Method for optimizing residence time in a magnetorheological processing of optical elements

Abstract

The application discloses a method for optimizing residence time in a magnetorheological processing of an optical element, which introduces a particle swarm algorithm into pulse iteration to calculate the residence time. Compared with the residence time calculated by original ordinary pulse iteration, the medium frequency error of the surface profile of the optical element is smaller, the instantaneous feed speed of the polishing wheel in the polishing process is reduced, and the influence on the stability of the machine tool is reduced. The application reduces the frequent acceleration and deceleration movement of the polishing wheel in the processing process, thereby reducing the surface profile error, especially the medium frequency error, and has great application value.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of optical element processing, and particularly relates to a method for optimizing dwell time in a magnetorheological processing of an optical element. BACKGROUND

[0002] With the promotion of space optical technology and civil optical technology, various optical elements are increasingly applied to space exploration and civil fields. Especially in some high-tech fields, the optical elements are widely used, but the requirements for surface shape precision and surface roughness of the optical elements are also increasingly high. As the last process of super-precision optical element processing, polishing technology restricts the surface quality of the workpiece and the whole processing flow. In the polishing process, a removal function is generated by a polishing head to scan the surface of the optical element according to a designed track and dwell time to correct the surface shape error. The dwell time of the polishing wheel at each discrete point is the dwell time. The basic model for solving the dwell time is that the expected material removal amount is equal to the convolution of the removal function of the polishing head and the dwell time. Therefore, the solving and post-processing algorithm of the dwell time are the basis for obtaining and realizing the accurate dwell time, and are also the key to super-precision numerical control processing.

[0003] In the prior art, the method for solving the dwell time mainly includes two kinds, one is an iterative method, and the other is a linear equation set method.

[0004] 1. Iterative method

[0005] The iterative algorithm is a fast solving method based on the linear time-invariant processing principle. According to the linear time-invariant material removal theory, the dwell time of the surface of the optical element is proportional to the surface shape error removal. Therefore, the iterative method is used until the condition is met. The iterative method has small calculation amount, fast calculation speed, and ideal solving result, and is most used in computer control processing. However, the iterative method has low precision, obvious medium and high frequency errors and other problems.

[0006] 2. Linear equation set method

[0007] The linear equation set algorithm is a process of linear equation solving after the surface shape error and the dwell time are discretized according to the motion track. The establishment of the coefficient matrix of the linear equation set needs to know the material removal of the removal function around the area of each dwell position. In the calculation process, the data needs to be continuously discretized according to the change of the position, which greatly reduces the calculation speed. The linear equation set method has very large calculation amount, and the coefficient matrix is generally ill-conditioned, which has slow calculation speed and limits the further application of the method. SUMMARY

[0008] The present application aims to overcome the shortcomings in the above method, and provides a method for optimizing the residence time in the magnetorheological processing of optical elements, which optimizes the overall surface residual by introducing a particle swarm algorithm, thereby determining the overall residence time, and then optimally selecting each residence time point, and realizing the optimization of the residence time on the basis of the iterative method, with fast calculation speed, high precision, and effective improvement of the intermediate frequency error.

[0009] The technical scheme adopted by the present application is as follows: a method for optimizing the residence time in the magnetorheological processing of optical elements, which optimizes the overall surface residual by introducing a particle swarm algorithm, thereby determining the overall residence time, and then optimally selecting each residence time point, and realizing the optimization of the residence time on the basis of the iterative method, with the specific steps being as follows:

[0010] Step 1: the surface error of the element to be processed is Z(x, y), the removal function generated by the polishing head on the surface of the optical element per unit time is R(x, y), and the residence time obtained by single iteration in the iterative calculation process is T(x, y). In the process of solving the residence time T(x, y), the removal amount calculated theoretically and the removal amount expected according to the surface error are not equal, and the difference between them is the residual E(x, y), which is expressed as:

[0011] E(x, y) = Z(x, y) - R(x, y) * T(x, y) (1)

[0012] In the formula, * represents convolution, and the convolution of the removal function R(x, y) and the residence time T(x, y) represents the removal of the material of the optical element within the residence time T(x, y). The solving of the residence time T(x, y) is actually a deconvolution process.

