Dynamic Stability of a System Including Three Shafts

Abstract — A system including three torsionally elastic shafts which they have been linked through two universal joints with different rotation axises is analyzed. The system stability has been studied by means of a three degree-of-freedom model in a spatial coordinate (three dimensional). Equations of motion for the system were derived. The differential equations consist of a set of Mathieu–Hill equations. Their stability is analyzed via a monodromy matrix method. Finally dynamic stability regions have been shown on system parameters such as rotational velocity, misalignment angle’s of shaft axis, shaft’s stiffness and rigidity. The results are presented in the form of stability maps constructed on different parameters and have been discussed