Investigation of torsional teeth stiffness and second moment of area calculations for an analytical model of spline coupling behaviour

Abstract

Torque distribution from within spline coupling is an important matter for design engineers, who wish to study the behaviour of spline couplings. This distribution can be estimated because of an analytical equation, based on material, torsional teeth stiffness, and second moments of area of the shaft and sleeve. These parameters have to be determined precisely. The material properties can be readily determined but calculation of the other parameters requires finite-element calculations or complex algorithms. The aim is to propose simplified equations so as rapidly to obtain values for both teeth stiffness and second moments of area. Experimental designs were implemented to determine the most appropriate equations. Torsional stiffness is the first parameter studied in the present paper. This is the result of rotations due to various phenomena involving distortions such as bending, shear, compression, rotation of the foundation of the teeth, and the teeth sliding. Two simplified equations are finally expressed to define torsional stiffness. The first equation takes into account the first four phenomena and the second one the teeth sliding. The second topic in the present paper covers the influence on torque distribution of various formulae for calculating second moments of area. A solution, which takes into account the shear of the teeth, is highlighted.