Set No. 1
Code No: RR320304
III B.Tech II Semester Regular Examinations, Apr/May 2007
DYNAMICS OF MACHINES
( Common to Mechanical Engineering, Mechatronics, Production
Engineering and Automobile Engineering)
Time: 3 hours
Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
⋆⋆⋆⋆⋆
1. A racing motor cyclist travels at 140km/hr round a curve of 120 m radius measured
horizontally. The cycle and rider have a mass of 150 kg and their center of gravity
lies at 0.7 m above the ground level when the motor cycle is vertical. Each wheel
is 0.6m in diameter and has moment of inertia about its axis of rotation 1.5 kg-m2 .
The engine has rotating parts whose moment of inertia about their axis of rotation
is 0.25 kg-m2 and it rotates at five times the wheel speed in the same direction.
Find;
(a) The correct angle of banking of the track so that there is no tendency to side
slip, and
(b) The correct angle of inclination of the cycle and rider to the vertical.
[16]
2. An engine is coupled to a machine. The engine produces a torque given by the
expression TE = (8000 + 1000 sin 2θ) N-m where θ is the angle of rotation of shaft.
The machine requires a torque to run it and is given by the expression TM = (8000
+ 800 sin θ ) N-m where θ is angle of rotation of shaft. The engine runs at a mean
speed of 250 rpm and has a flywheel of mass 400 kg and radius of gyration 0.4 m
fixed to it. Determine
(a) The fluctuation of energy
(b) Percentage fluctuation of speed, and
(c) The maximum and minimum acceleration of the flywheel and the corresponding angular positions of the engine shaft.
[16]
3. (a) A car moving on a level road at a speed 60 kmph, has a wheel base 3 m,
distance of C.G from ground level 600mm, and the distance of C.G from rear
wheels is 1.2 m. Find the distance travelled by the car before coming to rest
when brakes are applied,
i. to the front wheels only,
ii. to the rear wheels only and
iii. to all the four wheels. Take coefficient of friction between the tyres and
the road as 0.6
(b) What is self-energizing brake? Derive ‘self locking conditions’ for a differential
band brake when drum rotates in clockwise direction.
[10+6]
4. (a) Differentiate between static friction and dynamic friction with suitable examples.
1 of 2
Set No. 1
Code No: RR320304
(b) An effective diameter of the cone clutch is 75 mm. The semi-angle of the cone
is 180 . Find the torque required to produce slipping of the clutch if an axial
force applied is 200 N. This clutch is employed to connect an electric motor
running uniformly at 100 r.p.m with a flywheel which is initially stationary.
The flywheel has a mass of 13.5 kg and its radius of gyration is 150 mm.
Calculate the time required for the flywheel to attain full speed, and also the
energy lost in the slipping of the clutch. Take coefficient of friction as 0.3
[6+10]
5. (a) Derive an expression for the height of Pro ell governor.
(b) Calculate the minimum speed of a Proell governor, which has equal arms each
200mm and are pivoted on the axis of rotation. The mass of each ball is 4kg
and the central mass on the sleeve is 20kg. The extension arms of the lower
links are each 60mm long and parallel to the axis when the minimum radius
of the ball is 100mm.
[8+8]
6. (a) Distinguish the static balance and dynamic balance with appropriate examples.
(b) A,B,C and D are four masses carried by a rotating shaft at radii 100mm,
l50mm, 150 mm and 200 mm respectively. The planes in which masses rotate
are spaced at 500 mm apart and the magnitude of the masses B,C and D are
9 kg, 5 kg and 4 kg respectively. Find the required mass A and the relative
angular settings of the 4 masses so that the shaft shall be in complete balance.
[6+10]
7. An air compressor has four vertical cylinders 1,2,3 and 4 inline and the driving
cranks at 90 intervals reach their upper most positions in this order. The cranks
are of 150mm radius, the connecting rods 500mm long and the cylinder centre line
400mm apart. The mass of the reciprocating parts of each cylinder is 22.5kg and
the speed of rotation is 400r.p.m. Show that there are no out-of-balance primary or
secondary forces and determined the corresponding couples, indicating the positions
of No. 1 crank for maximum values. The central plane of the machine may be taken
as reference plane.
[16]
8. (a) A steel bar 25mm wide and 50 mm deep is freely supported at two points
of meter apart, and carries a mass of 200 kg mid-way between them. Find
the frequency of the natural transverse vibrations, neglecting the mass of the
bar. Take E= 28 x 105 bar. What will be the frequency of vibration, if any
additional mass of 200 kg is distributed uniformly along the length of the shaft
?
