Optical performance-oriented key geometric error identification method for large aspheric element multi-axis numerical control machine tool

Abstract

The invention discloses an optical performance-oriented key geometric error identification method for a large aspheric element multi-axis numerical control machine tool. According to the method, a tool setting point is used as a key node to establish a surface shape error model, geometric errors and surface shape errors of a machine tool are accurately associated, multi-error coupling analysis is simplified, and targeted compensation, online monitoring and real-time correction are achieved. On the basis, a machine tool space error model is constructed in combination with a multi-body system theory, a mapping relation between a surface shape error and wavefront aberration is established by utilizing a ray tracing theory, the wavefront aberration is fitted through a Zernike polynomial, and the contribution degree of each geometric error to the aberration is quantified by means of principal component analysis, so that a key geometric error is identified and compensation is implemented. According to the method, the machining error and the final optical performance are directly associated, and the machining precision and the performance quality of the large aspheric element can be improved. The method is suitable for the manufacturing field of large complex optical elements machined by a multi-axis numerical control machine tool.

Description

Technical Field

[0001] This invention belongs to the field of optical manufacturing and precision control technology of CNC machine tools. In particular, it is a key geometric error identification and compensation method based on optical performance evaluation parameters in the process of machining large aspherical optical components by multi-axis CNC machine tools. It is applicable to the ultra-precision CNC machining of aspherical optical components and the manufacturing of complex freeform surface optical devices. Background Technology

[0002] With the widespread application of high-end optical systems in aerospace, astronomical observation, laser systems, and advanced manufacturing, large aspherical optical elements have become core optical components due to their excellent optical performance and compact system structure. Multi-axis CNC machine tools, as the "mother machines" for processing large aspherical optical elements, directly affect the surface accuracy and final optical performance of the optical elements, thus impacting the imaging quality and performance stability of the optical system.

[0003] Multi-axis CNC machine tools inevitably generate geometric errors during operation due to the complexity of their structure, manufacturing and assembly errors, and wear and tear from long-term use. These geometric errors include straightness errors of guideways, perpendicularity errors between coordinate axes, and positioning and rotation errors of rotary axes. These errors are interconnected and severely affect the machining accuracy of the machine tool. Traditional methods relying on improving the manufacturing and assembly accuracy of key components are no longer sufficient to meet the ever-increasing precision requirements of multi-axis CNC machine tools. Therefore, exploring a new, low-cost method to improve machine tool machining accuracy is imperative. In this context, error compensation has emerged. Error compensation involves analyzing, summarizing, statistically analyzing, and understanding the different sources of error affecting the machine tool. It uses a reasonable mathematical model to characterize the machining error and, based on the calibrated machine tool results and the error mathematical model, artificially creates an error that is equal in value but opposite in direction to the original error, thereby improving the machining accuracy of the machine tool. However, machine tools have numerous error sources. Among the many error influencing factors, how to accurately quantify the contribution of each geometric error source, identify the key factors causing machine tool machining errors, and thus accurately correct the coordinates of each interpolation motion point of the machine tool, enhance the error compensation effect and reliability, and improve the machining accuracy of the machine tool has significant engineering application value and theoretical significance.

[0004] Currently, the performance evaluation of optical components often relies on surface topography errors, especially in the fabrication of large aspherical optical components. The relationship between surface topography errors and optical performance is complex; even if two surfaces have similar topography errors, their final optical performance can differ significantly due to different error distributions. Therefore, simply considering the surface topography error of the component is insufficient; focusing on the evaluation and control of the component's optical performance is essential. Wavefront aberration can quantify the degree of phase distortion of a beam after passing through an optical component and decompose the error information into various typical error modes (such as tilt, spherical aberration, coma, astigmatism, etc.) using methods such as Zernike polynomials. By evaluating and analyzing wavefront aberration, key geometric errors affecting optical performance during machine tool processing can be accurately identified. This not only provides a new perspective for the identification and compensation of key geometric errors in machine tools but also lays the foundation for realizing error compensation strategies based on optical performance.

