptical vibration cutting system is used to perform ultrasonic elliptical vibration cutting processing on the surface of the cylindrical workpiece according to the theoretical rotating speed curve. Under the condition that the frequency of the ultrasonic elliptical vibration and the ultrasonic tool parameters are selected, the rotating speed of the cylindrical workpiece corresponds to the grating spacing. Therefore, the structural color pattern corresponding to the to-be-processed pattern can be processed on the surface of the cylindrical workpiece according to the theoretical rotating speed curve. In the processing process, there is no idle time, the whole process is cutting, the continuity is better, and the processing is more efficient.

Description

Technical Field

[0001] This invention relates to the field of cutting and machining technology, and specifically to a method for machining structural color patterns on the surface of a cylinder. Background Technology

[0002] Colors can be categorized into pigment colors and structural colors based on their generation method. Pigment colors are produced by the selective absorption, reflection, and projection of different wavelengths of light by the pigments present in the object itself. Therefore, pigment colors lack luster and do not change with the viewing angle. Structural colors, on the other hand, are produced by the scattering, diffraction, or interference of visible light on the surface of objects with specific micro- and nano-structural features. These colors can be observed at a certain angle, and their color changes with the viewing angle. Compared to dye and pigment coloring, structural color processing is pollution-free, stable, energy-efficient, and produces vibrant colors with high saturation. It has already played an important role in display imaging, information encryption, color printing, and color decoration.

[0003] Fabricating micro / nano grating structures on metal surfaces can produce structural colors. Fabrication methods include mechanical engraving, holographic lithography, electron beam lithography, holographic ion beam etching, and nanoimprint lithography. These methods are characterized by complex processes, low efficiency, and high manufacturing costs. However, ultrasonic elliptical vibration cutting can machine structural color patterns onto metal surfaces with high precision and efficiency, making it widely applicable in aerospace, aviation, and military fields. However, current ultrasonic elliptical vibration cutting methods can only create structural color patterns on planar surfaces, making it difficult to create such patterns on cylindrical surfaces. Summary of the Invention

[0004] In order to overcome the shortcomings of the prior art, the present invention aims to provide a method for processing structural color patterns on the surface of a cylinder, which can process micro-nano structures with blazed grating features on the surface of a cylindrical workpiece.

[0005] To solve the above problems, the technical solution adopted by the present invention is as follows: A method for processing structural color patterns on the surface of a cylinder, comprising the following steps:

[0006] Step S100: The pattern to be processed is pixelated to obtain multiple pixel grids, each pixel grid corresponding to its own hue value. h All hue values h Arranged according to the cutting order h Row vectors;

[0007] Step S200: Take the contents of step S100... h Row vectors converted to light wavelengths λ Row vectors;

[0008] Step S300: The light wavelength in step S200 λ Row vectors converted to grating spacing d Row vectors;

[0009] Step S400: Adjust the grating spacing in step S300. d Row vectors converted to theoretical rotational speed ω Row vectors, to obtain theoretical rotational speed ω Theoretical rotational speed curve as the cutting pixel points change;

[0010] Step S500: The ultrasonic vibration cutting system is used to cut the required structural color pattern on the surface of the cylindrical workpiece. The ultrasonic vibration cutting system includes a rotating device, an ultrasonic vibration cutting device and a three-dimensional motion platform. The rotating device is used to position and install the cylindrical workpiece and provide the rotation speed to the cylindrical workpiece according to the theoretical rotation speed curve in step S400. The ultrasonic vibration cutting device is used to provide ultrasonic elliptical vibration to the ultrasonic tool. The three-dimensional motion platform is used to provide the ultrasonic tool with a feed speed along the axis of the cylindrical workpiece.

[0011] Compared with the prior art, the beneficial effects of the present invention are as follows: This method obtains multiple pixel grids by pixelating the pattern to be processed, and extracts hue values ​​from the pixel grids. h Row vectors, and the hue values ​​corresponding to each pixel grid. h Row vector, light wavelength λ Row vector, grating spacing d Row vector and theoretical rotational speed ω The row vectors are calculated and transformed sequentially to obtain the theoretical rotational speed curve corresponding to the pattern to be processed. An ultrasonic vibration cutting system is then used to perform ultrasonic elliptical vibration cutting on the surface of the cylindrical workpiece according to this theoretical speed curve. Given the selected frequency of the ultrasonic elliptical vibration and the parameters of the ultrasonic tool, the rotational speed of the cylindrical workpiece corresponds to the grating spacing. Therefore, by performing cutting according to the theoretical speed curve, the structural color pattern corresponding to the pattern to be processed can be machined onto the surface of the cylindrical workpiece. Compared to conventional dye or pigment dyeing methods, this method uses ultrasonic elliptical vibration cutting to obtain structural colors, resulting in more stable and durable colors, no pollution, and more vibrant, saturated, and glossy colors. Compared to machining structural color patterns on a plane, this method can machine structural color patterns on a cylindrical surface. The continuous rotation of the cylindrical workpiece, combined with the elliptical vibration of the ultrasonic tool and the feed along the axis of the cylindrical workpiece, eliminates idle time during processing, allowing for continuous cutting, better continuity, and higher processing efficiency.

[0012] In the above-described method for processing structural color patterns on a cylindrical surface, step S300 first obtains the incident angle and observation angle corresponding to the current pixel grid, and then sets the light wavelength... λThe grating pitch is calculated using the following formula (1). d :

[0013] (1)

[0014] in, θ 1 represents the incident angle corresponding to the current pixel grid. θ 2 represents the observation angle corresponding to the current pixel grid. k For diffraction order, and | k |=1;

[0015] In step S400, the grating spacing d The theoretical rotational speed is calculated using the following formula (2). ω :

[0016] (2)

[0017] in, r Let be the radius of the cylindrical workpiece. f The frequency of the elliptical vibration of the ultrasonic cutter.

