# Machine Dynamics Questions and Answers – Free Torsional Vibrations of a Geared System

This set of Machine Dynamics Multiple Choice Questions & Answers (MCQs) focuses on “Free Torsional Vibrations of a Geared System”.

1. For the free torsional vibration of a geared system which of the following statement is true?
a) Backlash in geared system
b) High inertia of shaft
c) Gearing teeth always in contact
d) High inertia of gear

Explanation: For the free torsional vibration of a geared system there should be no backlash in geared system and the inertia of the shaft, gears should be considered negligible and the gearing system should always be in contact.

2. In a geared system free torsional vibration will take place when the Inertia of gear is taken into consideration.
a) True
b) False

Explanation: In a geared system free torsional vibration will take place when the Inertia of gear and shaft is not taken into consideration.

3. If the pinion has 20 teeth and the gear has 32 teeth, then what is the gear ratio?
a) 5/8
b) 8/5
c) 25/64
d) 64/25

Explanation: Gear ratio is defined as the ratio of no. of teeth on the pinion to the no. of teeth on the gear, there in this question the gear ratio is 5/8.

4. A geared system possessed a kinetic energy if 200kJ, later it was converted into a two-rotor system connected by a shaft. The kinetic energy of the equivalent system will be_____
a) 200 kJ
b) less than 200 kJ
c) more than 200 kJ
d) Dependent on the length of the equivalent shaft

Explanation: If the geared system is converted into an equivalent system of rotors connected by a shaft then the kinetic energy of the original and the equivalent system must be same.

5. A geared system possessed a strain energy if 150kJ, later it was converted into a two-rotor system connected by a shaft. The Strain energy of the equivalent system will be _____
a) 150 kJ
b) less than 150 kJ
c) more than 150 kJ
d) Dependent on the length of the equivalent shaft

Explanation: If the geared system is converted into an equivalent system of rotors connected by a shaft then the Strain energy of the original and the equivalent system must be same.
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6. When inertia of gearing is taken into consideration, then which of the following should be taken into account.

Explanation: When inertia of gearing is taken into consideration, then an additional rotor must be introduced in the equivalent system of the rotors connected by the shaft.

7. 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 Kg-m2, C = 80Gn/m2. Neglecting the inertia of shaft and gears calculate the frequency of free torsional vibrations in Hz.
a) 4.7
b) 5.7
c) 4.5
d) 5.5

Explanation: Moment of inertia of rotor B : Ib = 166.7 Kg-m2
total length of equivalent shaft = 1000mm = 1m
Position of node = 294mm from left end (from same frequency condition)
J = 1.27×106 m4
substituting the values into the free torsional vibration relation we get
f = 4.7 Hz.

8. When inertia of gearing is taken into consideration, then an additional shaft must be introduced in the equivalent system of the rotors connected by the shaft.
a) True
b) False

Explanation: For gearing system, if the inertia of the gear is taken into consideration then an additional rotor must be placed in the equivalent system of vibration.

9. At a nodal point in the shaft, the frequency of vibration is _________
a) Zero
b) Double than at the ends
c) Minimum
d) Maximum

Explanation: A point of zero vibration is known as a node, hence at a nodal point the amplitude of frequency of free torsional vibration is zero.

10. For a gearing system, the equivalent system is made consisting of two rotors. How many nodes will this new equivalent system will have?
a) 0
b) 1
c) 2
d) 3

Explanation: When a gearing system is converted into an equivalent system consisting of two rotors, it will have only a single node on the shaft as the two rotor systems only produce one node.

11. For a gearing system, the equivalent system is made consisting of three rotors. How many nodes will this new equivalent system will have?
a) 0
b) 1
c) 2
d) 3

Explanation: When a gearing system is converted into an equivalent system consisting of three rotors, it will have two nodes on the shaft as the three-rotor system produces two nodes.

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