A null-coupling complete error model in gear hobbing and error prediction

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.