Complex ultrasonic vibration polishing path planning method based on entropy increase principle

Abstract

The invention relates to an optical element surface polishing method, in particular to a complex ultrasonic vibration polishing path planning method based on the entropy increase principle, and solves the technical problem that an existing ultrasonic vibration auxiliary polishing method cannot effectively solve intermediate frequency error accumulation. According to the method, the coupling polishing path is obtained by superposing complex ultrasonic vibration on the regular polishing path, and the optimal coupling polishing path is selected based on the entropy increase principle; the information entropy of different coupling polishing paths is compared, the coupling polishing path with the maximum information entropy is selected as the complex ultrasonic vibration polishing path, the obtained complex ultrasonic vibration polishing path has high randomness, the polishing effect can be further optimized, and the quality of the polished surface is improved; and particularly, the method has obvious advantages in the aspect of inhibiting intermediate-frequency error accumulation.

Description

Technical Field

[0001] The present invention relates to a method for polishing the surface of an optical element, and more particularly to a complex ultrasonic vibration polishing path planning method based on the principle of entropy increase. Background Art

[0002] Both mechanical grinding and Computer Controlled Optical Surfacing (CCOS) polishing technologies are widely used in the polishing of the surface of high-precision optical elements. However, due to the repeatability of the regular polishing paths (such as raster trajectories, Archimedes spiral trajectories) adopted by precision grinding and CCOS polishing technologies, significant mid-frequency errors will be formed on the surface of high-precision optical elements during the polishing process, resulting in a regular residual convolution effect in the feed direction of the polishing tool for the polishing removal function. This kind of mid-frequency error is difficult to eliminate in subsequent processes, which may lead to an increase in the scattering rate of high-precision optical elements and even cause self-interference phenomena, affecting the performance of the optical system.

[0003] In order to suppress the mid-frequency errors formed by regular polishing paths, the current mainstream method is to introduce pseudo-random paths for polishing. Pseudo-random paths can destroy the periodicity of regular polishing paths, effectively weaken the accumulation of mid-frequency errors, and improve the quality of the surface of high-precision optical elements. However, the implementation of pseudo-random paths places higher requirements on the number of linked axes and dynamic performance of the polishing tool machine tool, restricting its popularization and application in the manufacturing of high-precision optical elements. Therefore, although there are problems with the accumulation of mid-frequency errors in regular polishing paths, due to its stable polishing performance, it is still the preferred solution for the surface polishing of high-precision optical elements.

[0004] To further optimize the polishing effect of regular polishing paths, in recent years, researchers have begun to explore ultrasonic vibration-assisted polishing technology. Ultrasonic vibration-assisted polishing technology improves the removal rate and material removal characteristics by superimposing high-frequency vibrations during the polishing process, which helps to suppress the accumulation of mid-frequency errors to a certain extent. However, traditional one-dimensional ultrasonic vibrations (such as longitudinal vibrations) have limited ability to suppress the residual convolution effect of regular polishing paths due to the single motion direction, and still cannot effectively solve the problem of mid-frequency error accumulation. Summary of the Invention

[0005] The purpose of the present invention is to solve the technical problem that the existing ultrasonic vibration-assisted polishing method cannot effectively solve the accumulation of mid-frequency errors, and to provide a complex ultrasonic vibration polishing path planning method based on the principle of entropy increase.

[0006] To achieve the above purpose, the technical solution adopted by the present invention is as follows: A complex ultrasonic vibration polishing path planning method based on the principle of entropy increase, characterized in that it includes the following steps: Step 1. Preset N polishing paths for the polishing tool to polish along a regular polishing path, where N is an integer and N≥2; Step 2. Superimpose complex ultrasonic vibrations onto the N polishing paths preset in Step 1 to obtain N coupled polishing paths; Step 3. Based on kinematic analysis, perform trajectory simulation modeling on the N coupled polishing paths obtained in Step 2 under the same complex ultrasonic vibration conditions to obtain 3D trajectory diagrams of the N coupled polishing paths; Step 4. Based on the 3D trajectory diagrams obtained in Step 3, extract 2D scatter plots of the N coupled polishing paths at the same polishing removal depth; Step 5. Based on the entropy increase principle, calculate the information entropy of the 2D scatter plots of the N coupled polishing paths respectively, and select the coupled polishing path corresponding to the 2D scatter plot with the maximum information entropy as the complex ultrasonic vibration polishing path to complete the planning of the complex ultrasonic vibration polishing path.

