A special aspheric equation fitting method for CNC machining

Abstract

The present invention relates to the technical field of optical detection devices, and specifically to a special aspheric equation fitting method for CNC machining. The detection fixture and process designed in this scheme of the present application fully simulate the actual use scenario of the microscope, making the detection results more practical. This method not only improves the reliability of detection, but also enhances the fit between product design and actual customer needs. Through the improved detection scheme, the imaging blur and distortion caused by transmission eccentricity can be effectively eliminated, and the imaging clarity and accuracy of the microscope are improved. This improvement is of great significance for high-precision observation and shooting of tiny objects.

Description

Technical Field

[0001] The invention relates to the technical field of optical detection devices, and in particular to a special aspheric equation fitting method for CNC machining. Background Art

[0002] In the rapid development of modern manufacturing, computer numerical control (CNC) technology has become an indispensable core force, especially when dealing with various complex shapes and curved lens processing tasks. The widespread application of CNC technology has not only improved production efficiency, but also greatly improved the accuracy and quality of products. Whether it is precision optical components or complex mechanical parts, CNC equipment can achieve high-precision and high-efficiency processing with its precise motion control and programming flexibility. However, the popularization and application of this technology also faces certain limitations, especially when dealing with special aspheric equations, the applicability of CNC equipment is significantly restricted.

[0003] This limitation is mainly reflected in the current CNC equipment's reliance on standard aspheric equations. Most CNC equipment is designed and programmed based on standard aspheric equations, which makes them incapable of processing special aspheric equations. The complexity and uniqueness of special aspheric equations make them difficult to be directly recognized and processed by existing CNC programs. Summary of the invention

[0004] In order to solve the above problems, the present invention discloses a special aspheric equation fitting method for CNC machining.

[0005] In order to achieve the above object, the present application discloses a special aspheric equation fitting method for CNC machining, comprising the following steps:

[0006] Convert the aspheric formula given in the drawing into the standard aspheric formula and perform unit conversion;

[0007] The converted standard aspheric formula is sampled to obtain a discrete point data set;

[0008] Perform polynomial fitting according to the discrete point data set to obtain a fitting polynomial;

[0009] Adjust the coefficient of the quadratic term in the fitting polynomial so that the data at the sampling point of the standard aspheric formula meets the range of processing requirements;

[0010] The adjusted fitting polynomial is used for the processing and inspection of aspheric surfaces.

[0011] In the above scheme, the aspheric formula given in the drawing is converted into the standard aspheric formula, and the unit conversion is performed. The specific steps include:

[0012] Convert the units in the aspheric formulas given in the drawings from meters to millimeters;

[0013] Convert the aspheric formula given in the drawing to the standard aspheric formula, where the coefficient of the conic term is 0.

[0014] The processing module is used to fit the special aspheric equation into a parametric equation that can be processed by CNC, and it is ensured that the maximum error between the fitted equation and the original equation is less than 10nm.

[0015] The method further comprises:

[0016] The aspheric surface equation is input into a processing module, and a graph of the equation is plotted using the processing module to visualize the shape of the aspheric surface.

[0017] The aspheric surface is fitted into a polynomial with the minimum residual using a fitting algorithm to meet the machining accuracy requirements.

[0018] The method further comprises:

[0019] The fitted polynomial equation is input into the CNC equipment, and the quadratic term coefficient is modified to ensure that the maximum surface error is less than 10 nm.

[0020] The method of the present application simplifies the complex aspheric equations into a form that the CNC equipment can quickly understand and execute through sampling and polynomial fitting. This process reduces programming and debugging time, allowing the CNC equipment to be put into production faster, significantly improving the efficiency of the production line.

