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

Abstract

This invention provides an efficient simulation method for multi-axis laser processing of complex surfaces based on keypoint interpolation. It addresses the technical problem that existing pulse-by-pulse laser processing simulation methods for complex surfaces, while improving simulation efficiency through parallel computing, suffer from limited efficiency gains due to the dependence of the number of parallel operations on the efficiency gain. The proposed method decomposes the processing trajectory of the complex surface into stable and unstable segments. Discretely sampled keypoint pulses are selected for iterative calculation within the stable segment, and interpolation is performed on non-keypoint pulses between two adjacent keypoint pulses. The interpolated morphology is almost identical to that calculated using the iterative method. By replacing iterative calculations with interpolation while maintaining simulation accuracy, the computational load is effectively reduced, significantly improving computational efficiency.

Description

Technical Field

[0001] This invention relates to a laser processing simulation method for complex curved surfaces, and more particularly to an efficient simulation method for multi-axis laser processing of complex curved surfaces based on key point interpolation. Background Technology

[0002] Pulsed laser processing is a precision manufacturing technology that uses high peak power to instantaneously act on materials to remove or deposit material. The process involves complex multiphysics coupling phenomena, including light-matter interaction, heat conduction, phase transitions, and molten material ejection. Numerical simulation has become a key research tool for gaining a deeper understanding of the processing mechanism and optimizing process parameters. However, pulsed laser ablation simulation models face significant computational challenges in achieving high fidelity. Simulating a single pulse ablation requires dense mesh discretization and extremely small time steps, especially when considering nonlinear effects (such as plasma shielding and phase explosion), where the computational load increases exponentially. In complex curved surface multi-axis laser processing scenarios, thousands to millions of pulses are often superimposed. Multi-pulse simulation struggles to capture the curvature changes of the workpiece surface and the dynamic adjustment of the laser incident angle and defocus caused by multi-axis motion, resulting in significant differences in the action area, energy distribution, and material response of each pulse. Furthermore, existing simulation methods are insufficiently adaptable to such dynamic conditions, further exacerbating the efficiency bottleneck and accuracy deviation of multi-pulse simulation.

[0003] To address the aforementioned issues, the industry has developed a pulse-by-pulse laser processing simulation method for complex curved surfaces. This method decomposes the multi-pulse ablation process into localized ablation at different pulse locations and simplifies the iterative calculation of the entire pulse sequence into independent calculations at each pulse position, thereby improving simulation efficiency through parallel computing. However, since the efficiency improvement is related to the number of parallel operations, the effect of the pulse-by-pulse laser processing simulation method on improving simulation efficiency is quite limited. Summary of the Invention

[0004] The purpose of this invention is to solve the technical problem that existing simulation methods for pulse-by-pulse laser processing of complex curved surfaces improve simulation efficiency through parallel computing, but the improvement effect is very limited because the improvement factor is related to the number of parallel operations. The invention provides a high-efficiency simulation method for multi-axis laser processing of complex curved surfaces based on key point interpolation.

[0005] To achieve the above objectives, the technical solution provided by the present invention is as follows:

[0006] A highly efficient simulation method for multi-axis laser processing of complex curved surfaces based on key point interpolation is characterized by the following steps:

[0007] Step 1: Define the trajectory segment in the machining trajectory where the ablation range of both the preceding and following pulses has a critical overlap with that of the current pulse as a stable segment, and define the remaining trajectory segments as unstable segments; calculate the ablation morphology of the unstable segments.

[0008] 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;

[0009] Step 3: Calculate the ablation morphology at all key pulse points;

[0010] Step 4: Calculate the non-key point pulses between two adjacent key point pulses. The ablation morphology at the location;

[0011] 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 ;

[0012] 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;

[0013] 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;

[0014] Step 4.4: Following the methods in steps 4.2 to 4.3, calculate the non-critical point pulses sequentially. The machining amount along the optical axis of all machining points within the machining boundary is used to obtain non-critical point pulses. The ablation morphology at the location;

[0015] Step 4.5: Traverse all non-critical pulses between the two adjacent critical pulses using the methods in Steps 4.1 to 4.4 to obtain the ablation morphology at all non-critical pulses between the two adjacent critical pulses.

