A method and system for deterministic polishing dwell time collaborative optimization oriented to kinematic constraints of five-axis machine tools

Abstract

The application discloses a kind of certainty polishing dwell time collaborative optimization method and system for five-axis machine tool kinematics constraint, method includes: obtaining the polishing tool influence function of optical element to be processed, five-axis machine tool kinematics parameter and reference dwell time control vector;With B spline, dwell time is continuously parameterized, and VAJ mapping of dwell time and surface and five-axis solid axle kinematics quantity is established;Surface and solid axle speed, acceleration and jerk are calculated and normalized processing is carried out;With dwell time increment as variable, collaborative optimization is carried out;Each round re-computes evaluation point and VAJ index, establishes dynamic out-of-tolerance set, carries out local elimination with adaptive RMS budget, and joint compensation is carried out to coupling index;After global constraint check and independent review, final dwell time control vector, surface figure residual and surface and five-axis VAJ index are output.The application improves the matching between dwell time result and actual five-axis polishing machine tool movement ability.

Description

Technical Field

[0001] This invention relates to a deterministic polishing dwell time collaborative optimization method and system for kinematic constraints of five-axis machine tools, belonging to the fields of deterministic optical polishing, optical element surface shape correction, polishing dwell time inversion, and multi-axis machine tool kinematic control technology. Background Technology

[0002] In the field of modern high-end optical manufacturing, computer-controlled optical surface forming technology has become an important technical means for processing large-diameter aspherical and complex freeform surface components. With the increasing demands on optical system performance from aerospace, high-energy lasers, and extreme ultraviolet lithography, optical components not only need to meet higher surface accuracy requirements but also need to handle surface errors with local features and spatial non-uniformity. How to balance processing efficiency, processing safety, and machine tool motion operability while correcting complex local features is a crucial issue in ultra-precision optical manufacturing.

[0003] Deterministic optical polishing establishes a quantitative mapping relationship between dwell time and material removal based on the error between the measured surface shape and the target surface shape, the influence function of the polishing tool, and the processing path. It also calculates the dwell time of the polishing tool at each position along the path to ensure that the expected material removal amount approximates the surface shape error to be corrected. Dwell time is typically constrained by process limitations such as material removal accuracy, over-polishing prevention, non-negativity of dwell time, and surface shape residuals.

[0004] However, the dwell time solution that satisfies material removal and surface shape constraints does not necessarily satisfy the kinematic constraints of a practical five-axis polishing machine. The dwell time distribution affects the surface feed motion and the velocity, acceleration, and jerk of the X, Y, Z, A, and B solid axes through path geometry, tool posture, machine tool structure, and time parameterization. Rapid local changes in dwell time may cause kinematic peaks to exceed the machine tool's allowable range, resulting in trajectory execution risks and machining instability.

[0005] If a general feed rate planning or time parameterization method is directly used, it often changes the original correspondence between residence time and material removal, causing the surface correction results to deviate from expectations. In addition, the out-of-tolerance points may shift during the optimization process, and evaluation points that were not originally out of tolerance may become out of tolerance due to local compensation; optimizing only fixed out-of-tolerance points or a single VAJ index may cause other evaluation points or other entity axis indices to deteriorate.

[0006] Therefore, there is an urgent need to develop a deterministic polishing dwell time collaborative optimization method for kinematic constraints of five-axis polishing machine tools: taking dwell time as a unified variable, establishing a collaborative optimization relationship between material removal, surface accuracy and five-axis kinematics, and constructing a closed-loop control mechanism that integrates global back-calculation, dynamic updating and candidate back-off. Summary of the Invention

[0007] The purpose of this invention is to provide a deterministic polishing dwell time co-optimization method and system oriented towards kinematic constraints of five-axis machine tools. By combining dwell time increment adjustment, material removal constraints, and five-axis machine tool kinematic evaluation, the method reduces the degree of exceeding limits of surface and solid axis velocities, accelerations, and jerks while maintaining controllable surface correction results, thereby improving the matching between dwell time results and actual five-axis polishing machine tool kinematic capabilities.

[0008] To achieve the above objectives, the present invention is implemented using the following technical solution.

[0009] In a first aspect, the present invention provides a deterministic polishing dwell time collaborative optimization method oriented towards kinematic constraints of a five-axis machine tool, comprising:

[0010] Obtain the polishing tool influence function, five-axis machine tool kinematic parameters, and reference dwell time control vector of the optical element to be processed;

[0011] A basis function matrix and derivative matrix are established based on B-splines; a material removal mapping between residence time and material removal amount is established based on the polishing tool influence function and basis function matrix.

[0012] Based on the kinematic parameters, basis function matrix, and derivative matrix of a five-axis machine tool, a VAJ mapping is established between dwell time and surface feed and the kinematic quantities of the five-axis solid axis.

[0013] The baseline residence time control vector is used as the current control vector, and the residence time increment is used as the optimization variable for iterative optimization. Global constraints are applied based on the material removal map.

[0014] In each iteration, the current control vector is substituted into the VAJ mapping to calculate the surface feed and five-axis solid axis kinematics of each evaluation point set along the polishing path. The normalized VAJ ratio is obtained by normalizing it according to the corresponding allowable limit. When the VAJ ratio reaches the set threshold, the out-of-tolerance tool contact point and kinematic out-of-tolerance index are determined. The dynamic out-of-tolerance set is established and updated to determine the target item, protection item, active control point and coupling index.

[0015] Under the absolute RMS budget of the remaining surface shape, the dwell time increment optimization is implemented for the local area corresponding to the active control point, and the coupling index is jointly compensated to obtain the candidate dwell time control point vector.

[0016] Based on material removal mapping and VAJ mapping, the surface residuals and VAJ indices corresponding to the candidate residence time control point vectors are calculated, and global constraint checks are performed.

[0017] If the global constraints are met and the target and protection conditions are met, the candidate result is accepted; otherwise, it is rejected, rolled back, or the incremental step size is reduced and the optimization is repeated. The process is repeated until the preset stopping condition is met. After global verification, the final residence time control vector, surface residual, and surface and five-axis VAJ indices are output.

[0018] Furthermore, the optical workpiece to be processed also includes initial surface shape data, target surface shape data, processing path, and tool posture.

[0019] The method of this invention uses the relevant parameters and the kinematic parameters of the five-axis machine tool as the common data basis for subsequent material removal and kinematic calculations.

[0020] Furthermore, the continuous movement of the machining tool along the scanning path is defined as a path parameter. A one-dimensional parameterized curve, based on the path parameters, constructs a B-spline basis function matrix. First derivative matrix and second derivative matrix And based on the dwell time control point vector The dwell time and its path parameter derivatives at each actual path sampling point are calculated using the following expression:

[0021]

[0022] in, The actual dwell time of the sampling point along the path, expressed in seconds; This is the first derivative of the actual path sampling point dwell time with respect to the path parameters; This is the second derivative of the actual path sampling point dwell time with respect to the path parameters; The conversion factor for converting dwell time in minutes to dwell time in seconds.

[0023] The method of this invention pre-constructs the B-spline matrix, material removal mapping, and kinematic numerical evaluation relationship, reducing the overhead of repeatedly performing complete trajectory generation and data processing in multiple rounds of candidate evaluation.

[0024] Furthermore, the VAJ mapping between dwell time and surface feed and five-axis solid axis kinematics is used to determine the corresponding surface feed kinematics based on the dwell time control point vector, and to determine the kinematics of each machine tool solid axis based on the surface feed kinematics, machining path, tool posture, and five-axis machine tool kinematic parameters; the surface feed kinematics include surface feed speed, acceleration, and jerk, and the five-axis solid axis kinematics are the speed, acceleration, and jerk of the X-axis, Y-axis, Z-axis, A-axis, and B-axis;

[0025] Substituting the reference dwell time control point vector into the VAJ mapping, we obtain the surface feed kinematic vector corresponding to the reference dwell time and the first... The kinematic vectors of the machine tool's physical axes are expressed as follows:

[0026] ;

[0027] in, The surface feed kinematics vector corresponding to the baseline dwell time; , as well as These are surface feed rate, surface feed acceleration, and surface feed jerk, respectively; superscript Indicates the baseline dwell time status; This is the transpose symbol.

