1. ME8594 - DYNAMICS OF MACHINES
UNIT –I (Part –B)
Prepared By: N. E. Godwin Pithalis Page 1
1.The lengths of crank and connecting rod of horizontal steam engine are 300 mm and 1.2 m
respectively. When the crank has moved 30° from the inner dead center, the acceleration of piston is
35 m/s2
. The average frictional resistance to the motion of piston is equivalent to a force of 550 N and
net effective steam pressure on piston is 500 kN/m2
. The diameter of piston is 0.3 m and mass of
reciprocating parts is 160 kg. Determine (i) Reaction on the cross-head guides; (ii) Thrust on the
crankshaft bearings; and (iii) Torque on the crank shaft. (DEC-2010)
2. The torque delivered by two-stroke engine is represented by T = (1000 + 300 sin 2θ — 500 cos2θ)
N.m Where θ is the angle turned by the crank from the inner-dead center. The engine speed is 250
rpm. The mass of the flywheel is 400 kg and radius of gyration 400 mm. Determine (i) the power
developed; (ii) the total percentage fluctuation of speed; (iii) the angular acceleration of flywheel
when the crank has rotated through an angle of 60° from the inner-dead center; and (iv) the maximum
angular acceleration and retardation of the flywheel. (DEC-2010)
3. The crank and connecting rod of a petrol engine, running at 1800 rpm are 50 mm and 200 mm
respectively. The diameter of the piston is 80 mm and the mass of the reciprocating parts is 1 kg- at a
point during the power stroke, the pressure on the piston is 0.7 N/mm2
, when it has moved 10 mm
from the inner dead centre. Determine the net load on the gudgeon pin, thrust on the connecting rod,
reaction between the piston and cylinder and the engine speed at which the above values become
zero. (DEC-2011)
4. A three cylinder single acting engine has its cranks set equally at 120o
and it runs at 600 r.p.m. The
torque Vs crank angle diagram for each cycle is a triangle for the power stroke with maximum torque
of 90 N-m at 60o
from dead centre of corresponding crank. The torque on return stroke is sensibly
zero. Determine the power developed, co-efficient of fluctuation of speed, if the mass of the flywheel
is 12 kg and a radius gyration of 80 mm, co-efficient fluctuation of energy and maximum angular
acceleration of the flywheel. (DEC-2011)
5. Deduce an expression for the inertia force in the reciprocating parts, neglecting the weight of the
connecting rod. (DEC-2012)
6. The turning moment curve for an engine is represented by the equation T = (20000 + 9500 sin 2θ -
5700 cos2θ) N-m Where θ is the angle moved by the crank from the inner-dead center. If the resisting
torque is constant, find (i) the power developed by the engine (ii) moment of inertia of flywheel in
kg-m2
, if the total fluctuation of speed is not exceed 1% of mean speed which is 180 rpm and (iii) the
angular acceleration of flywheel when the crank has turned through 45° from inner-dead center.
(DEC-2012)
7. (i) Derive the equation of forces on the reciprocating parts of an engine, neglecting the weight of the
connecting rod (12)
(ii) What is turning moment diagram and draw it’s for four stroke IC engine? (4) (DEC-2013)
8. A single cylinder, single acting, four stroke gas engine develops 25 KW at 320 rpm. The work done
by the gases during the expansion stroke is three times the work done on the gases during the
compression stroke. The work done during the suction and exhaust stroke being negligible. The
fluctuation of speed is not to exceed ±2% of the mean speed. The turning moment diagram during
compression and expansion is assumed to be triangular in shape. Find the weight of the flywheel if its
radius of gyration is 0.5m. (DEC-2013)
2. ME6505 - DYNAMICS OF MACHINES
UNIT –I (Part –B)
Prepared By: N. E. Godwin Pithalis Page 2
9. A horizontal steam engine running at 120rpm has a bore of 250 mm and a stroke of 400mm. The
connecting rod is 0.6 m and mass of the reciprocating parts is 60 kg. When the crank has turned
through an angle of 45° from the Inner Dead Centre, the steam pressure on the cover end side is
550KN/m2
and that on the crank end side is 60KN/m2
. Considering the diameter of the piston rod
equal to 50 mm, Determine,
(i). Turning moment on the crank shaft (ii). Thrust on the bearing and
(iii).Acceleration of the flywheel, if the power of the engine is 20 kW, mass of the flywheel 60 kg and
radius of gyration of 0.6m. (MAY-2014)
10. A shaft fitted with a flywheel rotates at 250 rpm and drives a machine. The torque of machine
varies in a cyclic manner over a period of 3 revolutions. The torque rises from 750 Nm to 3000 Nm
uniformly during 1⁄2 revolutions and remains constant for the following revolution. It then falls
uniformly to 750 Nm during next 1⁄2 revolution and remain constant for one revolution, the cycle being
repeated thereafter.
