基于径轴向Tchebichef矩函数三维曲面非对称结构的模型修正

Model validation of three-dimensional curved asymmetric structure by radial axial Tchebichef moments

采用积分的思想,将曲面机匣看作由若干圆柱机匣积累而成,将曲面机匣振型数据插值到一个圈数×点数×层数的三维像素空间内,能够实现径轴向Tchebichef矩(RAT矩)对曲面机匣模态振型的识别。利用RAT矩函数从曲面结构模态振型数据提取矩特征值,实现对振型数据的压缩,基于矩特征值的相关性分析能够很好地描述重模态现象,弥补了传统模态置信准则(MAC)值对于重模态描述的缺陷。进而将矩特征值代替振型数据,作为目标函数,应用于模型修正。矩特征值的数据量远小于振型数据,能够提高计算效率、避免修正结果不收敛。考虑到工程部件大多非完全轴对称,以一个带有非对称凸台的航空发动机机匣为例,基于RAT矩进行模态计算、相关分析和模型修正,发现同时利用频率与RAT矩进行模型修正,相关性有明显的提升,例如第9阶模态的相关性由35.35%提升到67.21%。各阶模态对的频差也都明显降低,最大频差由14.56%降至9.09%。证明了RAT矩函数能够应用在三维曲面非对称机匣的模型确认中。

Using the idea of integral, the curved case was considered to be accumulated by a number of cylindrical cases. The mode shape data were interpolated into a three-dimensional pixel space of circle×points×layer, which can realize the identification of the mode shape of curved case by radial axial Tchebichef moment(RAT moment). The feature moment set was extracted from the mode shape data by using the RAT moment function to achieve compression of the mode shape data. Correlation analysis based on RAT moment can well describe the double modes phenomenon, which can make up for the defects of traditional modal assurance critertiom(MAC)values for double modes description. The eigenvalue of the moment was used as the objective function instead of the mode data, which was applied to model verification. The data amount of the moment eigenvalue was much smaller than the mode shape data, which can improve the calculation efficiency and avoid the non-convergence of the updating result. Considering that most engineering components were not completely axisymmetric, an aero-engine casing with an asymmetric boss was taken as an example. Based on RAT moments for mode calculation, correlation analysis and model updating, it was found that both frequency and RAT moments were used for model verification. Correlation was significantly improved, for example, the correlation of the ninth-order mode was increased from 35.35% to 67.21%. The frequency difference of each mode pair was also significantly reduced, and the maximum frequency difference was reduced from 14.56% to 9.09%. It was proved that the RAT moment function can be used in the model confirmation of asymmetrical three-dimensional surface.