High-precision deterministic polishing method for dynamically regulating and controlling scanning speed and immersion depth

Abstract

The invention discloses a high-precision deterministic polishing method for dynamically regulating and controlling scanning speed and immersion depth, and belongs to the field of optical polishing. The implementation method comprises the following steps: establishing a relation model between the immersion depth of the magnetorheological polishing method and the balloon polishing method and a controllable time-varying removal function based on a Reynolds equation and a Hertz contact model, and realizing the time-varying property of the removal function by accurately regulating and controlling the immersion depth according to the relation model between the immersion depth and the removal function. The material removal efficiency and controllability are further improved; a processing mode that constant-speed control is adopted in a single-line scanning process and a variable-speed adjusting mechanism is introduced in a line-feed scanning stage is provided, so that the path stability is ensured, and the influence of a dynamic load of a machine tool on precision is reduced; a residence time solving method of single-row constant-speed scanning and line-feed speed changing is constructed, and the accuracy and reliability of residence time solving are guaranteed; and a technology implementation path for dynamically regulating and controlling the scanning speed and the immersion depth is determined, and efficient convergence of the surface shape error and high-precision control over the polishing process are achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of optical polishing, and relates to a high-precision deterministic polishing method for dynamically regulating the scanning speed and immersion depth. Background Art

[0002] Ultra-precision optical components, as the cornerstone of strategic scientific and technological fields such as aerospace, national defense, and military industries, as well as new-era national high-tech industries such as microelectronic integrated circuits and advanced lithography technologies, the demand quantity and precision requirements are continuously rising. The processing process of optical components, especially the polishing link, is the key to realizing the high-efficiency manufacturing of high-precision components.

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

[0004] Currently, pressure-controlled polishing technologies such as balloon polishing and magnetorheological polishing are based on the Preston equation, and solve the dwell time through a stable removal function and the surface shape error distribution obtained by precise detection to achieve controllable material removal. However, the calculated dwell time often has mutations, resulting in frequent sudden stops and starts of the machine tool, which poses extremely high requirements on the mechanical precision and dynamic performance of the magnetorheological polishing machine tool. Frequent sudden stops and accelerations not only increase the machine tool wear and maintenance costs, but also affect the processing stability and efficiency. Therefore, how to avoid mutations in the dwell time and reduce the dynamic burden of the machine tool without affecting the processing precision is a key problem that current technologies urgently need to solve. Summary of the Invention

[0005] The invention aims to solve the problems of processing discontinuity and limited precision caused by sudden changes in residence time in existing pressure-controlled polishing methods such as magnetorheological polishing and balloon polishing. The invention provides a high-precision deterministic polishing method for dynamically controlling scanning speed and immersion depth, establishes a relationship model between immersion depth and removal function, substitutes the relationship model into Preston's equation, and solves the residence time of single-line constant speed scanning and line-changing speed change jointly; uses an optimization algorithm to determine the optimal distribution of immersion depth, combines the dynamically controlled scanning speed, and forms a highly coordinated polishing control strategy. Based on the highly coordinated polishing control strategy, the influence of the dynamic performance of the machine tool on the processing precision is alleviated, the stability and uniformity of the material removal process are improved, and the processing precision and efficiency of the pressure-controlled polishing method are thereby improved.

[0006] Pressure-controlled polishing methods include magnetorheological polishing method and balloon polishing method.

[0007] For the magnetorheological polishing method, the relationship model between the immersion depth and the removal function is established based on fluid mechanics.

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

[0009] The purpose of the present invention is achieved through the following technical solutions:

[0010] The present invention discloses a high-precision deterministic polishing method for dynamically controlling scanning speed and immersion depth, and establishes a relationship model between the immersion depth and a controllable time-varying removal function of a magnetorheological polishing method and a balloon polishing method based on the Reynolds equation and the Hertz contact model. According to the relationship model between the immersion depth and the removal function, the time-varying nature of the removal function is achieved by precisely controlling the immersion depth, thereby further improving the efficiency and controllability of material removal. A processing method is proposed in which a constant speed control is adopted in the single-line scanning process and a variable speed adjustment mechanism is introduced in the line-feed scanning stage to ensure path stability and reduce the influence of the dynamic load of the machine tool on the accuracy. A dwell time solution method for single-line constant speed scanning and line-feed variable speed is constructed to ensure the accuracy and reliability of the dwell time solution. A technical implementation path for dynamically controlling the scanning speed and immersion depth is established to achieve efficient convergence of surface errors and high-precision control of the polishing process.