[0018] In the above-described method for processing structural color patterns on a cylindrical surface, in step S300, the incident angle and observation angle corresponding to the current pixel grid are obtained in the following manner:

[0019] Using the middle plane of the parallel light source as the dividing interface, the pattern to be processed is divided into upper and lower parts, each part occupying a circular angle of . α Then the angle of the circle occupied by the upper and lower parts is 2. α The total number of pixels in a column of the two parts is m The plane corresponding to the point closest to the parallel light source from the cylinder is . plane ;

[0020] When the pixel grid is in the lower half, the first from the bottom up i Angle of incidence of a pixel grid α 1 and observation angle β 1 satisfies the following formulas (3) and (4):

[0021] (3)

[0022] 4

[0023] in, h 1 is the first i The vertical distance of each pixel grid from the horizontal line at the midpoint satisfies the following formula (5):

[0024] (5)

[0025] H The vertical distance from the observation position to the center line of the parallel light source;

[0026] L From the observation position to the plane plane The distance;

[0027] f 1 is the first i The horizontal distance of each pixel grid from the leftmost point of the cylinder satisfies the following formula (6):

[0028] 6

[0029] In step S400, the grating spacing d The theoretical rotational speed is calculated using the following formula (7). ω :

[0030] 7

[0031] When the pixel grid is in the upper half, the first from the bottom up... i Angle of incidence of a pixel grid α 2 and observation angle β 2 satisfies the following formulas (8) and (9):

[0032] (8)

[0033] (9)

[0034] in, h 2 is the first i The vertical distance of each pixel grid from the horizontal line at the midpoint satisfies the following formula (10):

[0035] 10

[0036] f 2 is the first i The horizontal distance of each pixel grid from the leftmost point of the cylinder satisfies the following formula (11):

[0037] 11

[0038] In step S400, the grating spacing d The theoretical rotational speed is calculated using the following formula (12). ω :

[0039] 12.

[0040] The above-described method for machining structural color patterns on a cylindrical surface includes the following steps in step S600: "providing a rotational speed to the cylindrical workpiece according to the theoretical rotational speed curve in step S500":

[0041] Step S610: Use multi-segment continuous pvt The speed curve is fitted to the theoretical speed curve to obtain... pvt Fitting the rotational speed curve;

[0042] Step S620, will pvt The fitted speed curve corresponding to pvt The code format output is as follows pvt The equipment operating code is determined by the rotating device according to... pvt The equipment operation code provides the rotational speed to the cylindrical workpiece.

[0043] The above-described method for processing structural color patterns on the surface of a cylinder includes the following steps in step S610:

[0044] Step S611: After the pattern to be processed is pixelated, the pixel matrix is ​​converted into a pixel row vector containing multiple pixel grids according to the cutting order. Then, the pixel row vector is divided into multiple equal pixel segments, each containing the same number of pixel grids.

[0045] Step S612: Each pixel segment uses a segment pvt The rotational speed curve was fitted, and the result was obtained after fitting all pixel segments. pvt Fitting the rotational speed curve;

[0046] In one section pvt Within the speed curve, t This refers to the time required for this segment of operation. p This refers to the period of time t The angle of rotation of the inner axis of rotation, v This refers to this section. pvt The final velocity of the rotational speed curve. pvt The speed curve satisfies the following formula (13):

[0047] 13

[0048] Among them, the parameters of each segment a i , b i , c i It can be obtained using the following formulas (14), (15) and (16):

[0049] 14

[0050] 12

[0051] ⒃

[0052] in, In order to be in The rotation angle of the axis of rotation at any given moment, a segment pvt The initial time point of the speed curve is The corresponding position is The corresponding speed is The end time point is The corresponding position is The corresponding speed is The initial velocity of each segment is the same as the final velocity of the previous segment.

[0053] In the above-described method for processing structural color patterns on a cylindrical surface, in step S612, for each pixel segment, the minimum time within that pixel segment is determined. T min and maximum time T max and in the minimum time T min and maximum time T max Obtain the corresponding integer time one by one within the integer range between them. t of pvt The rotational speed curve is generated, and the integer time is calculated separately. t of pvt The standard deviation between the rotational speed and the theoretical rotational speed is used, and the time corresponding to the smallest standard deviation is taken as the time for that pixel segment. pvt Code time, thus obtaining the final whole pvt Fitting the rotational speed curve;

[0054] In each pixel segment, V max This represents the maximum theoretical rotational speed within this pixel segment. V min This represents the minimum theoretical rotational speed within that pixel segment. P The minimum time required for the rotation angle of the rotation axis of the pixel segment rotation device. T min and maximum time T max Satisfy the following formulas (17) and (18):

[0055] T min = P / V max 14

[0056] T max = P / Vmin 18.

[0057] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments. Attached Figure Description

[0058] Figure 1 This is a step diagram of Embodiment 1 of the present invention;

[0059] Figure 2 This is a schematic diagram of ultrasonic elliptical vibration cutting a cylindrical surface.

[0060] Figure 3 A schematic diagram of the grid division of a blazed grating on a cylindrical surface;

[0061] Figure 4 A schematic diagram of pixel grid division for the pattern to be processed;

[0062] Figure 5 A schematic diagram showing the incident angle and observation angle of a cylindrical surface with a fixed observation position and light source position;

[0063] Figure 6 This is a partial graph showing the theoretical rotational speed as a function of pixel grid order, calculated using the observation angle and the incident angle.

