 # Static and Dynamic Balancing of Rigid Rotors

Unbalance is the most common source of vibration in machines with rotating parts. It is a very important factor to be considered in modern machine design, especially where high speed and reliability are significant considerations. Balancing of rotors prevents excessive loading of bearings and avoids fatigue failure, thus increasing the useful life of machinery. “STATIC AND DYNAMIC BALANCING OF RIGID ROTORS”
MACDARA MACCAMHAOIL | BRÜEL & KJÆR

Unbalance in a rotor is the result of an uneven distribution of mass, which causes the rotor to vibrate.

The vibration is produced by the interaction of an unbalanced mass component with the radial acceleration due to rotation, which together generate a centrifugal force. Since the mass component rotates, the force also rotates and tries to move the rotor along the line of action of the force. The vibration will be transmitted to the rotor's bearings, and any point on the bearing will experience this force once per revolution. Balancing
is the process of attempting to improve the mass distribution of a rotor, so that it rotates in its bearings without uncompensated centrifugal forces. This is usually done by adding compensating masses to the rotor at prescribed locations. It can also be done by removing fixed quantities of material, for example by drilling.

Field Balancing is the process of balancing a rotor in its own bearings and supporting structure, rather than in a balancing machine.

Static Unbalance is defined as the eccentricity of the centre of gravity of a rotor, caused by a point mass at a certain radius from the centre of rotation (see Fig. 1). An equal mass, placed at an angle of 180° to the unbalanced mass and at the same radius, is required to restore the centre of gravity to the centre of rotation.

Static Balancing
involves resolving primary forces into one plane and adding a correction mass in that plane only. Many rotating parts which have most of their mass concentrated in or very near one plane, such as flywheels, grindstones, car wheels, etc., can be treated as static balancing problems. If a rotor has a diameter of more than 7 to 10 times its width, it is usually treated as a single-plane rotor.

## Dynamic Rotor: Unbalance Calculations

The calculation of the maximum allowable residual specific unbalance assumes that the mass of the rotor is evenly distributed about the centre of gravity. If the mass of the rotor is unevenly distributed, the calculations are a little more complicated.

In a perfectly balanced rotor, equal forces act on both ends of the rotor when it rotates. If the rotor is shaped as in Fig. 8, however, the forces at each end will be equal, but the allowable residual specific unbalance will be different for each bearing. The position of the centre of gravity divides the rotor in the ratio V3 : 2 /3. The sum of the moments about the centre of gravity must be zero. Therefore the residual specific unbalance at bearing A is 2 /3 of the total residual specific unbalance, while at bearing B it is V3 of the total.

### Selection of Trial Masses

The specific unbalance is used to calculate the size of trial masses, which are used during balancing to make temporary alterations to the mass distribution of the rotor, to determine the relationship between the specific unbalance and the bearing vibrations.

To estimate the value ol a suitable trial mass, the mass oi the rotor in kg and the radius m mm at which the corrections are to be made must be determined. The Maximum Residual MMR, in grammes, is given by: A suitable trial mass is five to ten times the value of the Maximum Residual Mass.

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