Smooth transition based rotation angle optimization method for additive manufacturing turntable

CN117583622BActive Publication Date: 2026-08-07NANJING ZHONGKE RAYCHAM TECH
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
NANJING ZHONGKE RAYCHAM TECH
Filing Date
2023-12-19
Publication Date
2026-08-07

AI Technical Summary

Technical Problem

[0004]本发明目的在于提供一种基于平滑过渡的增材制造转台旋转角度优化方法,针对开光打印路径对角度跳动较大的区域进行打印路径的平滑过渡,优化调整转台旋转角度,减少因为激光加工头等待转台从而减速导致融化材料堆积过多的问题,以此来提高打印零件的质量

Benefits of technology

[0004] The purpose of this invention is to provide a method for optimizing the rotation angle of an additive manufacturing turntable based on smooth transition. This method smooths the printing path in areas with large angle jumps, optimizes and adjusts the turntable rotation angle, and reduces the problem of excessive accumulation of molten material due to the laser processing head slowing down while waiting for the turntable, thereby improving the quality of printed parts.

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Abstract

The application provides a kind of additive manufacturing rotary table rotation angle optimization method based on smooth transition, comprising the following steps: according to the pre-planned additive manufacturing printing process, target point and corresponding tool axis vector T are obtained, and the angle of B axis and the angle of C axis are calculated accordingly;According to the selected starting target point and the end target point, the original planning path of the rotation angle of C axis is obtained;From the starting target point, the positive solution of the tool axis vector is calculated according to each target point, and the included angle between the tool axis vector of the target point and its positive solution is determined;According to the comparison result of the included angle and the preset threshold value, the C axis angle of the target point in the original planning path is smoothly transitioned, the optimized planning path is obtained and updated;The additive manufacturing printing process is executed with the updated additive manufacturing printing process.
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Description

Technical Field

[0001] This invention relates to the field of additive manufacturing technology, and in particular to an optimization method for designing additive manufacturing printing paths, specifically to an optimization method for the rotation angle of an additive manufacturing turntable based on smooth transition. Background Technology

[0002] Additive manufacturing is a novel manufacturing technology that shapes materials layer by layer based on a geometric model. It features rapid prototyping, customization, high material utilization, and the ability to form complex structures, making it a preferred process for material processing. One of the most prominent technologies in additive manufacturing is laser metal deposition, where powder or wire materials undergo high-temperature melting and cooling solidification in an extremely short time, resulting in the accumulation of solid metal tracks to form a solid body.

[0003] For example, in an additive manufacturing process using a five-axis CNC machine tool, in a dual-rotor five-axis additive manufacturing system, both rotary axes are rotary tables. The B-axis rotates along the XZ plane, and the C-axis rotates along the XY plane. Typically, the two rotary axes are combined into a single unit to form a dual-rotor structure, placed on the worktable. After initial planning of the tool path, the angles of motion of the two rotary tables around the machine tool axes can be calculated using the target points and tool axis directions provided by the CAM system. Then, the well-tuned laser system is turned on for laser metal deposition. However, we found that during the process, there are instances where the tool travels a relatively small distance while the C-axis rotary table rotates significantly. Before the C-axis rotary table reaches the designated position, the tool speed slows down, meaning that excessive material is melted within this distance. This situation leads to abnormal protrusions on the surface of the formed part, ultimately affecting the deposition quality. Summary of the Invention

[0004] The purpose of this invention is to provide a method for optimizing the rotation angle of an additive manufacturing turntable based on smooth transition. This method smooths the printing path in areas with large angle jumps, optimizes and adjusts the turntable rotation angle, and reduces the problem of excessive accumulation of molten material due to the laser processing head slowing down while waiting for the turntable, thereby improving the quality of printed parts.

[0005] According to a first aspect of the present invention, a method for optimizing the rotation angle of an additive manufacturing turntable based on smooth transition is proposed, comprising the following steps:

[0006] Step 1: According to the pre-planned additive manufacturing printing process, obtain the target point and the corresponding tool axis vector T, and calculate the angle b of the A-axis or B-axis, and the angle c of the C-axis accordingly.

[0007] Step 2: Based on the selected starting and ending target points, obtain the original planned path for the C-axis rotation angle;

[0008] Step 3: On the original planned path, starting from the initial target point, calculate the positive solution T' of the tool axis vector based on each target point and the corresponding angle b, and determine the angle n between the tool axis vector T of the target point and its positive solution T'.

