Optical mold thermal deformation compensation method and system based on finite element analysis

Abstract

The application relates to the technical field of data processing, in particular to an optical mold thermal deformation compensation method and system based on finite element analysis, which comprises the following steps: obtaining an initial three-dimensional model of an optical mold; performing finite element analysis on the initial three-dimensional model to obtain a normal error vector of each node of the optical mold; performing iterative correction on the initial three-dimensional model to obtain a corrected optical mold until the root mean square value of the normal error vector is smaller than a preset threshold value. The application solves the problem of low compensation precision in the prior art.

Description

Technical Field

[0001] This invention relates to the field of data processing technology. More specifically, this invention relates to a method and system for compensating for thermal deformation of optical molds based on finite element analysis. Background Technology

[0002] In the field of modern optical device manufacturing, especially in the production of aspherical optical molds, freeform optical molds, and precision injection molded optical molds, the surface accuracy of the mold directly affects the imaging quality, optical transmission efficiency, and overall system performance of the final optical element. With the trend towards higher precision, miniaturization, and complex curved surfaces in optical elements, even minute geometric errors in the mold are amplified, leading to imaging distortion, beam shift, or light energy loss, and in severe cases, even affecting the functional reliability of the optical system. During mold processing, heat treatment, and use, the material's thermal expansion or local temperature gradients cause thermal deformation of the surface, typically manifesting as local warping between nodes, curvature changes, and overall surface shift. Since even minute deviations in the optical surface can significantly impact imaging quality, accurately predicting and compensating for this thermal deformation before mold processing or use has become a core technical problem in optical mold manufacturing and a crucial step in ensuring the performance of the optical system and the product yield rate.

[0003] In existing technologies, finite element analysis is applied to the prediction and compensation of thermal deformation in optical molds. Its main principle is to establish a finite element mesh based on the mold's three-dimensional geometric model, and then calculate the overall or local deformation of the mold under thermal action by applying thermal loads, boundary constraints, and material property parameters. Traditional methods typically use the overall deformation or average nodal displacement as the basis for compensation, and perform a one-time correction to the mold based on the calculation results, or adopt a unified convergence strategy with a fixed step size and multiple iterations for geometric compensation.

[0004] However, existing technologies mostly use overall or global indicators as the basis for iteration, which cannot fully reflect the local sensitivity of each node on the mold surface under thermal load. For areas with drastic curvature changes or uneven heat distribution, it is easy to cause undercompensation or overcompensation, resulting in new surface errors and reducing compensation accuracy. Secondly, existing technologies generally use fixed global convergence parameters and lack adaptive adjustment mechanisms for each node. This can lead to problems such as node oscillation, deviation of correction direction from the design trend, or slow convergence speed during the iteration process, thus affecting the stability and efficiency of compensation and resulting in low compensation accuracy. Summary of the Invention

[0005] To address the problem of low compensation accuracy mentioned in the background art, the present invention provides solutions in the following aspects.

[0006] In a first aspect, the present invention provides a method for compensating for thermal deformation of an optical mold based on finite element analysis, comprising: obtaining an initial three-dimensional model of the optical mold; performing finite element analysis on the initial three-dimensional model to obtain the normal error vector of each node of the optical mold; iteratively correcting the initial three-dimensional model to obtain a corrected optical mold, until the root mean square value of the normal error vector is less than a preset threshold; the iterative correction specifically involves: calculating the target node of the optical mold at the ... The local thermal stress intensity in the iteration, the local thermal stress intensity is related to the first iteration. In the next iteration, the stress value and curvature at the target node are positively correlated, and negatively correlated with the average temperature at each node within the neighborhood centered on the target node; the optical mold target node is calculated in the 1st iteration. The degree of anomaly in the iteration, which is positively correlated with the local thermal stress intensity, and with the... The second iteration and the first The dot product of the normal error vectors in the nth iteration is inversely correlated; the target node of the optical mold is obtained in the nth iteration. The adaptive local convergence factor in the nth iteration, which is inversely correlated with the degree of anomaly, is based on the adaptive local convergence factor and the nth iteration. The normal error vector of each iteration corrects the target node position of the optical mold until the set number of iterations is reached. The target node is any node among the nodes of the optical mold.