[0007] Further, in Step 5, the information entropy of the 2D scatter plot is calculated by the following method: Step A1. Divide the 2D scatter plot into k grid regions with the same size, k is an integer, and 5≤ k ≤50; Step A2. According to the number of scatter points in each grid region, obtain the probability density of each grid region of the 2D scatter plot respectively: where, p i is the probability density of the i th grid region of the 2D scatter plot, expressed as the proportion of the number of scatter points in this grid region, 1≤ i ≤ k ; l i is the number of scatter points in the i th grid region of the 2D scatter plot, L is the total number of scatter points in the 2D scatter plot; Step A3. According to the probability density of each grid region of the 2D scatter plot, calculate the information entropy of this 2D scatter plot through the following formula: where, is the information entropy of the 2D scatter plot, representing a measure of the uncertainty of the 2D scatter plot; p 1 is the probability density of the first grid region of the 2D scatter plot, p k is the probability density of the k th grid region of the 2D scatter plot.

[0008] Further, in step 2, the complex ultrasonic vibration is a longitudinal-torsional composite ultrasonic vibration formed by compounding high-frequency longitudinal ultrasonic vibration and torsional ultrasonic vibration.

[0009] Further, in step 3, the three-dimensional trajectory diagram is obtained by the following formula: where X , Y , Z are the X axis, Y axis, Z axis coordinates of the trajectory points on the coupled polishing path respectively, R is the radius of the polishing tool, v is the feed rate of the polishing tool, n is the rotational speed of the polishing tool, f 1, f 2 are the frequencies of the high-frequency longitudinal ultrasonic vibration and the torsional ultrasonic vibration respectively, A 1, A 2 are the amplitudes of the high-frequency longitudinal ultrasonic vibration and the torsional ultrasonic vibration respectively, is the phase difference between the high-frequency longitudinal ultrasonic vibration and the torsional ultrasonic vibration, t is the polishing time.

[0010] Further, in step 4, the two-dimensional scatter plot is extracted by the following method: At the same polishing removal depth, the three-dimensional trajectory diagram is projected onto a two-dimensional plane according to the polishing removal direction, the coordinates of all the trajectory points where polishing removal occurs in the three-dimensional trajectory diagram on the two-dimensional plane are extracted, and a two-dimensional scatter plot is generated accordingly.

[0011] Further, in step 1, the polishing path satisfies: the polishing path is continuous, the polishing scan spacing is consistent, all the points to be polished are covered, and each point to be polished is only passed through once.

[0012] Further, in step 1, the polishing path includes a raster trajectory and an Archimedes spiral trajectory.

