反射镜组件模态分析的误差评价

Error valuation for mode analysis of reflective mirror set

对有限元法在反射镜组件模态分析中产生的误差进行了定量评价及试验验证。阐述了算法误差、材料参数误差以及连接关系的简化处理等3个主要误差源对分析结果带来的影响。从模态分析的基本原理出发,得出算法选择引入的误差<1%;材料参数误差的传递因子可从公式推导以及试算数据拟合的方法得到,误差的参与权重因子可通过模态振型来获得;而螺钉连接关系简化处理引入的误差则通过简化处理螺钉连接关系与详细分析两种有限元模型的结果来获得。试验结果表明,在有限元分析中,若对连接关系进行了简化处理,反射镜组件模态分析结果的误差将达到10%左右;若对螺钉进行有限元建模,在组件的分析中考虑螺钉刚度的贡献,误差可以控制在5%以内。分析结果与试验结果基本吻合,表明对螺钉连接关系的处理方式是决定分析结果误差的关键因素,在高精度的分析中,螺钉连接的刚度贡献是不能忽略的。本文提出的组件模态分析误差的定量分析方法,对采用有限元法进行的重力变形分析、动力学响应分析以及热变形分析等误差定量分析亦有指导意义。

The error caused by Finite Element Analysis（FEA） in the mode analysis of a reflective mirror set was evaluated quantitatively and identified by an experiment.The influence of source factors,arithmetic error,material parameter error and the simplification of the bolt connection on the FEA results were introduced in detail.It shows that the arithmetic error is less than one percent;the deliver factors of the material parameter errors can be calculated by the formula and test calculation dada,respectively,and the participation factors of the material parameter errors are estimated by the modal plot;the error caused by the simplification of the bolt connection is calculated by the contrast of the results of the simplification finite element model and the detailed finite element model.The results show that the FEA error would be 10% if the bolt connection is simplified.However,if the bolt connection is considered in detail,the FEA error would be decreased to 5%.The experiment results prove that the error analysis results are correct.Moreover,the trade method of the bolt connection is the key factor in the mode analysis of the reflective mirror set and it can＇t be ignored apparently in the high precision analysis.It concludes that the quantitative error valuation method can be applied to the other cases,such as gravity transformation analysis,dynamic response analysis and thermal analysis.