[0007] The above technical solution introduces an iterative correction mechanism combining local thermal stress intensity, node anomaly degree, and adaptive local convergence factor during the thermal deformation compensation process of optical molds. This enables precise control of each node of the mold under thermal load. Highly sensitive areas are identified by utilizing local thermal stress and curvature characteristics. At the same time, the local thermal non-uniformity is reflected by combining the neighborhood temperature distribution. The degree of node anomaly is quantified by dynamic analysis of error direction and amplitude in continuous iteration. Then, the node correction amplitude is adaptively adjusted so that high-risk nodes avoid overcompensation and low-risk nodes converge faster. This significantly improves the stability of the compensation process, the convergence efficiency, and the accuracy and consistency of the final optical mold surface. It achieves high-precision thermal deformation control and reliable engineering application results under complex curved surface and non-uniform thermal field conditions.

[0008] Furthermore, optical mold target node In the Local thermal stress intensity in the next iteration for: , , These are the target nodes of the optical mold. Stress value, curvature , These represent the maximum stress value and the maximum curvature, respectively. For the natural constant An exponential function with base 0. For the target node Within the neighborhood of the center Temperature values ​​at each node The mean value of the temperature at all nodes within the neighborhood is given. The total number of nodes within the neighborhood.

[0009] The above technical solution integrates the stress level, local curvature, and neighborhood temperature distribution of optical mold nodes into the calculation of local thermal stress intensity, thereby achieving a quantitative assessment of the node's sensitivity and potential deformation risk under thermal load. The stress value reflects the direct driving force of thermal load on material deformation, the curvature reflects the sensitivity of geometry to local deformation, and the neighborhood temperature dispersion reflects the influence of thermal field inhomogeneity on local stability. This multi-factor comprehensive calculation can accurately identify areas with high thermal deformation risk, providing a scientific basis for adaptively adjusting the node correction amplitude during iterative correction, thereby improving the pertinence and accuracy of thermal deformation compensation, avoiding local over- or under-correction, and significantly improving the surface accuracy and compensation reliability of optical molds under complex curved surfaces and non-uniform thermal field conditions.

[0010] Furthermore, optical mold target node In the Anomalies in the next iteration for: , For optical mold target node In the Local thermal stress intensity in the next iteration , These are the target nodes of the optical mold. In the sequence The normal error vector in the next iteration. The threshold for the normal error vector. For dot product, To find the magnitude of the vector.

[0011] The above technical solution constructs an anomaly index by combining the local thermal stress intensity of a node with the changes in the direction and amplitude of the normal error vector during continuous iteration. This allows the potential risks of each node during the iteration process to be quantified. The change in the direction of the error vector reflects whether the node correction deviates from the expected trend or oscillates. The ratio of the error amplitude to the threshold reflects the severity of the node's deviation from the design target. Furthermore, by combining the local thermal stress intensity with weighted high-sensitivity areas, the anomaly index can accurately identify nodes with high thermal deformation risk that require key correction. This provides a targeted basis for the iterative correction process and enables node-level adaptive adjustment.

[0012] Furthermore, optical mold target node In the Adaptive local convergence factor in the next iteration for: , , These are the preset minimum convergence factor and the preset global convergence factor, respectively. For the natural constant An exponential function with base 0. For optical mold target node In the The degree of anomaly in the next iteration.

[0013] The above technical solution achieves dynamic adjustment of the iterative correction step by coupling the anomaly degree of the nodes with the adaptive local convergence factor. The convergence factor corresponding to the nodes with high anomaly degree decays exponentially, thereby limiting their correction amplitude to prevent local overcompensation and oscillation. Meanwhile, the nodes with low anomaly degree maintain a larger correction step to accelerate the convergence process. This adaptive adjustment mechanism based on node risk assessment enables each node of the optical mold to autonomously adjust the correction amplitude according to the thermal deformation sensitivity and error trend during the iteration process, which significantly improves the stability of thermal deformation compensation, convergence efficiency and the accuracy and consistency of the final surface shape.

[0014] Furthermore, it also includes updating the positions of each node of the optical mold using an adaptive local convergence factor, specifically: , For optical mold target node In the Spatial position coordinates at the next iteration For optical mold target node In the Spatial position coordinates at the next iteration For optical mold target node In the The adaptive local convergence factor in the next iteration For optical mold target node In the The normal error vector at the next iteration.

