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中文核心期刊

陶瓷基复合材料涡轮叶盘轴对称热力耦合拓扑优化研究

RESEARCH ON AXISYMMETRIC THERMO-MECHANICAL COUPLED TOPOLOGY OPTIMIZATION OF CERAMIC MATRIX COMPOSITE TURBINE BLISKS

  • 摘要: 针对连续纤维增强陶瓷基复合材料(Ceramic Matrix Composites, CMC)涡轮叶盘在高转速和给定温度场条件下的轻量化与高刚度设计问题, 提出一种考虑热力拓扑相关载荷和最大尺寸约束的轴对称热力耦合拓扑优化方法. 根据涡轮叶盘径向和周向为主要承载方向的特点, 假定连续纤维分别沿其径向和周向布置, 并将CMC等效为温度相关正交各向异性材料. 利用三维叶盘几何、材料分布及主要载荷沿叶盘周向均匀分布的特性, 以叶盘子午面为分析域, 建立给定温度场下的二维轴对称热力耦合有限元模型. 针对盘体离心载荷和热膨胀等效载荷随材料布局变化的特点, 采用RAMP模型对材料刚度及拓扑相关载荷进行插值, 并以轮缘边界节点径向位移均方值为目标, 表征热力载荷共同作用下的轮缘变形水平. 进一步, 考虑CMC化学气相渗透制备工艺对叶盘局部构件特征尺寸的限制, 采用Helmholtz偏微分方程过滤构造局部材料聚集度量约束, 并结合增广拉格朗日法处理大规模局部最大尺寸约束. 建立综合考虑CMC涡轮叶盘热力耦合变形响应与最大尺寸控制的拓扑优化问题数学列式, 基于伴随变量法推导灵敏度信息, 并采用数学规划算法求解优化问题. 数值算例分析了给定温度场、转速、体积分数和最大尺寸控制参数对优化构型及轮缘位移水平的影响. 结果表明, 温度场变化主要影响叶盘的轮缘位移水平, 而转速和体积分数对主承载路径及其拓扑构型具有更显著的影响; 随着转速提高, 叶盘优化构型可由单辐板式承载路径逐渐变化为双辐板式构型. 最大尺寸约束能够抑制局部实体材料的过度聚集, 并改变叶盘承载路径的分布形式. 所提出的优化方法可为CMC涡轮叶盘构型的概念设计提供参考.

     

    Abstract: To address the lightweight and high-stiffness design of continuous fiber-reinforced ceramic matrix composite (CMC) turbine blisks under high rotational speeds and specified temperature fields, an axisymmetric thermo-mechanical coupled topology optimization method considering thermo-mechanical topology-dependent loads and maximum size constraints is proposed. Based on the feature that the radial and circumferential directions are the primary load-bearing directions of the turbine blisk, continuous fibers are assumed to be arranged along the radial and circumferential directions, respectively, and the CMC is modeled as a temperature-dependent orthotropic material. Utilizing the characteristics that the 3D blisk’s geometry, material distribution, and primary loads are uniformly distributed along the circumferential direction, a 2D axisymmetric thermo-mechanical coupled finite element model under a given temperature field is established using the meridional plane of the blisk as the analysis domain. To account for the dependency of centrifugal loads and thermal expansion equivalent loads on material layout, the RAMP model is employed to interpolate the material stiffness and topology-dependent loads. The mean square value of the radial displacement at the outer rim boundary nodes is defined as the objective function to characterize the rim deformation level under combined thermo-mechanical loading. Furthermore, considering the limitations imposed by the chemical vapor infiltration (CVI) process of CMCs on the feature size of local blisk components, a Helmholtz partial differential equation filter is adopted to construct local material aggregation measures, and an Augmented Lagrangian Method is combined to handle large-scale local maximum size constraints. A mathematical formulation for the topology optimization problem is established, comprehensively considering the thermo-mechanical coupled deformation response and maximum size control of the CMC turbine blisk. The sensitivity information is derived using the adjoint variable method, and the optimization problem is solved via mathematical programming algorithms. Numerical examples analyze the effects of the specified temperature field, rotational speed, volume fraction, and maximum size control parameters on the optimized layout and rim displacement level. The results demonstrate that changes in the temperature field primarily affect the rim displacement level, whereas rotational speed and volume fraction exert a more significant influence on the main load-bearing paths and topology. As the rotational speed increases, the optimized blisk layout gradually transitions from a single-web to a double-web load-bearing configuration. Maximum size constraints effectively suppress excessive local solid material aggregation and alter the distribution of the load-bearing paths. The proposed optimization method provides a helpful reference for the conceptual design of CMC turbine blisk structures.

     

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