Understanding Quasi-Static Unbalance

1. Definition: What is Quasi-Static Unbalance?

Quasi-Static Unbalance is a specific and less common type of dynamic unbalance. It occurs when a rotor’s principal axis of inertia intersects the shaft’s rotational axis, but not at the rotor’s center of gravity.

In simpler terms, it’s a condition that has both static unbalance and couple unbalance, but the angular position of the static unbalance is exactly 90 degrees away from the plane containing the couple unbalance. This specific alignment gives it unique characteristics.

Like all forms of dynamic unbalance, it can only be fully measured and corrected when the rotor is spinning and requires correction in at least two planes.

2. Relationship to Other Unbalance Types

To understand quasi-static unbalance, it helps to place it in context:

• Static Unbalance: Purely a displacement of the center of gravity. Generates forces that are in-phase at the bearings.
• Couple Unbalance: Purely a “wobble” effect. Generates forces that are 180 degrees out-of-phase at the bearings.
• Dynamic Unbalance: The general case, which is a combination of static and couple unbalance at any random phase angle relative to each other.
• Quasi-Static Unbalance: A special case of dynamic unbalance where the static and couple components are physically locked at a 90-degree phase separation.

3. Practical Example: The Overhung Rotor

The classic textbook example of a machine that exhibits quasi-static unbalance is an overhung rotor where the unbalance is in a single plane that is far from the machine’s center of gravity. Consider a large industrial fan with a heavy set of blades mounted on the end of a long shaft.

If there is a single heavy spot on the fan (a pure static unbalance on the fan disk itself), the way this force is transmitted to the two bearings is different:

• The bearing closer to the fan will experience a large vibration force.
• The bearing further from the fan will also experience a force, but because the unbalance is “overhung,” this force creates a pivoting action over the nearby bearing.

The result is a complex motion at the bearings that combines both a shaking (static) and a rocking (couple) component. Because they originate from a single source, these components have a fixed relationship, creating the quasi-static condition.

4. Correction

Even though it has a specific definition, the correction for quasi-static unbalance is the same as for any general dynamic unbalance. The balancing procedure will involve:

1. Measuring the vibration amplitude and phase at 1X running speed at two bearing locations.
2. Calculating the required correction weights and their angular placement for two selected correction planes.
3. Placing the weights to counteract both the static and the couple components of the unbalance.

While an analyst might identify a condition as quasi-static based on the phase readings, the practical balancing process remains the same as for any two-plane balance job.

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