A theoretical procedure for the stress state assessment of hyper-static crankshafts

Crankshafts with many rods and crankpins for mechanical and industrial applications can be designed with first-order-approximation theoretical procedures in the literature. Numerical boundary element method (BEM) or finite element method (FEM) procedures can be used, with the latter models having a 3D tetrahedral, wire beam or hexahedral finite elements. To the best of the author's knowledge, the literature does not contain accurate evaluations of hyper-static reactions at the restraints of a crankshaft with four crankpins and five supports. The principle of virtual work is implemented to allow calculation of the reactions at the bearings of the shaft and to determine the internal actions (bending, torsion, shear and axial force) for each section of the shaft. The developed procedure does not give better results than a numerical BEM or 3D FEM code, but it is less expensive and less time consuming when implemented in a mathematical commercial code. Furthermore, the procedure gives results that have a better approximation with respect to the theoretical literature models. The theoretical model was validated through comparison with the results of a finite-element linear beam model developed using a commercial FEM code.