Static balancing

Before we start to learn about static balancing you know about balancing. Balancing is the process of designing or modifying machinery so that the unbalance is reduced to an acceptable level and if possible is eliminated entirely. 

What is static balancing?

The combined mass centre of the system lies on the axis of rotation then a system of rotating mass is said to be in static balance.

Static balancing

Explanation of static balancing :

The figure shows a rigid rotor revolving with a constant angular velocity of ω rad/s. A number of masses are depicted by point masses at different radii in the same transverse plane. They may represent different kinds of rotating masses such as turbine blades, eccentric discs etc. 

If m1, m2 and m3 are the masses revolving at radii r1, r2 and r3 respectively in the same the plane, then each mass produces a centrifugal force acting radially outwards from the axis of rotation. 
Let F be the vector sum of these forces.

F = m1r1ω2 + m2r2ω2 + m3r3ω

The rotor is said to be statically balanced if the vector sum F is zero. 

The rotor is said to be unbalanced if vector sum F is not zero. 

Graphical solution :

In graphical solution, vectors, m1r1, m2r2, m3r3 are added. If they close in a loop, the system is balanced. Otherwise, the closing vector will be giving mcrc.

Its direction identifies the angular position of the countermass relative to the other masses.