[0011] The high-precision deterministic polishing method for dynamically controlling scanning speed and immersion depth disclosed in the present invention comprises the following steps:

[0012] Step 1: Use a pressure-controlled polishing method to process the optical element, and establish a relationship model between the corresponding immersion depth and the removal function according to the pressure-controlled polishing method. The pressure-controlled polishing method includes a magnetorheological polishing method and a balloon polishing method.

[0013] For the magnetorheological polishing method, the relationship model between the immersion depth and the removal function is established based on hydrodynamics, and the specific implementation method is as follows:

[0014] Step 1.1. According to the set immersion depth H l and ribbon thickness H d , divide the spacing H h between the workpiece and the polishing wheel into several equal intervals to obtain the corresponding height h for each interval; and preset the over-relaxation factor, pressure convergence condition, and nucleation range convergence condition to determine the shear yield strength τ 0 of the magnetorheological fluid; utilize the property that the magnetorheological fluid has Bingham fluid, discretize the Reynolds equation corresponding to each height h based on the difference method; use the over-relaxation iteration method to solve the Reynolds equation corresponding to each height h to obtain the analytical solution of the pressure. If the preset convergence condition is not satisfied, combine the pressure distribution with the over-relaxation factor and substitute it back into the Reynolds equation for solution until the preset pressure convergence condition is satisfied to obtain the convergent pressure and shear stress; define the solid-state nucleation range between the workpiece and the polishing wheel in the polishing area according to the shear yield strength. When the shear stress is less than the shear yield strength, the magnetorheological fluid presents a solid state, otherwise it is a liquid state; update the apparent viscosity distribution according to the solid-state nucleation range, and re-solve the Reynolds equation based on the new apparent viscosity distribution. Through iterative solution, improve the solution accuracy of the shear stress and pressure analytical solution until the preset nucleation range condition converges to obtain the pressure and shear stress in the stable state.

[0015] The immersion depth H l , ribbon thickness H d , and the spacing H h between the workpiece and the polishing wheel mentioned in Step 1.1 satisfy the following equation relationship, as shown in Equation (1):

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

[0017] The relationship between the shear yield strength τ 0 and the magnetic field strength mentioned in Step 1.1 is as 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 ferromagnetic particles, δ is the net distance between adjacent ferromagnetic particles, μ 0 is the vacuum permeability, χ is the magnetic susceptibility of ferromagnetic particles, and ψ is the shear stress coefficient.

[0020] The Reynolds equation mentioned in Step 1.1 is as shown in Equation (3):

[0021]

[0022]

[0023]

[0024] In the formula, represents the dimensionless interval height, P represents the pressure distribution in the polishing area, represents the dimensionless pressure distribution in the polishing area, 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, h 0 represents the minimum spacing between the polishing wheel and the workpiece surface, R represents the polishing tool size, and U represents the linear velocity of the polishing wheel surface.

[0025] Step 1.2: Change the magnetic field strength, immersion depth, polishing tool size, and polishing wheel speed. According to Step 1.1, iteratively solve to obtain the pressure and shear stress, and analyze the following rules from the solution results: The effects of the magnetic field strength, immersion depth, tool size, and polishing wheel speed on the magnitude and distribution dimension of the pressure and shear stress all show a monotonicity rule, which is defined as the monotonicity rule.

[0026] Step 1.3: According to Preston's classical removal model, the dominant factor causing material removal during the polishing process is pressure. In the magnetorheological polishing process, the shear force is the core element that dominates the material removal efficiency, and pressure is a necessary factor for the existence of the shear force. Based on the monotonicity rule analyzed in Step 1.2, modify the removal function model by increasing the influence factor of the shear stress on the material removal efficiency to obtain the modified removal function model. Obtain the removal function at different immersion depths through the spot experiment method, use the data fitting method to determine the fitting parameters in the modified removal function model, obtain the fitted modified removal function model, and solve the corresponding removal function for the aspherical element according to the fitted modified removal function model to improve the prediction accuracy of the magnetorheological removal function.