[0013] Step 2: the removal function R(x, y) is idealized as a removal pulse, and the intensity I of the removal pulse is equal to the intensity R(x, y) of the removal function, that is:

[0014]

[0015] In the formula, a and b respectively represent the effective range interval of the removal function R(x, y).

[0016] The initial value of the residence time T(x, y) is set as:

[0017] T0(x, y) = Z(x, y) / I (3)

[0018] The initial residual is:

[0019] E0(x, y) = Z(x, y) - R(x, y) * T0(x, y) (4)

[0020] Step 3: For each obtained residence time T k (x, y), a particle swarm optimization algorithm is introduced to optimize the new residence time T' k (x, y), the particle swarm optimization algorithm is to take each residence time point position as a particle, and the particle swarm optimization algorithm optimizes the overall surface residual, thereby realizing the overall residence time determination, and then selecting the optimal residence time point. On the basis of iteration, the residence time optimization processing is realized.

[0021] x(k) = (x1(k), x2(k), x3(k)…x i (k)) is used to represent the particle swarm, i represents the particle number, k represents the kth generation particle, that is, the iteration number of the particle, and x i (k) is substituted into the fitness function, the pros and cons of the position of the kth generation particle can be measured. The step of the kth generation particle individual is represented by v(k) = (v1(k), v2(k), v3(k)…v i (k)). The historical optimal position of a single particle is represented by p best = (p 1，best , p 2，best , p 3，best …p i，best ), that is, the optimal residence time at each residence point. In each iteration, the particle's speed, position, individual optimal solution and global optimal solution are updated, and the particle's speed and position update formula is:

[0022] v i (k+1) = w·v i (k) + c1r1·(p i，best -x i (k)) + c2r2·(p best -x i (k)) (5)

[0023] x i (k+1) = x i (k) + v i (k+1) (6)

[0024] In the formula, w is the inertia weight, k represents the iteration number, r1 and r2 are two random numbers independent of each other and subject to uniform distribution between 0 and 1. It is the introduction of these two random numbers that makes the algorithm evolution process have a certain uncertainty and gives the algorithm a certain spatial exploration ability, which is beneficial to find the optimal solution of the problem. c1 and c2 are learning factors, representing the particle's learning ability of its own experience memory and the best particle in the group, so that the particle can approach the optimal position in the group, that is, the optimal residence time at each residence time point. The residence time obtained after each iteration is:

[0025] T' k (x,y) =∑p i，best (7)

[0026] Step 4: the difference between the surface error Z(x,y) to be processed and the removal amount corresponding to the residence time distribution T'(x,y) processed by the particle swarm algorithm is the residual error E'(x,y) after single residence time processing:

[0027] E'(x,y) = Z(x,y) - R(x,y)*T'(x,y) (8)

[0028] Step 5: taking the calculated residual error E'(x,y) as the surface error Z(x,y) of the element to be processed, repeating steps 2 to 4, iterative calculation is performed, and in the optical element processing process, the residual error of the element surface is set to an expected value, and when the residual error obtained by processing does not reach the expectation, iterative processing is required, that is, the residence time is superimposed once.

[0029] T' k (x,y) = T' k-1 (x,y) + T' k (x,y) (9)

[0030] until the expected value is reached, the iteration ends, and the residual error obtained can be represented as:

[0031] E' k (x,y) = Z(x,y) - R(x,y)*T' k (x,y) (10)

[0032] Finally, the total residence time distribution T'(x,y) processed by the particle swarm algorithm is obtained:

[0033]

[0034] wherein n represents the total number of loop iterations, thereby realizing the processing of the residence time of the optical element processing.

