Complex curved surface multi-axis laser processing efficient simulation method based on key point interpolation

Abstract

The invention provides an efficient simulation method for multi-axis laser processing of a complex curved surface based on key point interpolation, which is used for solving the problems that the simulation efficiency is improved through parallel calculation in the conventional pulse-by-pulse laser processing simulation method for the complex curved surface, but the improvement multiple is related to the parallel number; and the simulation efficiency improvement effect is very limited. According to the key point interpolation-based complex curved surface multi-axis laser processing efficient simulation method provided by the invention, a processing track of a complex curved surface is decomposed into a stable section and a non-stable section, and discrete sampling key point pulses are selected on the stable section for iterative calculation; according to the method, two adjacent key point pulses are adopted, interpolation calculation is carried out on the non-key point pulses between the two adjacent key point pulses, the morphology obtained through interpolation is almost consistent with the morphology calculated through an iteration method, the iteration calculation is replaced with the interpolation calculation while the simulation precision is guaranteed, the simulation calculation amount is effectively reduced, and the calculation efficiency is greatly improved.

Description

TECHNICAL FIELD

[0001] The application relates to a laser processing simulation method for a complex curved surface, in particular to a high-efficiency simulation method for multi-axis laser processing of a complex curved surface based on key point interpolation. BACKGROUND

[0002] Pulse laser processing is a precision manufacturing technology that uses high peak power to remove or deposit materials instantaneously. The process involves complex multi-physical field coupling phenomena, including light-matter interaction, heat conduction, phase change, and molten material ejection. To deeply understand the processing mechanism and optimize the process parameters, numerical simulation has become a key research method. However, the simulation model of pulse laser ablation faces huge computational challenges in terms of high fidelity. The simulation of a single pulse ablation requires dense grid discretization and extremely small time steps. Especially when considering nonlinear effects such as plasma shielding and phase explosion, the computational load increases exponentially. In the scenario of multi-axis laser processing of a complex curved surface, thousands to millions of pulses are often superimposed. Multi-pulse simulation cannot achieve the dynamic adjustment of laser incidence angle and defocusing amount caused by the curvature change of the workpiece surface and multi-axis motion, resulting in significant differences in the action area, energy distribution, and material response of each pulse. In addition, the adaptability of existing simulation methods to this dynamic working condition is insufficient, further exacerbating the efficiency bottleneck and precision deviation of multi-pulse simulation.

[0003] To solve the above problems, the industry has developed a pulse-by-pulse laser processing simulation method for complex curved surfaces. This method divides the multi-pulse ablation process into local ablation at different pulse positions and simplifies the iterative calculation of the full pulse sequence into independent calculation at each pulse position to improve simulation efficiency through parallel computing. However, the improvement factor is related to the number of parallel computations, resulting in limited improvement in simulation efficiency for the pulse-by-pulse laser processing simulation method. SUMMARY

[0004] The purpose of the present application is to solve the technical problem that the existing pulse-by-pulse laser processing simulation method for complex curved surfaces improves simulation efficiency through parallel computing, but the improvement factor is related to the number of parallel computations, resulting in limited improvement in simulation efficiency, and to provide a high-efficiency simulation method for multi-axis laser processing of complex curved surfaces based on key point interpolation.

