Dynamic control of scanning speed and immersion depth for high precision deterministic polishing method

Abstract

Dynamic regulation scanning speed and immersion depth high precision deterministic polishing method belongs to the field of optical polishing.The method for realizing the present application is as follows: based on the Reynolds equation and Hertz contact model, the relationship model between immersion depth and controllable time-varying removal function of magnetorheological polishing method and balloon polishing method is established, according to the relationship model between immersion depth and removal function, the time-varying nature of removal function is realized by accurately regulating the immersion depth, and the efficiency and controllability of material removal are further improved; the processing mode of adopting constant speed control in single line scanning process and introducing variable speed adjusting mechanism in row scanning stage is proposed, the path stability is ensured, and the influence of machine tool dynamic load on precision is reduced; the dwell time solving method of single line constant speed scanning and row variable speed is constructed, the accuracy and reliability of dwell time solving are ensured; the technical realization path of dynamic regulation scanning speed and immersion depth is established, the efficient convergence of surface error and high precision control of polishing process are realized.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of optical polishing and relates to a high-precision deterministic polishing method for dynamically regulating a scanning speed and an immersion depth. BACKGROUND

[0002] Ultra-precision optical elements, as the cornerstone of strategic technology fields such as aerospace and national defense, and new era national cutting-edge industries such as microelectronic integrated circuits and advanced lithography technology, are in increasing demand in terms of quantity and precision. The processing flow of optical elements, especially the polishing link, is the key to achieving high-precision element high-efficiency manufacturing.

[0003] Pressure-controlled polishing technologies such as air bag polishing and magnetorheological polishing are an extension of computer-controlled optical surface forming technology. The material removal efficiency is closely related to the relative pressure between the tool head and the workpiece, and has the advantages of high machining precision and precise force control. In air bag polishing, the air bag rotation speed, polishing liquid concentration and air bag compression amount are key parameters that affect material removal efficiency. Magnetorheological polishing forms a polishing tool with a specific hardness by using magnetic particles in the polishing liquid. The shape, hardness and pressure of the tool are controlled by factors such as magnetic field strength, liquid viscosity, tool rotation speed and immersion depth, thereby accurately controlling the material removal amount. The complex coupling between the above factors makes the theoretical modeling of the material removal process more complex. Therefore, in-depth study of the interaction of these parameters and their influence on material removal efficiency is of great significance for optimizing the polishing process and improving machining precision.

[0004] Currently, pressure-controlled polishing technologies such as air bag polishing and magnetorheological polishing are based on the Preston equation. By using a stable removal function and the surface error distribution obtained by precise detection, the residence time is solved to achieve controllable material removal. However, the calculated residence time often has sudden changes, which leads to frequent emergency stops and starts of the machine tool, which puts extremely high requirements on the mechanical precision and dynamic performance of the magnetorheological polishing machine tool. Frequent emergency stops and accelerations not only increase the wear and maintenance cost of the machine tool, but also affect the stability and efficiency of the machining. Therefore, how to avoid the sudden change of the residence time and reduce the dynamic burden of the machine tool without affecting the machining precision is a key problem that needs to be solved in current technology. SUMMARY

[0005] The present application aims to provide a high-precision deterministic polishing method of dynamically regulating scanning speed and immersion depth, establish a relationship model of immersion depth and removal function, substitute the relationship model into the Preston equation, and solve the residence time of single-row constant-speed scanning and line-changing variable-speed scanning; the optimal distribution of immersion depth is determined by using an optimization algorithm, combined with the dynamically regulated scanning speed, to form a highly synergistic polishing control strategy, based on which the influence of machine tool dynamic performance on machining precision is relieved, the stability and uniformity of material removal process are improved, and the machining precision and efficiency of the pressure-controlled polishing method are improved.

[0006] The pressure-controlled polishing method includes a magneto-rheological polishing method and a balloon polishing method.

[0007] For the magneto-rheological polishing method, the relationship model of immersion depth and removal function is established based on fluid mechanics.

[0008] For the balloon polishing method, the relationship model of immersion depth and removal function is established based on the Hertz contact model.

[0009] The present application aims to achieve the following technical solutions:

[0010] The high-precision deterministic polishing method of dynamically regulating scanning speed and immersion depth disclosed by the present application establishes a relationship model between immersion depth and controllable time-varying removal function of the magneto-rheological polishing method and the balloon polishing method based on the Reynolds equation and the Hertz contact model, realizes the time-varying nature of the removal function by accurately regulating the immersion depth according to the relationship model between the immersion depth and the removal function, and further improves the efficiency and controllability of material removal; a machining mode of constant-speed control in single-row scanning and variable-speed adjustment mechanism in line-changing scanning is proposed to ensure path stability and reduce the influence of machine tool dynamic load on precision; a residence time solving method of single-row constant-speed scanning and line-changing variable-speed scanning is constructed to ensure the accuracy and reliability of residence time solving; and a technical implementation path of dynamically regulating scanning speed and immersion depth is established to realize efficient convergence of surface error and high-precision control of the polishing process.

