Ain Shams University Mechanical Vibrations

Faculty of Engineering MDP 311

7. Vibration Control
7.1 A rotating shaft carries four masses
arranged in different planes as
shown in the Fig. The masses at A,
B, C and D are 12, 20, 70 and 16 Kg,
respectively, and their respective
radii of rotation are 15, 12, 6 and 18
cm. The shaft speed is 120 rpm.
Find the magnitude and direction, relative to A, of the resultant force and resultant
moment at a plane midway between A and B.
7.2 A rotating shaft carries four masses A, B, C and D rigidly attached to it, the mass
centers are at 1.25, 1.5, 1.625 and 1.375 cm, respectively from the axis of rotation.
A, C and D are of mass 15, 10 and 18 Kg respectively, the axial distance between
A and B is 16 cm, and that between B and C is 20 cm, the eccentricities of A and
C are 90 deg. to one another. Find for complete balance :
a) The axial distance between the planes of revolution of C and D.
b) The angles between A, B and D.
c) The mass of B.

7.3 A rotating shaft carries four masses A, B, C and D rigidly attached to it, the mass
centers are at 30, 36, 39 and 33 mm respectively from the axis of rotation. A, C
and D are 7.5, 5 and 4 Kg, the axial distance between A and the other masses are
shown in the Fig., and the eccentricities of A and C are at 90 deg. to one another.

Find for complete balance:

1
Ain Shams University Mechanical Vibrations
Faculty of Engineering MDP 311
Design & Production Engineering
Department

7.4 Three concentrated masses A, B and C are attached to the same shaft. The mass of
them are 10, 15 and 20 Kg respectively. The mass center of these masses are at 40,
50 and 45 mm respectively from the axis of rotation. A and B are 3 cm apart, along
the shaft and C is 4 cm from B remote from A. the angular position of B and C
with respect to A are 79 and 194 deg. both measured in the same direction. Balance
masses can be located in a plane (T) 2 cm from A remote from B and in plane (S)
5 cm from B both at 7 cm radius. Find the magnitude of each balancing mass and
its angular position with respect to A.

7.5 A rough casting for a rotor is of mass 450 Kg and is mounted on centers 46 cm
apart, ready for machining. It is given static balance by two masses A and B in
planes which are situated 20 cm and 16 cm respectively on the either side of the
plane containing the mass center. The masses of A and B are 20 and 24 Kg
respectively, and their mass center are at 90 deg. to each other relative to the axis
of the casting, and at 15 and 18 cm respectively. Determine the eccentricity of the
mass center of the casting, its angular position relative to mass A, and the forces
on the centers when the rotor with attached masses A and B is run at 50 rpm.

7.6 Attached to a uniformly rotating shaft are four discs A, B, C and D, spaced at equal
intervals along the shaft, of mass 7.5, 12.5, 7 and 6 Kg, respectively, the mass
centers of the discs are at 4, 3, 5 and 8 mm respectively from the axis of rotation.
An additional mass M may be attached to D at an effective radius of 60 mm from
the axis of rotation. Find the minimum value of the mass of M, and the relative
angular positions of the mass centers of all the masses to ensure complete dynamic
balance for the rotating shaft.

7.7 A shaft rotating at 120 rpm is supported in bearings A and B 1.8 m apart. A being
at the left-hand end. Two unbalanced rotating masses of 7.5 and 10 Kg at radii of
75 mm and 50 mm respectively are situated between A and B at distances of 0.6
and 0.9 m respectively from A. The angle between the radii is 60 deg. when viewed
along the shaft. Find the magnitudes, directions and senses of the bearing reactions
due to the combined action of the dynamic forces and the gravity.

2
Ain Shams University Mechanical Vibrations
Faculty of Engineering MDP 311
Design & Production Engineering
Department

7.8 A machine, of mass 500 kg, is mounted on an elastic support with negligible
damping. The machine has an unbalanced rotor, with unbalance 10 kg.mm. It was
noticed that the maximum amplitude of vertical vibration occurs when the
unbalanced rotor is rotating at 1500 rpm. A vibration absorber, tuned to 1500 cpm,
is to be used in order that, the natural frequencies of the system become at least
16% away from the original natural frequency. Determine:
a) The mass and stiffness of the absorber.
b) The amplitude of the absorber mass during its steady state operation, when the
unbalanced rotor is rotating at 1500 rpm.

7.9 A machine is mounted on an elastic support with negligible damping. The machine
has an unbalanced rotor. It was noticed that the maximum amplitude of vertical
vibration occurs when the unbalanced rotor is rotating at 1600 rpm. In order to
determine the mass of the machine and the stiffness of the support, a spring-mass
system, of mass 3 kg, tuned to 1600 cpm, was attached to the machine to act as a
tuned vibration absorber. With this arrangement, resonance occurred at rotor
speeds 1505 rpm and 1701 rpm, and the steady state amplitude of the absorber
mass was 2 mm when the rotor was rotating at 1600 rpm. Determine the mass of
the machine and the stiffness of the support.
A vibration absorber, tuned to 1600 cpm, is to be used to provide a speed range 384
rpm between the resonance speeds. Determine:
a) The mass and stiffness of this absorber.
b) The amplitude of the mass of this absorber during its steady state operation,
when the unbalanced rotor is rotating at 1600 rpm.