Gear ultrasonic vibration grinding composite function curve distribution heat source model optimized based on particle swarm algorithm

Accurate thermal boundary modeling is essential for preventing grinding-induced damage in gear finishing. This work addresses the lack of an ultrasonic-specific heat-source model by proposing a Composite Function Curve Distribution (CFCD) that couples an exponential decay and a linear component to capture vibration-induced, high-frequency contact modulation in Ultrasonic Vibration Grinding (UVG). Building upon moving-point heat-source theory and grain-separation mechanisms, we optimize the shape coefficients of all candidate distributions—CFCD, Segmented Triangular (STD), Parabolic (PD), and Trapezoidal (TrD)—using a unified Particle Swarm Optimization (PSO) protocol with identical multi-objective criteria and constraints. A fast 3D transient solver provides temperature predictions that are validated against thermocouple measurements on 12Cr2Ni4A gears under both UVG and conventional grinding (CG). The PSO-optimized CFCD achieves the highest fidelity to measurements in UVG (average error≈3.06 %) and reproduces both the peak and the morphology of the temperature evolution, whereas PD/TrD yield errors >10 %. In CG, CFCD performs comparably to STD (error≈3–4 %), reflecting the differing physics between steady contact and vibration-modulated contact. The unified optimization and validation demonstrate that CFCD provides an accurate, physically interpretable thermal boundary for gear UVG, enabling near-real-time temperature prediction and actionable guidance for process planning and thermal-damage control in precision gear manufacturing.