In a gearing system, pump speed is one third of the motor. Shaft from motor is 6 cm in diameter and 30cm long, the impellar shaft is 10cm diameter and 60cm long. Mass moment of inertia is 1500 Kgm2, C = 80Gn/m2. Neglecting the inertia of shaft and gears calculate the frequency of free torsional vibrations in Hz.

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Quizplus · Accepted Answer

The frequency of free torsional vibrations can be calculated using the formula $ f = \frac{1}{2\pi} \sqrt{\frac{K}{I}} $, where $K$ is the torsional stiffness and $I$ is the mass moment of inertia. Given that $C = 80 \, \text{Gn/m}^2 = 80 \times 10^9 \, \text{N/m}^2$ and $I = 1500 \, \text{Kgm}^2$, we can calculate the torsional stiffness $K$ as $K = C \cdot L$, but since $L$ (length) is not directly involved in the calculation and the inertia of shaft and gears are neglected, we directly use $C$ and $I$ in our formula. Plugging the values into the formula gives $ f = \frac{1}{2\pi} \sqrt{\frac{80 \times 10^9}{1500}} \approx 4.7 \, \text{Hz}$.

In a Gearing System, Pump Speed Is One Third of the Motor