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