A Temperature-Based Statistical Model for Real-Time Thermal Deformation Prediction in End-Milling of Complex Workpiece

Thermally induced deformation is a major source of dimensional error in end-milling, especially under high-speed or high-load conditions. Direct measurement of workpiece deformation during machining is impractical, while temperature signals can be obtained with good stability using embedded thermocouples. This study proposes an indirect method for predicting milling-induced thermal deformation based on temperature measurements. A three-dimensional thermo-mechanical finite element model is established to simulate the transient temperature field and corresponding deformation of the workpiece during milling. The numerical model is validated using cutting experiments performed under the same boundary conditions and machining parameters. Based on the validated results, the relationship between deformation at critical machining locations and temperature responses at candidate monitoring points is analyzed. To improve applicability to complex workpieces, a statistical prediction model is developed. Temperature monitoring points are optimized, and significant temperature–deformation correlations are identified using multiple linear regression combined with information-criterion-based model selection. The final model is constructed using simulation-derived datasets and provides stable deformation prediction over the entire milling process.