[0005] To achieve the above purpose, the technical solution provided by the present application is as follows: A high-efficiency simulation method for multi-axis laser processing of complex curved surfaces based on key point interpolation, characterized by the following steps: Step 1, define the trajectory segment where the front and rear pulses of the processing trajectory have critical overlap with the current pulse ablation range as a stable segment, and define the remaining trajectory segments as non-stable segments; calculate the ablation morphology of the non-stable segments; Step 2: Discretely sample the laser pulses in the stable segment to obtain all key point pulses in the laser pulses in the stable segment; Step 3: Calculate the ablation morphology at all key pulse points; Step 4: Calculate the non-key point pulses between two adjacent key point pulses. The ablation morphology at the location; Step 4.1: Select any two adjacent keypoint pulses and calculate the non-keypoint pulses between the two adjacent keypoint pulses. Normal on the freeform surface S and the instantaneous ablation velocity along the tangential direction of the light spot's trajectory. And acquire non-critical point pulses. optical axis vector ; Step 4.2, select non-critical point pulses Any point within the processing boundary is taken as the processing point. And calculate the pulses at non-critical points. Point from origin to processing point unit vector ; around the normal direction Calculate non-critical point pulses From instantaneous ablation rate to unit vector rotation angle Then, based on the rotation angle The instantaneous ablation velocity of the two key point pulses along the tangential direction of the spot motion trajectory is rotated to obtain unit vectors pointing to their corresponding positions with the two key point pulses as the origin. The lengths of the two key point pulses along their corresponding unit vector directions to their machining boundaries are calculated, and then the non-key point pulses are calculated. Along its unit vector The length up to its processing boundary; Step 4.3, combining non-critical point pulses Along its unit vector To the length of its machining boundary, determine the corresponding machining points of the two key point pulses within its machining boundary. The coordinates of the processing points are obtained, and interpolation is performed along the optical axis of the two key point pulses in their ablation morphology to obtain the processing amount of the corresponding processing points within the processing boundary of the two key point pulses. This is then combined with the non-key point pulses obtained in step 4.1. Optical axis vector, calculate non-key point pulses Machining points within machining boundaries The machining amount along its optical axis; Step 4.4: Following the methods in steps 4.2 to 4.3, calculate the non-critical point pulses sequentially. the machining amount of all machining points within the machining boundary along the optical axis of the machining point, and then the ablation profile at the non-key point pulse is obtained. Step 4.5, traversing all non-key point pulses between the current two adjacent key point pulses according to the method of steps 4.1-4.4, to obtain the ablation profile at all non-key point pulses between the current two adjacent key point pulses; Step 5, traversing all adjacent two key point pulses on the stable section by the method of step 4, and calculating the ablation profile at all non-key point pulses corresponding thereto; performing Boolean operation on the ablation profiles at all key point pulses and all non-key point pulses on the stable section in the workpiece blank model, to obtain the ablation profile of the stable section, and complete the ablation profile simulation of the free-form surface S.

[0006] Further, in step 1, the ablation profile of the non-stable section is iteratively calculated by using a pulse laser ablation model.

[0007] Further, in step 2, the laser pulses on the stable section are discretely sampled by simultaneously controlling the arc length and chord height difference of adjacent pulses in the spot motion trajectory, to obtain all key point pulses in the laser pulses on the stable section.

[0008] Further, in step 3, the ablation profile at all key point pulses is iteratively calculated by using a pulse laser ablation model.

[0009] Further, in step 4.1, the instantaneous ablation speed of the non-key point pulse in the tangential direction of the spot motion trajectory is calculated by the following formula: ; wherein, is the scanning speed of the non-key point pulse in the focal point scanning trajectory, is the rotational speed of the ablation point of the non-key point pulse around the focal point of the non-key point pulse , is the translational speed of the ablation point of the non-key point pulse along the optical axis direction of the non-key point pulse relative to the focal point of the non-key point pulse , is the tangential direction of the ablation point of the non-key point pulse in the spot motion trajectory.

[0010] Further, in step 4.1, the optical axis vector of the non-key point pulse is obtained by using quaternion interpolation: ; wherein, is the arc length ratio, , and is the non-key point pulse adjacent to the key point pulse . and the key point pulse ; is the optical axis angle, , and are the optical axis vectors of the key point pulse and the key point pulse , respectively.

