• CN:11-2187/TH
  • ISSN:0577-6686

›› 2011, Vol. 47 ›› Issue (23): 135-143.

• 论文 • 上一篇    下一篇

元结构方法的理论建模和验证

郭垒;张辉;汪劲松;叶佩青   

  1. 清华大学精密仪器与机械学系
  • 发布日期:2011-12-05

Theoretical Modeling and Verifications of Unit Structure Method

GUO Lei;ZHANG Hui;WANG Jinsong;YE Peiqing   

  1. Department of Precision Instruments and Mechanology, Tsinghua University
  • Published:2011-12-05

摘要: 元结构方法在结构分析中得到了很多应用,但是很少文献对其理论建模做研究。使用集中参数法对元结构及其复制成的整体进行分析,推导两者间振动频率的关系,从而建立元结构方法的理论模型。理论模型中,不考虑弹簧质量的模型称为简单模型,误差较大;使用瑞利法考虑弹簧质量所建的瑞利模型,误差比简单模型小。使用元结构方法的理论模型,在已知元结构振动频率和整体结构尺寸的情况下,能够完成整体振动频率的计算和设计。在第一个仿真算例中,验证了瑞利模型的误差(5.7%)小于简单模型的误差(15.6%)。在第二个仿真算例中,使用元结构方法指导了机床床身的设计。在试验算例中,使用元结构方法对一个铸件振动频率做出计算和设计。三个算例证明,元结构方法可以减小有限元仿真的建模工作量,可以减小样机的试制成本,是一种由局部特性推导整体特性的有效方法。

关键词: 机床, 机械振动, 集中参数法, 建模, 模态试验, 有限元法, 元结构

Abstract: Unit structure method is broadly used in structure analysis, but its theoretical modeling research is rarely found in literature. Lumped parameter method is used to analyze the unit structure and the whole structure made up by repeating it. Theoretical models of the unit structure method are established based on the relationship between the vibration frequencies of the unit structure and the whole structure. The model which doesn’t consider the mass of the spring is called simple model, with relatively large error. The error of the Rayleigh model which considers the mass of the spring using Rayleigh method is less than that of the simple model. The calculation and design of the whole structure can be realized by using theoretical models of the unit structure method, when the vibration frequency of the unit structure and the dimensions of the whole structure are known. In the first simulation example, the fact is verified that the error of Rayleigh model (5.7%) is less than that of the the simple model (15.6%). In the second simulation example, a machine tool bed is designed by using the unit structure method. In an experiment example, the vibration frequency of a casting is calculated and designed by using the unit structure method. These examples show that the unit structure method is an effective way to deduce the performance of the whole from the part, which can reduce the simulation modeling work in finite element method and prototype construction cost.

Key words: Finite element method, Lumped parameter method, Machine tool, Mechanical vibration, Modal experiment, Modeling, Unit structure

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