[0015] The above technical solution combines the adaptive local convergence factor with the normal error vector of the node to dynamically update the spatial position of each node of the optical mold in each iteration. This allows the node correction amplitude to be automatically adjusted according to the degree of local anomaly. High-anomaly nodes have their update amplitude limited due to the decrease in the convergence factor, thus preventing over-correction and oscillation, while low-anomaly nodes maintain a larger update amplitude to accelerate the convergence speed. Overall, this forms a node-level adaptive iterative mechanism, enabling the optical mold to specifically correct local deformations under complex curved surfaces and non-uniform thermal field conditions. This significantly improves the stability of thermal deformation compensation, iterative convergence efficiency, and the accuracy and uniformity of the final surface shape.

[0016] Furthermore, the normal error vector is the difference vector between the actual deformation normal displacement of each node of the optical mold under thermal load conditions and the target design normal displacement.

[0017] Furthermore, the set number of iterations is the number of nodes.

[0018] Furthermore, the optical mold is at least one of an aspherical optical mold, a freeform surface optical mold, or a precision injection mold.

[0019] Furthermore, the curvature is obtained by fitting a quadratic surface to the target node and its neighboring nodes.

[0020] In a second aspect, the present invention provides an optical mold thermal deformation compensation system based on finite element analysis, comprising a memory and a processor, wherein the memory stores computer program instructions, and when the computer program instructions are executed by the processor, the optical mold thermal deformation compensation method based on finite element analysis described above is implemented.

[0021] The beneficial effects of this invention are as follows: This invention acquires an initial three-dimensional model of an optical mold and calculates the normal error vector of each node under thermal load using finite element analysis. It then constructs a thermal deformation compensation mechanism based on local node characteristics and iterative dynamic adjustment. The sensitivity of nodes to thermal load is quantified by the intensity of local thermal stress. The direction and amplitude changes of the error vector during continuous iteration are incorporated into the anomaly assessment. Based on the anomaly level, the convergence factor of the nodes is adaptively adjusted to achieve precise correction of each node's position. This prevents overcompensation in high-risk areas and allows for rapid convergence in low-risk areas, thus forming a node-level adaptive iterative optimization process. This not only improves compensation accuracy and convergence stability under complex curved surfaces and non-uniform thermal fields but also significantly improves the consistency and reliability of the optical mold's surface shape. Furthermore, it provides an efficient, predictable, and engineering-applicable solution for optical mold manufacturing and thermal deformation control. Attached Figure Description

[0022] Figure 1 This is a flowchart illustrating an optical mold thermal deformation compensation method based on finite element analysis according to an embodiment of the present invention; Figure 2 This is a schematic diagram illustrating the root mean square convergence curve of the normal error vector of an optical mold thermal deformation compensation method based on finite element analysis according to an embodiment of the present invention. Figure 3 This is a schematic diagram illustrating the structural block diagram of an optical mold thermal deformation compensation system based on finite element analysis according to an embodiment of the present invention. Detailed Implementation

[0023] An embodiment of a method for compensating for thermal deformation of optical molds based on finite element analysis.

[0024] like Figure 1 As shown, a flowchart of an optical mold thermal deformation compensation method based on finite element analysis according to an embodiment of the present invention is presented, including the following steps: S1: Obtain the initial 3D model of the optical mold.

[0025] In a preferred embodiment, the optical mold is at least one of an aspherical optical mold, a freeform surface optical mold, or a precision injection mold. The optical mold is three-dimensionally measured using a structured light measurement device, a laser interferometer, or a coordinate measuring machine to obtain spatial coordinate data of the mold surface, and the initial three-dimensional model is generated based on least-squares surface fitting or spline surface reconstruction.

[0026] By using structured light measurement equipment, laser interferometer, or coordinate measuring machine to perform three-dimensional measurement of the optical mold and obtain its surface spatial coordinate data, and then generating an initial three-dimensional model based on least squares surface fitting or spline surface reconstruction, the established three-dimensional model can truly reflect the real geometric shape of the optical mold under actual processing or use conditions. This effectively avoids the idealization error caused by relying solely on theoretical design models, thereby significantly improving the accuracy and consistency of node position, curvature distribution, and thermal deformation response calculations in subsequent finite element analysis, and enhancing the ability to perceive local geometric anomalies and high-precision surface errors during thermal deformation compensation.

