Mathematical Modelling for Vibration Evaluation of Powertrain Systems

Masoud SoltanRezaee, Mohammad Reza Ghazavi, and Asghar Nahafi


Power transmission system, numerical simulation, instability identification


Powertrains have been applied extensively in machines, energy systems and industry. A drive system can contain different parts like shafts, joints and disks. The shaft axes may be misaligned with each other (non-collinear), depending on the powertrain system application. Such two shafts can be connected through a non-constant velocity Hardy-Spicer joint, which transform a constant input velocity into a periodically fluctuating one. As a result, the mechanism is parametrically excited and may cause resonances. Herein, the shafts include a flexible rod with a torsional stiffness and viscous damping. The polar inertia moment of each shaft is simulated with two discrete disks at its ends. After linearization via McLaurin series, the equations of motion consist a set of Mathieu–Hill differential equations with periodic coefficients. The influence of the system geometry and inertia moment on the stability of shaft system are the chief subjects. Parametric instability diagrams were obtained by means of Floquet theory. The graphical-numerical results are validated with the frequency analytical results. Ultimately, the stability areas have revealed in the parameter spaces of angular velocity, misalignment angles and disks inertia. The results were illustrated that by changing the system inertia and geometry, stabilizing the system is achievable.

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