[0009] Step 4: Based on the comparison result between the included angle n and the preset threshold, the C-axis angle of the target point within the original planned path is smoothly transitioned to obtain the optimized planned path;

[0010] Step 5: Replace the original planned path between the starting target point and the ending target point in the additive manufacturing printing process with the optimized planned path, and perform additive manufacturing printing with the updated additive manufacturing printing process.

[0011] As an optional implementation, in step 1, angles b and c are obtained based on the inverse kinematics solution according to the target point coordinates and the corresponding tool axis vector T.

[0012] As an optional implementation, in step 3, the forward kinematics solution T' of the tool axis vector is obtained based on the target point and the corresponding angle b.

[0013] As an optional implementation, the method further includes the following steps:

[0014] The pre-planned additive manufacturing printing process is represented graphically, and the original planned path of the C-axis rotation angle is represented by a broken line.

[0015] As an optional implementation, different areas marked with color in the graph are used to characterize the change in the C-axis rotation angle and the allowable area:

[0016] The zones marked with the first color represent qualified areas where no light will leak during the laser melting process;

[0017] The zones marked with the second color indicate transition areas where there is a risk of light leakage during the laser melting process;

[0018] The zones marked with the third color indicate risk areas where there is a risk of light leakage during the laser melting process;

[0019] The graph shows a continuous broken line formed by connecting the C-axis rotation angles of each target point.

[0020] As an optional implementation, in the process of representing the graph, the change of the C-axis rotation angle of each target point is obtained by comparing the angle n between the positive solution T' of the tool axis vector and the tool axis vector T at each target point with a preset range, including the following process:

[0021] For any target point, if the angle n between the positive solution T' of the tool axis vector and the tool axis vector T is within the range of passing values, it means that it is located within the partition marked by the first color, that is, the safe passing area where no light will leak. The range of passing values ​​represents the safe passing angle threshold of the partition marked by the first color.

[0022] If the angle n between the positive solution T' of the tool axis vector and the tool axis vector T is within the transition value range, it indicates that it is located within the partition marked by the second color, i.e., the transition region. The transition value range represents the transition risk angle threshold of the partition marked by the second color.

[0023] If the angle n between the positive solution T' of the cutter axis vector and the cutter axis vector T is greater than the preset risk angle threshold, it is determined that it is located in the partition marked by the third color, that is, the area with the risk of light leakage. The risk angle threshold represents the risk angle threshold of the partition marked by the third color.

[0024] As an optional implementation, the step of smoothly transitioning the C-axis angle of the target point within the original planned path based on the comparison result of the included angle n and a preset threshold to obtain an optimized planned path includes:

[0025] For target points where the angle n between the positive solution T' of the tool axis vector and the tool axis vector T is greater than the preset risk angle threshold, the C-axis rotation angle of the target point is smoothly transitioned according to the preset algorithm.

[0026] It should be understood that all combinations of the foregoing concepts and the additional concepts described in more detail below may be considered part of the inventive subject matter of this disclosure, provided that such concepts do not contradict each other. Furthermore, all combinations of the claimed subject matter are considered part of the inventive subject matter of this disclosure.

[0027] The foregoing and other aspects, embodiments, and features of the teachings of the present invention will be more fully understood from the following description in conjunction with the accompanying drawings. Other additional aspects of the invention, such as features and / or beneficial effects of exemplary embodiments, will become apparent from the following description or may be learned through practice of specific embodiments according to the teachings of the present invention. Attached Figure Description

[0028] The accompanying drawings are not intended to be drawn to scale. In the drawings, each identical or nearly identical component shown in the various figures may be denoted by the same reference numeral. For clarity, not every component is labeled in each figure. Embodiments of various aspects of the invention will now be described by way of example and with reference to the accompanying drawings.

[0029] Figure 1 This is a flowchart of an additive manufacturing turntable rotation angle optimization method based on smooth transition according to an embodiment of the present invention.

[0030] Figure 2 This is a process diagram illustrating a method for optimizing the rotation angle of an additive manufacturing turntable, based on a specific example of an embodiment of the present invention.

[0031] Figure 3 A schematic diagram of the forward solution of the tool axis vector according to an embodiment of the present invention.