[0028] Furthermore, the normalized VAJ ratio expression is:

[0029] ;

[0030] in, For the first At the first evaluation point Normalized VAJ ratio for kinematic indices; This refers to the actual velocity, acceleration, or jerk at that point. These are the permissible limits for the corresponding kinematic quantities;

[0031] The process for determining the kinematic deviation index includes:

[0032] For each evaluation point, the velocity, acceleration, and jerk indices corresponding to the surface feed motion and the motion of each solid axis are traversed to determine the normalized VAJ ratio corresponding to each kinematic index. The maximum value among these indices is taken as the maximum normalized VAJ ratio for the corresponding evaluation point. The expression is as follows:

[0033] ;

[0034] in, For the first The maximum normalized VAJ ratio for each evaluation point; Index of kinematic parameters; Normalized VAJ ratio; This represents the maximum value of the kinematic index.

[0035] When the maximum normalized VAJ ratio is greater than a set threshold, the corresponding evaluation point is determined to be an out-of-tolerance tool contact point, and the velocity, acceleration or jerk index corresponding to the evaluation point with a normalized VAJ ratio greater than the set threshold is determined as a kinematic out-of-tolerance index item.

[0036] The method of this invention updates the out-of-tolerance set dynamically, deleting eliminated out-of-tolerance items and adding newly generated out-of-tolerance items, thus avoiding omissions caused by a fixed out-of-tolerance set.

[0037] Furthermore, the iterative optimization process, using the baseline residence time control vector as the current control vector and the residence time increment as the optimization variable, includes:

[0038] The dwell time increment vector relative to the reference dwell time control point vector As variables, a candidate residence time control point vector is constructed, expressed as follows:

[0039] ;

[0040] in, For the first The increment of each control point, j=1,2,…,P, where P is the total number of control points; It is the transpose symbol; The baseline residence time control point vector; For the candidate residence time control point vector, during optimization initialization, the residence time increment vector is set to a zero vector, expressed as:

[0041] ;

[0042] Based on the candidate residence time control point vector, calculate the surface residual, material removal amount and five-axis kinematic index corresponding to the candidate results, and determine the normalized VAJ ratio corresponding to each evaluation point based on the kinematic index.

[0043] Based on the normalized VAJ ratio, a kinematic overlimit penalty function is constructed, expressed as:

[0044] ;

[0045] in, Here is the kinematic overlimit penalty function; Optional penalty levels; and These are the evaluation point index and the kinematic index, respectively. For the first At the first evaluation point The normalized VAJ ratio of the kinematic index under the candidate residence time control point vector; when the normalized VAJ ratio When the threshold is exceeded, the corresponding item will penalize the objective function.

[0046] The candidate dwell time control point vector is iteratively optimized based on the kinematic over-limit penalty function, and a global constraint is applied to the candidate results after each iteration. The global constraint includes global anti-over-throw, minimum dwell time of actual path sampling points, non-negativity of dwell time control points, and absolute RMS one-sided constraint of the remaining surface shape.

[0047] If a candidate result does not meet any constraint, the dwell time increment is rolled back or the optimization step size is reduced and optimization is performed again; if a candidate result meets the constraint and the kinematic index meets the set condition, the candidate result is accepted.

[0048] Wherein, the penalty order To ensure adjustable parameters, the first penalty order is used. Perform global kinematic over-limit optimization, and apply a second penalty order after satisfying the preset constraints. Local kinematic over-limit peak suppression is performed; in the method of the present invention, the penalty order is selected in stages or other equivalent ways, and is not limited to a fixed order.

[0049] The global constraint check includes global overthrow prevention, minimum dwell time constraint of global actual path sampling points, non-negative constraint of dwell time control points, and absolute RMS unilateral constraint check of remaining surface shape.

[0050] Furthermore, the process of constructing and updating the dynamic deviation set includes:

[0051] In the Current stay time Next, all evaluation points and all corresponding velocities, accelerations, and jerk indicators are recalculated. Based on the relationship between the normalized VAJ ratio corresponding to each kinematic indicator and its allowable limit, the first... The dynamic deviation set of the wheel is expressed as:

[0052] ;

[0053] in, For the first The dynamic out-of-range set corresponding to the current dwell time of the round; Indicates the first The evaluation point of the first The kinematic index exceeds its permissible limit; For the first At the first evaluation point kinematic indicators in residence time Normalized VAJ ratio;

[0054] The dynamic deviation set is also used to record the deviation knife contact and the corresponding deviation index item: the evaluation point containing the deviation index item in the dynamic deviation set is determined as the deviation knife contact, and the kinematic index corresponding to the set element is determined as the kinematic deviation index item of the deviation knife contact.

[0055] In the After the candidate residence time control point vectors are accepted, the VAJ is recalculated for all evaluation points and all kinematic indices based on the updated residence time control point vectors, and the VAJ is constructed. The dynamic kinematic error set of the round; for kinematic error indicators that have been eliminated in the previous round, they are removed from the current dynamic kinematic error indicator set; for kinematic error indicators newly generated due to local dwell time compensation, they are added to the current dynamic kinematic error indicator set.

[0056] Furthermore, the remaining face shape RMS budget refers to:

[0057] Starting from the absolute RMS allowable range of currently accepted length of stay, establish progressively increasing RMS budget tiers; The absolute RMS upper limit of each budget layer is denoted as:

[0058] ;

[0059] in, The absolute RMS of the global remaining surface shape corresponding to the candidate residence time; This represents the maximum absolute RMS allowed in the current optimization round;

[0060] Within each residual surface absolute RMS budget layer, candidate residuals for local or small-area dwell time increments are generated based on the current dwell time control point vector, resulting in candidate dwell time control point vectors. Based on these candidate dwell time control point vectors, the global material removal amount, residual surface error, and VAJ index for all evaluation points are recalculated to generate candidate results.

[0061] When the candidate result meets the global constraint check, and the normalized VAJ ratio corresponding to the target item reaches the set condition and the protection item does not exceed the corresponding protection limit, the candidate result is accepted.

[0062] When a candidate result does not meet any constraint or the normalized VAJ ratio corresponding to the target item does not reach the set condition, the candidate result is rejected and the dwell time increment is rolled back or the increment step size is reduced.

[0063] When the number of consecutive failures to meet the set conditions reaches a preset number, a constraint risk occurs, or any of the preset budget limit is reached, the current budget layer search is stopped or the optimization is terminated. If the optimization is not terminated, the process proceeds to the next budget layer.

[0064] In the method of this invention, the purpose of progressively expanding the budget is not to relax the surface shape requirements themselves, but to find a compromise between the minimum surface shape loss and the minimum kinematic deviation within the feasible range.

[0065] Furthermore, the joint compensation process includes:

[0066] When the control points corresponding to the remaining out-of-tolerance indicators have a shared relationship, or when the local compensation of a single out-of-tolerance indicator has a coupling effect on other kinematic indicators with a preset threshold, the velocity, acceleration and jerk indicators corresponding to multiple A-axis and B-axis, as well as the kinematic indicators with coupling effects between them, are determined as joint optimization objectives, and a joint compensation task is constructed based on the joint optimization objectives.

[0067] Based on the joint compensation task, candidate dwell times are generated, and the material removal amount, remaining surface residual, and VAJ index of all evaluation points corresponding to the candidate dwell times are globally calculated. When the candidate result meets the global constraint check, and the normalized VAJ ratio corresponding to the target item reaches the set condition and the protection item does not exceed the corresponding protection upper limit, the candidate result is accepted. When the remaining out-of-tolerance index is mainly concentrated in the A-axis, B-axis and their coupled influence area, the corresponding A-axis and B-axis joint compensation candidates are constructed, and joint optimization is performed according to the above process.

[0068] The method of this invention further reduces the number of out-of-tolerance tool contacts and kinematic peak values ​​at the cost of controllable surface accuracy by adaptive absolute RMS budgeting, local out-of-tolerance elimination and coupled joint compensation.

