Aspherical lens grinding and polishing method based on curvature partition matching

Abstract

The present application relates to the technical field of optical processing, and specifically provides a kind of aspheric lens grinding and polishing method based on curvature partition matching, first determine the target surface shape and surface shape residual of aspheric lens, and calculate the curvature distribution of aspheric lens according to target surface shape, according to curvature distribution, the surface to be processed of aspheric lens is divided, and according to the size and curvature of each sub-processing area, the corresponding processing tool is selected, the initial residence time distribution on processing trajectory is calculated according to the removal function of processing tool, finally, through simulation, anti-collision iterative correction is carried out, finally, according to the adjusted processing trajectory, removal function and residence time distribution, parallel processing is carried out.The present application not only improves the processing efficiency through multi-robot collaborative processing, but also improves the removal function stability and processing precision by improving the grinding disc processing fit.

Description

Technical Field

[0001] This invention belongs to the field of optical processing technology, and in particular relates to a method for polishing aspherical lenses based on curvature partition matching. Background Technology

[0002] As our understanding of the universe deepens, higher demands are placed on telescope technology, requiring greater surface accuracy and larger effective apertures. Increasing the aperture of the primary mirror, either by enlarging individual lenses or by combining multiple lenses, significantly improves system resolution. Simultaneously, to eliminate aberrations, lenses are often designed as aspherical mirrors, such as quadratic surfaces. In optical processing, Computer-Controlled Optical Surface Forming (CCOS) technology achieves quantitative material removal by controlling the dwell time of a small grinding head on the lens surface, thereby improving processing accuracy and enabling the fabrication of aspherical mirrors.

[0003] Currently, in the process of polishing optical mirrors using industrial robots, a single robot drives a small tool head to process the aforementioned large-diameter aspherical optical components. This method is inefficient. Furthermore, the radius of curvature varies at different locations on the aspherical lens. Using a grinding wheel with a constant curvature to process the entire aspherical surface results in curvature mismatch during processing, leading to uneven pressure distribution on the grinding wheel, severe wear on the grinding wheel, and consequently, unstable removal function and reduced processing accuracy. Summary of the Invention

[0004] In view of this, the present invention aims to provide a method for polishing aspherical lenses based on curvature partition matching. By accurately partitioning the surface curvature of the lens and matching a grinding wheel with a suitable curvature to each partition, multiple robots control different grinding wheels to process multiple partitions simultaneously and collaboratively. This not only improves processing efficiency through multi-robot collaborative processing, but also improves the grinding wheel processing fit, and enhances the stability of the removal function and processing accuracy.

[0005] To achieve the above objectives, the technical solution created by this invention is implemented as follows: This invention provides a method for polishing aspherical lenses based on curvature partition matching, comprising: S1: Determine the target surface shape and initial surface shape of the aspherical lens, obtain the surface shape residual of the aspherical lens based on the target surface shape and initial surface shape, and calculate the curvature distribution of the aspherical lens based on the target surface shape; S2: Based on the curvature distribution, the surface to be processed of the aspherical lens is divided into N continuous sub-processing regions; S3: Select the corresponding machining tool based on the size and curvature of each sub-machining area, and measure the removal function of each machining tool under preset conditions; S4: Set the machining trajectory of the corresponding machining tool in each sub-machining area, and calculate the initial dwell time distribution on the machining trajectory based on the removal function of the corresponding machining tool; S5: Predict the risk of tool collisions during parallel machining through simulation, and adjust the process parameters and initial dwell time distribution according to the simulation prediction results to ensure that the distance between tools is always greater than the safe distance throughout the entire machining process. S6: After adjustment by S5, determine the processing trajectory, removal function, process parameters and final dwell time distribution of each processing tool, and control each processing tool accordingly to process aspherical lenses in parallel according to curvature zones.

