Research on Micro-Vibration Isolation Platform Based on Udwadia-Kalaba Theory

doi:10.7652/xjtuxb201701009

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Research on Micro-Vibration Isolation Platform Based on Udwadia-Kalaba Theory

更新时间：2025-07-09

- Research on Micro-Vibration Isolation Platform Based on Udwadia-Kalaba Theory
- Vol. 51, Issue 1, Pages: 51-58(2017)
- 作者机构：
  
  合肥工业大学机械与汽车工程学院,合肥,230009
- 作者简介：
- 基金信息：
- DOI：10.7652/xjtuxb201701009
  CLC： TH113.1
- Online First：10 January 2017，
  
  Published：2017
- 稿件说明：
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Research on Micro-Vibration Isolation Platform Based on Udwadia-Kalaba Theory[J]. 2017, 51(1): 51-58.
DOI：

Research on Micro-Vibration Isolation Platform Based on Udwadia-Kalaba Theory[J]. 2017, 51(1): 51-58. DOI： 10.7652/xjtuxb201701009.

摘要

针对微制造平台的隔振问题

建立基于Udwadia-Kalaba方程的动力学模型

其可以在不引入拉格朗日乘数等额外参数的情况下进行求解。将微振动平台的振动位移作为系统约束

建立微振动隔振平台的离散化模型

并在主动隔振与被动隔振的混合机制下进行微振动平台隔振系统的多体动力学分析与仿真; 用Udwadia-Kalaba方程建立了驱动条件的求解方法以满足系统约束

基于约束条件建立微振动隔振平台的动力学模型

且通过Matlab语言进行仿真计算。研究结果表明:根据仿真得到了8个自由度方向的约束力矩

由此可以求得致动器所要求的竖直方向力的大小; 在4个质点所受噪声干扰相同的条件下

微振动离散化模型4个致动器所需的约束力保持一致

而且可以达到良好的减振作用。

Abstract

Focusing on vibration isolation for micro manufacturing platform

a dynamic model is established based on Udwadia-Kalaba equations

which can be solved without introducing Lagrange multiplier or other additional parameters. The discrete model of micro-vibration isolation vibration platform is constructed by treating the vibration displacement as a system restraint

and the multi-body dynamics analysis and simulation of micro-vibration platform are carried out following the mixing mechanism of the active and passive vibration isolation. To satisfy the system constraints

the driving conditions for Udwadia-Kalaba equations are introduced. The dynamic model of the vibration isolation platform can be solved under the constraint conditions and numerically simulated by Matlab. The constraint torques of 8 DOFs are thus achieved and the needed vertical forces for actuators can be obtained. The proposed discrete model of the micro-vibration is effective as the noises on four mass points are same.

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references

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