[0032] Figure 4 This is a schematic diagram of the inverse kinematics of the tool axis according to an embodiment of the present invention.

[0033] Figure 5 This is a schematic diagram of the original planned path of the C-axis rotation angle of one segment of the additive manufacturing printing process according to an embodiment of the present invention.

[0034] Figure 6 , 7 They are in Figure 5 In the original planned path of the C-axis rotation angle shown, the starting target point and the ending target point are selected, and the path between them is taken as the part to be optimized.

[0035] Figure 8 This is a schematic diagram of the optimized C-axis rotation angle planning path provided by an embodiment of the present invention.

[0036] Figure 9 This is a comparative schematic diagram showing the printing effect of the additive manufacturing printing process before optimization and the printing effect of the additive manufacturing printing process after optimization according to the embodiments of the present invention. Detailed Implementation

[0037] To better understand the technical content of the present invention, specific embodiments are described below in conjunction with the accompanying drawings.

[0038] Various aspects of the invention are described in this disclosure with reference to the accompanying drawings, which illustrate numerous illustrative embodiments. The embodiments of this disclosure are not necessarily intended to encompass all aspects of the invention. It should be understood that the various concepts and embodiments described above, as well as those described in more detail below, can be implemented in any of many ways, because the concepts and embodiments disclosed herein are not limited to any particular implementation. Furthermore, some aspects of the invention disclosed may be used alone or in any suitable combination with other aspects of the invention disclosed.

[0039] Combination Figure 1 As shown, the additive manufacturing turntable rotation angle optimization method based on smooth transition according to an embodiment of the present invention includes the following steps:

[0040] Step 1: According to the pre-planned additive manufacturing printing process, obtain the target point and the corresponding tool axis vector T, and calculate the angle b of the A-axis or B-axis, and the angle c of the C-axis accordingly.

[0041] Step 2: Based on the selected starting and ending target points, obtain the original planned path for the C-axis rotation angle;

[0042] Step 3: On the original planned path, starting from the initial target point, calculate the positive solution T' of the tool axis vector based on each target point and the corresponding angle b, and determine the angle n between the tool axis vector T of the target point and its positive solution T'.

[0043] Step 4: Based on the comparison result between the included angle n and the preset threshold, the C-axis angle of the target point within the original planned path is smoothly transitioned to obtain the optimized planned path;

[0044] Step 5: Replace the original planned path between the starting target point and the ending target point in the additive manufacturing printing process with the optimized planned path, and perform additive manufacturing printing with the updated additive manufacturing printing process.

[0045] It should be understood that, in the embodiments of the present invention, taking a dual-rotary-table five-axis machine tool additive manufacturing system as an example, both rotary axes are rotary tables, with the B-axis rotation plane being the XZ plane and the C-axis rotation plane being the XY plane. The two rotary axes are combined into a single unit, forming a dual-rotary-table structure, which is placed on the worktable. After completing the initial planning of the laser tool machining trajectory, the angles of motion of the two rotary tables around the machine tool axes can be calculated using the target point and tool axis direction provided by the CAM system. Then, the calibrated laser system is turned on to perform the laser metal deposition process.

[0046] As an optional embodiment of the present invention, the conversion relationship between parameter b, representing the A-axis or B-axis turntable angle, parameter c, representing the C-axis turntable angle, and tool axis vector T can be obtained by relying on the principle of forward and inverse kinematics to obtain kinematic solutions. The solution from tool axis T to angle is the inverse solution, and the solution from angle to tool axis T' is the forward solution. The principle of forward and inverse kinematics is as follows. Figure 3 , 4 As shown.

[0047] Therefore, in step 1, angles b and c are obtained based on the target point coordinates and the corresponding tool axis vector T using inverse kinematics. In step 3, the forward kinematics solution T' of the tool axis vector is obtained based on the target point and the corresponding angle b using forward kinematics.

[0048] In embodiments of the present invention, the pre-planned additive manufacturing printing process is represented graphically, and the original planned path of the C-axis rotation angle is represented by a broken line. For example, after the initial planning of the tool machining trajectory is completed, the target point and tool axis direction are given by the CAM system, and then the angles of the two rotary tables moving around the machine tool axis are calculated. Then, the angle change of the C-axis rotation angle is visualized using a curve chart, and the area with large angle jumps in the printing path is optimized for smooth transition.