[0027] The Preston classical removal model described in Step 1.3 is shown in Equation (6):

[0028]

[0029] 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.

[0030] The modified removal function model described in Step 1.3 is shown in Equation (7):

[0031]

[0032] In the formula, C is the material removal coefficient, α represents the influence factor of pressure on the removal function, and C and α are fitting parameters. Substitute the pressure and shear stress obtained in Step 1.1 into Equation (7) to obtain the magnetorheological removal function in the polishing area.

[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. The specific implementation method is as follows:

[0034] 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 relatively small compared with the radius of curvature of the object at the contact point. The elliptical Hertz contact model is used to analyze the pressure distribution in the contact area of the polishing head. The pressure formula at a certain point (x, y) in the contact area is:

[0035]

[0036]

[0037] In the formula, P 0 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 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.

[0038] According to the Preston classical removal model, the main factor causing material removal during polishing is pressure. The material removal amount in the polishing area per unit time, that is, the removal function, is shown in Equation (6). Substitute the pressure distribution obtained based on the Hertz contact model into Equation (6) to establish the relationship model between the immersion depth and the material removal function in the balloon polishing method, and improve the accuracy of dynamically regulating the immersion depth and ultra-precision polishing.

[0039] Step 2: Set the maximum scanning speed and the minimum scanning speed according to the limiting 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 among the scanning speed, the scanning pitch, and the dwell time. Accurately measure the material removal amount ΔZ(x, y) of the workpiece surface material through an ultra-precision detection device, determine the removal function at each sampling point based on the immersion depth distribution, and solve the convolution equation according to the Preston equation to obtain the dwell time of the tool head at each sampling point. However, due to the difficulty in solving the convolution equation and the difficulty in achieving accurate analysis, construct a removal efficiency matrix M(x, y) at each sampling point, and transform the non-linear convolution equation into a system of linear equations for processing. The removal efficiency matrix is characterized by being large and sparse, and its solution process usually relies on numerical optimization techniques such as the least squares method to obtain an approximate solution of the linear equation, thereby significantly reducing the solution difficulty and improving the calculation efficiency. To meet the dynamic performance of CNC polishing machining, during the process of using the least squares method to solve the dwell time, add the constraint conditions of the maximum scanning speed and the minimum scanning speed of the machine tool, combine equality constraints and inequality constraints, and construct a method for dynamically regulating the scanning speed based on the scanning path: adopt constant speed control during single-line scanning to ensure path stability; introduce a variable speed adjustment mechanism during line-changing scanning to adapt to the removal requirements of path turning and complex regions. Through this method of dynamically regulating the scanning speed, accurately solve the dwell time and improve the uniformity of the removal efficiency distribution.

[0040] The relationship formula among the scanning speed v(x, y), the scanning pitch l, and the dwell time D(x, y) described in Step 2 is:

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

[0042] The Preston equation described in Step 2 indicates that the material removal amount ΔZ(x, y) on 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, represents convolution.

[0045] The system of linear equations described in Step 2 is:

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

[0047] Step 3: Determine the maximum value, minimum value, and their change resolution of the immersion depth according to the machine tool performance, and use the distribution of the immersion depth on the workpiece surface as the decision variable to be optimized. Given that the immersion depth has a direct proportional relationship with the material removal efficiency, that is, the greater the immersion depth, the larger the action area and the stronger the action ability of material removal. 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, map the initial value distribution of the immersion depth; adopt Step 1 to calculate the removal function at each sampling point according to the initial immersion depth at each sampling point; through Step 2, based on the removal function at each sampling point, solve the initial dwell time; according to the Preston equation, convolve the obtained initial dwell time with the removal function at each sampling point to predict the material removal amount, and compare and subtract it from the initial surface shape error to obtain the surface shape error distribution, and evaluate it using the root mean square value RMS; based on the surface shape error and the processing target, construct a multi-objective function; adopt an optimization algorithm to solve the optimal value of the objective function to obtain the optimal immersion depth distribution and the corresponding dwell time, improve the scientificity of dynamically regulating the immersion depth, and thus improve the precision and efficiency of optical element manufacturing.