[0035] The residence time optimization method of the optical element processing process can optimize the residence time in the iterative calculation process, reduce the instantaneous acceleration and deceleration movement, ensure the dynamic performance of the machine tool while reducing the medium frequency error introduced in the surface error in the processing process, and ensure the surface accuracy. BRIEF DESCRIPTION OF DRAWINGS

[0036] Figure 1 is a flow chart for realizing the residence time optimization method of the optical element processing process;

[0037] Figure 2is the surface form error distribution used in the example and removal function distribution, Figure 2 (a) is the surface form error distribution used in the example, Figure 2 (b) is the removal function distribution used in the example.

[0038] Figure 3 is the comparison chart of the calculated residual in the example, wherein Figure 3 (a) is the calculated residual when the optical element processing process resident time optimization method is not used, Figure 3 (b) is the calculated residual when the optical element processing process resident time optimization method is used.

[0039] Figure 4 is the power spectral density (PSD) curve of the calculated residual in the example, wherein the solid line is the power spectral density (PSD) curve of the residual when the optical element processing process resident time optimization method is not used, and the dotted line is the power spectral density (PSD) curve of the residual when the optical element processing process resident time optimization method is used.

[0040] Figure 5 is the comparison chart of the calculated polishing wheel feed speed after completion in the example, wherein Figure 5 (a) is the polishing wheel feed speed when the optical element processing process resident time optimization method is not used, Figure 5 (b) is the polishing wheel feed speed when the optical element processing process resident time optimization method is used.

[0041] Figure 6 is the power spectral density (PSD) curve of the calculated polishing wheel feed speed after completion in the example, wherein the solid line is the power spectral density (PSD) curve of the polishing wheel feed speed when the optical element processing process resident time optimization method is not used, and the dotted line is the power spectral density (PSD) curve of the polishing wheel feed speed when the optical element processing process resident time optimization method is used. DETAILED DESCRIPTION

[0042] The present application will be further described below in conjunction with the accompanying drawings and specific examples, and it is necessary to point out that the examples are only used to further describe the present application, and do not mean any limitation on the protection scope of the present application.

[0043] The optical element surface form processing process resident time optimization method proposed by the present application has the implementation process as shown in Figure 1 .

[0044] First step, according to the detection data, determine the surface error Z(x, y) to be processed and the removal function R(x, y);

[0045] Second step, processing path selection, according to the surface error Z(x, y) to be processed and the removal function R(x, y), through single iteration, solve the residence time T k (x, y);

[0046] Third step, using particle swarm algorithm to optimize the residence time, get the processed residence time T' k (x, y);

[0047] Fourth step, using the processed residence time T' k (x, y) and the surface error Z(x, y) to be processed, solve the residual error E' k (x, y);

[0048] Fifth step, take the calculated residual error E' k (x, y) as the surface error Z(x, y) to be processed, repeat the second step to the fourth step, and perform iterative calculation until the nth iteration calculation is completed, and the surface error meets the expected set value;

[0049] Sixth step, add up the residence time T' k (x, y) obtained each time to obtain the total residence time T'

[0050] Embodiment

[0051] In this embodiment, a circular aspheric mirror with a diameter of 156 mm is taken as a to-be-processed element, numerical control machining is performed on a magneto-rheological polishing machine, and the particle swarm optimization method is combined Figures 2 to 6 , to illustrate the specific embodiments of the present application. Figure 2 (a) is the initial surface error distribution Z(x, y) of the to-be-processed element, the surface error peak-to-valley value (PV) is 1161.69 nm, and the root mean square value (RMS) is 169.164 nm. The surface error distribution Z(x, y) of the to-be-processed element and the removal function R(x, y) are brought into formulas (3) and (4), so that the initial residence time T0(x, y) without using the optimization method and the corresponding surface residual error E0(x, y) can be obtained. According to the initial residence time T0(x, y), the optimized residence time distribution T'0(x, y) can be obtained by optimizing according to formulas (5)-(7), and the calculation residual error E'0(x, y) after using the optimization method can be calculated according to formula (8).