[0011] The high-precision deterministic polishing method of dynamically regulating scanning speed and immersion depth disclosed by the present application comprises the following steps:

[0012] Step one, using a pressure-controlled polishing method to process an optical element, and establishing a relationship model between immersion depth and removal function according to the pressure-controlled polishing method. The pressure-controlled polishing method includes a magneto-rheological polishing method and a balloon polishing method.

[0013] For the magnetorheological finishing method, the relationship model of the immersion depth and the removal function is established based on fluid mechanics, and the implementation method is as follows:

[0014] Step 1.1, according to the set immersion depth H l and the satin band thickness H d , the distance H h between the workpiece and the polishing wheel is divided into several equal intervals to obtain the height h corresponding to each interval; and the super relaxation factor, the pressure convergence condition, and the nucleation range convergence condition are preset to determine the shear yield strength τ0 of the magnetorheological fluid; the Reynolds equation corresponding to each height h is discretized based on the difference method by utilizing the Bingham fluid characteristics of the magnetorheological fluid; the super relaxation iterative method is used to solve the Reynolds equation corresponding to each height h to obtain the analytical solution of the pressure, and if the preset convergence condition is not met, the pressure distribution and the super relaxation factor are combined to be substituted into the Reynolds equation for solving until the preset pressure convergence condition is met to obtain the converged pressure and shear stress; according to the shear yield strength, the solid-state nucleation range of the workpiece and the polishing wheel in the polishing area is defined, and the magnetorheological fluid is in a solid state when the shear stress is less than the shear yield strength, otherwise it is in a liquid state; the apparent viscosity distribution is updated according to the solid-state nucleation range, and the Reynolds equation is solved again based on the new apparent viscosity distribution to improve the solving accuracy of the analytical solution of the shear stress and the pressure through iterative solving until the preset nucleation range condition converges to obtain the pressure and shear stress in the stable state.

[0015] The immersion depth H l , the satin band thickness H d , and the distance H h between the workpiece and the polishing wheel in step 1.1 satisfy the equation relationship as shown in equation (1):

[0016] H d =H h +H l (1)

[0017] The relationship between the shear yield strength τ0 and the magnetic field strength in step 1.1 is shown in equation (2):

[0018]

[0019] In the formula, represents the volume fraction of ferromagnetic particles in the magnetorheological fluid, B is the magnetic induction intensity, r is the radius of the ferromagnetic particle, δ is the net distance between adjacent ferromagnetic particles, μ0 is the vacuum permeability, χ is the magnetic susceptibility of the ferromagnetic particles, and ψ is the shear stress coefficient.

[0020] The Reynolds equation in step 1.1 is shown in equation (3):

[0021]

[0022]

[0023]

[0024] wherein, represents the dimensionless interval height, P represents the pressure distribution of the polishing area, represents the dimensionless pressure distribution of the polishing area, and represents the aspect ratio of the polishing area, represents the dimensionless apparent viscosity, represents the dimensionless surface spacing between the polishing wheel and the workpiece, h0 represents the minimum spacing between the polishing wheel and the workpiece surface, R represents the polishing tool size, and U represents the linear speed of the polishing wheel surface.

[0025] Step 1.2, change the magnetic field strength, the immersion depth, the polishing tool size, the polishing wheel speed, and solve the pressure and shear stress according to step 1.1 iteratively, and the following rules are obtained through analysis of the solving results: the magnetic field strength, the immersion depth, the tool size, and the polishing wheel speed all show a monotonicity rule in the size and distribution dimension of the pressure and shear stress, which is defined as the monotonicity rule.

[0026] Step 1.3, according to the classic Preston removal model, the dominant factor of material removal in the polishing process is pressure. In the magnetic fluid polishing process, shear force is the core element of material removal efficiency, and pressure is a necessary factor for the existence of shear force. Based on the monotonicity rule obtained in step 1.2, the removal function model is corrected by increasing the influence factor of shear stress on material removal efficiency, the removal function correction model is obtained, the removal function under different immersion depths is obtained by the spot experiment method, the fitting parameters in the removal function correction model are determined by using the data fitting method, the fitted removal function correction model is obtained, and the removal function corresponding to the aspheric element is solved according to the fitted removal function correction model, thereby improving the prediction accuracy of the magnetic fluid removal function.

[0027] The Preston classic removal model described in step 1.3 is shown in formula (6):

[0028]

[0029] wherein, E is the Preston coefficient, P is the pressure distribution of the polishing area, and V is the relative polishing speed between the polishing head and the workpiece.

[0030] The removal function correction model described in step 1.3 is shown in formula (7):

[0031]

[0032] where C is the material removal coefficient, and a represents the influence factor of pressure on the removal function, and C and a are fitting parameters. The pressure and shear stress obtained in step 1.1 are substituted into formula (7) to obtain the material removal function in the polishing area of the magnetorheological finishing.

