VIDHYADEEP INSTITUTE OF MANAGEMENT
AND TECHNOLOGY
Vidhyadeep Campus, Anita (Kim), Ta. Olpad, Dist. Surat
Subject Name: DOM Subject Code: 161901
Sem: 6th (2013-14)
Assignment 2
1
A, B, C and D are four masses attached on a shaft at radii 0.1 m, 0.225 m, 0.15 m
and 0.15 m respectively. Planes in which masses revolve are spaced 0.6 m apart
and the weights of B, C and D are 10 kg, 5.5 kg and 3.6 kg respectively. Find the
required mass at A and the relative angular positions of all the four masses so that
the shaft is in complete balance. Use any method.
2
A single cylinder engine has a mass of 100 kg and is acted upon by a vertical
t
having a stiffness 60 kN/m and a damper which gives a damping force of 700 N per
unit velocity. Find the damping ratio and force transmitted to the foundation.
3
A single cylinder engine runs at 250 rpm and has a stroke of 180 mm. The
reciprocating parts weigh 120 kg and revolving parts equivalent to 70 kg at a radius
of 90 mm. A mass is kept opposite to the crank at a radius of 150 mm to balance
the whole of revolving mass and two third of the reciprocating mass. Determine
the magnitude of balancing mass and the resultant residual unbalanced force
when the crank has turned 300 from the dead centre.
4
A five cylinder in-line engine running at 750 rpm has successive cranks 1440 apart,
the distance between the cylinder centre lines being 375 mm. The piston stroke is
225 mm and the ratio of the connecting rod to the crank is 4. Examine the engine
for balance of primary force and couple. Find the maximum values of these and
the position of the central crank at which these maximum values occurs. The
reciprocating mass for each cylinder is 15 kg.
5
Four masses A, B, C, and D are completely balanced. Masses C and D make angles
of 90 and 195 respectively with B in the same sense. The rotating masses have
following properties. mb = 25 kg ra = 150 mm mc = 40 kg rb = 200 mm md = 35 kg
rc = 100 mm rd = 180 mm Planes B and C are 250 mm apart. Determine using
analytical method, (i) The mass A and its angular position (ii) The positions of
planes A and D.
6
The three cranks of three cylinder locomotive are all on the same axle and are set
at 1200 .The pitch of the cylinders is 1 meter 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.
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VIDHYADEEP INSTITUTE OF MANAGEMENT
AND TECHNOLOGY
Vidhyadeep Campus, Anita (Kim), Ta. Olpad, Dist. Surat
2. The hammer blow per wheel when the axle makes 6 rps.
7
The reciprocating mass per cylinder in a 600 twin engine is 1.5 kg. The stroke and
connecting rod length are 100 mm and 250 mm respectively. If the engine runs at
2500 r.p.m. Determine the maximum and minimum values of the primary forces.
Also find out the resultant secondary force.
8
Four masses 150 kg, 200 kg, 100 kg and 250 kg are attached to a shaft revolving at
radii 150 mm, 200 mm, 100 mm and 250 mm ; in planes A, B, C and D respectively.
The planes B, C and D are at distances 350 mm, 500 mm and 800 mm from plane
A. The masses in planes B, C and D are at an angle 105o, 200o and 300o measured
anticlockwise from mass in plane A. It is required to balance the system by placing
the balancing masses in the planes P and Q which are midway between the planes
A and B, and between C and D respectively. If the balancing masses revolve at
radius 180 mm, find the magnitude and angular positions of the balance masses.
9
The crank radius and connecting rod length of a four cylinder inline engine are 200
mm and 900 mm respectively. The outer cranks are set at 120o to each other and
each has a reciprocating mass of 200 kg. The spacing between adjacent planes of
cranks are 400 mm, 600 mm and 500 mm. If the engine is in complete primary
balance, determine the reciprocating masses of the inner cranks and their angular
positions. Also find the secondary unbalanced force if the engine speed is 300 rpm.
For a twin V-engine the cylinder centerlines are set at 90. The mass of
reciprocating parts per cylinder is 2.5 kg. Length of crank is 100 mm and length of
connecting rod is 400 mm. Determine the primary and secondary unbalanced
forces when the crank bisects the lines of cylinder centerlines. The engine runs at
1000 rpm.
10
11
Four masses A, B, C and D carried by a rotating shaft are at radii 110, 140, 210 and
160 mm respectively. The planes in which the masses revolve are spaced 600 mm
apart and the masses of B, C and D are 16 kg, 10 kg and 8 kg respectively. Find the
required mass A and the relative angular positions of the four masses so that shaft
is in complete balance.
12
The following data refers to an inside cylinder locomotive: Mass of reciprocating
parts/cylinder:36 kg Revolving masses/cylinder:16 kg Pitch of the cylinder:700 mm
Angle between crank : 90 Length of each crank:320 mm Wheel tread
diameter:1900 mm Distance between planes of wheel:1800 mm Limiting speed of
locomotive:100 kmph. If total revolving masses and 2/3 of the reciprocating parts
are to be balanced, determine: (i) Variation of tractive force (ii) Maximum swaying
couple.
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VIDHYADEEP INSTITUTE OF MANAGEMENT
AND TECHNOLOGY
Vidhyadeep Campus, Anita (Kim), Ta. Olpad, Dist. Surat
13
The intermediate cranks of a four cylinder symmetrical engine, which is in
complete primary balance, are 90o to each other and each has a reciprocating
mass of 300 kg. The centre distance between intermediate cranks is 600 mm and
between extreme cranks it is 1800 mm. Lengths of the connecting rod and cranks
are 900 mm and 300 mm respectively. Calculate the masses fixed to the extreme
cranks with their relative angular positions. Also find the magnitudes of secondary
forces and couples about the centre line of the system if the engine speed is 1500
rpm.
14
A rotating shaft carries four masses A, B, C and D which are radially attached to it.
The mass centers are 30 mm, 40 mm, 35 mm and 38 mm respectively from the axis
of rotation. The masses A, C and D are 7.5 kg, 5 kg and 4 kg respectively. The axial
distances between the planes of rotation of A and B is 400 mm and between B and
C is 500 mm. The masses A and C are at right angles to each other. Find for a
complete balance, (i) the angles between the masses B and D from mass A, (ii) the
axial distance between the planes of rotation of C and D, and (iii) the magnitude of
mass B.
15
Four masses P, Q, R and S are carried by a rotating shaft at radii 100 mm, 125 mm,
200 mm and 150 mm respectively. The planes in which the masses revolve are
spaced 600 mm apart and the masses Q, R and S are 10 kg, 5 kg and 4 kg
respectively. Determine the required mass P and the relative angular positions of
four masses so that the shaft shall be in complete balance.
16
The cranks and connecting rods of a four-cylinder in-line engine running at 1800
rpm are 60 mm and 240 mm each respectively and the cylinders are spaced 150
mm apart. The reciprocating mass corresponding to each cylinder is 10 kg. If the
cylinders are numbered 1 to 4 in sequence from one end, the cranks appear at
intervals of 90o in an end view in order 1-4-2-3. Determine unbalanced primary
and secondary forces, if any and unbalanced primary and secondary couples with
reference to central plane of the engine.
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