[0064] Figure 7 For part pvt A comparison chart of simulated speed curves and theoretical speed curves;

[0065] Figure 8 For part pvt A comparison chart of simulated rotational speed curves and actual machining rotational speed curves;

[0066] Figure 9 This is a comparison chart of the predicted pattern and the actual processed pattern. Detailed Implementation

[0067] The embodiments of the present invention are described in detail below:

[0068] Example 1

[0069] Reference Figure 1 Embodiment 1 of the present invention provides a method for processing structural color patterns on the surface of a cylinder, comprising the following steps:

[0070] Step S100: The pattern to be processed is pixelated to obtain multiple pixel grids, each pixel grid corresponding to its own hue value. h All hue values h Arranged according to the cutting order h Row vectors;

[0071] Step S200: Take the contents of step S100... hRow vectors converted to light wavelengths λ Row vectors;

[0072] Step S300: The light wavelength in step S200 λ Row vectors converted to grating spacing d Row vectors;

[0073] Step S400: Adjust the grating spacing in step S300. d Row vectors converted to theoretical rotational speed ω Row vectors, to obtain theoretical rotational speed ω Theoretical rotational speed curve as the cutting pixel points change;

[0074] Step S500: The ultrasonic vibration cutting system is used to cut the required structural color pattern on the surface of the cylindrical workpiece. The ultrasonic vibration cutting system includes a rotating device, an ultrasonic vibration cutting device and a three-dimensional motion platform. The rotating device is used to position and install the cylindrical workpiece and provide the rotation speed to the cylindrical workpiece according to the theoretical rotation speed curve in step S400. The ultrasonic vibration cutting device is used to provide ultrasonic elliptical vibration to the ultrasonic tool. The three-dimensional motion platform is used to provide the ultrasonic tool with a feed speed along the axis of the cylindrical workpiece.

[0075] Reference Figure 2 The ultrasonic vibration cutting device provides the ultrasonic tool with a direction along... X Axial direction and along Y The vibrations in the axial direction at the micro-nano level combine to form the elliptical vibration of the ultrasonic tool. Simultaneously, the rotation of the cylindrical workpiece driven by the rotating axis provides the nominal cutting speed, and the three-dimensional motion platform provides the ultrasonic tool with a cutting speed along the axial direction. Z The feed rate along the axial direction. With a fixed observation angle and light source incident angle, the color displayed by the blazed grating corresponds to the grating spacing of the micro / nano structure. d Related, refer to Figure 3 When the frequency of elliptical vibration processing is fixed, the grating spacing on the cylindrical surface is... d Since it is related to rotational speed, different colors can be observed in each processing area by assigning different rotational speeds to different processing areas. Therefore, it is particularly important to determine the appropriate rotational speed for different areas based on the color characteristics of the pattern to be processed. Among these, in... Figure 3 In the diagram, n1, n2, n3, and n4 represent four different rotation speeds. Different rotation speeds correspond to different grating spacings, which in turn display different colors.

[0076] Reference Figure 4 For any photograph, it can be pixelated into a grid, and each pixel grid has a corresponding rgb (Color Standard) and h s v(Color Model) This method obtains multiple pixel grids by pixelating the pattern to be processed, and extracts hue values ​​from the pixel grids. h Row vectors, and the hue values ​​corresponding to each pixel grid. h Row vector, light wavelength λ Row vector, grating spacing d Row vector and theoretical rotational speed ω The row vectors are calculated and transformed sequentially to obtain the theoretical rotational speed curve corresponding to the pattern to be processed. An ultrasonic vibration cutting system is then used to perform ultrasonic elliptical vibration cutting on the surface of the cylindrical workpiece according to this theoretical speed curve. Given the selected frequency of the ultrasonic elliptical vibration and the parameters of the ultrasonic tool, the rotational speed of the cylindrical workpiece corresponds to the grating spacing. Therefore, by performing cutting according to the theoretical speed curve, the structural color pattern corresponding to the pattern to be processed can be machined onto the surface of the cylindrical workpiece. Compared to conventional dye or pigment dyeing methods, this method uses ultrasonic elliptical vibration cutting to obtain structural colors, resulting in more stable and durable colors, no pollution, and more vibrant, saturated, and glossy colors. Compared to machining structural color patterns on a plane, this method can machine structural color patterns on a cylindrical surface. The continuous rotation of the cylindrical workpiece, combined with the elliptical vibration of the ultrasonic tool and the feed along the axis of the cylindrical workpiece, eliminates idle time during processing, allowing for continuous cutting, better continuity, and higher processing efficiency.

[0077] Example 2

[0078] Embodiment 2 of the present invention provides a method for processing structural color patterns on the surface of a cylinder, comprising the following steps:

[0079] Step S100: The pattern to be processed is pixelated to obtain multiple pixel grids, each pixel grid corresponding to its own hue value. h All hue values h Arranged according to the cutting order h Row vectors;

[0080] Step S200: Take the contents of step S100... h Row vectors are converted into light wavelengths using the following formula (19). λ Row vectors:

[0081] 16

[0082] Step S300: Obtain the incident angle and observation angle corresponding to the current pixel grid, and then convert the light wavelength from step S200... λ The grating pitch is calculated using the following formula (1). d :

[0083] (1)

[0084] in, θ 1 represents the incident angle corresponding to the current pixel grid. θ 2 represents the observation angle corresponding to the current pixel grid. k For diffraction order, and | k |=1;

[0085] Step S400: Adjust the grating spacing in step S300. d The theoretical rotational speed is calculated using the following formula (2). ω Row vectors, to obtain theoretical rotational speed ω Theoretical rotational speed curve as the number of cutting pixels varies:

[0086] (2)

[0087] in, r Let be the radius of the cylindrical workpiece. f The frequency of the elliptical vibration of the ultrasonic cutter;

[0088] Step S500: The ultrasonic vibration cutting system is used to cut the required structural color pattern on the surface of the cylindrical workpiece. The ultrasonic vibration cutting system includes a rotating device, an ultrasonic vibration cutting device and a three-dimensional motion platform. The rotating device is used to position and install the cylindrical workpiece and provide the rotation speed to the cylindrical workpiece according to the theoretical rotation speed curve in step S400. The ultrasonic vibration cutting device is used to provide ultrasonic elliptical vibration to the ultrasonic tool. The three-dimensional motion platform is used to provide the ultrasonic tool with a feed speed along the axis of the cylindrical workpiece.

