What is an influence coefficient?

An influence coefficient describes how a unit weight at a specific location and angle affects the vibration of a rotor. It is a complex number (magnitude and phase) that relates the change in vibration to the trial weight that caused it. Once known, the coefficient can be used to calculate the exact correction weight needed.

How to do single-plane balancing?

Single-plane balancing involves three steps: 1) Measure initial vibration (amplitude and phase), 2) Add a known trial weight and measure the new vibration, 3) Use vector math to calculate the correction weight. The influence coefficient method automates step 3 by computing the vibration change vector and dividing to find the correction.

What if vibration increases after adding the trial weight?

An increase in vibration after adding the trial weight is normal and expected in many cases — it simply means the trial weight was placed in an unfavorable angular position. The vector math still works correctly regardless. However, if vibration increases dramatically (more than 3-4×), use a smaller trial weight for safety.

Can I do multiple runs to improve accuracy?

Yes. After placing the calculated correction weight, you can measure the residual vibration and perform another trim balance run using the same influence coefficient. Each iteration typically reduces residual vibration. Two to three runs usually achieve the desired balance quality.

What factors affect accuracy?

Key accuracy factors include: measurement repeatability (run the rotor to the same speed), sensor quality and mounting, phase reference stability, rotor thermal state consistency, and trial weight size (should produce a measurable change but not be dangerously large — typically 5-30% of the expected correction).

Free Engineering Tool — #010

Influence Coefficient Calculator

Single-plane rotor balancing using the influence coefficient method. Enter initial vibration, trial weight data, and get the exact correction mass and angle.

Single-Plane Vector Math Correction Weight

Initial Vibration (Run 1 — no trial weight)

Amplitude A₀ (mm/s, μm, or mils)

Phase φ₀ (degrees)

Trial Weight

Trial Mass m_t (g)

Trial Angle θ_t (degrees)

Vibration with Trial Weight (Run 2)

Amplitude A₁ (same units as A₀)

Phase φ₁ (degrees)

Correction Radius (optional)

Correction Radius R (mm, if different from trial)

Quick presets

Results

Correction Mass

—

Correction Angle

—

Influence Coefficient |C|

—

Influence Vector ΔV

—

Estimated Residual

—

Vibration Vectors

Vibration is represented as complex vectors with amplitude and phase:

Influence Vector

The change in vibration caused by the trial weight:

Correction Weight

The correction weight is computed by complex division:

ℹ️ Note: The negative sign ensures the correction weight opposes the unbalance. The result is a vector: magnitude gives the weight in grams, argument gives the angular position.

Practical Example

Example — Single-Plane Balancing

Given: V₀ = 5∠45°, Trial = 10g@0°, V₁ = 8∠120°

ΔV = V₁ − V₀ = (8∠120°) − (5∠45°) = complex subtraction

W_c = −m_t × V₀ / ΔV → magnitude and angle of correction

⚠️ Important: Always remove the trial weight before adding the correction weight. The correction weight replaces the trial weight — do not leave both on the rotor.

Influence Coefficient Calculator | Single-Plane Balancing

Published by Nikolai Shelkovenko on February 15, 2026 February 15, 2026