[0011] Further, step 4.2 is specifically as follows: Step 4.2.1, calculate the unit vector with the non-key point pulse as the origin pointing to the machining point by the following formula: ; Step 4.2.2, calculate the rotation angle of the non-key point pulse from the instantaneous ablation speed to the unit vector : ; Step 4.2.3, define the normal of the key point pulse and the key point pulse on the free-form surface S as and , respectively, and the instantaneous ablation speed in the tangent direction of the spot motion trajectory as and , respectively; rotate the instantaneous ablation speed at the key point pulse by the rotation angle around its normal to obtain the unit vector pointing to the corresponding position with the key point pulse as the origin: ; rotate the instantaneous ablation speed at the key point pulse by the rotation angle around its normal to obtain the unit vector pointing to the corresponding position with the key point pulse as the origin​​ : ; Step 4.2.4, calculating the key point pulse according to the geometric relationship along the unit vector in the direction to the length of its machining boundary , and the key point pulse along the unit vector in the direction to the length of its machining boundary , and then determining the non-key point pulse along the unit vector in the direction to the length of its machining boundary .

[0012] Further, in step 4.2.4, the non-key point pulse along the unit vector in the direction to the length of its machining boundary is determined by the following formula: .

[0013] Further, step 4.3 is specifically: Step 4.3.1, defining as the machining point of the key point pulse in the machining boundary corresponding to the machining point , and as the machining point of the key point pulse in the machining boundary corresponding to the machining point ; the position coordinates of the machining points and are determined according to the following formula respectively: ; wherein, is the distance from the machining point to the non-key point pulse ; Step 4.3.2, interpolating in the ablation topography of the two key point pulses respectively along the optical axis direction to obtain the machining amount of the machining point and the machining amount of the machining point ; and calculating the machining amount of the non-key point pulse along its optical axis in the machining boundary according to the following formula: .

[0014] Further, in step 4.2, when , then​ , .

[0015] Compared with the prior art, the application has the following advantages: 1. The complex curved surface multi-axis laser processing efficient simulation method based on key point interpolation provided by the application decomposes the processing track of the complex curved surface into stable sections and unstable sections, selects a few key point pulses for discrete sampling on the stable sections for iterative calculation, and interpolates a large number of non-key point pulses between two adjacent key point pulses for interpolation calculation, the morphology obtained by interpolation is almost consistent with the morphology calculated by the iterative method, while ensuring the simulation accuracy, the interpolation calculation is used to replace the iterative calculation, thereby effectively reducing the simulation calculation amount and greatly improving the calculation efficiency.

[0016] 2. The complex curved surface multi-axis laser processing efficient simulation method based on key point interpolation provided by the application is a local calculation method, and can further improve the calculation efficiency by combining parallel calculation. BRIEF DESCRIPTION OF DRAWINGS

[0017] Figure 1 FIG. 2 is a schematic diagram of laser processing of the free curved surface S in step 2 of the embodiment of the complex curved surface multi-axis laser processing efficient simulation method based on key point interpolation; Figure 2 FIG. 3 is a schematic diagram of obtaining the instantaneous ablation speed in step 2 of the embodiment of the method; Figure 3 FIG. 4 is a schematic diagram of calculating the ablation morphology of the non-key point pulses between two adjacent key point pulses by using the interpolation method in step 3 of the embodiment of the method; Figure 4 FIG. 5 is a schematic diagram of the final ablation morphology of the workpiece to be processed obtained by using the complex curved surface multi-axis laser processing efficient simulation method based on key point interpolation of the application; Figure 5 FIG. 6 is a simulation schematic diagram of laser processing on a plane in a single row scanning mode at different speeds by using the method; Figure 6 FIG. 7 is a simulation schematic diagram of laser processing on a plane in a double row scanning mode with different row distances by using the method; Figure 7 FIG. 8 is a simulation schematic diagram of laser processing on a complex curved surface in a multi-row scanning mode by using the method. DETAILED DESCRIPTION

[0018] In order to make the advantages and characteristics of the application more clear, the application will be further described in detail below in combination with the drawings and specific embodiments.

[0019] A complex curved surface multi-axis laser processing efficient simulation method based on key point interpolation, specifically comprising the following steps: Step 1, complex surface decomposition.