[0089] Example 3

[0090] When machining on cylindrical or curved surfaces, a crucial step is obtaining the observation angle and the angle of incidence. Unlike planar surfaces, the observation angle and the angle of incidence on a cylindrical surface continuously change with the observation position and the position of the pixel grid on the cylindrical or curved surface. To better obtain the observation angle and the angle of incidence, Embodiment 3 of this invention provides a method for machining structural color patterns on a cylindrical surface, comprising the following steps:

[0091] Step S100: The pattern to be processed is pixelated to obtain multiple pixel grids, each pixel grid corresponding to its own hue value. h All hue values h Arranged according to the cutting order h Row vectors;

[0092] Step S200: Take the contents of step S100... h Row vectors are converted into light wavelengths using the following formula (19). λ Row vectors:

[0093] 16

[0094] Step S300: Obtain the incident angle and observation angle corresponding to the current pixel grid using the following method:

[0095] Using the middle plane of the parallel light source as the dividing interface, the pattern to be processed is divided into upper and lower parts, each part occupying a circular angle of . α Then the angle of the circle occupied by the upper and lower parts is 2. α The total number of pixels in a column of the two parts is m The plane corresponding to the point closest to the parallel light source from the cylinder is . plane ;

[0096] When the pixel grid is in the lower half, the first from the bottom up i Angle of incidence of a pixel grid α 1 and observation angle β 1 satisfies the following formulas (3) and (4):

[0097] (3)

[0098] 4

[0099] in, h 1 is the first i The vertical distance of each pixel grid from the horizontal line at the midpoint satisfies the following formula (5):

[0100] (5)

[0101] H The vertical distance from the observation position to the center line of the parallel light source;

[0102] L From the observation position to the plane plane The distance;

[0103] f 1 is the first i The horizontal distance of each pixel grid from the leftmost point of the cylinder satisfies the following formula (6):

[0104] 6

[0105] In step S400, the grating spacing d The theoretical rotational speed is calculated using the following formula (7). ω :

[0106] 7

[0107] When the pixel grid is in the upper half, the first from the bottom up... iAngle of incidence of a pixel grid α 2 and observation angle β 2 satisfies the following formulas (8) and (9):

[0108] (8)

[0109] (9)

[0110] in, h 2 is the first i The vertical distance of each pixel grid from the horizontal line at the midpoint satisfies the following formula (10):

[0111] 10

[0112] f 2 is the first i The horizontal distance of each pixel grid from the leftmost point of the cylinder satisfies the following formula (11):

[0113] 11

[0114] In step S400, the grating spacing d The theoretical rotational speed is calculated using the following formula (12). ω :

[0115] 12

[0116] Step S400: Adjust the grating spacing in step S300. d The theoretical rotational speed is calculated using the following formula (2). ω Row vectors, to obtain theoretical rotational speed ω Theoretical rotational speed curve as the number of cutting pixels varies:

[0117] (2)

[0118] in, r Let be the radius of the cylindrical workpiece. f The frequency of the elliptical vibration of the ultrasonic cutter;

[0119] Step S500: The ultrasonic vibration cutting system is used to cut the required structural color pattern on the surface of the cylindrical workpiece. The ultrasonic vibration cutting system includes a rotating device, an ultrasonic vibration cutting device and a three-dimensional motion platform. The rotating device is used to position and install the cylindrical workpiece and provide the rotation speed to the cylindrical workpiece according to the theoretical rotation speed curve in step S400. The ultrasonic vibration cutting device is used to provide ultrasonic elliptical vibration to the ultrasonic tool. The three-dimensional motion platform is used to provide the ultrasonic tool with a feed speed along the axis of the cylindrical workpiece.

[0120] Furthermore, referring toFigure 5 In step S300, with α Taking 10° as an example, the circular angle occupied by a picture is 2. α =20°. Since the calculation methods for the incident angle and observation angle of the upper and lower halves are different, the pattern is divided into upper and lower parts, with the middle plane of the parallel light source as the dividing interface. The circular angle occupied by half a part is 10°. Let... i The number counting from the bottom up i If there are elements, then:

[0121] If in the second half, the first i The radius of the grid of pixels is (20*) i / m )°, and α 1 and α 1 ' Since they are interior angles on the same side, we have:

[0122]

[0123]

[0124]

[0125]

[0126] in, α 1 is the first i The incident angle corresponding to each pixel grid h 1 is the first i The vertical distance of each pixel grid from the midpoint of the horizontal line. f 1 is the first i The horizontal distance of each pixel grid from the leftmost point of the cylinder. β 1 is the first i The observation angle corresponding to each pixel grid L It is the distance from the observation position to the plane. plane The distance, when the observation point is outside the lower half of the 10° range. β The value of 1 is positive, and... α 1. Same sign; when the observation point is within the lower half of 10°, β The value of 1 is negative, and... α 1. Opposite signs satisfy the sign relationship between the observation angle and the incident angle. Therefore, for better observation results, the diffraction order of the grating equation should be | k If |=1, then:

[0127] 7

[0128] in, ω For the firsti Rotation speed of each pixel grid f The frequency of the elliptical vibration of the ultrasonic cutter. λ For the first i The light wavelength corresponding to each pixel grid r Let be the radius of the cylindrical workpiece.

