图 文 导 读

1. 提出了超精密飞切机床动力学有限元模态综合多体系统传递矩阵法；
   
2. 建立了超精密飞切机床多柔体系统动力学模型；
3. 推导了超精密飞切机床多柔体系统总传递方程；
4. 实现了超精密飞切机床振动特性快速仿真计算。

Highlights:

1. A hybrid multibody system method for the dynamic analysis of the ultra-precision fly-cutting machine tool is proposed.  
2. The dynamic model of the ultra-precision fly-cutting machine tool is developed.
3. The overall transfer equation for the ultra-precision fly-cutting machine tool is derived.
4. The vibration characteristics at a fast calculation speed are simulated.

超精密加工是指被加工零件的尺寸精度优于0.1微米，表面粗糙度优于0.01微米的加工技术。超精密加工技术是国家制造技术水平的重要标志。超精密机床动力学性能决定了超精密加工的加工质量，超精密机床动力学设计为提高超精密加工精度提供了技术支撑。鉴于超精密机床整机系统结构复杂，加工精度要求高，以往的多体系统动力学仿真设计理论因建模繁琐、计算效率低而难以满足超精密机床系统动力学快速仿真设计需求。

北京大学陆涵婧博士后、南京理工大学芮筱亭院士团队和丹麦奥胡斯大学Xuping Zhang副教授合作在《国际机械系统动力学学报（英文）》(International Journal of Mechanical System Dynamics, IJMSD)发表“超精密飞切机床动力学有限元模态综合多体系统传递矩阵法”研究论文。该文建立了超精密飞切机床动力学有限元模态综合多体系统传递矩阵法新方法，实现了超精密飞切机床多柔体系统快速仿真计算，计算结果得到了模态试验验证，为超精密机床动力学设计提供了有效的技术途径。该方法保持了多体系统传递矩阵法矩阵阶次低、计算速度快、内存占用小等优点，同时可应用于含复杂形状柔体的一般多柔体系统振动分析，扩大了多体系统传递矩阵法对一般多柔体系统的计算能力。

Abstract: A localized Fourier collocation method is proposed for solving certain types of elliptic boundary value problems. The method first discretizes the entire domain into a set of overlapping small subdomains, and then in each of the subdomains, the unknown functions and their derivatives are approximated using the pseudo-spectral Fourier collocation method. The key idea of the present method is to combine the merits of the quick convergence of the pseudo-spectral method and the high sparsity of the localized discretization technique to yield a new framework that may be suitable for large-scale simulations. The present method can be viewed as a competitive alternative for solving numerically large-scale boundary value problems with complex-shape geometries. Preliminary numerical experiments involving Poisson, Helmholtz, and modified-Helmholtz equations in both two and three dimensions are presented to demonstrate the accuracy and efficiency of the proposed method.