[0020] The complex surface of the workpiece to be processed in this embodiment is denoted as a free surface S. For a multi-pulse ablation process, the ablation morphology of any one pulse on the processing trajectory is affected by the surrounding pulses within a certain range. It is necessary to determine whether the front and rear pulses overlap with the ablation range of the current pulse. When the front and rear pulses on the processing trajectory both have a critical overlap with the ablation range of the current pulse, the trajectory segment is defined as a stable segment. The remaining trajectory segments are uniformly defined as non-stable segments, including a trajectory segment in which only any one of the front and rear pulses has a critical overlap with the ablation range of the current pulse, or a trajectory segment in which the front and rear pulses both do not have a critical overlap with the ablation range of the current pulse.

[0021] The pulses corresponding to the non-stable segments are generally located at the starting and ending positions of the trajectory, and account for a small proportion of the total number of pulses. The ablation morphology of the non-stable segments can be directly calculated by using the existing pulse laser ablation model. The ablation morphology of the stable segments, which account for a large proportion of the total number of pulses, can be calculated according to the subsequent method, thereby achieving efficient solution.

[0022] Step 2, key point pulse extraction.

[0023] As shown in FIG. 1, the free surface S is processed by laser, and the focal point scanning trajectory of the laser is denoted as L, the spot motion trajectory of the laser on the free surface S is denoted as S, the action positions of the i-2th pulse, the i-1th pulse, the ith pulse, the i+1th pulse and the i+2th pulse on the focal point scanning trajectory L are respectively denoted as L(i-2), L(i-1), L(i), L(i+1) and L(i+2), i≥3, i.e., the focal points of the corresponding pulses, the action positions of the i-2th pulse, the i-1th pulse, the ith pulse, the i+1th pulse and the i+2th pulse on the spot motion trajectory S are respectively denoted as S(i-2), S(i-1), S(i), S(i+1) and S(i+2), i.e., the ablation points of the corresponding pulses, the optical axis vectors of the corresponding pulses are respectively denoted as O(i-2), O(i-1), O(i), O(i+1) and O(i+2), and the ablation morphologies of the i-2th pulse, the i-1th pulse, the ith pulse, the i+1th pulse and the i+2th pulse on the focal point scanning trajectory L are respectively denoted as A(i-2), A(i-1), A(i), A(i+1) and A(i+2). Figure 1 ​​​​​​​​​​​​​​​​​​​​​​​​​The scanning speed on , , , , These are the corresponding pulse trajectories in the light spot. The instantaneous ablation rate on the surface.

[0024] In actual processing, in order to meet the high-precision processing requirements of freeform surface S, it is necessary to use multi-axis processing equipment to perform processing with variable axis, variable speed, and variable defocus. Therefore, the optical axis vector, scanning speed, instantaneous ablation speed, and defocus amount are constantly changing under different pulses during the processing.

[0025] The focal scan trajectory is usually known during processing. The laser's motion speed and optical axis vector are used to easily obtain the focal point of the i-th pulse. In the focal scan trajectory On the scanning speed and optical axis vector By focusing the i-th pulse The ablation point of the i-th pulse can be obtained by projecting it onto the freeform surface S along its optical axis. Then, based on the ablation point of the i-th pulse... Calculate the trajectory of the i-th pulse in the light spot. instantaneous ablation rate ,like Figure 2 As shown, combining the theory of rigid body motion, we have ( ) in, The ablation point of the i-th pulse Around the i-th pulse focus rotational speed, The ablation point of the i-th pulse Along its optical axis relative to the i-th pulse focus The translational speed.

[0026] Focus on the i-th pulse along the focal scan trajectory Move to the (i+1)th pulse focus The time is recorded as So, rotational speed It can be represented as: ( ) in, Let be the angular velocity of the i-th pulse.

[0027] when Without rotational motion, let .

