A semi-analytical load distribution model for side-fit involute splines

• A new semi-analytical spline load distribution model is developed.
• Arbitrary loading conditions and initial separations can be analyzed.
• A numerical efficient multi-step discretization solution scheme is proposed.

A semi-analytical load distribution model for side-fit involute splines has been proposed by extending the formulations of elastic bodies in contact. The spline compliances considered in the model consist of tooth bending and shear, tooth base flexibility, tooth contact, and torsional deformations. This model allows input of arbitrary loading components and arbitrary initial separations. With this, load distribution characteristics of splines under various combined loading conditions can be determined. In addition, the effects of design variations and manufacturing errors can also be quantified. Aside from the versatility of the model in terms of its capabilities, a new multi-step discretization solution scheme is devised to reduce computational effort thus qualifying the semi-analytical model as a design tool. Numerical results for an example spline under various loading conditions including: (i) pure torsion, (ii) combined torsion and radial loads, and (iii) combined torsion, radial loads and tilting moments, are presented and compared to those predicted by a deformable-body model for the verification of the results.