[0033] For the balloon polishing method, the relationship model between the immersion depth and the removal function is established based on the Hertz contact model, and the implementation method is as follows:

[0034] The balloon polishing is a flexible contact polishing method, the contact type between the polishing tool and the workpiece surface is approximately elastic contact, and the contact area is smaller than the characteristic radius of curvature of the object at the contact point, and the elliptical Hertz contact model is used to analyze the pressure distribution of the polishing head contact area. The pressure formula of a certain (x, y) point in the contact area is as follows:

[0035]

[0036]

[0037] where P0 is the pressure at the center of the balloon polishing head; F is the normal force of the polishing head on the workpiece, including the action of the surface distance between the polishing wheel and the workpiece; a and b are the long axis radius and the short axis radius of the elliptical contact area.

[0038] According to the classical Preston removal model, the dominant factor of material removal in the polishing process is pressure, and the material removal amount of the polishing area per unit time, i.e. the removal function, is shown in formula (6). The pressure distribution obtained based on the Hertz contact model is substituted into formula (6) to establish the relationship model between the immersion depth and the material removal function in the balloon polishing method, and to improve the accuracy of dynamic regulation of the immersion depth and ultra-precision polishing.

[0039] Step two, set the maximum scanning speed and the minimum scanning speed according to the limit conditions of the dynamic performance of the machine tool, and determine the upper and lower limit constraints of the dwell time based on the relationship formula of the scanning speed, the scanning pitch and the dwell time. The amount of material to be removed ΔZ(x, y) of the workpiece surface is obtained by accurate measurement of the ultra-precision detection equipment, the removal function at each sampling point is determined based on the immersion depth distribution, and the dwell time of the tool head at each sampling point is obtained by solving the convolution equation according to the Preston equation. However, due to the difficulty in solving the convolution equation and the difficulty in obtaining an accurate analytical solution, a removal efficiency matrix M(x, y) is constructed based on the removal function at each sampling point, and the nonlinear convolution equation is converted into a linear equation set for processing. The removal efficiency matrix has the characteristics of large size and sparsity, and its solving process usually relies on numerical optimization techniques such as least squares method to obtain an approximate solution of the linear equation, thereby significantly reducing the difficulty of solving and improving the calculation efficiency. In order to meet the dynamic performance of numerical control polishing processing, the constraint conditions of the maximum scanning speed and the minimum scanning speed of the machine tool are added in the process of solving the dwell time using the least squares method, and the equation constraint and the inequality constraint are combined to construct a method of dynamically regulating the scanning speed based on the scanning path: constant speed control is adopted in the single scanning process to ensure the stability of the path; variable speed adjustment mechanism is introduced in the row scanning stage to adapt to the removal requirements of the path turning and complex area. Through this method of dynamically regulating the scanning speed, the dwell time is accurately solved, and the uniformity of the removal efficiency distribution is improved.

[0040] The relationship formula of the scanning speed v(x, y), the scanning pitch l and the dwell time D(x, y) in step two is:

[0041] v(x, y) = l / D(x, y) (10)

[0042] The Preston equation in step two shows that the material removal amount ΔZ(x, y) of the surface of the optical element is the two-dimensional convolution D(x, y) of the removal function R(x, y) and the dwell time, that is:

[0043]

[0044] In the formula, Indicates convolution.

[0045] The linear equation set in step two is:

[0046] ΔZ(x, y) = M(x, y)*T(x, y) (12)

[0047] Step three, according to the performance of the machine tool, determine the maximum value, minimum value and change resolution of the immersion depth, and the distribution of the immersion depth on the workpiece surface as the decision variable to be optimized. In view of the proportional relationship between the immersion depth and the material removal efficiency, that is, the larger the immersion depth, the larger the material removal area and the stronger the material removal ability, according to the initial surface shape error of the workpiece and the dynamic range and limit resolution of the machine tool in the z direction displacement, the initial value distribution of the immersion depth is mapped; according to step one, the removal function of each sampling point is calculated according to the initial immersion depth of each sampling point; through step two, the initial residence time is solved based on the removal function of each sampling point; according to the Preston equation, the initial residence time is convolved with the removal function of each sampling point to predict the material removal amount, and the surface shape error distribution is obtained by comparing the initial surface shape error; based on the surface shape error and the machining target, a multi-objective function is constructed; the optimal value of the objective function is solved by using the optimization algorithm, and the optimal immersion depth distribution and the corresponding residence time are obtained, which improves the scientificity of dynamic control of immersion depth, and further improves the precision and efficiency of optical element manufacturing.

[0048] The machining target includes minimizing low frequency error, minimizing medium frequency error, maximizing machining efficiency, or simultaneously optimizing the convergence of low frequency and medium frequency error.

[0049] The optimization algorithm includes gradient descent method, genetic algorithm, particle swarm algorithm or simulated annealing method.

[0050] It also includes step four, obtaining the surface shape error distribution of the optical element to be machined by high-precision measurement means such as interference detection and Hartmann detection as the input parameter of the material to be removed; based on the optimal immersion depth and the corresponding residence time obtained in step three, the polishing path is set according to the machining requirement, and the polishing tool completes the scanning operation along the preset path; and then the high-efficiency convergence of the surface shape error and the high-precision control of the polishing process are realized.

