Bipod反射镜支撑结构的柔度计算及分析

Flexibility calculation and analysis of Bipod reflector support structure

为了改善反射镜在环境温度波动情况下的面形精度下降问题,设计了一种联杆型双轴Bipod柔性支撑结构,并基于柔度理论对它进行了参量优化。首先,对支撑结构的柔度进行了分析和计算,推导出柔性支腿以及反射镜组件的柔度理论公式。然后,以保证反射镜轴向支撑刚度和卸载能力为目的,计算得到一组针对口径为200mm反射镜的柔性支撑结构尺寸参数。最后,通过有限元分析和振动试验,对支撑结构的柔度公式、动态特性、温度适应性进行了分析验证。分析结果显示,在一定作用力下,柔性支腿的理论值与有限元分析值的误差在10%以内;振动试验得到组件的一阶频率为358.5Hz,与理论计算值的相对误差为8.8%;在20℃温差下,反射镜面形精度为7.7nm(rms)。试验结果验证了理论模型的有效性,同时说明Bipod柔性支撑结构能够降低温度波动对反射镜面形的影响。

A biaxial bipod flexible support structure was designed based on flexibility analysis parameter optimization to improve the accuracy of a mirror surface subject to ambient temperature fluctuations.First,the flexibility of the mirror support structure was calculated and analyzed,and a flexibility formula for the leg-and-mirror assembly was deduced.Then,to ensure the axial support stiffness and unloading ability of the mirror,a set of flexible support structure size parameters were calculated with a diameter of 200 mm.Finally,the flexibility formula,dynamic characteristics,and temperature adaptability of the support structure were analyzed and verified by finite element analysis and vibration tests.The results show that the error between the theoretical and finite element analysis values is less than 10%,under a certain force.The first-order frequency of the component,obtained by the vibration test,is 358.5 Hz,and the relative error of the theoretical calculation is 8.9%.Atatemperature difference of 20 ℃,the value of the mirror surface accuracy is 0.8.The validity of the theoretical model was verified,thus proving that the bipod flexible support structure can reduce the influence of temperature fluctuation on a mirror surface.