# Static and Dynamic Balancing

What is Balancing

The technique of correcting or eliminating unwanted inertia forces and moments is called balancing. Production of machine components with tight tolerances, though desirable, generally leads to a higher cost of production. In general, a more economical proposition is to produce parts with reasonable tolerances, subject them to balancing procedures and apply corrections as and where needed. It is possible to balance either wholly or partly the inertia forces in the machine component by either introducing additional masses to counteract original forces or by removing masses from reference planes from positions diametrically opposite to those of balancing masses.

Static Balancing

Machine components in motion may be either in (i) static or standing balance; or (ii) dynamic or running balance. The static imbalance is due to gravity or a centrifugal force. A 'static imbalance' in a rotating system is the effect of an eccentric (or unbalanced) mass which can be detected by quasi-static methods in which the weight of out-of-balance mass itself reveals its position. One such arrangement used for this purpose is illustrated in the following figure (a) which consists of a disc fixed to a straight shaft, resting on rigid rails, which permit the shaft to roll freely without friction. A reference system XOY is assumed to be described on the disc which moves with the disc.

To examine the disc for static imbalance, if any, the disc along with the shaft is rolled over rails gently by hand and permitted to assume equilibrium position of its own accord. A chalk mark is placed at a point that is considered to be in static balance. If all the chalk marks coincide at a particular point, the disc is said to have static imbalance.

 Static Balancing

Static balance exists if the forces acting on the parts are in equilibrium among themselves when not running, irrespective of the position in which the parts may be placed. Note that this is possible only when the position of the center of mass of all moving parts remains unchanged relative to the machine frame. This is possible only when the c.g. coincides with the geometric centre. When all the chalk marks in the experimental set-up coincide, the center of mass of the disc lies on the radial line joining the chalk mark to the geometric centre of the disc. In the lowest peripheral position, the gravitational pull acts downwards along this radial line and therefore, the same point occupies the lower most position in all trials. Theoretically it is possible to obtain static equilibrium with the unbalance above the shaft axis. However, it is practically impossible to obtain a condition in which two chalk marks are 180° apart.

When a static imbalance exists, it is possible to correct the same by drilling out material at the chalk mark. Static balancing can also be achieved by adding weights until the disc remains 'static' when the shaft is placed on knife edges as shown in figure above. Static balancing process is thus equivalent to bringing the center of mass of the system to its axis of rotation by adding correction masses or by drilling out material suitably.

Dynamic Balancing

Even when a rotor is statically balanced, it may exhibit unwanted vibration when allowed to rotate about its axis. A static balance of machine components is not enough to eliminate inertia forces because these forces may act in various planes (particularly when the disc is not thin) or in various directions depending on the directions and magnitudes of the accelerations (see Fig. where equal and opposite inertia forces constitute a couple). A dynamic imbalance is thus indicated by the presence of a couple with its axis perpendicular to that of rotation for the body. For complete dynamic balancing therefore, in addition to inertia force, inertia couples must also be balanced.

 Dynamic Balancing

A dynamically balanced rotor statically balances automatically but, in general, the opposite is not true. As a general rule, a rotor whose thickness is significant in relation to its diameter should be balanced dynamically. For thin disc static balancing is generally enough.