A Complex Ultrasonic Vibration Polishing Path Planning Method Based on the Principle of Entropy Increase

Abstract

The present invention relates to a method for polishing the surface of an optical element, specifically to a complex ultrasonic vibration polishing path planning method based on the principle of entropy increase, which solves the technical problem that the existing ultrasonic vibration assisted polishing method cannot effectively solve the accumulation of medium-frequency errors. The present invention superimposes complex ultrasonic vibrations on the regular polishing path to obtain a coupled polishing path, and selects the optimal coupled polishing path based on the principle of entropy increase; by comparing the information entropy of different coupled polishing paths, the coupled polishing path with the largest information entropy is selected as the complex ultrasonic vibration polishing path. The obtained complex ultrasonic vibration polishing path has a high degree of 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.

Description

Technical Field

[0001] The present invention relates to a method for polishing the surface of an optical element, and 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 grating trajectories, Archimedean 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. The pseudo-random paths can destroy the periodicity of the regular polishing paths, effectively weaken the accumulation of mid-frequency errors, and improve the surface quality of high-precision optical elements. However, the implementation of pseudo-random paths poses higher requirements on the number of linked axes and dynamic performance of the polishing tool machine tool, restricting its popularization and application in the manufacture 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 polishing the surface 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 technologies. The 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 their single movement 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:

[0007] A complex ultrasonic vibration polishing path planning method based on the principle of entropy increase, which is characterized in that it includes the following steps:

[0008] 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;

[0009] Step 2: Superimpose complex ultrasonic vibrations onto the N polishing paths preset in Step 1 to obtain N coupled polishing paths;

[0010] 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 three-dimensional trajectory diagrams of the N coupled polishing paths;

[0011] Step 4: Based on the three-dimensional trajectory diagrams obtained in Step 3, extract two-dimensional scatter plots of the N coupled polishing paths respectively under the same polishing removal depth;

[0012] Step 5: Based on the principle of entropy increase, calculate the information entropy of the two-dimensional scatter plots of the N coupled polishing paths respectively, and select the coupled polishing path corresponding to the two-dimensional 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.

[0013] Further, in Step 5, the information entropy of the two-dimensional scatter plot is calculated by the following method:

[0014] Step A1: Divide the two-dimensional scatter plot into k grid regions of the same size, k is an integer, and 5≤ k ≤50;

[0015] Step A2: According to the number of scatter points in each grid region, obtain the probability density of each grid region of the two-dimensional scatter plot respectively:

[0016]

[0017] where, p i is the probability density of the i th grid region of the two-dimensional 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 two-dimensional scatter plot, L is the total number of scatter points in the two-dimensional scatter plot;

[0018] Step A3: According to the probability density of each grid region of the two-dimensional scatter plot, calculate the information entropy of this two-dimensional scatter plot through the following formula:

[0019]

[0020] Among them, is the information entropy of the two-dimensional scatter plot, representing the 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.

[0021] Furthermore, in step 2, the complex ultrasonic vibration is a longitudinal-torsional composite ultrasonic vibration composed of high-frequency longitudinal ultrasonic vibration and torsional ultrasonic vibration.

[0022] Furthermore, in step 3, the three-dimensional trajectory diagram is obtained through the following formula:

[0023]

[0024] Among them, X , Y , Z are the X axis, Y axis, Z axis coordinates of the trajectory points on the coupling polishing path respectively, R is the radius of the polishing tool, v is the feed speed 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.

[0025] Furthermore, in step 4, the two-dimensional scatter plot is extracted through the following method:

[0026] At the same polishing removal depth, project the three-dimensional trajectory diagram onto the 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 plot based on this.

[0027] Furthermore, in step 1, the polishing path satisfies: the polishing path is continuous, the polishing scan spacing is consistent, it covers all the points to be polished, and each point to be polished is only passed through once.

[0028] Furthermore, in step 1, the polishing path includes a raster trajectory and an Archimedean spiral trajectory.

[0029] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0030] 1. A complex ultrasonic vibration polishing path planning method based on the principle of entropy increase provided by the present invention superimposes complex ultrasonic vibrations 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, selects the coupled polishing path with the largest information entropy as the complex ultrasonic vibration polishing path. The finally obtained complex ultrasonic vibration polishing path has 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;

[0031] 2. A complex ultrasonic vibration polishing path planning method based on the principle of entropy increase provided by the present invention evaluates the randomness of the coupled polishing path by calculating the information entropy of the two-dimensional scatter plot of different coupled polishing paths, and quantifies it by using a mathematical modeling method, which can effectively characterize the influence of superimposing complex ultrasonic vibrations on the regular polishing path on the spatial coverage uniformity, so as to achieve the suppression of the accumulation of medium-frequency errors;

[0032] 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 on the regular polishing path, it can increase the complexity of the polishing path and enhance the randomness of the polishing path;

[0033] 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 improvement of the polishing quality;