[0005] In the ultra-precision machining of large aspherical components, the tool setting point serves as the reference point for tool-workpiece contact and a key node for machining path generation and error propagation. Modeling surface errors based on this point offers significant advantages: it can accurately correlate machine tool geometric errors (such as guideway straightness and spindle runout) with surface errors by establishing a mapping relationship between tool setting point error and cutting point position deviation, quantifying the impact of machine tool errors on the surface accuracy of specific cutting points, and avoiding analytical biases caused by ambiguity in error propagation paths in traditional modeling; furthermore, it can transform numerous interconnected and dispersed geometric errors (such as perpendicularity error and rotary axis error) in multi-axis CNC machine tools into a comprehensive deviation at the tool setting point. The displacement method simplifies the complexity of multi-error coupling analysis by modeling with a single reference point, improving model interpretability. It can also accurately locate error-sensitive areas (such as high-curvature parts of aspherical surfaces) and achieve targeted error compensation for specific areas by combining the dynamic position change of the tool setting point, avoiding the waste of resources in global compensation. It is especially suitable for the local high-precision machining requirements of large aspherical components. At the same time, the position of the tool setting point can be obtained in real time through machine tool sensors. Based on its error model, the real-time changes of surface shape error can be quickly calculated, providing a direct basis for online error compensation, realizing closed-loop control of the machining process, and significantly improving the consistency and pass rate of batch machining of large aspherical components.

[0006] In summary, the existing technologies mainly suffer from the following problems: 1. Traditional methods primarily focus on the spatial errors of CNC machine tools. However, this approach focuses on analyzing the positioning and orientation accuracy of CNC machine tools; 2. The accuracy and efficiency of current research on real-time feedback and error compensation may be limited, which may affect processing accuracy and efficiency in the mass production of high-end optical components; 3. Traditional error identification methods emphasize surface topography errors, neglecting the impact of topography error distribution on optical performance, ignoring wavefront quality and imaging performance, and failing to achieve error identification for practical optical applications; 4. Traditional research methods may be affected by the complexity of geometric errors during the error identification process, leading to insufficient accuracy of compensation in some cases; 5. Traditional research focuses on surface shape errors, failing to establish a complete error propagation model, making it difficult to correlate machine tool errors with optical performance, resulting in compensation that lacks specificity and efficiency, often leading to situations where the topography meets the standards but the optical performance is insufficient.

[0007] This invention proposes a method for identifying key geometric errors in multi-axis CNC machine tools for machining large aspherical components, focusing on optical performance. This method analyzes the propagation path of machine tool geometric errors to the component surface and ultimately affecting optical performance, enabling the reverse identification of key geometric errors based on optical performance requirements. This improves machine tool machining accuracy and the performance quality of large aspherical optical components. Summary of the Invention

[0008] This invention provides a method for identifying key geometric errors in multi-axis CNC machine tools for large aspherical components with optical performance, comprising the following steps: S1: Establish a spatial error model for multi-axis CNC machine tools; S2: Establish an optical element surface shape error model based on the tool setting point; S3: Establish an optical performance analysis model; S4: Identify key geometric errors using principal component analysis; S5: Implement critical error compensation and verify its effectiveness.

[0009] Furthermore, step S2 is specifically as follows: S21: Solve for the tool setting point position in the workpiece coordinate system; S22: Convert spatial error to surface error.

[0010] Furthermore, step S4 is specifically as follows: S41: Construct a data matrix relating geometric errors and wavefront aberrations; S42: Preprocess the data and calculate the principal component analysis matrix; S43: Identify key geometric error terms.

[0011] Furthermore, step S5 is specifically as follows: S51: Compensation for key error terms; S52: Effect Comparison and Verification.

[0012] Compared with the prior art, the present invention has the following advantages: 1. Modeling surface shape error based on tool setting point This invention is based on surface error modeling of tool points, which can better model and locate errors in a more refined manner, establish a complete error propagation path, and identify and compensate for geometric errors more accurately and quickly.