[0069] Secondly, the present invention provides a deterministic polishing dwell time collaborative optimization system for kinematic constraints of a five-axis machine tool, comprising:

[0070] The data acquisition module is used to acquire the polishing tool influence function, five-axis machine tool kinematic parameters, and reference dwell time control vector of the optical element to be processed;

[0071] The parameterization and material mapping module is used to establish the basis function matrix and derivative matrix based on B-splines; and to establish the material removal mapping between residence time and material removal amount based on the polishing tool influence function and basis function matrix.

[0072] The kinematic mapping pre-calculation module is used to establish the VAJ mapping between dwell time and surface feed and the kinematic quantities of the five-axis solid axis based on the kinematic parameters, basis function matrix and derivative matrix of the five-axis machine tool.

[0073] The global incremental collaborative optimization module is used to iteratively optimize with the baseline residence time control vector as the current control vector and the residence time increment as the optimization variable, and to apply global constraints based on the material removal map.

[0074] The dynamic out-of-tolerance set update module is used in each iteration to substitute the current control vector into the VAJ mapping, calculate the surface feed and five-axis solid axis kinematics of each evaluation point set along the polishing path, and normalize them according to the corresponding allowable limit to obtain the normalized VAJ ratio. When the VAJ ratio reaches the set threshold, the out-of-tolerance tool contact point and kinematic out-of-tolerance index item are determined, the dynamic out-of-tolerance set is established and updated, and the target item, protection item, active control point and coupling index are determined.

[0075] The joint compensation module is used to perform incremental optimization of dwell time for the local area corresponding to the active control point under the absolute RMS budget of the remaining surface shape, and to perform joint compensation for the coupling index to obtain the candidate dwell time control point vector.

[0076] The candidate result determination and verification module is used to calculate the surface residual and VAJ index corresponding to the candidate residence time control point vector based on the material removal mapping and VAJ mapping, and to perform global constraint checks.

[0077] If the global constraints are met and the target and protection conditions are met, the candidate result is accepted; otherwise, it is rejected, rolled back, or the incremental step size is reduced and the optimization is repeated. The process is repeated until the preset stopping condition is met. After global verification, the final residence time control vector, surface residual, and surface and five-axis VAJ indices are output.

[0078] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0079] 1. The deterministic polishing dwell time collaborative optimization method for kinematic constraints of five-axis machine tools provided by the present invention unifies the feasible dwell time of surface shape, material removal, anti-over-polishing, minimum dwell time, absolute RMS of remaining surface shape and five-axis kinematic constraints into the same dwell time optimization process, avoiding the destruction of the original material removal relationship by independent feed planning;

[0080] 2. The method of the present invention avoids the problem of omission of excess tolerance caused by a fixed excess tolerance set by dynamically updating the excess tolerance set, deleting eliminated excess tolerance items and adding newly generated excess tolerance items;

[0081] 3. The method of the present invention, through the combined effect of the target term and the protection term, reduces the current kinematic deviation while avoiding performance degradation in other regions and other indicators;

[0082] 4. This invention also improves the interpretability and repeatability of dwell time optimization results, as well as the reliability of actual execution on five-axis machine tools, by performing global back-calculation, acceptance, rejection, and rollback operations on candidate solutions, and a final independent back-verification step. Attached Figure Description

[0083] Figure 1This is a flowchart illustrating the overall process of a deterministic polishing dwell time co-optimization method for kinematic constraints of a five-axis machine tool, as provided in an embodiment of the present invention.

[0084] Figure 2 This is a flowchart of the global optimization of dwell time increment and candidate solution rollback in the deterministic polishing dwell time collaborative optimization method for kinematic constraints of a five-axis machine tool provided in an embodiment of the present invention.

[0085] Figure 3 The flowchart shows the dynamic out-of-tolerance set update, local out-of-tolerance elimination, and joint compensation closed-loop process in the deterministic polishing dwell time collaborative optimization method for kinematic constraints of a five-axis machine tool provided in an embodiment of the present invention.

[0086] Figure 4 This is a comparison of surface dwell time and surface VAJ before and after optimization in the deterministic polishing dwell time collaborative optimization method for kinematic constraints of five-axis machine tools provided in an embodiment of the present invention.

[0087] Figure 5 This is a comparison diagram of the five-axis solid axis velocity before and after optimization in the deterministic polishing dwell time collaborative optimization method for kinematic constraints of a five-axis machine tool provided by an embodiment of the present invention.

[0088] Figure 6 This is a comparison diagram of the acceleration of the five-axis solid axis before and after optimization in the deterministic polishing dwell time collaborative optimization method for kinematic constraints of a five-axis machine tool provided by an embodiment of the present invention.

[0089] Figure 7 This is a comparison diagram of the jerk of the five-axis solid axis before and after optimization in the deterministic polishing dwell time collaborative optimization method for kinematic constraints of a five-axis machine tool provided by an embodiment of the present invention.

[0090] Figure 8 The distribution diagrams of the initial surface shape, the reference residual surface shape, the global collaborative optimization residual surface shape, and the final residual surface shape in the deterministic polishing dwell time collaborative optimization method for kinematic constraints of a five-axis machine tool provided in the embodiments of the present invention are shown.

[0091] Figure 9 This is a comparison of the technical effects of each optimization stage in the deterministic polishing dwell time collaborative optimization method for kinematic constraints of a five-axis machine tool provided according to an embodiment of the present invention.

[0092] Figure 10 The image shows the evaluation results of the budget layer in the adaptive absolute RMS budget search stage of the deterministic polishing dwell time collaborative optimization method for kinematic constraints of a five-axis machine tool provided in an embodiment of the present invention.

[0093] Figure 11This diagram illustrates the process of eliminating local deviations and jointly compensating for errors in a deterministic polishing dwell time optimization method for kinematic constraints of a five-axis machine tool, provided by an embodiment of the present invention. Detailed Implementation

[0094] It should be noted that:

[0095] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present invention and the specific features in the embodiments are detailed descriptions of the technical solution of the present invention, rather than limitations thereof. In the absence of conflict, the embodiments of the present invention and the technical features in the embodiments can be combined with each other.

[0096] The term "and / or" simply describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A alone, A and B simultaneously, or B alone. Additionally, the character " / " generally indicates that the preceding and following related objects have an "or" relationship.

[0097] Example 1

[0098] like Figure 1-3 As shown, this embodiment uses a reference dwell time control vector that already meets the surface shape correction requirements. As a starting point for kinematic collaborative optimization, this paper introduces a deterministic collaborative optimization method for polishing dwell time oriented towards the kinematic constraints of a five-axis machine tool, including:

[0099] Obtain the polishing tool influence function, five-axis machine tool kinematic parameters, and reference dwell time control vector of the optical element to be processed;

[0100] A basis function matrix and derivative matrix are established based on B-splines; a material removal mapping between residence time and material removal amount is established based on the polishing tool influence function and basis function matrix.

[0101] Based on the kinematic parameters, basis function matrix, and derivative matrix of a five-axis machine tool, a VAJ mapping is established between dwell time and surface feed and the kinematic quantities of the five-axis solid axis.

[0102] The baseline residence time control vector is used as the current control vector, and the residence time increment is used as the optimization variable for iterative optimization. Global constraints are applied based on the material removal map.

[0103] In each iteration, the current control vector is substituted into the VAJ mapping to calculate the surface feed and five-axis solid axis kinematics of each evaluation point set along the polishing path. The normalized VAJ ratio is obtained by normalizing it according to the corresponding allowable limit. When the VAJ ratio reaches the set threshold, the out-of-tolerance tool contact point and kinematic out-of-tolerance index are determined. The dynamic out-of-tolerance set is established and updated to determine the target item, protection item, active control point and coupling index.

[0104] Under the absolute RMS budget of the remaining surface shape, the dwell time increment optimization is implemented for the local area corresponding to the active control point, and the coupling index is jointly compensated to obtain the candidate dwell time control point vector.

[0105] Based on material removal mapping and VAJ mapping, the surface residuals and VAJ indices corresponding to the candidate residence time control point vectors are calculated, and global constraint checks are performed.

[0106] If the global constraints are met and the target and protection conditions are met, the candidate result is accepted; otherwise, it is rejected, rolled back, or the incremental step size is reduced and the optimization is repeated. The process is repeated until the preset stopping condition is met. After global verification, the final residence time control vector, surface residual, and surface and five-axis VAJ indices are output.

