Stress Assessment of Filleted Stepped Shafts under Combined Bending and Torsion

Abstract

Stepped shafts require diameter transitions for bearings, gears, couplings, and other mounted components, but the resulting shoulder fillet may govern the local stress. This study presents a dimensionless assessment of circular filleted shafts under combined bending and torsion. A finite-element-based correlation for the von Mises stress-concentration factor was applied to 60 combinations of diameter ratio , fillet-radius ratio , and nominal torsion-to-bending stress ratio , covering , , and . For a 30 mm steel shaft with a nominal bending stress of 70 MPa and a yield strength of 355 MPa, the calculated stress-concentration factor ranged from 1.440 to 2.934. Increasing  from 0.02 to 0.10 reduced the factor by 32.8–42.5%, whereas increasing  from 1.2 to 1.8 raised it by 5.5–15.2%. Although the normalized factor decreased with increasing torsional contribution, the maximum local equivalent stress increased because of the higher nominal multiaxial stress. Under equal nominal bending and torsional stresses, the most severe case reached 343.4 MPa with a static safety factor of 1.03. For a required safety factor of 1.5, the minimum  increased from 0.0479 to 0.0653 as  increased from 1.2 to 1.8. Benchmark and representative finite-element comparisons showed deviations below 2.1%. The resulting design charts provide a practical tool for preliminary shaft assessment without requiring a separate finite-element model for each geometry.