考虑激光粉末床熔融成形铺粉过程的自支撑拓扑优化算法

Self-Supporting Topological-Optimization Algorithm Considering Powder-Recoating Process in Laser Powder-Bed Fusion

悬角约束是面向增材制造的零件拓扑优化设计中考虑最多的一种约束,且以45°等值约束为主,其虽然能够实现零件自支撑设计且具有较好的通用性,但与具体的增材制造工艺及装备性能脱节,在一定程度上限制了拓扑优化设计的应用潜力。本课题组结合激光粉末床熔融(LPBF)成形工艺及装备特点,提出了一种考虑铺粉过程的自支撑拓扑优化设计方法。该方法基于变值悬角约束改进现有变密度拓扑优化方法,扩大了寻优空间,从而提高了拓扑优化的性能。二维与三维算例证明了该方法的有效性:在相同的约束和边界条件下,是否添加悬角约束与拓扑结构刚度变化之间没有明显的规律。与基于等值悬角约束的自支撑拓扑优化方法相比,基于变值悬角约束的自支撑拓扑优化方法获得的拓扑结构的刚度明显提升。

Objective Additive manufacturing(AM)enables the fabrication of extremely complex structures,which can reveal the full potential of topological optimization(TO).However,it presents certain limitations that should be considered in TO.A typical example is that an overhang structure cannot be easily formed in AM without incorporating additional support structures.Therefore,many selfsupporting TO algorithms have been proposed to avoid generating components with overhanging structures by considering the incline angle constraint(IAC).The IAC is usually set to a constant value,typically 45°,at all polar angles.Although it can realize the selfsupporting design of components and features high versatility,the effects of the AM process and equipment performance on the IAC are typically disregarded,thus resulting in a self-supporting TO algorithm with subpar performance.To fully understand the active role of TO,a self-supporting TO design method that considers the powder-recoating process is proposed based on the characteristics of the laser powder-bed fusion(LPBF)process and equipment.Methods In this study,based on the authors’previous study where the changing law of the IAC due to the powder-recoating process in LPBF was investigated,a new self-supporting TO design method is proposed.First,the method for determining the IAC was reviewed;notably,the IAC is not constant but changes with the polar angle.Subsequently,a variable-value IAC was proposed after a mathematical formula for the change in the IAC with the polar angle was derived.Second,a variable-value IAC was integrated into an improved solid isotropic material with penalization(SIMP)TO algorithm in the form of a filter using the min–max operator.Third,the proposed algorithm was validated using two-dimensional(2D)and three-dimensional(3D)MBB beam examples and supplemented with additional examples using an L-beam,a compression structure,and a cantilever beam to generalize the results.Finally,a set of 3D TO MBB beams was selected to be formed via LPBF to further validate the effectiveness of the variable-value IAC.Results and Discussions In this study,we used 2D and 3D MBB beams as examples to investigate the change rule of component performance during component change while maintaining the volume fraction within 0.2‒0.7 under the conditions of variable-value IAC,equal-value IAC,and no IAC.The examples show that in the MBB beams,the advantage of having no IAC is the most significant,followed by that of the variable-value IAC.Additionally,the final flexibility curves corresponding to the three TO methods converge gradually as the retained volume fraction increases.In particular,when the retained volume fraction is greater than 0.6,the three curves almost overlapped.An L-beam,a compression structure,and a cantilever beam were added as supplementary calculation examples for validation.The final flexibility value of the L-beam using the variable-value IAC is 2.252×10^(−3),which is lower than those using the equal-value IAC(2.383×10^(−3))and without the IAC(2.315×10^(−3)),where the stiffnesses increase by 5.5%and 2.72%,respectively.This indicates that the variable-value IAC can better unleash the potential of TO.However,combining the above with the aforementioned MBB beam optimization results,one cannot conclude that the TO structures without the IAC are better than those with the IAC.The final flexibility value of the TO compression structure using the variable-value IAC is 1.21093,which is lower than those using the equal-value IAC(1.28939)and without the IAC(1.44747),where the stiffnesses increase by 6.09%and 16.34%,respectively.This indicates that the addition of the IAC does not necessarily change the stiffness of the topological structure;however,using a variable-value IAC can better unleash the potential of TO compared with using an equalvalue IAC.The final flexibility value of the TO cantilever beam using the variable-value IAC is 5.0745×10^(−4),which is lower than those using the equal-value IAC(5.4169×10^(−4))and without the IAC(5.1878×10^(−4)),where the stiffnesses increases by 6.32%and 2.18%,respectively.The results show that using a variable-value IAC is better for achieving higher stiffness compared with using an equal-value IAC when the retained volume fraction is lower than 0.5.The 3D TO MBB beams designed using equal-value and variable-value IACs are completely formed via LPBF,which further validates the effectiveness of the proposed method.Conclusions The existing self-supporting TO method for AM does not account for the related process and equipment.Based on a review of the effect of the powder-recoating process on the IAC in LPBF,a self-supporting TO algorithm considering the variablevalue IAC was proposed,and its effectiveness in enhancing TO performance was demonstrated via a series of specific examples.The conclusions are as follows:(1)Improving the SIMP method using IAC filters can realize a self-supporting TO design for LPBF,thus enabling the formation of designed components without incorporating additional support;additionally,the IAC significantly affects the optimization space.(2)A comparative analysis of the optimization results of MBB beams and the remaining three validation cases shows no clear pattern between the use of IAC filters and changes in the topology stiffness.(3)Compared with a self-supporting TO algorithm with an equal-value IAC,a variable-value IAC significantly enhances the structural stiffnesses of topological MBB beams,L-beams,compression structures,and cantilever beams,where the stiffness enhancement becomes more evident as the retained volume fraction decreases.