Case study: Evaluation of stress concentration factors in shaft keyways through FE analysis

Abstract

The finite element method (FEM) is utilised in evaluating stresses in keyways of shafts loaded in torsion. These stress values are divided by their corresponding nominal stresses to arrive at so-called stress concentration factors, which are compared against published charts and experimental results for specific reference cases. FEM has become ubiquitous in the analysis and design of mechanical systems. While simple and well-known formulas for analytical solutions are employed to calculate nominal stresses in static design, dynamic or fatigue design is typically concerned with higher-than-nominal stresses that are associated with localised geometric stress raisers present in the system. These higher stresses are derived from nominal stresses by multiplication with an appropriate stress concentration factor. At present, though, the application of a multiplier to a nominal value seems somewhat redundant since the complete stress distribution – which includes the maximum stresses in areas of stress concentration – is a direct result from a finite element analysis (FEA). In this paper it is shown that FEA results not only compare favourably with available known results for commonly encountered stress raisers such as fillets and keyways but provide resolution to the stress distribution and paves the way for analysis and design of mechanical devices exhibiting uncommonly encountered stress raisers for which charts and formulas are not available.