Fatigue Performance of a 30CrMoA Gear Shaft Strengthened by Laser Quenching Combined with Ultrasonic Surface Rolling: A Theoretical S–N Curve Approach

Marine gear shafts strengthened by multi-track overlapping laser quenching–ultrasonic rolling composite treatment exhibit complex torsional fatigue damage evolution due to the multi-layer gradient structure of the meshing interface, making quantitative fatigue life evaluation under mean shear stress challenging. Taking 30CrMoA steel as the research object, this study establishes a torsional fatigue S–N model modified by mean shear stress and a layered finite element model comprising the matrix, hardened layer, and tempered zone. Symmetric (R = −1) and asymmetric (R = 0.14435) cyclic torsional fatigue simulations were performed to clarify load effects on fatigue life distribution and attenuation. A second-order response surface model based on the Box–Behnken design was employed to reveal the interactive effects of hardened layer depth, tempered zone width, and surface residual compressive stress on fatigue life, yielding the sensitivity ranking: residual compressive stress > hardened layer depth > tempered zone width. With maximum fatigue life as the objective, the optimal parameters were determined (0.85 mm hardened layer, 1.60 mm tempered zone, −650 MPa residual stress). Torsional fatigue tests and fracture observations validated the simulations, with a relative error below 15%, providing a theoretical basis for anti-torsional-fatigue design of composite-strengthened shafts.