[0107] In summary, this embodiment directly adjusts the dwell time distribution within the neighborhood of the existing feasible dwell time of the surface shape. Under the premise of maintaining global material removal, anti-over-throwing, minimum dwell time of actual path sampling points, non-negative control points, and absolute RMS constraints of the remaining surface shape, it reduces the degree of exceeding the limits of surface and five-axis solid axis kinematics, and handles the remaining local deviations through dynamic closed-loop processing.

[0108] Preferably, the reference dwell time control vector is obtained by the surface shape correction solution process and maintains the same coordinate and parameter domain definition as the initial surface shape data, target surface shape data, polishing tool influence function, machining path, tool posture, and five-axis machine tool kinematic parameters.

[0109] Preferably, the measured height data of the surface of the optical element to be processed is obtained through interferometry, contour scanning, or other surface shape measurement methods, and the target surface shape or optical design theoretical data is also obtained. Spatial coordinate alignment, effective aperture selection, and discrete mesh unification are performed on the measured height data and the target surface shape or optical design theoretical data to form an initial surface shape error distribution.

[0110] Obtain the polishing tool influence function, tool effective boundary, machining path, path parameters, tool posture, and the structural and kinematic parameters of the five-axis machine tool.

[0111] Preferably, the continuous movement of the machining tool along the scanning path is defined as the path parameter. The one-dimensional parameterized curve is obtained, and multiple path evaluation points are obtained according to the preset sampling rules. The residence time control point vector is used as the basis for this. Representing the continuous residence time distribution, a B-spline basis function matrix is ​​constructed based on the path parameters. First derivative matrix and second derivative matrix The expression is:

[0112] ;

[0113] in, The number of path evaluation points. Number of stay time control points; Used to reconstruct the actual sampling point dwell time from the control point.

[0114] This embodiment employs a total of 34,777 path evaluation points, 2,000 residence time control points, and 27,729 material monitoring points. Residence time basis function matrix. First derivative matrix and second derivative matrix The dimensions are all 34777×2000, and the material removal mapping matrix is... The dimensions are 27729×2000. Dwell time control point vector. In the internal optimization and storage processes, the unit is uniformly set to minutes. When calculating the VAJ index of the surface and five-axis solid axes, it is converted to seconds using a coefficient of 60. The dwell time and its path parameter derivative at each actual path sampling point are calculated using the following relationship, expressed as follows:

[0115] ;

[0116] in, The actual dwell time of the sampling point along the path, expressed in seconds; This is the first derivative of the actual path sampling point dwell time with respect to the path parameters; 60 represents the second derivative of the actual path sampling point dwell time with respect to the path parameters; 60 is the conversion factor for converting the dwell time in minutes to the dwell time in seconds.

[0117] Preferably, a material removal mapping matrix is ​​constructed based on the parameterized relationship between the polishing tool influence function, processing path, and residence time. This is used to establish a material removal mapping between residence time and material removal amount. For any residence time control vector... , This represents the amount of material removed at each global surface shape monitoring point; the amount of material removed is compared with the initial surface shape error distribution to obtain the remaining surface shape distribution and calculate the absolute RMS of the remaining surface shape. For example... Figure 8 As shown, Figure 8 (a) Figure 8 (b) Figure 8 (c) and Figure 8 The middle (d) section displays the initial surface shape, the baseline residual surface shape, the globally collaboratively optimized residual surface shape, and the final residual surface shape, respectively. The specific content includes:

[0118] In the residence time optimization, a global anti-overthrow constraint is applied to ensure that the amount of material removed does not exceed the allowable removal range; simultaneously, a non-negativity constraint for the residence time control point is established, expressed as:

[0119] ;

[0120] in, The reference dwell time control point vector, This is the current candidate increment vector; used to ensure that the candidate dwell time control point is non-negative.

[0121] Through the B-spline basis function matrix Map the dwell time control points to all actual path sampling points, and establish a global minimum dwell time constraint for actual path sampling points, expressed as:

[0122] ;

[0123] Of these, 60 is used for the conversion from minutes to seconds; This is the minimum allowed dwell time at the actual path sampling point; this constraint is used to establish a constraint on all actual path sampling points globally.

[0124] One-sided constraints are established based on the absolute RMS of the remaining surface shape, and the expression is:

[0125] ;

[0126] in, The absolute RMS of the global remaining surface shape corresponding to the candidate residence time; This represents the maximum absolute RMS allowed in the current optimization round; This is the candidate residence time control point vector; this constraint is used to limit the loss of surface accuracy.

[0127] In this embodiment, the global anti-overthrow constraint, the minimum dwell time constraint of the actual path sampling point, the non-negativity constraint of the dwell time control point, and the absolute RMS constraint of the remaining surface shape are all established on the global surface shape monitoring point or all actual path sampling points, rather than only for the local kinematic error region.

[0128] Preferred, such as Figure 5-7 As shown, before kinematic co-optimization, this embodiment establishes a VAJ mapping between dwell time and surface feed kinematics and the kinematics of the five-axis solid axes (X, Y, Z, A, B) based on the dwell time control point vector, path geometry, tool posture, machine tool structure, and five-axis machine tool kinematic parameters. Figure 5 (a) Figure 6 (a) and Figure 7 (a) shows the X-axis velocity, acceleration, and jerk before and after optimization, respectively; Figure 5 (b) Figure 6 (b) and Figure 7 (b) shows the Y-axis velocity, acceleration, and jerk before and after optimization, respectively; Figure 5 (c) Figure 6 (c) and Figure 7 (c) shows the Z-axis velocity, acceleration, and jerk before and after optimization, respectively; Figure 5 (d) Figure 6 (d) and Figure 7 (d) shows the A-axis velocity, acceleration, and jerk before and after optimization, respectively; Figure 5 (e) Figure 6 (e) and Figure 7 (e) shows the B-axis velocity, acceleration, and jerk before and after optimization, respectively. The black curve is the baseline dwell time result, the blue curve is the final optimization result, the red dashed line is the corresponding kinematic limit, the horizontal axis is the B-spline path parameter u, and the vertical axis is the corresponding kinematic quantity and its unit.

[0129] The VAJ mapping is used to sequentially calculate the surface feed rate, acceleration, jerk, and the velocity, acceleration, and jerk of each solid axis based on the change of the dwell time control point vector along the machining path. The X, Y, and Z axes use linear motion units, while the A and B axes use angular motion units, and are compared with their corresponding kinematic limits.

[0130] Preferred, such as Figure 4 As shown, the baseline dwell time control point vector and the finally accepted optimized dwell time control point vector are substituted into the VAJ mapping respectively, and the results are compared. Figure 4 (a) Surface residence time Figure 4 (b) Surface feed rate Figure 4 (c) Surface feed acceleration and Figure 4 (d) Surface feed jerk; Figure 4 The black and blue curves represent the baseline and final optimization results, respectively; the red dashed line in the residence time subplot represents the minimum actual residence time, and the red dashed line in the surface VAJ subplot represents the corresponding kinematic limit, expressed as:

[0131] ;

[0132] in, The surface feed kinematics vector corresponding to the baseline dwell time; , as well as These are surface feed rate, surface feed acceleration, and surface feed jerk, respectively; superscript Indicates the baseline dwell time status; This is the transpose symbol.

[0133] Preferably, the normalized VAJ ratio is expressed as:

[0134] ;

[0135] in, For the first At the first evaluation point Normalized VAJ ratio for kinematic indices; This refers to the actual velocity, acceleration, or jerk at that point. These are the permissible limits for the corresponding kinematic quantities;

[0136] The process for determining the kinematic deviation index includes:

[0137] For each evaluation point, the velocity, acceleration, and jerk indices corresponding to the surface feed motion and the motion of each solid axis are traversed to determine the normalized VAJ ratio corresponding to each kinematic index. The maximum value among these indices is taken as the maximum normalized VAJ ratio for the corresponding evaluation point. The expression is as follows:

[0138] ;

[0139] in, For the first The maximum normalized VAJ ratio for each evaluation point; The kinematic index corresponds to the surface feed and the velocity, acceleration, and jerk indices of the five axes: X, Y, Z, A, and B. Normalized VAJ ratio; Refers to the maximum value;

[0140] When the maximum normalized VAJ ratio is greater than 1, the corresponding evaluation point is determined to be an out-of-tolerance tool contact point, and the velocity, acceleration or jerk index with a normalized VAJ ratio greater than 1 corresponding to the evaluation point is determined as a kinematic out-of-tolerance index item.

