Overhanging angle optimization method considering additive manufacturing constraints
By combining multi-attribute decision-making with feedback control, the printing direction is adjusted, and a multi-dimensional evaluation index system is constructed. This solves the limitations of the overhang angle constraint in additive manufacturing, achieves effective control of the overhang area and balance of multiple attribute objectives, and improves the accuracy and controllability of the printing direction.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- BEIJING INST OF TECH
- Filing Date
- 2026-02-09
- Publication Date
- 2026-06-19
AI Technical Summary
Existing technologies struggle to effectively control the suspended region without disrupting the optimal force transmission path when dealing with the cantilever angle constraints in additive manufacturing. Furthermore, existing methods are difficult to achieve precise balance and closed-loop control among multiple attribute objectives.
A multi-attribute decision-making and feedback control approach is adopted. By adjusting the printing direction and using a quaternion rotation matrix for continuous rotation, a multi-dimensional evaluation index system is constructed, including the volume of the supporting structure, surface quality, printing accuracy, printing time, and manufacturing cost. Optimization is achieved using the TOPSIS model and a variable speed integral PID controller.
While maintaining structural mechanical properties, the printing direction is optimized to achieve effective control of the suspended area, thereby improving the accuracy and controllability of the printing direction and solving the limitations of the suspended angle processing and the balance problem of multi-attribute targets in the existing technology.
Smart Images
Figure CN122241899A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of additive manufacturing data processing and computer-aided design technology, specifically relating to a method for optimizing the overhang angle considering additive manufacturing constraints. Background Technology
[0002] Additive manufacturing technology boasts advantages such as high degree of freedom in forming, high digitalization, and no need for molds, making it widely used in aerospace and defense industries. It is the preferred process for the rapid manufacturing of complex and heterogeneous components. The final performance of topology-optimized structures is closely related to their manufacturing process. Efficiently and accurately handling the unique process constraints of additive manufacturing plays a crucial role in ensuring the manufacturability and performance of the structure. Overhang angle constraints are among the most critical geometric process constraints in additive manufacturing. Areas that do not meet the overhang angle requirements will collapse or deform during the forming process due to lack of support. Usually, support structures are needed to assist in forming, but these support structures not only increase printing time and material costs, but their removal process can also seriously affect the surface quality of the part.
[0003] The overhang angle optimization technique transforms topology optimization results from purely theoretical design into manufacturing-oriented engineering design, improving the feasibility and cost-effectiveness of the design, and has received widespread attention in the field of additive manufacturing data processing.
[0004] In recent years, the handling of overhang angle constraints has mainly focused on two aspects: optimizing structural configuration and optimizing printing direction. While modifying the structural configuration to meet overhang angle constraints can achieve self-support, it often disrupts the optimal force transmission path, leading to a decline in mechanical performance. In contrast, optimizing the printing direction can reduce the overhang area by adjusting the placement posture while maintaining the optimal topological configuration of the structure, providing a new approach to solving the overhang angle problem. Multi-attribute decision modeling (MCDM) is a classic method for solving complex engineering trade-offs. Because it can comprehensively consider multiple conflicting evaluation indicators such as printing time, manufacturing cost, and surface quality, it has been gradually introduced into additive manufacturing process planning. However, traditional methods are often limited to a finite number of discrete alternatives, making it difficult to obtain a globally optimal solution.
[0005] It is evident that pre-processing methods for constraining overhang angles in additive manufacturing primarily achieve self-support by forcibly modifying the structural configuration during the topology optimization stage. This approach often disrupts the optimal force transmission path of the structure, resulting in limited applicability for structural designs aiming for ultimate mechanical performance (such as maximizing stiffness). Furthermore, existing post-processing methods based on printing direction optimization face challenges such as a limited discrete search space and the difficulty in achieving precise balance and closed-loop control among multiple attributes, including overhang angle constraints, printing time, manufacturing cost, and surface quality. Summary of the Invention
[0006] In view of this, the present invention provides a method for optimizing the overhang angle considering the constraints of additive manufacturing, which can optimize the printing direction and control the overhang angle based on multi-attribute decision and feedback control for additive manufacturing.
[0007] To achieve the objectives of this invention, the following technical solutions are provided.