[0129] Similarly, if in the upper part, let... i The number counting from the bottom up i One element, i The angle of the circle occupied by each pixel is (20* i / m )°, α 2 and α 2 ' Since it is an interior angle on the same side, therefore:

[0130]

[0131]

[0132]

[0133]

[0134] in, α 2 is the first i The incident angle corresponding to each pixel grid h 2 is the first i The vertical distance of each pixel grid from the midpoint of the horizontal line. f 2 is the first i The horizontal distance of each pixel grid from the leftmost point of the cylinder. β 2 is the first i The observation angle corresponding to the pixel of each element, and α The two diffraction orders are of the same sign, satisfying the sign relationship between the observation angle and the incident angle. Therefore, for better observation results, the diffraction order of the grating equation should be | k If |=1, then:

[0135] 12

[0136] Therefore, after calculating the observation angle and incident angle at a fixed position on the cylindrical surface, the theoretical rotational speed required for each pixel grid of the pattern can be obtained using the above formulas (7) and (12). By arranging the theoretical rotational speeds of all pixel grids into a row vector according to the cutting order, the curve of the theoretical rotational speed changing with the cutting pixel points can be obtained. Figure 6 As shown, in this embodiment, the structural color pattern is an 1800*175 matrix pixel. From the above step S300, the rotational speed curve of the workpiece requiring elliptical vibration processing on the cylindrical surface can be obtained.Figure 6 The diagram shows the theoretical rotation speed curves of the pixel grid for the first three images of the 100th column of the structural color pattern. This verifies that the required rotation speed varies depending on the position of the same color on the circumference, which is significantly different from the algorithm for planar structural color patterns. This invention allows for the processing of desired structural color patterns on cylindrical surfaces, achieving a new technological breakthrough. Furthermore, by observing the designed and processed structural color pattern on the cylindrical surface from a defined angle, the dynamic pattern can still be observed as the cylinder rotates—a function impossible for planar patterns. When the cylindrical surface pattern is used as a template, the cylinder can be continuously rolled and imprinted, making it more efficient and convenient.

[0137] Example 4

[0138] Embodiment 4 of the present invention provides a method for processing structural color patterns on the surface of a cylinder. The difference between this method and Embodiments 1, 2, or 3 is that, after obtaining the theoretical rotational speed curve, the method is applied to the equipment... pvt The code instructions process the cylindrical workpiece, enabling... pvt The rotational speed curve is fitted to the theoretical rotational speed curve to reduce machining errors.

[0139] In one section pvt Within the speed curve, t This refers to the time required for this segment of operation. p This refers to the period of time t The angle of rotation of the inner axis of rotation, v This refers to this section. pvt The final velocity of the rotational speed curve. pvt The speed curve satisfies the following formula (13):

[0140] 13

[0141] in, In order to be in The rotation angle of the rotation axis at any given time, and the parameters for each segment. a i , b i , c i It can be obtained using the following formulas (14), (15) and (16):

[0142] 14

[0143] 12

[0144] ⒃

[0145] in, In order to be in The rotation angle of the axis of rotation at any given moment, a segment pvt The initial time point of the speed curve is The corresponding position is The corresponding speed is The end time point is The corresponding position is The corresponding speed is The initial velocity of each segment is the same as the final velocity of the previous segment.

[0146] for pvt The code requires the following three parameters to determine the velocity curve for that time period:

[0147] P : The angle (in degrees) of rotation of the rotation axis of this pixel segment;

[0148] V : The angular velocity (in ° / s) at the end of the pixel segment.

[0149] T The processing time (in units) required for this pixel segment. m s);

[0150] exist pvt In the code, the initial velocity of each segment is the final velocity of the previous segment, and the velocities of each segment are continuous and interconnected. pvt The initial and final velocities of the rotational speed curve are consistent with those of the corresponding theoretical rotational speed curve. Therefore, by giving... P , V , T The system's internal algorithm can calculate the cubic polynomial (13) for this segment, along with the final velocity of the previous segment, using these four parameters to obtain the velocity curve for that time period. In this embodiment, when processing the structural color pattern on the cylindrical surface, step S600, "providing the rotational speed to the cylindrical workpiece according to the theoretical rotational speed curve in step S500" includes the following steps:

[0151] Step S610: Use multi-segment continuous pvt The speed curve is fitted to the theoretical speed curve to obtain... pvt Fitting the rotational speed curve;

[0152] Step S620, will pvt The fitted speed curve corresponding to pvt The code format output is as follows pvt The equipment operating code is determined by the rotating device according to... pvt The equipment operation code provides the rotational speed to the cylindrical workpiece.

[0153] In this embodiment, multiple continuous segments are required. pvtThe rotational speed curve is fitted to the theoretical rotational speed curve; therefore, step S610 includes the following steps:

[0154] Step S611: After the pattern to be processed is pixelated into a mesh, the pixel matrix is ​​converted into a pixel row vector containing multiple pixel meshes according to the cutting order. Then, the pixel row vector is divided into multiple equal pixel segments, each containing the same number of pixel meshes. For example, when processing... Figure 4 When creating 18 consecutive motion images of galloping horses, the image resolution is 1800*175 pixels, totaling 31,500 pixels. These are divided into 10-pixel segments, meaning each segment contains 10 pixels. The resulting pixel color values... h The row vectors are as follows:

[0155] h =

[0156] (0.473,0.473,0.473,0.473,0.473,0.473,0.473,0.473,0.473,0.473,0.473,0.473,0.473,0.69,0.69,0.69,0.69,0.69,0.69,0.69,0.69,0.69,0.69,0.473,0.473,0.473,0.473,0.473,0.473,......0.69,0.69,0.69,0.69,0.69,0.69,0.69,0.473,0.473,0.473,0.473,0.473);

[0157] Equal pixel segments:

[0158] L1=(0.473,0.473,0.473,0.473,0.473,0.473,0.473,0.473,0.473,0.473);

[0159] L2=(0.473,0.473,0.473,0.69,0.69,0.69,0.69,0.69,0.69,0.69);

[0160] L3=(0.69,0.69,0.69,0.473,0.473,0.473,0.473,0.473,0.473,0.473); ......