[0034] 5. A complex ultrasonic vibration polishing path planning method based on the principle of entropy increase provided by the present invention extracts a two-dimensional scatter plot 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 path and reveal the influence law of ultrasonic vibration on the coupled polishing path;

[0035] 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, thus ensuring both the uniform distribution and higher randomness of the polishing path. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 is a flowchart of the method according to an embodiment of the present invention;

[0037] Figure 2Schematic diagram of the polishing path set in step 1 of the embodiment of the present invention. Among them, (a) is a schematic diagram of the grating trajectory for transverse feed, (b) is a schematic diagram of the grating trajectory for longitudinal feed, and (c) is a schematic diagram of the Archimedes spiral trajectory;

[0038] Figure 3 3D trajectory comparison diagram obtained in step 3 of the embodiment of the present invention. Among them, (a) is Figure 2 the 3D trajectory comparison diagram corresponding to (a) in Figure 2 , (b) is Figure 2 the 3D trajectory comparison diagram corresponding to (b) in

[0039] Figure 4 2D scatter plot obtained in step 4 of the embodiment of the present invention. Among them, (a) is Figure 3 the 2D scatter plot corresponding to (a) in Figure 3 , (b) is Figure 3 the 2D scatter plot corresponding to (b) in

[0040] Figure 5 2D scatter plot corresponding to the polishing path set in step 1 of the embodiment of the present invention. (a) is Figure 2 the 2D scatter plot corresponding to (a) in Figure 2 , (b) is Figure 2 the 2D scatter plot corresponding to (c) in Detailed implementation manners

[0041] 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.

[0042] A complex ultrasonic vibration polishing path planning method based on the principle of entropy increase, as Figure 1 shown, includes the following steps:

[0043] Step 1: Preset 3 polishing paths for the polishing tool to polish along a regular polishing path, as Figure 2As shown, it includes a grating trajectory for transverse feed, a grating trajectory for 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 pitch in the three polishing paths is consistent. In this embodiment, the polishing scan pitches of the grating trajectory for transverse feed, the grating trajectory for 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 three polishing paths need to meet the following requirements: the polishing path is continuous, the polishing scan pitch 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.

[0044] Step 2: Superimpose the longitudinal-torsional composite ultrasonic vibration composed of high-frequency longitudinal ultrasonic vibration and torsional ultrasonic vibration onto the three polishing paths preset in Step 1 to obtain three coupled polishing paths.

[0045] In this step, the longitudinal-torsional composite ultrasonic vibration composed of high-frequency longitudinal ultrasonic vibration and torsional ultrasonic vibration is superimposed onto 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 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 three preset polishing paths are consistent.

[0046] Step 3: Based on kinematic analysis, respectively perform trajectory simulation modeling on the three coupled polishing paths obtained in Step 2 under the same longitudinal-torsional composite ultrasonic vibration conditions, and obtain the three-dimensional trajectory diagrams of the three coupled polishing paths through the following formulas:

[0047]

[0048] 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 speed 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 torsional ultrasonic vibration respectively, A 1、 A 2 are the amplitudes of the high-frequency longitudinal ultrasonic vibration and torsional ultrasonic vibration respectively, is the phase difference between the high-frequency longitudinal ultrasonic vibration and torsional ultrasonic vibration, tis the polishing time.

[0049] 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.

[0050] As Figure 3 shown, it is a comparison diagram of three-dimensional trajectories after superimposing longitudinal-torsional composite ultrasonic vibration on three polishing paths. It can be seen that the randomness and complexity of the coupled polishing path obtained after superimposing longitudinal-torsional composite ultrasonic vibration on the polishing path have been significantly increased.

[0051] Step 4: Based on the three-dimensional trajectory diagram obtained in Step 3, at the same polishing removal depth, two-dimensional scatter plots of three coupled polishing paths are extracted respectively. Among them, the method for extracting the two-dimensional scatter plot is as follows: at the same polishing removal depth, project the three-dimensional trajectory diagram onto a two-dimensional plane according to the polishing removal direction, extract the coordinates of all trajectory points where polishing removal occurs in the three-dimensional trajectory diagram on the two-dimensional plane, and generate a two-dimensional scatter plot based on this. The two-dimensional scatter plot is as Figure 4 shown.

[0052] Step 5: Based on the principle of entropy increase, calculate the information entropy of the two-dimensional scatter plots of three coupled polishing paths respectively, and select the coupled polishing path corresponding to the two-dimensional scatter plot 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 plot is calculated by the following method:

[0053] Step A1: Divide the two-dimensional scatter plot into k grid regions with the same size, k is an integer, and 5 ≤ k ≤ 50;

[0054] Step A2: According to the number of scatter points in each grid region, obtain the probability density of each grid region of the two-dimensional scatter plot respectively:

[0055]

[0056] Among them, p i is the probability density of the i th grid region of the two-dimensional 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 two-dimensional scatter plot, L is the total number of scatter points in the two-dimensional scatter plot;

[0057] Step A3. According to the probability density of each grid area in the two-dimensional scatter plot, calculate the information entropy of the two-dimensional scatter plot through the following formula:

[0058]

[0059] 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.