[0008] A method for optimizing dangling angles considering additive manufacturing constraints includes the following steps:
[0009] Step S1: Model preprocessing. The STL model file generated after topology optimization is parsed to extract the vertex coordinates and normal vector information of all triangular faces. Step S2: Identify suspended areas. Based on the current printing direction, calculate the angle between the normal vector of each triangular facet and the horizontal direction. If the angle is less than the preset suspended angle threshold, then the triangular facet is determined to be in a suspended area. Step S3: Quantization of suspended regions. For each of the identified suspended triangular facets, calculate the volume of the required support structure and sum them up to obtain the total volume of the support structure. Step S4: Calculate multi-attribute evaluation index. Based on the current printing direction, calculate the values of each index in a multi-dimensional evaluation index system. The multi-dimensional evaluation index system includes at least the total support structure volume, surface quality index, printing accuracy index, printing time index, and manufacturing cost index. Step S5: Decision optimization based on feedback control. The multi-attribute evaluation index value calculated in step S4 is input into an optimization model based on multi-attribute decision and feedback control. The optimization model outputs the adjustment amount for the current printing direction. Using the adjustment amount, the STL model is continuously rotated in three-dimensional space through a quaternion rotation matrix to update the printing direction. Step S6: Iteration and output. Repeat steps S2 to S5 until the comprehensive evaluation result of the multi-dimensional evaluation index system meets the preset convergence condition. Output the corresponding printing direction as the optimal printing direction.
[0010] In step S3, the method for calculating the volume of the supporting structure required for a single suspended triangular facet is to project the triangular facet onto the printing bottom surface along the current printing direction and calculate the volume of the geometry enclosed by the triangular facet and its projection surface.
[0011] In step S4, the multidimensional evaluation index system specifically includes: Support structure volume: that is, the total support structure volume calculated in step S3; Surface quality index: Based on the principle of step effect, the index is calculated by taking into account the effects of layer thickness, printing angle and roughness of the contact surface of the support structure; Printing accuracy indicators: Indicators reflecting the errors in feature dimensions or flatness caused by the step effect; Printing time metric: Total printing time of a part predicted based on additive manufacturing process parameters; Manufacturing cost indicators: Indicators calculated by combining material consumption, machine depreciation, and energy consumption.
[0012] In step S5, the optimization model based on multi-attribute decision-making and feedback control includes: Multi-attribute decision module: Using the TOPSIS method, it calculates in real time the relative closeness between the values of each attribute index and the user-defined ideal target value under the current printing orientation; Feedback control module: Employs a PID controller, which takes the deviation between the relative closeness and the ideal value as an input signal, and outputs a control variable based on this deviation; The control variables are converted into rotation angle increments in three-dimensional space, and the quaternion rotation matrix drives the model to rotate according to the rotation angle increments.
[0013] The PID controller is a variable-speed integral PID controller, which dynamically adjusts the cumulative speed of the integral term according to the magnitude of the input deviation.
[0014] In step S2, the critical value of the suspension angle is 45°.
[0015] Beneficial effects 1. This invention adopts a step-by-step strategy of "optimizing the structure first and then the direction". Compared with the existing technology that forces the structural configuration to change by applying geometric constraints (such as AM filters), this invention controls the size of the suspended area by adjusting the printing direction without destroying the optimal force transmission path of the structure. This maximizes the preservation of the overall stiffness and mechanical properties of the topology optimization results and solves the problem of sacrificing structural performance to meet manufacturing constraints in the existing technology.
[0016] 2. This invention introduces a variable speed integral PID controller and a quaternion rotation mechanism into a multi-attribute decision model, expanding the search space for printing direction from a finite discrete angle to an infinite continuous space. Through feedback control, the optimization process can automatically approach the user-set target value, thereby improving the accuracy and controllability of finding the optimal printing direction. This solves the problems of existing technologies that easily miss the global optimal solution and are difficult to meet customized printing needs due to the use of discrete angle search.
[0017] 3. This invention constructs a multi-dimensional evaluation index system that includes overhang angle constraints, surface quality, printing accuracy, printing time, and manufacturing cost. It uses the TOPSIS model to achieve a comprehensive trade-off between multiple objectives and evaluates the manufacturability of the printing direction from a global perspective. This avoids the situation where poor surface quality or high manufacturing cost is caused by simply pursuing the minimization of support volume, and alleviates the local optimum problem caused by the single evaluation index in the prior art. Attached Figure Description
[0018] Figure 1 This is a flowchart of a method according to an embodiment of the present invention.
[0019] Figure 2 This is a schematic diagram illustrating the volume calculation of the triangular facet support structure in the suspended region according to an embodiment of the present invention.
