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Stress Concentration Factor Solutions for Shoulder Filleted Shafts in Bending, including the Influence of Tapering
Abstract:
An accurate set of solutions is presented for stress concentration factors in shoulder filleted shafts under bending, tension and torsion. Solutions were obtained from extensive elastic finite element analyses for both plain stepped shafts, and for shafts in bending with a variety of tapered shoulders.
For plain stepped shafts, conventional stress concentration factor graphs are presented, along with a convenient equation to facilitate numerical analyses. Sets of constants are provided for the equation to compute either the maximum principal stress or the maximum von Mises equivalent stress in the fillet, under each loading mode. This defines the complete state of biaxial stress at the root of the fillet. Furthermore, another convenient equation is provided to accurately compute the location of the maximum stress in the fillet, which varies with geometry. This information can be invaluable for experimental analysis or failure analysis.
With the newly established solutions for shoulder filleted shafts as a baseline, the influence of adding a conical taper to the shoulder was examined using a matrix of over 4000 FEA runs. It is demonstrated that tapering can reduce the stress concentration factors in the fillet significantly, but only over a small range of geometries. A sample calculation is used with notch strain analysis to demonstrate the fatigue life improvement that can be achieved with tapering. This example problem addresses some important factors for notch strain analysis, including the proper application of the Smith-Watson-Topper parameter and the use of maximum principal stress versus von Mises equivalent stress in the notch root.