CN109227226A - Uniform-sliding method for residence time in optical element processing process - Google Patents

Abstract

The invention discloses a method for levelling the residence time in the process of optical element processing. The method adopts a time diffusion model to spread the residence time distribution obtained by conventional calculation, so as to realize the levelling treatment of the residence time. Compared with the original residence time, the dwell time after leveling treatment has a relatively small time difference between adjacent discrete points, so as to achieve a smooth transition between adjacent discrete points and reduce the frequency of polishing tools during processing. The influence of acceleration and deceleration on the stability of the machine tool. The method for smoothing the residence time in the optical element processing process of the present invention can not only improve the convergence effect of the calculation through time diffusion processing, but also reduce the residence time between adjacent discrete points through the smoothing processing of the residence time. The degree of jumping is conducive to improving the stability of CNC machining, thereby reducing the medium and high frequency errors caused by the frequent shaking of the polishing tool.

Description

A method for levelling the residence time in the optical element processing

technical field

The invention belongs to the processing field of optical elements, and particularly relates to a method for levelling the residence time during the processing of optical elements.

Background technique

With the rapid development of optical technology and the continuous expansion of its application range, people have put forward higher and higher requirements for technical indicators such as surface accuracy and surface roughness of optical components. The development trend of modern optical components. In order to effectively improve the surface processing quality of optical components and meet the needs of modern high-precision processing technology, technicians began to use high-precision CNC machining machines to process optical components. During the CNC machining process, the polishing tool forms a certain relative movement speed and pressure on the surface of the machined element, thereby removing excess material on the surface of the machined element. Due to the introduction of digital technology, the motion trajectory of the polishing tool on the surface of the workpiece to be processed can be approximately regarded as a continuous movement at each discrete point. For the removal function, the dwell time of the polishing tool at each discrete point is the dwell time. Therefore, how to plan the residence time distribution of the polishing tool on the surface of the machined component is the key to achieve high-precision CNC machining.

In the prior art, the method for solving the dwell time is mainly divided into a global optimal solution method and a local optimal solution method:

1. Global optimal solution

When the removal function and the amount to be removed of the processed component are known, a set of optimal residence time distributions can be calculated by classical algorithms such as the least squares method to minimize the residual surface shape of the processed component surface. The optimal residence time distribution is the global optimal solution. However, in the actual high-precision machining, the amount of data and computation involved in the calculation process is very large, which makes it difficult to obtain the global optimal solution.

2. Local optimal solution

In order to obtain a set of optimal dwell time distribution within a limited time, and to make the surface shape residual on the surface of the component as small as possible after machining, algorithms such as proportional estimation iteration method and pulse iteration method are usually used to solve the dwell time. This set of residence time distributions is the local optimal solution. However, this method is mainly suitable for the case that the removal function of the polishing tool on the surface of the element is distributed in a circular symmetry. When the removal function of the magnetorheological polishing machine is a polishing device with a non-circular symmetry distribution, the calculation convergence effect of this method needs to be improve.

However, neither of the above two methods considers the smoothness of the residence time distribution; when the variation of the residence time between adjacent discrete points is too large, that is, the residence time distribution is not smooth enough, and the polishing tool may appear during the movement process. Frequent acceleration, deceleration and other phenomena, which will affect the stability of the machine tool, and then leave movement marks on the surface of the machined component. Typically, the spatial size of this motion trace is comparable in magnitude to the spacing of adjacent discrete points, corresponding to mid- and high-frequency surface shape errors. Since the surface shape error is introduced by the processing equipment during the processing, and the correction of the medium and high frequency surface shape error is the technical difficulty of the current CNC machining, it is difficult to correct it through secondary processing.

SUMMARY OF THE INVENTION

The purpose of the present invention is to overcome the deficiencies in the prior art, and provide a method for levelling the residence time in the optical element processing process. The obtained residence time distribution is diffused, so as to realize the smoothing treatment of the residence time; and inherits the advantages of the local optimal solution method, and the calculation amount is much smaller than that of the global optimal solution method.

The technical scheme adopted in the present invention is as follows: a method for levelling the residence time in the optical element processing process, by introducing a time diffusion model to spread the residence time distribution obtained by conventional calculation, so as to realize the levelling treatment of the residence time , the specific steps are:

Step 1: Establish a time diffusion model D(x,y), the center of which is D(x ₀ ,y ₀ ), and D(x,y) meets the total normalization requirements:

∑ _i,j D(x _i , y _j )=1 (1)

where D(x _i , y _j ) represents the relative time rate of change of (x _i , y _j ) position after time diffusion; for any time amount t, its position is taken as the center point (x ₀ , y ₀ ), Using the diffusion model D(x,y) to spread the time amount t, then t·D(x _i ,y _j ) represents the time amount of the (x _i ,y _j ) position after the time diffusion.

