范数最优控制理论在植树挖坑机钻头主轴纵向振动系统中的应用  

Application of theory of norm optimal control on the longitudinal vibration system of drill bit main shaft of pit digger for tree planting

作　　者：孟庆华[1] 于建国[1] 

机构地区：[1]东北林业大学机电工程学院

出　　处：《机械设计》2006年第9期25-27,共3页Journal of Machine Design

基　　金：教育部博士点基金项目(20040225005)

摘　　要：首先利用弹性动力学理论和Hamilton变分原理建立了植树挖坑机钻头主轴及钻尖在进给过程中钻尖与土壤互相作用而产生纵向振动的动力学模型,同时给出边界条件和初始条件。其次通过把系统阻尼函数当作控制变量,利用算子半群理论和Banach空间几何方法,以“范数最小”来证明系统最优控制的存在性和唯一性,为有效地预测和控制钻头的运动规律,改善钻头主轴的动力学特性,提高钻头工作效率及改进设计方法提供了新的理论依据。Utilizing the theory of elastic dynamics and Hamilton variation principle, the dynamics model was firstly established for the longitudinal vibration produced by mutual action between drill tip and soil during the feeding course of drill-bit main shaft and drill tip of the pit digger for tree planting, and at the same time the boundary conditions and preliminary conditions were presented. Secondly, by means of taking the damping function of system as the controlling variable and using the operator semi-group theory and the method of Banach spatial geometry, the existence and uniqueness of optimal control of system were testified by ＂norm minimum＂. Thus provided a new theoretical basis for effectively predict and control the moving low of drill bit, improve the dynamics characteristics of drill-bit main shaft, enhance the working efficiency of drill-hit and improve the designing method.

关 键 词：挖坑机 钻头主轴 纵向振动 范数最小 最优控制 

分 类 号：O175[理学—数学] TG52[理学—基础数学]