[0051] Advantages:

[0052] 1. The dynamic control scanning speed and immersion depth high-precision deterministic polishing method disclosed by the application adopts immersion depth and scanning speed as the control parameters when polishing machine tool machined optical elements, which effectively alleviates the influence of machine tool dynamic performance on machining precision compared with the machining method using only scanning speed as a single control parameter, and balances the dynamic performance limitation of the machine tool and the demand for machining precision and efficiency. The material removal efficiency can be significantly improved by increasing the immersion depth, so as to realize the machining target of high precision and high efficiency.

[0053] 2. The high-precision deterministic polishing method of dynamically regulating the scanning speed and the immersion depth, adopts the scanning mode of single-row constant speed and line-changing variable speed to replace the scanning mode of frequent speed changing between workpiece surface sampling points, and significantly reduces the dynamic load of the machine tool in the polishing process. Compared with the global constant speed scanning mode, the polishing efficiency adjustability can be increased, so that the controllability and process adaptability of the polishing efficiency are greatly improved.

[0054] 3. The high-precision deterministic polishing method of dynamically regulating the scanning speed and the immersion depth, for the dwell time solving method of single-row constant speed and line-changing variable speed, increases the equality constraint and inequality constraint in the process of solving the dwell time by using linear equations, ensures the consistency of the dwell time of each row during path scanning, ensures that the dwell time remains constant in single-row scanning and is flexibly adjusted in line-changing scanning, so that the solved dwell time directly meets the requirements without further processing, and the accuracy, scientificity and reliability of the dwell time solving are ensured.

[0055] 4. Since the immersion depth has a significant impact on the peak removal efficiency and volume removal efficiency of the airbag polishing and the magnetorheological polishing. Specifically, the increase of the immersion depth can significantly improve the material removal efficiency. The high-precision deterministic polishing method of dynamically regulating the scanning speed and the immersion depth disclosed by the present application realizes the time-varying nature of the removal function by accurately regulating the immersion depth according to the relationship model between the immersion depth and the removal function, and further improves the efficiency and controllability of the optical material removal. BRIEF DESCRIPTION OF DRAWINGS

[0056] Figure 1 The flowchart of the high-precision deterministic polishing method of dynamically regulating the scanning speed and the immersion depth of the present application.

[0057] Figure 2 The magnetorheological removal function of different immersion depths on the quartz plane element obtained by the spot method in the embodiment.

[0058] Figure 3 The surface error distribution of the to-be-processed element used in the embodiment.

[0059] Figure 4 The surface error distribution of the optical element after processing in the embodiment of the present application. DETAILED DESCRIPTION

[0060] The technical solutions in the embodiments of the present application will be described clearly and completely in combination with the drawings in the embodiments of the present application. The described embodiments are only a part of the embodiments of the present application, not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the protection scope of the present application.

[0061] Example 1

[0062] This embodiment uses 50×50mm 2 Using a plane mirror as the component to be processed, magnetorheological polishing technology is employed to correct the surface shape error with a root mean square value of 0.344 μm. This further illustrates the high-precision deterministic polishing method of the present invention, which dynamically controls the scanning speed and immersion depth.

[0063] like Figure 1 As shown in the figure, the high-precision deterministic polishing method for dynamically controlling scanning speed and immersion depth disclosed in this embodiment is implemented in the following specific steps:

[0064] Step 1: For the magnetorheological polishing method, the relationship model between the immersion depth and the removal function is established based on fluid mechanics.

[0065] Step 1.1: Set the immersion depth to 0.1mm and the ribbon thickness to 0.6mm, and define the spacing H between the workpiece and the polishing wheel. h The system is divided into 20 equally divided regions, and the height h of each region is obtained. The over-relaxation factor is preset to 1.6, and the convergence accuracy of the pressure is set to tol. P Convergence accuracy tol for nucleation range of 0.0001 H The shear yield strength τ0 of the magnetorheological fluid is determined by calculation, with a value of 0.01. Utilizing the Bingham fluid characteristics of the magnetorheological fluid, the Reynolds equations corresponding to each height h are discretized using the finite difference method. The Reynolds equations corresponding to each height h are solved using the over-relaxation iterative method to obtain analytical solutions for pressure. If the preset convergence condition is not met, the pressure distribution is combined with the over-relaxation factor and resubstituted into the Reynolds equations for solving until the preset pressure convergence condition is met, yielding converged pressure and shear stress. Based on the shear yield strength, the solid nucleation range between the workpiece and the polishing wheel within the polishing area is defined. When the shear stress is less than the shear yield strength, the magnetorheological fluid is solid; otherwise, it is liquid. The apparent viscosity distribution is updated based on the solid nucleation range, and the Reynolds equations are resolved based on the new apparent viscosity distribution. Iterative solutions are used to improve the accuracy of the analytical solutions for shear stress and pressure until the preset nucleation range conditions converge, yielding the pressure and shear stress in the steady state.

