The Influence Coefficient Method for Field Balancing

Definition: What is an Influence Coefficient?

An influence coefficient is a complex vector (containing both an amplitude and a phase angle) that describes how a rotor system responds to a known unbalance. Specifically, it represents the change in vibration at a specific measurement point that results from adding a known trial weight at a specific location on a correction plane. In simpler terms, the coefficient tells you: “For a trial weight of this size, placed at this angle, the vibration at the bearing changed by this much and in this direction.”

This method is the foundation of modern field balancing because it allows for precise balancing without needing to know the complex physical properties of the rotor (like its mass, stiffness, or damping).

Why is the Influence Coefficient Method So Effective?

The power of this method lies in the fact that it treats the machine as a “black box.” Instead of trying to theoretically model the rotor, it uses a practical test to directly measure the system’s unique response. Key advantages include:

• High Accuracy: It accounts for all the real-world dynamic effects of the system, including bearing stiffness, support structure flexibility, and aerodynamic forces.
• Versatility: It works equally well for both single-plane and complex multi-plane balancing problems on both rigid and flexible rotors.
• No Disassembly Required: It is the standard for in-situ or field balancing, allowing machines to be balanced in their final installed condition under normal operating loads and temperatures.

The Single-Plane Balancing Procedure (Step-by-Step)

For a simple single-plane balance, the influence coefficient method follows a clear, logical process:

1. Initial Run (Run 1): With the machine under normal operating conditions, measure the initial vibration vector (amplitude A1 and phase P1) at the bearing. This represents the vibration caused by the original unbalance (O).
2. Trial Weight Run (Run 2): Stop the machine and attach a known trial weight (T) at a known angular position (e.g., 0 degrees) on the correction plane.
3. Measure the New Response: Start the machine and measure the new vibration vector (amplitude A2 and phase P2). This new vibration is the vector sum of the original unbalance plus the effect of the trial weight (O+T).
4. Calculate the Vibration Change: The balancing instrument performs a vector subtraction (A2 – A1) to find the vector representing the effect of the trial weight alone (T_effect).
5. Calculate the Influence Coefficient (α): The influence coefficient is calculated by dividing the trial weight’s effect by the trial weight itself: α = T_effect / T. This vector now represents the vibration response per unit of unbalance (e.g., mm/s per gram).
6. Calculate the Required Correction: To cancel the original unbalance, we need a correction weight that produces a vibration vector exactly opposite to the initial vibration (-A1). The required correction weight (W) is calculated as: W = -A1 / α.
7. Install Correction and Verify: The trial weight is removed, and the calculated correction weight (W) is permanently installed. A final run is performed to verify that the vibration has been reduced to an acceptable level.

Multi-Plane Balancing

The same principle extends to two-plane and multi-plane balancing, but the mathematics becomes more complex. For a two-plane balance, the instrument calculates four influence coefficients (the effect of a weight in plane 1 on both bearings, and the effect of a weight in plane 2 on both bearings). It then solves a set of simultaneous equations to find the correct weights for both planes. This powerful capability allows it to be used on virtually any type of rotating machine.

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