GATE ME 2020 Set 1 — Question 31
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Theory of Machines & Vibrations → Balancing, Flywheels & Gyroscopes → Balancing of Rotating Masses
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Question
A balanced rigid disc mounted on a rigid rotor has four identical point masses, each of , attached to four points on the radius circle shown in the figure.
The rotor is driven by a motor at uniform angular speed of . If one of the masses gets detached then the magnitude of the resultant unbalance force on the rotor is ______ (round off to 2 decimal places).
Correct answer
0.09 to 0.11
Solution
Initially, the four identical masses are placed symmetrically at 90-degree intervals (A, B, C, and D). Due to symmetry, the net centrifugal force is zero, and the rotor is balanced.
When one mass is detached, the system becomes unbalanced. The resultant unbalance force is equal in magnitude to the centrifugal force that was exerted by the detached mass:Given:
Substituting the values:
.
When one mass is detached, the system becomes unbalanced. The resultant unbalance force is equal in magnitude to the centrifugal force that was exerted by the detached mass:Given:
Substituting the values:
.
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