基于瑞利-里兹法的复合材料转子叶片模拟件力学分析与铺层优化

Mechanical analysis and layup optimization of simulating specimen for composite rotor blades based on Rayleigh-Ritz method

摘要

复合材料转子叶片由于质轻、比强度高、比模量大、力学性能可调等优势，正逐渐替代传统金属件成为航空、能源动力等领域的关键承载部件。明确材料参数、铺层形式等对该类结构承载性能的影响具有重要的工程意义。本工作应用能量法，提出一种适用于复合材料转子叶片模拟件的刚度、强度分析，以及铺层优化设计的高效数值计算方法。基于 Rayleigh-Ritz 变分原理，建立等厚度与变厚度梯度（削层结构）层合梁在不同载荷工况（单一离心场、离心-侧压耦合场）下的平面应力分析模型。应用有限元仿真，验证理论模型在结构力学性能预测方面的准确性。通过引入高阶多项式位移形函数，实现了各载荷工况下结构的位移场与应力场的精确预测。最后，针对单一离心场作用下的变厚度复合材料转子叶片模拟件进行了铺层优化设计。数值分析表明，该理论模型对结构径向变形量的平均预测误差不高于 6%，横向变形量的平均预测误差不高于 15%。对于应力分布趋势的预测，理论计算与仿真值吻合良好。此外，铺层角度对转子叶片结构的应力与变形量有着较大影响。其中，[0]_n 铺层沿径向的变形量最小，[0/90]_ns 与 [±30]_ns 对称铺层结构次之，[±45]_ns 对称铺层结构变形最大。应力方面，[0/90]_ns 对称铺层结构中的 0°铺层沿纤维方向应力较大，其他 3 种铺层结构的应力相近。结果表明，该力学分析模型能够对等厚度、变厚度复合材料转子叶片结构的力学响应进行快速评估。相较于传统方法，该理论模型能够显著提升计算效率，在推进复合材料动力构件的优化设计方面具有工程应用价值。

Abstract

Composite rotor blade becomes one of the important components in the aerospace and energy industries，owing to its advantages of lightweight， high specific strength and modulus， and tunable mechanical properties. Determining the effects of material parameters and layup on structural load-bearing capacity is valuable for engineering application. With energy method，a theoretical model for strength evaluation， stiffness analysis， and layup optimization of this structure are proposed. Based on Rayleigh-Ritz method，theoretical models about the simulating specimen for composite rotor blade under different loading conditions are established，including the blade solely under centrifugal force and the blade under combined centrifugal force and uniform pressure. The theoretical model is verified by the finite element method (FEM). And a higher order of the trial function induces higher prediction accuracy of the model. Finally，the effects of different layups on the strength and stiffness of the rotor blade simulator with ply drops are evaluated with this model. The results show that the prediction error of the theoretical model in radial deformation is lower than 6%. And for transverse deformation prediction，the error is no higher than 15%. The theoretical analysis aligns well with simulation results in predicting stress distribution. Besides，it shows that the layup significantly influence the mechanical performance of the structure. The deformation in x-direction of the structure with [0]_n layup is the smallest，followed by the structure with [0/90]_ns layup and [±30]_ns layup. The deformation in x-direction of the structure with [±45]_ns layup is the largest. The increase in proportion of 0° plies improves the structural stiffness. As for stress along the principal material axes，the structures with [0]_n，[±30]_ns and [±45]_ns layups have similar magnitude，which are smaller than that of the structure with [0/90]_ns layup. The theorical model proposed in this paper provides a method for efficiently evaluating the mechanical properties of the composite rotor blade. Compared to traditional method，this model can shorten the design period and improve the efficiency，which is helpful for optimal design of composite power components.

关键词

复合材料 / 转子叶片 / 力学分析 / 瑞利-里兹法 / 铺层优化

Key words

composites / rotor blade / mechanical analysis / Rayleigh-Ritz method / layup optimization

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基金资助

中国航发集团产学研合作项目(HFZL2022CXY026-2)

中国航发集团应用创新项目(2023-05-2016-ZB)