[0013] 2. Suitable for batch processing and online monitoring It enables online error monitoring and closed-loop correction in the mass production of high-end optical components. By acquiring wavefront aberration data in real time and feeding it back to the error compensation stage, processing parameters can be dynamically adjusted to improve the yield rate of optical components.

[0014] 3. Error identification based on optical performance Traditional compensation methods primarily target reducing surface topography errors. However, the same topography error can lead to different optical performances due to variations in distribution, neglecting wavefront quality and imaging performance. This invention directly optimizes wavefront aberrations, achieving error identification for final optical applications and ensuring that the fabricated optical components meet actual optical requirements.

[0015] 4. Efficient error identification and compensation mechanism Principal component analysis quantifies the contribution of each geometric error to the Zernike coefficients (aberration types), quickly identifying the range of key geometric error terms (such as guide straightness in a specific direction or spindle radial runout) that have the greatest impact on optical performance. By combining geometry and optics, efficient error compensation can be achieved, improving the timeliness and accuracy of the compensation strategy.

[0016] 5. Introduce optical error compensation technology based on wavefront aberration. Using wavefront aberration as the core indicator, this paper establishes a complete transfer model of geometric error, surface shape error, and wavefront aberration by decomposing aberration types (such as tilt, spherical aberration, astigmatism, etc.) using Zernike polynomials. This model directly correlates machine tool errors with final optical performance, avoiding the problem of meeting shape requirements but failing to meet optical performance standards, and ensuring that processed components meet the requirements of actual optical systems. A real-time wavefront aberration feedback mechanism is proposed, generating Zernike coefficients online and feeding them back to the compensation stage. This supports dynamic adjustment of machining parameters (such as tool path and motion compensation), achieving closed-loop control and significantly improving the yield and consistency of mass-produced optical components. By introducing principal component analysis, a correlation matrix of "geometric error → Zernike coefficients" is constructed. Through PCA dimensionality reduction, the geometric error term that contributes the most to wavefront aberration (such as guide rail straightness error in a specific direction) is identified, accurately pinpointing the core error source, avoiding the waste of resources in global compensation, and improving compensation efficiency. This application optimizes wavefront aberrations directly through a compensation strategy. It compensates key geometric errors based on PCA results. During verification, the degree of improvement in wavefront aberrations and Zernike coefficients is used as the core indicators to ensure that the optical performance of the optical components (such as imaging resolution and energy concentration) is substantially improved after compensation, rather than just meeting the surface morphology requirements. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of a five-axis CNC machine tool mechanism; Figure 2 It is a five-axis ultra-precision machining tool topology; Figure 3 It is a vector diagram of the key points; Figure 4 This is a diagram of the ray tracing theorem, the law of reflection, and the law of refraction; Figure 5 It is a three-dimensional topographic image of an aspherical surface; Figure 6 These are the coefficients of the first 21 Zernike polynomials; Figure 7 It is the effect of each error term on wavefront aberration; Figure 8 It is a comparison of coefficients and wavefront aberrations before and after compensation; Figure 9 This is a schematic diagram of the process for identifying key geometric errors in multi-axis CNC machine tools for large aspherical components with optical performance, as proposed in this application. Detailed Implementation

[0018] like Figure 1-9 As shown, taking a five-axis CNC machine tool as an example, this embodiment provides a method for identifying key geometric errors in multi-axis CNC machine tools for large aspherical components with optical performance, including the following steps: S1: Establish a spatial error model for a five-axis CNC machine tool Based on multibody system theory and combined with the motion of multi-axis CNC machine tools, this paper analyzes the geometric errors of each motion axis and classifies them according to motion form and installation position. A coordinate system is established on the components, and a low-order volume array is used to describe the relationship between the components. The motion error transmission relationship between adjacent bodies is derived using a homogeneous transformation matrix. The actual and ideal position deviation of the tool is constructed, and a machining error model is built, providing a foundation for the spatial error model analysis of large aspherical optical components. The five-axis CNC machine tool includes a bed 0, a workpiece holder fixedly mounted on the upper surface of the bed 0, a workpiece 3 placed above the workpiece holder, a tool holder above the bed 0, a spindle 7 fixedly mounted on the tool holder, and a tool fixedly mounted at the end of the spindle 7. The workpiece holder can move along the X-axis 1 and rotate around the C-axis 2. The tool holder can move along the Y-axis 4 or Z-axis 5. The spindle 7 and the tool 8 can rotate around the A-axis 6.

