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The thermal error in the spindle unit is substantial and necessitates mitigation. Current models, being predominantly static in nature, have limited efficacy in error control. Integrating digital twin technology for modeling and controlling spindle unit thermal error holds promise in enhancing the machining accuracy of machine tools. Yet, the notion of a digital twin system specifically tailored for spindle unit thermal characteristics remains uncharted territory. To navigate these challenges, this study introduces a novel digital twin system tailored for spindle unit thermal characteristics. This system is poised to revolutionize thermal error modeling and compensation by harnessing the capabilities of digital twin technology. Within this digital twin framework, both the thermal error control model and the analytical thermal characteristic model are seamlessly integrated. The control model is devised as an exponential function, utilizing operational time, inherent time constants, and both initial and equilibrium thermal errors as parameters. Delving deeper, the analytical thermal characteristic model for the spindle system is rooted in a thermal resistance network approach. This leads to a closed-loop thermal characteristic modeling process, culminating in the derivation of a steady-state thermal error. Intricate heat transfer dynamics between spindle components are dissected, and a comprehensive thermal equilibrium equation set is formulated for the spindle unit. This equation set comprehensively accounts for dynamic variations in key parameters such as preload, lubricant viscosity, thermal load intensity, thermal contact resistance, and convective coefficients. To ascertain the time constant, a meticulously designed set of thermal characteristic experiments is executed. Subsequently, the digital twin system embarks on predictive modeling of thermal errors across varied operational conditions. This prediction then forms the foundation for thermal error compensation. With the integration of the present model into the digital twin system, the results are impressive: the absolute average and maximum deviations in thermal elongation, post-error control, stand at approximately 0.40 μm and 1.24 μm, respectively. [ABSTRACT FROM AUTHOR]

The thermal errors in ball screws present complex spatial-temporal characteristics and exhibit persistent long-term memory, significantly affecting the machining accuracy of the whole machine tool in applications. Deep learning has emerged as a promising approach to predict these errors using thermal data. However, the scarcity of extensive thermal datasets, typically due to the prohibitive costs and time required for experimental acquisition, hampers the comprehensive exploitation of spatial-temporal and long-term memory attributes. Moreover, the current thermal error compensation system does not support the deployment of deep learning-based thermal error models due to its weak real-time performance. These limitations lead to suboptimal prediction accuracy and inadequate error compensation. Addressing this challenge, a novel spatial-temporal interactive integration network is proposed, and this is a sophisticated model that synergistically blends a time memory gate and a spatial-temporal fusion gate within an advanced attention-based spatial-temporal graph convolutional framework. Our network ingeniously leverages spatial data to anchor long-term memory while employing temporal data for selective memory feature extraction, facilitating a refined integration of spatial-temporal features. Concurrently, the integration of gated recurrent units and a time attention layer meticulously extracts and enhances temporal features, bolstered by our innovative time memory gate, which is adept at handling small-sample scenarios and refining thermal error predictions. Critically, the digital twin system for thermal error compensation is constructed to improve the system's real-time performance. The integration of this network into the digital twin system marks a pivotal advancement in thermal error compensation. Our empirical results underscore the system's remarkable robustness and superior predictive accuracy, demonstrating a significant reduction in positioning and machining errors (over 90% and 80% respectively) even with constrained thermal data inputs. These advancements not only delineate a substantial leap in predictive accuracy but also underscore our contribution to reducing operational costs and enhancing the efficacy of machine tools. [Display omitted] • Spatial-temporal fusion gate is proposed to extract spatiotemporal features. • STIIN is proposed to extract spatiotemporal features of thermal error. • Digital twin system for thermal error compensation is established. • STIIN model is embedded into digital twin system. • Robust compensation is realized with small-volume thermal information data. [ABSTRACT FROM AUTHOR]

The heat generation is significant in the machining process, leading to thermal errors, and finally the geometric precision of machined parts is reduced. So the precision machine tool is a key factor in determining the geometric precision of complex parts. In recent years, the error control method is applied. But the method fails in reducing thermal errors because it cannot effectively process large-volume data, resulting from its low executing efficiency. To solve above issues, a new intelligent digital-twin prediction and reverse control system is designed for thermally induced errors based on the user-edge-cloud architecture to expedite the executing efficiency. The data-driven error modeling method is augmented by an error mechanism-based modeling to express the thermal error as a function with the temperature, armature current, rotational speed, and ambient temperature as independent variables, and then the long-term memorizing behavior of thermal errors is demonstrated. The error model is established based on an improved wavelet threshold denoising (IWTD) and a (long short-term memory) LSTM network to describe the memorizing behavior, and IWTD-LSTM network error prediction model is embedded into the digital-twin system. The digital-twin system and IWTD-LSTM network model were verified on a precision machine tool. With the implementation of the digital-twin system, the thermal error and the volume of the transferred data are reduced by 88.72% and 56.36%, respectively. [ABSTRACT FROM AUTHOR]

[Display omitted] • Four-terminal-architecture CEDTS is proposed for thermal error control. • Hyper-parameters of ILSTM network are optimized by ISOA. • Comprehensive machining error model is constructed according to HCT theory. • Data services, including clustering analysis, status monitoring, and data funsion, are provided. • GPU-based cloud computing layer is used to expedite executing process. 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. [ABSTRACT FROM AUTHOR]