As the integration of mechanical engineering and deep learning elds becomes increasingly intertwined, the application of experimental thermal error modeling in intelligent manufacturing has gained signi cant importance. In this paper, the issue of spindle thermal error is treated as a multivariate time series problem due to the thermal transfer characteristics. This study aims to address the challenge of modeling intermittent multivariate time series spindle thermal errors under a wide range of environmental temperatures and various operational scenarios. To tackle this challenge, a substantial volume of experimental data, capable of effectively re ecting the patterns of spindle thermal error variations, was collected through experiments conducted at multiple speeds and under various operational scenarios.Subsequently, the acquired thermal error data underwent intermittent multivariate time series transformation (IMTS) to suit the serialized deep learning model. The study introduces the Crossformer model into the eld of thermal error modeling for the rst time, which is a variant of the Transformer model. The Crossformer model exhibits remarkable adaptability to temporal aspects while effectively maintaining its focus on data features. Ultimately, this study resulted in the development of the IMTS-CrossformerR experimental thermal error model. Throughout the research, a comprehensive examination of various models was undertaken, including two traditional Transformer models, and other thermal error deep learning and machine learning models. The results indicate that the proposed model outperforms its counterparts across multiple model metrics and predictive capabilities. Particularly noteworthy is its substantial improvement in the Range (± 5) ratio of residual uctuations reaching 95.7%, a key engineering metric. These ndings emphasize the signi cant engineering application value of this research, offering novel methods and insights for the precise prediction of spindle thermal errors in the manufacturing industry.
