考虑SLM约束的井下小尺寸涡轮结构优化

Structural Optimization of a Downhole Small-Size Turbine Considering SLM Manufacturing Constraints

摘要: 针对井下小尺寸涡轮叶片结构复杂、传统加工难度较大以及金属增材制造过程中易产生支撑结构等问题，提出一种考虑选择性激光熔化(SLM)几何制造约束的涡轮叶片结构优化方法。以叶片前缘半径、后缘半径、前缘楔角、后缘楔角、入口角、出口角和叶片高度为设计变量，采用五次多项式曲线与圆弧相切方法建立涡轮定、转子叶片参数化模型。基于拉丁超立方抽样获得100组叶片结构样本，通过计算流体力学(CFD)方法获得各样本的输出扭矩和压降，并进一步计算效率。在此基础上，建立叶片结构参数与涡轮性能之间的径向基函数(RBF)代理模型，并采用扭矩、压降和效率加权综合评价函数对叶片结构进行优化。结果表明：扭矩、压降和效率代理模型测试集的决定系数分别为0.8110、0.8619和0.7319；优化方案的扭矩、压降和效率分别为1.12 N∙m、24,821 Pa和0.709，与代理模型预测值6.67%、5.90%和1.25%。在本文设定的最小特征尺寸、叶片边缘尺寸和悬垂角约束下，优化方案具有SLM无支撑成形可行性。

Abstract: To address the challenges associated with the complex structure of downhole small-scale turbine blades, the difficulty of conventional machining, and the tendency to generate support structures during metal additive manufacturing, this study proposes a turbine blade structural optimization method considering the geometric manufacturability constraints of selective laser melting (SLM). The leading-edge radius, trailing-edge radius, leading-edge wedge angle, trailing-edge wedge angle, inlet angle, outlet angle, and blade height were selected as design variables. A parametric model of the turbine stator and rotor blades was established using a method in which quintic polynomial curves are tangent to circular arcs. Based on Latin hypercube sampling, 100 sets of blade-structure samples were generated. The output torque and pressure drop of each sample were obtained using computational fluid dynamics (CFD), and the corresponding efficiency was further calculated. On this basis, radial basis function (RBF) surrogate models were established to describe the relationship between blade structural parameters and turbine performance. The blade structure was then optimized using a weighted comprehensive evaluation function incorporating torque, pressure drop, and efficiency. The results show that the coefficients of determination of the surrogate models for torque, pressure drop, and efficiency on the test set are 0.8110, 0.8619, and 0.7319, respectively. The torque, pressure drop, and efficiency of the optimized design are 1.12 N∙m, 24,821 Pa, and 0.709, respectively, with relative errors of 6.67%, 5.90%, and 1.25% compared with the surrogate-model predictions. Under the constraints of minimum feature size, blade edge size, and overhang angle specified in this study, the optimized design demonstrates the feasibility of support-free SLM fabrication.