[0006] Preferably, in S1, the formula for calculating the curvature distribution of the aspherical lens based on the target surface shape is: ; Where C represents the curvature of the aspherical lens at a radial distance r, and r represents the radial distance from any point on the aspherical lens to the optical axis of the mirror. , Represents the coordinates of any point. Represents the target surface shape function of an aspherical lens The first derivative, Represents the target surface shape function of an aspherical lens The second derivative of .

[0007] Preferably, the range of mirror curvature distribution within any sub-processing area is... Represented as: ; in, Indicates any sub-processing region; The mirror curvature distribution range within each sub-processing area must meet the following requirements: ; in, This indicates the curvature tolerance of the grinding wheel of the machining tool corresponding to the sub-machining area.

[0008] Preferably, adjacent sub-processing areas and There is a pre-defined overlapping area between the two sub-processing areas. The width of the overlapping area is set according to the grinding wheel size of the processing tools in the corresponding two sub-processing areas.

[0009] Preferably, the width of the overlapping area is equal to the sum of the grinding disc diameters of the machining tools in the corresponding two sub-machining areas.

[0010] Preferably, in S3, the dimensions of each machining tool need to meet the following requirements: ; in, This represents the diameter of any machining tool. This represents the minimum width of the sub-processing area corresponding to any given processing tool; The curvature of each machining tool must satisfy: Within each sub-processing area, the machining tool selects the curvature with the largest machining area within that sub-processing area, or selects the median of the curvature within that sub-processing area.

[0011] Preferably, in S4, the initial dwell time distribution on the processing trajectory is calculated using the following set of convolution equations: ; in, This represents the convolution operation, where z represents the discretized surface residual. This represents the removal function for N processing tools within N sub-processing regions. This represents the initial dwell time distribution of these N machining tools under the removal function condition.

[0012] Preferably, in S5, by changing the rotation speed of the corresponding machining tools within the sub-machining area, the distance between the machining tools is always greater than the safe distance throughout the entire machining process.

[0013] Preferably, S5 includes: The parallel machining process is simulated based on the machining trajectory, rotation speed, and initial dwell time distribution of each machining tool obtained from S4, to determine the position of each machining tool and the distance between machining tools after machining time t. Mark all processing times and corresponding processing tools where the distance between processing tools is less than the safe distance; Adjust the rotational speed of at least one of the two machining tools whose distance is less than the safe distance; The dwell time distribution of all machining tools is updated based on the adjusted rotation speed. The machining trajectory, removal function, rotation speed and final dwell time distribution of each machining tool are determined through iterative updates, so that the distance between machining tools is always greater than the safe distance throughout the entire machining process.

[0014] Preferably, each processing tool is controlled by an independent robot.

[0015] Compared with the prior art, the present invention can achieve the following beneficial effects: This invention effectively solves the problems of poor fit and uneven pressure distribution caused by curvature mismatch when processing with a single constant curvature grinding wheel by precisely dividing the curvature of large-diameter aspherical lenses and matching a grinding wheel with a suitable curvature to each sub-region. This ensures the stability of the removal function and thus significantly improves the surface processing accuracy. Furthermore, by employing multiple robots to control grinding wheels with different curvatures and simultaneously processing each sub-region in parallel, the traditional single-tool processing mode is transformed into multi-region, multi-tool parallel processing, effectively shortening the mirror polishing cycle and greatly improving processing efficiency.

[0016] This invention uses grinding discs with different curvatures to adapt to different curvature zones of the mirror surface, making the contact pressure between the grinding disc and the mirror surface more uniform and the grinding effect better. In addition, overlapping areas are set between adjacent sub-processing areas to achieve a smooth transition of material removal amount and avoid the seams or abrupt changes in surface shape that may occur during zone processing.