Step 2: The surface shape error of the component to be processed is M(x,y), and the removal function of the polishing tool in unit time is I(x,y). The time is T ₁ (x, y); within the dwell time T ₁ (x, y), the difference between the theoretical removal amount and the surface error M(x, y) of the component to be processed is the calculated residual E ₁ (x,y), which can be expressed as:

E ₁ (x, y)=M(x, y)-T ₁ (x, y)**I(x, y) (2)

In the formula, ** represents convolution, T ₁ (x,y)**I(x,y) represents the removal amount of the element to be processed by the polishing tool within the dwell time T ₁ (x, y);

Step 3: For each discrete coordinate point (x _i , y _j ) in T ₁ (x, y), translate the time diffusion model D(x, y) in the X and Y directions to make its center position ( x ₀ ,y ₀ ) moves to (x _i ,y _j ), denoted as _{Di ij} (x,y):

D _ij (x, y)=D(xx _i , yy _j ) (3)

Then, the point T ₁ (x _i ,y _j ) is diffused from point to surface using the diffusion function D _ij (x,y) to obtain the diffused time distribution K _ij (x,y):

K _ij (x, y)=D _ij (x, y)·T ₁ (x _i , y _j ) (4)

Since D _ij (x, y) also satisfies the total normalization requirement shown in formula (1), there are:

∑ _i,j K _ij (x, y)=T ₁ (x _i , y _j ) (5)

k _ij (x, y)**I(x, y)≈T ₁ (x _i , y _j )·I(x, y) (6)

Step 4: According to step 3, the time distribution K _ij (x, y) after diffusion processing for each discrete point (x _i , y _j ) can be obtained, then the residence time distribution T ₁ '(x, y after leveling) ) can be expressed as:

T′ ₁ (x, y)=∑ _{i, j} K _ij (x, y) (7)

And the removal amount corresponding to the residence time distribution T ₁ '(x, y) after level slip should be approximately equal to the removal amount corresponding to the residence time distribution T ₁ (x, y) before level slip:

T′ ₁ (x, y)**I(x, y)≈T ₁ (x, y)**I(x, y) (8)

Step 5: The difference between the surface shape error M(x, y) to be processed and the removal amount corresponding to the residence time distribution T ₁ '(x, y) after level-slipping is the result of a single residence-time level-slipping process. Compute the residual E ₁ '(x,y):

E' ₁ (x, y)=M(x, y)-T' ₁ (x, y)**I(x, y) (9)

Step 6: Take the calculation residual E ₁ ' as the surface shape M to be processed, repeat steps 2 to 5, and perform iterative calculation until the nth iteration calculation is completed, and the corresponding calculation residual E _n ' meets the requirements, thereby obtaining: The total residence time distribution T'(x,y) after the smoothing treatment:

In the formula, n represents the total number of loop iterations; thus, the smoothing process of the optical element processing dwell time is realized.

Compared with the prior art, the advantages and beneficial technical effects of the present invention are as follows:

(1) The method for levelling the residence time in the optical element processing process of the present invention can compensate for the situation that the removal function of the polishing tool on the surface of the element is non-circular symmetric, and improve the convergence of the iterative calculation. Effect.

(2) The method for levelling the residence time in the optical element processing process of the present invention can reduce the residence time between adjacent discrete points by means of levelling the residence time in the iterative calculation process. The degree of jump, thereby reducing the influence of frequent acceleration and deceleration of the polishing tool on the stability of the machine tool during the processing process, thereby reducing the medium and high frequency surface error introduced by the equipment to the processed components during the processing process.