[0049] In an optional embodiment, different areas are marked with color in the graph to characterize the change in the C-axis rotation angle and the allowable area:

[0050] The zones marked with the first color represent qualified areas where no light will leak during the laser melting process;

[0051] The zones marked with the second color indicate transition areas where there is a risk of light leakage during the laser melting process;

[0052] The zones marked with the third color indicate risk areas where there is a risk of light leakage during the laser melting process;

[0053] The lines connecting the C-axis rotation angles of each target point in the chart form a continuous broken line.

[0054] Combination Figure 4 In the example shown, the chart is divided into three categories of partitions using white (rgb(255,255,255)), orange (rgb(237,145,33)) and cyan (rgb(0,255,255)) pixels. The dark blue line shown in the diagram represents the target that needs to be operated on.

[0055] For example, white zones represent acceptable areas where light will not leak during processing, orange zones represent transitional areas where light will not leak during processing but there is a risk, cyan zones represent unacceptable areas where light will leak.

[0056] Of course, in other embodiments, different colors can also be used to mark different partition areas.

[0057] It should be understood that the pixel color of a region is determined by comparing the positive solution of the tool axis vector with the angle between the tool axis vector and a preset threshold.

[0058] The new tool axis vector (i.e., the forward solution T' of the tool axis vector) is obtained by combining the C-axis rotary table angle from 0 degrees to 360 degrees with the B-axis rotary table angle, i.e., by forward solution calculation.

[0059] In an optional embodiment, during the representation of the graph, the change in the C-axis rotation angle of each target point is obtained by comparing the angle n between the positive solution T' of the tool axis vector at each target point and the tool axis vector T with a preset range, including the following process:

[0060] For any target point, if the angle n between the positive solution T' of the tool axis vector and the tool axis vector T is within the range of the passing value, it means that it is located in the partition marked by the first color, that is, the safe passing area where no light will leak. The range of passing value represents the safe passing angle threshold of the partition marked by the first color.

[0061] If the angle n between the positive solution T' of the tool axis vector and the tool axis vector T is within the transition value range, it means that it is located within the partition marked by the second color, that is, the transition area. The transition value range represents the transition risk angle threshold of the partition marked by the second color.

[0062] If the angle n between the positive solution T' of the cutter axis vector and the cutter axis vector T is greater than the preset risk angle threshold, it is determined that it is located in the partition marked by the third color, that is, the area with the risk of light leakage. The risk angle threshold represents the risk angle threshold of the partition marked by the third color.

[0063] Specifically, based on the comparison between the included angle n and a preset threshold, the C-axis angle of the target point within the original planned path is smoothly transitioned to obtain an optimized planned path, including:

[0064] For target points where the angle n between the positive solution T' of the tool axis vector and the tool axis vector T is greater than a preset risk angle threshold, the C-axis rotation angle of the target point is smoothly transitioned according to a preset algorithm.

[0065] Therefore, for the portion requiring optimization between the two selected target points, a pre-defined smoothing algorithm is used to smoothly transition the area, and the optimized C-axis rotary table angle is saved. The dark blue line in the graph is then updated. The smoothed-transition optimized C-axis rotary table angle is updated in the original path file, and the five-axis CNC machine tool applies the updated path file. Ultimately, this resolves the issue of the laser processing head slowing down while waiting for the rotary table, thereby improving the quality of printed parts.

[0066] In an optional embodiment, based on the C-axis rotation angles of the selected starting and ending target points, a smooth transition of the C-axis rotation angle of the target point is performed according to a preset algorithm, including:

[0067] Calculate the average of the two C-axis rotation angles based on the selected starting and ending target points;

[0068] The mean value is used as the C-axis rotation angle of the smoothing target point to achieve a smooth transition to the smoothing target point.

[0069] like Figure 8 The figure shows a schematic diagram of the updated C-axis rotation angle change curve obtained by assigning values ​​based on the average C-axis rotation angles of the starting and ending target points.

[0070] In an optional embodiment, combining the actual C-axis rotation angles of the endpoints of the original planned path and the optimized segment, and based on the C-axis rotation angles of the selected starting and ending target points, a smooth transition of the C-axis rotation angles of the target points is performed according to an improved algorithm, including:

[0071] Calculate the average of the two C-axis rotation angles based on the selected starting and ending target points;

[0072] The weighting coefficients of the smoothed target point are obtained by performing a weighted calculation based on the changing trend of the included angle.