[0017] This invention predicts the collision risk between tools through simulation and actively avoids these risks by adjusting parameters, ensuring the safety and reliability of the machining process. The design scheme is feasible. Attached Figure Description

[0018] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments and descriptions of the invention are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 This is a flowchart of an aspherical lens polishing method based on curvature partition matching according to an embodiment of the present invention; Figure 2 This is a target surface shape diagram of a rotationally symmetric aspherical lens provided according to an embodiment of the present invention; Figure 3 This is a curvature distribution diagram of a rotationally symmetric aspherical lens provided according to an embodiment of the present invention; Figure 4 This is a target surface shape diagram of an off-axis aspherical lens provided according to an embodiment of the present invention; Figure 5 This is a curvature distribution diagram of an off-axis aspherical lens provided according to an embodiment of the present invention; Figure 6 This is a schematic diagram of the partition trajectory of a rotationally symmetric aspherical lens according to an embodiment of the present invention; Figure 7 This is a schematic diagram of the partition trajectory of an off-axis aspherical lens according to an embodiment of the present invention.

[0019] The reference numerals in the figures include: Mirror boundary 1, machining trajectory 2, overlapping area 3, sub-machining area Boundary 4, Sub-processing Area Boundary 5, Sub-processing Area Boundary 6. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only for explaining the invention and do not constitute a limitation thereof. Similar elements in different embodiments are referred to by associated similar element reference numerals. In the following embodiments, many details are described to facilitate a better understanding of the invention. However, those skilled in the art will readily recognize that some features may be omitted in different situations, or may be replaced by other elements, materials, or methods. In some cases, some operations related to the invention are not shown or described in the specification. This is to avoid obscuring the core parts of the invention with excessive description. For those skilled in the art, detailed description of these related operations is not necessary; the relevant operations can be fully understood based on the description in the specification and general technical knowledge in the art.

[0021] It should be noted that, unless otherwise specified, the embodiments and features described in this invention can be combined to form various implementations. Furthermore, the order of the steps or actions in the method description can be changed or adjusted in a manner readily apparent to those skilled in the art. Therefore, the various orders in the specification and drawings are merely for the clear description of a particular embodiment and do not imply a mandatory order, unless otherwise stated that a particular order must be followed.

[0022] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," and "counterclockwise," etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on this invention. Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, features defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0023] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0024] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0025] Please see Figure 1 In one embodiment of the present invention, a method for polishing aspherical lenses based on curvature partition matching is provided, comprising the following steps: S1: Determine the target surface shape and initial surface shape of the aspherical lens, obtain the surface shape residual of the aspherical lens based on the target surface shape and initial surface shape, and calculate the curvature distribution of the aspherical lens based on the target surface shape; S2: Based on the curvature distribution, the surface to be processed of the aspherical lens is divided into N continuous sub-processing regions; S3: Select the corresponding machining tool based on the size and curvature of each sub-machining area, and measure the removal function of each machining tool under preset conditions; S4: Set the machining trajectory of the corresponding machining tool in each sub-machining area, and calculate the initial dwell time distribution on the machining trajectory based on the removal function of the corresponding machining tool; S5: Predict the risk of tool collisions during parallel machining through simulation, and adjust the process parameters and initial dwell time distribution according to the simulation prediction results to ensure that the distance between tools is always greater than the safe distance throughout the entire machining process. S6: After adjustment by S5, determine the processing trajectory, removal function, process parameters and final dwell time distribution of each processing tool, and control each processing tool accordingly to process aspherical lenses in parallel according to curvature zones.

[0026] In step S1, the target surface shape of the aspherical lens is first determined, and the target surface shape function is... Represented as: ; in This is the off-axis offset, representing the displacement of the center of the current aspherical lens surface region relative to the vertex of the "parent aspherical surface"; for coaxial (non-off-axis) aspherical surfaces, ;parameter Let be the curvature of the vertex of the parent aspherical surface; Let be the conic constant of the parent aspherical surface. is the even-order aspheric coefficient of the parent aspheric surface.