[0141] like Figure 9 As shown, Figure 9 Figure (a) illustrates the evolution of the out-of-tolerance tool contact. Figure 9 Figure (b) illustrates the evolution of the maximum normalized VAJ ratio. Figure 9 Figure (c) illustrates the process of sacrificing surface accuracy. Figure 9Figure (d) illustrates the evolution of the out-of-tolerance index. In this embodiment, the baseline dwell time result, after global back-calculation, yielded 3066 out-of-tolerance tool contacts and 7113 out-of-tolerance index items. The maximum normalized VAJ ratio was 13.121715781, the remaining surface absolute RMS was 20.650027637 nm, and the machining time was 2083.532261 s. The results indicate that although the baseline dwell time meets the requirements for surface correction and anti-over-scraping, there are still significant surface or solid axis kinematic out-of-tolerances. Therefore, incremental adjustments are needed without compromising surface constraints.

[0142] Preferred, such as Figure 2 As shown, the construction and collaborative optimization process of the candidate residence time control vector includes:

[0143] The reference dwell time control point vector is used as the currently accepted solution, with the increment vector relative to the reference dwell time control point vector. As variables, a candidate residence time control point vector is constructed, expressed as follows:

[0144] ;

[0145] in, For the first The increment of each control point, j=1,2,…,P, where P is the total number of control points; It is the transpose symbol; The baseline residence time control point vector; For the candidate residence time control point vector, during optimization initialization, the residence time increment vector is set to a zero vector, expressed as:

[0146] ;

[0147] Therefore, this embodiment adjusts the dwell time in the neighborhood of the existing feasible benchmark solution for the surface shape, without resolving the absolute dwell time which is unrelated to the original dwell time.

[0148] Based on the candidate residence time control point vector, the surface residual, material removal amount and five-axis kinematic index corresponding to the candidate results are calculated, and the normalized VAJ ratio corresponding to each evaluation point is determined based on the kinematic index.

[0149] Based on the normalized VAJ ratio, a kinematic overlimit penalty function is constructed, expressed as:

[0150] ;

[0151] in, Here is the kinematic overlimit penalty function; Optional penalty levels; and These are the evaluation point index and the kinematic index, respectively. For the first At the first evaluation point The normalized VAJ ratio of the kinematic index under the candidate residence time control point vector; when the normalized VAJ ratio When the value exceeds 1, the corresponding term penalizes the objective function;

[0152] The candidate dwell time control point vector is iteratively optimized based on the kinematic over-limit penalty function, and a global constraint check is performed on the candidate results after each iteration.

[0153] If a candidate result does not meet any constraint, the dwell time increment is rolled back or the optimization step size is reduced and optimization is performed again; if a candidate result meets the constraint and the kinematics are improved, the candidate result is accepted.

[0154] Wherein, the penalty order To ensure adjustable parameters, the first penalty order is used in this embodiment. Perform global kinematic over-limit optimization, and apply a second penalty order after satisfying the preset constraints. Suppress local kinematic over-limit peak values.

[0155] Preferably, in the global collaborative optimization process, the following steps are performed sequentially: "candidate solution generation - material removal and surface shape back calculation - surface and five-axis VAJ back calculation - global constraint check - objective function comparison". Each candidate solution is subject to global anti-overshooting, minimum dwell time of global actual path sampling points, non-negativity of dwell time control points, and absolute RMS unilateral constraint of the remaining surface shape. When a candidate result does not meet any constraint condition, the current candidate result is rejected, and the dwell time increment is rolled back or the optimization step size is reduced before regenerating the candidate result. When the candidate result meets all constraints and the kinematic index is improved, the current candidate result is accepted and used as the current accepted solution for the next round of optimization.

[0156] In this embodiment, the backoff coefficient of the candidate results is gradually reduced based on feasibility to ensure that the candidate increment always meets the feasibility requirements of global anti-overthrow, minimum dwell time of actual path sampling points, non-negativity of control points, and absolute RMS unilateral constraints. The saved candidate audit is used to record the dwell time of multiple types of candidates and their global constraint states; for candidate solutions that pass the geometric constraint check, their kinematic over-limit penalty, maximum normalized VAJ ratio, and absolute RMS are further compared; if the candidate solution does not improve the kinematic objective or causes unacceptable surface changes, the candidate solution is directly rejected, and the valid candidate solutions from the previous round are retained.

[0157] In this embodiment, the final global collaborative result includes 87 out-of-tolerance tool contacts and 88 out-of-tolerance index items. The maximum normalized VAJ ratio is reduced to 1.284282575, the absolute RMS is 21.269425226nm, and the processing time is 2070.345106s.

[0158] Preferred, such as Figure 3 As shown, this embodiment, based on the obtained global collaborative optimization results, selects to perform dynamic out-of-tolerance set update, adaptive RMS budget, local out-of-tolerance elimination, joint compensation of coupled control points, and final independent backtesting according to the current remaining out-of-tolerance status. Specifically, it includes:

[0159] The process of constructing and updating the dynamic deviation set includes:

[0160] In the Current stay time Next, all evaluation points and all corresponding velocities, accelerations, and jerk indicators are recalculated. Based on the relationship between the normalized VAJ ratio corresponding to each kinematic indicator and its allowable limit, the first... The dynamic deviation set of the wheel is expressed as:

[0161] ;

[0162] in, For the first The dynamic out-of-range set corresponding to the current dwell time of the round; Indicates the first The evaluation point of the first The kinematic index exceeds its permissible limit; For the first At the first evaluation point kinematic indicators in residence time The normalized VAJ ratio.

[0163] The dynamic deviation set is also used to record the deviation knife contact and the corresponding deviation index item: the evaluation point containing the deviation index item in the dynamic deviation set is determined as the deviation knife contact, and the kinematic index corresponding to the set element is determined as the kinematic deviation index item of the deviation knife contact.

[0164] In the After the candidate residence time control point vectors are accepted, the VAJ is recalculated for all evaluation points and all kinematic indices based on the updated residence time control point vectors, and the VAJ is constructed. The dynamic kinematic error set of the round; for kinematic error indicators that have been eliminated in the previous round, they are removed from the current dynamic kinematic error indicator set; for kinematic error indicators newly generated due to local dwell time compensation, they are added to the current dynamic kinematic error indicator set.

[0165] The out-of-tolerance indicators in the dynamic out-of-tolerance set are divided into target indicators and protection indicators: target indicators are used to reduce the current out-of-tolerance level and decrease the number of out-of-tolerance tool contacts or out-of-tolerance indicators; protection indicators include indicators that are not currently out of tolerance but are close to the limit, indicators that may be affected by local compensation in non-target areas, and indicators that have material or kinematic coupling with the active control point. Both target and protection indicators are dynamically updated with the results of each round of global back-calculation.

[0166] Preferably, based on the basis function matrix First derivative matrix and second derivative matrix The local non-zero support relationship maps the out-of-tolerance tool contact to the dwell time control point that affects its kinematics, and adds buffer control points on both sides of the relevant control point.

[0167] The active control point is used to perform the current local dwell time increment adjustment, and the buffer control point is used to maintain the continuous adjustment capability of the local dwell time distribution. Its range is determined according to the B-spline order, path sampling density and processing requirements.

[0168] In this embodiment, when the control point sets corresponding to multiple out-of-tolerance tool contacts overlap, or when the corresponding material removal action areas have obvious shared relationships, the corresponding control points are merged into a material coupling block; when multiple VAJ indices have common sensitivity to the same set of control points, the corresponding control points are merged into a kinematic coupling block. The local active control points are only used to reduce the dimension of a single solution and will not reduce the inspection range of global surface shape and dwell time constraints.