(b) A steel shaft 100 mm in diameter is loaded and supported in shaft bearings
0.4m apart. The shaft carries three loads: first mass of 12 kg at the centre,
second mass of 10 kg at a distance 0.12 m from the left bearing and third
mass of 7 kg at a distance 0.09 m from the right bearing. Find the value of
the critical speed by using Dunkerley’s method.
[8+8]
⋆⋆⋆⋆⋆
2 of 2
Set No. 2
Code No: RR320304
III B.Tech II Semester Regular Examinations, Apr/May 2007
DYNAMICS OF MACHINES
( Common to Mechanical Engineering, Mechatronics, Production
Engineering and Automobile Engineering)
Time: 3 hours
Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
⋆⋆⋆⋆⋆
1. A four wheel trolley car of total mass 2000 kg running on rails of 1m gauge, rounds
a curve of 25m radius at 40 km/hr. the track is banked at 100. The wheels have
an external diameter of 0.6 m and each pair of an axle has a mass of 200 kg. The
radius of gyration for each pair is 250mm. The height of C.G of the car above the
wheel base is 0.95m. Allowing for centrifugal force and gyroscopic couple action,
determine the pressure in each rail.
[16]
2. An engine is coupled to a machine. The engine produces a torque given by the
expression TE = (8000 + 1000 sin 2θ) N-m where θ is the angle of rotation of shaft.
The machine requires a torque to run it and is given by the expression TM = (8000
+ 800 sin θ ) N-m where θ is angle of rotation of shaft. The engine runs at a mean
speed of 250 rpm and has a flywheel of mass 400 kg and radius of gyration 0.4 m
fixed to it. Determine
(a) The fluctuation of energy
(b) Percentage fluctuation of speed, and
(c) The maximum and minimum acceleration of the flywheel and the corresponding angular positions of the engine shaft.
[16]
3. (a) Name different types of dynamometers. Explain function of prony brake.
(b) In a band and block Brake, the band is lined with 14 blocks, each of which
subtends an angle of 200 at the drums centre. One end of the band is attached
to the fulcrum of the brake lever and the other to a pin 150mm from the
fulcrum. Find the force required at the end of the lever 1m long from the
fulcrum to give a torque of 4k N-m. The diameter of the brake drum is 1m
and the coefficient of friction between the blocks and the drum is 0.25.[6+10]
4. (a) Distinguish between torque transmitted in multi collar bearing, and torque
transmitted in multi plate clutch.
(b) A conical pivot bearing supports a vertical shaft of 200 mm diameter. It is
subjected to a load of 30 kN. The angle of the cone is 1200 and the coefficient
of friction is 0.025. Find the power lost in friction when the speed is 120
r.p.m., assuming uniform pressure and uniform wear conditions.
[8+8]
5. (a) A spring controlled governor of the Hartnell type has the following data: Mass
of the ball = 1.8 kg; Mall of the sleeve= 6kg; Ball and sleeve arms of the bell
crank lever = 150 mm and 120 mm respectively. The equilibrium speed and
1 of 2
Set No. 2
Code No: RR320304
radius of rotation for the lowest position of the sleeve are 400r.p.m. and
150mm respectively. The sleeve lift is 10 mm and the change in speed for full
sleeve lift is 5%. During an overhaul, the spring was compressed 2 mm more
than the correct compression for the initial setting. Determine the stiffness of
the spring and the new equilibrium speed for the lowest position of the sleeve.
(b) The upper arms of a Porter governor are pivoted on the axis of rotation and
the lower arms are pivoted to the sleeve at a distance of 30 mm from the axis
of rotation. The length of each arm is 300 mm and the mass of each ball is
6 kg. If the equilibrium speed is 200 r.p.m. when the radius of rotation is
200 mm, find the required mass on the sleeve. If the friction is equivalent to
a force of 40 N at the sleeve, find the coefficient of insensitiveness at 200 rpm
radius.
[8+8]
6. The cranks 2 to 9 of a nine cylinder engine running at 1000 r.p.m. make 240,
120, 160, 280, 40, 80, 320 and 2000 respectively with crank 1, when measured in
a counter clock direction. The rotating masses for each cylinder are estimated to
be 20 kg at 0.15m radius. The distance between centre lines of cranks is 0.4 m.
Determine the unbalanced movement due to the rotating parts about the mid plane
(cylinder S) of the crank craft.
