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The gear profile grinder is important to ensure the geometric accuracy of tooth surfaces. However, its machining accuracy is significantly reduced by the geometric and thermal errors. So the geometric and thermal errors should be controlled simultaneously. The geometric error modeling and decoupling of the gear profile grinder are studied, and the mapping relationship between the geometric accuracy of tooth surfaces and machine errors is constructed. To establish a robust thermal error model, a physically-based model is established to prove the feasibility of using the bidirectional long short term memory network (Bi-LSTMN) to establish a self-learning error model. The high-frequency noises are filtered and singular values are reduced by the Savitzky–Golay (SG) filtering algorithm. An attention-gate-based Bi-LSTMN (AGBi-LSTMN) is proposed to reduce the time complexity. Then the mixed-variants whale optimization algorithm (MVWOA) is proposed to optimize the hyper-parameters, and SG-MVWOA-AGBi-LSTMN is proposed for the thermal error prediction. Finally, the simultaneous geometric and thermal error control is implemented. The results show that the total tooth profile precision is increased by ISO level 3, and the tooth profile tilt precision is increased by ISO level 5 with the simultaneous geometric and thermal error control.

Production lines are important for the high-accuracy and efficient machining of parts. The thermal error of key machining equipment in production lines has a significant effect on the geometric accuracy of machined parts. To improve the geometric accuracy of machined parts, the thermal error of key machining equipment in a production line should be controlled. Then the collection, storage, analysis, and calculation of the large-volume manufacturing data are essential. But the processing involving the large-volume manufacturing data is time-consuming and challenging, which leads to low executing efficiency. To solve the problem that the system is inefficient in the processing of the large-volume manufacturing data, a four-terminal-architecture cloud-edge-based digital twin system (CEDTS) is proposed with a reasonable functional division of four terminals, and thus the executing efficiency of CEDTS is expedited. Then the error mechanism is studied to prove the long-term memorizing behavior, and an improved seagull optimization algorithm (ISOA) is proposed based on the chaos thought to optimize the weights, thresholds, and the number of iterations of an improved long short term memory (ILSTM) network with the attention mechanism. The ISOA-ILSTM error model is embedded into the intelligent decision-making terminal of CEDTS to predict the thermal error. Moreover, a comprehensive machining error model is proposed and embedded into the intelligent decision-making terminal of CEDTS to control the thermal error. Finally, the effectiveness of CEDTS is verified on a production line. The results show that the reduction of the large-volume manufacturing data for the collection, storage, analysis, and calculation is significant. With the implementation of CEDTS, the fluctuation range of geometric errors of machined parts is reduced significantly. The executing time is reduced by more than half by CEDTS with the GPU acceleration.