Understanding the Four-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 Four-Run Method?

The four-run method is a systematic procedure for two-plane balancing that uses four distinct measurement runs to establish a complete set of influence coefficients for both correction planes. The method involves measuring the rotor’s initial condition, then testing each correction plane independently with a trial weight, followed by testing both planes together with trial weights simultaneously.

This comprehensive approach provides complete characterization of the rotor-bearing system’s dynamic response, allowing for accurate calculation of correction weights that minimize vibration at both bearing locations simultaneously.

The Four-Run Procedure

The method consists of precisely four sequential test runs, each serving a specific purpose:

Run 1: Initial (Baseline) Run

The machine is operated at its balancing speed in its as-found condition. Vibration measurements (both amplitude and phase) are recorded at both bearing locations (Bearing 1 and Bearing 2). This establishes the baseline vibration signature caused by the original unbalance.

Record: Vibration at Bearing 1 = A₁, ∠θ₁
Record: Vibration at Bearing 2 = A₂, ∠θ₂

Run 2: Trial Weight in Plane 1

The machine is stopped, and a known trial weight (T₁) is attached at a specified angular position in Correction Plane 1. The machine is restarted and vibration is again measured at both bearings. The change in vibration reveals how a weight in Plane 1 affects both measurement locations.

Trial weight T₁ added to Plane 1 at angle α₁
Record: New vibration at Bearing 1 and Bearing 2
Calculate: Effect of T₁ on Bearing 1 (primary effect)
Calculate: Effect of T₁ on Bearing 2 (cross-coupling effect)

Run 3: Trial Weight in Plane 2

Trial weight T₁ is removed, and a different trial weight (T₂) is attached at a specified position in Correction Plane 2. Another measurement run is performed. This reveals how a weight in Plane 2 affects both bearings.

Trial weight T₁ removed from Plane 1
Trial weight T₂ added to Plane 2 at angle α₂
Record: New vibration at Bearing 1 and Bearing 2
Calculate: Effect of T₂ on Bearing 1 (cross-coupling effect)
Calculate: Effect of T₂ on Bearing 2 (primary effect)

Run 4: Trial Weights in Both Planes

Both trial weights are installed simultaneously (T₁ in Plane 1 and T₂ in Plane 2), and a fourth measurement run is performed. This provides additional data that helps verify the system’s linearity and can improve calculation accuracy, particularly when cross-coupling effects are significant.

Both T₁ and T₂ installed simultaneously
Record: Combined vibration response at both bearings
Verify: Vector sum of individual effects matches combined measurement (validates linearity)

Mathematical Foundation

The four-run method establishes four influence coefficients that form a 2×2 matrix describing the complete system behavior:

The Influence Coefficient Matrix

α₁₁: Effect of a unit weight in Plane 1 on vibration at Bearing 1 (direct effect)
α₁₂: Effect of a unit weight in Plane 2 on vibration at Bearing 1 (cross-coupling)
α₂₁: Effect of a unit weight in Plane 1 on vibration at Bearing 2 (cross-coupling)
α₂₂: Effect of a unit weight in Plane 2 on vibration at Bearing 2 (direct effect)

Solving for Correction Weights

With all four coefficients known, the balancing software solves a system of two simultaneous vector equations to calculate the correction weights (W₁ for Plane 1, W₂ for Plane 2) that will minimize vibration at both bearings:

α₁₁ · W₁ + α₁₂ · W₂ = -V₁ (to cancel vibration at Bearing 1)
α₂₁ · W₁ + α₂₂ · W₂ = -V₂ (to cancel vibration at Bearing 2)

Where V₁ and V₂ are the initial vibration vectors at the two bearings. The solution uses vector mathematics and matrix inversion.

Advantages of the Four-Run Method

The four-run method offers several important benefits:

1. Complete System Characterization

By testing each plane independently and then both together, the method fully characterizes both direct effects and cross-coupling effects. This is critical when planes are close together or when bearing stiffness varies significantly.

2. Built-In Verification

Run 4 provides a check on system linearity. If the combined effect of both trial weights doesn’t match the vector sum of their individual effects, this indicates non-linear behavior (looseness, bearing play, foundation issues) that should be corrected before proceeding.

3. Improved Accuracy

When cross-coupling effects are significant (one plane strongly affecting the other bearing), the four-run method provides more accurate results than simpler three-run methods.

4. Redundant Data

Having four measurements for four unknowns provides some redundancy, allowing the software to detect and potentially compensate for measurement errors.

5. Confidence in Results

The systematic approach and built-in verification give the technician confidence that the calculated corrections will be effective.

When to Use the Four-Run Method

The four-run method is particularly appropriate in these situations:

Significant Cross-Coupling: When correction planes are closely spaced or when the rotor-bearing system has asymmetric stiffness, one plane significantly affects both bearings.
High-Precision Requirements: When tight balancing tolerances must be met.
Unknown System Characteristics: When balancing a machine for the first time and the system’s behavior is not well understood.
Critical Equipment: High-value machinery where the additional time for a fourth run is justified by increased confidence in the result.
Establishing Permanent Calibration: When creating permanent calibration data for future use, the thoroughness of the four-run method ensures accurate stored coefficients.

Comparison with the Three-Run Method

The four-run method can be compared to the simpler three-run method:

Three-Run Method

Run 1: Initial condition
Run 2: Trial weight in Plane 1
Run 3: Trial weight in Plane 2
Calculate corrections directly from three runs

Four-Run Method Advantages

Linearity Verification: Run 4 confirms the system behaves linearly
Better Cross-Coupling Characterization: More complete data when cross-coupling is strong
Error Detection: Anomalies are more readily identified

Three-Run Method Advantages

Time Savings: One less run reduces balancing time by ~20%
Sufficient Accuracy: For many applications, three runs provide adequate results
Simplicity: Less data to manage and process

In practice, the three-run method is more commonly used for routine balancing work, while the four-run method is reserved for high-precision applications or problem situations.

Practical Execution Tips

For successful four-run method execution:

Trial Weight Selection

Choose trial weights that produce 25-50% change in vibration from baseline
Use similar magnitude weights for both planes for consistent measurement quality
Ensure weights are securely attached for all runs

Measurement Consistency

Maintain identical operating conditions (speed, temperature, load) for all four runs
Allow thermal stabilization between runs if necessary
Use the same sensor locations and mounting for all measurements
Take multiple readings per run and average them to reduce noise

Data Quality Checks

Verify that trial weights produce clearly measurable vibration changes (at least 10-15% of initial level)
Check that Run 4 results approximately match the vector sum of Runs 2 and 3 effects (within 10-20%)
If linearity check fails, investigate mechanical issues before proceeding

Troubleshooting

Common issues with the four-run method and their solutions:

Run 4 Doesn’t Match Expected Response

Possible Causes:

Non-linear system behavior (looseness, soft foot, bearing play)
Trial weights too large, driving system into non-linear regime
Measurement errors or inconsistent operating conditions

Solutions:

Check for and correct mechanical problems
Use smaller trial weights
Verify measurement system calibration
Ensure consistent operating conditions across all runs

Poor Final Balance Results