Understanding the Three-Run Method in Rotor Balancing

Devices

Portable balancer & Vibration analyzer Balanset-1A

Parts

Optical Sensor (Laser Tachometer)

Complete vibration diagnostics and balancing kit from Vibromera, including four vibration sensors with cables, a signal interface module, laser tachometer with magnetic stand, digital scale, USB cable, and a carrying case. The system is designed for field rotor balancing and condition monitoring on industrial equipment.

Devices

Dynamic balancer “Balanset-1A” OEM

Definition: What is the Three-Run Method?

The three-run method is the most widely used procedure for two-plane (dynamic) balancing. It determines the correction weights needed in two correction planes using exactly three measurement runs: one initial run to establish the baseline unbalance condition, followed by two sequential trial weight runs (one for each correction plane).

This method provides an optimal balance between accuracy and efficiency, requiring fewer machine starts and stops than the four-run method while providing sufficient data to calculate effective corrections for most industrial balancing applications.

The Three-Run Procedure: Step-by-Step

The procedure follows a straightforward, systematic sequence:

Run 1: Initial Baseline Measurement

The machine is operated at its balancing speed in its unbalanced, as-found condition. Vibration measurements are taken at both bearing locations (designated as Bearing 1 and Bearing 2), recording both amplitude and phase angle. These measurements represent the vibration vectors caused by the original unbalance distribution.

Measure at Bearing 1: Amplitude A₁, Phase θ₁
Measure at Bearing 2: Amplitude A₂, Phase θ₂
Purpose: Establishes the baseline vibration condition (O₁ and O₂) that must be corrected

Run 2: Trial Weight in Correction Plane 1

The machine is stopped, and a known trial weight (T₁) is temporarily attached at a precisely marked angular position in the first correction plane (typically near Bearing 1). The machine is restarted at the same speed, and vibration is measured again at both bearings.

Add: Trial weight T₁ at angle α₁ in Plane 1
Measure at Bearing 1: New vibration vector (O₁ + effect of T₁)
Measure at Bearing 2: New vibration vector (O₂ + effect of T₁)
Purpose: Determines how a weight in Plane 1 affects vibration at both bearings

The balancing instrument calculates the influence coefficients for Plane 1 by vector subtraction of the initial measurements from these new measurements.

Run 3: Trial Weight in Correction Plane 2

The first trial weight is removed, and a second trial weight (T₂) is attached at a marked position in the second correction plane (typically near Bearing 2). Another measurement run is performed, again recording vibration at both bearings.

Remove: Trial weight T₁ from Plane 1
Add: Trial weight T₂ at angle α₂ in Plane 2
Measure at Bearing 1: New vibration vector (O₁ + effect of T₂)
Measure at Bearing 2: New vibration vector (O₂ + effect of T₂)
Purpose: Determines how a weight in Plane 2 affects vibration at both bearings

The instrument now has a complete set of four influence coefficients describing how each plane affects each bearing.

Calculating the Correction Weights

After the three runs are complete, the balancing software performs vector mathematics to solve for the correction weights:

The Influence Coefficient Matrix

From the three measurement runs, four coefficients are determined:

α₁₁: How Plane 1 affects Bearing 1 (primary effect)
α₁₂: How Plane 2 affects Bearing 1 (cross-coupling)
α₂₁: How Plane 1 affects Bearing 2 (cross-coupling)
α₂₂: How Plane 2 affects Bearing 2 (primary effect)

Solving the System

The instrument solves two simultaneous equations to find W₁ (correction for Plane 1) and W₂ (correction for Plane 2):

α₁₁ · W₁ + α₁₂ · W₂ = -O₁ (to cancel vibration at Bearing 1)
α₂₁ · W₁ + α₂₂ · W₂ = -O₂ (to cancel vibration at Bearing 2)

The solution provides both the mass and angular position required for each correction weight.