[0016] Step 5: Traverse all adjacent key point pulses on the stable segment using the method in Step 4, and calculate the ablation morphology at all corresponding non-key point pulses; perform Boolean operations on the ablation morphology 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 freeform surface S.

[0017] Furthermore, in step 1, the ablation morphology of the unstable segment is calculated iteratively using a pulsed laser ablation model.

[0018] Furthermore, in step 2, the laser pulses on the stable segment are discretely sampled by simultaneously controlling the arc length and chord height difference of adjacent pulses in the laser spot motion trajectory, thereby obtaining all key point pulses in the laser pulses of the stable segment.

[0019] Furthermore, in step 3, the ablation morphology at all key point pulses is calculated iteratively using a pulsed laser ablation model.

[0020] Furthermore, in step 4.1, non-critical point pulses Instantaneous ablation velocity along the tangential direction of the light spot's trajectory Calculated using the following formula:

[0021] ;

[0022] in, Non-critical point pulse Scanning speed on the focal scan trajectory, Non-critical point pulse ablation points around non-critical points pulse The rotational speed of the focal point, Non-critical point pulse The ablation point along its optical axis relative to the non-critical point pulse The translation speed of the focal point, Non-critical point pulse The tangential direction of the ablation point on the trajectory of the light spot.

[0023] Furthermore, in step 4.1, quaternion interpolation is used to obtain non-critical point pulses. optical axis vector :

[0024] ;

[0025] in, It is the ratio of arc length. , and For two adjacent key point pulses, Key point pulse and key point pulse Non-critical point pulses between; The angle between the optical axes, , and Key point pulses and key point pulse The optical axis vector.

[0026] Furthermore, step 4.2 specifically includes:

[0027] Step 4.2.1, calculate the non-critical point pulse using the following formula. Point from origin to processing point unit vector :

[0028] ;

[0029] Step 4.2.2, around the normal direction Calculate non-critical point pulses From instantaneous ablation rate to unit vector rotation angle :

[0030] ;

[0031] Step 4.2.3, Define key point pulses and key point pulse The normals on the freeform surface S are respectively and Its trajectory of light spot movement The instantaneous ablation rates in the tangential direction are respectively and ;

[0032] 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. :

[0033] ;

[0034] 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. :

[0035] ;

[0036] Step 4.2.4: Calculate key point pulses based on geometric relationships. Along unit vector Length from direction to its machining boundary and key point pulses Along unit vector Length from direction to its machining boundary Then, a distance-weighted average method is used to determine the non-critical point pulses. Along unit vector Length from direction to its machining boundary .

[0037] Furthermore, in step 4.2.4, the non-critical point pulses are determined using the following formula. Along unit vector Length from direction to its machining boundary :

[0038] .

[0039] Furthermore, step 4.3 specifically includes:

[0040] 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:

[0041] ;

[0042] in, For processing point Pulse to non-critical point The distance;

[0043] Step 4.3.2: Interpolate along the optical axis of the two key point pulses in their ablation morphology to obtain the processing points. Processing volume and processing point Processing volume ; and calculate the non-critical point pulse using the following formula. Machining points within machining boundaries Machining amount along its optical axis :

[0044] .

[0045] Furthermore, in step 4.2, when At that time, , .

[0046] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0047] 1. This invention provides an efficient simulation method for multi-axis laser processing of complex curved surfaces based on key point interpolation. The processing trajectory of the complex curved surface is decomposed into stable and unstable segments. On the stable segment, discretely sampled key point pulses (a small number) are selected for iterative calculation, and interpolation calculation is performed on non-key point pulses (a large number) between two adjacent key point pulses. The morphology obtained by interpolation is almost consistent with the morphology calculated by the iterative method. While ensuring the simulation accuracy, the interpolation calculation replaces the iterative calculation, which effectively reduces the amount of simulation calculation and greatly improves the calculation efficiency.

[0048] 2. The efficient simulation method for multi-axis laser processing of complex curved surfaces based on key point interpolation provided by this invention is a local calculation method, which can be combined with parallel computing to further improve the calculation efficiency. Attached Figure Description

[0049] Figure 1 This is a schematic diagram of laser processing of freeform surface S in step 2 of an embodiment of an efficient simulation method for multi-axis laser processing of complex curved surfaces based on key point interpolation according to the present invention.