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

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

[0050] It further includes Step 4: Obtain the surface shape error distribution of the optical element to be processed as the input parameter of the material to be removed through high-precision measurement means such as interference detection and Hartmann detection; based on the optimal immersion depth and the corresponding dwell time optimized in Step 3, set the polishing path according to the processing requirements, and the polishing tool completes the scanning operation along the preset path; thus, achieve the efficient convergence of the surface shape error and the high-precision control of the polishing process.

[0051] Beneficial effects:

[0052] 1. The high-precision deterministic polishing method for dynamically regulating the scanning speed and immersion depth disclosed in the present invention uses the immersion depth and scanning speed as the regulation parameters when the polishing machine tool processes optical elements. Compared with the processing method that only uses the scanning speed as a single regulation parameter, it effectively alleviates the influence of the machine tool's dynamic performance on the processing precision, and balances the dynamic performance limitations of the machine tool and the requirements for processing precision and efficiency. The present invention can significantly improve the material removal efficiency by increasing the immersion depth, thereby achieving the processing goal of both high precision and high efficiency.

[0053] 2. The high-precision deterministic polishing method for dynamically regulating the scanning speed and immersion depth disclosed by the present invention adopts a scanning method with a constant speed for a single row and a variable speed for line change instead of the scanning method with frequent speed change between the sampling points on the workpiece surface, significantly reducing the dynamic load of the machine tool during the polishing process. Compared with the global constant-speed scanning method, the present invention can increase the adjustability of the polishing efficiency, thereby greatly improving the controllability of the polishing efficiency and the process adaptability.

[0054] 3. For the high-precision deterministic polishing method for dynamically regulating the scanning speed and immersion depth disclosed by the present invention, regarding the method for solving the dwell time of a single row with a constant speed and line change with a variable speed, equality constraints and inequality constraints are added during the process of solving the dwell time using a system of linear equations to ensure the consistency of the dwell time for each row during the path scanning, ensuring that the dwell time remains constant during the single-row scanning and is flexibly adjusted during the line change scanning, so that the obtained dwell time directly meets the requirements without further processing, ensuring the accuracy, scientificity, and reliability of the dwell time solution.

[0055] 4. Given that the immersion depth has a significant impact on the peak removal efficiency and volumetric removal efficiency of bladder polishing and magnetorheological polishing. Specifically, the increase in the immersion depth can significantly improve the material removal efficiency. The high-precision deterministic polishing method for dynamically regulating the scanning speed and immersion depth disclosed by the present invention, according to the relationship model between the immersion depth and the removal function, realizes the time-variation of the removal function by precisely regulating the immersion depth, further improving the efficiency and controllability of optical material removal. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 It is a flowchart of the high-precision deterministic polishing method for dynamically regulating the scanning speed and immersion depth of the present invention.

[0057] Figure 2 It is the magnetorheological removal function at different immersion depths on the quartz planar element obtained by the speckle method in the embodiment.

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

[0059] Figure 4 It is the surface shape error distribution of the optical element after processing in the embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0060] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. The described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without making creative efforts shall fall within the protection scope of the present invention.

[0061] Example 1

[0062] In this example, a plane mirror with a size of 50×50 mm 2 is used as the component to be processed. The magnetorheological finishing technology is adopted to correct the surface shape error with a root mean square value of 0.344 μm, so as to further illustrate a high-precision deterministic polishing method for dynamically regulating the scanning speed and immersion depth of the present invention.