Description of drawings

Fig. 1 is the flow chart that realizes the leveling method of dwell time in a kind of optical element processing process of the present invention;

Fig. 2 is the removal function distribution and time diffusion model used in the embodiment, Fig. 2 (a) is the removal function distribution used in the embodiment, Fig. 2 (b) is the time diffusion model used in the embodiment;

Fig. 3 is the initial surface shape error to be processed in the embodiment;

4 is a graph showing the variation trend of the root mean square value (RMS) of the calculated residuals with the number of iterations in the embodiment (wherein the solid line is when the method for leveling the residence time in the optical element processing according to the present invention is not used) The variation law of the root mean square value (RMS) of the calculated residual with the number of iterations, the dotted line is the root mean square value (RMS) of the calculated residual when the method of the present invention is used for the level-slip method of the residence time in the optical element processing process. ) changes with the number of iterations);

Fig. 5 is a comparison diagram of the calculated residuals in the embodiment, wherein Fig. 5(a) is the calculated residuals without using the method of level-slipping of the dwell time in the optical element processing process of the present invention, Fig. 5(b) ) is the calculated residual error when using the level-slip method of the residence time in the optical element processing process of the present invention;

6 is the power spectral density (PSD) distribution of the residual calculated in the embodiment (wherein the solid line is the power spectral density of the residual calculated without using the method of the present invention for the leveling of the residence time in the optical element processing process) (PSD) distribution, the dotted line is the power spectral density (PSD) distribution of the residual calculated when the method of the present invention is used for the method of leveling the residence time in the optical element processing process);

FIG. 7 is a comparison diagram of the dwell time obtained by iterative calculation in the embodiment, wherein FIG. 7(a) is the dwell time distribution without using the method of the present invention for the level-smoothing of the dwell time in the optical element processing process. , Fig. 7(b) is the residence time distribution when using the method of level-smoothing the residence time in the optical element processing process of the present invention;

8 is the power spectral density (PSD) distribution of the dwell time in the embodiment (wherein the solid line is the power spectral density of the dwell time without using the method of the present invention for the leveling of the dwell time in the optical element processing process) (PSD) distribution, the dotted line is the power spectral density (PSD) distribution of the dwell time when using the method of the present invention for a method of skidding the dwell time during optical element processing.

Detailed ways

The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It is necessary to point out that the embodiments are only used to further describe the present invention, and are not intended to limit the protection scope of the present invention.

A method for levelling the residence time in the optical element processing process proposed by the present invention, the realization flow of which is shown in FIG. 1 .

The first step, according to the removal function model I(x, y) corresponding to the used processing machine tool and processing equipment, establish a time diffusion model D used to realize a method of leveling the residence time in the optical element processing process of the present invention. (x,y);

In the second step, according to the surface shape to be processed M(x,y) and the removal function I(x,y), the dwell time Tn( _x ,y) is obtained through a single iterative solution;

The third step is to use the time diffusion model D(x, y) to perform a smoothing process on the residence time T _n (x, y) to obtain the residence time T _n '(x, y) after the smoothing;

The fourth step, from the residence time T _n '(x, y) after the levelling treatment and the surface shape M(x, y) to be processed, the calculation residual E _n '(x, y) is obtained by solving;

The fifth step is to take the calculated residual E _n '(x, y) as the surface shape M(x, y) to be processed, repeat the second to fourth steps, and perform iterative calculation until the nth iteration calculation is completed, Calculate the residual E _n '(x, y) to meet the requirements;

In the sixth step, the dwell time T _n '(x, y) obtained by each calculation is accumulated to obtain the total dwell time T'(x, y) after level slip, and the subsequent processing step is entered.

Example

In this embodiment, a magnetorheological numerical control polishing machine is used as the processing equipment, and a circular plane mirror with a diameter of 100 mm is used as the element to be processed. In the following description process, the method of the present invention for the levelling of the residence time in the optical element processing process is simply referred to as the levelling method. Under normal circumstances, the removal function of the magnetorheological polishing machine is non-circularly symmetrical. Figure 2(a) shows the removal function of the magnetorheological polishing head when the magnetorheological polishing head resides at the coordinate point of x=0, y=0 for 3 seconds Distribution I(x,y). In this embodiment, the shape distribution of the removal function distribution shown in Fig. 2(a) rotated 180 degrees about the coordinate point of x=0, y=0 is used as the time diffusion model D(x, y), and its distribution shape is shown in Fig. 2(b) ); and normalize the total amount of the time diffusion model to make it satisfy formula (1).

Figure 3 shows the initial surface shape error M(x, y) of the component to be processed, the surface shape peak-valley (PV) is 200.076nm, and the root mean square (RMS) is 36.115nm. Substituting the surface shape error M(x,y) and the removal function I(x,y) into formula (2), the residence time distribution T ₁ (x, y) can be obtained when the time level slip method is not used. and the corresponding computed residual E ₁ (x,y). For the above dwell time T ₁ (x, y), use the time diffusion model D(x, y) shown in Fig. 2(b) to perform a smoothing process on it according to formulas (3) to (8) to obtain The residence time distribution T ₁ '(x, y) after using the level slip method can be calculated from the formula (9) to obtain the calculated residual E ₁ '(x, y) after using the level slip method.

