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 — informational only: the calculated correction mass applies at the trial-weight radius)

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.

An influence coefficient is a complex number that describes how a unit weight placed at a specific radius and angle affects the vibration of a rotor. It is the ratio of vibration change to the weight that caused it:

C = ΔV / W_trial

Once known, it can be used to calculate the exact correction weight needed to reduce vibration to zero (theoretically).

The process has three steps:

Run 1: Measure the initial vibration amplitude and phase (V₀)
Run 2: Attach a known trial weight, measure new vibration (V₁)
Calculate: ΔV = V₁ − V₀, then correction = −m_t × V₀ / ΔV

Remove the trial weight, place the correction weight at the calculated angle, and verify with a final run.

This is normal and not a problem. An increase means the trial weight happened to be placed near the heavy spot, adding to the unbalance. The vector calculation still produces the correct correction.

However, if vibration increases by more than 3–4×, use a smaller trial weight for safety, especially on equipment with limited bearing capacity.

Yes, this is standard practice. After placing the correction weight:

Measure the residual vibration
Use the same influence coefficient for a trim run
Calculate a small additional correction

Two to three iterations typically achieve the target balance quality. The influence coefficient remains valid as long as operating conditions don't change.

Key factors:

Speed stability — measurements must be at the same RPM
Phase reference — tachometer signal must be stable
Thermal state — let the machine warm up consistently
Trial weight size — should produce 20–50% vibration change
Sensor mounting — rigid, repeatable sensor position
Nonlinearity — very high vibration may introduce errors

The procedures described on this page were developed and field-tested by the Vibromera team using the Balanset-1A, a portable dual-channel balancer and vibration analyzer for on-site rotor balancing.