[0063] As Figure 1 shown, the specific implementation steps of the high-precision deterministic polishing method for dynamically regulating the scanning speed and immersion depth disclosed in this example are as follows:

[0064] Step 1: For the magnetorheological finishing 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 0.1 mm, the ribbon thickness to 0.6 mm, and divide the distance H h between the workpiece and the polishing wheel into 20 equal division regions to obtain the corresponding height h for each region; and preset the over-relaxation factor to 1.6, the convergence accuracy tol P of the pressure to 0.0001, and the convergence accuracy tol H of the nucleation range to 0.01. Determine the shear yield strength τ 0 of the magnetorheological fluid through calculation; utilize the property that the magnetorheological fluid has Bingham fluid, discretize the Reynolds equation corresponding to each height h based on the difference method; adopt the over-relaxation iteration method to solve the Reynolds equation corresponding to each height h to obtain the analytical solution of the pressure. If the preset convergence condition is not satisfied, combine the pressure distribution with the over-relaxation factor and substitute it back into the Reynolds equation for solution until the preset pressure convergence condition is satisfied to obtain the convergent pressure and shear stress; define the solid-state nucleation range between the workpiece and the polishing wheel in the polishing area according to the shear yield strength. When the shear stress is less than the shear yield strength, the magnetorheological fluid presents a solid state, otherwise it is a liquid state; update the apparent viscosity distribution according to the solid-state nucleation range, and re-solve the Reynolds equation based on the new apparent viscosity distribution. Improve the solution accuracy of the shear stress and the pressure analytical solution through iterative solution until the preset nucleation range condition converges to obtain the pressure and shear stress in the stable state.

[0066] The immersion depth H l , ribbon thickness H d and the distance H h between the workpiece and the polishing wheel in Step 1.1 satisfy the following equation relationship, as shown in Equation (1):

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

[0068] The shear yield strength τ described in Step 1.1 0 The relationship with the magnetic field strength 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 intensity, r is the particle radius of the ferromagnetic particles, δ is the net distance between adjacent ferromagnetic particles, μ 0 is the magnetic permeability of vacuum, 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 in the polishing area, represents the dimensionless pressure distribution in the polishing area, 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, h 0 represents the minimum spacing 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.

[0076] Step 1.2: Taking the polishing wheel radius of 100 mm, the polishing wheel rotation speed of 300 r / min, the magnetic field current of 10 A, and the immersion depth of 0.1 mm as the reference values, set control experiments with the polishing wheel radius, polishing wheel rotation speed, magnetic field strength, and immersion depth as single variables respectively. Change the magnetic field strength, immersion depth, polishing tool size, and polishing wheel rotation speed, and iteratively solve to obtain the pressure and shear stress according to Step 1.1. Among them, the value range of the polishing wheel radius is 90 mm to 160 mm, and the sampling interval is 10 mm; the value range of the rotation speed is 100 r / min to 700 r / mm, and the sampling interval is 100 r / min; the value range of the magnetic field strength is 120 mT to 260 mT, and the sampling interval is 20 mT; the value range of the immersion depth is 0.07 mm to 0.14 mm, and the sampling interval is 0.01 mm. The following rules are obtained through the analysis of the solution results: The effects of the magnetic field strength, immersion depth, tool size, and polishing wheel rotation speed on the magnitude and distribution dimension of the pressure and shear stress all show a monotonicity rule, which is defined as the monotonicity rule.

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

[0078] The Preston classical removal model described in Step 1.3 is shown in Equation (6):

[0079]

[0080] where 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.

[0081] The corrected removal function model described in Step 1.3 is shown in Equation (7):

[0082]

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

[0084] Step 2: According to the limiting conditions of the dynamic performance of the machine tool, set the maximum scanning speed to 3000 mm / min and the minimum scanning speed to 100 mm / min, and determine the upper and lower limit constraints of the dwell time based on the relationship formula among the scanning speed, scanning pitch, and dwell time. The material removal amount ΔZ(x, y) of the workpiece surface material is accurately measured through the ZYGO interferometer system, and invalid points in the measurement results are removed, such as Figure 3 As shown, the root mean square value of the initial surface shape error is 0.344 μm. Based on the immersion depth distribution, the removal function at each sampling point is determined. According to the Preston equation, solving the convolution equation can obtain the dwell time of the tool head at each sampling point. However, due to the difficulty in solving the convolution equation and the difficulty in achieving accurate analysis, a removal efficiency matrix M(x, y) is constructed based on the removal function at each sampling point, and the nonlinear convolution equation is transformed into a system of linear equations for processing. The removal efficiency matrix is characterized by being large and sparse. The lsqlin function in Matlab is used to solve the dwell time, thus significantly reducing the solving difficulty and improving the calculation efficiency. To meet the dynamic performance of CNC polishing machining, during the process of using the lsqlin function to solve the dwell time, the constraint conditions of the maximum and minimum scanning speeds of the machine tool are added, and a method for dynamically regulating the scanning speed based on the scanning path is constructed by combining equality constraints and inequality constraints: constant speed control is adopted during single-line scanning to ensure path stability; a variable speed adjustment mechanism is introduced during line-changing scanning to meet the removal requirements of path turning and complex regions. Through this method of dynamically regulating the scanning speed, the distribution of the dwell time is accurately solved, and the uniformity of the removal efficiency distribution is improved.

