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Abstract- 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. Keywords: Dynamic Stability, Shaft System, Torsional Vibration, Hooke’s Joint

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In the paper, a three-axis power transmission system is modeled mathematically and simulated by software. In mathematically method, a system consisting of three flexible shafts with different rotation axis which connected through two universal joints is investigated via a three degree-of-freedom model. The stability is analyzed by means of a monodromy matrix technique. This is verified by comparing the results with dynamic analytical software AdamsView simulation and the results of the previous research. Then, the effects of rotational velocity, non-aligned angles, shaft's properties (stiffness and damping) on the stability are investigated. Finally, the stability charts constructed on various parameters is presented. It is observed that decreasing shaft stiffness and universal joint angle due to more stability, while decreasing shaft damping has the opposite effect.