[0027] Then, the initial surface shape of the aspherical lens before processing is obtained using measuring equipment such as an interferometer. The initial surface shape measured by the interferometer is a set of discrete data, which can be represented as... ,in The coordinates of a discrete surface point on the aspherical lens before processing are given. This represents the total number of discrete surface shape points on the aspherical lens. Simultaneously, the surface shape residual is obtained based on the target surface shape and the initial surface shape of the aspherical lens. , ,in, Discrete points on the aspherical lens before processing The sag difference relative to the target surface shape, i.e., during optical processing Target removal amount at location. When A positive value indicates that the point is convex and more material needs to be removed, while a negative value indicates that it is concave and less or no material needs to be removed.

[0028] To facilitate subsequent calculations of curvature distribution, the aforementioned target surface shape function needs to be... Convert to polar coordinates. Let Then the target surface shape function can be written in polar coordinates as follows: .

[0029] Using the curvature formula in differential geometry, calculate the discrete points on the full aperture of the aspherical lens. The curvature distribution along the meridian of the parent aspherical surface is as follows: ; Where C represents the curvature of the aspherical lens at a radial distance r, and r represents the radial distance from any point on the aspherical lens to the optical axis of the mirror. , Represents the coordinates of any point. Represents the target surface shape function of an aspherical lens The first derivative, Represents the target surface shape function of an aspherical lens The second derivative of .

[0030] This yields the curvature distribution matrix corresponding one-to-one with the discrete points of the surface. This serves as the basis for subsequent partitioning processes.

[0031] Depending on the type of aspherical lens, the calculated curvature distribution will also differ, such as... Figure 2 As shown, this is the target surface shape of a rotationally symmetric aspherical lens. Figure 3correspond Figure 2 The curvature distribution of rotationally symmetric aspherical lenses. For example... Figure 4 The image shown is the target surface shape of an off-axis aspherical lens. Figure 5 correspond Figure 4 Curvature distribution of off-axis aspherical lenses.

[0032] In step S2, based on the curvature distribution obtained in step 1 The surface to be processed of the aspherical lens is divided into N consecutive sub-processing regions. ( Define each sub-processing area. Curvature distribution range within for: ; in, Indicates any sub-processing region. Indicates the upper limit of curvature. This indicates the lower limit of curvature.

[0033] Each sub-processing area The range of mirror curvature distribution within the interior must meet the following conditions: ; in, This indicates the curvature tolerance of the grinding wheel corresponding to the sub-machining area, representing the grinding wheel's ability to effectively adapt to changes in the workpiece's surface curvature. Different grinding wheels are required for different processing stages of optical lenses (e.g., rough grinding, fine grinding, polishing). Correspondingly, different grinding wheels... And so it changes. Grinding disc curvature tolerance The specific values ​​are related to factors such as the size and material of the grinding disc, the processing pressure, and the type of abrasive. These values ​​can be determined by calculating the actual processing parameters. This constraint ensures that the grinding disc matched to each sub-processing area can better fit the lens surface of that area, guaranteeing the stability of the removal function at each point on the grinding disc.

[0034] In the process of dividing sub-processing areas, an iterative segmentation method can be adopted, specifically through iterative segmentation from the outside in or from the inside out. For example, starting from the edge of the lens, with a curvature change not exceeding... To constrain the region, the area is gradually expanded until the constraint boundary is reached, thus completing the division of a sub-region; then the division of the next sub-region begins from that boundary, until the entire mirror surface is covered.

[0035] As an optional embodiment, considering the need to select appropriate processing tools based on the curvature distribution characteristics of different sub-processing regions, and the fact that the removal functions of the grinding discs in different sub-processing regions are generally different, if an absolutely isolated partitioning method is adopted, with different grinding discs on both sides of the boundary of the sub-processing region, the abrupt change in the removal function at the boundary will cause discontinuity in the amount of material removed, thus creating seams. Therefore, in this embodiment of the invention, adjacent sub-processing regions are partitioned... and Set to non-absolute isolation, i.e.: ; The above formula shows that adjacent sub-processing areas and An overlapping area is pre-defined between the two tools. Within this area, both tools will perform processing. Optimizing subsequent dwell time allows for a smooth transition, suppressing the seam effect caused by partitioned processing. The width of the overlapping area... That is, after iterative segmentation, two adjacent sub-processing regions expand outward along the region boundary by a certain width. The expansion width of the two sub-processing regions is equal to the grinding disc diameter of the corresponding processing tool in their respective regions. Finally, the width of the overlapping region is equal to the sum of the grinding disc diameters of the processing tools in the two corresponding sub-processing regions.

