MBC COLLEGE OF ENGINEERING
& TECHNOLOGY
, PEERMADE
SECOND
SERIES EXAMINATION
7
th
Semester Mechanical Engineering
DYNAMICS OF MACHINERY
For second series test, questions should be asked only from module 1, module 4
and module 5.
MODULE 1
1)
Define the expression for balancing of a Single Rotating Mass By a Single Mass Rotating in
the Same
Plane?
2)
Balancing of a Single Rotating Mass By Two Masses Rotating in
Different Plane
3)
Balancing of Several Masses Rotating in the Same Plane?
4)
Explain stati
c and dynamic balancing?
5)
Four masses A, B, C and D as shown below are to be completely balanced.
The planes containing masses B and C are 300 mm apart. The angle between planes
containing B
and C is 90°. B and C make angles of 210° and 120° respectively
with D in the same sense. Find
:
1.
The magnitude and the angular position of mass A ; and
2.
The position of planes A and D
PART B
1.
A, B, C and D are four masses carried by a rotating shaft at radii 100,125, 200 and 150 mm
respectively. The planes in which the masses revolve are spaced 600 mm apart and the mass of
B, C and D are 10 kg, 5 kg, and 4 kg respectively.Find the required mass
A and the relative
angular settings of the four masses so that the shaft shall be in complete balance.
2.
A shaft carries four masses in parallel planes A, B, C and D in this order
along its length. The
masses at B and C are 18 kg and 12.5 kg respectively,
and each has an
eccentricity of 60 mm.
The masses at A and D have an eccentricity of 80 mm. The angle between
the masses at B and C
is 100° and that between the masses at B and A is 190°, both being
measured in the same
direction. The axial distance betwee
n the planes A and B is 100 mm and
that between B and C is
200 mm. If the shaft is in complete dynamic balance,
determine: 1
.
The magnitude of the
masses at A and D ;
2.
the distance between planes A and D ; and
3.
the angular position of the
mass at D.
3.
Four masses
A
,
B
,
C
and
D
are attached to a shaft and revolve in the same plane. The masses are
12kg, 10 kg, 18 kg and 15 kg respectively and their radii of rotations are 40 mm, 50 mm, 60 mm
and 30 mm. The angular position of the masses
B
,
C
and
D
are 60°,
135° and 270° from the mass
A
. Find the magnitude and position of the balancing mass at a radius of 100 mm.
4.
A shaft carries five masses
A
,
B
,
C
,
D
and
E
which revolve at the same radius in planes which are
equidistant from one another. The magnitude of the masses in planes
A
,
C
and
D
are 50 kg, 40
kg
and 80 kg respectively. The angle between
A
and
C
is 90° and that between
C
and
D
is 135°.
Determine the magnitude of the masses in planes
B
and
E
and their
positions to put the shaft in
complete rotating balance.
MODULE 2
Part A (4 marks)
1.
Find the natural frequency of longitudinal vibrations using energy method?
2.
Find the natural frequency of longitudinal vibrations using Rayleigh’s method?
3.
Derive the expres
sion for effect of inertia constraint in torsional vibrations?
4.
What you mean by critical or whirling speed of a shaft?
5.
Derive the expression for balancing of several masses rotating in different planes?
6.
Derive the expression for finding equivalent length i
n a three rotor system?
7.
Find the natural frequency of longitudinal vibrations using equilibrium method?
8.
Derive the expression for effect of inertia constraint in longitudinal vibrations?
9.
What you mean by critical or whirling speed of a shaft?
10.
Find the nat
ural frequency of free tensional vibrations?
11.
Define frequency, cycle, period and free vibration?
Part B (12 marks)
1.
An instrument vibrates with a frequency of 1Hz when there is no damping. When the damping is
provided, the frequency of damped vibrat
ion was observed to be 0.9Hz.
Find, (i) damping factor
(ii) logarithmic decrement
2.
A shaft of length 0.75m supported freely at the ends is carrying a body of mass 90 Kg at 0.25m
from one end. Find the natural frequency of transverse vibration, Assume
E=200GN/m² and the
shaft diameter 50mm.
3.
A flywheel is mounted on a vertical shaft as shown in figure. The both ends of a shaft are fixed
and its diameter is 50mm. The flywheel has a mass of 500kg and its radius of gyration is 0.5m.
Find the natural freque
ncy of torsional vibrations, if the modulus of rigidity for the shaft material
is 80GN
.
4.
Calculate the whirling speed of a shaft 20 mm diameters and 0.6m long carrying a mass of 1kg at
its mid