[0169] Preferably, in this embodiment, the remaining surface RMS budget is adjusted adaptively step by step, and the specific process includes:

[0170] Starting from the absolute RMS allowable range of currently accepted length of stay, establish progressively increasing RMS budget tiers; The absolute RMS upper limit of each budget layer is denoted as:

[0171] ;

[0172] in, The absolute RMS of the global residual surface shape corresponding to the candidate residence time control point vector; This represents the maximum absolute RMS allowed in the current optimization round;

[0173] Within each budget layer, candidate local or small-area residence time increments are generated based on the current residence time, and the global material removal amount, remaining surface residual, and VAJ index for all evaluation points are recalculated based on the candidate residence times.

[0174] Within each residual surface absolute RMS budget layer, candidate residuals for local or small-area dwell time increments are generated based on the current dwell time control point vector, resulting in candidate dwell time control point vectors. Based on these candidate dwell time control point vectors, the global material removal amount, residual surface error, and VAJ index for all evaluation points are recalculated to generate candidate results.

[0175] When the candidate result meets the global constraint check, and the normalized VAJ ratio corresponding to the target item reaches the set condition and the protection item does not exceed the corresponding protection limit, the candidate result is accepted.

[0176] When a candidate result does not meet any constraint or the normalized VAJ ratio corresponding to the target item does not reach the set condition, the candidate result is rejected and the dwell time increment is rolled back or the increment step size is reduced.

[0177] When the number of consecutive failures to meet the set conditions reaches a preset number, a constraint risk occurs, or any of the preset budget limit is reached, the current budget layer search is stopped or the optimization is terminated. If the optimization is not terminated, the process proceeds to the next budget layer.

[0178] like Figure 10 As shown, Figure 10 (a) shows the changes in budget and kinematic deviation. Figure 10 (b) illustrates the changes in budget and surface accuracy costs. After completing the budget layer evaluation at this stage, further local point-by-point or small-area deviation elimination is performed in subsequent budget layers, and the candidate results corresponding to each budget layer are recorded:

[0179] In this embodiment, the point-by-point elimination history records a total of 95 local candidate rounds. Each round records the current budget, target out-of-tolerance items, number of eliminated tool contacts, change in the number of out-of-tolerance items, total out-of-tolerance amount, maximum normalized VAJ ratio, absolute RMS, step scaling factor, and solution status.

[0180] Within the 0.34nm budget layer, the number of out-of-tolerance tool contacts is gradually reduced from 31 to 9;

[0181] In the subsequent local deviation elimination process, when the budget was 0.36nm, 0.38nm, 0.40nm, 0.42nm and 0.44nm, the number of deviations further decreased from 9 to 7, 6, 5, 4 and 3 respectively.

[0182] Within the 0.46nm, 0.48nm, and 0.50nm budget layers, the number of out-of-tolerance items remained at 3, but the total out-of-tolerance amount continued to decrease, ultimately resulting in 3 out-of-tolerance tool contacts and 3 out-of-tolerance index items. The maximum normalized VAJ ratio was 1.041582411, the absolute RMS was 21.768528349nm, and the processing time was 2066.767051s.

[0183] Preferably, during the local deviation elimination process, when the number of remaining deviation tool contacts is small, a single-point or small-area optimization task is constructed based on the set of local support control points; and corresponding active control points and buffer control points are selected to reduce the target deviation degree and reduce the number of deviation tool contacts.

[0184] Candidate results will be filtered based on the number of out-of-pocket points eliminated, the reduction in out-of-pocket level, and the absolute RMS cost. In this embodiment, after each local candidate update, all evaluation points and all VAJ indices will be recalculated: if the local processing reduces the target out-of-pocket level but generates new unacceptable out-of-pocket levels at other evaluation points, the candidate result will be rejected and the parameters will be rolled back.

[0185] Preferably, the joint compensation process includes:

[0186] When the control points corresponding to the remaining out-of-tolerance indicators have a shared relationship, or when the local compensation of a single out-of-tolerance indicator has a coupling effect on other kinematic indicators with a preset threshold, the velocity, acceleration and jerk indicators corresponding to multiple A-axis and B-axis, as well as the kinematic indicators with coupling effects between them, are determined as joint optimization objectives, and a joint compensation task is constructed based on the joint optimization objectives.

[0187] Based on the joint compensation task, candidate dwell times are generated, and the material removal amount, remaining surface residual, and VAJ index of all evaluation points corresponding to the candidate dwell times are globally calculated. When the candidate result satisfies the global constraint check, the target deviation item is improved, and no new deviation tool contact or new deviation index item is introduced, the candidate result is accepted. When the remaining deviation index is mainly concentrated in the A-axis, B-axis and their coupled influence area, the corresponding A-axis and B-axis joint compensation candidates are constructed, and joint optimization is performed according to the above process.

[0188] like Figure 11 As shown, Figure 11 (a) shows the distribution of dwell time increments caused by local deviation elimination and joint compensation. The blue and orange curves represent the local elimination increment and the joint compensation increment, respectively. The horizontal axis is the B-spline control point number, and the vertical axis is the dwell time increment, in seconds. Figure 11 Figure (b) shows the changes in the number of remaining out-of-tolerance tool contacts and the number of out-of-tolerance index items as the processing stage progresses.

[0189] In this embodiment, the joint compensation process recorded a total of 37 candidate rounds: the initial compensation control point scale was 80, the active control point scale was 150, and then it was gradually expanded to 136, 215, 373 and 549 active control points according to the shared local support relationship; the target optimization item was always dynamically selected from the currently remaining A and B axis indicators, while the protection item covered all other indicators that may be affected by the same control point.

[0190] The first round of joint compensation reduced the number of out-of-tolerance tool contacts from 3 to 2, and the maximum normalized VAJ ratio from 1.041582411 to 1.02265. After further expanding the range of coupling control points and reducing the step size, the remaining out-of-tolerance amount gradually decreased. After entering the 0.52nm budget layer, the candidate solution first reduced the number of out-of-tolerance points from 2 to 1, and then eliminated the last out-of-tolerance point. The final maximum normalized VAJ ratio was 0.999983741, the number of out-of-tolerance tool contacts and the out-of-tolerance index were both 0, the absolute RMS was 21.789021136nm, and the processing time was 2066.101845s.

[0191] From the statistical results of the index items, the number of out-of-tolerance items for A-axis velocity, A-axis acceleration, A-axis jerk, and B-axis jerk in the baseline solution gradually decreased in subsequent closed-loop optimization; the original main out-of-tolerance items such as surface jerk, Y-axis velocity, Y-axis acceleration, and Y-axis jerk were completely eliminated in the global collaborative optimization stage. In this embodiment, both index-level changes and tool contact-level changes are independently backtested simultaneously to avoid judging the optimization effect solely based on a single maximum peak value.

[0192] Preferably, during the dynamic out-of-tolerance closed-loop process, the operation is terminated when the preset number of out-of-tolerance tool contacts, the maximum normalized VAJ ratio, the absolute RMS budget limit, the lack of improvement in continuous iterations, or other preset stopping conditions are met.

[0193] When the dynamic deviation set is empty, constrained RMS recovery can be performed based on whether there is a feasible direction; the recovery step accepts the iterative results only if all VAJs do not exceed the allowable limit and the absolute RMS is improved.

[0194] After the preset stopping condition is reached, the final dwell time control vector is reread, and the material removal, remaining surface shape, actual path dwell time, surface feed, and VAJ indexes of the five solid axes (X, Y, Z, A, B) for all evaluation points are recalculated. The recalculated results are then compared with the saved results for consistency. In this embodiment, this final independent backtest is only used to verify the validity of the results and does not undertake any new optimization tasks.

[0195] In this embodiment, the independent backtest does not invoke the intermediate cache during the optimization process. Instead, it recalculates the total material removal amount, remaining surface shape, path dwell time, and the surface and the five-axis VAJ indices (X, Y, Z, A, B). The backtest results show that the final dwell time control vector satisfies the global anti-overthrow constraint, the minimum dwell time constraint for actual path sampling points, the non-negativity constraint for dwell time control points, and the absolute RMS one-sided constraint for remaining surface shape. The difference between the final maximum normalized VAJ ratio and 1 is approximately 1.63 × 10⁻⁶. -5 The absolute RMS margin is approximately 5.07 × 10⁻⁶. -4 nm, and the independent recalculation results are completely consistent with the saved results.

