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## The Basics Of Balancing

26-09-2557 10:49:50น. Why Balance? Rotating components experience significant quality and performance
improvements when balanced. Balancing is the process of aligning a principal inertia axis
with the geometric axis of rotation through the addition or removal of material. By doing so,
the centrifugal forces are reduced, minimizing vibration, noise and associated wear.

Virtually all rotating components experience significant improvements when balanced.
Consumers throughout the global market continue to demand value in the products they
purchase. They demand performance - smaller, lighter, more efficient, more powerful,
quieter, smoother running and longer lasting. Balancing can contribute to each of these and
is one of the most cost effective means of providing value to the consumer.

FUNDAMENTAL TERMS
For a better understanding of balancing, it is necessary to have an understanding of its
terminology and its fundamental concepts. For additional terminology see ISO 1925,
Mechanical Vibration  Balancing - Vocabulary.

MASS CENTER:
The center of mass is the point about which the total mass of a rigid body is equally
distributed. It is useful to assume that all the mass is concentrated at this one point for
simple dynamic analyses. A force vector that acts through this point will move the body in a
straight line, with no rotation, according to Newtons second law of motion, F = m·a. The
sum of all forces acting on a body, F, cause a body to accelerate at a rate, a, proportional
to its mass, m.

CENTER OF GRAVITY:
For normal commercial balancing applications, the mass center and the center of gravity
occur at the same point. This does not hold true for applications involving a non-uniform
gravitational field, however, the scale of most balancing applications is very small with
respect to gradients in the earths gravitational field and the terms are synonymous.

AXIS OF ROTATION:
The axis of rotation is the true centerline of rotation  the instantaneous line about which a
part rotates. It is also referred to as the shaft axis or the geometric axis. The axis of
rotation is generally determined by geometric features on the rotor or by its support
bearings. The quality of the mounting datums greatly influence the ability to balance a part.
Non-circular surfaces, non-flat surfaces, irregular or loose bearings all allow or cause
variations in the position of the rotation axis. Any variation of the axis appears to be motion
of the mass center with respect to the axis and contributes to non-repeatability.

PRINCIPAL INERTIA AXIS:
The mass moment of inertia is the rotational counterpart of mass and is a measure of mass
distribution about an axis. For a particle it is the product of mass times the square of the
distance from the axis to the particle, I = m·r². For a rigid body it is an integral, I = ∫ r²·dm.
Since the mass moment of inertia is calculated with respect to an arbitrarily specified axis, it
can have just about any value depending on the axis chosen. It turns out that all rigid
bodies have at least one set of axes about which the body is perfectly balanced. These
axes are known as the principal axes. They are mutually orthogonal and have their origin at
the mass center. There are corresponding principal moments of inertia for each.
In balancing, it is useful to describe the central principal axis as the principal axis that is
most closely in line with the axis of rotation. It is also known as the balance axis or the
mass axis. A rotor with an axis of rotation that is not coincident with the central principal
axis has unbalance. The magnitude of unbalance will be a function of the angle between
the axes and the distance of the origin (mass center) from the axis of rotation.

CENTER OF GRAVITY:
For normal commercial balancing applications, the mass center and the center of gravity
occur at the same point. This does not hold true for applications involving a non-uniform
gravitational field, however, the scale of most balancing applications is very small with
respect to gradients in the earths gravitational field and the terms are synonymous.

AXIS OF ROTATION:
The axis of rotation is the true centerline of rotation  the instantaneous line about which a
part rotates. It is also referred to as the shaft axis or the geometric axis. The axis of
rotation is generally determined by geometric features on the rotor or by its support
bearings. The quality of the mounting datums greatly influence the ability to balance a part.
Non-circular surfaces, non-flat surfaces, irregular or loose bearings all allow or cause
variations in the position of the rotation axis. Any variation of the axis appears to be motion
of the mass center with respect to the axis and contributes to non-repeatability.

PRINCIPAL INERTIA AXIS:
The mass moment of inertia is the rotational counterpart of mass and is a measure of mass
distribution about an axis. For a particle it is the product of mass times the square of the
distance from the axis to the particle, I = m·r². For a rigid body it is an integral, I = ∫ r²·dm.
Since the mass moment of inertia is calculated with respect to an arbitrarily specified axis, it
can have just about any value depending on the axis chosen. It turns out that all rigid
bodies have at least one set of axes about which the body is perfectly balanced. These
axes are known as the principal axes. They are mutually orthogonal and have their origin at
the mass center. There are corresponding principal moments of inertia for each.
In balancing, it is useful to describe the central principal axis as the principal axis that is
most closely in line with the axis of rotation. It is also known as the balance axis or the
mass axis. A rotor with an axis of rotation that is not coincident with the central principal
axis has unbalance. The magnitude of unbalance will be a function of the angle between
the axes and the distance of the origin (mass center) from the axis of rotation.

CENTRIFUGAL FORCE:
A particle made to travel along a circular path generates a centrifugal force directed
outward along the radial line form the center of rotation to the particle. As the particle
rotates about the center point, so does the centrifugal force.
F (centrifugal) = m·r·ω2
Centrifugal force is an inertia force and is actually the bodys reaction to an externally
applied force. For circular motion the external force is known as centripetal force. The
centripetal force acts on the particle in a radially inward direction. They both have the same
magnitude but differ in the direction of action.
Centrifugal force is an inertia force and is actually the bodys reaction to an externally
applied force. For circular motion the external force is known as centripetal force. The
centripetal force acts on the particle in a radially inward direction. They both have the same
magnitude but differ in the direction of action.
With rigid bodies the unbalance remains the same although an increase in speed causes
an increase in force. The increased force will in turn cause increased motion depending on
the stiffness of the shaft or the shaft supports. Force increases exponentially as the square
of the change in speed. Twice the speed equates to four times the force and four times the
motion.
F = m·r·ω2 = U·ω2
Unbalance force for various unbalances are depicted in the following chart:

It should be noted that system flexibility limits the growth of centrifugal force. This is
discussed in greater detail in a later section, MOTION OF UNBALANCED PARTS.