[0028] Similarly, the translation velocity can be approximated as: ( ) In the calculation of formula and formula , the process of the i-th pulse optical axis vector to the i+1-th pulse optical axis vector is approximated as uniform rotation around the i-th pulse focal point , and the relative motion of the ablation point of the i-th pulse along the direction of the i-th pulse optical axis vector is approximated as uniform translation, resulting in a certain deviation in the calculation of the rotation speed and the translation speed , and further resulting in a large deviation in the direction of the speed when calculating the beam motion speed using formula . Therefore, the present application defines the tangent of the ablation point of the i-th pulse on the spot motion trajectory as , and corrects the direction of the calculation result, thereby obtaining the instantaneous ablation speed of the i-th pulse on the spot motion trajectory , i.e. ( ) Under the condition that the laser parameters are unchanged, the main factors affecting the ablation morphology include the beam motion speed, the optical axis vector, the surface normal, and the defocusing amount, etc. Generally, to obtain all the key point pulses in the laser pulse, it is necessary to establish a corresponding discrete control function by comprehensively considering the above influencing factors, so as to discretely sample the spot motion trajectory based on the ablation morphology change amount of adjacent positions. Considering that the optical axis of the general laser processing changes little, and the surface of the processed material and the curvature of the scanning trajectory line will not change greatly, the present application discretely samples the laser pulses on the stable section by simultaneously controlling the arc length and chord height difference of adjacent pulses in the spot motion trajectory , thereby quickly obtaining all the key point pulses in the laser pulses of the stable section.

[0029] Step 3, calculate the ablation morphology at all key point pulses.

[0030] By combining the surrounding pulses that affect the key point pulses, the existing pulse laser ablation model is used to iteratively calculate the ablation morphology at all key point pulses, which will not be described here.

[0031] Step 4, interpolation method is used to calculate the ablation profile at non-key point pulse between two adjacent key point pulses.

[0032] Definition and Two adjacent key point pulses, the key point pulse The ablation profile at the key point pulse is The ablation profile at the key point pulse is , where is the removal profile at the key point pulse , is the redeposition profile at the key point pulse , is the removal profile at the key point pulse , is the redeposition profile at the key point pulse . .

[0033] The non-key point pulse between the key point pulse and the key point pulse is denoted as , and the ablation profile of the non-key point pulse is calculated by interpolation.

[0034] As shown in Figure 3 , the normal of the key point pulse and the key point pulse on the freeform surface S are and respectively, the instantaneous ablation velocity of the key point pulse in the tangential direction of the spot motion trajectory is and , the optical axis vector of the key point pulse is and , and the machining boundary of the key point pulse is

[0035] and . The normal of the non-key point pulse on the freeform surface S is calculated as , and the instantaneous ablation velocity of the non-key point pulse in the tangential direction of the spot motion trajectory is calculated as . The instantaneous ablation velocity of the non-key point pulse in the tangential direction of the spot motion trajectory is combined with formula (4) for calculation, and has:

[0036] wherein, is the non-critical point pulse the scanning speed on the focal point scanning trajectory, is the rotation speed of the ablation point of the non-critical point pulse around the non-critical point pulse focal point, is the translation speed of the ablation point of the non-critical point pulse along its optical axis direction relative to the non-critical point pulse focal point, is the tangential direction of the ablation point of the non-critical point pulse on the spot motion trajectory.

[0037] and the optical axis vector of the current non-critical point pulse is obtained by using quaternion interpolation, i.e.: ( ) wherein, is the arc length ratio, , is the optical axis angle, .

[0038] Definition is the processing boundary of the non-critical point pulse , is the position coordinate of any processing point in the processing boundary , is the unit vector pointing to the processing point from the non-critical point pulse , , is the processing amount along the optical axis vector direction, the negative value is the removal amount, and the positive value is the redeposition amount, is the distance from the processing point to the non-critical point pulse .