[0036] In step S3, for the sub-processing regions obtained in step S2, a suitable processing tool is selected based on the size and curvature of each sub-processing region. The size of the processing tool corresponding to each sub-processing region needs to meet the following requirements: ; in, This represents the diameter of any machining tool. This indicates the minimum width of the sub-processing area corresponding to any processing tool; this condition ensures that the grinding wheel of the processing tool can move flexibly within the sub-processing area, avoiding the inability to cover the edge or interference due to the grinding wheel size being too large.

[0037] After selecting the grinding wheel size of the machining tool, it is also necessary to select the grinding wheel curvature of the machining tool according to the curvature distribution of each sub-machining area to achieve curvature matching between the sub-machining area and the grinding wheel of the machining tool, thereby improving the fit rate and grinding accuracy during the machining process. Typically, the grinding wheel curvature of the machining tool within each sub-machining area is selected based on the curvature of the largest machining area within that sub-machining area, or the median of the curvature within that sub-machining area. Other curvature matching methods may also be used depending on the machining design requirements.

[0038] For the sub-processing area, select the area within a certain curvature tolerance range. Internal processing area Maximum curvature First, define a judgment function. It is represented as: ; The above formula considers surface points within a preset curvature tolerance range as constraints. Points outside this tolerance range are not considered during the tool curvature selection process. Therefore, each curvature corresponds to an effective machining area. It can be represented as: ; Furthermore, the optimal matching curvature of the grinding wheel for the machining tool can be determined. for: ; The median curvature within the sub-processing region can be directly determined using the following formula: [Median Curvature within the processing region]. for: .

[0039] At this point, each sub-processing area has been assigned a corresponding processing tool. After the processing tools and sub-processing areas are bound together, the removal function of each processing tool needs to be measured under certain preset conditions. Specifically, a test piece with the same material and parameters as the aspherical lens to be processed is used, and a single-point processing experiment is conducted under determined process parameters. The initial pressure of the processing tool on the sub-processing area is set to... The initial rotational speed of the machining tool itself is Under these preset conditions, the selected processing tool's grinding disc is used to perform point polishing on the experimental piece to form polishing spots.

[0040] By measuring the depth profile of the polishing spot, the removal function of the tool is obtained. The removal function is a discretized distribution of data. The discretized data of the removal function is then processed. (Removal function) is expressed as: ; in, Indicates sub-processing area The position of the grinding disc of the matched machining tool on the experimental piece Material removal rate at the site This is to remove the total number of discrete data points for the function.

[0041] In step S4, after determining the partitioning of the sub-processing areas, the processing tools and their removal functions for each sub-processing area, and the surface residual before processing the aspherical lens, the processing trajectory of the corresponding processing tool can be set in each sub-processing area. The form of the processing trajectory includes, but is not limited to, grating trajectories, spiral trajectories, or circular trajectories. The spacing between dwell points on the processing trajectory and the spacing between adjacent trajectories can be determined according to the shape of the sub-processing area, the grinding wheel size of the processing tool, and the processing requirements. Taking the processing trajectory corresponding to any nth processing tool as an example, J dwell points are set on the trajectory, and the three-dimensional coordinates of each dwell point... Represented as: .

[0042] Since each machining tool corresponds to an independent robot responsible for drive and control, to ensure the safe start-up of multi-robot collaborative parallel processing, the starting machining point of the machining tool in each sub-machining area is determined. The spatial distance between them must be greater than the preset safety distance. To prevent collisions during startup, the starting points of all machining tools must satisfy the following conditions: ; in, and This represents the starting point of any two machining tools.