[0196] In this embodiment, as the absolute RMS budget gradually increases, and through global kinematic collaborative optimization, dynamic error update, local error elimination, and A- and B-axis coupled kinematic joint compensation, the number of kinematic errors and the maximum normalized VAJ ratio continuously decrease. The final result achieves zero kinematic errors under the conditions of satisfying global over-throwing, minimum dwell time of actual path sampling points, non-negativity of control points, and all absolute RMS constraints. The total processing time is reduced from the initial 2083.532261s to 2066.101845s, a reduction of 17.430416s, or approximately -0.836580%. The specific values ​​mentioned above are only used to illustrate the technical effects of this embodiment and do not constitute a fixed limitation on the scope of protection, nor do they imply that strictly zero errors must be achieved under all operating conditions.

[0197] Example 2

[0198] Based on the deterministic polishing dwell time collaborative optimization method for kinematic constraints of a five-axis machine tool described in Example 1, this example introduces a deterministic polishing dwell time collaborative optimization system for kinematic constraints of a five-axis machine tool, including:

[0199] The data acquisition module is used to acquire the polishing tool influence function, five-axis machine tool kinematic parameters, and reference dwell time control vector of the optical element to be processed;

[0200] The parameterization and material mapping module is used to establish the basis function matrix and derivative matrix based on B-splines; and to establish the material removal mapping between residence time and material removal amount based on the polishing tool influence function and basis function matrix.

[0201] The kinematic mapping pre-calculation module is used to establish the VAJ mapping between dwell time and surface feed and the kinematic quantities of the five-axis solid axis based on the kinematic parameters, basis function matrix and derivative matrix of the five-axis machine tool.

[0202] The global incremental collaborative optimization module is used to iteratively optimize with the baseline residence time control vector as the current control vector and the residence time increment as the optimization variable, and to apply global constraints based on the material removal map.

[0203] The dynamic out-of-tolerance set update module is used in each iteration to substitute the current control vector into the VAJ mapping, calculate the surface feed and five-axis solid axis kinematics of each evaluation point set along the polishing path, and normalize them according to the corresponding allowable limit to obtain the normalized VAJ ratio. When the VAJ ratio reaches the set threshold, the out-of-tolerance tool contact point and kinematic out-of-tolerance index item are determined, the dynamic out-of-tolerance set is established and updated, and the target item, protection item, active control point and coupling index are determined.

[0204] The joint compensation module is used to perform incremental optimization of dwell time for the local area corresponding to the active control point under the absolute RMS budget of the remaining surface shape, and to perform joint compensation for the coupling index to obtain the candidate dwell time control point vector.

[0205] The candidate result determination and verification module is used to calculate the surface residual and VAJ index corresponding to the candidate residence time control point vector based on the material removal mapping and VAJ mapping, and to perform global constraint checks.

[0206] If the global constraints are met and the target and protection conditions are met, the candidate result is accepted; otherwise, it is rejected, rolled back, or the incremental step size is reduced and the optimization is repeated. The process is repeated until the preset stopping condition is met. After global verification, the final residence time control vector, surface residual, and surface and five-axis VAJ indices are output.

[0207] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0208] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0209] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A deterministic polishing dwell time collaborative optimization method oriented towards kinematic constraints of a five-axis machine tool, characterized in that, include: Obtain the polishing tool influence function, five-axis machine tool kinematic parameters, and reference dwell time control vector of the optical element to be processed; A basis function matrix and derivative matrix are established based on B-splines; a material removal mapping between residence time and material removal amount is established based on the polishing tool influence function and basis function matrix. Based on the kinematic parameters, basis function matrix, and derivative matrix of a five-axis machine tool, a VAJ mapping is established between dwell time and surface feed and the kinematic quantities of the five-axis solid axis. The baseline residence time control vector is used as the current control vector, and the residence time increment is used as the optimization variable for iterative optimization. Global constraints are applied based on the material removal map. In each iteration, the current control vector is substituted into the VAJ mapping to calculate the surface feed and five-axis solid axis kinematics of each evaluation point set along the polishing path. The normalized VAJ ratio is obtained by normalizing it according to the corresponding allowable limit. When the VAJ ratio reaches the set threshold, the out-of-tolerance tool contact point and kinematic out-of-tolerance index are determined. The dynamic out-of-tolerance set is established and updated to determine the target item, protection item, active control point and coupling index. Under the absolute RMS budget of the remaining surface shape, the dwell time increment optimization is implemented for the local area corresponding to the active control point, and the coupling index is jointly compensated to obtain the candidate dwell time control point vector. Based on material removal mapping and VAJ mapping, the surface residuals and VAJ indices corresponding to the candidate residence time control point vectors are calculated, and global constraint checks are performed. If the global constraints are met and the target and protection conditions are met, the candidate result is accepted; otherwise, it is rejected, rolled back, or the incremental step size is reduced and the optimization is repeated. The process is repeated until the preset stopping condition is met. After global verification, the final residence time control vector, surface residual, and surface and five-axis VAJ indices are output.

2. The deterministic polishing dwell time collaborative optimization method for kinematic constraints of five-axis machine tools according to claim 1, characterized in that, The optical workpiece to be processed also includes initial surface shape data, target surface shape data, processing path, and tool posture.

3. The deterministic polishing dwell time collaborative optimization method for kinematic constraints of five-axis machine tools according to claim 1, characterized in that, The continuous movement of the machining tool along the scanning path is defined as the path parameter. A one-dimensional parameterized curve, based on the path parameters, constructs a B-spline basis function matrix. First derivative matrix and second derivative matrix And based on the dwell time control point vector The dwell time and its path parameter derivatives at each actual path sampling point are calculated using the following expression: ； in, The actual dwell time of the sampling point along the path, expressed in seconds; This is the first derivative of the actual path sampling point dwell time with respect to the path parameters; This is the second derivative of the actual path sampling point dwell time with respect to the path parameters; The conversion factor for converting dwell time in minutes to dwell time in seconds.

4. The deterministic polishing dwell time collaborative optimization method for kinematic constraints of five-axis machine tools according to claim 1, characterized in that, The VAJ mapping between dwell time and surface feed and five-axis solid axis kinematics is used to determine the corresponding surface feed kinematics based on the dwell time control point vector, and to determine the kinematics of each machine tool solid axis based on the surface feed kinematics, machining path, tool posture, and five-axis machine tool kinematic parameters; the surface feed kinematics include surface feed speed, acceleration, and jerk, and the five-axis solid axis kinematics are the speed, acceleration, and jerk of the X-axis, Y-axis, Z-axis, A-axis, and B-axis; Substituting the reference dwell time control point vector into the VAJ mapping, we obtain the surface feed kinematic vector corresponding to the reference dwell time and the first... The kinematic vectors of the machine tool's physical axes are expressed as follows: ； in, The surface feed kinematics vector corresponding to the baseline dwell time; , as well as These are surface feed rate, surface feed acceleration, and surface feed jerk, respectively; superscript Indicates the baseline dwell time status; This is the transpose symbol.

5. The deterministic polishing dwell time collaborative optimization method for kinematic constraints of five-axis machine tools according to claim 1, characterized in that, The normalized VAJ ratio expression is: ； in, For the first At the first evaluation point Normalized VAJ ratio for kinematic indices; This refers to the actual velocity, acceleration, or jerk at that point. These are the permissible limits for the corresponding kinematic quantities; The process for determining the kinematic deviation index includes: For each evaluation point, the velocity, acceleration, and jerk indices of the surface feed and each solid axis motion are iterated to determine the normalized VAJ ratio corresponding to each kinematic index, and the maximum value among them is taken as the maximum normalized VAJ ratio of the corresponding evaluation point. The expression is: ； in, For the first The maximum normalized VAJ ratio for each evaluation point; Index of kinematic parameters; Normalized VAJ ratio; This represents the maximum value of the kinematic index. When the maximum normalized VAJ ratio is greater than a set threshold, the corresponding evaluation point is determined to be an out-of-tolerance tool contact point, and the velocity, acceleration or jerk index corresponding to the evaluation point with a normalized VAJ ratio greater than the set threshold is determined as a kinematic out-of-tolerance index item.