[0039] around the normal , the rotation angle of the non-critical point pulse from the instantaneous ablation speed to the unit vector is calculated, wherein ( ) the instantaneous ablation speed at the critical point pulse is rotated around its normal ​​​By rotation angle Rotate to obtain keypoint pulses The unit vector pointing from the origin to the corresponding position. ,Right now ( ) Calculate key point pulses based on geometric relationships. Along unit vector Direction to its processing boundary length Similarly, the above method is used to obtain key point pulses. Along unit vector Direction to its processing boundary length Non-critical point pulses are determined using a distance-weighted average method. Along unit vector Direction to its processing boundary length ,Right now ( ) definition Key point pulse Processing boundary Internal corresponding processing point Processing point, Key point pulse Processing boundary Internal corresponding processing point The processing points. Based on non-critical point pulses. Along unit vector Direction to its processing boundary length Key point pulse Along unit vector Direction to its processing boundary length Key point pulse Along unit vector Direction to its processing boundary length Determine the processing point and processing point The position coordinates, i.e. ( ) Then along the optical axis vector respectively and optical axis vector Direction at key point pulse ablation morphology at the site and key point pulse ablation profile at the machining point . the machining amount at the machining point and the machining point . the machining boundary the machining point the machining amount along its optical axis at the machining point .

[0040] According to the above method, the machining amount along the optical axis at all machining points within the machining boundary is calculated in turn, and the ablation profile at the non-key point pulse is determined. . Figure 3 , , are the coordinates after machining at the key point pulse , the key point pulse , and the non-key point pulse , respectively.

[0041] Similarly, according to the above method, all the remaining non-key point pulses between the key point pulse and the key point pulse are traversed, and the ablation profile at all non-key point pulses between the key point pulse and the key point pulse is obtained.

[0042] It is worth noting that when the selected is at the center of the pulse action position, i.e., , then the machining amount and the machining amount are directly accessed to obtain the machining amount and the machining amount , and finally the machining amount along the optical axis vector at the machining point is determined using the above method. .

[0043] Step 5: Complete the ablation profile simulation of the free-form surface S.

[0044] All adjacent two key point pulses on the stable section are traversed, and the ablation profile at all non-key point pulses between the two adjacent key point pulses is calculated using the above interpolation method. Finally, the ablation profiles at all key point pulses and all non-key point pulses on the stable section are subjected to Boolean operation in the workpiece blank model to obtain the ablation profile of the stable section. Combined with the previously calculated ablation profile of the non-stable section, the ablation profile of the free-form surface S is obtained as​Figure 4 the final ablation morphology of the free surface S of the workpiece to be processed.

[0045] In the calculation of the ablation morphology of the workpiece to be processed, if each pulse is calculated by using the existing iterative model, the calculation time of each pulse is 75.05 ms, and for 1250 pulses, the average calculation time of each pulse is still 75.05 ms. If the complex curved surface multi-axis laser processing high-efficiency simulation method based on key point interpolation of the present application is used, among the 1250 pulses in the stable stage, the pulses at the starting, middle and ending positions are selected as the three key point pulses, and the remaining pulses are interpolated and calculated as the processing points in the non-key point pulses. The calculation time of the three key point pulses is 75.05 ms, and the interpolation calculation time of the processing points in the remaining non-key point pulses is 16.58 ms. Therefore, the average calculation time of 1250 pulses is only 16.72 ms, and the calculation efficiency is improved by several times. It is worth noting that the above method is the ablation morphology calculation process under single line scanning processing. For multi-line processing, only the ablation morphology under each line scanning processing is calculated by the above method, and then the ablation morphologies of multiple lines are subjected to Boolean operation in the workpiece blank model, so that the final ablation morphology of the workpiece to be processed under multi-line scanning processing can be obtained. For multi-layer processing, the above method is still used.