[0043] like Figure 6 As shown, for rotationally symmetric aspherical lenses, the above constraint design can be used to design lenses as follows. Figure 6 The partitioning and processing trajectory 2 in the diagram divide the mirror surface of the rotationally symmetric aspherical lens into three sub-processing regions, and these sub-processing regions are marked. Boundary 4, Sub-processing Area Boundary 5 and sub-processing area Boundary 6, along the sub-processing area Boundary 4 and Sub-processing Area The boundary 5 is extended to include overlapping areas 3.

[0044] Similarly, for off-axis aspherical lenses, such as Figure 7 As shown, after the above constraint design, the following can be designed: Figure 7 The partitioning and processing trajectory 2 in the diagram divide the off-axis aspherical lens into three sub-processing areas within the lens boundary 1, and these sub-processing areas are marked. Boundary 4, Sub-processing Area Boundary 5 and sub-processing area Boundary 6, along the sub-processing area Boundary 4 and Sub-processing Area The boundary 5 is extended to include overlapping areas 3.

[0045] After the processing trajectory 2 is designed, a dwell time solution model needs to be established and solved to obtain the final dwell time at each dwell point. In this embodiment of the invention, a multi-tool material removal model based on convolution is used to solve the dwell time. The removal amount of the aspherical lens is represented by z. In the processing stage, z is the discretized surface residual obtained in step S1. After achieving this removal amount z, the aspherical lens achieves the target surface shape. The removal functions of each processing tool are expressed as follows: Let the initial dwell time distribution of these N machining tools under the removal function condition be expressed as follows: Therefore, the following set of convolution equations can be obtained: ; in, The above formula represents the convolution operation, which can be used to calculate the initial dwell time distribution of the corresponding machining tool on each machining trajectory.

[0046] Discretizing the above convolution equations at discrete lens surface data points and discrete dwell points of the machining trajectories of each machining tool can transform them into a large system of linear equations: ; Where I represents the total number of discrete surface shape data points of the lens, and N corresponds to N sub-processing areas and N processing tools, or N processing trajectories. This indicates the number of dwell points of these N machining tools on the corresponding machining trajectory. This represents the amount of target material removed (i.e., surface residual) for each surface data point on the mirror surface. , , ..., These represent the dwell time distribution of each machining tool on its corresponding machining trajectory, with each element in the matrix corresponding to the dwell time at each specific dwell point on the machining trajectory. , , ..., These represent the influence coefficient matrices of the removal rate of each processing tool on the surface data points. For any element in these matrices... Indicates the first The tool on its trajectory During processing at each station, the first [item] on the lens The amount of material removed per unit time at each surface data point location.

[0047] Furthermore, the amount of material removed at any surface data point during multi-tool, multi-path machining processes will be further analyzed. Represented as:

[0048] ; The linear equations from the previous section can then be further transformed into: .

[0049] Since each dwell point needs to satisfy the non-negativity requirement of dwell time during the processing, solving for the initial dwell time distribution becomes solving for the optimal non-negativity solution of the above linear equation system:

[0050] Where λ is the Tikhonov regularization coefficient, which is introduced to improve the stability of the solution and obtain the solution of the optimal dwell time distribution of each machining tool. This formula allows us to obtain an optimal residence time distribution while ensuring that all residence times are non-negative, thus minimizing the sum of the squared error and the regularization term.