[0050] Figure 2 This is a schematic diagram illustrating the instantaneous ablation rate obtained in step 2 of this embodiment of the method.

[0051] Figure 3 This is a schematic diagram illustrating the ablation morphology at non-critical point pulses between two adjacent critical point pulses calculated using the interpolation method in step 3 of this embodiment of the method.

[0052] Figure 4 This is a schematic diagram of the final ablation morphology of the workpiece to be processed, obtained by using the efficient simulation method for multi-axis laser processing of complex curved surfaces based on key point interpolation of the present invention.

[0053] Figure 5 This is a simulation diagram of laser processing on a plane using this method with single-line scanning at different speeds;

[0054] Figure 6 This is a simulation diagram of laser processing on a plane using this method with double-line scanning at different line spacings;

[0055] Figure 7 This is a simulation diagram illustrating laser processing on complex curved surfaces using this method with multi-line scanning. Detailed Implementation

[0056] To make the advantages and features of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0057] An efficient simulation method for multi-axis laser processing of complex curved surfaces based on key point interpolation, specifically including the following steps:

[0058] Step 1: Complex surface decomposition.

[0059] In this embodiment, the complex curved surface of the workpiece to be processed is denoted as the free surface S. For the multi-pulse ablation process, the ablation morphology of any pulse on the processing trajectory is affected by the pulses within a certain range around it. It is necessary to determine whether the ablation range of the preceding and following pulses overlaps with that of the current pulse. The trajectory segment on the processing trajectory where the ablation ranges of the preceding and following pulses and the current pulse both have critical overlap is defined as a stable segment. The remaining trajectory segments are uniformly defined as unstable segments, including trajectory segments where only the ablation range of any one of the preceding and following pulses has critical overlap with that of the current pulse, or trajectory segments where the ablation ranges of the preceding and following pulses and the current pulse do not have critical overlap.

[0060] The pulses corresponding to the unstable segments are generally located at the beginning and end of the trajectory and account for a small proportion of the total number of pulses. The existing pulsed laser ablation model can be used to iteratively calculate and obtain the ablation morphology of the unstable segments. For the stable segments, which account for the majority of the total number of pulses, the ablation morphology can be calculated according to the subsequent methods, thereby achieving efficient solution.

[0061] Step 2, key point pulse extraction.

[0062] like Figure 1 As shown, laser processing is performed on the freeform surface S, defining... This represents the focal scanning trajectory of the laser. The trajectory of the laser beam on the freeform surface S. , , , , The focal scanning trajectories of the (i-2)th pulse, (i-1)th pulse, ith pulse, (i+1)th pulse, and (i+2)th pulse are respectively located at the focal point. The position of action on the pulse, i≥3, corresponds to the focal point of the pulse. , , , , The pulses i-2, i-1, i, i+1, and i+2 are respectively located on the trajectory of the light spot. The point of action on the pulse corresponds to the ablation point of the pulse. , , , , These are the optical axis vectors of the corresponding pulses. , , , , These are the corresponding pulse scanning trajectories at the focal point. The scanning speed on , , , , These are the corresponding pulse trajectories in the light spot. The instantaneous ablation rate on the surface.

[0063] 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.

[0064] 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

[0065] ( )

[0066] 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.

[0067] 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:

[0068] ( )

[0069] in, Let be the angular velocity of the i-th pulse.

[0070] when There is no rotational motion, so .

[0071] Similarly, translation speed It can be approximated as:

[0072] ( )

[0073] In the formula Japanese style In the calculation, the optical axis vector of the i-th pulse is... up to the (i+1)th pulse optical axis vector The process is approximately centered around the i-th pulse focus. The uniform rotation will ablate the i-th pulse point. Along the optical axis vector of the i-th pulse The relative motion in the direction is approximately uniform translation, which leads to a change in rotational speed. Translation speed There is a certain deviation in the calculation, which leads to the use of formula... Calculate the speed of the beam This can cause a significant deviation in the velocity direction. Therefore, this invention defines the ablation point of the i-th pulse. In the trajectory of the light spot Tangential direction on The calculation results are then corrected for direction to obtain the trajectory of the i-th pulse in the light spot. instantaneous ablation rate ,Right now