[0046] The complex curved surface multi-axis laser processing high-efficiency simulation method based on key point interpolation of the present application is used for laser processing on different surfaces in different scanning modes. Figure 5 The simulation diagram for laser processing on a plane in a single line scanning mode at different speeds is shown. The single line vertical scribing processing without defocusing is carried out on the plane at a speed of 200 mm / s, 400 mm / s and 600 mm / s under the condition that the laser power is 4 W and the repetition frequency is 100 kHz. Figure 6 The simulation diagram for laser processing on a plane in a double line scanning mode with different line distances is shown. The double line vertical scribing processing without defocusing is carried out on the plane at a speed of 400 mm / s and line distances of 5 μm, 10 μm and 15 μm under the condition that the laser power is 4 W and the repetition frequency is 100 kHz. Figure 7 The simulation diagram for laser processing on a complex curved surface in a multi-line scanning mode is shown. The vertical scribing processing without defocusing is carried out on the complex curved surface at a speed of 400 mm / s and a line distance of 10 μm under the condition that the laser power is 4 W and the repetition frequency is 100 kHz. Figures 5-7 It can be seen that the complex curved surface multi-axis laser processing high-efficiency simulation method based on key point interpolation of the present application can not only realize fast laser processing simulation on a plane, but also realize fast laser processing simulation on a complex curved surface.

[0047] The above merely aims to explain the technical solutions of the present application, and is not intended to limit the same. Those skilled in the art can make modifications to the specific technical solutions described in the above embodiments, or make equivalent replacements to some of the technical features, and these modifications or replacements do not cause the corresponding technical solutions to deviate from the scope of the technical solutions protected by the present application.

Claims

1. A key point interpolation-based efficient simulation method for multi-axis laser processing of complex curved surfaces, characterized in that, The method comprises the following steps: Step 1, define the track segment with critical overlap between the current pulse and the previous and subsequent pulses in the machining track as a stable segment, and define the remaining track segments as unstable segments; calculate the ablation morphology of the unstable segments; Step 2, discretely sample the laser pulses on the stable segment to obtain all key point pulses; Step 3, calculate the ablation morphology at all key point pulses; Step 4, calculating the ablation profile of the non-key point pulse between two adjacent key point pulses at the non-key point pulse Step 4.1, optionally two adjacent key point pulses, calculate the non-key point pulse between two adjacent key point pulses Normal on the free-form surface S And the instantaneous ablation speed in the tangential direction of the spot motion trajectory , and obtain the optical axis vector of the non-key point pulse ;​ Step 4.2, select non-critical point pulses Any point within the processing boundary is taken as the processing point. And calculate the pulses at non-critical points. Point from origin to processing point unit vector ; around the normal direction Calculate non-critical point pulses From instantaneous ablation rate to unit vector rotation angle Then, based on the rotation angle The instantaneous ablation velocity of the two key point pulses in the tangential direction of the spot motion trajectory is rotated to obtain a unit vector pointing to the corresponding position with the two key point pulses as the origin. The length of each key point pulse to its machining boundary along its corresponding unit vector direction is calculated, and then the non-key point pulse is obtained along its unit vector to its machining boundary; Step 4.3, combining non-critical point pulses along its unit vector to its processing boundary, respectively determine the processing point coordinates of the two critical point pulses at the corresponding processing points within their processing boundaries , and respectively interpolate in the ablation topography along the optical axis direction of the two critical point pulses to obtain the processing amount of the corresponding processing points within the processing boundaries of the two critical point pulses, and then combine the optical axis vectors of the non-critical point pulses obtained in step 4.1 to calculate the processing amount of the processing points within the processing boundaries of the non-critical point pulses along their optical axes; Step 4.4, calculate the non-critical point pulse in turn according to the method of step 4.2~step 4.3 The machining amount of all machining points in the machining boundary along the optical axis is calculated, and the ablation morphology at the non-critical point is obtained ​ Step 4.5, traverse all non-key point pulses between the current two adjacent key point pulses according to the method of steps 4.1-4.4 to obtain the ablation morphology at all non-key point pulses between the current two adjacent key point pulses; Step 5, traverse all adjacent two key point pulses on the stable segment by the method of step 4, and calculate the ablation morphology at all non-key point pulses corresponding thereto; Perform Boolean operation on the ablation morphologies at all key point pulses and all non-key point pulses on the stable segment in the workpiece blank model to obtain the ablation morphology of the stable segment, and complete the ablation morphology simulation of the free-form surface S.

