A Finite Element Study of Stresses in Stepped Splined Shafts, and Partially Splined Shafts Under Bending, Torsion, and Combined Loadings
The maximum von Mises stress is calculated for solid finite element models of splined shafts with straight-sided teeth. One spline shaft is stepped with larger diameter section containing spline teeth and the smaller diameter section circular and cylindrical with no spline teeth. A second shaft is not stepped, but contains incomplete spline teeth.
Finite element analyses are performed for the cases of a stepped shaft of three different step size ratios (d/D). The second set of models consists of a solid cylindrical shaft with incomplete spline teeth. The incomplete regions of the spline teeth are modeled in three radii (R). Bending, torsion, and combined loads are applied to each model, including several combinations of bending and torsion between pure bending and pure torsion. Finite element stress results are converged to within 2% for verification.
The stresses in the stepped splined shafts are up to 50% greater than nominal stresses in the non-splined section and up to 88% greater than nominal stresses splined section. Stresses in the partially splined shaft showed little or no correlation between the hob radius and the magnitude of the peak von Mises stress, but show a strong correlation between the peak stress and the proportion of bending to torsion. The peak von Mises stress occurs when the applied load consists of greater proportions of torsion as opposed to bending. Stresses in the partially splined shaft are up to 42% greater than the well-developed nominal stress in the non-splined section of the shaft, and up to 7% greater than the nominal stresses in the splined section.