[0085] The relationship formula among the scanning speed v(x, y), scanning pitch l, and dwell time D(x, y) described in Step 2 is:

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

[0087] The Preston equation described in Step 2 shows that the material removal amount ΔZ(x, y) on 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, represents convolution.

[0090] The system of linear equations described in Step 2 is:

[0091] ΔZ(x, y) = M(x, y) * T(x, y) (10)

[0092] Step 3: According to the performance of the machine tool, determine that the maximum immersion depth is 0.5 mm, the minimum is 0.05 mm, and the change resolution is 0.02 mm. Take the distribution of the immersion depth on the workpiece surface as the decision variable to be optimized. Given that the immersion depth has a direct proportional relationship with the material removal efficiency, that is, the greater the immersion depth, the larger the action area and the stronger the action ability of material removal. According to the initial surface shape error of the workpiece and the dynamic range and limit resolution of the machine tool's z-direction displacement, map the initial value distribution of the immersion depth; adopt Step 1 to calculate the removal function at each sampling point based on the initial immersion depth at each sampling point; through Step 2, based on the removal function at each sampling point, solve the initial dwell time; according to the Preston equation, convolve the obtained initial dwell time with the removal function at each sampling point to predict the material removal amount, and compare and subtract it from the initial surface shape error to obtain the surface shape error m(x, y), and evaluate it using the root mean square value; based on the surface shape error and the processing objective of minimizing the RMS of the surface shape error, construct an objective function; use the genetic algorithm to solve the optimal value of the objective function to obtain the optimal immersion depth distribution and the corresponding dwell time, improve the scientific nature of dynamically regulating the immersion depth, and thus improve the accuracy and efficiency of optical element manufacturing.

[0093] The objective function of the genetic algorithm described in Step 3 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 to find the optimal value of the immersion depth of the magnetorheological polishing head using the genetic algorithm are as follows:

[0096] Set the immersion depth of the polishing head at each sampling point on the workpiece surface as the decision variable; take the RMS of the workpiece surface shape error as the objective function and convert it into a fitness function; set the population size to 20, the maximum number of genetic iterations to 50, the chromosome length to 30, the crossover probability to 0.8, the mutation probability to 0.02, and the target best fitness value to less than 0.0001 μm; based on the generated initial value of the immersion depth, use binary coding to construct chromosomes containing decision variables; calculate the dwell time corresponding to each chromosome and evaluate the surface shape error after material removal, so as to obtain the fitness values of each chromosome in the population; according to the fitness values, select excellent chromosomes as parents, and perform crossover and mutation operations through the set crossover probability and mutation probability to update the population and generate the next generation. During the iteration process, continuously record the chromosome with the best fitness value in each generation of the population until the maximum number of iterations is reached, and finally obtain the optimal immersion depth distribution.

[0097] Step 4: Obtain the surface error distribution of the optical element to be processed by the ZYGO interferometer system as the input parameter of the material to be removed; based on the optimal immersion depth and the corresponding dwell time optimized in Step 3, set the polishing path according to the processing requirements, and the polishing tool completes the scanning operation along the preset path; thereby achieving the efficient convergence of the surface error and the high-precision control of the polishing process. After the deterministic processing is completed on the magnetorheological polishing machine tool, use the ZYGO interferometer to precisely measure the processing result to obtain the surface error distribution of the processed workpiece. The measurement results show that the root mean square value of the surface error of the workpiece has converged to 0.071 μm, specifically as Figure 4 shown, which is the surface error distribution diagram of the polished workpiece in this embodiment. The results show that by dynamically adjusting the scanning speed and immersion depth, the dynamic load of the machine tool is effectively reduced, and the accuracy and efficiency of the magnetorheological polishing method are improved.