[0051] In step S5, since multiple robots perform parallel synchronous grinding, this embodiment of the invention also needs to predict the collision risk between various processing tools through simulation, and ensure a safe distance by dynamically adjusting process parameters (such as rotational speed) and initial dwell time distribution. Adjusting the process parameters will cause the removal function obtained in step S3 to change. In this embodiment of the invention, the removal function is changed by adjusting the rotational speed of the processing tool itself, and the initial dwell time distribution of the processing tool is also changed to ensure that the distance between all processing tools is always greater than the safe distance throughout the entire processing stage. The specific simulation and adjustment process is as follows: S51: Simulate the entire parallel machining process based on the initial dwell time distribution of each machining tool, the removal function, and the planned machining trajectory. Calculate the position of each machining tool after machining time t. Distance between and processing tools , and This represents the distance between two corresponding machining tools in any two sub-machining regions after machining time t.

[0052] S52: On the complete machining timeline, examine all moments to determine the tool spacing. Less than or equal to the safe distance time period And the corresponding two processing tools will appear The two machining tools are denoted as Toola and Toolb.

[0053] S53: Adjust the rotational speed of Toola and / or Toolb, changing the rotational speed of the two machining tools at their dwell points during the conflict period and the preceding and following buffer periods. ,in These are the speed adjustment parameters. Depending on the actual operating conditions, the following adjustment strategies can be selected: Increasing the speed of a single machining tool ( ); Reduce the speed of a single machining tool ( ); Simultaneously adjust the speed of two machining tools: (One increases, one decreases); Simultaneously reduce the speed of two machining tools, but with different changes in speed: ; Simultaneously increasing the speed of two machining tools, but with different changes in speed: .

[0054] S54: Update the dwell time distribution of all machining tools based on the adjusted rotational speed to ensure that the removal amount remains unchanged. The update of the dwell time distribution is based on the convolution-based removal model of the machining tools. The convolution-based removal model is as follows: ; in, This represents the amount of data points removed from any surface shape. This represents the removal function. Indicates the distribution of stay time. Indicates the rotational speed of the machining tool. This indicates the pressure exerted by the machining tool on the grinding point.

[0055] While maintaining a constant removal rate, the rotational speed of the machining tools is adjusted using the above formula, thereby altering the residence time distribution. After each update of the rotational speed and residence time distribution, it cannot be determined whether the distance between the machining tools remains greater than the safe distance throughout the entire machining process. Therefore, steps 51 and 52 need to be repeated based on the updated residence time until the entire machining time is reached. Thus, the machining trajectory, removal function, rotation speed, and final dwell time distribution of each machining tool were obtained.

[0056] In step S6, the machining trajectory, removal function, rotation speed, and final dwell time distribution of each machining tool obtained after adjustment in step S5 are used to generate a mod file for each robot to execute. Each robot controls each machining tool to execute the corresponding mod file to polish each sub-machining area. Aspherical lenses are processed in parallel according to curvature zones.

[0057] Furthermore, when the target surface shape of the aspherical lens is a rotationally symmetric surface shape, the sub-processing areas divided in step 2... In the case of multiple concentric rings, the robot's movement can be controlled without controlling it. Instead, the aspherical lens can be placed on a turntable, and the turntable can be used to drive the aspherical lens to achieve relative movement between the processing tool and the aspherical lens. This also allows multiple robots to process in parallel according to curvature zones.

[0058] In summary, the above description is merely a preferred embodiment of this specification and is not intended to limit the scope of protection of this specification. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this specification should be included within the scope of protection of this specification.

[0059] The systems, apparatuses, modules, or units described in one or more of the above embodiments may be implemented by a computer chip or entity, or by a product having a certain function. A typical implementation device is a computer. Specifically, a computer may be, for example, a personal computer, a laptop computer, a cellular phone, a camera phone, a smartphone, a personal digital assistant, a media player, a navigation device, an email device, a game console, a tablet computer, a wearable device, or any combination of these devices.

[0060] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0061] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to interchangeably. Each embodiment focuses on describing the differences from other embodiments. In particular, the system embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions in the method embodiments.

