基于NiTi合金丝的反射镜柔性支撑结构的应力补偿

Stress compensation of flexible supporting structures for mirrors using NiTi shape memory alloy

针对大口径反射镜柔性支撑结构中柔性槽根部的应力集中问题,提出将NiTi记忆合金丝复合于柔性槽周边的结构方案,借助其预应变产生的拉应力来降低柔性槽根部的应力并保证支撑结构柔性。首先,建立了柔性槽根部的应力分布方程,得出了柔性槽危险截面位置。然后,建立了NiTi合金丝的一维本构方程,设计了桥型和U型两种复合方案,并对其进行了有限元分析。结果表明,采用U型复合的柔性支撑结构的应力改善明显优于桥型复合结构,且对结构柔性影响较小。以NiTi合金丝的拉力F为设计变量,以支撑结构的最大应力p及变形量δ为优化目标,对U型复合结构进行了参数优化设计。优化结果表明,在F为200N时有最优解,p由76 MPa降到37.9 MPa,δ由0.031mm微降到0.028mm,并且最大应力位置偏离柔性槽根部危险区域。对所提出的U型复合方案进行了随机振动试验,试验结果表明,该应力补偿设计有效降低了柔性支撑结构的最大应力。

Abstract： For the stress concentration regularly occured in the flexible supporting structures for largeaperture mirrors, a new method that composed the NiTi Shape Memory Alloy （SMA） around the flexible slots of the supporting structures was proposed, by which the tensile stress caused by prestrain of the SMA can reduce the stress concentration greatly without decreasing the flexibility of the structure. Firstly, the stress distribution equation for the flexible supporting structure was established, and the dangerous cross-sections were analyzed. Then, the one-dimensional constitutive equation of the NiTi alloy wires was derived, and two composition schemes, cross-type layout and U-type layout, were designed accordingly. The finite element analysis was applied to the two schemes, and the results show that the U-type composition is superior to the cross-type one in both peak stress and structural flexibility. A parameterized optimization was applied to the U-type layout by taking the tension F of NiTi alloy wires as design variable and the maximum stress p and the distortion 8 as optimization objectives. The results demonstrate that the optimum solution is obtained when F is 200 N, which shows that the p is reduced from 76.0 MPa to 37.9 MPa while g from 0. 031 mm to 0.028 mm slightly, and the maximum stress occurs away from the flexible slots. Random vibration tests were conducted for the U-type composition scheme, and the results verify the effectiveness of this method for the stress compensation.