[0052] When the optimization method is not used, the calculated residual error E0(x, y) is taken as the surface error Z(x, y) to be processed, and the iteration calculation is entered into the loop; when the optimization method is used, the calculated residual error E'0(x, y) is taken as the surface error Z(x, y) to be processed, and the iteration calculation is entered into the loop;

[0053] Figure 3 (a) is the surface residual error E6(x, y) after 7 iterations of calculation when the optimization method is not used, and the corresponding surface peak-to-valley value (PV) is 837.9057 nm, and the root mean square value (RMS) is 28.6086 nm; Figure 3 (b) is the surface residual error E'6(x, y) after 7 iterations of calculation when the optimization method is used, and the corresponding surface peak-to-valley value (PV) is 807.2156 nm, and the root mean square value (RMS) is 23.4925 nm; and Figure 3 (a) compared with, Figure 3 (b) the corresponding surface distribution is smoother, and the peak-to-valley value (PV) and the root mean square value (RMS) are smaller, indicating that the optimization method can improve the surface error of the element. Figure 4 The power spectral density (PSD) curve of the residual error E6(x, y) when the optimization method is used is compared with the power spectral density (PSD) curve of the residual error E'6(x, y) when the optimization method is not used, and it can be seen from the figure that after using the optimization method, the spatial frequency in the 0.03mm -1 -0.16mm -1 band is reduced, indicating that the optimization method can reduce the corresponding low-frequency surface error in the machining process, although the spatial frequency in the 0.03mm -1 band is increased, but the overall surface error peak-to-valley value (PV) and root mean square value (RMS) are reduced, so this part can not be considered.

[0054] Figure 5 The polishing wheel feed speed distribution obtained by not using the optimization method and using the optimization method is compared. Figure 5 (a) is the total residence time T(x, y) distribution obtained after the 7th iteration calculation when the optimization method is not used, which satisfies The corresponding peak-to-valley value (PV) is 4000 rpm / min, and the root mean square value (RMS) is 507.199 rpm / min; Figure 5 (b) is the total residence time T'(x, y) distribution obtained after the 7th iteration calculation when the optimization method is used, which satisfies The corresponding peak-to-valley value (PV) is 4000 rpm / min, and the root mean square value (RMS) is 188.1263 rpm / min. It can be seen that, after using the optimization method, although the peak-to-valley value (PV) of the polishing wheel feed speed obtained by solving does not change, the root mean square value (RMS) of the polishing wheel feed speed obtained is reduced, and the speed distribution is more gentle. Figure 6 The power spectral density (PSD) curve of the polishing wheel feed speed obtained by using the optimization method is compared with the power spectral density (PSD) curve of the polishing wheel feed speed obtained without using the optimization method. It can be seen that, after using the optimization method, the spatial frequency in the range of 0.02mm -1 -0.18mm -1 The part in the frequency band is reduced, indicating that the optimization method can make the polishing wheel feed speed in the machining process more uniform, reduce the instantaneous acceleration and deceleration movement, increase the stability of the machining bed during machining, and thus reduce the introduction of medium frequency error.

[0055] Through the above examples, it is shown that the optimization method of the residence time in the optical element machining process can improve the convergence of the surface error in the residence time calculation process, make the polishing wheel feed speed in the machining process more uniform, reduce the instantaneous acceleration and deceleration movement, increase the stability of the machining bed during machining, and thus reduce the introduction of medium frequency error.

