This document discusses balancing rotating masses on a shaft. It provides examples of balancing a single mass, balancing multiple masses in the same plane, and balancing masses in different planes. It then gives two example problems: 1) A shaft carries four masses rotating at different radii and angles, and asks to find the balancing mass and its position if placed at a given radius. 2) A shaft carries four masses at different radii and angles across three planes, and asks to find the magnitudes and positions of balancing masses placed at a given radius in two other planes.

1. BALANCING OF ROTATING
MASSES
Unit - II

2. BALANCING OF ROTATING
MASSES NOTATION
Centrifugal Disturbing Force Newton
M Unbalanced Disturbing Mass Kg
Counter Balanced Mass Kg
R Distance Of C.G of mass from axis of
ration
M
Distance Of C.G of balancing mass from
axis of ration
M
Angular velocity Rad/sec

3. Balancing Of Single Rotating Mass By
Single Mass In Same Plane

4. Balancing of a Single Rotating Mass By two
rotating Masses In Different Planes

6. Balancing Of several masses rotating
in Same Plane

14. 2. A shaft is rotating at a uniform angular speed. Four masses
M1, M2 and M3 and M4 of magnitudes 300kg, 450kg, 360kg and
390kg respectively are attached rigidly to the shaft. The masses
are rotating in the same plane. The corresponding radii of
rotation are 200mm, 150mm, 250mm and 300mm respectively.
The angle made by these masses with horizontal are 0°, 45°, 120°
and 255° respectively. Find (i) the magnitude of balancing mass
(ii) the position of balancing mass if the radius of rotation is
200mm. [May/June 2012]

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24. K.M.Kumar ME2302-Dynamics of Machinery 24

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3. 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
4. Four masses 200kg, 300kg, 240kg and 260kg are attached to a shaft. These
masses are revolving at radii 270mm, 210mm, 300mm and 360mm respectively in
planes measured from A1at 270mm, 420mm and 720mm respectively. The angles
measured anticlockwise are m1 to m2 is 45°, m2 to m3 is 70ºand m3 to m4 is 135° and
the distance between the planes L and M in which the balance masses are to be
placed is 500mm. The distance between planes A1 and L is 120mm and M and A4 is
100mm. If the balancing masses revolve at a radius of 72mm, find their magnitude
and angular positions