高速主轴动态性能数值模拟的小波有限元理论新研究

项目名称： 高速主轴动态性能数值模拟的小波有限元理论新研究

项目编号： No.50805028

项目类型： 青年科学基金项目

立项/批准年度： 2009

项目学科： 数理科学和化学

项目作者： 向家伟

作者单位： 桂林电子科技大学

项目金额： 22万元

中文摘要： 本项目针对高速主轴动态性能数值模拟问题，系统地研究新型小波有限元方法。提出高维非张量积提升小波单元簇构造方法；研究小波多尺度迭代算法，结合小波单元簇构造技术和多尺度提升框架，提出高维多尺度小波单元的构造方法；研究多尺度小波单元与传统自适应有限元分析的切入点，提出自适应小波有限元理论框架；建立高速主轴动态性能数值模拟的自适应小波有限元核心算法，弥补传统自适应有限元在模拟多物理场问题时存在的计算精度差、计算效率低、难以收敛到精确解等不足。本项目研究的先进的自适应小波有限元理论与技术，重点突破解决了高速主轴（转子）高精度数值模拟的技术难点，同时研究了主轴（转子）裂纹定量诊断问题，为高速主轴动态优化设计的研究和深入发展提供新颖的高性能数值分析手段，取得有价值的基础理论和实用技术。

中文关键词： 高速主轴；提升小波；小波单元簇；多尺度小波单元；自适应

英文摘要： Aiming at the numerical simulation of dynamic characteristics for high speed spindle, a new wavelet finite element method is systematically studied. Firstly, the construction method of high dimensional non-tensor product wavelet-based elements is proposed. Secondly, the wavelet-based multi-scale iterative algorithm is studied. By combination of the construction technique of wavelet-based elements and the multi-scale lifting scheme, the construction method of high dimensional multi-scale wavelet-based is presented. Thirdly, the breakthrough point of multi-scale wavelet-based element and the traditional adaptive finite element analysis method is studied to present the theoretical framework of adaptive wavelet finite element method. Finally, the core algorithm of adaptive wavelet finite element method is established for the numerical simulation of dynamic characteristics of high-speed spindle. The disadvantages of traditional adaptive finite element analysis method for analyzing multi-physics field problems, such as poor accuracy, low efficiency and bad converge ratio, can be enormously remedied. The project aims to study advanced adaptive wavelet finite element theory and technology. The key breakthrough is to solve the difficult of high-precision and all-digital modeling of high-speed spindle components. At the same time, the crack quantitative detection of spindle (shaft) is investigated. The research results can be applied to the dynamic optimization and in-depth development of innovative high performance numerical analysis method and to obtain valuable basic theory and practical technology.

英文关键词： High-speed spindle; Lifting wavelet;Wavelet-based elements; Multi-scale wavelet-based element; Adaptivity