point. The density of the shaft material is 40Mg/
. And E
=200GN
. Assume the
shaft to be freely supported.
MODULE 3
Part A (4 marks)
1)
Define damping ratio or damping factor.
2)
Define logarithmic decrement
3)
What is meant by dynamic magnifier or magnification factor
4)
Define transmissibility ratio or isolation
factor
5)
Define following damping conditions?
1.
Over damping 2. Under damping 3.critical damping coefficient.
6)
A cantilever shaft 50mm diameter and 300mm long has a disc of mass 100kg. The
E=200 GN/m². Determine the frequency of longitudinal and transverse vib
rations?
7)
A body of mass 20kg is suspended from a spring which deflects 15mm under this
load.
Calculate the frequency of free vibrations and verify that a viscous damping force is
1000N at a speed of 1m/s
is just sufficient to make the motion aperiodic.
8)
Derive the expression for effect of inertia constraint on torsional vibrations?
9)
Derive the expression for torsionally equivalent shaft?
10)
Derive the expression for the amplitude of forced vibrations?
Part B
(12
marks)
1)
A mass of 10kg is suspended from one
end of a helical spring, the other end being fixed. The
stiffness of the spring is10N/mm.The viscous damping causes the amplitude to decreases to one

tenth of the initial value in four complete oscillations. If a periodic force of 150cos50t N is applied
at
the mass in the vertical direction .Find the amplitude of the forced vibrations? What is its value
of resonance?
2)
A single cylinder vertical petrol engine of total mass of 200kg is mounted upon a steel chassis
frame. Thevertical static deflection of the fr
ame is 2.4mm due to the weight of the engine .The
mass of the reciprocating parts is 18kg and stroke of piston 160mm with S.H.M.If dashpot of
damping coefficient of 1N/mm/s used to damped the vibrations, calculate al steady state
(i)Amplitude of vibrations
at 500rpm engine speed.(ii)The speed of the driving shaft at which
resonance will occurs.
3)
The mass of an electric motor is 120kg and it runs at 1500rpm.The armature mass is 35kg and its
centre of gravity lies 0.5mm from axis of rotation. The motor is moun
ted on five springs of
negligible damping. So that the force transmitted is one

eleventh of the impressed force.
Assume that the mass of the motor is equally distributed among the five springs. Determine (i)
the stiffness of the spring (ii) Natural frequen
cy of system.
4)
The following data are given for a vibratory system with viscous
damping.
Mass=2.5kg
s=3N/mm
x6=0.25x1
.
Determine the damping
coefficient of
the damper in the system?
5)
A machine part of mass 2kg vibrates in a viscous
medium.
Determine the damping coefficient
when a harmonic exciting force of 25N results in
resonant
amplitude of 12.5 mm with a period
of 0.2 seconds. If the system is excited by a harmonic force of frequency 4Hz what will be the
percentage increase in the amplit
ude of vibration when damper is removed as
compared with
that with damping?
MODULE 4
PART A
1.
Discuss how a single revolving mass is balanced by two masses revolving in different
planes
2.
Why is balancing of rotating parts necessary for high speed engines
3.
Explain the method of balancing of different masses revolving in the same plane.
4.
How the different masses rotating in different planes are
balanced?
5.
What
you mean by
unbalanced force
or
shaking force?
6.
Write the expression for
Primary and Secondary Unb
alanced Forces of Reciprocating
Masses
?
PART B
1.
The three cranks of a three cylinder locomotive are all on the same axleand are set at 120°. The
pitch of the cylinders is 1 metre
and the stroke of each piston is 0.6 m. The
reciprocating masses
are 300 kg for inside cylinder and 260 kg for each outside cylinder and the
planes of rotation of
the balance masses are 0.8 m from the inside crank.
If 40% of the reciprocating parts are to
be
balanced, find :
1. the magnitude and the position of the balancing masses required at a radius of
0.6 m ;
And
2. the hammer blow per wheel when the axle makes 6 r.p.s.
2.
The following data refer to two cylinder locomotive with cranks at 90° :Reciprocat
ing mass per
cylinder = 300 kg ; Crank radius = 0.3 m ; Driving wheel
diameter = 1.8 m ; Distance between
cylinder centre lines = 0.65 m ; Distance between the driving
wheel central planes = 1.55 m.
Determine : 1. the fraction of the reciprocating masses t
o be balanced, if the hammer blowis not
to exceed 46 kN at 96.5 km. p.h. ; 2. the variation in tractive effort ; and 3. the maximum
swaying
couple
3.
The following particulars relate to a two