6. The deterministic polishing dwell time collaborative optimization method for kinematic constraints of five-axis machine tools according to claim 1, characterized in that, The iterative optimization process, using the baseline residence time control vector as the current control vector and the residence time increment as the optimization variable, includes: The dwell time increment vector relative to the reference dwell time control point vector As variables, a candidate residence time control point vector is constructed, expressed as follows: ； in, For the first The increment of each control point, j=1,2,…,P, where P is the total number of control points; It is the transpose symbol; The baseline residence time control point vector; For the candidate residence time control point vector, during optimization initialization, the residence time increment vector is set to a zero vector, expressed as: ； Based on the candidate residence time control point vector, calculate the surface residual, material removal amount and five-axis kinematic index corresponding to the candidate results, and determine the normalized VAJ ratio corresponding to each evaluation point based on the kinematic index. Based on the normalized VAJ ratio, a kinematic overlimit penalty function is constructed, expressed as: ； in, Here is the kinematic overlimit penalty function; Optional penalty levels; and These are the evaluation point index and the kinematic index, respectively. For the first At the first evaluation point The normalized VAJ ratio of the kinematic index under the candidate residence time control point vector; when the normalized VAJ ratio When the threshold is exceeded, the corresponding item will penalize the objective function. The candidate dwell time control point vector is iteratively optimized based on the kinematic over-limit penalty function, and a global constraint is applied to the candidate results after each iteration. The global constraint includes global anti-over-throw, minimum dwell time of actual path sampling points, non-negativity of dwell time control points, and absolute RMS one-sided constraint of the remaining surface shape. If a candidate result does not meet any constraint, the dwell time increment is rolled back or the optimization step size is reduced and optimization is performed again; if a candidate result meets the constraint and the kinematic index meets the set condition, the candidate result is accepted. Wherein, the penalty order To ensure adjustable parameters, the first penalty order is used. Perform global kinematic over-limit optimization, and apply a second penalty order after satisfying the preset constraints. Suppress local kinematic over-limit peak values.

7. The deterministic polishing dwell time collaborative optimization method for kinematic constraints of five-axis machine tools according to claim 1, characterized in that, The process of constructing and updating the dynamic deviation set includes: In the Current stay time Next, the evaluation points and their corresponding velocities, accelerations, and jerk indicators are recalculated. Based on the relationship between the normalized VAJ ratio and the allowable limits of each kinematic indicator, the first... The dynamic deviation set of the wheel is expressed as: ； in, For the first The dynamic out-of-range set corresponding to the current dwell time of the round; Indicates the first The evaluation point of the first The kinematic index exceeds its permissible limit; For the first At the first evaluation point kinematic indicators in residence time Normalized VAJ ratio; The dynamic deviation set is also used to record the deviation knife contact and the corresponding deviation index item: the evaluation point containing the deviation index item in the dynamic deviation set is determined as the deviation knife contact, and the kinematic index corresponding to the set element is determined as the kinematic deviation index item of the deviation knife contact. In the After the candidate residence time control point vectors are accepted, the VAJ is recalculated for all evaluation points and all kinematic indices based on the updated residence time control point vectors, and the VAJ is constructed. The dynamic kinematic error set of the round; for kinematic error indicators that have been eliminated in the previous round, they are removed from the current dynamic kinematic error indicator set; for kinematic error indicators newly generated due to local dwell time compensation, they are added to the current dynamic kinematic error indicator set.

8. The deterministic polishing dwell time collaborative optimization method for kinematic constraints of five-axis machine tools according to claim 1, characterized in that, The absolute RMS budget of the remaining face shape refers to: Starting from the absolute RMS allowable range of the accepted length of stay, set up progressively increasing RMS budget tiers; The absolute RMS upper limit of each budget layer is denoted as: ； in, The absolute RMS of the global residual surface shape corresponding to the candidate residence time control point vector; This represents the maximum absolute RMS allowed in the current optimization round; Within each residual surface absolute RMS budget layer, candidate residuals for local or small-area dwell time increments are generated based on the current dwell time control point vector, resulting in candidate dwell time control point vectors. Based on these candidate dwell time control point vectors, the global material removal amount, residual surface error, and VAJ index for all evaluation points are recalculated to generate candidate results. When the candidate result meets the global constraint check, and the normalized VAJ ratio corresponding to the target item reaches the set condition and the protection item does not exceed the corresponding protection limit, the candidate result is accepted. When a candidate result does not meet any constraint or the normalized VAJ ratio corresponding to the target item does not reach the set condition, the candidate result is rejected and the dwell time increment is rolled back or the increment step size is reduced. When the number of consecutive failures to meet the set conditions reaches a preset number, a constraint risk occurs, or any of the preset budget limit is reached, the current budget layer search is stopped or the optimization is terminated. If the optimization is not terminated, the process proceeds to the next budget layer.

9. The deterministic polishing dwell time collaborative optimization method for kinematic constraints of five-axis machine tools according to claim 1, characterized in that, The joint compensation process includes: When the control points corresponding to the remaining out-of-tolerance indicators have a shared relationship, or when the local compensation of a single out-of-tolerance indicator has a coupling effect on other kinematic indicators with a preset threshold, the velocity, acceleration and jerk indicators corresponding to multiple A-axis and B-axis, as well as the kinematic indicators with coupling effects between them, are determined as joint optimization objectives, and a joint compensation task is constructed based on the joint optimization objectives. Based on the joint compensation task, candidate dwell times are generated, and the material removal amount, remaining surface residual, and VAJ index of all evaluation points corresponding to the candidate dwell times are globally calculated. When the candidate result meets the global constraint check, and the normalized VAJ ratio corresponding to the target item reaches the set condition and the protection item does not exceed the corresponding protection upper limit, the candidate result is accepted. When the remaining out-of-tolerance index is mainly concentrated in the A-axis, B-axis and their coupled influence area, the corresponding A-axis and B-axis joint compensation candidates are constructed, and joint optimization is performed according to the above process.

10. A deterministic polishing dwell time collaborative optimization system for kinematic constraints of a five-axis machine tool, characterized in that, include: The data acquisition module is used to acquire the polishing tool influence function, five-axis machine tool kinematic parameters, and reference dwell time control vector of the optical element to be processed; The parameterization and material mapping module is used to establish the basis function matrix and derivative matrix based on B-splines; and to establish the material removal mapping between residence time and material removal amount based on the polishing tool influence function and basis function matrix. The kinematic mapping pre-calculation module is used to establish the VAJ mapping between dwell time and surface feed and the kinematic quantities of the five-axis solid axis based on the kinematic parameters, basis function matrix and derivative matrix of the five-axis machine tool. The global incremental collaborative optimization module is used to iteratively optimize with the baseline residence time control vector as the current control vector and the residence time increment as the optimization variable, and to apply global constraints based on the material removal map. The dynamic out-of-tolerance set update module is used in each iteration to substitute the current control vector into the VAJ mapping, calculate the surface feed and five-axis solid axis kinematics of each evaluation point set along the polishing path, and normalize them according to the corresponding allowable limit to obtain the normalized VAJ ratio. When the VAJ ratio reaches the set threshold, the out-of-tolerance tool contact point and kinematic out-of-tolerance index item are determined, the dynamic out-of-tolerance set is established and updated, and the target item, protection item, active control point and coupling index are determined. The joint compensation module is used to perform incremental optimization of dwell time for the local area corresponding to the active control point under the absolute RMS budget of the remaining surface shape, and to perform joint compensation for the coupling index to obtain the candidate dwell time control point vector. The candidate result determination and verification module is used to calculate the surface residual and VAJ index corresponding to the candidate residence time control point vector based on the material removal mapping and VAJ mapping, and to perform global constraint checks. If the global constraints are met and the target and protection conditions are met, the candidate result is accepted; otherwise, it is rejected, rolled back, or the incremental step size is reduced and the optimization is repeated. The process is repeated until the preset stopping condition is met. After global verification, the final residence time control vector, surface residual, and surface and five-axis VAJ indices are output.

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