A novel thermal error compensation framework towards precision manufacturing: integrating digital twin technology and edge server deployment

The dynamic variation of spindle thermal error has a significant impact on the overall machining accuracy of machine tools. Therefore, effective compensation and control of thermal error are essential. However, existing systems still suffer from limitations in terms of real-time performance and compensation effectiveness. To address these issues, on the one hand, the generation mechanism of spindle thermal error is analyzed, and its correlation with the spatial characteristics of sensor data is verified. On this basis, a long-term spatiotemporal fusion parallel network model for thermal error prediction is proposed. In the temporal modeling stage, the thermal dynamics-aware temporal encoding network, which is able to embed physical characteristics such as heat conduction, memory hysteresis, and multiscale temporal patterns, is designed to effectively capture the dynamic dependencies in thermal error data. In the spatial modeling stage, a graph convolutional network guided by physical weights is employed to extract spatial distribution features from sensor data. Subsequently, a multiscale temporal encoder is used to jointly model short-term fluctuations and long-term drift and a spatiotemporal gate fusion module is used to enable dynamic and adaptive allocation of spatiotemporal feature weights, maintaining high efficiency without introducing additional computational overhead. In particular, the cross-scale spatiotemporal aggregation module can achieve cross-scale modeling across different temporal and spatial levels, enhancing model robustness under varying thermal operating conditions. The final prediction is constrained by a physics-embedded prediction head, which further improves the prediction accuracy and robustness. On the other hand, a digital twin-based compensation system framework is developed based on cloud-edge collaboration, and a general deployment scheme suitable for embedded environments is proposed. With an emphasis on deploying deep learning models, the framework is proposed to provide forward-propagation interface for various neural network layers without relying on mainstream deep learning frameworks. Importantly, the limitations of traditional wireless sensor network nodes in terms of insufficient performance and high energy consumption, which prevent them from supporting deep learning libraries such as TensorFlow and PyTorch, are overcome, thereby enabling the universal deployment of computationally complex models. A resource-efficient cyclic double-buffering mechanism is proposed to enable layered execution of multiple network modules. Additionally, a one-dimensional container for the model storage and a parameter indexing pointer mechanism that enables precise addressing of computational parameters during the inference process is introduced into the framework. Moreover, a high-performance edge computing intelligent gateway node is developed based on the ARM Cortex-A73 low-power processor architecture. The proposed long-term spatiotemporal fusion parallel network model is integrated into the edge server, enabling efficient execution of complex edge computing models. Experimental results demonstrate that the proposed model achieves superior prediction accuracy and robustness compared with traditional temporal and spatiotemporal models. Using the proposed compensation framework, spindle thermal error is reduced by up to 80%, and the response latency of the compensation system is improved by approximately 40% compared with conventional methods.