中文摘要：

研究数控加工精度优化控制问题，由于滚齿加工过程中机床关键部件发热导致主轴热变形、实际加工点发生偏移，引起齿轮加工误差。针对零传动数控滚齿机存在的热误差，对机床结构特征进行分析，并确定热误差形成的原因和关键热源点。为解决上述问题，提出分别在工件轴向、水平径向和滚刀轴向针对热变形量与热源点温度关系建立非线性误差补偿模型。采用支持向量机回归方法建模，并结合贝叶斯理论，实现了估计系统噪声水平，同时提出确定模型超参数的方法，将超参数搜索范围限定在二维直线上，可避免搜索的盲目性，时间开销小于传统方法。实验结果表明，改进模型比常用最小二乘法有更好的误差拟合效果且效率较高，模型输出值作为误差补偿量可有效提高齿轮加工精度。

英文摘要：

This paper focused on the precision optimal control problem for CNC hobbing machines： heats pro- duced by some machine parts lead to the thermal deformation of principal spindles, which will lead to machining er- rors. For solving this problem, the structural features of the direct-driving hobbing machine were analyzed, and the factors of thermal deformation and the key thermal fountainheads were determined. Finally, the non-linear models a- bout the relation between thermal deformations in three directions of two principal spindles and temperatures at ther- mal fountainheads were founded based on support vector machine regression theory. In the modeling process, the method to evaluate system noise and estimate the model hyper-parameters was achieved from the Bayesian point of view. It ensures that the hyper-parameters searching scope is limited to a certain line in the two-dimensional plane, which indicates the less blindness and lower time overheads. Comparative experimental results show that this im- proved model has higher efficiency and better fitting precision than the least square one. Using this model as thermal error compensation mechanism can increase the bobbing precision effectively.