Balancing single rotating mass

Procedure of Balancing single rotating mass when disturbing mass in same plane

Fig. shows single rotating mass ‘m’ which is attached to a shaft rotating with angular velocity ‘ω’. Let ‘r’ = distance of centre of gravity of ‘m’ from axis of rotation of shaft

 Due to rotation of shaft, centrifugal force ‘mrω2 ‘acts  radially outwards due to inertia of mass. This force is called disturbing force which will produce bending moment on the shaft.  

   

Diagram:-

A balance mass mb is introduced in the plane of rotation of disturbing mass, such that, it neutralizes the effect of inertia force due to disturbing mass. 

Thus , the inertia forces of mass ‘m’ and mass ‘mb’ must be equal and opposite.       mrω2  = mbrbω2               mr  = mbrb.

Thus the balancing mass mb is used at convenient radius rb  .Generally, rb is considered as large as possible so that balance mass mb required is very small.