When the level slip method is not used, the above calculation residual E ₁ (x, y) is used as the surface shape error M(x, y) to be processed, and is substituted into the loop for iterative calculation; when the level slip method is used, the above calculation The residual E ₁ '(x, y) is used as the surface shape error M(x, y) to be processed, and is substituted into the loop for iterative calculation.

Figure 4 shows the variation law of the root mean square (RMS) of the calculated residuals with the number of iterations in 20 iterative calculations; the solid line is the RMS value of the residuals calculated when the level slip method is not used ( RMS) with the number of iterations, and the dotted line is the change rule of the root mean square (RMS) of the residual calculated after using the level slip method with the number of iterations. It can be seen from Figure 4 that the root mean square value (RMS) of the calculated residual shows a decreasing trend with the increase of the number of iterations, and after using the smoothing method, the root mean square value (RMS) of the residual calculated ), the convergence speed and the convergence effect are better than those without the use of the level-slip method. When the level-slip method is not used, the calculated residual E ₂₀ (x, y) after the 20th iteration calculation is shown in Figure 5(a), and the corresponding peak-to-valley (PV) value is 96.258 nm, the root mean square value (RMS) is 12.263nm; after using the level slip method, the calculated residual E ₂₀ '(x, y) after the 20th iteration calculation is shown in Figure 5(b), the corresponding peak-to-valley value (PV ) is 86.432 nm, and the root mean square (RMS) value is 7.835 nm. Compared with Fig. 5(a), the surface distribution corresponding to Fig. 5(b) is more uniform and gentle, and its peak-to-valley (PV) and root mean square (RMS) are also smaller, indicating that the levelling method can improve the The convergence effect of the iterative calculation, even if the removal function of the polishing tool on the surface of the element is a non-circular symmetrical distribution, a better convergence effect can be achieved after using the leveling method. As shown in Figure 6, the power spectral density of the calculated residual E ₂₀ (x, y) without the use of the level slip method and the calculated residual error E ₂₀ '(x, y) after the use of the level slip method are compared (Power Spectral density) , PSD) distribution. Power Spectral Density (PSD) is well known in the art, and will not be further described here. Its numerical calculation formula is:

In the formula, Δx=L/N is the sampling interval, L is the sampling length, N is the number of valid sampling points, and M(n) is the error function. It can be seen from Figure 6 that, compared with the case where the crossfading method is not used, after using the crossfading method, the part of the spatial frequency lower than 0.2mm ^-1 (usually corresponding to the middle and low frequency errors) in the residual surface shape is calculated. are reduced, which further indicates that the levelling method can improve the processing effect of the processing equipment in the middle and low frequency parts.

Figure 7 shows a comparison of the residence time distributions solved for without and with the use of the levelling method. Among them, the space size corresponding to each discrete point is 0.0383mm ² , that is, 512×512 discrete points are used to discretize a square area with a side length of 100mm; Fig. 7(a) is the first step when the leveling method is not used. The total residence time T(x,y) distribution obtained after 20 iterations is calculated, T(x,y) satisfies The corresponding peak-to-valley value (PV) is 0.107 seconds, and the root mean square value (RMS) is 0.013 seconds; 7(b) is the total dwell time T after the 20th iterative calculation after the time smoothing method is used. '(x,y) distribution, T'(x,y) satisfies It corresponds to a peak-to-valley (PV) value of 0.038 seconds and a root mean square value (RMS) of 0.006 seconds. From this, it can be seen that the dwell time calculated using the cross-fade method has a lower peak-to-valley (PV) and root mean square (RMS) value than the dwell time calculated without the use of the cross-fade method. decreases, the time distribution is more uniform and smooth. Figure 8 compares the distribution characteristics of dwell times T(x,y) and T'(x,y) over spatial frequencies from the perspective of power spectral density. It can be seen from Fig. 8 that, compared with when the cross-fading method is not used, in the dwell time distribution after using the cross-fading method, the part of the spatial frequency higher than 0.05mm ^-1 (usually corresponding to the mid- and high-frequency errors) It shows that the smoothing method can reduce the frequent movement of the polishing tool in the small space, thereby reducing the medium and high frequency errors caused by the frequent shaking of the polishing tool during the processing.

