Ali Asghar Jafari - Mech. Eng., K. N. Toosi Univ. of Tech., ۴۷۰ Mirdamad Ave, P.O.B. ۱۹۳۹۵-۱۹۹۹, Tehran, Iran
Masoud Soltan Rezaee - Mech. Eng., Tarbiat Modares Univ., Jalal Ale Ahmad Ave, P.O.B. ۱۴۱۱۵-۱۱۱, Tehran, Iran
Mohammad Reza Ghazavi

Shaft system is one of the power transmission systems, which has many applications due to the high rotational speed and low weight. The system includes some shafts that based on theapplication of the system can be non-aligned. A common way to link the non-aligned shafts is using universal joint. This joint has many advantages but transforming a constant input speed to a periodically fluctuating one. As a result, the system is parametrically excited and hasdynamic instability (or resonance) conditions. Therefore, introduces several special unstable regions to the system.In this work, dynamic stability of a three-axis power transmission system is investigated.This system consists of three torsionally elastic shafts with different rotation axes. The systemstability has been investigated by means of a three degree-of-freedom model in a spatialcoordinate (three-dimensional). Each shaft carrying a rigid disk at one end and have been linked through two universal joints. Equations of motion for the system are derived andlinearized. The differential equations consist of a set of Mathieu–Hill equations. Their stability is analyzed by means of a reliable, exact numerical technique so-called monodromymatrix method. The validation of the model is obtained by comparing the areas of nstability with natural frequencies of the system or their combinations. Also harmonic, sub-harmonic, sum combination and difference type combination parametric resonance regionscorresponding to different vibration modes are calculated. Finally, dynamic stability regions have been shown on system parameters such as rotational velocity, misalignment angle’s of shaft axis, stiffness and rigidity of shafts. It is observed that increasing inertia ratio of disks and decreasing universal joint angle leads to more stability.

Stability Analysis; Power Transmission System; Three-Axis System