数控机床热误差的改进型灰色DGM(2,1)模型建模  

Modeling of Machine Tool Thermal Error Using Modified Grey DGM(2,1) Model

作　　者：闫嘉钰[1] 范嘉桢[1] 杨建国[1] 

机构地区：[1]上海交通大学机械与动力工程学院,上海200240

出　　处：《武汉理工大学学报（交通科学与工程版）》2009年第5期835-838,共4页Journal of Wuhan University of Technology（Transportation Science & Engineering）

基　　金：高等学校全国优秀博士学位论文作者专项资金项目(批准号:200131);上海市引进技术的吸收与创新年度计划项目(批准号:05-12)资助

摘　　要：针对机床热误差补偿的建模问题,提出了基于灰色DGM(2,1)模型对数控机床热误差进行分析、预测的方法.该模型在通过对原始数据序列进行累加、累减处理以减小其随机性,建立微分方程的方式建立动态模型以揭示数据序列的长期发展趋势的基础上,利用函数变换法改善数据序列的光滑性.通过对1台数控机床的实际切削加工实验数据进行建模分析,对该方法进行了验证.结果表明该方法克服了传统灰色GM(1,1)模型的不足,获得了更高的建模和预测精度,且具有计算简单,便于在线补偿应用等优点.This paper presents a new methodology for the analysis and prediction of machine tool thermal error based on the grey DGM（2,1） model. This model can decrease the randomicity of thermal error data series by accumulation and descending operations to reveal the long term＇ developing trend of the data series by establishing differential equations. Function transformation strategy is also used to make the data series smoother. This method is verified by modeling the thermal error data under real cutting conditions on a Computer Numerical Control（CNC） machine. The result show that the new model can perform superior to traditional GM（1,1） model in terms of model and prediction accuracy, that it has the advantage that the calculation procedure is simple and timesaving and it is quite suitable for the application of on-line compensation.

关 键 词：数控机床 热误差 建模 灰色系统 DGM模型 

分 类 号：TH161[机械工程—机械制造及自动化]