Rotating unbalance is the uneven distribution of mass around an axis of rotation. A rotating mass, or rotor, is said to be out of balance when its center of mass (inertia axis) is out of alignment with the center of rotation (geometric axis). Unbalance causes a moment which gives the rotor a wobbling movement characteristic of vibration of rotating structures.

Causes of imbalance

Distortion from stress

Routine manufacturing processes can cause stress on metal components. Without stress relief, the rotor will distort itself to adjust.

Thermal distortion

Thermal distortion often occurs with parts exposed to increased temperatures. Metals are able to expand when in contact with heat, so exposure to warmer temperatures can cause either the entire piece of machinery to expand, or just certain parts, causing distortion.

Buildups and deposits

Rotating parts involved in material handling almost always accumulate buildup. Moreover, when exposed to oil, these parts can be very easily distorted. Without adhering to a maintenance routine or implementing an inspection process, oil can seep into the parts, causing unbalance.^[1]

By design

In some cases, vibration is desired, and a rotor is deliberately unbalanced to serve as a vibrator. An example of this is an aircraft's stick shaker.

Effects of unbalance

• Vibration
• Noise
• Decreased life of bearings
• Unsafe work conditions
• Reduced machine life
• Increased maintenance

Units used to express unbalance

• In terms of the mass eccentricity ${\displaystyle e}$: µm, mm, cm, ...; µin, mil, in, ...
• In terms of mass ${\displaystyle m}$ at a given radius: µg, mg, g, kg, ...; moz, oz, ...
• In terms of mass × radius moment (mR): mg-mm, g-mm, mg-cm, g-cm, kg-mm, ...; oz-in, g-in, ...

Types of balance

How to correct or compensate balance

• Mass addition.
• Mass removal.
• Mass shifting.
• Mass centering.

The measurement of existing vibration and calculation of the change of mass required is typically carried out using some form of balancing machine.

Grades

ISO 21940^[6] classifies vibration in terms of G codes. Unfortunately, it is the theoretical value assuming the rotor was spinning in free space so it does not relate to actual operating conditions. Rotors of the same type having permissible residual specific unbalance value e_per, varies inversely with the speed of the rotor.

e_per × ω = Constant,

where ω = angular velocity (radians per second) e_per = permissible residual specific unbalance

This constant is quality grade G. Balance Grades are used to specify the allowable residual imbalance for rotating machinery. The ISO 1940 standard defines balance grades for different classes of machinery. A rotor balanced to G2.5 will vibrate at 2.5 mm/s at operating speed if rotating in a suspended state with no external influences.

U_per = (9.54 × G number × mass)/rpm

Where U_per = balance tolerance (or) residual imbalance

Important formulas

${\displaystyle F=U\omega ^{2}}$

${\displaystyle U=mass(unbalance)r}$

${\displaystyle e={\frac {U}{m(rotor)}}}$

Where F = force due to unbalance, U = unbalance. ω = angular frequency. e = specific unbalance. m = mass. r = distance between unbalance and the axis of rotation of the object.

References