[0027] S2: Perform finite element analysis on the initial three-dimensional model to obtain the normal error vector of each node of the optical mold.

[0028] In a preferred embodiment, the normal error vector is the difference vector between the actual deformation normal displacement of each node of the optical mold under thermal load conditions and the target design normal displacement.

[0029] By comparing the actual deformation displacement of each node of the optical mold along the node normal direction with the normal displacement corresponding to the target design surface under thermal load conditions, and using the difference vector between the two as the normal error vector, the obtained error information can directly characterize the substantial impact of thermal deformation on the effective optical surface. This avoids invalid interference introduced by tangential displacement or overall rigid body displacement, improves the correlation between error characterization and optical performance degradation, and makes the subsequent compensation iteration process more focused on the key directions affecting imaging quality and surface accuracy. This enhances the pertinence and effectiveness of geometric correction, thereby improving the reliability and stability of thermal deformation compensation results in optical precision control and engineering applications.

[0030] S3: Iteratively correct the initial three-dimensional model to obtain the corrected optical mold until the root mean square value of the normal error vector is less than a preset threshold.

[0031] like Figure 2 The figure shows a schematic diagram of the root mean square convergence curve of the normal error vector of an optical mold thermal deformation compensation method based on finite element analysis according to an embodiment of the present invention.

[0032] In a preferred embodiment, the iterative correction specifically involves: calculating the optical mold target node at the ... Local thermal stress intensity in the next iteration, optical mold target node In the Local thermal stress intensity in the next iteration for: , , These are the target nodes of the optical mold. Stress value, curvature , These represent the maximum stress value and the maximum curvature, respectively. For the natural constant An exponential function with base 0. For the target node Within the neighborhood of the center Temperature values ​​at each node The mean value of the temperature at all nodes within the neighborhood is given. This represents the total number of nodes within the neighborhood. The curvature is obtained by fitting a quadratic surface to the target node and its neighboring nodes.

[0033] Local thermal stress intensity is introduced during the iterative correction process. The stress level, surface geometry, and neighborhood temperature distribution at the target node are coupled and modeled. The stress term describes the direct driving effect of thermal load on material deformation, the curvature term amplifies the influence of high curvature regions on thermal deformation sensitivity, and the neighborhood temperature dispersion reflects the disturbance effect of local thermal field inhomogeneity on deformation stability. At the same time, a quadratic surface fitting method is used to obtain the node curvature to ensure the continuity and noise resistance of geometric feature extraction. Thus, the obtained local thermal stress intensity can more realistically characterize the comprehensive risk level of abnormal deformation in different regions under thermal action.

[0034] Calculate the target node of the optical mold at the th Anomaly level in the next iteration, optical mold target node In the Anomalies in the next iteration for: , For optical mold target node In the Local thermal stress intensity in the next iteration , These are the target nodes of the optical mold. In the sequence The normal error vector in the next iteration. The threshold for the normal error vector. For dot product, To find the magnitude of the vector.

[0035] By combining the local thermal stress intensity of a node with the changing characteristics of the normal error vector during the iteration process, the thermal deformation sensitivity of a node in the current iteration is comprehensively evaluated with the consistency of the displacement direction in the previous iteration and the relative magnitude of the error amplitude. The change in the direction of the error vector reflects whether the node correction has oscillated or deviated from the expected trend, and the ratio of the error amplitude to the threshold reflects the severity of the deformation deviation from the design target. Combined with the weight of the local thermal stress intensity, the degree of anomaly can accurately quantify the potential risks and correction priorities of each node in the iteration process, thereby enabling targeted adjustment of the node correction step in subsequent iterations to avoid over-correction in highly sensitive areas or under-correction in low-sensitive areas.

[0036] Obtain the target node of the optical mold at the first The adaptive local convergence factor in the next iteration, the optical mold target node In the Adaptive local convergence factor in the next iteration for: , , These are the preset minimum convergence factor and the preset global convergence factor, respectively. For the natural constant An exponential function with base 0. For optical mold target node In the The degree of anomaly in the next iteration.

