A progressive mechanism-data-knowledge integration approach for generalizable thermal error perception and prediction of motorized spindles under high-variability CNC operations

• A progressive mechanism–data–knowledge integration framework is proposed for spindle thermal error perception and prediction, enabling effective modeling of nonlinear heat conduction and robust generalization under time-varying conditions. • A two-stage hybrid modeling approach combines ridge regression and BiLSTM networks to achieve linear–nonlinear decoupling, significantly enhancing prediction accuracy and stability for constant operating conditions. • A knowledge graph-based embedding and Gaussian kernel weighting strategy enables quantitative similarity assessment and adaptive transfer of thermal behavior knowledge, improving multi-source model integration under variable conditions. Under increasingly demanding and complex CNC machining processes, achieving precise prediction and compensation of motorized spindle thermal errors is crucial for maintaining stable machining quality. Traditional thermal error prediction models demonstrate inherent constraints in their capability for cross-condition generalization and knowledge transfer. These constraints primarily stem from the highly nonlinear behavior and condition-dependent characteristics of thermal error variations. To address these challenges, this study proposes a general framework for spindle thermal error prediction modeling based on progressive integration of mechanisms, data, and knowledge. Firstly, the proposed approach integrates spindle thermal deformation mechanisms and extracts physically interpretable state features from multi-source sensor data, and the developed two-stage hybrid modeling strategy combines ridge regression for linear thermal response modeling with a BiLSTM network for nonlinear residual compensation. This mechanism-data synergistic approach balances theoretical interpretability with local generalization capability, establishing knowledge source models for subsequent reasoning processes. Subsequently, thermal state characteristics of representative operating conditions are organized into a knowledge graph, with knowledge embedding learning quantitatively assessing thermal state similarities between different conditions. Finally, a knowledge-driven dynamic weight optimization strategy is established using Gaussian kernel weighting, forming an intelligent reasoning system for adaptive transfer and integrated prediction of multi-source models. Experimental results demonstrate that under high-speed and variable-load milling conditions, the method maintains average prediction errors below 2.8 μm, validating its generalization performance and practical value in complex operating environments. This study provides an effective technical framework for generalized prediction modeling of spindle thermal errors under complex machining conditions.