[0066] The immersion depth H mentioned in step 1.1 l Ribbon thickness H d and the distance H between the workpiece and the polishing wheel h The equation relationship is satisfied, as shown in equation (1):

[0067] H d =H h +H l (1)

[0068] The relationship between the shear yield strength τ0 and the magnetic field strength described in step 1.1 is shown in equation (2):

[0069]

[0070] In the formula, represents the volume fraction of ferromagnetic particles in the magnetorheological fluid, B is the magnetic induction strength, r is the particle radius of the ferromagnetic particles, δ is the net distance between adjacent ferromagnetic particles, μ0 is the vacuum permeability, χ is the magnetic susceptibility of the ferromagnetic particles, and ψ is the shear stress coefficient.

[0071] The Reynolds equation described in step 1.1 is shown in equation (3):

[0072]

[0073]

[0074]

[0075] In the formula, represents the dimensionless interval height, P represents the pressure distribution of the polishing area, represents the dimensionless pressure distribution of the polishing area, and Λ represents the aspect ratio of the polishing area. represents the dimensionless apparent viscosity, represents the dimensionless surface spacing between the polishing wheel and the workpiece, h0 represents the minimum spacing between the polishing wheel and the workpiece surface, R represents the polishing tool size, and U represents the linear speed of the polishing wheel surface.

[0076] Step 1.2, taking the polishing wheel radius as 100 mm, the polishing wheel speed as 300 r / min, the magnetic field current as 10 A, and the immersion depth as 0.1 mm as the baseline values, and setting the polishing wheel radius, the polishing wheel speed, the magnetic field strength, and the immersion depth as single variables for the control experiment. Change the magnetic field strength, the immersion depth, the polishing tool size, and the polishing wheel speed, and solve the pressure and shear stress according to step 1.1. Among them, the polishing wheel radius is 90 mm to 160 mm, the sampling interval is 10 mm; the speed is 100 r / min to 700 r / mm, the sampling interval is 100 r / min; the magnetic field strength is 120 mT to 260 mT, the sampling interval is 20 mT; the immersion depth is 0.07 mm to 0.14 mm, the sampling interval is 0.01 mm. Through the analysis of the solving results, the following rules are obtained: the magnetic field strength, the immersion depth, the tool size, and the polishing wheel speed all show a monotonicity rule in the size and distribution dimension of the pressure and shear stress, which is defined as the monotonicity rule.

[0077] Step 1.3. According to the classic Preston removal model, the dominant factor of material removal in the polishing process is pressure. In the process of magnetorheological polishing, shear force is the core element of material removal efficiency, and pressure is the necessary factor for the existence of shear force. Based on the monotonicity rule obtained in step 1.2, the removal function model is modified by increasing the influence factor α of shear stress on material removal efficiency, and the modified removal function model is obtained. Through the spot experiment method, the removal function under different immersion depths is obtained. In this embodiment, the processing time is set to 8 seconds, the change rate of immersion depth is 0.02 mm, and the diamond is used as the abrasive on the quartz plane mirror with a diameter of 100 mm. The magnetorheological removal function under the immersion depth of 0.05 mm to 0.49 mm is collected. The ZYGO interferometer is used for measurement, and the results are shown in Figure 2 According to the Reynolds equation, the pressure distribution and shear stress distribution under the conditions of the initial set magnetic field current 10 A, tool rotation speed 260 r / min, polishing wheel radius 100 mm, and immersion depth value 0.05 mm to 0.49 mm, change rate 0.02 mm are calculated, and substituted into formula (7). The fitting parameters C=5.0161 -10 , α=0.1191 in the modified removal function model are determined by using the data fitting method. The fitting parameters are substituted into formula (7) to obtain the fitted modified removal function model. According to the fitted modified removal function model, the removal function corresponding to the aspheric element is solved, and the prediction accuracy of the magnetorheological removal function is improved.

[0078] The Preston classic removal model described in step 1.3 is shown in formula (6):

[0079]

[0080] In the formula, E is the Preston coefficient, P is the pressure distribution of the polishing area, and V is the relative polishing speed between the polishing head and the workpiece.

[0081] The modified removal function model described in step 1.3 is shown in formula (7):

[0082]

[0083] In the formula, C is the material removal coefficient, and α represents the influence factor of pressure on the removal function. C and α are fitting parameters. The pressure and shear stress obtained in step 1.1 are substituted into formula (7) to obtain the magnetorheological removal function in the polishing area.

