Parametric resonances for torsional vibration of excited rotating machineries with nonconstant velocity joints

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Abstract
The shaft system is a rotating machinery with many applications due to its high speed. The angle between shafts may not be zero. So the shafts can be connected to each other through a nonconstant velocity U-joint, which transforms a constant input angular velocity into a periodically fluctuating velocity. Consequently, the mechanism is parametrically excited and may face resonance conditions. Herein, a power transmission system including three elastic shafts is considered. The polar inertia moment of each shaft is modeled as a dynamic system with two discrete disks at the shaft ends. The equations of motion consist of a set of Mathieu–Hill differential equations with periodic coefficients. The dynamic stability and torsional vibration of the shaft system are analyzed. The system geometry and inertia moment effect are the main issues in this contribution. Parametric instability charts are achieved via the monodromy matrix technique. The graphical numerical results are validated with the frequency analytical results. Finally, the stability regions are shown in the parameter spaces of velocity, misalignment angles and the inertia of disks. The results demonstrated that by changing the system inertia and geometry, stabilizing the whole system is possible. Moreover, to check the precision of the model, the results are compared with a basic single-disk model, which is prevalent in two-shaft systems.

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