[0020] Figure 3 This is a block diagram of a multi-attribute decision control model based on feedback control according to an embodiment of the present invention. Figure 4 This is a schematic diagram illustrating the identification and optimization results of the suspended area of the motor gantry bracket in an embodiment of the present invention.
[0021] Figure 5(a) shows the initial printing direction of multiple parts before optimization in an embodiment of the present invention; Figure 5(b) shows the optimized printing direction of multiple parts after optimization in an embodiment of the present invention. Detailed Implementation
[0022] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.
[0023] To address the shortcomings of existing topology optimization methods in handling additive manufacturing overhang constraints, which often sacrifice structural mechanical properties or result in low manufacturing efficiency due to considering only a single constraint, this invention provides an overhang constraint optimization method that considers additive manufacturing constraints. The process is as follows: Figure 1 As shown, the process includes model preprocessing, suspended region identification, suspended region quantification, multi-attribute evaluation index calculation, decision optimization based on feedback control, continuous iteration, and finally outputting the optimal printing direction.
[0024] The model preprocessing involves parsing the STL file generated from the topology optimization results to extract the vertex coordinates and normal vector information of the triangular facets.
[0025] The identification of the suspended region is based on the angle between the normal vector of the triangular facet and the horizontal direction. If the angle is less than a set threshold (such as 45°), the facet is determined to be in a suspended region.
[0026] The quantification of the suspended region is achieved by calculating the volume of the supporting structure. The volume calculation of the supporting structure for the triangular facets of the suspended region is as follows: Figure 2As shown, for each identified suspended triangular facet, the volume of the triangular prism or pyramid formed by its projection onto the printed bottom surface is calculated, and the supports of all suspended facets are accumulated as a quantitative indicator to measure the severity of the suspension.
[0027] The calculation of the multi-attribute evaluation index is based on a multi-attribute evaluation index system, which includes not only the volume of the supporting structure, but also surface quality, printing accuracy, printing time, and manufacturing cost. The surface quality index is based on the principle of the step effect, comprehensively considering the influence of layer thickness, printing angle, and the removal of the supporting structure on surface roughness. The printing accuracy index considers the flatness tolerance caused by the step effect. The printing time and manufacturing cost indexes are based on the process characteristics of additive manufacturing, covering coating time, scanning time, material consumption, and machine depreciation costs.
[0028] The core optimization algorithm used in the feedback control-based decision optimization is based on a multi-attribute decision model, the structure of which is as follows: Figure 3 As shown, the model combines TOPSIS (Top-Solution Ranking Method) with a variable-speed integral PID controller. First, the user sets a desired comprehensive evaluation target value (i.e., the ideal solution). The TOPSIS model calculates in real-time the relative distance (i.e., the difference) between each attribute index and the ideal solution in the current printing direction. This difference is then used as the input deviation of the PID controller. To address the oscillation problem of conventional PID controllers during parameter updates, this invention employs a variable-speed integral PID controller, dynamically adjusting the accumulation rate of the integral term according to the magnitude of the deviation: weakening the integral action when the deviation is large and strengthening the integral action when the deviation is small, thereby achieving fast and stable convergence. The control variable output by the PID controller is converted into a rotation angle, and a quaternion rotation matrix is used to drive the part to rotate continuously in three-dimensional space. The use of quaternions avoids the gimbal lock-up problem and expands the limited alternative directions to an infinite continuous space.
[0029] The process of continuously iterating and finally outputting the optimal printing direction is specifically achieved through a continuous "rotation-evaluation-feedback" process until the evaluation index falls within the set maximum allowable range (MPR). The printing direction at this point is then output as the optimal printing direction.
[0030] Figure 4The optimized printing direction of the motor gantry bracket obtained using this invention is shown. Compared with the initial printing direction, the optimized direction significantly reduces the area of the suspended region marked in red, greatly reduces the volume of the support structure, and achieves the user-defined balance between printing time and manufacturing cost. This verifies that the method effectively improves the manufacturability of the part while ensuring the mechanical properties of the part's topological configuration. The support structures of the printed parts before and after optimization are shown in Figures 5(a) and 5(b). Figure 5(a) shows the initial printing direction of multiple parts before optimization in this embodiment of the invention; Figure 5(b) shows the optimized printing direction of multiple parts after optimization in this embodiment of the invention.