[0084] Step two, according to the dynamic performance of the machine tool limit conditions, set the maximum scanning speed is 3000mm / min, the minimum scanning speed is 100mm / min, based on the scanning speed, scanning pitch and dwell time relationship formula to determine the upper and lower limit of the dwell time constraints. Through the ZYGO interferometer system accurate measurement of the material to be removed from the workpiece surface ΔZ(x, y), remove the invalid points in the measurement results, such as Figure 3 As shown in the initial surface error root mean square value is 0.344μm. Based on the immersion depth distribution to determine the removal function at each sampling point, according to the Preston equation, the convolution equation can be obtained. However, due to the difficulty of solving the convolution equation and the difficulty of accurate analysis, the removal efficiency matrix M(x, y) is constructed based on the removal function at each sampling point, and the nonlinear convolution equation is converted into a linear equation set. The removal efficiency matrix has the characteristics of large and sparse, and the lsqlin function in Matlab is used to solve the dwell time, so as to significantly reduce the difficulty of solving and improve the calculation efficiency. In order to meet the dynamic performance of numerical control polishing processing, in the process of using lsqlin function to solve the dwell time, the constraint conditions of maximum scanning speed and minimum scanning speed of machine tool are increased, and the equation constraint and inequality constraint are combined to construct a dynamic control scanning speed method based on scanning path: in the process of single scanning, constant speed control is adopted to ensure the stability of the path; In the row scanning stage, variable speed adjustment mechanism is introduced to adapt to the removal demand of path turning and complex area. Through this dynamic control scanning speed method, the distribution of dwell time is accurately solved, and the uniformity of removal efficiency distribution is improved.

[0085] The relationship formula of scanning speed v(x, y), scanning pitch l and dwell time D(x, y) in step two is:

[0086] v(x, y)=l / D(x, y) (8)

[0087] The Preston equation described in step two shows that the material removal amount ΔZ(x, y) of the surface of the optical element is the two-dimensional convolution D(x, y) of the removal function R(x, y) and the dwell time, that is:

[0088]

[0089] In the formula, Indicates convolution.

[0090] The linear equation set described in step two is:

[0091] ΔZ(x, y)=M(x, y)*T(x, y) (10)

[0092] Step three, according to the performance of the machine tool, the maximum value of the immersion depth is 0.5mm, the minimum value is 0.05mm, the variation resolution is 0.02mm, and the distribution of the immersion depth on the surface of the workpiece is taken as the decision variable to be optimized. In view of the proportional relationship between the immersion depth and the material removal efficiency, that is, the larger the immersion depth, the larger the material removal area and the stronger the material removal ability, according to the initial surface shape error of the workpiece and the dynamic range and limit resolution of the machine tool in the z direction displacement, the initial value distribution of the immersion depth is mapped; according to step one, the removal function of each sampling point is calculated according to the initial immersion depth at each sampling point; through step two, the initial residence time is solved based on the removal function of each sampling point; according to the Preston equation, the initial residence time is convolved with the removal function of each sampling point to predict the material removal amount, and compared with the initial surface shape error to obtain the surface shape error m(x, y), and evaluated by using the root mean square value; based on the surface shape error and the machining target of minimizing the RMS of the surface shape error, a target function is constructed; the optimal value of the target function is solved by using genetic algorithm, and the optimal immersion depth distribution and the corresponding residence time are obtained, which improves the scientificity of dynamic control of immersion depth, and further improves the precision and efficiency of optical element manufacturing.

[0093] The target function of the genetic algorithm in step three can be expressed as:

[0094]

[0095] In the formula, n is the total number of samples, m i is the value of the surface shape error at the i th sampling point, is the average value of the surface shape error. The specific steps of finding the optimal value of the immersion depth of the magnetorheological polishing head by using the genetic algorithm are as follows:

[0096] The immersion depth of the polishing head at each sampling point on the surface of the workpiece is taken as the decision variable; the RMS of the surface shape error of the workpiece is taken as the target function, and is converted into the fitness function; the population size is set to 20, the maximum genetic iteration number is set to 50, the chromosome length is set to 30, the crossover probability is set to 0.8, the mutation probability is set to 0.02, and the target optimal fitness value is set to less than 0.0001μm; based on the generated initial value of the immersion depth, a chromosome containing the decision variable is constructed by using binary coding; the residence time corresponding to each chromosome is calculated, and the surface shape error after material removal is evaluated, so as to obtain the fitness value of each chromosome in the population; according to the fitness value, the excellent chromosomes are selected as the parents, and the crossover and mutation operations are performed through the set crossover probability and mutation probability, the population is updated and the next generation is generated. In the iteration process, the chromosome with the optimal fitness value in each generation population is continuously recorded until the maximum iteration number is reached, and finally the optimal immersion depth distribution is obtained.

[0097] Step four, the surface error distribution of the optical element to be processed is obtained by the ZYGO interferometer system as the input parameter of the material to be removed; based on the optimal immersion depth and the corresponding residence time obtained in step three, the polishing path is set according to the processing requirements, and the polishing tool completes the scanning operation along the preset path; and then the efficient convergence of the surface error and the high-precision control of the polishing process are realized. After the deterministic processing is completed on the magnetorheological polishing machine tool, the ZYGO interferometer is used to measure the processing result, and the surface error distribution of the processed workpiece is obtained. The measurement result shows that the root mean square value of the surface error of the workpiece has converged to 0.071 μm, and the specific surface error distribution diagram of the workpiece after polishing in this embodiment is shown in Figure 4 The results show that by dynamically adjusting the scanning speed and the immersion depth, the dynamic load of the machine tool is effectively reduced, and the precision and efficiency of the magnetorheological polishing method are improved.