[0019] Figure 1 This is a schematic diagram of a five-axis ultra-precision machining tool mechanism, such as... Figure 2 The diagram shows the topology of a five-axis ultra-precision machining center. The low-order volume array of the machine tool is obtained from its topology, as shown in Table 1.

[0020] According to the definition of low-order volume arrays, a typical nth order low-order body number satisfy:

[0021] in The low-order body operator L represents the relationship between adjacent low-order bodies.

[0022] Table 1 shows the low-order volume array of a five-axis ultra-precision machining center.

[0023] The actual position vector of the tool center point in the machine coordinate system It can be represented as:

[0024] in: : Ideal position transformation matrix between adjacent bodies; Position error matrix between adjacent bodies; Ideal motion transformation matrix; Motion error matrix; : The vector representing the position of the tool tip in the tool coordinate system. l represents the tool length.

[0025] S2: Establish an optical element surface shape error model based on the tool setting point. The tool setting point is a key point for tool path generation and error identification, and its error is expressed as the difference between the actual machining position and the ideal position.

[0026] S21: Solve for the tool setting point position in the workpiece coordinate system Establish vector relationship diagrams of key points in the machine tool coordinate system and workpiece coordinate system, such as... Figure 3 As shown, the tool setting point in the workpiece coordinate system is... The actual position vector of the tool setting point in the machine coordinate system is The ideal location is The actual offset of the tool setting point relative to the workpiece coordinate origin is: The vector form is The ideal offset of the tool setting point relative to the workpiece coordinate origin is: The offset of the workpiece coordinate system relative to the machine tool coordinate system is: The ideal cutting point is located in the workpiece coordinate system as follows: The position vector of the point to be machined in the workpiece coordinate system within the machine tool coordinate system is: .

[0027] The error equation for the tool setting point is:

[0028] in: This represents the difference between the position error matrix and the identity matrix, where I is the identity matrix.

[0029] Considering the actual machining position of the workpiece at the tool setting point, the actual position of the workpiece cutting point in the workpiece coordinate system is... for:

[0030] in: This is the ideal transformation matrix from the workpiece coordinate system to the machine tool coordinate system.

[0031] S22: Convert spatial error to surface error The positional deviation between the ideal cutting point and the actual cutting point is:

[0032] The ball end mill model is represented using the surface shape error expression:

[0033] in: R: Tool radius; : Workpiece normal; ; The direction of the tool axis Establish a surface shape error model for discrete points, specifically as follows: The error at point j in the i-th tool position is:

[0034] in: Ideal cutting point compensation Unit normal vector of the workpiece surface at the cutting point The angle between the tool and the surface at this point S3: Establish an optical performance analysis model Combining the actual process path and spatial error model, simulations are used to generate three-dimensional topographic data of the aspherical surface after processing, such as... Figure 4 As shown, based on ray tracing theory, an optical performance model was established. After superimposing surface shape errors, ray deflection and wavefront changes were obtained through simulation calculations, leading to a wavefront aberration distribution map. Ray tracing theorem is a core theory in geometrical optics describing the laws of light propagation.

[0035] Based on the laws of reflection and refraction and their vector forms, an optical performance model is established, and the influence of processing errors on optical performance is analyzed. For example... Figure 5 As shown, denoted as the refractive index of the incident medium; is the refractive index of the refracting medium; Angle of incidence; The angle of reflection, The angle of refraction. Through the optical path difference. surface shape error With optical performance (wavefront aberration) ( ) are linked together.