[0073] The C-axis rotation angle of the corresponding smooth target point is updated by multiplying the weighting coefficient of the smooth target point with the average of the two C-axis rotation angles, thereby achieving a smooth transition to the smooth target point.

[0074] In an optional embodiment, a weighted calculation is performed based on the changing trend of the included angle, including:

[0075] Calculate the mean of the included angles corresponding to all smoothed target points;

[0076] Calculate the difference between the included angle and the mean for each smoothed target point, and use the ratio of the difference to the mean of the included angle as the weighting coefficient for each smoothed target point.

[0077] Therefore, the C-axis rotation angle change line after smooth transition avoids guiding the machining directly as a straight line. Instead, it uses the average value of the two C-axis rotation angles (within the white area) as the basis, and balances and weights the angle difference with the average value of the angle to obtain a more reasonable curve movement and achieve a better smoothing effect.

[0078] {Example 1}

[0079] The process of optimizing the rotation angle of the additive manufacturing turntable, as shown in Figure 2, is combined with... Figure 5 The original planned path for one segment of the C-axis rotation angle is shown.

[0080] according to Figure 2 The method shown imports the NC program file and visualizes it using icons. Based on the target point and tool axis in the path file, the C-axis angle value and three types of partitions are obtained. The three types of partitions are composed of white (rgb(255,255,255)), orange (rgb(237,145,33)) and cyan (rgb(0,255,255)) pixels, and the dark blue broken line represents the target that needs to be operated.

[0081] The horizontal axis represents the target point, and the vertical axis represents the angle (i.e., the C-axis rotation angle). The dark blue line is the line connecting the changes in the C-axis angle. The white area represents a safe and qualified zone, the orange area represents a slightly risky transition zone, and the cyan area represents a qualified zone that will leak light.

[0082] The preset values ​​are pass value, transition value, and step size. The pass value represents the angle threshold of the white safety zone, and the transition value represents the angle threshold of the orange transition zone. The aforementioned step size is the increment for angle calculation, i.e., the spacing of the x-axis coordinates. If set to 10, only the tool axis vector synthesized by the BC axes when the C-axis is used as an angle of 0, 10, 20…360 degrees is calculated. If set to 1, the tool axis vector synthesized by the BC axes when the C-axis is used as an angle of 0, 1, 2…, 359, 360 degrees is calculated.

[0083] The changes in the C-axis rotation angle were observed in different sedimentary regions.

[0084] We select two target points as the starting and ending points, and combine them... Figure 6 , 7 As shown, the printing path is selected to optimize the smooth transition of areas with large angle jumps. After the smooth transition, the polyline is updated, as shown. Figure 8 As shown.

[0085] Combination Figure 6 , 7 As shown, select the start and end target points of the part to be optimized, and perform smoothing optimization according to the preset smoothing algorithm, combined with... Figure 8 As shown, the average C-axis rotation angle between the starting and ending target points is used as the new value, where the C-axis angle line within the red box becomes smoother after significant fluctuations. The optimized C-axis angle is then automatically saved and updated in the NC program file, and the machine tool is driven to continue additive manufacturing operations based on the modified NC forming file.

[0086] Therefore, in the actual machining process, the C-axis rotary table rotation angle output after a smooth transition operation is used for additive manufacturing, preventing the C-axis rotary table from experiencing large rotations during five-axis linkage. Ultimately, the C-axis rotary table rotation angle remains stable, and the machining speed does not need to be reduced to avoid heat accumulation at this point. Figure 9 The comparison of the morphology and quality of the printed parts before and after optimization clearly shows that when the optimized smooth transition C-axis rotation angle is used for processing, the raised defects in the red box of the original unoptimized printed parts disappear, the surface of the printed parts is smooth and uniform, and the deposition quality is significantly improved.

[0087] While the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the invention. Those skilled in the art can make various modifications and refinements without departing from the spirit and scope of the invention. Therefore, the scope of protection of the present invention shall be determined by the claims.