[0013] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. A complex ultrasonic vibration polishing path planning method based on the principle of entropy increase provided by the present invention superimposes complex ultrasonic vibration on a regular polishing path to form a coupled polishing path, and then based on the principle of entropy increase, by comparing the information entropy of different coupled polishing paths, the coupled polishing path with the maximum information entropy is selected as the complex ultrasonic vibration polishing path. The finally obtained complex ultrasonic vibration polishing path has a high randomness, can further optimize the polishing effect, improve the polishing surface quality, and has obvious advantages especially in suppressing the accumulation of medium-frequency errors; 2. A complex ultrasonic vibration polishing path planning method based on the principle of entropy increase provided by the present invention can effectively characterize the influence of the superposition of regular polishing paths and complex ultrasonic vibrations on the spatial coverage uniformity by calculating the information entropy of the two-dimensional scatter plots of different coupled polishing paths, evaluating the randomness of the coupled polishing paths, and quantifying it using mathematical modeling methods, thereby realizing the suppression of intermediate frequency error accumulation; 3. A complex ultrasonic vibration polishing path planning method based on the principle of entropy increase provided by the present invention combines high-frequency longitudinal ultrasonic vibration with torsional ultrasonic vibration to form a two-dimensional longitudinal-torsional composite ultrasonic vibration path. After being superimposed with the regular polishing path, it can increase the complexity of the polishing path and enhance the randomness of the polishing path; 4. A complex ultrasonic vibration polishing path planning method based on the principle of entropy increase provided by the present invention generates a three-dimensional trajectory map through kinematic analysis to facilitate further optimization of the polishing path and improve the polishing quality; 5. A complex ultrasonic vibration polishing path planning method based on the principle of entropy increase provided by the present invention extracts two-dimensional scatter plots at the same polishing removal depth to reflect the trajectory distribution characteristics of different coupled polishing paths at a specific polishing removal depth, which can intuitively display the distribution of the coupled polishing paths and reveal the influence law of ultrasonic vibration on the coupled polishing paths; 6. A complex ultrasonic vibration polishing path planning method based on the principle of entropy increase provided by the present invention has a continuous polishing path that covers all points to be polished, and each point to be polished is only passed through once, which can avoid the coupled polishing path passing through a certain point to be polished multiple times, thereby ensuring both the uniform distribution and higher randomness of the polishing path. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 is the flowchart of the method according to the embodiment of the present invention; Figure 2 is the schematic diagram of the polishing path set in step 1 in the embodiment of the present invention. Among them, (a) is the schematic diagram of the raster trajectory of the transverse feed, (b) is the schematic diagram of the raster trajectory of the longitudinal feed, and (c) is the schematic diagram of the Archimedes spiral trajectory; Figure 3 is the three-dimensional trajectory comparison diagram obtained in step 3 in the embodiment of the present invention. Among them, (a) is Figure 2 the three-dimensional trajectory comparison diagram corresponding to (a) in Figure 2 and (b) is Figure 2 the three-dimensional trajectory comparison diagram corresponding to (b) in Figure 4 is the two-dimensional scatter plot obtained in step 4 in the embodiment of the present invention. Among them, (a) is Figure 3 the two-dimensional scatter plot corresponding to (a) in Figure 3The two-dimensional scatter plot corresponding to (b) in [Chinese], and (c) is Figure 3 the two-dimensional scatter plot corresponding to (c) in [Chinese]; Figure 5 the two-dimensional scatter plot corresponding to the polishing path set in Step 1 in the embodiments of the present invention. (a) is Figure 2 the two-dimensional scatter plot corresponding to (a) in [Chinese], (b) is Figure 2 the two-dimensional scatter plot corresponding to (b) in [Chinese], and (c) is Figure 2 the two-dimensional scatter plot corresponding to (c) in [Chinese]. Detailed implementation manners

[0015] The following further elaborates in detail a complex ultrasonic vibration polishing path planning method based on the principle of entropy increase proposed by the present invention in conjunction with the accompanying drawings and specific implementation manners. Those skilled in the art should understand that these implementation manners are only used to explain the technical principle of the present invention, and the purpose is not to limit the protection scope of the present invention.

[0016] A complex ultrasonic vibration polishing path planning method based on the principle of entropy increase, as Figure 1 shown, includes the following steps: Step 1, preset 3 polishing paths for the polishing tool to polish along regular polishing paths, as Figure 2 shown, including a raster trajectory with transverse feed, a raster trajectory with longitudinal feed, and an Archimedean spiral trajectory. Each polishing path is a trajectory with adjustable parameters and can be dynamically adjusted according to different processing requirements to ensure that the feed spacing in the 3 polishing paths is consistent. In this embodiment, the polishing scan spacings of the raster trajectory with transverse feed, the raster trajectory with longitudinal feed, and the Archimedean spiral trajectory are all set to 2 mm to ensure that the polished surface is uniformly processed. The polishing tool uses mechanical grinding or CCOS polishing technology for polishing. All 3 polishing paths need to meet the following requirements: the polishing path is continuous, the polishing scan spacing is consistent, all points to be polished are covered, and each point to be polished is only passed through once, which can ensure the uniform distribution and higher randomness of the polishing path at the same time.

[0017] Step 2, superimpose the longitudinal-torsional composite ultrasonic vibration composed of high-frequency longitudinal ultrasonic vibration and torsional ultrasonic vibration on the 3 polishing paths preset in Step 1 to obtain 3 coupled polishing paths.

[0018] In this step, the longitudinal-torsional composite ultrasonic vibration composed of high-frequency longitudinal ultrasonic vibration and torsional ultrasonic vibration is superimposed on the traditional regular polishing path to form a longitudinal-torsional composite ultrasonic vibration polishing path, which can improve the complexity and randomness of the polishing path. The amplitudes and frequencies of the high-frequency longitudinal ultrasonic vibration and the torsional ultrasonic vibration can be dynamically adjusted according to different polishing requirements to ensure that the amplitudes and frequencies of the longitudinal-torsional composite ultrasonic vibration superimposed on the preset 3 polishing paths are consistent.

