Understanding Eccentricity in Rotating Machinery

Definition: What is Eccentricity?

In the context of rotor dynamics, eccentricity refers to the radial distance or offset between a rotor’s center of mass (also called the center of gravity) and its geometric center (the true center of its form or shaft). In a perfectly balanced rotor, these two centers would coincide. However, due to manufacturing imperfections and non-uniform material density, there is almost always some inherent eccentricity. When an eccentric rotor spins, the offset mass center generates a centrifugal force, which is the root cause of vibration due to unbalance.

The Direct Relationship Between Eccentricity and Unbalance

Eccentricity and unbalance are fundamentally linked. Unbalance is the *measure* of the effect of eccentricity at a given speed, while eccentricity is the *physical cause*. The amount of unbalance is directly proportional to the mass of the rotor and its eccentricity.

The formula is simple:

Unbalance (U) = Mass (M) × Eccentricity (e)

This relationship highlights why eccentricity is so critical. Even a very small eccentricity (just a few micrometers) on a heavy, high-speed rotor can create a massive unbalance force, leading to severe vibration and rapid wear on bearings.

Types of Eccentricity

It’s important to distinguish between different forms of eccentricity and related geometric imperfections:

1. Mass Eccentricity

This is the true eccentricity as defined above—the offset between the mass center and the geometric center. This is the type that causes unbalance and is the target of all balancing procedures. It cannot be seen or measured directly with a dial indicator when the rotor is stationary.

2. Geometric Eccentricity (Runout)

This refers to a deviation of the rotor’s surface from a perfect circle. It is a measure of how “out-of-round” a shaft or rotor is. This is also known as mechanical runout. For example, a shaft journal may be slightly oval, or a pulley may be machined slightly off-center on a shaft. This type of imperfection *can* be measured with a dial indicator during a slow roll. While it doesn’t represent mass unbalance directly, an eccentric geometric form often contributes to mass unbalance.

3. Electrical Runout

This is not a physical imperfection but an error in measurement that occurs with non-contact proximity probes. If the rotor’s surface has variations in magnetic permeability or electrical conductivity, the probe can give a false reading that mimics geometric runout. This “noise” must be accounted for during rotor dynamic testing.

Causes of Eccentricity

Mass eccentricity is introduced into rotors through various means:

• Manufacturing Tolerances: No manufacturing process is perfect. There will always be slight errors in machining, casting, and assembly.
• Non-Uniform Material Density: Inclusions, voids, or porosity within a casting or forging mean that the material is not perfectly homogeneous, causing the mass center to shift.
• Asymmetric Design: Components like crankshafts are inherently asymmetric.
• Assembly Errors: A pulley or bearing that is not perfectly centered on a shaft will create an eccentric mass.
• Thermal Distortion: Uneven heating or cooling can cause a rotor to bow, temporarily shifting its mass center. This is known as a thermal vector.

How Eccentricity is Addressed

Since mass eccentricity is the cause of unbalance, it is corrected through the process of balancing. By adding or removing small amounts of weight, a technician creates an opposing force that effectively pulls the rotor’s mass centerline back into alignment with its geometric centerline, minimizing the net centrifugal force and the resulting vibration.

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