基于数字孪生控制的精密机床热误差模型

Thermal error model for precision machine tools based on digital twin control

已有的研究结果表明,机床的热误差约占其总加工误差的40%~70%,且机床越精密,其热误差所占比例就越大,因此,通过控制热误差以提升机床的加工精度很有必要。针对机床热误差模型的预测精度不高和泛化能力不强的问题,提出了一种引入主轴转速,并可嵌入数字孪生控制系统的机床热误差建模方法。首先,对模糊聚类分析(FCA)、灰色关联分析(GCA)及主成分回归(PCR)方法进行了理论分析;然后,以某立式加工中心为对象,通过热特性实验,获得了转速图谱下的温度数据和热误差数据,并采用模糊聚类分析结合灰色关联分析的方法选取了其温度敏感点;最后,以主轴转速和温度敏感点的温升值为输入变量,采用PCR方法建立了机床热误差模型,并将其与多元线性回归(MLR)模型进行了效果对比。研究结果表明:相比于MLR模型,所建立的PCR模型的预测精度提升9.5%,证明该模型拥有更高的预测精度和更强的泛化能力;可将模型嵌入到数字孪生控制系统中,对机床进行实时热误差预测和热误差控制。

The results of studies have shown that the thermal error of the machine tool accounts for about 40%to 70%of its total machining error,and the more precise the machine tool is,the greater the proportion of its thermal error is.Therefore,it is necessary to improve the machining accuracy of the machine by controlling the thermal error.Aiming at the problem that the prediction accuracy and generalization ability of machine tool thermal error model were not strong,a thermal error modeling method which introduced spindle speed and could be embedded in the digital twin control system was presented.Firstly,the fuzzy cluster analysis(FCA),grey correlation analysis(GCA)and principal component regression(PCR)method were theoretically analyzed.Then,a vertical machining center was used as the object,and the temperature data and thermal error data under the rotational speed chart were obtained through the thermal characteristic experiment,fuzzy cluster analysis combined with grey correlation analysis were used to select temperature sensitive points.Finally,the spindle speed and the temperature appreciation of the temperature sensitive points were used as input variables.The thermal error model was established by PCR method,and the effect was compared with multiple linear regression(MLR)model.The results show that the prediction accuracy of the established PCR model is 9.5%higher than that of the MLR model,which proves that the model has higher prediction accuracy and stronger generalization ability.It can be embedded into the digital twin control system to predict thermal error in real time and realize thermal error control.