[0019] Step 3. Based on kinematic analysis, under the same longitudinal-torsional composite ultrasonic vibration conditions, trajectory simulation models are respectively established for the three coupling polishing paths obtained in Step 2, and three-dimensional trajectory diagrams of the three coupling polishing paths are obtained respectively through the following formula: where X , Y , Z are respectively the X axis, Y axis, Z axis coordinates of the trajectory points on the coupling polishing path, R is the radius of the polishing tool, v is the feed rate of the polishing tool, n is the rotational speed of the polishing tool, f 1, f 2 are respectively the frequencies of the high-frequency longitudinal ultrasonic vibration and the torsional ultrasonic vibration, A 1, A 2 are respectively the amplitudes of the high-frequency longitudinal ultrasonic vibration and the torsional ultrasonic vibration, is the phase difference between the high-frequency longitudinal ultrasonic vibration and the torsional ultrasonic vibration, t is the polishing time.

[0020] This formula is used to describe the motion trajectory of the polishing tool under given conditions, and a three-dimensional trajectory diagram of the polishing tool motion is generated through kinematic analysis.

[0021] As shown in Figure 3 , it is a comparison diagram of the three-dimensional trajectories of the three polishing paths and the longitudinal-torsional composite ultrasonic vibration superimposed thereon. It can be seen that the randomness and complexity of the coupling polishing path obtained after superimposing the longitudinal-torsional composite ultrasonic vibration on the polishing path have been significantly increased.

[0022] Step 4. Based on the three-dimensional trajectory diagram obtained in Step 3, under the same polishing removal depth, two-dimensional scatter diagrams of the three coupling polishing paths are respectively extracted. Among them, the method for extracting the two-dimensional scatter diagram is as follows: under the same polishing removal depth, project the three-dimensional trajectory diagram onto a two-dimensional plane in the polishing removal direction, extract the coordinates of all the trajectory points where polishing removal occurs in the three-dimensional trajectory diagram on the two-dimensional plane, and generate a two-dimensional scatter diagram based on this. The two-dimensional scatter diagram is as shown in Figure 4 .

[0023] Step 5. Based on the principle of entropy increase, calculate the information entropy of the two-dimensional scatter diagrams of the three coupling polishing paths respectively, and select the coupling polishing path corresponding to the two-dimensional scatter diagram with the largest information entropy as the complex ultrasonic vibration polishing path to complete the planning of the complex ultrasonic vibration polishing path. Among them, the information entropy of the two-dimensional scatter diagram is calculated through the following method: Step A1. Divide the two-dimensional scatter diagram into k grid regions with the same size,k is an integer, and 5 ≤ k ≤ 50; Step A2: According to the number of scatter points in each grid area, obtain the probability density of each grid area of the two-dimensional scatter plot respectively: where p i is the probability density of the i th grid area of the two-dimensional scatter plot, expressed as the proportion of the number of scatter points in this grid area, 1 ≤ i ≤ k ; l i is the number of scatter points in the i th grid area of the two-dimensional scatter plot, L is the total number of scatter points in the two-dimensional scatter plot; Step A3: According to the probability density of each grid area of the two-dimensional scatter plot, calculate the information entropy of this two-dimensional scatter plot through the following formula: where is the information entropy of the two-dimensional scatter plot, representing a measure of the uncertainty of the two-dimensional scatter plot; p 1 is the probability density of the first grid area of the two-dimensional scatter plot, p k is the probability density of the k th grid area of the two-dimensional scatter plot.

[0024] Information entropy is an important concept in information theory, used to quantify the magnitude of uncertainty in a random variable or system. The larger the information entropy, the higher the uncertainty and complexity of the system. For the discrete probability distribution of the coupled polishing path in this embodiment, the randomness is evaluated by calculating the information entropy of the two-dimensional scatter plot. In this embodiment, the information entropy theory is applied to the polishing process of the coupled polishing path with superimposed longitudinal-torsional composite ultrasonic vibration. Based on the principle of entropy increase, the information entropy of its two-dimensional scatter plot is calculated to quantify the randomness of each coupled polishing path, so as to evaluate the clutter and uniform densification of the coupled polishing path, and select the optimal coupled polishing path as the final complex ultrasonic vibration polishing path. The larger the information entropy, the higher the randomness, thus optimizing the polishing effect and improving the polishing surface quality, which helps to improve the intermediate frequency convergence of the polishing surface and suppress the accumulation of intermediate frequency errors.