Through the above-mentioned embodiments, it is shown that the method of the present invention for a method of levelling the residence time in the optical element processing process can improve the convergence effect of the iterative calculation in the process of solving the residence time, and improve the accuracy of the processing equipment on the surface of the processed element, The processing capability of low-frequency error; in addition, the method for levelling the residence time in the optical element processing process of the present invention reduces the variation of the residence time between adjacent discrete points through the levelling processing of the residence time. The degree of jumping, thereby reducing the influence of frequent acceleration and deceleration of the polishing tool on the stability of the machine tool during the processing process, thereby reducing the medium and high frequency errors introduced by the frequent shaking of the polishing tool to the processed components.

Claims (2)

1. a kind of smoothing method of residence time in the optical element processing process, it is characterized in that: by introducing a time diffusion model, the residence time distribution that conventional calculation is obtained is diffused, thereby realizes the smoothing process of residence time, its The specific steps are: Step 1: Establish a time diffusion model D(x,y), the center of which is D(x ₀ ,y ₀ ), and D(x,y) meets the total normalization requirements: ∑ _i,j D(x _i , y _j )=1 (1) where D(x _i , y _j ) represents the relative time rate of change of (x _i , y _j ) position after time diffusion; for any time amount t, its position is taken as the center point (x ₀ , y ₀ ), Using the diffusion model D(x,y) to diffuse the time amount t, then t·D(x _i ,y _j ) represents the time amount of the (x _i ,y _j ) position after time diffusion; Step 2: The surface shape error of the component to be processed is M(x,y), and the removal function of the polishing tool in unit time is I(x,y). The time is T ₁ (x, y); within the dwell time T ₁ (x, y), the difference between the theoretical removal amount and the surface error M(x, y) of the component to be processed is the calculated residual E ₁ (x,y), which can be expressed as: E ₁ (x, y)=M(x, y)-T ₁ (x, y)**I(x, y) (2) In the formula, ** represents convolution, T ₁ (x,y)**I(x,y) represents the removal amount of the element to be processed by the polishing tool within the dwell time T ₁ (x, y); Step 3: For each discrete coordinate point (x _i , y _j ) in T ₁ (x, y), translate the time diffusion model D(x, y) in the X and Y directions to make its center position ( x ₀ ,y ₀ ) moves to (x _i ,y _j ), denoted as _{Di ij} (x,y): D _ij (x, y)=D(xx _i , yy _j ) (3) Then, the point T ₁ (x _i ,y _j ) is diffused from point to surface using the diffusion function D _ij (x,y) to obtain the diffused time distribution K _ij (x,y): K _ij (x, y)=D _ij (x, y)·T ₁ (x _i , y _j ) (4) _{Di ij} (x,y) also satisfies the total normalization requirement shown in formula (1), so there are: ∑ _i,j K _ij (x, y)=T ₁ (x _i , y _j ) (5) k _ij (x, y)**I(x, y)≈T ₁ (x _i , y _j )-I(x, y) (6) Step 4: According to step 3, the time distribution K _ij (x, y) after diffusion processing for each discrete point (x _i , y _j ) can be obtained, then the residence time distribution T ₁ '(x, y after leveling) ) can be expressed as: T′ ₁ (x, y)=∑ _{i, j} K _ij (x, y) (7) And the removal amount corresponding to the residence time distribution T ₁ '(x, y) after level slip should be approximately equal to the removal amount corresponding to the residence time distribution T ₁ (x, y) before level slip: T′ ₁ (x, y)**I(x, y)≈T ₁ (x, y)**I(x, y) (8) Step 5: The difference between the surface shape error M(x, y) to be processed and the removal amount corresponding to the residence time distribution T ₁ '(x, y) after level-slipping is the result of a single residence-time level-slipping process. Compute the residual E ₁ '(x,y): E' ₁ (x, y)=M(x, y)-T' ₁ (x, y)**I(x, y) (9) Step 6: Take the calculation residual E ₁ ' as the surface shape M to be processed, repeat steps 2 to 5, and perform iterative calculation until the nth iteration calculation is completed, and the corresponding calculation residual E _n ' meets the requirements, thereby obtaining: The total residence time distribution T'(x,y) after the smoothing treatment: In the formula, n represents the total number of loop iterations; thus, the smoothing process of the optical element processing dwell time is realized. 2. The method for levelling the residence time in a processing process of an optical element according to claim 1, characterized in that: the residence time is levelled by using a time diffusion model, and can be improved by adjusting the time diffusion model. Smoothing effect of dwell time.