Spindle unit thermal error modeling and compensation based on digital twin

Abstract

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.