[0025] In this embodiment, longitudinal-torsional composite ultrasonic vibration is superimposed on the regular polishing path to form a coupled polishing path. Combining the perturbation effect of longitudinal-torsional composite ultrasonic vibration, the polishing path is optimized based on the principle of entropy increase, which can effectively improve the quality of the polishing surface, optimize the intermediate frequency convergence, and solve the problem that the existing polishing path cannot suppress the accumulation of intermediate frequency errors.

[0026] In this embodiment, the type of the polishing tool is not limited. The polishing tool can be a grinding wheel, a polishing disc, a polishing wheel or an airbag tool, and its loading device is a machine tool or a six-degree-of-freedom robot. Longitudinal-torsional composite ultrasonic vibration can be added to all of them, and then path optimization is carried out based on the principle of entropy increase to select a trajectory with stronger randomness.

[0027] The following further illustrates the technical principle of this embodiment by comparing the traditional regular polishing path with the complex ultrasonic vibration polishing path obtained by the method of this embodiment.

[0028] The information entropy of each coupled polishing path is calculated through the information entropy principle to quantify the randomness and complexity of the coupled polishing path and reflect the uniform distribution characteristics of the coupled polishing path. The specific calculation method is to analyze the two-dimensional scatter plot of each coupled polishing path to obtain the information entropy and make a comparison. The larger the information entropy of the coupled polishing path, the stronger its randomness, so that the regular error can be effectively reduced. To quantify the uniformity and compactness of the polishing path, the two-dimensional scatter plot of the coupled polishing path is divided into multiple grid regions, and the proportion of the number of scatter points in each grid region to the total number of scatter points is calculated, so as to obtain the information entropy.

[0029] Extract the two-dimensional scatter plots of the 3 preset polishing paths in step 1, as Figure 5 shown, and then calculate the information entropy of the 3 polishing paths according to the method of step 5 of this embodiment. As shown in Table 1, it is the information entropy of the 3 polishing paths in step 1 and the information entropy of the 3 coupled polishing paths calculated in step 5 of this embodiment.

[0030] Table 1 In the raster trajectory of the transverse feed, the information entropy without vibration is 5.654, and the information entropy after superimposing the longitudinal-torsional composite ultrasonic vibration is 7.641. The entropy increase value under the longitudinal-torsional composite ultrasonic vibration is about 35.1%; in the raster trajectory of the longitudinal feed, the information entropy without vibration is 5.126, and the information entropy after superimposing the longitudinal-torsional composite ultrasonic vibration is 7.329. The entropy increase value under the longitudinal-torsional composite ultrasonic vibration is about 43.0%; in the Archimedes spiral trajectory, the information entropy without vibration is 5.388, and the information entropy after superimposing the longitudinal-torsional composite ultrasonic vibration is 7.564. The entropy increase value under the longitudinal-torsional composite ultrasonic vibration is about 40.4%. It can be seen that the longitudinal-torsional composite ultrasonic vibration can significantly increase the information entropy and improve the uniformity and randomness of the polishing trajectory.

[0031] Under the condition of superimposing longitudinal-torsional composite ultrasonic vibration, the information entropy of the Archimedes spiral trajectory is 7.564, the information entropy of the grating trajectory of the transverse feed is 7.641, and the improvement of the grating trajectory of the transverse feed relative to the Archimedes spiral trajectory is about 1.02%; while the information entropy of the grating trajectory of the longitudinal feed is 7.329, which is 3.10% lower than that of the Archimedes spiral trajectory.

[0032] It can be seen that the grating trajectory of the transverse feed is superior to the Archimedes spiral trajectory under both the conditions of no vibration and superimposing longitudinal-torsional composite ultrasonic vibration, and is superior to the grating trajectory of the longitudinal feed. Therefore, the combined path method of superimposing longitudinal-torsional composite ultrasonic vibration on the grating trajectory of the transverse feed is preferably selected.

[0033] Based on the traditional regular polishing path, the present invention superimposes longitudinal-torsional composite ultrasonic vibration to obtain a coupled polishing path, so as to optimize the randomness and complexity of the regular polishing path. Then, based on the principle of entropy increase, the randomness and complexity of the coupled polishing path are quantified, and the coupled polishing path with the maximum information entropy is selected, so as to obtain a complex ultrasonic vibration polishing path with the highest randomness and complexity, which can suppress the accumulation of intermediate frequency errors, reduce the intermediate frequency errors, effectively improve the polishing quality, overcome the common intermediate frequency error accumulation problem in the traditional mechanical polishing method, and has good practical application potential.