[0037] By mapping the anomaly level of nodes to an adaptive local convergence factor, the dynamic adjustment of the iterative correction step size is achieved. For nodes with higher anomaly levels, the corresponding convergence factor decays exponentially, thereby reducing the correction amplitude to avoid overcompensation of high-risk areas. Nodes with low anomaly levels, on the other hand, maintain a larger correction step size to accelerate the convergence speed. Overall, an automatic adjustment iterative control mechanism is formed, enabling each node to adaptively adjust the correction amplitude according to the local thermal deformation sensitivity and error trend during the iteration process, thereby improving the stability of thermal deformation compensation, convergence efficiency, and the accuracy and consistency of the final optical surface shape.

[0038] Based on the aforementioned adaptive local convergence factor and the first The normal error vector of each iteration corrects the target node position of the optical mold until a set number of iterations is reached. The target node is any node among the nodes of the optical mold. The set number of iterations is the number of nodes, but it can also be set according to the actual situation.

[0039] It also includes updating the positions of each node of the optical mold using an adaptive local convergence factor, specifically: , For optical mold target node In the Spatial position coordinates at the next iteration For optical mold target node In the Spatial position coordinates at the next iteration For optical mold target node In the The adaptive local convergence factor in the next iteration For optical mold target node In the The normal error vector at the next iteration.

[0040] By combining the adaptive local convergence factor with the normal error vector of the nodes, the spatial position of each node of the optical mold is updated in each iteration. This allows the correction amplitude of the nodes to be automatically adjusted according to the degree of local anomaly. Nodes with high anomaly levels have limited update amplitudes due to the decrease in the convergence factor, thus avoiding overcorrection that could cause oscillations or local shifts. Nodes with low anomaly levels maintain larger update amplitudes to accelerate the convergence process. This forms a node-level adaptive iterative mechanism that enables the optical mold to specifically correct local deformations during the iteration process, thereby improving the stability and convergence efficiency of thermal deformation compensation.

[0041] The present invention constructs an iterative compensation method and system based on finite element analysis, which realizes precise control of each node of an optical mold under thermal load. It utilizes an initial three-dimensional model combined with local thermal stress, curvature characteristics, and neighborhood temperature distribution of the nodes to assess local sensitivity. Through continuous iterative calculation of node anomalies and adaptive adjustment of local convergence factors, the correction magnitude of each node can dynamically match its thermal deformation risk, thereby avoiding over- or under-correction. Simultaneously, the normal error vector guides the node position update, gradually bringing the mold surface closer to the design target. This achieves stable convergence and surface optimization under high-precision, multi-node, complex surface, and non-uniform thermal field conditions. This method not only improves the accuracy and uniformity of thermal deformation compensation for optical molds but also enhances the stability and efficiency of the iterative process, providing a reliable engineering application solution for the manufacturing of complex optical components. Furthermore, the compensation process can be automated through computer system implementation, significantly improving production efficiency and controllability.

[0042] An embodiment of an optical mold thermal deformation compensation system based on finite element analysis: like Figure 3 As shown, a structural block diagram of an optical mold thermal deformation compensation system based on finite element analysis according to an embodiment of the present invention is presented. The system includes a processor and a memory. The memory stores computer program instructions. When the computer program instructions are executed by the processor, the above-described optical mold thermal deformation compensation method based on finite element analysis according to the present invention is implemented.

[0043] The optical mold thermal deformation compensation system based on finite element analysis also includes other components well known to those skilled in the art, such as communication interfaces. Their settings and functions are known in the art and will not be described in detail here.

[0044] In this invention, the aforementioned memory can be any tangible medium containing or storing a program that can be used or combined with an instruction execution system, apparatus, or device. For example, a computer-readable storage medium can be any suitable magnetic or magneto-optical storage medium, such as Resistive Random Access Memory (RRAM), Dynamic Random Access Memory (DRAM), Static Random Access Memory (SRAM), Enhanced Dynamic Random Access Memory (EDRAM), High-Bandwidth Memory (HBM), Hybrid Memory Cube (HMC), etc., or any other medium that can be used to store desired information and can be accessed by an application, module, or both. Any such computer storage medium can be part of a device or accessible to or connected to a device. Any application or module described in this invention can be implemented using computer-readable / executable instructions stored or otherwise maintained by such a computer-readable medium.

