Optimization of straight-sided spline design

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Spline connection of shaft and hub is commonly applied when large torque capacity is needed together with the possibility of disassembly. The designs of these splines are generally controlled by different standards. In view of the common use of splines, it seems that few papers deal with splines and the subject of improving the design. The present paper concentrates on the optimization of splines and the predictions of stress concentrations, which are determined by finite element analysis (FEA). Using different design modifications, that do not change the spline load carrying capacity, it is shown that large reductions in the maximum stress are possible. Fatigue life of a spline can be greatly improved with up to a 25% reduction in the maximum stress level. Design modifications are given as simple analytical functions (modified super elliptical shape) with only two active design parameters and the designs are practical realizable. Some generality is found in the design parameters.
Original languageEnglish
JournalArchive of Applied Mechanics
Issue number10
Pages (from-to)1393-1407
Publication statusPublished - 2011


  • Straight-sided spline
  • Stress concentration
  • Laplace equation
  • Torsion
  • Optimization

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