[16]
7. An air compressor has four vertical cylinders 1,2,3 and 4 inline and the driving
cranks at 90 intervals reach their upper most positions in this order. The cranks
are of 150mm radius, the connecting rods 500mm long and the cylinder centre line
400mm apart. The mass of the reciprocating parts of each cylinder is 22.5kg and
the speed of rotation is 400r.p.m. Show that there are no out-of-balance primary or
secondary forces and determined the corresponding couples, indicating the positions
of No. 1 crank for maximum values. The central plane of the machine may be taken
as reference plane.
[16]
8. (a) Explain the term ‘Damping factor’
(b) A mass suspended from a helical spring vibrates is a viscous fluid medium
whose resistance varies directly with the speed. It is observed that the frequency of damped vibration is 90 per minute and that the amplitude decreases
to 20% of its initial value in one complete vibration. Find the frequency of
the free undamped vibration of the system.
[4+12]
⋆⋆⋆⋆⋆
2 of 2
Set No. 3
Code No: RR320304
III B.Tech II Semester Regular Examinations, Apr/May 2007
DYNAMICS OF MACHINES
( Common to Mechanical Engineering, Mechatronics, Production
Engineering and Automobile Engineering)
Time: 3 hours
Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
⋆⋆⋆⋆⋆
1. The turbine rotor of a ship has a mass of 20 tones and a radius of gyration of 0.75m.
Its speed is 2000 rpm. The ship pitches 60 above and below the horizontal position. One complete oscillation takes 18 seconds and the motion is simple harmonic.
Determine.
(a) The maximum couple tending to shear the holding down bolts of the turbine
(b) The maximum angular acceleration of the ship during pitching and
(c) The direction in which the bow will tend to turn while rising, if the rotation
of the rotor is clockwise when looking from rear.
[16]
2. The torque delivered by two stroke engine represented by T=1000+300 sin 2θ 500 cosθ N-m where θ is the angle made by the crank from IDC. The engine
speed is 250rpm. The mass of flywheel is 400 kg and radius of gyration is 400mm.
Determine:
(a) Total percentage of fluctuation of speed.
(b) The angular acceleration of flywheel when the crank has rotated through an
angle of 600 from IDC.
(c) The maximum angular retardation of flywheel.
[16]
3. A band and block brake having 12 blocks, each of which subtends 150 at the centre,
is applied to a rotating drum of 600 mm diameter. The blocks are 75 mm thick.
The drum and the flywheel mounted on the same shaft have a mass of 1800 kg
and have combined radius of gyration of 600 mm. The two ends of the band are
attached to pins on the opposite sides of the brake fulcrum at distances of 40 mm
and 150 mm from the fulcrum. Calculate
(a) the maximum braking torque,
(b) the angular retardation of the drum,
(c) the time taken by the system to be stationary from the rated speed of 300
r.p.m. Take coefficient of friction is 0.3
[16]
4. A car engine has its rated output of 10kW. Maximum torque developed is 100Nm.
The clutch used is of single plate type having two active surfaces. Axial pressure
is not to exceed 0.85 bar. External diameter of the friction plate is 1.25 times the
internal diameter. Determine the dimensions of the friction plate and the axial
force exerted by the springs. Assume uniform wear and coefficient of friction as
O.3.
[16]
1 of 2
Set No. 3
Code No: RR320304
5. A loaded governor of the Porter type has equal arms and links each 250 mm long.
The mass of each ball is 2 kg and the central mass is 12 kg. When the ball radius is
150mm, the valve is fully’ open and when the radius is 185 mm, the valve is closed.
Find the maximum speed and the range of speed. If the maximum speed is to be
increased 20% by an addition of mass to the central load, find what additional mass
is required.
[16]
6. (a) Distinguish the static balance and dynamic balance with appropriate examples.
(b) A,B,C and D are four masses carried by a rotating shaft at radii 100mm,
l50mm, 150 mm and 200 mm respectively. The planes in which masses rotate
are spaced at 500 mm apart and the magnitude of the masses B,C and D are
9 kg, 5 kg and 4 kg respectively. Find the required mass A and the relative
angular settings of the 4 masses so that the shaft shall be in complete balance.
[6+10]
7. An air compressor has four vertical cylinders 1,2,3 and 4 inline and the driving
cranks at 90 intervals reach their upper most positions in this order. The cranks
are of 150mm radius, the connecting rods 500mm long and the cylinder centre line
400mm apart. The mass of the reciprocating parts of each cylinder is 22.5kg and
the speed of rotation is 400r.p.m. Show that there are no out-of-balance primary or
secondary forces and determined the corresponding couples, indicating the positions
of No. 1 crank for maximum values. The central plane of the machine may be taken
as reference plane.
[16]
8. (a) Define the term ‘node’ and explain how it is obtained.