Final Steps

Remove both trial weights
Install the calculated permanent correction weights in both planes
Perform a verification run to confirm vibration has been reduced to acceptable levels
If necessary, perform a trim balance to fine-tune the results

Advantages of the Three-Run Method

The three-run method has become the industry standard for two-plane balancing due to several key advantages:

1. Optimal Efficiency

Three runs represent the minimum needed to establish four influence coefficients (one initial condition plus one trial run per plane). This minimizes machine downtime while providing complete system characterization.

2. Proven Reliability

Decades of field experience demonstrate that three runs provide sufficient data for reliable balancing in the vast majority of industrial applications.

3. Time and Cost Savings

Compared to the four-run method, eliminating one trial run reduces balancing time by approximately 20%, translating to reduced downtime and labor costs.

4. Simpler Execution

Fewer runs mean less handling of trial weights, fewer opportunities for errors, and simpler data management.

5. Adequate for Most Applications

For typical industrial machinery with moderate cross-coupling effects and acceptable balancing tolerances, three runs consistently deliver successful results.

When to Use the Three-Run Method

The three-run method is appropriate for:

Routine Industrial Balancing: Motors, fans, pumps, blowers—the majority of rotating equipment
Moderate Precision Requirements: Balance quality grades from G 2.5 to G 16
Field Balancing Applications: In-situ balancing where minimizing downtime is important
Stable Mechanical Systems: Equipment with good mechanical condition and linear response
Standard Rotor Geometries: Rigid rotors with typical length-to-diameter ratios

Limitations and When Not to Use

The three-run method may be inadequate in certain situations:

When Four-Run Method is Preferred

High-Precision Requirements: Very tight tolerances (G 0.4 to G 1.0) where the additional verification of linearity is valuable
Strong Cross-Coupling: When correction planes are very close together or stiffness is highly asymmetric
Unknown System Characteristics: First-time balancing of unusual or custom equipment
Problem Machinery: Equipment showing signs of non-linear behavior or mechanical issues

When Single-Plane Might Be Sufficient

Narrow, disc-type rotors where dynamic unbalance is minimal
When only one bearing location shows significant vibration

Comparison with Other Methods

Three-Run vs. Four-Run Method

Aspect	Three-Run	Four-Run
Number of Runs	3 (initial + 2 trials)	4 (initial + 2 trials + combined)
Time Required	Shorter	~20% longer
Linearity Check	No	Yes (Run 4 verifies)
Typical Applications	Routine industrial work	High-precision, critical equipment
Accuracy	Good	Excellent
Complexity	Lower	Higher

Three-Run vs. Single-Plane Method

The three-run method is fundamentally different from single-plane balancing, which uses only two runs (initial plus one trial) but can only correct one plane and cannot address couple unbalance.

Best Practices for Three-Run Method Success

Trial Weight Selection

Choose trial weights that produce 25-50% change in vibration amplitude
Too small: Poor signal-to-noise ratio and calculation errors
Too large: Risk of non-linear response or unsafe vibration levels
Use similar sizes for both planes to maintain consistent measurement quality

Operational Consistency

Maintain exact same speed for all three runs
Allow for thermal stabilization between runs if necessary
Ensure consistent process conditions (flow, pressure, temperature)
Use identical sensor locations and mounting methods

Data Quality

Take multiple measurements per run and average them
Verify phase measurements are consistent and reliable
Check that trial weights produce clearly measurable changes
Look for anomalies that might indicate measurement errors

Installation Precision

Carefully mark and verify trial weight angular positions
Ensure trial weights are securely attached and won’t shift during runs
Install final correction weights with same care and precision
Double-check masses and angles before final run

Troubleshooting Common Issues

Poor Results After Correction

Possible Causes:

Correction weights installed at wrong angles or with wrong masses
Operating conditions changed between trial runs and correction installation
Mechanical problems (looseness, misalignment) not addressed before balancing
Non-linear system response

Trial Weights Produce Small Response

Solutions:

Use larger trial weights or place them at greater radius
Check sensor mounting and signal quality
Verify operating speed is correct
Consider if the system has very high damping or very low response sensitivity

Inconsistent Measurements