[0045] In the description of this specification, "multiple" or "several" means at least two, such as two, three or more, unless otherwise explicitly specified.

[0046] While this specification has shown and described numerous embodiments of the invention, it will be apparent to those skilled in the art that such embodiments are provided by way of example only. Many modifications, alterations, and alternatives will occur to those skilled in the art without departing from the spirit and essence of the invention. It should be understood that various alternatives to the embodiments of the invention described herein may be employed in the practice of this invention.

Claims

1. A method for compensating for thermal deformation of optical molds based on finite element analysis, characterized in that, include: Obtain the initial 3D model of the optical mold; Finite element analysis is performed on the initial three-dimensional model to obtain the normal error vector of each node of the optical mold. The normal error vector is the difference vector between the actual deformation normal displacement of each node of the optical mold under thermal load and the target design normal displacement. The initial three-dimensional model is iteratively corrected. When the root mean square value of the normal error vector is less than a preset threshold, or when the current iteration number reaches the set iteration number, the iterative correction is stopped, and the corrected optical mold is obtained. The iterative correction specifically involves: calculating the optical mold target node at the [number]th [time]. Local thermal stress intensity in the next iteration, optical mold target node In the Local thermal stress intensity in the next iteration for: , , These are the target nodes of the optical mold. Stress value, curvature , These represent the maximum stress value and the maximum curvature, respectively. For the natural constant An exponential function with base 0. For the target node Within the neighborhood of the center Temperature values ​​at each node The mean value of the temperature at all nodes within the neighborhood is given. The total number of nodes within the neighborhood; Calculate the target node of the optical mold at the th The degree of anomaly in the iteration, which is positively correlated with the local thermal stress intensity, and with the... The second iteration and the first The dot product of the normal error vectors in the nth iteration is inversely correlated; the target node of the optical mold is obtained in the nth iteration. The adaptive local convergence factor in the nth iteration, which is inversely correlated with the degree of anomaly, is based on the adaptive local convergence factor and the nth iteration. The normal error vector of each iteration corrects the target node position of the optical mold until the set number of iterations is reached. The target node is any node among the nodes of the optical mold.

2. The method for compensating for thermal deformation of optical molds based on finite element analysis according to claim 1, characterized in that, Optical mold target node In the Anomalies in the next iteration for: , For optical mold target node In the Local thermal stress intensity in the next iteration , These are the target nodes of the optical mold. In the sequence The normal error vector in the next iteration. The threshold for the normal error vector. For dot product, To find the magnitude of the vector.

3. The method for compensating for thermal deformation of optical molds based on finite element analysis according to claim 1, characterized in that, Optical mold target node In the Adaptive local convergence factor in the next iteration for: , , These are the preset minimum convergence factor and the preset global convergence factor, respectively. For the natural constant An exponential function with base 0. For optical mold target node In the The degree of anomaly in the next iteration.

4. The method for compensating for thermal deformation of optical molds based on finite element analysis according to claim 1, characterized in that, This also includes updating the positions of each node of the optical mold using an adaptive local convergence factor, specifically: , For optical mold target node In the Spatial position coordinates at the next iteration For optical mold target node In the Spatial position coordinates at the next iteration For optical mold target node In the The adaptive local convergence factor in the next iteration For optical mold target node In the The normal error vector at the next iteration.

5. The method for compensating for thermal deformation of optical molds based on finite element analysis according to claim 1, characterized in that, The set number of iterations is the number of nodes.

6. The method for compensating for thermal deformation of optical molds based on finite element analysis according to claim 1, characterized in that, The optical mold is at least one of an aspherical optical mold, a freeform surface optical mold, or a precision injection mold.

7. The method for compensating for thermal deformation of optical molds based on finite element analysis according to claim 1, characterized in that, The curvature is obtained by fitting a quadratic surface to the target node and its neighboring nodes.

8. A thermal deformation compensation system for optical molds based on finite element analysis, characterized in that, It includes a memory and a processor, wherein the memory stores computer program instructions, and when the computer program instructions are executed by the processor, it implements the optical mold thermal deformation compensation method based on finite element analysis as described in any one of claims 1 to 7.

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