Determine the power required to drive the machine and percentage fluctuation in speed, if the driving
torque applied to the shaft is constant and the mass of the flywheel is 500 kg with radius of gyration of
600 mm. (MAY-2013, 2014)
11. The piston diameter of an IC engine is 125 mm and the stroke is 220 mm. The connecting rod is
4.5 times the crank length and has a mass of 50 kg. The mass of the reciprocating parts is 30 kg. The
center of mass of the connecting rod is 170 mm from the crank pin center and the radius of gyration
about an axis through the center of mass is 148 mm. The engine runs at 320 rpm. Determine the
magnitude and direction of the inertia force and the corresponding torque on the crank shaft when the
angle turned by the crank is 140 degrees from the inner dead center. (MAY-2008)
12. The torque delivered by a two stroke engine is represented by, T= (1000 +300 sin2θ -500 cos2θ)
N.m, where θ is the angle turned by the crank from the inner dead centre. The mass of the flywheel is
400 Kg and the radius of gyration 400 mm. Determine
(i) The power developed when the engine speed is 250 rpm and
(ii) The maximum fluctuations of speed in terms of percentage. (MAY-2008)
13. A horizontal steam engine running at 240rpm has a bore of 300 mm and stroke 600mm. The
connecting rod is 1.25 m long and mass of the reciprocating parts is 60 kg. When the crank is 60° past
its Inner Dead Centre, the steam pressure on the cover side of the piston is 1.125 N/mm2
while that on
the crank side is 0.125N/mm2
. Neglecting the area of the piston rod, Determine,
(i) the force on the piston rod, and (ii).Turning moment on the crank shaft. (MAY-2013)
14. The crank and connecting rod of an engine are 125 mm and 500 mm respectively. The mass of the
connecting rod is 60 kg and its center of gravity is 275 mm from the cross head pin center. The radius
of gyration about center of gravity being 150 mm. If the engine speed is 600 rpm for a crank position
of 45o
from the inner dead centre. Determine the acceleration of the piston and the magnitude, position
and direction of inertia force due to the mass of the connecting rod. (MAY-2011)
3. ME6505 - DYNAMICS OF MACHINES
UNIT –I (Part –B)
Prepared By: N. E. Godwin Pithalis Page 3
15. A punching press is required to punch 30 mm diameter holes in a plate of 20 mm thickness at the
rate of 20 holes/mm. It requires 6 Nm energy /mm2
of sheared area. If punching takes places in 1/10 of
a second and the speed of the flywheel varies from 160 to 140 rpm, determine the mass of the flywheel
having radius of gyration 1m. (MAY-2011)
16. The turning moment diagram for a multi cylinder engine has been drawn to a scale of 1mm =325
Nm vertically and 1mm = 3o
horizontally. The areas above and below the mean torque line are -26,
+378, -306, -302, -244, -380, -261 and -225 mm2
the engine is running at a mean speed of 600 rpm.
The total fluctuation of speed is not to exceed ±1.8% of the mean speed. If the radius of flywheel is
0.7m, find the mass of the flywheel. (DEC-2009)
17. The dimensions of a four four-link mechanism are AB=50 mm, BC =66 mm, CD =560 mm, and
AD =1000 mm the link AB has an angular velocity of 10.5 rad/s counter-clockwise and an angular
retardation of 26 rad/s2
at the instant when it makes an angle of 60o
with AD, the fixed link. The mass
of the links BC and CD is 4.2 kg/m length. The link AB has a mass of 3.54 kg, the center of which lies
at 200 mm from A and a moment of inertia of 88500 kgmm2
neglecting the gravity and friction effects,
determine the instantaneous value of the drive torque required to be applied on AB to overcome the
inertia forces. (DEC-2009)
18. The equation of the turning moment curve of a three crank engine is (5000+1500sin3θ) N-m,
where θ is the crank and in radians. The moment of inertia of the flywheel is 1000 kg-m2
and the mean
speed is 300 rpm. Calculate
(i) Power of the engine and (8)
(ii) The maximum fluctuation of the speed of the flywheel in percentage when
(a) The resisting torque is constant, and (4)
(b) The resisting torque is (5000 + 600sinθ) N-m. (4)
(DEC-2014)
19. A certain machine requires a torque of (5000 + 500sinθ) N-m to drive it, where θ is the angle of
rotation of shaft measured from certain datum. The machine is directly coupled to an engine which
produces a torque of (5000 + 600sin2θ) N-m. The flywheel and the other rotating parts attached to the
engine have a mass of 500 kg at a radius of gyration of 0.4 m. If the mean speed is 150 rpm, find
(i) the fluctuation of energy
(ii) the total percentage fluctuation of speed, and
(iii) the maximum and minimum angular acceleration of the flywheel and the corresponding shaft
position. (DEC-2014)