2. The efficient simulation method of multi-axis laser machining of complex curved surfaces based on key point interpolation according to claim 1, wherein: In step 1, the ablation morphology of the unstable segment is iteratively calculated by using a pulse laser ablation model.

3. The efficient simulation method of multi-axis laser machining of complex curved surfaces based on key point interpolation according to claim 2, wherein: In step 2, all key point pulses are obtained by discretely sampling the laser pulses on the stable segment by simultaneously controlling the arc length and chord height difference of adjacent pulses in the spot movement track.

4. The efficient simulation method of multi-axis laser machining of complex curved surfaces based on key point interpolation according to claim 3, wherein: In step 3, the ablation morphology at all key point pulses is iteratively calculated by using a pulse laser ablation model.

5. The efficient simulation method of multi-axis laser machining of complex curved surfaces based on key point interpolation according to claim 4, wherein: In step 4.1, the non-critical point pulses Instantaneous ablation velocity in the tangential direction of the spot motion trajectory This is calculated by the formula: ； wherein is the non-critical point pulse is the scanning speed of the focal spot on the focal scan trajectory, is the non-critical point pulse is the translation speed of the ablation spot of the non-critical point pulse around the focal spot is the rotation speed of the focal spot, is the non-critical point pulse is the translation speed of the ablation spot of the non-critical point pulse along its optical axis direction is the translation speed of the focal spot, is the non-critical point pulse is the tangential component of the ablation spot of the non-critical point pulse on the spot motion trajectory.

6. The efficient simulation method of multi-axis laser machining of complex curved surfaces based on key point interpolation according to claim 5, wherein: In step 4.1, the non-critical point pulses are obtained using quaternion interpolation of the optical axis vector : ； wherein is the arc length ratio, , and is a non-key point pulse between key point pulses is a key point pulse and key point pulse ; is the optical axis angle, , and are optical axis vectors of key point pulse and key point pulse , respectively.

7. The method of claim 6, wherein the method further comprises: Step 4.2 is specifically: Step 4.2.1, calculate with non-key point pulses to the machining point unit vector : ； Step 4.2.2, around normal Computing non-critical point pulses From instantaneous ablation velocity To unit vector Rotation angle : ； Step 4.2.3, defining key point pulses and key point pulses The normal on the freeform surface S is respectively and The instantaneous ablation speed in the tangential direction of the spot motion trajectory is respectively and and ; Key point pulse instantaneous ablation rate at the point Around its normal direction By rotation angle Rotate to obtain keypoint pulses The unit vector pointing from the origin to the corresponding position. : ； Key point pulse instantaneous ablation rate at the point Around its normal direction By rotation angle Rotate to obtain keypoint pulses The unit vector pointing from the origin to the corresponding position. : ； Step 4.2.4, calculating the key point pulse according to the geometric relationship along the unit vector in the direction to the length of its machining boundary , and the key point pulse along the unit vector in the direction to the length of its machining boundary , and then determining the non-key point pulse in the distance weighted average manner along the unit vector in the direction to the length of its machining boundary .

8. The efficient simulation method of multi-axis laser machining of complex curved surfaces based on key point interpolation according to claim 7, wherein: In step 4.2.4, the non-critical point pulses are determined using the following formula along the unit vector to the length of its processing border : 。 9. The method of claim 8, wherein, Step 4.3 is specifically: Step 4.3.1, Define Key point pulse corresponding machining points within the machining boundary Processing point, Key point pulse corresponding machining points within the machining boundary The processing points are determined according to the following formulas. and processing point Location coordinates: ； wherein, is a processing point to a non-critical point pulse distance; Step 4.3.2, interpolate the machining amount of the machining point along the optical axis direction of the two key point pulses in its ablation morphology respectively, and obtain the machining point The machining amount of the machining point and the machining point The machining amount of the machining point ; and calculate the non-key point pulse machining point The machining amount of the machining point along its optical axis : 。 10. The efficient simulation method of multi-axis laser machining of complex curved surfaces based on key point interpolation according to claim 9, wherein: In step 4.2, when then , .

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