[0161] L3150=(0.69,0.69,0.69,0.473,0.473,0.473,0.473,0.473,0.473,0.473);

[0162] Step S612: Each pixel segment uses a segmentpvt The rotational speed curve was fitted, and the result was obtained after fitting all pixel segments. pvt Fitting the rotational speed curve;

[0163] In step S612, for each pixel segment, the minimum time within that pixel segment is determined. T min and maximum time T max and in the minimum time T min and maximum time T max Obtain the corresponding integer time one by one within the integer range between them. t of pvt The rotational speed curve is generated, and the integer time is calculated separately. t The standard deviation between the PVT rotation speed and the theoretical rotation speed is used, and the time corresponding to the smallest standard deviation is taken as the time for that pixel segment. pvt Code time, thus obtaining the final whole pvt Fitted speed curve;

[0164] In each pixel segment, V max This represents the maximum theoretical rotational speed within this pixel segment. V min This represents the minimum theoretical rotational speed within that pixel segment. P The minimum time required for the rotation angle of the rotation axis of the pixel segment rotation device. T min and maximum time T max Satisfy the following formulas (17) and (18):

[0165] T min = P / V max 14

[0166] T max = P / V min 18

[0167] For example, in the L2 pixel segment, the theoretical rotational speed can be obtained from steps S200 to S400. ω row vector is

[0168] W 2=

[0169] (158.189250137658,155.969179769376,153.813075770135,

[0170] 151.718243517935, 149.682137688774, 147.702352058745,

[0171] 145.776610130772, 143.902756509206, 142.078748953583,

[0172] 140.302651049971), there are a total of 1800 pixels corresponding to one circumference of the cylinder, and the circumferential angle P = 2° is occupied by 10 pixels in the equal pixel segment. Since t in the pvt code must be an integer, by calculating and rounding the above formulas (17) and (18), we can obtain the minimum time. T min and maximum time T max The integer interval between these intervals is [12ms, 15ms]. The initial velocity of this segment is the final velocity of the previous segment, which is V = 140.302651049971° / s. Within the integer interval [12ms, 15ms], we take 12, 13, 14, and 15 as t in the PVT speed curves to obtain the PVT speed curves at times 12, 13, 14, and 15. We then calculate the standard deviation corresponding to each integer time within the integer interval [12ms, 15ms]. The standard deviation corresponding to 13ms is the smallest, at 7.4338. Therefore, the T = 13 corresponds to the PVT code of the L2 pixel segment.

[0173] Example 4

[0174] Embodiment 4 of the present invention provides a method for processing structural color patterns on the surface of a cylinder, wherein... Figure 4 The 18 images of horses in continuous motion were machined onto the surface of a cylinder. During the machining process, the following techniques were used: ac s-axis rotation EL -50 ΣHP Ultrasonic vibration cutting device and ANT 130 XYZ Three-dimensional motion platform. The tip radius of the diamond tool selected during machining. R n For 500 μm Rake angle of the cutting tool γ = 0° The back angle of the cutting tool α=20° The tool vibration frequency is a fixed 40. khz Amplitude in the bending direction Ax =0.5 μm, Amplitude in the axial direction Ay =2.5 μm Phase difference φ =90°. The material used in the experiment was 50 mm in length. mm, with a diameter of 30 mm A brass cylinder. The following steps are in matlab The software performs the processing calculations, and the processing steps include the following:

[0175] Step 1: Import the image matlad Extract the pixel matrix corresponding to the image rgb A 3D matrix will be transformed and extracted to obtain the pixel matrix corresponding to the image. h The matrix is ​​obtained by transforming it according to the cutting order. h Row vectors, where the extracted portion h The row vectors are as follows:

[0176] h=

[0177] (0.641830065359477, 0.641830065359477, 0.641830065359477, 0.641830065359477, 0.641830065359477, 0.641830065359477, 0.64183) 0065359477, 0.641830065359477, 0.641830065359477, 0.641830065359477, 0.641830065359477, 0.641830065359477, 0.641830065359477, 0.641830065359477 7, 0.641830065359477, 0.643044619422572, 0.641830065359477, 0.641830065359477, 0.642857142857143, 0.642857142857143, 0.6411764705882350, 6405228 75816994, 0.6411764705882350, 641830065359477, 0.643044619422572, 0.642857142857143, 0.640000000000000, 0.639892904953146, 0.6400000000000000);

[0178] Step 2: Obtain the results from Step 1 h Row vectors are converted to wavelengths using formula (19). λ Row vectors are used, and wavelengths are optimized to improve stability. For example, colors in the blue range have their wavelengths converted to 473. nm This is to facilitate the subsequent fitting of the rotational speed curve, in which a portion of the wavelength is extracted. λ The row vectors are as follows:

[0179] λ =

[0180] (0.473, ...

[0181] Step 3, according to Example 3 and Figure 5 Based on the principle, the incident angle and observation angle of a given cylindrical image position and observation position are calculated, and the wavelength is... λ Row vectors converted to corresponding rotational speeds ω Row vectors are used to obtain the theoretical rotational speed curve, where a portion of the incident angle is extracted. α Row vector, observation angle β Row vector, grating spacing d Row vector and rotational speed ω The row vectors are as follows:

[0182] α = (

[0183] 0.172787595947439,0.169296937443450,0.165806278939461,0.162315620435473,0.158824961931484,0.155334303427495, 0.151843644923507,0.148352986419518,0.144862327915529, 0.141371669411541,0.137881010907552,0.134390352403563, 0.130899693899575,0.127409035395586,0.123918376891597,0.120427718387609,0.116937059883620,0.113446401379631, 0.109955742875643,0.106465084371654,0.102974425867665, 0.0994837673636768,0.0959931088596881,0.0925024503556995, 0.0890117918517108,0.0855211333477222,0.0820304748437335,0.0785398163397448,0.0750491578357562,0.0715584993317675）；