Claims

1. A method for optimizing the rotation angle of an additive manufacturing turntable based on smooth transition, characterized in that, Includes the following steps: Step 1: According to the pre-planned additive manufacturing printing process, obtain the target point and the corresponding tool axis vector T, and calculate the angle b of the A-axis or B-axis, and the angle c of the C-axis accordingly. Step 2: Based on the selected starting and ending target points, obtain the original planned path for the C-axis rotation angle; Step 3: On the original planned path, starting from the initial target point, calculate the positive solution T' of the tool axis vector based on each target point and the corresponding angle b, and determine the angle n between the tool axis vector T of the target point and its positive solution T'. Step 4: Based on the comparison result between the included angle n and the preset threshold, the C-axis angle of the target point within the original planned path is smoothly transitioned to obtain the optimized planned path; Step 5: Replace the original planned path between the starting target point and the ending target point in the additive manufacturing printing process with the optimized planned path, and perform additive manufacturing printing with the updated additive manufacturing printing process; The method further includes the following steps: The pre-planned additive manufacturing printing process is represented graphically, and the original planned path of the C-axis rotation angle is represented by a line graph. Furthermore, different areas in the graph are color-coded to characterize variations in the C-axis rotation angle and the allowable area, specifically including: The zones marked with the first color represent qualified areas where no light will leak during the laser melting process; The zones marked with the second color indicate transition areas where there is a risk of light leakage during the laser melting process; The zones marked with the third color indicate risk areas where there is a risk of light leakage during the laser melting process; The lines connecting the C-axis rotation angles of each target point in the chart form a continuous broken line. In the process of representing the chart, the change of the C-axis rotation angle of each target point is obtained by comparing the angle n between the positive solution T' of the tool axis vector and the tool axis vector T at each target point with a preset range, including the following process: For any target point, if the angle n between the positive solution T' of the tool axis vector and the tool axis vector T is within the passing value range, it means that it is located within the partition marked by the first color, that is, the safe passing area where no light will leak. The passing value range represents the safe passing angle threshold of the partition marked by the first color. If the angle n between the positive solution T' of the tool axis vector and the tool axis vector T is within the transition value range, it indicates that it is located within the partition marked by the second color, i.e., the transition region. The transition value range represents the transition risk angle threshold of the partition marked by the second color. If the angle n between the positive solution T' of the cutter axis vector and the cutter axis vector T is greater than the preset risk angle threshold, it is determined that it is located within the partition marked by the third color, i.e., the area with a risk of light leakage. The risk angle threshold represents the risk angle threshold of the partition marked by the third color. Furthermore, for target points where the angle n between the positive solution T' of the cutter axis vector and the cutter axis vector T is greater than the preset risk angle threshold, they are used as smoothing target points. Based on the C-axis rotation angle of the selected starting target point and ending target point, the C-axis rotation angle of the smoothing target point is smoothly transitioned according to the preset algorithm.

2. The method for optimizing the rotation angle of an additive manufacturing turntable based on smooth transition according to claim 1, characterized in that, In step 1, angles b and c are obtained based on the target point coordinates and the corresponding tool axis vector T using inverse kinematics.

3. The method for optimizing the rotation angle of an additive manufacturing turntable based on smooth transition according to claim 1, characterized in that, In step 3, the forward kinematics solution T' of the tool axis vector is obtained based on the target point and the corresponding angle b.

4. The method for optimizing the rotation angle of an additive manufacturing turntable based on smooth transition according to claim 1, characterized in that, Calculate the average of the two C-axis rotation angles based on the selected starting and ending target points; The mean value is used as the C-axis rotation angle of the smoothing target point to achieve a smooth transition to the smoothing target point.

5. The method for optimizing the rotation angle of an additive manufacturing turntable based on smooth transition according to claim 1, characterized in that, Calculate the average of the two C-axis rotation angles based on the selected starting and ending target points; The weighting coefficients of the smoothed target point are obtained by performing a weighted calculation based on the changing trend of the included angle n. The C-axis rotation angle of the corresponding smooth target point is updated by multiplying the weighting coefficient of the smooth target point with the average of the two C-axis rotation angles, thereby achieving a smooth transition to the smooth target point.

6. The method for optimizing the rotation angle of an additive manufacturing turntable based on smooth transition according to claim 5, characterized in that, The weighted calculation based on the changing trend of the included angle n includes: Calculate the mean of the included angle n corresponding to all smoothed target points; Calculate the difference between the included angle n and the mean for each smoothing target point, and use the ratio of the difference to the mean of the included angle n as the weighting coefficient for each smoothing target point.

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