[0098] The above specific description further details the purpose, technical scheme and beneficial effects of the application. It should be understood that the above description is only a specific embodiment of the application and is not used to limit the protection scope of the application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the application should be included in the protection scope of the application.

Claims

1. A high-precision deterministic polishing method with dynamic control of scanning speed and immersion depth, characterized in that: Includes the following steps, Step 1: Process the optical components using the pressure-controlled polishing method, and establish a relationship model between the immersion depth and the removal function based on the pressure-controlled polishing method; Step 2: Based on the limitations of the machine tool's dynamic performance, set the maximum and minimum scanning speeds. Determine the upper and lower limits of the dwell time based on the formula relating scanning speed, scanning spacing, and dwell time. Accurately measure the amount of material to be removed from the workpiece surface using ultra-precision inspection equipment. The removal function at each sampling point is determined based on the immersion depth distribution. The dwell time of the tool head at each sampling point can be obtained by solving the convolution equation according to the Preston equation. A removal efficiency matrix is ​​constructed based on the removal function at each sampling point. The nonlinear convolution equations are transformed into a system of linear equations. To meet the dynamic performance requirements of CNC polishing, constraints on the maximum and minimum scanning speeds of the machine tool are added during the process of solving the dwell time using the least squares method. Combining equality and inequality constraints, a method for dynamically adjusting the scanning speed based on the scanning path is constructed: constant speed control is used during single-line scanning to ensure path stability; a variable speed adjustment mechanism is introduced during the line-changing scanning stage to adapt to the needs of path turns and removal of complex areas. By using the method of dynamically adjusting the scanning speed, the dwell time can be accurately calculated, thereby improving the uniformity of the removal efficiency distribution. Step 3: Based on the machine tool performance, determine the maximum and minimum values ​​of the immersion depth and its variation resolution, and use the distribution of the immersion depth on the workpiece surface as the decision variable to be optimized. Given the direct correlation between immersion depth and material removal efficiency (i.e., the greater the immersion depth, the larger the material removal area and the stronger the effect), map the initial distribution of the immersion depth based on the initial surface shape error of the workpiece and the dynamic range and limit resolution of the machine tool in the z-direction displacement. Using the relationship model from Step 1, calculate the removal function for each sampling point based on the initial immersion depth. Through Step 2, solve for the initial dwell time based on the removal function of each sampling point. According to the Preston equation, convolve the initial dwell time with the removal function of each sampling point to predict the amount of material removed, and compare it with the initial surface shape error to obtain the surface shape error distribution, which is then evaluated using the root mean square (RMS) value. Based on the surface shape error and processing objectives, construct a multi-objective function. Use an optimization algorithm to solve for the optimal value of the objective function, obtaining the optimal immersion depth distribution and corresponding dwell time, improving the scientific nature of dynamically controlling the immersion depth, and thus improving the accuracy and efficiency of optical component manufacturing.

2. The high-precision deterministic polishing method for dynamically controlling scanning speed and immersion depth as described in claim 1, characterized in that: Pressure-controlled polishing methods include magnetorheological polishing and ball-blade polishing.

