This set of Machine Dynamics Multiple Choice Questions & Answers (MCQs) focuses on “Free Torsional Vibrations of a Three Rotor System”.
Explanation: The torsional vibrations occur in a three rotor system only if there are one node or two nodes, at points N1 and N2 there is no vibration hence they are known as nodes.
2. In a three rotor system, free torsional vibration cannot occur if there is only one node.
Explanation: In a three rotor system there may occur one or two nodes, free torsional vibration may occur in presence of either one or two nodes.
3. In which of the following condition torsional vibration will not take place, considering 3 rotors A, B and C. A is rotating in clockwise direction.
a) B in clockwise C in anticlockwise
b) C in clockwise B in anticlockwise
c) B and C in clockwise
d) B and C in anticlockwise
Explanation: For a three rotor system torsional vibration will occur only if two of the three rotors are rotating in the same direction and the third one is rotating in the opposite direction.
4. For occurrence of free torsional vibration in a three rotor system which of the condition is necessary?
a) Rotors moving in same direction
b) Rotors having same frequency
c) Rotors having different frequency
d) Rotors rotate in the same sense
Explanation: In a three rotor torsional vibration system, the system will rotate if the two rotors are rotating in same direction and the third one with opposite direction all with the same frequency.
5. the given figure, considering left end has one rotor, If the mass moment of inertia of the shaft till node N1 is increased to four times, then what will be the effect on free torsional vibrations of a rotor at left end of N1?
a) Increases 4 times
b) Increases 2 times
c) Decreases 4 times
d) Decreases 2 times
Explanation: If N1 is the node then left end and N1 can be considered as a shaft of single rotor system, since the free torsional vibrations of a single motor system depends on the inverse of square root of the mass moment of inertia of the system, increasing 4 times will lead to decrease in two times the initial vibration.
Explanation: If N1 is the node in the given figure, then N1 can act as a fixed end of the shaft N1N2 where the rotor is connected at Q and N1, hence it acts like a two rotor system.
7. Keeping the mass moment of inertia of left end and the right end shafts in a three rotor system same, if the length of one shaft is doubled what should be the effect on the length of other shaft?
d) Increased to 4 times
Explanation: The vibration will occur in a two rotor system only if the frequencies of both the rotors are same, hence L(a)I(a) = L(c)I(c). Therefore the relation is directly proportional.
8. Free torsional vibrations will occur in a three rotor system only if all rotors have same frequency.
Explanation: In a three rotor system the free torsional vibration will occur only if all the rotors have the same frequency of vibration and two have common rotation sense.
9. What is the total number of nodes formed in a three rotor system if the rotors at one of the ends and the one in the middle rotate in the same direction?
Explanation: In a three rotor system, if the rotor at one of the ends and the one in the middle are rotating in the same direction, then there is formation of only one node.
10. For a three rotor system in the figure given below, the length of one shaft(P) is twice the other(Q), then what is the relation between the Mass moment of inertia of the shafts.
a) 2I(P) = I(Q)
b) I(P) = 2I(Q)
c) I(P) = I(Q)
d) 2I(P) = 3I(Q)
Explanation: For a two rotor system, we have L(P)I(P) = L(Q)I(Q)
Therefore, 2I(P) = I(Q).
11. In a three rotor system, for the middle rotor, if the stiffness of both the length either side of the rotor is increased to two times what will be the effect on total stiffness of the middle rotor?
a) Remains constant
b) Decreases by two times
c) Increases by two times
d) Increases by 4 times
Explanation: In a three rotor system, each length to either side of the middle rotor is twisted through the same angle therefore the total stiffness is the sum of individual stiffness.
Sanfoundry Global Education & Learning Series – Machine Dynamics.
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