[0098] The above specific description further details the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above is only a specific embodiment of the present invention and is not used to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A high-precision deterministic polishing method with dynamic control of scanning speed and immersion depth, characterized in that: The following steps are included: Step 1: Processing the optical element by using a pressure-controlled polishing method, and establishing a relationship model between the corresponding immersion depth and the removal function according to the pressure-controlled polishing method; Step 2: According to the constraints of the dynamic performance of the machine tool, the maximum scanning speed and the minimum scanning speed are set, and the upper and lower limit constraints of the dwell time are determined based on the relationship formula between the scanning speed, the scanning interval and the dwell time; The amount of material to be removed from the workpiece surface ΔZ(x,y) is accurately measured by ultra-precision detection equipment. The removal function at each sampling point is determined based on the immersion depth distribution. According to the Preston equation, the dwell time of the tool head at each sampling point can be obtained by solving the convolution equation. Based on the removal function at each sampling point, the removal efficiency matrix M(x,y) is constructed, and the nonlinear convolution equation is converted into a linear equation system for processing; in order to meet the dynamic performance of CNC polishing processing, the constraints 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 method of dynamically controlling the scanning speed based on the scanning path is constructed by combining the equality constraint and the inequality constraint: constant speed control is adopted in the single-line scanning process to ensure the path stability; a variable speed adjustment mechanism is introduced in the line-changing scanning stage to meet the removal requirements of path turning and complex areas; By using the method of dynamically controlling the scanning speed, the residence time is accurately solved to improve the uniformity of the removal efficiency distribution; Step 3: According to the performance of the machine tool, 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; in view of the proportional relationship between the immersion depth and the material removal efficiency, that is, the greater the immersion depth, the larger the effective area of ​​material removal and the stronger the effective capacity, the initial value distribution of the immersion depth is mapped according to the initial surface error of the workpiece and the dynamic range and limiting resolution of the machine tool in the z-direction displacement; using step 1, calculate the removal function of each sampling point according to the initial immersion depth at each sampling point; through step 2, solve the initial residence time based on the removal function of each sampling point; according to the Preston equation, the removal function of each sampling point convolved with the initial residence time is used to predict the material removal amount, and the surface error distribution is obtained by comparison and difference with the initial surface error, and the root mean square value RMS is used for evaluation; based on the surface error and processing objectives, a multi-objective function is constructed; the optimization algorithm is used to solve the optimal value of the objective function, and the optimal immersion depth distribution and the corresponding residence time are obtained, so as to improve the scientific nature of the dynamic control of the immersion depth, thereby improving the accuracy and efficiency of optical component manufacturing.