3. The high-precision deterministic polishing method for dynamically controlling scanning speed and immersion depth as described in claim 2, characterized in that: For the magnetorheological polishing method, the relationship model between the immersion depth and the removal function is established based on fluid dynamics, and the specific implementation method is as follows: Step 1.1: According to the set immersion depth and ribbon thickness Define the spacing between the workpiece and the polishing wheel. The system divides the region into several equal parts and obtains the corresponding height h for each region. It then predetermines the shear yield strength of the magnetorheological fluid by setting the over-relaxation factor, pressure convergence condition, and nucleation range convergence condition. ; Utilizing the Bingham fluid properties of magnetorheological fluids, the Reynolds equations corresponding to various heights h are discretized using the finite difference method. An over-relaxation iterative method is employed to solve the Reynolds equations at each height h, yielding analytical solutions for pressure. If the preset convergence conditions are not met, the pressure distribution is combined with an over-relaxation factor and resubmitted into the Reynolds equations for solving until the preset pressure convergence conditions are met, yielding converged pressure and shear stress. Based on the shear yield strength, the solid nucleation range between the workpiece and the polishing wheel within the polishing area is defined. When the shear stress is less than the shear yield strength, the magnetorheological fluid exhibits a solid state; otherwise, it remains liquid. The apparent viscosity distribution is updated based on the solid nucleation range, and the Reynolds equations are resolved based on the new apparent viscosity distribution. Iterative solutions are used to improve the accuracy of the analytical solutions for shear stress and pressure until the preset nucleation range conditions converge, yielding the pressure and shear stress in a steady state. The immersion depth described in step 1.1 ribbon thickness and the distance between the workpiece and the polishing wheel The equation relationship is satisfied, as shown in equation (1): （1） The shear yield strength mentioned in step 1.1 The relationship between the magnetic field strength and the magnetic field strength is shown in equation (2): （2） In the formula, The volume fraction of ferromagnetic particles in the magnetorheological fluid is represented by , B is the magnetic flux density, and r is the radius of the ferromagnetic particle. This is the net distance between adjacent ferromagnetic particles. The permeability of free space, Let be the magnetic susceptibility of the ferromagnetic particles. It is the shear stress coefficient; The Reynolds equation described in step 1.1 is shown in equation (3): （3） （4） （5） In the formula, P represents the dimensionless height interval, and P represents the pressure distribution in the polished area. The dimensionless pressure distribution representing the polished area. The aspect ratio of the polished area Represents dimensionless apparent viscosity. The dimensionless distance between the polishing wheel and the workpiece surface. R represents the minimum distance between the polishing wheel and the workpiece surface, R represents the size of the polishing tool, and U represents the linear velocity of the polishing wheel surface. Step 1.2: Change the magnetic field strength, immersion depth, polishing tool size, and polishing wheel speed. Iterate and solve for the pressure and shear stress according to Step 1. Analyze the solution results to find the following pattern: The influence of magnetic field strength, immersion depth, tool size, and polishing wheel speed on the pressure and shear stress in terms of magnitude and distribution dimension all show a monotonicity pattern, which is defined as a monotonicity pattern. Step 1.3: According to the Preston classical removal model, the dominant factor in material removal during polishing is pressure. In magnetorheological polishing, shear force is the core element that dominates material removal efficiency, and pressure is a necessary factor for the existence of shear force. Based on the monotonicity law obtained in Step 2, the removal function model is modified by increasing the influence factor of shear stress on material removal efficiency, resulting in a modified removal function model. The removal function at different immersion depths is obtained through spot experiment. The fitting parameters in the modified removal function model are determined using data fitting methods, resulting in a fitted modified removal function model. The removal function corresponding to the aspherical element is obtained by solving the fitted modified removal function model, thus improving the prediction accuracy of the magnetorheological removal function. The Preston classic removal model described in step 1.3 is shown in equation (6): （6） In the formula, E is the Preston coefficient, P is the pressure distribution in the polishing area, and V is the relative polishing speed between the polishing head and the workpiece. The removal function correction model described in step 1.3 is shown in equation (7): （7） In the formula, C is the material removal coefficient. C represents the influence factor of pressure on the removal function. The fitting parameters are obtained by substituting the pressure and shear stress obtained in step one into equation (7) to obtain the magnetorheological removal function in the polishing area. For the balloon polishing method, the relationship between the immersion depth and the removal function is established based on the Hertzian contact model, and the specific implementation method is as follows: Ball bearing polishing is a flexible contact polishing method. The contact between the polishing tool and the workpiece surface is approximately elastic, and the contact area is relatively small compared to the radius of curvature of the object at the contact point. An elliptical Hertzian contact model is used to analyze the pressure distribution in the contact area of ​​the polishing head. The pressure formula at a point (x, y) within the contact area is: （8） （9） In the formula, P0 is the pressure at the center of the ball-shaped polishing head; F is the normal force exerted by the polishing head on the workpiece, including the effect of the surface distance between the polishing wheel and the workpiece; a and b are the major axis radius and minor axis radius of the elliptical contact area. According to the Preston classical removal model, the dominant factor in material removal during polishing is pressure. The amount of material removed from the polished area per unit time, i.e. the removal function, is shown in Equation (6). Substituting the pressure distribution obtained based on Hertz contact theory into Equation (6), a relationship model between the immersion depth and the material removal function in the ball-blade polishing method is established to improve the accuracy of ultra-precision polishing by dynamically controlling the immersion depth.

4. The high-precision deterministic polishing method for dynamically controlling scanning speed and immersion depth as described in claim 3, characterized in that: The scanning speed mentioned in step two Scanning interval l and dwell time The relationship formula is: （10） The Preston equation described in step two indicates the amount of material removed from the surface of the optical element. It is a removal function Two-dimensional convolution with dwell time ,Right now: （11） In the formula, To represent convolution, the system of linear equations mentioned in step two is: （12）。 5. The high-precision deterministic polishing method for dynamically controlling scanning speed and immersion depth as described in claim 4, characterized in that: The processing objectives include minimizing low-frequency errors, minimizing mid-frequency errors, maximizing processing efficiency, or simultaneously optimizing the convergence of low-frequency and mid-frequency errors.

6. The high-precision deterministic polishing method for dynamically controlling scanning speed and immersion depth as described in claim 5, characterized in that: The optimization algorithms include gradient descent, genetic algorithm, particle swarm optimization, or simulated annealing.

7. The high-precision deterministic polishing method for dynamically controlling scanning speed and immersion depth as described in claim 1, 2, 3, or 4, characterized in that: The process also includes step four, which uses high-precision measurement methods such as interferometric detection and Hartmann detection to obtain the surface shape error distribution of the optical element to be processed as an input parameter for the amount of material to be removed; based on the optimal immersion depth and corresponding residence time obtained in step three, a polishing path is set according to the processing requirements, and the polishing tool completes the scanning operation along the preset path; thereby achieving efficient convergence of surface shape error and high-precision control of the polishing process.

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