[0074] ( )

[0075] With laser parameters remaining constant, the main factors affecting the ablation morphology include beam velocity, optical axis vector, surface normal, and defocusing. Typically, to obtain all key pulse points within the laser pulse, a corresponding discrete control function needs to be established, taking into account these influencing factors. This allows for the control of the beam trajectory while managing the changes in ablation morphology at adjacent positions. Discrete sampling is performed. Considering that the optical axis change is generally small in laser processing and the surface curvature of the processed material and the scanning trajectory line will not change significantly, this invention simultaneously controls adjacent pulses on the spot movement trajectory. The laser pulses in the stable segment are discretely sampled by taking the arc length and chord height difference, thereby quickly obtaining all key point pulses in the stable segment laser pulses.

[0076] Step 3: Calculate the ablation morphology at all key pulse points.

[0077] Combining the surrounding pulses that affect the key point pulse, the existing pulsed laser ablation model is used to iteratively calculate the ablation morphology at all key point pulses, which will not be elaborated here.

[0078] Step 4: Use interpolation to calculate the ablation morphology at the non-critical point pulses between two adjacent critical point pulses.

[0079] definition and If there are two adjacent keypoint pulses, then the keypoint pulses The ablation morphology at the location is Key point pulse The ablation morphology at the location is ,in Key point pulse The morphology of the removed area Key point pulse The redeposition morphology at the location, Key point pulse The morphology of the removed area Key point pulse redeposition morphology at the location .

[0080] Key point pulse and key point pulse Non-critical point pulses between are denoted as Non-critical point pulse The ablation morphology was calculated by interpolation in the following way.

[0081] like Figure 3 As shown, the pulse of the known beam at a key point on the freeform surface S. and key point pulse The normals on the freeform surface S are respectively and Its trajectory of light spot movement The instantaneous ablation rates in the tangential direction are respectively and The optical axis vectors are respectively and The processing boundaries are respectively and .

[0082] Calculate non-critical point pulses Normal on the freeform surface S and non-critical point pulses In the trajectory of the light spot tangential instantaneous ablation rate Among them, non-critical point pulses In the trajectory of the light spot tangential instantaneous ablation rate Combining equation (4) with the calculation, we have:

[0083]

[0084] in, Non-critical point pulse In the focus scan trajectory The scanning speed on Non-critical point pulse ablation points around non-critical points pulse The rotational speed of the focal point, Non-critical point pulse The ablation point along its optical axis relative to the non-critical point pulse The translation speed of the focal point, Non-critical point pulse The ablation point is on the trajectory of the light spot. Tangential direction.

[0085] The optical axis vector of the current non-key point pulse is obtained by quaternion interpolation. ,Right now:

[0086] ( )

[0087] in, It is the ratio of arc length. , The angle between the optical axes, .

[0088] definition Non-critical point pulse The processing boundary, For processing boundaries The position coordinates of any processing point within the area, For non-critical point pulses Point from origin to processing point unit vector, , Vector along the optical axis The processing amount in the direction is defined as follows: negative values ​​represent the removal amount, and positive values ​​represent the re-deposition amount. For processing point Pulse to non-critical point The distance.

[0089] Around the normal direction Calculate non-critical point pulses From instantaneous ablation rate to unit vector rotation angle ,in

[0090] ( )

[0091] 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. ,Right now

[0092] ( )

[0093] 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

[0094] ( )

[0095] 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.

[0096] ( )

[0097] 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 morphology at the site Interpolation can be used to obtain the processing point. Processing volume and processing point Processing volume Then the processing boundary Internal processing point Machining amount along its optical axis .

[0098] Calculate the processing boundaries sequentially using the method described above. The amount of machining along the optical axis at all machining points within the cavity can be used to determine the non-critical point pulses. ablation morphology at the site . Figure 3 middle , , Key point pulses Key point pulse Pulse at key points and non-critical points The coordinates after processing.

[0099] Similarly, the keypoint pulses are traversed using the method described above. and key point pulse The key point pulses can be obtained from the remaining non-key point pulses. and key point pulse The ablation morphology at all non-critical pulse points.