Claims

1. A complex ultrasonic vibration polishing path planning method based on the entropy increase principle, characterized in that: The following steps are involved: Step 1, presetting N polishing paths for polishing by a polishing tool along a regular polishing path, wherein N is an integer and N≥2; Step 2, superimposing complex ultrasonic vibrations onto the N polishing paths preset in step 1 to obtain N coupled polishing paths; Step 3: Based on kinematic analysis, trajectory simulation modeling is performed on the N coupled polishing paths obtained in step 2 under the same complex ultrasonic vibration conditions to obtain three-dimensional trajectory diagrams of the N coupled polishing paths; Step 4: Based on the three-dimensional trajectory diagram obtained in step 3, two-dimensional scatter plots of N coupled polishing paths are extracted at the same polishing removal depth; Step 5: Based on the entropy increase principle, the information entropy of the two-dimensional scatter diagrams of N coupled polishing paths is calculated respectively, and the coupled polishing path corresponding to the two-dimensional scatter diagram with the largest information entropy is selected as the complex ultrasonic vibration polishing path to complete the planning of the complex ultrasonic vibration polishing path.

2. A complex ultrasonic vibration polishing path planning method based on the entropy increase principle according to claim 1, characterized in that: In step 5, the information entropy of the two-dimensional scatter plot is calculated by the following method: Step A1: Divide the two-dimensional scatter plot into k grid areas of equal size, k is an integer, and 5≤ k ≤50; Step A2: According to the number of scattered points in each grid area, the probability density of each grid area of ​​the two-dimensional scatter plot is obtained: ； in, For the two-dimensional scatter plot i The probability density of a grid area is expressed as the proportion of scattered points in the grid area, 1≤ i ≤ k ; For the two-dimensional scatter plot i The number of scattered points in a grid area, L is the total number of scattered points in the two-dimensional scatter plot; Step A3: Calculate the information entropy of the two-dimensional scatter plot using the following formula based on the probability density of each grid area of ​​the two-dimensional scatter plot: ； in, is the information entropy of the two-dimensional scatter plot, which represents the measure of uncertainty of the two-dimensional scatter plot; p 1 is the probability density of the first grid area of ​​the two-dimensional scatter plot, p k For the two-dimensional scatter plot k The probability density of a grid area.

3. The complex ultrasonic vibration polishing path planning method based on the entropy increase principle according to claim 1 is characterized in that: In step 2, the complex ultrasonic vibration is a longitudinal-torsional composite ultrasonic vibration formed by combining high-frequency longitudinal ultrasonic vibration and torsional ultrasonic vibration.

4. A complex ultrasonic vibration polishing path planning method based on the entropy increase principle according to claim 3, characterized in that: In step 3, the three-dimensional trajectory graph is obtained by the following formula: ； in, X , Y , Z are the trajectory points on the coupled polishing path. X axis, Y axis, Z Axis coordinates, R is the radius of the polishing tool, v is the feed speed of the polishing tool, n is the speed of the polishing tool, f 1. f 2 are the frequencies of high-frequency longitudinal ultrasonic vibration and torsional ultrasonic vibration, respectively. A 1. A 2 are the amplitudes of high-frequency longitudinal ultrasonic vibration and torsional ultrasonic vibration, respectively. is the phase difference between high-frequency longitudinal ultrasonic vibration and torsional ultrasonic vibration, t It's polishing time.

5. The complex ultrasonic vibration polishing path planning method based on the entropy increase principle according to claim 1 is characterized in that: In step 4, the two-dimensional scatter plot is extracted by the following method: At the same polishing removal depth, the three-dimensional trajectory diagram is projected onto a two-dimensional plane according to the polishing removal direction, the coordinates of all trajectory points where polishing removal occurs in the three-dimensional trajectory diagram on the two-dimensional plane are extracted, and a two-dimensional scatter plot is generated accordingly.

6. A complex ultrasonic vibration polishing path planning method based on the entropy increase principle according to any one of claims 1 to 5, characterized in that: In step 1, the polishing path satisfies: the polishing path is continuous, the polishing scanning interval is consistent, all points to be polished are covered, and each point to be polished is passed only once.

7. The complex ultrasonic vibration polishing path planning method based on the entropy increase principle according to claim 6 is characterized in that: In step 1, the polishing path includes a grating track and an Archimedean spiral track.

Images