Claims

1. A method for polishing aspherical lenses based on curvature partition matching, characterized in that, include: S1: Determine the target surface shape and initial surface shape of the aspherical lens, obtain the surface shape residual of the aspherical lens based on the target surface shape and the initial surface shape, and calculate the curvature distribution of the aspherical lens based on the target surface shape; S2: Based on the curvature distribution, the surface to be processed of the aspherical lens is divided into N continuous sub-processing regions; S3: Select the corresponding machining tool based on the size and curvature of each sub-machining area, and measure the removal function of each machining tool under preset conditions; S4: Set the machining trajectory of the corresponding machining tool in each sub-machining area, and calculate the initial dwell time distribution on the machining trajectory based on the removal function of the corresponding machining tool; S5: Predict the risk of tool collisions during parallel machining through simulation, and adjust the process parameters and initial dwell time distribution according to the simulation prediction results to ensure that the distance between tools is always greater than the safe distance throughout the entire machining process. include: The parallel machining process is simulated based on the machining trajectory, machining speed and initial dwell time distribution of each machining tool obtained in S4, and the position of each machining tool and the distance between machining tools are determined after machining time t. Mark all processing times and corresponding processing tools where the distance between processing tools is less than the safe distance; Adjust the rotational speed of at least one of the two machining tools whose distance is less than the safe distance; The dwell time distribution of all machining tools is updated based on the adjusted rotation speed. The machining trajectory, removal function, rotation speed and final dwell time distribution of each machining tool are determined through iterative updates, so that the distance between machining tools is always greater than the safe distance throughout the entire machining process. S6: After the adjustment in S5, the processing trajectory, removal function, process parameters and final dwell time distribution of each processing tool are determined, and each processing tool is controlled accordingly to process the aspherical lens in parallel according to curvature partition.

2. The aspherical lens polishing method based on curvature partition matching according to claim 1, characterized in that, In step S1, the formula for calculating the curvature distribution of the aspherical lens based on the target surface shape is as follows: ； Where C represents the curvature of the aspherical lens at a radial distance r, and r represents the radial distance from any point on the aspherical lens to the optical axis of the mirror. , Represents the coordinates of any point. Represents the target surface shape function of an aspherical lens The first derivative, Represents the target surface shape function of an aspherical lens The second derivative of .

3. The aspherical lens polishing method based on curvature partition matching according to claim 1, characterized in that, The range of mirror curvature distribution within any sub-processing region Represented as: ； in, Indicates any sub-processing region; The mirror curvature distribution range within each sub-processing area must meet the following requirements: ； in, This indicates the curvature tolerance of the grinding wheel of the machining tool corresponding to the sub-machining area.

4. The aspherical lens polishing method based on curvature partition matching according to claim 1, characterized in that, Adjacent sub-processing areas and There is a pre-defined overlapping area between the two sub-processing areas. The width of the overlapping area is set according to the grinding wheel size of the processing tools in the corresponding two sub-processing areas.

5. The aspherical lens polishing method based on curvature partition matching according to claim 4, characterized in that, The width of the overlapping area is equal to the sum of the grinding disc diameters of the machining tools in the corresponding two sub-machining areas.

6. The aspherical lens polishing method based on curvature partition matching according to claim 1, characterized in that, In step S3, the dimensions of each machining tool must meet the following requirements: ； in, This represents the diameter of any machining tool. This represents the minimum width of the sub-processing area corresponding to any given processing tool; The curvature of each machining tool must satisfy: Within each sub-processing area, the machining tool selects the curvature with the largest machining area within that sub-processing area, or selects the median of the curvature within that sub-processing area.

7. The aspherical lens polishing method based on curvature partition matching according to claim 1, characterized in that, In step S4, the initial dwell time distribution on the processing trajectory is calculated using the following set of convolution equations: ； in, This represents the convolution operation, where z represents the discretized surface residual. This represents the removal function for N processing tools within N sub-processing regions. This represents the initial dwell time distribution of these N machining tools under the removal function condition.

8. The aspherical lens polishing method based on curvature partition matching according to claim 1, characterized in that, Each machining tool is controlled by a separate robot.

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