SARDAR VALLABHBHAI NATIONAL INSTITUTE OF TECHNOLOGY, SURAT
Mechanical Engineering Department
B. Tech. - III (Mechanical Eng.) Sem.-V
10 Dec 2020 (End-Semester Examination)
Subject: Dynamics of Machines (ME 301)
Time: 2.30 Hrs
Max. Marks: 80
SECTION – B (SUBJECTIVE TYPE)
Instructions:
1. Write your roll number & other essential details and then start writing answers on ONE SIDE of A4
size white sheets.
2. Answers of this section may be in descriptive and involve calculations. Assume the missing data
suitably. Clearly write used notations and symbols.
3. On top & bottom of each page, there must be signature of student, roll number & page number.
4. On the 1st page there should be also mentioned that answers of SUBJECTIVE SECTION and Total
number of pages.
5. Scan the answer sheet pages & prepare a pdf file. Name this file as - "AdminNo-Div-SUB-DOM". For
example - "U18ME001-Div-A-SUB-DOM". All students must submit prepared pdf file of SUBJECTIVE
section latest by 12.30 pm.
6. There are total 3 (three) pages in this section.
--- QUESTIONS --Q. 1
The links 3 and 4 of a four bar mechanism are subjected to forces of Q = 100 N at 600 and P = 50 N
at 450. The dimensions of various links are O2O4 = 800 mm, O2B = 500 mm, BC = 450 mm, O4C = 300
mm, BD = 200 mm, O4E = 150 mm. Calculate the shaft torque T2 on link 2 for static equilibrium of
the mechanism. Also find the forces in the joints. Also draw following diagrams:
(10)
1. Forces acting on various links,
2. Force polygons.
Figure - 1
Page 1 of 5
(P.T.O.)
Q. 2
A spring loaded governor of the Hartnell type has arms of equal length. The masses rotate in a circle
of 130 mm diameter when the sleeve is in the mid position and the ball arms are vertical. The
equilibrium speed for this position is 450 r.p.m., neglecting friction. The maximum sleeve
movement is to be 25 mm and the maximum variation of speed taking in account the friction to be
5 per cent of the mid position speed. The mass of the sleeve is 4 kg and the friction may be
considered equivalent to 30 N at the sleeve. The power of the governor must be sufficient to
overcome the friction by one per cent change of speed either way at mid-position. Determine,
neglecting obliquity effect of arms;
1. The value of each rotating mass,
2. The spring stiffness in N/mm and
3. The initial compression of spring.
(10)
OR
Q. 2
The arms of a Porter governor are 250 mm long. The upper arms are pivoted on the axis of rotation
and the lower arms are attached to the sleeve at a distance of 40 mm from the axis of rotation. The
load on the sleeve is 525 N and the weight of each ball is 75 N. Determine the equilibrium speed
when the radius of the balls is 200 mm. What will be the range of speed for this position, if the
frictional resistance to the motion of the sleeve is equivalent to a force of 30 N?
Q. 3
Fig. 2 shows diagrammatically a centrifugal governor. The masses ‘m’ are directly connected to one
another by two parallel and identical close coiled springs, one on either side. In the position shown,
with the mass arms parallel to the axis of rotation, the equilibrium speed is 900 r.p.m. Given:
Ball circle radius = 70 mm ;
Length of ball arm = 85 mm and
Length of sleeve arm = 50 mm.
(10)
1. When the speed is increased by 1% without any change of radius for the given position, an axial
force of 30 N is required at the sleeve to maintain equilibrium. Determine the mass of each ball.
2. Find the stiffness and initial extension of each spring, if the rate of sleeve movement, when in
mid position is 20 mm for 480 r.p.m. change of speed.
Figure – 2
Page 2 of 5
(P.T.O.)
OR
Q. 3
A Porter governor (Figure 3) has equal arms each 250 mm long and pivoted on the axis of rotation.
