采用离散余弦变换的复合材料构件制造偏差建模方法  

Modeling Method for Manufacturing Deviation of Composite Components Using Discrete Cosine Transform

作　　者：常正平[1] 李学文 严康赫 李晓锋 罗群 王仲奇[1] CHANG Zhengping;LI Xuewen;YAN Kanghe;LI Xiaofeng;LUO Qun;WANG Zhongqi(School of Mechanical Engineering,Northwestern Polytechnical University,Xi’an 710072,China;AVIC Xi’an Aircraft Industry Group Co.,Ltd.,Xi’an 710089,China)

机构地区：[1]西北工业大学机电学院,西安710072 [2]中航西安飞机工业集团股份有限公司,西安710089

出　　处：《西安交通大学学报》2025年第3期201-209,共9页Journal of Xi'an Jiaotong University

基　　金：国家自然科学基金资助项目(51905443);陕西省自然科学基础研究计划资助项目(2024JC-YBMS-318)。

摘　　要：为能够更精确、高效地表达碳纤维增强复合材料构件制造偏差,提出了一种基于离散余弦变换的制造偏差建模方法。首先,对构件理论表面进行离散化得到网格模型,计算网格模型节点与对应区域实测点云数据的法向距离以表征制造偏差,进而得到复合材料构件制造偏差场,实现了理论模型与实测数据的融合。其次,采用二维离散余弦正变换,将制造偏差场分解为一系列偏差模态的线性组合,并结合离散余弦变换的能量集中特性与核函数的正交性,对复合材料构件制造偏差场组成模态进行识别与筛选,确定了构成制造偏差场的关键模态。然后,对确定的制造偏差场关键模态进行离散余弦逆变换,并重构制造偏差场,实现了构件制造偏差场的数据精简,该方法在保证重构模型精度的同时减少了计算复杂度与数据存储量。最后,通过复合材料蒙皮构件开展实例验证。结果表明:点云数据网格尺寸与重构精度、偏差模态总数成反比,当数据删减率为60.54%时,其相对重构误差为7.62%。研究结果证明了基于离散余弦变换的偏差建模方法可精确、高效地表征复合材料构件的制造偏差特征。To more accurately and efficiently express the manufacturing deviations of carbon fiber reinforced composite components,a modeling method based on discrete cosine transform is proposed.Firstly,the theoretical surface of the component is discretized to obtain a mesh model.The normal distances between the mesh model nodes and the corresponding region’s measured point cloud data are calculated to characterize the manufacturing deviations,thereby obtaining the manufacturing deviation field of the composite component and achieving the fusion of theoretical models and measured data.Secondly,using the two-dimensional discrete cosine transform,the manufacturing deviation field is decomposed into a linear combination of a series of deviation modes.By combining the energy concentration characteristics of the discrete cosine transform with the orthogonality of the kernel function,the modal composition of the manufacturing deviation field of composite components is identified and selected,determining the key modes that constitute the manufacturing deviation field.Subsequently,the identified key modes of the manufacturing deviation field are subjected to discrete cosine inverse transform to reconstruct the manufacturing deviation field,achieving data simplification of the component’s manufacturing deviation field.This method reduces computational complexity and data storage while ensuring reconstruction model accuracy.Finally,an example verification is conducted on a composite skin component.The results show that the mesh size of point cloud data is inversely proportional to reconstruction accuracy and the total number of deviation modes.When the data reduction rate is 60.54%,the relative reconstruction error is 7.62%.The research results demonstrate that the deviation modeling method based on discrete cosine transform can accurately and efficiently characterize the manufacturing deviation characteristics of composite components.

关 键 词：离散余弦变换 复合材料构件 制造偏差 模态识别 

分 类 号：TH124[机械工程—机械设计及理论]