Analytical Modeling of a Material Efficient Hollow Shaft Design

Abstract

This paper discusses the optimal distribution of material across the cross-section of a shaft under pure uniform torsional loads such that the factor of safety and thereby the shear stresses generated at any point in the cross-section remain largely the same irrespective of their radial distance from the centre of the shaft. An analytical mathematical relationship is deduced to relate the material distribution as a function of the radial distance. The relationship is then used to plot the corresponding variation in MATLAB. Finally, several CAD models of the proposed cross-sectional shapes are prepared in SolidWorks, and then simulated in ANSYS simulation software by employing the Static Structural analysis platform. The graphical and statistical results of the shear stress distributions are then compared with a solid shaft of the exact same radial and axial dimensions. It is found that the proposed 3-Branched model is about 25% more efficient in material utilization than the conventionally employed solid shaft of similar dimensions.