DYNAMICS OF MACHINES
UNIT-02
PART-A
1. Write the importance of balancing?
2. Define static balancing.
3. State the condition for static balancing & complete balancing.
4. Define Dalby’s method of balancing masses.
5. Why complete balancing is not possible in reciprocating masses?
6. Define tractive force.
7. Define swaying couple.
8. What is the effect of hammer blow and what is the cause it?
9. Give the reason for selecting different firing orders.
10. Why radial engines are preferred?
PART-B
11. Three masses are attached to a shaft as follows: 10 kg at 90 mm radius, 15 kg at 120 mm radius and 9
kg at 150 mm radius. The masses are to be arranged so that the shaft is in complete balance. Determine
the angular position of masses relative to 10 kg mass. All the masses are in the same plane. Solve by both
methods.
12) A shaft carries four masses A, B, C and D of magnitude 200 kg, 300 kg, 400 kg and 200 kg
respectively and revolving at radii 80 mm, 70 mm, 60 mm and 80 mm in planes measured from A at 300
mm, 400 mm and 700 mm. The angles between the cranks measured anticlockwise are A to B 45°, B to C
70° and C to D 120°. The balancing masses are to be placed in planes X and Y. The distance between the
planes A and X is 100 mm, between X and Y is 400 mm and between Y and D is 200 mm. If the balancing
masses revolve at a radius of 100 mm, find their magnitudes and angular positions.
13) A rotating shaft carries four masses of magnitude 18kg, 14kg, 16kg and 12 kg respectively and
revolving at radii 5cm, 6cm, 7cm and 6cm.The 2nd, 3rd, 4th masses revolved in planes 8cm, 16cm and
28cm respectively measured from the plane of the first mass and are angularly located at 60°,135°,and 270°
respectively measured clock wise from the first mass. The shaft is dynamically balanced by two masses,
both located at 5cm radii and revolving in planes mid-way between first&second masses and mid-way
between third & fourth masses. Find their magnitudes and angular positions.
14) A shaft carries four rotating masses A, B, C and D which are completely balanced. The
masses B, C and Dare 50kg, 80kg and 70kg respectively. The masses C and D make angles of 90° and
195° respectively with mass B in the same sense. The masses A,B,C and D are concentrated at radius
75mm,100mm,50mm and 90mmrespectively.The plane of rotation of masses B and C are 250mm apart.
Determine (i) the magnitude of mass A and its angular position (ii) the position of planes A and D.
15) A, B, C and D are four masses carried by a rotating shaft at radii 100, 125, 200 and 150 mm
respectively. The planes in which the masses revolve are spaced 600 mm apart and the mass of B, C and D
are 10 kg, 5 kg, and 4 kg respectively. Find the required mass A and the relative angular settings of the four
masses so that the shaft shall be in complete balance.
16) A shaft carries four masses in parallel planes A, B, C and D in this order along its length. The masses at
B and C are 18 kg and 12.5 kg respectively, and each has an eccentricity of 60 mm. The masses at A and D
have an eccentricity of 80 mm. The angle between the masses at B and C is 100° and that between the
masses at B and A is 190°, both being measured in the same direction. The axial distance between the
planes A and B is 100 mm and that between B and C is 200 mm. If the shaft is in complete dynamic
balance, determine: 1. The magnitude of the masses at A and D ; 2. the distance between planes A and D ;
and 3. the angular position of the mass at D.
17) Four masses A, B, C and D revolves at equal radii and equally spaced along a shaft. The mass B is
7kg and the radii of C and D make angle of 90° and 240°respectively with the radius of B. Find the
magnitude of masses A,C and D and angular position of A . So that the system may be completely
balanced.
18) Vee-twin engine has the cylinder axes at right angles and the connecting rods operate a common crank.
The reciprocating mass per cylinder is 11.5 kg and the crank radius is 75 mm. The length of the connecting
rod is 0.3 m. Show that the engine may be balanced for primary forces by means of a revolving balance
mass. If the engine speed is 500 r.p.m. What is the value of maximum resultant secondary force ?
19) A shaft is supported in bearings 1.8 m apart and projects 0.45 m beyond bearings at each end. The shaft
carries three pulleys one at each end and one at the middle of its length. The mass of end pulleys is 48 kg
and 20 kg and their centre of gravity are 15 mm and 12.5 mm respectively from the shaft axis. The centre
pulley has a mass of 56 kg and its centre of gravity is 15 mm from the shaft axis. If the pulleys are arranged
so as to give static balance, determine: 1. relative angular positions of the pulleys, and 2. dynamic forces
produced on the bearings when the shaft rotates at 300 r.p.m.
20) An inside cylinder locomotive has its cylinder centre lines 0.7 m apart and has a stroke of 0.6 m. The
rotating masses per cylinder are equivalent to 150 kg at the crank pin, and the reciprocating masses per
cylinder to 180 kg. The wheel centre lines are 1.5 m apart. The cranks are at right angles. The whole of the
rotating and 2/3 of the reciprocating masses are to be balanced by masses placed at a radius of 0.6 m. Find
the magnitude and direction of the balancing masses. Find the fluctuation in rail pressure under one wheel,
variation of tractive effort and the magnitude of swaying couple at a crank speed of 300 r.p.m.
21) The cranks of a three-cylinder locomotive are set at 120 o.The reciprocating masses are 450 kg for the
inside cylinder and 390 kg for each outside cylinder. The pitch of the cylinder is 1.2 m and the stroke of
each piston 500 mm. The planes of rotation of the balance masses are 960 mm from the inside cylinder. If
40% of the reciprocating masses are to be balanced, determine The magnitude and the position of the
balancing masses required at a radial distance of 500 mm; and The hammer blow per wheel when the axle
rotates at 350 rpm.
22) The cranks and connecting rods of a 4-cylinder in-line engine running at 1800 r.p.m. are 60 mm and
240 mm each respectively and the cylinders are spaced 150 mm apart. If the cylinders are numbered 1 to 4
in sequence from one end, the cranks appear at intervals of 90° in an end view in the order 1-4-2-3. The
reciprocating mass corresponding to each cylinder is 1.5 kg. Determine: 1. Unbalanced primary and
secondary forces, if any, and 2. Unbalanced primary and secondary couples with reference to central plane
of the engine.
