Indirect online estimation of friction torque for ball screws in CNC machine tools under varying operating conditions based on hybrid-driven heterogeneous model fusion

Friction torque (FT) is an important measurand for evaluating the operating condition and degradation of ball screws in CNC feed systems. However, direct FT measurement usually requires machine shutdown and component disassembly, which limits its practical application. Indirect online estimation based on operational measurements is therefore more feasible, but accurate estimation under varying operating conditions remains challenging due to limited generalization and vulnerability to abnormal predictions. To address these issues, this paper proposes an anomaly-aware hybrid-driven heterogeneous model fusion (AA-HD-HMF) method for online FT estimation of CNC ball screws under varying operating conditions. A parametric physical model integrating Coulomb friction, viscous friction, and the Stribeck effect is first established to describe speed-dependent FT characteristics and provide physically meaningful constraints for condition transformation. Multi-source signals acquired from the feed system are then processed and encoded by a variational autoencoder, and the encoder, latent-space, and decoder features are respectively introduced into three broad learning systems to generate multiple FT estimates. A confidence-weighted and outlier-aware dynamic fusion strategy is further developed to improve robustness against local abnormal outputs. A dedicated reference FT measurement procedure and a 300-hour degradation experiment were conducted on a dual-ball-screw torsional loading test bench over a speed range of 25–1000 r/min. The proposed method achieved mean absolute percentage errors of 1.54% and 1.60% on two test sets, respectively, and maintained stable performance under out-of-distribution speeds.