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    What is the power needed to accelerate a flywheel?

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    Please see the attached file for full problem description.

    I need to calculate torque for this question:

    A gearbox and flywheel are as shown in FIGURE 4 (attached). The output shaft rotates in the opposite direction to the input shaft at 5 times its speed. The gearbox has an efiiciency of 92%.

    If the flywheel is solid, has a mass of 50 kg, a diameter of 1.5 m and is to accelerate from rest to 300 revs min^-1 in 1 minute:
    (a) Calculate the torque required at input T_1.
    (b) Calculate the magnitude and direction of the torque required to hold the gearbox stationary (holding torque T_h). Show the direction of the holding torque applied to the shaft with the aid of a sketch.
    (c) Plot a graph of the input power against time when taking the flywheel from rest to 300 revs min^-1.

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    Solution Preview

    Please see the attached file for full problem description.

    (a) From the power balance, it follows that:
    where Plost = lost power, which can be determined from the gearbox efficiency:

    The required input torque related to the output torque will be:

    One assumes that acceleration of flywheel is uniform, that means, in our case:
    where t = acceleration time and (n2)max = maximum rotating speed after the given acceleration time. Based on the aforementioned assumption, the required torque to accelerate the flywheel of a given ...

    Solution Summary

    In this problem, the input torque and the needed input power is computed, given that a flywheel is accelerated from rest to a speed of n = 300 rpm during t = 1 min. The holding torque is computed as well.