Unbalance results from the uneven distribution of mass around an axis of rotation. It occurs when the center of mass is not aligned with the center of rotation resulting in centrifugal forces acting on the rotor.
What is balancing?
To balance a shaft, mass must be added or removed from specific locations on the shaft.
Balancing involves determining the location and mass of these weights on the rotor to remove/reduce the unbalance.
Causes of Unbalance:
There are many causes of unbalance:
Non-symmetric mass: The rotating shaft may not have symmetric mass distribution around the axis of rotation.Figure 1: The mass is unevenly distributed around the center of rotation.
Not straight: The shaft itself may not be straight. The shaft may have been manufactured this way or the shaft may have deformed over time due to its elastic nature.Figure 2: The shaft is bent over the axis of rotation.
Clearance: Operating clearances of universal joints, splines, bearings, and other components will allow the shaft to move off center.Figure 3: Extra clearance between bearings allows for shaft wobble.
Bending: The shaft will deflect if a bending resonance is excited at a certain operating speed. Figure 4: The shaft could be excited in a bending mode.
What are the effects of unbalance?
Unbalance leads to excessive vibration which can cause:
Excessive noise due to vibration
Decreased lifetime of bearings and other components
Additional losses in efficiency
There are three kinds of unbalance: static, coupled, and dynamic.
Static Unbalance (single plane):
Static unbalance occurs when the principal mass axis is displaced parallel to the axis of rotation.
Figure 5: The axis of rotation is not aligned with the center of gravity. Rather is it displaced parallel to the axis of rotation.
For static unbalance, the centrifugal force (F) caused by unbalance is calculated as follows:
Where U is the unbalance, M is the rotor mass, re is the distance between the center of gravity (COG) and the center of rotation, m is the unbalance mass, ru is the distance between the center of rotation and the balance circle, ω is the angular velocity of the rotor, and F is the centrifugal force. See Figure 6 below for a pictorial representation of the terms.
The units of unbalance are [mass]x[distance]. Common units are the gram-centimeter [gm-cm] and ounce-inch [oz-in].
Figure 6: Pictorial representation of terms in unbalance equations. Above is a cross section of a shaft. The black circle represents a mass. The addition of the mass moves the center of mass away from the center of rotation. After balancing, re should be zero, thus moving the center of mass back to the center of rotation (the center of the blue circle).
Below is a graph of the centrifugal force vs. the shaft speed in RPM. It is clear that as the unbalance increases and the speed increases, the centrifugal force increases. Notice that doubling the unbalance mass at a certain speed doubles the centrifugal force. Notice that doubling the speed results in a 4X increase in the centrifugal force.
Figure 7: As the unbalance and shaft speed increase, the centrifugal force increases.
To correct for static unbalance, mass must be added or removed along a single plane in the shaft.
Coupled Unbalance (dual plane):
A coupled unbalance results when a rotating shaft has two equal unbalance masses in two different planes that are 180° apart from one another. See Figure 8 below. This results in the axis of rotation passing through the principal mass axis, but it is not parallel to it.
Figure 8: Two weights are on two different planes and are 180° apart from one another.
To compensate for coupled unbalance, weights must be added in two planes.
Dynamic Unbalance (dual plane):
Dynamic unbalance is the most common type of unbalance. It is a combination of static and coupled unbalance.
Dynamic unbalance results in the principal mass axis and the axis of rotation not crossing and not being parallel.
Figure 9: Dynamic unbalance is a combination of static and coupled unbalance.
Dynamic unbalance causes the system to tilt or wobble. To compensate for this, weights must be added in two planes.
Single Plane and Dual Plane Balancing:
Balancing involves adding weight to a single plane or multiple planes along a shaft.
Figure 10: A single plane through a shaft and a dual planes through a shaft.
Single plane balancing involves adding weights to only one plane along the rotor. This can only compensate for static unbalance.
Dual plane balancing involves adding weights to two planes along the rotor. This can compensate for coupled and dynamic unbalance.
The techniques for balancing single or dual plane are somewhat similar. Siemens Simcenter Testlab balancing application provides a solution for single and dual plane balancing issues.