Mass unbalance and vibration at 1X running speed

The term mass unbalance, as used in rotating assembly (rotor) of centrifugal
pump, refers to the uneven mass distribution in the rotor that will cause its axis of
inertia to shift away from the shaft centerline. When the rotor axis of inertia does
not coincide with the shaft centerline the rotor will vibrate due to centrifugal force
when the pump rotates.

The vibration due to mass unbalance will peak at a frequency equal to one times
(1X ) the rotational speed of the pump, and is directly proportional to the square of
the speed. Example, for the same amount of mass unbalance a rotor will vibrate
four times as much at 3560 RPM than it will at 1780 RPM.

Residual unbalance

Residual unbalance is defined as the mass unbalance remaining on a rotor after
it has been balanced on a balancing machine. The magnitude of unbalance is
calculated by multiplying the unbalance mass with its radial distance from the
shaft centerline. (It is commonly expressed in ounce-inches, in U.S. customary
units.

No matter how well a rotor is balanced it will always have some amount of
residual unbalance due to many factors, such as:

• eccentricity of machined rotor components such as shaft, shaft sleeves,
wear rings, etc.
• casting defects such as the presence of porous areas, bubbles, blow
holes, etc.
• material defects such as erosion, corrosion, lack of homogeneity, etc.
• bent or cracked shaft
• uneven heating or expansion of  rotating element when in operation
• machining tolerance of mating parts of the rotor
• unfilled sections of keyways
• dirt or scale build-up on the rotor
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Types of residual unbalance:

Static unbalance

Static unbalance, also called force unbalance, exists when the rotor centerline
(axis of inertia) is displaced parallel to the shaft centerline, as opposed to an
angular displacement. The rotor centerline does not intersect the shaft centerline.
Static unbalance commonly occurs in rotors with a narrow disk element such as a
flywheel.

Couple unbalance

Couple unbalance, also called moment unbalance, exists when the rotor axis of
inertia intersects the shaft centerline at its center of gravity. Couple unbalance
occurs when two unbalance mass of the same amount exist at opposite ends of a
rotor and are located 180 degrees apart from each other.

Static unbalance and couple unbalance are rarely encountered in centrifugal
pumps, so it will not be discussed here in details.

Dynamic unbalance

Dynamic unbalance exists when the rotor axis of inertia is not parallel to, and
does not intersects, the shaft centerline. The unbalance exists in at least two
planes, and can be corrected in at least two planes perpendicular to the shaft
centerline. Dynamic unbalance is the most common type of mass unbalance
occurring in centrifugal pumps.

Since the magnitude of vibration increases proportionately by the square of the
increase in rotor speed, the speed is taken into account when calculating the
amount of acceptable residual dynamic unbalance. The unbalance is calculated
from the equation:

U = K x W / N

where:

U  - acceptable residual unbalance, per plane, in ounce-inches
K  - constant, ranging from 4 to 8 depending on balance quality
W - rotor static weight, in pounds
N - rotor speed, in revolutions per minute (RPM)

Use K=4 for balance equal to ISO 1940-1 grade G1, and K=8 for ISO Grade G2.5.

The vibration caused by residual unbalance is indicated on a vibration spectrum
by a peak at frequency equal to one times (1X) the running or rotational speed.
The peak will show predominantly in both vertical and horizontal directions; it is
often higher in horizontal direction due to increased rotor flexibility in that direction,
whereas the vertical direction is slightly suppressed by the stiffness provided by
the casing feet.

Questions:

1. Is there a difference in the vibration signature, from residual unbalance,
between an overhung pump and a between bearing pump?

2. What should be done if a pump showed unacceptable high vibration due to
residual unbalance even after its rotor was dynamically balanced in a balancing
machine?

The answers to these questions can be found in our Facebook page.

R: 0511-MAUN
C: assembly, operation, trouble-shooting
F: Unbalance

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