[0036] The relationship between optical path difference and wavefront aberration is as follows:

[0037] In the case of reflection, the incident light is incident at an angle (the angle of reflection equals the angle of incidence):

[0038] in: I is the unit incident direction vector; N is the unit normal vector; R is the unit reflected ray direction vector; Surface shape error is the offset in the vertical direction. The actual increase in the path is projected in the direction of the light. The optical path difference is the difference between two reflections. The relationship with surface shape error is as follows:

[0039] Relationship between wavefront aberration and surface shape error:

[0040] Oblique incidence under refraction:

[0041] in: , T: Unit refraction direction vector The actual travel path in the medium is:

[0042] The path of reduction in air is:

[0043] Optical path difference The relationship with surface shape error is as follows:

[0044] Relationship between wavefront aberration and surface shape error:

[0045] Discrete wavefront aberration data is obtained by relating surface shape error to wavefront aberration. The discrete data of wavefront aberrations were fitted using Zernike polynomials to obtain the Zernike polynomial coefficients.

[0046] The Zernike polynomial wavefront fitting formula is:

[0047] : The coefficients of the j-th Zernike polynomial; : The j-th standard Zernike polynomial; : Planar coordinates Mapped to polar coordinates within the unit circle; M: Number of selected Zernike polynomials N: Number of discrete data points for wavefront aberrations Zernike polynomials are orthogonal polynomials within the unit circle, defined as follows:

[0048] in: n: principal order, ; m: secondary order, ,and It is an even number; : Radial polynomial.

[0049] The specific steps for solving the Zernike polynomial coefficients using the least squares method are as follows: (1) Obtaining discrete points Wavefront aberration data at the location .

[0050] (2) Coordinate transformation: Transform Cartesian coordinates Convert to polar coordinates ,in , R is the maximum radius of the entire pupil (or effective aperture); It is the polar angle of the i-th data point, representing its angular position within the unit circle. (3) Normalization: Normalization to Range (within the unit circle).

[0051] (4) Construct the Zernike function matrix A For each data point Calculate the value of each Zernike polynomial at that point. Construct matrix A

[0052] (5) Construct the target vector W

[0053] (6) Solve the Zernike polynomial coefficients c using the least squares method.

[0054] The objective function is constructed as follows:

[0055] The least squares solution is obtained as follows:

[0056] in These are the Zernike coefficients obtained from the fitting. For example... Figure 6 The figure shows the coefficients of the Zernike polynomial for the first 21 terms.

[0057] The coefficients of the Zernike polynomial fitting are obtained. Different processing errors will cause different aberration coefficients. When wavefront aberrations exist in the processed device, the magnitude of these coefficients can be used to roughly determine the tolerance range of the main processing errors, providing initial values ​​for the processing error identification process. The m, n, and the aberrations they represent for the first nine Zernike polynomials are shown in Table 2.

[0058] Table 2 shows the m, n, and their corresponding aberrations for the first nine Zernike polynomials.

[0059] S4: Identify key geometric errors using principal component analysis. Different geometric errors have varying degrees and patterns of influence on machine tool machining accuracy, resulting in different final optical performance. To better understand the influence of various geometric errors on the machining performance of aspherical optical elements, it is necessary to calculate the wavefront aberrations caused by each geometric error parameter and the coefficients of the Zernike polynomial fitting, and analyze the influence of each geometric error individually on the wavefront aberrations formed on the aspherical optical element. Finally, principal component analysis is performed to identify key geometric error terms, such as... Figure 7 The diagram shows the impact of each error term on wavefront aberrations. By comparing the changes in Zernike coefficients obtained under different error term interferences, the geometric error that contributes the most to changes in optical performance (especially key aberrations such as focus and astigmatism) is identified.

[0060] S41: Construct a data matrix relating geometric errors and wavefront aberrations Each time, only one geometric error is introduced and simulated; each set of errors generates a wavefront; Zernike polynomials are fitted to each wavefront to obtain a set of Zernike coefficients; the Zernike coefficient matrix is ​​constructed.

[0061]

[0062] in: m: the number of geometric error samples Each sample yields n Zernike polynomial coefficients, where each row represents a Zernike fit coefficient under geometric error perturbation; each column corresponds to a Zernike mode term.