[0021] By adjusting the coefficient of the quadratic term in the fitting polynomial, the present invention ensures that the data at the sampling point meets the range of processing requirements, thereby ensuring the surface accuracy of aspheric surface processing. This precise control ensures the quality of the final product and meets the high standard requirements for precision optical components. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 This is a schematic diagram of a lens processing drawing in an embodiment of the present application;

[0023] Figure 2 This is a flow chart of the method in the embodiment of the present application. DETAILED DESCRIPTION

[0024] In order to make the purpose, features and advantages of the present invention more obvious and easy to understand, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the embodiments described below are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention. The principles and features of the present invention are described below in conjunction with the drawings. The examples are only used to explain the present invention and are not used to limit the scope of the present invention.

[0025] The terms "including" and other expressions with similar meanings in the specification or claims of the present invention and the above-mentioned drawings are intended to cover non-exclusive inclusions, such as a process, method or system, or device comprising a series of steps or units is not limited to the listed steps or units.

[0026] Example: Figure 2 As shown, a special aspheric equation fitting method for CNC machining includes the following steps:

[0027] S101: converting the aspheric surface formula given in the drawing into a standard aspheric surface formula, and performing unit conversion;

[0028] In CNC machining, millimeters are usually used as standard units, so it is necessary to convert meter units in design drawings into millimeters to ensure the consistency of machining parameters.

[0029] S102: Sampling the converted standard aspheric formula to obtain a discrete point data set;

[0030] S103: Perform polynomial fitting according to the discrete point data set to obtain a fitting polynomial;

[0031] S104: adjusting the coefficient of the quadratic term in the fitting polynomial so that the coefficient and the data of the standard aspheric formula at the sampling point meet the range of processing requirements;

[0032] The quadratic term coefficient has the greatest impact on the entire equation, so consider fine-tuning the quadratic term coefficient to achieve a maximum error of at least less than one in 100,000;

[0033] S105: Using the adjusted fitting polynomial for processing and testing the aspheric surface.

[0034] Convert the aspheric formula given in the drawing to the standard aspheric formula and perform unit conversion. The specific steps include:

[0035] Convert the units in the aspheric formulas given in the drawings from meters to millimeters;

[0036] Convert the aspheric formula given in the drawing to the standard aspheric formula, where the coefficient of the conic term is 0.

[0037] Example 2: In a possible implementation, the method includes the following steps: using a processing module to fit the special aspheric equation into a parametric equation that can be processed by CNC, and ensuring that the maximum error between the fitted equation and the original equation is less than 10 nm.

[0038] In a specific solution, the processing module may integrate a computing processing unit having a plurality of fitting algorithms, for example, a least squares polynomial fitting algorithm and a multivariate nonlinear regression algorithm, or a functional module in a software processing system configured with the same functional characteristics; wherein the least squares polynomial fitting algorithm is used to achieve accurate fitting of the parametric equation by minimizing the square difference between the data points and the fitting curve;

[0039] The multivariate nonlinear regression algorithm is suitable for processing nonlinear data sets with multiple independent variables and complex functional relationships to obtain high-precision fitting results.

[0040] The method further comprises:

[0041] The aspheric surface equation is input into a processing module, and a graph of the equation is plotted using the processing module to visualize the shape of the aspheric surface.

[0042] The aspheric surface is fitted into a polynomial with the minimum residual using a fitting algorithm to meet the machining accuracy requirements.

[0043] The method further comprises:

[0044] The fitted polynomial equation is input into the CNC equipment, and the quadratic term coefficient is modified to ensure that the maximum surface error is less than 10 nm.

[0045] For example, Figure 1 The example of the machining drawing in the figure does not give the standard aspheric formula. The standard formula is: When operating, the coefficient of the high-order term on the s2 surface is 0

[0046]

[0047] It can be directly converted to the standard aspheric equation:

[0048]

[0049] Before entering the correlation coefficient in the drawing, the unit needs to be converted to millimeters (the units of the formulas in the drawing are all meters) before processing can be carried out according to the normal process. The results after unit conversion are as follows:

[0050] Towards S1

[0051] Due to the existence of high-order terms, the corresponding standard aspheric formula cannot be directly derived. The aspheric formula that can be processed and tested is obtained by fitting.