Each ball has a mass of 5 kg and the mass of the central load on the sleeve is 25 kg. The radius of
rotation of the ball is 150 mm when the governor begins to lift and 200 mm when the governor is at
maximum speed. Find the range of speed, sleeve lift, governor effort and power of the governor in
the following cases :
1. When the friction at the sleeve is neglected, and
2. When the friction at the sleeve is equivalent to 10 N.
Figure – 3
Q. 4
Ship propelled by a turbine rotor which has a mass of 3 tonnes and a speed of 3000 r.p.m. The rotor
has a radius of gyration of 0.6 m and rotates in a clockwise direction when viewed from the stern.
Find the gyroscopic effects in the following conditions: (i) The ship sails at a speed of 60 km/h and
steers to the left in a curve having 60 m radius.(ii) The ship pitches 3 degree above and 3 degree
below the horizontal position. The bow is descending with its maximum velocity. The motion due to
pitching is simple harmonic and the periodic time is 12 seconds. (iii) The ship rolls and at a certain
instant it has an angular velocity of 0.06 rad/s clockwise when viewed from stern. (iv) Determine
also the maximum angular acceleration during pitching. Also explain how the direction of motion
due to gyroscopic effect is determined in conditions.
(10)
OR
Q. 4
An aeroplane makes a complete half circle of 120 metres radius, towards left, when flying at 300 km
per hour. The rotary engine and the propeller of the plane has a mass of 400 kg with a radius of
gyration of 500 mm. The engine runs at 1800 r.p.m. clockwise, when viewed from the rear. Find the
gyroscopic couple on the aircraft and state its effect on it. How this effect will be changed: (i) if the
aeroplane turns to its right instead of to the left ? (ii) if the engine runs at the same speed but in
counter-clockwise direction instead of clockwise direction while taking left turn ? (iii) if the engine
runs at the same speed in counter-clockwise direction & and the aeroplane turns toward its right ?
(P.T.O.)
Page 3 of 5
Q. 5
The torque delivered by a two-stroke engine is represented by T = (1000 + 1200 Sin θ + 180 Sin 2θ +
18 Sin 3θ) Nm where θ is the angle turned by the crank from the inner-dead centre. The engine
speed is 180 rpm. Determine: (i) Mean power of the engine (ii) Minimum mass of the flywheel is if
the radius of the gyration is 600 mm and the maximum fluctuation of speed is ± 1.2 % of the mean.
(10)
OR
Q. 5
The equation of the turning moment curve of a three crank engine is (4000 + 2000 Sin 3θ) N-m,
where θ is the crank angle in radians. The moment of inertia of the flywheel is 800 kg-m2 and the
mean speed is 240 r.p.m. Calculate: 1. power of the engine, and 2. the maximum fluctuation of the
speed of the flywheel in percentage when (i) the resisting torque is constant, and (ii) the resisting
torque is (4000 + 500 sin θ) N-m.
Q. 6
A horizontal single cylinder gas engine running at 180 rpm has a bore of 200 mm and a stroke of 400
mm. The length of the connecting rod is 900 mm while the mass of the reciprocating parts is 24 kg.
When the crank has turned through and angle 60° from the inner dead centre, the gas pressure on
the cover end is 400 kN/m2 and the same on the crank side is 50 kN/m2 respectively. Diameter of
the piston rod is 50 mm.
(10)
Calculate:
(i) Inertia force on the piston
(ii) Net piston effort
(iii) Turning moment on the crankshaft
(iv) Crank effort
(v) Force (thrust) along the crankshaft
Neglect frictional resistance for all calculations.
Q. 7
Answer the following questions (ANY TWO):
(10)
1. What is dynamic balancing? Explain with neat sketch.
2. What are the necessary conditions for balancing of connecting rod in four bar mechanism?
3. Explain unbalance in engine due to inertia force of piston?
Q. 8
Examine the balancing condition, both shaking force and moment, as it apply to the four cylinder
inline engine shown in figure 4 and 5. Comment on the effect of crank position on balancing.
(P.T.O.)
Page 4 of 5
(10)
Figure - 4
Figure - 5
END OF THE SUBJECTIVE SECTION
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