[0100] It is worth noting that when the selected At that time, that is, when it is at the position of the pulse center, , Then access directly and Obtain processing volume and processing volume Finally, the processing boundary is determined using the above method. Internal processing point Vector along the optical axis Processing volume .

[0101] Step 5: Complete the ablation morphology simulation of the freeform surface S.

[0102] The ablation morphology of all non-critical pulses between all adjacent critical pulses in the stable segment is calculated using the interpolation method described above. Finally, Boolean operations are performed on the ablation morphologies of all critical and non-critical pulses in the stable segment within the workpiece blank model to obtain the ablation morphology of the stable segment. Combined with the previously calculated ablation morphology of the unstable segment, the following can be obtained: Figure 4 The final ablation morphology of the free-form surface S of the workpiece to be processed is shown.

[0103] When calculating the ablation morphology of the workpiece, if the existing iterative model is used for each pulse, the calculation time for each pulse is 75.05 ms. Taking 1250 pulses as an example, the average calculation time for each pulse is still 75.05 ms. However, if the efficient simulation method for multi-axis laser processing of complex curved surfaces based on key point interpolation of this invention is adopted, pulses at the start, middle, and end positions are selected as three key point pulses from the 1250 pulses in the stable segment, and the remaining pulses are used as processing points within non-key point pulses for interpolation calculation. The calculation time for the three key point pulses is 75.05 ms, and the interpolation calculation time for the processing points within the remaining non-key point pulses is 16.58 ms. Therefore, the average calculation time for 1250 pulses is only 16.72 ms, which improves the calculation efficiency by several times. It is worth noting that the above method is for calculating the ablation morphology under single-line scanning machining. For multi-line machining, it is only necessary to calculate the ablation morphology of each line of scanning machining according to the above method, and finally perform Boolean operations on the ablation morphology of multiple lines in the workpiece blank model to obtain the final ablation morphology of the workpiece under multi-line scanning machining. For multi-layer machining, the above method is still used.

[0104] The following uses the efficient simulation method for multi-axis laser processing of complex curved surfaces based on key point interpolation of the present invention to perform laser processing on different surfaces with different scanning methods. Figure 5 This is a simulation diagram of laser processing on a plane using a single-line scanning method at different speeds. It shows single-line unfocused vertical scribing processing on a plane at speeds of 200mm / s, 400mm / s, and 600mm / s, with a laser power of 4W and a repetition rate of 100kHz. Figure 6 This is a simulation diagram of laser processing on a plane using a double-line scanning method with different line spacing. It shows that the laser power is set to 4W, the repetition rate is 100kHz, and the speed is 400mm / s with line spacing of s=5μm, 10μm, and 15μm. The laser performs double-line unfocused vertical scribing on the plane. Figure 7 This is a simulation diagram of laser processing on a complex curved surface using multi-line scanning. It shows a laser power of 4W, a repetition rate of 100kHz, a speed of 400mm / s, and a line spacing of 10μm, performing focusless scanning processing along the surface normal on the complex curved surface. Based on... Figures 5-7 As can be seen, the efficient simulation method for multi-axis laser processing of complex curved surfaces based on key point interpolation of this invention can not only realize rapid laser processing simulation of planar surfaces, but also realize rapid laser processing simulation of complex curved surfaces.

[0105] The above description is only used to illustrate the technical solutions of the present invention, and is not intended to limit them. For those skilled in the art, modifications can be made to the specific technical solutions described in the above embodiments, or equivalent substitutions can be made to some of the technical features. However, these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions protected by the present invention.

Claims

1. A highly efficient simulation method for multi-axis laser processing of complex curved surfaces based on key point interpolation, characterized in that, Includes the following steps: Step 1: Define the trajectory segment in the machining trajectory where the ablation range of both the preceding and following pulses has a critical overlap with that of the current pulse as a stable segment, and define the remaining trajectory segments as unstable segments; calculate the ablation morphology of the unstable segments. Step 2: Discretely sample the laser pulses on the stable section to obtain pulses at all key points; 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 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. Calculate the lengths of the pulses at two key points along their corresponding unit vector directions to their machining boundaries, and then calculate the pulses at non-key points. 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 along the optical axis of all machining points within the machining boundary is used to obtain non-critical point pulses. The ablation morphology at the location; Step 4.5: Traverse all non-critical pulses between the two adjacent critical pulses using the methods in Steps 4.1 to 4.4 to obtain the ablation morphology at all non-critical pulses between the two adjacent critical pulses. Step 5: Traverse all adjacent key point pulses on the stable segment using the method in Step 4, and calculate the ablation morphology at all corresponding non-key point pulses. In the workpiece blank model, Boolean operations are performed on the ablation morphology at all key point pulses and all non-key point pulses on the stable segment to obtain the ablation morphology of the stable segment, thus completing the ablation morphology simulation of the freeform surface S.

