Revolutionizing gear hobbing machine precision: Innovative thermal error compensation and intelligent error control with enhanced crystal structure algorithm and self-attention bidirectional minimal gated unit network

Abstract

The thermal error stands as a pivotal determinant, significantly impacting both the precision and its stability of gear hobbing processes. Thus far, conspicuous delays in compensation and insufficiencies in precision have been duly noted. To achieve a proficient and exceedingly precise thermal error compensation, an intricate mathematical correlation is expounded, delineating the connection between the spatial pose error of the hob and the inherent thermal error in the gear hobbing machine. In addressing the thermal error linked to the B-axis, a bidirectional-minimal gated unit network is harnessed to characterize long-term memory attributes. An advanced crystal structure algorithm is introduced, encompassing components such as the population initialization mechanism, the nonlinear convergence factor, the Gaussian perturbation mechanism, and an enhanced optimization equation. The weights of the bidirectional-minimal gated unit network are judiciously assigned via the self-attention mechanism. This innovation, recognized as the improved crystal structure algorithm-self-attention-bidirectional-minimal gated unit network, is introduced for the training of the thermal error model for the B-axis. Subsequently, thermal analysis models are formulated, yielding the thermal errors of the X- and Z- axes. An error control model and an error decoupling model are established, employing the thermal errors of the B-, X-, and Z- axes as their input. Ultimately, an intelligent error control system is crafted, in which the error control model, error decoupling model, and thermal error model are seamlessly integrated. The aim is to mitigate tooth flank errors. With the integration of the intelligent error control system, the levels of precision pertaining to gear helix deviation, maximum deviation of a single pitch, and cumulative total pitch deviation are elevated by one, one, and two levels, respectively. More significantly, the geometric error reduction of the tooth flank achieved by the meticulously designed intelligent error control system surpasses that of traditional pitch compensation by a substantial margin. Furthermore, the execution efficiency of the intelligent error control system, when operating within the machine-edge-fog-cloud framework, exhibits a remarkable improvement of 24.18%, 16.20%, and 57.84% when compared to the intelligent error control system operating within the machine-edge-cloud, machine-fog-cloud, and machine-cloud frameworks, respectively.