(^592) A Textbook of Engineering Mechanics
29.9.GRAPHICAL METHOD FOR THE BALANCING OF SEVERAL ROTATING
MASSES IN ONE PLANE BY ANOTHER MASS IN THE SAME PLANE
Fig. 29.4.
The magnitude and position of the balancing body may also be obtained graphically as
discussed below :
- First of all, draw the space diagram with the given masses of the bodies and their positions
as shown in Fig. 29·4 (a). - Find out the centrifugal forces (or assumed forces) exerted by each body on the rotating
shaft. - Now draw the vector diagram with the obtained centrifugal forces (or assumed forces),
such that ab represents in magnitude and direction the force exerted by the mass m 1 to
some scale. Similarly draw bc, cd and de which may represent in magnitude and direction
the forces exerted by the masses m 2 , m 3 , m 4 ....... and so on. - Now, as per polygon law of forces, ea represents in magnitude and direction of the resultant
force. - The balancing force is, then equal to the resultant force; but in the opposite direction.
- Now find out the magnitude of the balancing mass. This can be done by calculating the
mass of a body, which can produce a force or assumed force equal to the resultant force.
Example 29.4. Three bodies A, B and C of mass 10 kg, 9 kg and 16 kg revolve in the same
plane about an axis at radii of 100, 125 and 50 mm respectively with a speed of 100 r.p.m. The
angular positions of B and C are 60° and 135° respectively from A.
Find the position and magnitude of a body D, at a radius of 150 mm, to balance the system.
Solution. Given : Mass of body A (m 1 ) = 10 kg ; Radius of the rotating body A (r 1 ) = 100 mm;
Angle which the body A makes with the horizontal (θ 1 ) = 0 ; Mass of body B (m 2 ) = 9 kg ; Radius of
the rotating body B (r 2 ) = 125 mm ; Angle which the body B makes with the horizontal (θ 2 ) = 60°;
Mass of body C (m 3 ) = 16 kg ; Radius of rotating body C (r 3 ) = 50 mm ; Angle which the body C
makes with the horizontal (θ 3 ) = 135° ; Angular velocity (ω) = 100 r.p.m. and radius of balancing
mass D (r) = 150 mm.