[0060] 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, which can optimize the polishing effect and improve the polishing surface quality, contribute to improving the intermediate-frequency convergence of the polishing surface, and inhibit the accumulation of intermediate-frequency errors.

[0061] 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 and optimizing the polishing path based on the principle of entropy increase can effectively improve the quality of the polishing surface, optimize the intermediate-frequency convergence, and solve the problem that the existing polishing path cannot inhibit the accumulation of intermediate-frequency errors.

[0062] This embodiment does not limit the type of polishing tool. The polishing tool can be a grinding wheel, a polishing disc, a polishing wheel or an airbag tool, and its carrying device is a machine tool or a six-axis robot. Longitudinal-torsional composite ultrasonic vibration can be added, and then the path can be optimized based on the principle of entropy increase to select a trajectory with stronger randomness.

[0063] 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.

[0064] Calculate the information entropy of each coupled polishing path through the principle of information entropy 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 comparisons. The larger the information entropy of the coupled polishing path, the stronger its randomness, and thus the regular error can be effectively reduced. To quantify the uniformity and compactness of the polishing path, divide the two-dimensional scatter plot of the coupled polishing path into multiple grid regions and calculate the proportion of the number of scatter points in each grid region to the total number of scatter points, thereby obtaining the information entropy.

[0065] 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 in 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.

[0066] Table 1

[0067]

[0068] In the grating trajectory of transverse feed, the information entropy without vibration is 5.654, and the information entropy after superimposing longitudinal-torsional composite ultrasonic vibration is 7.641. The entropy increment under longitudinal-torsional composite ultrasonic vibration is about 35.1%; in the grating trajectory of longitudinal feed, the information entropy without vibration is 5.126, and the information entropy after superimposing longitudinal-torsional composite ultrasonic vibration is 7.329. The entropy increment under 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 longitudinal-torsional composite ultrasonic vibration is 7.564. The entropy increment under longitudinal-torsional composite ultrasonic vibration is about 40.4%. It can be seen that longitudinal-torsional composite ultrasonic vibration can significantly increase the information entropy and improve the uniformity and randomness of the polishing trajectory.

[0069] 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 transverse feed is 7.641, and the improvement of the grating trajectory of transverse feed relative to the Archimedes spiral trajectory is about 1.02%; while the information entropy of the grating trajectory of longitudinal feed is 7.329, which is 3.10% lower than that of the Archimedes spiral trajectory.

[0070] It can be seen that the grating trajectory of transverse feed is better than the Archimedes spiral trajectory under both the conditions of no vibration and superimposing longitudinal-torsional composite ultrasonic vibration, and is better than the grating trajectory of longitudinal feed. Therefore, the combined path method of superimposing longitudinal-torsional composite ultrasonic vibration on the grating trajectory of transverse feed is preferably selected.

[0071] Based on the traditional regular polishing path, a longitudinal-torsional composite ultrasonic vibration is superimposed 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 largest information entropy is selected, thus obtaining a complex ultrasonic vibration polishing path with the highest randomness and complexity. This can suppress the accumulation of medium-frequency errors, reduce medium-frequency errors, effectively improve the polishing quality, overcome the problem of medium-frequency error accumulation commonly found in traditional mechanical polishing methods, 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: Preset N polishing paths for polishing along regular polishing paths by a polishing tool, where 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, extract two-dimensional scatter plots of N coupled polishing paths at the same polishing removal depth; Step 5: Based on the entropy increase principle, the information entropy of the two-dimensional scatter plots of N coupled polishing paths is calculated respectively, and the coupled polishing path corresponding to the two-dimensional scatter plot 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. The complex ultrasonic vibration polishing path planning method based on the entropy increase principle according to claim 1 is 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: Based on the number of scattered points in each grid area, obtain the probability density of each grid area in the two-dimensional scatter plot: ； 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 uncertainty measure 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. The complex ultrasonic vibration polishing path planning method based on the entropy increase principle according to claim 3 is characterized in that: In step 3, the three-dimensional trajectory graph is obtained by the following formula: ； in, X 、 Y 、 Z They 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 rotation speed of the polishing tool, f 1. f 2 are the frequencies of high-frequency longitudinal ultrasonic vibration and torsional ultrasonic vibration, A 1. A 2 are the amplitudes of high-frequency longitudinal ultrasonic vibration and torsional ultrasonic vibration, is the phase difference between high-frequency longitudinal ultrasonic vibration and torsional ultrasonic vibration, t 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 based on the coordinates.

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 following conditions: 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 method for planning a complex ultrasonic vibration polishing path based on the entropy increase principle according to claim 6, wherein: In step 1, the polishing path includes a grating track and an Archimedean spiral track.

Images