B.E / B.
Tech DEGREE END SEMESTER EXAMINATIONS, APRIL/MAY 2014
MECHANICAL ENGINEERING
FOURTH SEMESTER
ME 9253 DYNAMICS OF MACHINES
( REGULATION 2009)
Time:3hr. Max. Mark: 100
Answer ALL Questions
P a r t A ( 1 0 x 2 = 20 Marks)
1 What do you understand by the term 'angle of heel'? What is the significance in
stability analysis?
2 Explain the term 'maximum fluctuation of energy". How is it established from a
known T.M diagram?
3 Explain the terms 'controlling force' and 'Effort' as applied to a governor
mechanism.
4 Explain the term hammer blow. How it can be reduced in locomotives?
5 In the case of unbalanced masses revolving in different planes, what are the
conditions to be fulfilled in order to obtain a complete balance.
6 Explain the term 'effective force' and explain D'Alembert's principle for analyzing a
dynamic force/couple system.
7 Depict 'under-damped vibrations', 'over-damped vibrations' and 'critically damped
vibrations' with the help of amplitude vs time plot.
8 What do you understand by whirling motion? Does it involve transverse or torsional
vibrations?
9 Why is it customary to make an assumption of small amplitude of oscillations? Give
justification.
10 State the effect of gyroscopic couple on a naval ship during rolling.
PART B ( 5 x 1 6 = 80 Marks)
11 (i) For the linkage shown below, find all constraints forces and torque T
required if F=120N in the direction shown. The dimensions of linkages
are as follows: (10)
c
F = 120N
^0
B, 40°
Magnitude T
unknown
0
60 "5
0
0 80
(ii) A vertical petrol engine 150 mm diameter and 200 mm stroke has a
connecting rod 350mm long. The mass of the piston is 1.6kg and the
engine speed is 1800 rpm. On the expansion stroke with crank angle 30°
from the top dead centre, the gas pressure is 750kN/m . Determine the 2
net trust on the piston. (6)
12a (i) How are the cylinders arranged in uncoupled three cylinder reciprocating
engine locomotive?
(ii) A,B,C and D are four masses carried by a rotating shaft at radii 100mm,
150mm, 150mm and 200mm respectively. The planes in which the
masses rotate are spaced at 500 mm apart and magnitude of the
masses B,C and D are 9Kg,5kg, and 4kg respectively. Find the required
mass A and the relative angular settings of the four masses so that the
shaft be in complete balance.
12b The following data apply to two cylinder locomotive with cranks at right angles:
Reciprocating mass per cylinder = 300 kg
Crank radius = 0.3 m
Distance between the driving wheel control planes = 1.55 m
Distance between cylinder centers = 0.65 m
Distance between driving wheel centers = 1.8 m
Determine :
(i) The fraction of reciprocating masses to be balanced if the hammer blow
i
is not to exceed 40kN at 100 km/hr.
(ii) The variation in tractive effort
(iii) The maximum swaying couple
(16)
13a (i) The frequency of damped vibration is 70 per minute and the amplitude
decreases by 70% of its initial value after two complete oscillations. Find
the frequency of the froe undamped vibrations of the system. (6)
(ii) A shaft 1.6 m long is 95 mm diameter for the first 0.6m of its length
60mm in diameter for the next 0.5 m of the iength and 50 mm in
diameter for the remaining length. The shaft carries two rotors at two
ends, the first having a mass of 800kg and 0.85 m radius of gyration
located at the other end. Determine the location of the node. Take
(10)
C=80GN/m . 2
[OR]
13b (i) A shaft 12.5 mm diameter rotates in long bearings and a disc of mass
16kg is secured to a shaft at the middle of its length. The span of the
shaft between the bearing is 0.5m. The mass centre of the disc is 0.5
mm from the axis of the shaft. Neglecting the mass of the shaft and
taking E=200GN/m find the critical speed of rotation in rpm. (6)
(ii) Mass of a single degree damped vibrations system measures 6kg and
makes 25 free oscillations in 11 seconds. The amplitude of vibration
reduces by 30% of its initial value after 5 oscillations. Determine
The stiffness of the spring
Logarithmic decrement
Damping factor
Critical damping coefficient and
Actual damping coefficient. (10)
14a A mass of 50kg suspended from a spring produces a statical deflection of 17 mm
and when in motion experiences a viscous damping force of value 250N at a
velocity of 0.3m/s. Calculate the periodic time of damped vibration. If the mass is
then subjected to a periodic disturbing force of maximum value of 200N and making (16)
2 Cycles/sec. find the amplitude of ultimate motion.
[OR]
A machine having a mass of 100kg and supported on spring of total stiffness 7.84 x
10 N/m has an unbalanced rotating element which results in a disturbing force of
5
392 N at a speed of 3000 rpm. Assuming the damping factor as 0.2 determine the
amplitude of motion due to unbalance, transmissibility and force transmitted.
(i) A heavy turbine rotor of a sea vessel rotates at 1500 rpm clockwise
looking from the stern, its mass being 800 kg. The vessel pitches with an
angular velocity of 1 rad/s. Determine the gyroscopic couple transmitted
to the hull when bow is rising, if the radius of gyration for the rotor is 275
mm. Also show in what direction the couple acts on the hull.
(ii) A porter governor has two balls each of mass 3kg and a central load of
mass 15kg. The arms area all 200mm long, pivoted on the axis. If the
maximum and minimum radius of rotation of the balls is 160mm and
120mm respectively, find the minimum and maximum speeds and range
of speed.
[OR]
(i) For the same values of mass of the sleeve and height at a given instant,
Proell governor requires smaller mass than that in Porter governor to
obtain the same equilibrium speed. Why?
(ii) A rear engine automobile is travelling along a curved track of 120m
radius. Each of the four wheels has a moment of inertia of 2.2kgm and 2
an effective diameter of 600 mm. The rotating parts of the engine have a
moment of inertia of 1.25kgm . The gear ratio of the engine to the back
2
wheel is 3.2. The engine axis is parallel to the rear axle and the crank
shaft rotates in the same sense as the road wheels. The mass of the
vehicle is 2050 kg and the centre of the mass 520 mm above the road
level.The width of the track is 1.6m. What will be the limiting speed of the
vehicle if all the four wheels maintain contact with the road surface?