[0184] β =（

[0185] 0.598433041961003,0.602232780443210,0.606031647349773,0.609829638429552,0.613626749453890,0.617422976216672, 0.621218314534395,0.625012760246227,0.628806309214071, 0.632598957322628,0.636390700479449,0.640181534615003, 0.643971455682727,0.647760459659086,0.651548542543627,0.655335700359030,0.659121929151167,0.662907224989146, 0.666691583965368,0.670475002195572,0.674257475818882, 0.678039000997860,0.681819573918546,0.685599190790504, 0.689377847846867,0.693155541344377,0.696932267563429,0.700708022808110,0.704482803406235,0.708256605709390）；

[0186] d =（

[0187] 1.20842243097332,1.18845869999089,1.16916364351177, 1.15050448701051,1.13245056372995,1.11497314792814, 1.09804530370943,1.08164174776694,1.06573872456516, 1.05031389266695,1.03534622106113,1.02081589447895,1.00670422680314,0.992993581773943,0.979667300284724, 0.966709633636845,0.954105682191787,0.941841338918007, 0.929903237382930,0.918278703787004,0.906955712678005, 0.895922846020310,0.885169255326321,0.874684626586055,0.864459147756614,0.854483478596164,0.844748722647511, 0.835246401194663,0.825968429032159,0.816907091901647）；

[0188] ω =（

[0189] 184.633347103228, 181.583113693553, 178.635046222300, 175.784137110842, 173.025700823832, 170.355348391194, 167.768964311229, 165.262685579199, 162.832882616637, 160.476141903393, 158.189250137658, 155.969179769376, 153.813075770135, 151.718243517935, 149.682137688774, 147.702352058745, 145.776610130772, 143.902756509206, 142.078748953583, 140.302651049971, 138.572625444612, 136.886927590168, 135.243899959830, 133.641966688953, 132.079628607813, 130.555458632580, 129.068097484719, 127.616249711853, 126.198679985583, 124.814209654053);

[0190] Step 4: Output the maximum and minimum rotational speeds. ω and the maximum and minimum grating spacing d If the equipment cannot achieve the maximum and minimum speeds under these conditions, further modifications to the previous conditions are required. In this embodiment, the equipment... pvt Under the machining experiment code, the maximum rotational speed is 380° / s. By using the maximum and minimum grating spacing, the potential for the tool's back angle to plow the grating can be roughly estimated based on the elliptical vibration amplitude of the tool, thus reducing the impact of the tool's back angle on the grating.

[0191] Step 5, in matlab The output section contains representative theoretical speed curves to verify the results of steps one through four. matlab The correctness of the code, and its implications for subsequent actions. pvt The code performs preliminary pixel segmentation checks, such as determining whether equal pixel segmentation is suitable, and whether the maximum rotation speed and maximum acceleration exceed device limits.

[0192] Step Six: According to step S611 in Example Three, select the 15-pixel segmentation method and obtain... pvt The code fits a curve of rotational speed as a function of image pixels, with some curves as shown below.Figure 6 As shown;

[0193] Step 7, in matlab The output section also features representative theoretical speed curves and pvt The fitted rotational speed curves are then compared visually to determine the better fit. If the fit is insufficient, the optimal conditions are obtained by continuously changing the observation position and the size of the evenly divided pixel segments. In this embodiment, some theoretical rotational speed curves and... pvt The fitted speed curve is as follows Figure 7 As shown, it is important to note that in Figure 7 In the middle, through the equipment pvt The algorithm code can fit the theoretically required rotational speed curve very well. Although there is an error in the rotational speed, since the wavelength can display the same color within a certain range, the results are relatively accurate as long as the experimental error is below a certain range.

[0194] Step 8: Inspection pvt The shortest time corresponding to the segment, the maximum mean square error within the segment, and the overall mean square error. pvt Code experiment maximum rotational speed acceleration, pvt Code experiment maximum speed and pvt The code experiment detects parameters such as minimum rotation speed. pvt Reasonableness and thereby improve and optimize results;

[0195] Step Nine, use pvt Algorithm fitting obtained pvt The fitted rotational speed was obtained by reverse calculation. matlab Predicting images allows for a visual understanding of the quality of the results in advance, and enables comparison with the final processed image for verification. pvt The accuracy of the code;

[0196] Step 10: After the inspection is completed, place the required equipment... pvt The code format output is as follows pvt The device runs the code and saves it to the specified file;

[0197] Step 11: The ultrasonic vibration cutting system, based on... pvt The equipment operating code cuts and processes the required structural color pattern on the cylindrical surface.

[0198] In this embodiment, some pvt Comparison of simulated speed curves and actual speed curves Figure 8 As shown, you can see pvtThe fitted speed curve and the actual machining speed curve show a very good fit; the theoretical speed curve and the actual machining speed curve are very close, and the fitting effect is even better than the speed curve under no-load conditions. The reason why the speed under no-load conditions differs significantly from the actual machining speed curve is because the control parameters for the rotating shaft are different when it is unloaded and when clamping the cylindrical workpiece (within the equipment). digital s cope Inside ea s ytune Regulation pid Since this control parameter is the parameter when the workpiece is mounted, it causes an error in the rotational speed when unloaded. This indirectly shows that the theoretical and actual machining rotational speeds fit very well, and the error is even smaller than that between unloaded and workpiece-clamped speeds. matlab Calculated using software pvt The expected effect of code processing patterns is as follows: Figure 9 As shown in columns 1 and 3, the actual processed pattern presentation is shown in columns 2 and 4, which are derived from... Figure 9 It can be seen that the pixels are evenly divided into 15 segments. pvt The fitting method yielded good processing results, with most color areas being accurate. The horse's outline was a transitional zone between blue and red, with distinct colors.

[0199] 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.

[0200] 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.

[0201] 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.

