Understanding Two-Plane Balancing

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Portable balancer & Vibration analyzer Balanset-1A

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Dynamic balancer “Balanset-1A” OEM

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Definition: What is Two-Plane Balancing?

Two-plane balancing is a dynamic balancing procedure in which correction weights are placed in two separate planes along the rotor’s length to eliminate both static unbalance and couple unbalance. This method is required for most industrial rotating machinery, particularly for rotors where the axial length is comparable to or greater than the diameter.

Unlike single-plane balancing, which only addresses the rotor’s mass center offset, two-plane balancing corrects both the translational force unbalance and the moment (couple) that causes the rotor to wobble or rock during rotation.

When is Two-Plane Balancing Required?

Two-plane balancing is necessary in the following situations:

1. Long or Slender Rotors

Any rotor with a length-to-diameter ratio greater than approximately 0.5 to 1.0 requires two-plane balancing. This includes:

• Electric motor armatures
• Pump and compressor shafts
• Multi-stage fan rotors
• Drive shafts and couplings
• Spindles and rotating tooling
• Turbine rotors

2. Presence of Couple Unbalance

When vibration measurements show significant out-of-phase motion between the two bearing supports (indicating a rocking or tilting motion), couple unbalance is present and must be corrected using two-plane balancing.

3. When Single-Plane Balancing is Inadequate

If an attempt at single-plane balancing reduces vibration at one bearing but increases it at another, this is a clear indication that two-plane balancing is needed.

4. Rigid Rotors with Distributed Mass

Even for rigid rotors operating below their first critical speed, if the mass is distributed over a significant axial length, two-plane balancing ensures vibration is minimized at all bearing locations.

The Two-Plane Balancing Procedure

Two-plane balancing is more complex than single-plane balancing because corrections in one plane affect vibration at both bearings. The procedure uses the influence coefficient method with multiple trial weights:

Step 1: Initial Measurement

Run the machine at its balancing speed and measure the initial vibration vectors (amplitude and phase) at both bearing locations. Label these as “Bearing 1” and “Bearing 2.” This data represents the combined effect of all unbalance present in the rotor.

Step 2: Define Correction Planes

Select two correction planes along the rotor where weights can be added or removed. These planes should be as far apart as practical and accessible. Common locations include near each end of the rotor, at coupling flanges, or at fan hubs.

Step 3: Trial Weight in Plane 1

Stop the machine and attach a trial weight at a known angular position in the first correction plane. Run the machine and measure the new vibration at both bearings. The change in vibration at each bearing, caused by the trial weight in Plane 1, is recorded. This establishes two influence coefficients: the effect of Plane 1 on Bearing 1, and the effect of Plane 1 on Bearing 2.

Step 4: Trial Weight in Plane 2

Remove the first trial weight and attach a trial weight at a known position in the second correction plane. Run the machine again and measure vibration at both bearings. This establishes two more influence coefficients: the effect of Plane 2 on Bearing 1, and the effect of Plane 2 on Bearing 2.

Step 5: Calculate Correction Weights

The balancing instrument now has four influence coefficients, forming a 2×2 matrix that describes how the rotor system responds to weights in each plane. Using vector mathematics and matrix inversion, the instrument solves a system of simultaneous equations to calculate the exact mass and angle required in each correction plane to minimize vibration at both bearings simultaneously.

Step 6: Install Corrections and Verify

Install both calculated correction weights permanently and run the machine for final verification. Ideally, vibration at both bearings should be reduced to acceptable levels. If not, a trim balance can be performed to refine the corrections.

Understanding the Influence Coefficient Matrix

The power of two-plane balancing lies in the influence coefficient matrix. Each correction plane influences vibration at both bearings, and these cross-coupling effects must be accounted for:

• Direct Effects: A weight in Plane 1 has the strongest influence on vibration at nearby Bearing 1, and a weight in Plane 2 has the strongest effect on nearby Bearing 2.
• Cross-Coupling Effects: However, a weight in Plane 1 also affects Bearing 2 (though usually to a lesser extent), and a weight in Plane 2 also affects Bearing 1.

The balancing instrument’s calculations account for all four of these effects simultaneously, ensuring that the correction weights work together to minimize vibration at all measurement points.

Advantages of Two-Plane Balancing

• Complete Correction: Addresses both static and couple unbalance, providing a thorough balancing solution for most rotor types.
• Minimizes Vibration at All Bearings: Unlike single-plane balancing, two-plane balancing optimizes vibration reduction across the entire rotor system.
• Extends Component Life: By reducing vibration at both bearing locations, wear on bearings, seals, and couplings is minimized.
• Industry Standard: Two-plane balancing is the standard approach for most industrial machinery and is required by many equipment manufacturers and industry standards.
• Suitable for Rigid Rotors: Effectively balances rigid rotors operating below their first critical speed, which represents the vast majority of industrial equipment.

Comparison with Single-Plane and Multi-Plane Balancing

• vs. Single-Plane: Two-plane balancing is more complex and time-consuming but provides superior vibration reduction for all but the narrowest disc-type rotors.
• vs. Multi-Plane: For flexible rotors operating above critical speeds, three or more correction planes may be required. However, two-plane balancing is sufficient for the vast majority of industrial machinery.

Common Challenges and Solutions

1. Inaccessible Correction Planes

Challenge: Sometimes the ideal correction plane locations are not accessible on an assembled machine.
Solution: Use available locations such as coupling hubs, fan blades, or external flanges. Modern instruments can mathematically account for less-than-optimal plane spacing.

2. Insufficient Trial Weight Response

Challenge: If the trial weight produces very little change in vibration, the influence coefficients will be inaccurate.
Solution: Use a larger trial weight or place it at a larger radius to increase its effect.

3. Non-Linear System Behavior

Challenge: Some rotors (especially those with loose components, soft foot, or operating near resonance) do not respond linearly to correction weights.
Solution: Address mechanical issues first (tighten bolts, correct soft foot), and perform balancing away from critical speeds when possible.

Field Balancing Applications

Two-plane balancing is the standard method for field balancing of industrial machinery. With portable vibration analyzers and balancing instruments, technicians can perform two-plane balancing directly on-site without disassembling or shipping the rotor to a balancing shop. This approach saves time, reduces cost, and ensures the rotor is balanced under actual operating conditions, accounting for factors like bearing stiffness, foundation flexibility, and process loads.

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