2. The efficient simulation method for multi-axis laser processing of complex curved surfaces based on key point interpolation according to claim 1, characterized in that: In step 1, the ablation morphology of the unstable section is calculated iteratively using a pulsed laser ablation model.

3. The efficient simulation method for multi-axis laser processing of complex curved surfaces based on key point interpolation according to claim 2, characterized in that: In step 2, the laser pulses on the stable segment are discretely sampled by simultaneously controlling the arc length and chord height difference of adjacent pulses in the laser spot motion trajectory to obtain all key point pulses.

4. The efficient simulation method for multi-axis laser processing of complex curved surfaces based on key point interpolation according to claim 3, characterized in that: In step 3, the ablation morphology at all key points is calculated iteratively using a pulsed laser ablation model.

5. The efficient simulation method for multi-axis laser processing of complex curved surfaces based on key point interpolation according to claim 4, characterized in that: In step 4.1, non-critical point pulses Instantaneous ablation velocity along the tangential direction of the light spot's trajectory Calculated using the following formula: ； in, Non-critical point pulse Scanning speed on the focal scan trajectory, Non-critical point pulse ablation points around non-critical points pulse The rotational speed of the focal point, Non-critical point pulse The ablation point along its optical axis relative to the non-critical point pulse The translation speed of the focal point, Non-critical point pulse The tangential direction of the ablation point on the trajectory of the light spot.

6. The efficient simulation method for multi-axis laser processing of complex curved surfaces based on key point interpolation according to claim 5, characterized in that: In step 4.1, quaternion interpolation is used to obtain non-critical point pulses. optical axis vector : ； in, It is the ratio of arc length. , and For two adjacent key point pulses, Key point pulse and key point pulse Non-critical point pulses between; The angle between the optical axes, , and Key point pulses and key point pulse The optical axis vector.

7. The efficient simulation method for multi-axis laser processing of complex curved surfaces based on key point interpolation according to claim 6, characterized in that, Step 4.2 specifically involves: Step 4.2.1, calculate the non-critical point pulse using the following formula. Point from origin to processing point unit vector : ； Step 4.2.2, around the normal direction Calculate non-critical point pulses From instantaneous ablation rate to unit vector rotation angle : ； Step 4.2.3, Define key point pulses and key point pulse The normals on the freeform surface S are respectively and Its trajectory of light spot movement The instantaneous ablation rates in the tangential direction are respectively 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: Calculate key point pulses based on geometric relationships. Along unit vector Length from direction to its machining boundary and key point pulses Along unit vector Length from direction to its machining boundary Then, a distance-weighted average method is used to determine the non-critical point pulses. Along unit vector Length from direction to its machining boundary .

8. The efficient simulation method for multi-axis laser processing of complex curved surfaces based on key point interpolation according to claim 7, characterized in that: In step 4.2.4, the non-critical point pulses are determined using the following formula. Along unit vector Length from direction to its machining boundary : 。 9. The efficient simulation method for multi-axis laser processing of complex curved surfaces based on key point interpolation according to claim 8, characterized in that, Step 4.3 specifically involves: 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: ； in, For processing point Pulse to non-critical point The distance; Step 4.3.2: Interpolate along the optical axis of the two key point pulses in their ablation morphology to obtain the processing points. Processing volume and processing point Processing volume ; and calculate the non-critical point pulse using the following formula. Machining points within machining boundaries Machining amount along its optical axis : 。 10. The efficient simulation method for multi-axis laser processing of complex curved surfaces based on key point interpolation according to claim 9, characterized in that: In step 4.2, when At that time, , .

Images