Claims

1. A method for optimizing residence time in a magnetorheological processing of optical elements, characterized in that, The particle swarm algorithm is introduced to calculate the residence time distribution on the basis of the ordinary pulse iteration, and a new residence time calculation is realized, and the specific steps are as follows: Step 1: the surface error of the processed element is Z(x, y), the removal function generated by the polishing head on the optical element surface per unit time is R(x, y), and the residence time obtained by single iteration in the iteration calculation process is T(x, y). In the process of solving the residence time, the removal amount calculated in theory and the removal amount expected according to the surface error are not equal, and the difference between them is the residual error E(x, y), which is expressed as: E(x, y) = Z(x, y) - R(x, y) * T(x, y) (1) In the formula, * represents convolution, and the convolution of the removal function R(x, y) and the residence time T(x, y) represents the material removal of the optical element within the residence time T(x, y). The solution of the residence time T(x, y) is actually a deconvolution process; Step 2: the removal function R(x, y) is idealized as a removal pulse, and the intensity I of the removal pulse is equal to the intensity R(x, y) of the removal function, that is: In the formula, a and b represent the effective range interval of the removal function R(x, y) respectively; Set the initial value of the residence time T(x, y) as: T0(x, y) = Z(x, y) / I (3) The initial residual error is: E0(x, y) = Z(x, y) - R(x, y) * T0(x, y) (4) Step 3: for each obtained residence time T k (x, y), a particle swarm algorithm is introduced for optimization to obtain a new residence time T' k (x, y), the particle swarm algorithm takes each residence time point position as a particle, and the particle swarm algorithm optimizes the overall surface residual, thereby realizing the overall residence time determination, and then performing the optimal selection of each residence time point, and realizing the optimization processing of the residence time on the basis of the iteration method; Use x(k)=(x1(k), x2(k), x3(k)…x i Let (k) represent the particle swarm, where i represents the particle index, k represents the k-th generation particle, i.e., the number of iterations of the particle, and x i Substituting (k) into the fitness function, we can measure the quality of the position of the k-th generation particle. The step size of the k-th generation particle is represented by v(k) = (v1(k), v2(k), v3(k)...v i (k)), the historical optimal position of a single particle is represented by p. best =(p 1，best p 2，best p 3，best ...p i，best This represents the optimal dwell time at each dwell point. In each iteration, the particle's velocity, position, individual optimal solution, and global optimal solution are updated. The formulas for updating the particle's velocity and position are: v i (k+1) = w · v i (k) + c1r1 · (p i，best -x i (k) + c2r2 · (p best -x i (k) (5) x i (k+1) = x i (k) + v i (k+1) (6) In the formula, w is the inertia weight, k represents the iteration number, r1 and r2 are two random numbers independent of each other and obeying uniform distribution between 0 and 1. It is just the introduction of the two random numbers that makes the evolution process of the algorithm have a certain uncertainty and gives the algorithm a certain spatial exploration ability, which is conducive to finding the optimal solution of the problem. C1 and C2 are learning factors, representing the particle's ability to learn from its own experience memory and the best particle in the group, so that the particle can move towards the optimal position in the group, that is, the optimal residence time at each residence time point. The residence time obtained after each iteration is: T' k (x, y) = ∑p i，best (7) Step 4: the difference between the removal amount corresponding to the surface error Z(x, y) to be processed and the residence time distribution T′0(x, y) processed by the particle swarm algorithm is the residual error E′0(x, y) after single residence time processing: E′0(x, y) = Z(x, y) - R(x, y) * T′0(x, y) (8) Step 5: take the calculated residual error E′0(x, y) as the surface error Z(x, y) of the processed element, repeat steps 2 to 4, and perform iteration calculation. In the process of processing the optical element, the residual error of the element surface is set to the expected value. When the processed residual error does not reach the expected value, the residence time needs to be added once, T' k (x, y) = T' k-1 (x, y) + T' k (x, y) (9) Until the expected value is reached, the iteration is ended, and the residual error obtained can be expressed as: E′ k (x, y) = Z(x, y) - R(x, y) * T' k (x, y) (10) The total residence time distribution T′(x, y) processed by the particle swarm algorithm is finally obtained: In the formula, n represents the total number of loop iterations, and thus the residence time processing of the optical element processing is realized.

2. The method of claim 1, wherein the method is used in a process of optimizing the residence time of an optical element in a magnetorheological fluid. The particle swarm algorithm is used to process the residence time of the general pulse iteration calculation, and the residence time can be changed by controlling the population number and the maximum evolution generation particle swarm model parameters, so as to improve the machining surface type precision and the medium frequency error. ​

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