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

3. The high-precision deterministic polishing method for dynamically controlling scanning speed and immersion depth according to 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 mechanics, and the specific implementation method is as follows: Step 1.1: According to the set immersion depth H l and ribbon thickness H d , divide the distance H between the workpiece and the polishing wheel h The magnetorheological fluid is divided into several equal regions, and the height h corresponding to each region is obtained; and the super-relaxation factor, pressure convergence condition, and nucleation range convergence condition are preset to determine the shear yield strength τ0 of the magnetorheological fluid; the magnetorheological fluid has the characteristics of Bingham fluid, and the Reynolds equation corresponding to each height h is discretized based on the difference method; the super-relaxation iteration method is used to solve the Reynolds equation corresponding to each height h to obtain the analytical solution of the pressure. If the preset convergence condition is not met, the pressure distribution is combined with the super-relaxation factor and re-substituted into the Reynolds equation for solution until the preset pressure convergence condition is met to obtain the converged pressure and shear stress; according to the shear yield strength, the solid nucleation range of the workpiece and the polishing wheel in 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 according to the solid nucleation range, and the Reynolds equation is re-solved based on the new apparent viscosity distribution. The solution accuracy of the shear stress and pressure analytical solution is improved through iterative solution until the preset nucleation range condition converges to obtain the pressure and shear stress in the stable state; The immersion depth H described in step 1.1 l , Ribbon thickness H d And the distance H between the workpiece and the polishing wheel h Satisfy the equation relationship, as shown in formula (1): H d =H h +H l (1) The relationship between the shear yield strength τ0 and the magnetic field strength described in step 1.1 is shown in formula (2): 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 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; The Reynolds equation described in step 1.1 is shown in equation (3): In the formula, represents the dimensionless interval height, the pressure distribution in the polishing area of ​​the P table, represents the dimensionless pressure distribution in the polishing area, Λ represents the aspect ratio of the polishing area, represents the dimensionless apparent viscosity, represents the dimensionless distance between the polishing wheel and the workpiece surface, h0 represents the minimum distance 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; Step 1.2, changing the magnetic field intensity, immersion depth, polishing tool size, and polishing wheel speed, and iteratively solving the pressure and shear stress according to step 1, and analyzing the solution results to obtain the following law: the influence of magnetic field intensity, immersion depth, tool size, and polishing wheel speed on pressure and shear stress in terms of size and distribution dimension all show a monotonic law, which is defined as a monotonic law; Step 1.3, according to Preston's classic removal model, the dominant factor of material removal during polishing is pressure; in the magnetorheological polishing process, shear force is the core factor that dominates the material removal efficiency, and pressure is a necessary factor for the existence of shear force; based on the monotonicity law obtained by the analysis of step 2, the removal function model is corrected by increasing the influencing factor of shear stress on material removal efficiency to obtain a removal function correction model, the removal function at different immersion depths is obtained by the spot experiment method, the fitting parameters in the removal function correction model are determined by the data fitting method, and the fitted removal function correction model is obtained, and the removal function corresponding to the non-spherical component is solved according to the fitted removal function correction model to improve the prediction accuracy of the magnetorheological removal function; The Preston classic removal model described in step 1.3 is shown in equation (6): Where 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 formula (7): Where C is the material removal coefficient, α represents the influence factor of pressure on the removal function, and C and α are fitting parameters. Substitute the pressure and shear stress obtained in step 1 into formula (7) to obtain the magnetorheological removal function in the polishing area. 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 specific implementation method is as follows: 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 the object curvature at the contact point. The elliptical Hertz contact model is used to analyze the pressure distribution in the contact area of ​​the polishing head; the pressure formula at a certain (x, y) point in the contact area is: 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 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 Preston's classic removal model, the dominant factor that causes material removal during polishing is pressure. The amount of material removed from the polishing area per unit time, i.e., the removal function, is shown in formula (6). Substituting the pressure distribution obtained based on the Hertz contact theory into formula (6), a relationship model between the immersion depth and the material removal function in the balloon polishing method is established to improve the accuracy of dynamically controlling the immersion depth to achieve ultra-precision polishing.

4. The high-precision deterministic polishing method for dynamically controlling scanning speed and immersion depth as claimed in claim 3, characterized in that: The relationship between the scanning speed v(x, y), the scanning interval l and the dwell time D(x, y) described in step 2 is: v(x,y)=l / D(x,y) (10) The Preston equation described in step 2 shows that the material removal ΔZ(x,y) on 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: In the formula, Represents convolution. The linear equations described in step 2 are: ΔZ(x,y)=M(x,y)*T(x,y) (12).

5. The high-precision deterministic polishing method for dynamically controlling scanning speed and immersion depth according to claim 4, characterized in that: The processing objectives include minimizing low-frequency errors, minimizing medium-frequency errors, maximizing processing efficiency, or optimizing the convergence of low-frequency and medium-frequency errors at the same time.

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

7. The high-precision deterministic polishing method for dynamically controlling scanning speed and immersion depth according to claim 1, 2, 3 or 4, characterized in that: The method also includes step 4, obtaining the surface error distribution of the optical element to be processed as an input parameter of the amount of material to be removed through high-precision measurement methods such as interference detection and Hartmann detection; setting the polishing path according to the processing requirements based on the optimal immersion depth and the corresponding dwell time optimized in step 3, and completing the scanning operation along the preset path by the polishing tool; thereby achieving efficient convergence of the surface error and high-precision control of the polishing process.

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