数控机床热误差变参数GM(1,1)的建模

Thermal error modeling of numerical control machine based on grey GM(1,1) model with variable parameters

为提高数控机床的加工精度,减少热误差对零件加工质量的影响,对热误差变参数灰色GM(1,1)在线预测模型进行研究。变参数灰色GM(1,1)在线预测模型能直接运用热误差时间序列值进行单序列建模,并给出模型参数的逐步迭代公式,根据不断输入的新数据,变参数模型能利用迭代公式,及时修正模型参数。以某精密卧式加工中心为研究对象,对所提出的变参数灰色GM(1,1)模型进行应用验证,并与传统的GM(1,1)模型和新陈代谢GM(1,1)模型进行对比研究。对比分析的结果表明:变参数灰色GM(1,1)模型很好地解决了传统的GM(1,1)模型难以预测大样本数据和非线性变化趋势的问题,且比新陈代谢GM(1,1)模型建模运算量小、求解时间短。变参数灰色GM(1,1)模型的预测值与实验结果对比表明,该模型预测精度高、通用性好,适用于机床热误差建模预测,进而提高机床的加工精度。

To improve processing precision of numerical machine tool and reduce the influence of thermal error on part quality,research on an on-line grey GM（1,1） prediction model with variable parameters was carried out.The variable parameters modeling method set up single sequence model on the basis of thermal error time sequence,and provided parameter iterative formula which constantly modified model parameters in accordance with continuous input data.A precise horizontal machining centre was used as a research platform to testify the variable parameters GM（1,1） model.Then,a comparison was made of three models as conventional GM（1,1）,metabolic GM（1,1） and variable parameters GM（1,1）.Comparative analysis shows that the variable parameters model solves the problem that conventional GM（1,1） has difficulty in predicting mass data and forecasting nonlinear variation trend.Furthermore,the new model has less computation and shorter computing time than metabolic GM（1,1）.Comparison between predicted value and experiment value indicates that the variable parameters model has high predict accuracy and good popularity.Thus,the proposed model is quite fit for thermal error prediction so as to improve machine tool processing precision.