[0202] 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 processing structural color patterns on the surface of a cylinder, characterized in that, Includes the following steps: Step S100: The pattern to be processed is pixelated to obtain multiple pixel grids, each pixel grid corresponding to its own hue value. h All hue values h Arranged according to the cutting order h Row vectors; Step S200: Take the contents of step S100... h Row vector converted to light wavelength λ Row vectors; Step S300: The light wavelength in step S200 λ Row vectors converted to grating spacing d Row vectors; Step S400: Adjust the grating spacing in step S300. d Row vectors converted to theoretical rotational speed ω Row vectors, to obtain theoretical rotational speed ω Theoretical rotational speed curve as the cutting pixel points change; Step S500: The ultrasonic vibration cutting system is used to cut the required structural color pattern on the surface of the cylindrical workpiece. The ultrasonic vibration cutting system includes a rotating device, an ultrasonic vibration cutting device and a three-dimensional motion platform. The rotating device is used to position and install the cylindrical workpiece and provide the rotation speed to the cylindrical workpiece according to the theoretical rotation speed curve in step S400. The ultrasonic vibration cutting device is used to provide ultrasonic elliptical vibration to the ultrasonic tool. The three-dimensional motion platform is used to provide the ultrasonic tool with a feed speed along the axis of the cylindrical workpiece. In step S300, the incident angle and observation angle corresponding to the current pixel grid are first obtained, and then the light wavelength is... λ The grating pitch is calculated using the following formula (1). d : ⑴ in, θ 1 represents the incident angle corresponding to the current pixel grid. θ 2 represents the observation angle corresponding to the current pixel grid. k For diffraction order, and | k |=1; In step S400, the grating spacing d The theoretical rotational speed is calculated using the following formula (2). ω : ⑵ in, r Let be the radius of the cylindrical workpiece. f The frequency of the elliptical vibration of the ultrasonic cutter; In step S300, the incident angle and observation angle corresponding to the current pixel grid are obtained in the following way: Using the middle plane of the parallel light source as the dividing interface, the pattern to be processed is divided into upper and lower parts, each part occupying a circular angle of . α Then the angle of the circle occupied by the upper and lower parts is 2. α The total number of pixels in a column of the two parts is m The plane corresponding to the point closest to the parallel light source from the cylinder is . plane ; When the pixel grid is in the lower half, the first from the bottom up i Angle of incidence of a pixel grid α 1 and observation angle β 1 satisfies the following formulas (3) and (4): ⑶ ⑷ in, h 1 is the first i The vertical distance of each pixel grid from the horizontal line at the midpoint satisfies the following formula (5): ⑸ H The vertical distance from the observation position to the center line of the parallel light source; L From the observation position to the plane plane The distance; f 1 is the first i The horizontal distance of each pixel grid from the leftmost point of the cylinder satisfies the following formula (6): ⑹ In step S400, the grating spacing d The theoretical rotational speed is calculated using the following formula (7). ω : ⑺ When the pixel grid is in the upper half, the first from the bottom up... i Angle of incidence of a pixel grid α 2 and observation angle β 2 satisfies the following formulas (8) and (9): ⑻ ⑼ in, h 2 is the first i The vertical distance of each pixel grid from the horizontal line at the midpoint satisfies the following formula (10): ⑽ f 2 is the first i The horizontal distance of each pixel grid from the leftmost point of the cylinder satisfies the following formula (11): ⑾ In step S400, the grating spacing d The theoretical rotational speed is calculated using the following formula (12). ω : ⑿。 2. The method for processing structural color patterns on the surface of a cylinder according to claim 1, characterized in that, In step S600, "providing a rotational speed to the cylindrical workpiece according to the theoretical rotational speed curve in step S500" includes the following steps: Step S610: Use multi-segment continuous pvt The speed curve is fitted to the theoretical speed curve to obtain... pvt Fitting the rotational speed curve; Step S620, to pvt The fitted speed curve corresponding to pvt The code format output is as follows pvt The equipment runs the code and saves it to a specified file, which is then used by the rotating device according to... pvt The equipment operation code provides the rotational speed to the cylindrical workpiece.

3. The method for processing structural color patterns on the surface of a cylinder according to claim 2, characterized in that, Step S610 includes the following steps: Step S611: After the pattern to be processed is pixelated, the pixel matrix is ​​converted into a pixel row vector containing multiple pixel grids according to the cutting order. Then, the pixel row vector is divided into multiple equal pixel segments, each containing the same number of pixel grids. Step S612: Each pixel segment uses a segment pvt The rotational speed curve was fitted, and the result was obtained after fitting all pixel segments. pvt Fitting the rotational speed curve; In one section pvt Within the speed curve, t This refers to the time required for this segment of operation. p This refers to the period of time t The angle of rotation of the inner axis of rotation, v This refers to this section. pvt The final velocity of the rotational speed curve. pvt The speed curve satisfies the following formula (13): ⒀ Among them, the parameters of each segment a i , b i , c i It can be obtained using the following formulas (14), (15) and (16): ⒁ ⒂ ⒃ in, In order to be in The rotation angle of the axis of rotation at any given moment, a segment pvt The initial time point of the speed curve is The corresponding position is The corresponding speed is The end time point is The corresponding position is The corresponding speed is The initial velocity of each segment is the same as the final velocity of the previous segment.

4. The method for processing structural color patterns on the surface of a cylinder according to claim 3, characterized in that, In step S612, for each pixel segment, the minimum time within that pixel segment is determined. T min and maximum time T max and in the minimum time T min and maximum time T max Obtain the corresponding integer time one by one within the integer range between them. t of pvt The rotational speed curve is generated, and the integer time is calculated separately. t of pvt The standard deviation between the rotational speed and the theoretical rotational speed is used, and the time corresponding to the smallest standard deviation is taken as the time for that pixel segment. pvt Code time, thus obtaining the final whole pvt Fitting the rotational speed curve; In each pixel segment, V max This represents the maximum theoretical rotational speed within this pixel segment. V min This represents the minimum theoretical rotational speed within that pixel segment. P The minimum time required for the rotation angle of the rotation axis of the pixel segment rotation device. T min and maximum time T max Satisfy the following formulas (17) and (18): T min = P / V max ⒄ T max = P / V min ⒅。

Images