[0031] As can be seen, this invention employs an optimization model combining multi-attribute decision-making and feedback control to construct a decision control model based on a TOPSIS multi-attribute decision-making model and a variable-speed integral PID controller. This transforms the selection process of the printing direction into a closed-loop dynamic control process, achieving automatic approximation of the predetermined target value. Furthermore, it introduces quaternion rotation and a geometric calculation mechanism based on facet normals. Quaternions are used to describe rotation in three-dimensional space, enabling continuous and infinite resolution adjustment of the printing direction. Simultaneously, a geometric algorithm based on STL model triangular facet normals is employed to achieve rapid identification of overhanging areas and quantization of support volumes without the need for slicing.
[0032] In this invention, the evaluation system adopted is an evaluation function that integrates multi-dimensional manufacturing constraints. The evaluation function is not limited to the overhang angle constraint (support volume), but establishes a comprehensive evaluation index system that covers surface quality (roughness), printing accuracy (flatness error), printing time and manufacturing cost.
[0033] This invention includes, but is not limited to, the above embodiments. Any equivalent substitutions or partial improvements made under the spirit and principles of this invention shall be considered within the scope of protection of this invention.
Claims
1. A method for optimizing the overhang angle considering additive manufacturing constraints, characterized in that, Includes the following steps: Step S1: Model preprocessing. The STL model file generated after topology optimization is parsed to extract the vertex coordinates and normal vector information of all triangular faces. Step S2: Identify suspended areas. Based on the current printing direction, calculate the angle between the normal vector of each triangular facet and the horizontal direction. If the angle is less than the preset suspended angle threshold, then the triangular facet is determined to be in a suspended area. Step S3: Quantization of suspended regions. For each of the identified suspended triangular facets, calculate the volume of the required support structure and sum them up to obtain the total volume of the support structure. Step S4: Calculate multi-attribute evaluation index. Based on the current printing direction, calculate the values of each index in a multi-dimensional evaluation index system. The multi-dimensional evaluation index system includes at least the total support structure volume, surface quality index, printing accuracy index, printing time index, and manufacturing cost index. Step S5: Decision optimization based on feedback control. The multi-attribute evaluation index value calculated in step S4 is input into an optimization model based on multi-attribute decision and feedback control. The optimization model outputs the adjustment amount for the current printing direction. Using the aforementioned adjustment amount, the STL model is continuously rotated in three-dimensional space via a quaternion rotation matrix to update the printing orientation; Step S6: Iteration and output. Repeat steps S2 to S5 until the comprehensive evaluation result of the multi-dimensional evaluation index system meets the preset convergence condition. Output the corresponding printing direction as the optimal printing direction.
2. The overhang angle optimization method considering additive manufacturing constraints according to claim 1, characterized in that, In step S3, the method for calculating the volume of the supporting structure required for a single suspended triangular facet is to project the triangular facet onto the printing bottom surface along the current printing direction and calculate the volume of the geometry enclosed by the triangular facet and its projection surface.
3. The method for optimizing the overhang angle considering additive manufacturing constraints according to claim 1, characterized in that, In step S4, the multidimensional evaluation index system specifically includes: Support structure volume: that is, the total support structure volume calculated in step S3; Surface quality index: Based on the principle of step effect, the index is calculated by taking into account the effects of layer thickness, printing angle and roughness of the contact surface of the support structure; Printing accuracy indicators: Indicators reflecting the errors in feature dimensions or flatness caused by the step effect; Printing time metric: Total printing time of a part predicted based on additive manufacturing process parameters; Manufacturing cost indicators: Indicators calculated by combining material consumption, machine depreciation, and energy consumption.
4. The method for optimizing the overhang angle considering additive manufacturing constraints according to claim 1, characterized in that, In step S5, the optimization model based on multi-attribute decision-making and feedback control includes: Multi-attribute decision module: Using the TOPSIS method, it calculates in real time the relative closeness between the values of each attribute index and the user-defined ideal target value under the current printing orientation; Feedback control module: Employs a PID controller, which takes the deviation between the relative closeness and the ideal value as an input signal, and outputs a control variable based on this deviation; The control variables are converted into rotation angle increments in three-dimensional space, and the quaternion rotation matrix drives the model to rotate according to the rotation angle increments.
5. The overhang angle optimization method considering additive manufacturing constraints according to claim 4, characterized in that, The PID controller is a variable speed integral PID controller, which dynamically adjusts the accumulation speed of the integral term according to the magnitude of the input deviation.
6. The method for optimizing the overhang angle considering additive manufacturing constraints according to claim 1, characterized in that, In step S2, the critical value of the suspension angle is 45°.