Stability of a system consisting of three-axis connected through Hooke's joints

In this study، dynamic stability of a system consisting of three torsionally elastic shafts with different rotation axises is analyzed. The system stability have been investigated by means of a three degree-of-freedom model in a spatial coordinate (three dimensional). Each shaft carrying a rigid disk at one end and have been linked through two Hooke''s joints. Equations of motion for the system were derived. These equations are linearised. After linearization of the differential equations are shown to consist of a set of Mathieu–Hill equations. Their stability are analyzed by means of a monodromy matrix method. Finally dynamic stability regions have been shown on different system parameters such as rotational velocity، misalignment angle’s of shaft axis، stiffness and rigidity of shafts. The stability charts constructed on various parameters. It was observed that with increasing inertia disk ratio and decreasing Hooke''s joint angle، the stable region increases.