cylinder locomotive with two
coupled wheels on each
side :
Stroke
= 650 mm
Mass of reciprocating parts per cylinder = 240 kg
Mass of revolving parts per cylinder = 200 kg
Mass of each coupling rod = 250 kg
Radius of centre of coupling rod pin = 250 mm
Distances between cylinders = 0.6 m
Distance between wheels = 1.5 m
Di
stance between coupling rods = 1.8 m
The main cranks are at right angles and the coupling rod pins are at 180° to their respective
main cranks. The balance masses are to be placed in the wheels at a mean radius of 675 mm
in
order to balance whole of the re
volving and 3/4th of the reciprocating masses. The
balance
mass
for the reciprocating
masses are
to be divided equally between the driving wheels and the
coupled wheels. Find : 1. The magnitudes and angular positions of the masses required for the
driving
and trailing wheels, and 2. The hammer blow at 120 km/h, if the wheels are 1.8 metre
diameter
.
4.
A four cylinder vertical engine has cranks 150 mm long. The planes of
rotation of the first, second
and fourth cranks are 400 mm, 200 mm and 200 mm respectively
from the third crank and their
reciprocating masses are 50 kg, 60 kg and 50 kg respectively. Find the mass of the reciprocating
parts for the third cylinder and the relative angular positions of the cranks in order that the
engine may be in complete primar
y balance.
MODULE 5
PART A
1)
Derive the expression for balancing of V engine
.
2)
Write a short note on primary and secondary balancing.
3)
Explain why only a part of the unbalanced force due to reciprocating masses is balanced
by revolving
mass.
4)
Derive the
following expressions, for an uncoupled two cylinder locomotive engine
a.
Variation is tractive force ; (b) Swaying couple ; and (c) Hammer blow.
5)
What are in

line engines ? How are they balanced ? It is possible to balance them
completely ?
6)
Explain the
‘direct and reverse crank’ method for determining unbalanced forces in radial
engines.
7)
Discuss the balancing of V

engines.
PART B
1)
The reciprocating masses of the first three cylinders of a four cy
linder engine are 4.1, 6.2 and 7.4
tonnes respectively. The centre lines of the three cylinders are 5.2 m, 3.2 m and 1.2 m from the
fourth cylinder. If the cranks for all the cylinders are equal, determine the reciprocating mass of
the fourth cylinder and
the angular position of the cranks such that the system is completely
balanced for the primary force and couple.
If the cranks are 0.8 m long, the connecting rods 3.8
m, and the speed of the engine 75 r.p.m. ; find
the maximum unbalanced secondary force
and
the crank angle at which it occurs.
2)
A four cylinder inline marine oil engine has cranks at angular displacement of 90°. The outer
cranks are 3 m apart and inner cranks are 1.2 m apart. The inner cranks are placed symmetrically
between the outer cranks
. The length of each crank is 450 mm. If the engine runs at 90 r.p.m. and
the mass of reciprocating parts for each cylinder is 900 kg, find the firing order of the cylinders for
the best primary balancing force of reciprocating masses. Determine the maximu
m unbalanced
primary couple for the best arrangement.
3)
In a four crank symmetrical engine, the reciprocating masses of the two outside cylinders
A
and
D
are each 600 kg and those of the two inside cylinders
B
and
C
are each 900 kg. The distance
between th
e cylinder axes of
A
and
D
is 5.4 metres. Taking the reference line to bisect the angle
between the cranks
A
and
D
, and the reference plane to bisect the distance between the cylinder
axes of
A
and
D
, find the angles between the cranks and the distance bet
ween the cylinder axes
of
B
and
C
for complete balance except for secondary couples.
Determine the maximum value of
the unbalanced secondary couple if the length of the crank is 425
mm, length of connecting rod
1.8 m and speed is 150 r.p.m.
4)
A three cylind
er radial engine driven by a common crank has the cylinders spaced at 120°. The
stroke is 125 mm, length of the connecting rod 225 mm and the mass of the reciprocating parts
per
cylinder 2 kg. Calculate the primary and secondary forces at crank shaft speed
of 1200 r.p.m.
5)
The pistons of a 60° twin
V

engine has strokes of 120 mm. The connecting rods driving a common
crank has a length of 200 mm. The mass of the reciprocating parts per cylinder is 1 kg and the
speed of the crank shaft is 2500 r.p.m. Determine
the magnitude of the primary and secondary
forces.
6)
A twin cylinder
V

engine has the cylinders set at an angle of 45°, with both pistons connected to
the single crank. The crank radius is 62.5 mm and the connecting rods are 275 mm long. The
reciprocating mass per line is 1.5 kg and the total rotating mass is equivalent to 2
kg at the crank
radius. A balance mass fitted opposite to the crank, is equivalent to 2.25 kg at a radius of 87.5
mm. Determine for an engine speed of 1800 r.p.m. ; the maximum and minimum values of the
primary and secondary forces due to the inertia of r
eciprocating and rotating masses
.
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Solution no 6 part B module 5