(b) A shaft 1.5 m long has a diameter of 5 cm for the first 75 cm and a diameter
7.5 cm for the remaining 75 cm. If one end of the shaft is fixed and the other
end carries a disc of mass 25 kg and the radius of gyration 50 cm. What is the
frequency of the free torsional vibration? Modulus of rigidity of shaft material
may be taken as 80 GN/m2 .
[6+10]
⋆⋆⋆⋆⋆
2 of 2
Set No. 4
Code No: RR320304
III B.Tech II Semester Regular Examinations, Apr/May 2007
DYNAMICS OF MACHINES
( Common to Mechanical Engineering, Mechatronics, Production
Engineering and Automobile Engineering)
Time: 3 hours
Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
⋆⋆⋆⋆⋆
1. A steam engine 200 mm bore and 300 mm stroke has a connecting rod 625 mm
long. The mass of the reciprocating parts is 15 kg and the speed is 250 rpm when
the crank is at 300 to the inner dead center and moving outwards, the difference in
steam pressures is 840 kN/m2 . if the crank pin radius is 30mm, determine:
(a) The force on the crankshaft; and
(b) The torque acting on the frame.
[16]
2. (a) What is Turning Movement diagram? Mention its uses.
(b) A certain machine requires a torque of (1500+200 sinθ)N-m to drive it where
θ is the angle of rotation of shaft. The machine is directly connected to an
engine which produces a torque (1500+250 sinθ)N-m. The flywheel and other
rotating parts have a mass 300 kg at radius of gyration 200mm. Mean speed
is 200 rpm. Find:
i. Kinetic Energy of flywheel
ii. Percentage coefficient of fluctuation of speed
iii. Crank angle at Maximum Turning Moment.
[4+12]
3. (a) Describe the construction and operation of a rope brake absorption dynamometer.
(b) A lorry is moving on a level road at a sped of 36 kmph. Its centre of gravity
lies at a distance of 0.6m from ground level. The wheel base is 204m and the
distance of centre of gravity from the rear wheels is 0.9m. Find the distance
travelled by the car before coming to rest when brakes are applied,
i. to the rear wheels
ii. to the front wheels &
iii. to all the four wheels. The coefficient of friction between the tyres and
the road surface is 0.45.
[6+10]
4. (a) Differentiate between static friction and dynamic friction with suitable examples.
(b) An effective diameter of the cone clutch is 75 mm. The semi-angle of the cone
is 180 . Find the torque required to produce slipping of the clutch if an axial
force applied is 200 N. This clutch is employed to connect an electric motor
running uniformly at 100 r.p.m with a flywheel which is initially stationary.
1 of 2
Set No. 4
Code No: RR320304
The flywheel has a mass of 13.5 kg and its radius of gyration is 150 mm.
Calculate the time required for the flywheel to attain full speed, and also the
energy lost in the slipping of the clutch. Take coefficient of friction as 0.3
[6+10]
5. In a Porter governor, the arms and links are each 25cm long and intersect on the
main axis. Each ball weighs 45N and the central load is 200N. The sleeve is in
its lowest position when the arms are inclined at 30 degrees to the axis. The lift
of sleeve is 5cm. What is the force of friction at the sleeve, if the speed at ascent
from the lowest position is equal to the speed at the beginning of descent from the
highest position? What is then the range of speed, all other things remaining the
same?
[16]
6. The cranks 2 to 9 of a nine cylinder engine running at 1000 r.p.m. make 240,
120, 160, 280, 40, 80, 320 and 2000 respectively with crank 1, when measured in
a counter clock direction. The rotating masses for each cylinder are estimated to
be 20 kg at 0.5m radius. The distance between centre lines of cranks is 0.4 m. It
is proposed to balance this engine by two masses, one in the damper at a distance
of 0.6 m from cylinder one and the other located in the fly wheel at a distance of
0.6 m from cylinder nine. Determine the kg-m magnitudes and the locations of the
balancing masses.
[16]
7. (a) Prove that maximum secondary unbalanced forces is l/n times maximum primary unbalanced for n cylinder reciprocating engine.
(b) For radial engines with an odd number of cylinders prove that the primary
force may be balanced by attaching single mass of km where ‘k’ is number of
cylinders and ‘m’ is mass of reciprocating parts.
[8+8]
8. (a) Derive an equation for the transverse vibration of a uniformly loaded shaft.
(b) A rigid massless bar of length L is hinged at its end and carries a spring K2
with mass at its right end. The bar is also supported by a spring K1 at a
distance from the left hinge. Determine the natural frequency of the bar.
[8+8]
⋆⋆⋆⋆⋆
2 of 2