[0052] The standard aspheric formula consists of (quadratic curve + high-order polynomial). At the beginning, we considered fitting with the standard aspheric formula, but the result was not ideal and the error was large (the maximum error reached 2um). Later, we considered setting the quadratic curve term to zero and approximating the aspheric surface shape with a high-order polynomial. The result was very ideal and the error was negligible (the maximum error was 1nm). The following is the fitting process:

[0053] Will Figure 1 After the coefficient is brought into the formula to convert the unit (the original formula unit is meter, the processing unit is millimeter), it is input into the processing module. The operation instructions are as follows:

[0054] function x = myf1(y);

[0055] x = sqrt(84.8110400298. * y+0.329409. * y·∧2)+0.0045993646. * y ∧1.466;

[0056] according to Figure 1 The formula for the vector height y from 0 to 7.125mm (according to the formula on the drawing, the maximum aperture vector height is 7.12405mm) is sampled every 0.5nm, and the operation is as follows:

[0057] The following polynomial is obtained by basic fitting of the sampled points:

[0058] The operation instructions are:

[0059] >>y=0:0-0000005=7.125;

[0060] x = myf(y);

[0061] plot(x,y);1

[0062] The polynomial is:

[0063] 10 times: y = -5.2132e-18 * x 10 +8.6452e-16 * x 9 -6.2843e-14 * x 8 +2.0019e-12 * x 7+1.7193e-11 * x 6 +1.2704e-09 * x 5 -6.8256e-07 * x 4 -4.5781e-08 * x 3 +0.011791 * x 2 -4.2561e-08 * x+1.213e-08

[0064] Substituting the polynomial into the processing simulation software, the results of the sagitta (left) and the sagitta of the original drawing (right) are as follows:

[0065]

[0066] It can be seen from the table that the maximum error reaches 17nm, which is not satisfactory. Considering that the coefficient of the quadratic term in the polynomial has the greatest impact on the result, the coefficient of the quadratic term is fine-tuned and the other terms remain unchanged to obtain the new result as follows:

[0067] The new sagitta are shown in the following table:

[0068]

[0069] Comparing the vector height with the original drawing, the maximum error of the vector height is 1nm. This precision has no effect on the processing, so the S1 surface can be processed normally.

[0070] The technical means disclosed in the scheme of the present invention are not limited to the technical means disclosed in the above-mentioned implementation mode, but also include technical schemes composed of any combination of the above-mentioned technical features. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications are also regarded as the protection scope of the present invention.

Claims

1. A special aspheric equation fitting method for CNC machining, characterized in that: The following steps are involved: Convert the aspheric formula given in the drawing into the standard aspheric formula and perform unit conversion; The converted standard aspheric formula is sampled to obtain a discrete point data set; Perform polynomial fitting according to the discrete point data set to obtain a fitting polynomial; Adjust the coefficient of the quadratic term in the fitting polynomial so that the data at the sampling point of the standard aspheric formula meets the range of processing requirements; The adjusted fitting polynomial is used for the processing and inspection of aspheric surfaces.

2. The method according to claim 1, characterized in that The aspheric surface formula given in the drawing is converted into a standard aspheric surface formula, and the unit conversion is performed. The specific steps include: converting the unit in the aspheric surface formula given in the drawing from meter to millimeter; Convert the aspheric formula given in the drawing to the standard aspheric formula, where the coefficient of the conic term is 0.

3. The method according to claim 1 or 2, characterized in that: The processing module is used to fit the special aspheric equation into a parametric equation that can be processed by CNC, and it is ensured that the maximum error between the fitted equation and the original equation is less than 10nm.

4. The method according to claim 3, characterized in that The method further comprises: The aspheric surface equation is input into a processing module, and a graph of the equation is plotted using the processing module to visualize the shape of the aspheric surface. The aspheric surface is fitted into a polynomial with the minimum residual using a fitting algorithm to meet the machining accuracy requirements.

5. The method according to claim 4, characterized in that The method further comprises: The fitted polynomial equation is input into the CNC equipment, and the quadratic term coefficient is modified to ensure that the maximum surface error is less than 10 nm.

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