[0063] S42: Preprocess the data and calculate the principal component analysis matrix The Zernike coefficient matrix is ​​standardized, the covariance matrix is ​​calculated and eigenvalues ​​are decomposed, and principal components are extracted to reveal key influences.

[0064] Perform mean normalization (Z-score standardization) on each column of matrix Z:

[0065] in: : The average of each column (each Zernike item) across all samples; Standard deviation of each column (measures the magnitude of change of the Zernike term under various error disturbances).

[0066] Covariance matrix calculation, specifically the standardized covariance matrix:

[0067] This is The matrix reflects the cooperative changes among different Zernike terms.

[0068] Eigenvalue decomposition: Performing eigenvalue decomposition on the covariance matrix.

[0069] in: Each column represents the principal component direction (principal axis), also known as the load vector. A diagonal matrix representing the variance (contribution rate) of each principal component.

[0070] S43: Identify key geometric error terms By combining principal component loadings and contribution rates, and correlating them with the original geometric errors, key terms significantly affecting optical performance are identified. The principal component loading vectors are analyzed ( (Column vectors), the larger the absolute value of the loading, the stronger the correlation between the corresponding Zernike term and the principal component; combined with the principal component contribution rate ( (Diagonal elements) focus on Zernike terms associated with high-contribution principal components. By mapping Zernike terms to geometric errors, the original geometric errors that have the greatest impact on high-contribution principal components are identified, which are the key geometric error terms, thus completing the identification target.

[0071] S5: Implement key error compensation and verify its effectiveness. S51: Compensation for key error terms: Based on the principal component analysis results, corresponding compensation strategies were formulated for the key geometric error terms that significantly affect optical performance. These strategies include adjusting machine tool motion parameters, correcting interpolation point coordinates, and optimizing machining processes to compensate for the key errors.

[0072] S52: Effect Comparison and Verification After compensation, the surface topography and wavefront aberrations of the processed optical components were re-measured. The compensated surface topography error data were compared with those before compensation to observe whether the surface shape error decreased. Simultaneously, the wavefront aberration distribution maps before and after compensation were compared to evaluate the improvement in wavefront quality. Zernike coefficient analysis: The focus was on the main terms in the Zernike coefficients corresponding to key aberrations (such as focal aberration, astigmatism, spherical aberration, etc.). Figure 8 The figures show a comparison of coefficients and wavefront aberrations before and after compensation. If the compensation is effective, the coefficients of these key terms should decrease significantly, indicating that the optical performance is also optimized. The above embodiments are exemplary and are intended to illustrate the technical concept and features of the present invention, so that those skilled in the art can understand the content of the present invention and implement it accordingly. They should not be construed as limiting the scope of protection of the present invention. All equivalent changes or modifications made according to the spirit and essence of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A method for identifying key geometric errors in multi-axis CNC machine tools for large aspherical components with optical performance characteristics, characterized in that... Includes the following steps: S1: Establish a spatial error model for multi-axis CNC machine tools; S2: Establish an optical element surface shape error model based on the tool setting point; S3: Establish an optical performance analysis model; S4: Identify key geometric errors using principal component analysis; S5: Implement critical error compensation and verify its effectiveness.

2. The method for identifying key geometric errors in multi-axis CNC machine tools for large aspherical components oriented towards optical performance, as described in claim 1, is characterized in that... Step S2 is as follows: S21: Solve for the tool setting point position in the workpiece coordinate system; S22: Convert spatial error to surface error.

3. The method for identifying key geometric errors in multi-axis CNC machine tools for large aspherical components oriented towards optical performance, as described in claim 1, is characterized in that... Step S4 is as follows: S41: Construct a data matrix relating geometric errors and wavefront aberrations; S42: Preprocess the data and calculate the principal component analysis matrix; S43: Identify key geometric error terms.

4. The method for identifying key geometric errors in multi-axis CNC machine tools for large aspherical components oriented towards optical performance, as described in claim 1, is characterized in that... Step S5 is as follows: S51: Compensation for key error terms; S52: Effect Comparison and Verification.

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