一种零耦合滚齿全误差模型及其预测方法
A Null-Coupling Complete Error Model in Gear Hobbing and Error PredictionL

为了降低滚齿全误差模型的求解难度,建立了机床误差模型与工件加工精度之间的映射关系,同时对滚齿加工误差进行准确辨识与预测,提出了一种将滚齿全误差模型分解为两个完全独立的子模型并进行协同计算的方法,可以提高滚齿全误差模型在误差辨识、预测中的可操作性。利用齐次坐标变换建立机床误差传递模型,依据共轭曲面的空间啮合特性,对滚齿加工理论齿廓进行了精确计算。利用齿廓误差的折算方法,将机床误差参量折算成齿廓误差,从而得到实际加工齿廓,通过对比,即可得到齿形、齿向、齿距等误差值,从而建立起了机床各误差参量与齿轮加工误差之间的完整映射关系。进一步在滚刀存在偏心的情况下进行直齿滚切实验,并将齿轮检测结果与文中模型的预测结果进行对比,表明该模型的计算结果与检测结果高度契合(相对误差≤5％),充分说明了该模型的正确性与实用性。滚齿加工误差的准确辨识与预测也使滚齿加工虚拟化成为可能,为构建机床信息物理系统模型和实现预测式制造提供了重要的技术支撑。
To reduce the complexity of gear hobbing error model, establish a mapping relationship between the machine tool error model and the machining precision, and accurately identify and predict gear hobbing error, a method is proposed where the complete error model of gear hobbing is divided into two completely independent submodels for cooperative computing, and the maneuverability of the error model for gear hobbers is improved for engineering application. The deviations in transmission model are evaluated by homogeneous coordinate transformation. Following the space meshing principle of the conjugate surfaces in gear hobbing, the ideal tooth surface functions are calculated. By means of tooth profile conversion, the profile error of gear tooth from the deviations in transmission model and the actual tooth profile are obtained. The errors of gear profile, lead and index can be obtained through comparison. The complete mapping relationship between the machine tool error and the machining error is thus established. A hobbing experiment of a spur gear with hob eccentric error shows that the prediction from this model and detection from the experiment coincide well, verifying the correctness and availability of this model, and the relative error is no more than 5％. The accurate error identification and prediction make virtualization for gear hobbing possible, and provide significant technical support for the construction of machine tool cyber？？physical system to realize of predictable manufacturing