BIZOMAT MAKEOS · Mechanics
Two-Plane (Dynamic) Balance Corrections
What correction masses in two planes give this rotor a running (dynamic) balance?
Correction masses and angles in two chosen correction planes that balance up to three masses lying in different planes along a rotor, by taking moments about one correction plane.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Distance between correction planes A and B | mm | Axial distance between the two correction planes. |
| Masses (axial position measured from plane A) | ||
| Mass 1 | g | First unbalanced mass. |
| Radius 1 | mm | Its radius. |
| Angle 1 | ° | Its angle. |
| Axial position 1 | mm | Its axial distance from plane A (negative if outside, beyond A). |
| Mass 2 | g | Second mass. |
| Radius 2 | mm | Its radius. |
| Angle 2 | ° | Its angle. |
| Axial position 2 | mm | Its axial position. |
| Mass 3 | g | Third mass (0 if unused). |
| Radius 3 | mm | Its radius. |
| Angle 3 | ° | Its angle. |
| Axial position 3 | mm | Its axial position. |
| Correction radii | ||
| Correction radius in plane A | mm | Radius for the correction mass in plane A. |
| Correction radius in plane B | mm | Radius for the correction mass in plane B. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Distance between correction planes A and B
- What it is
- The axial distance along the rotor between correction plane A and correction plane B, the two planes where correction masses will be fitted.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 400 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Choose planes where mass can actually be added or removed, such as the faces of a rotor or pulley.
Masses (axial position measured from plane A)
What this means: Mass 1
- What it is
- An unbalanced mass somewhere along the rotor, with its radius, angle and axial position given in the same row. Zero leaves the row out.
- Units and format
- Enter a number in g: grams. The form accepts 0 g to 10000000 g. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 40 g as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use only the eccentric mass; material symmetrical about the axis causes no unbalance.
What this means: Radius 1
- What it is
- The distance from the rotor axis to the centre of gravity of the matching mass.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Angle 1
- What it is
- The angular position of the matching mass, measured from one reference line on the rotor in a consistent direction.
- Units and format
- Enter a number in °: degrees of angle. The form accepts -360° to 360°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the same reference line and direction for every mass; the correction angles are reported on that basis.
What this means: Axial position 1
- What it is
- The distance along the axis from correction plane A to the plane of the matching mass, positive towards plane B and negative for a mass lying beyond plane A.
- Units and format
- Enter a number in mm: millimetres. The form accepts -100000 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Measure every position from plane A; a mass beyond plane B has a position greater than the distance between the planes.
What this means: Mass 2
- What it is
- An unbalanced mass somewhere along the rotor, with its radius, angle and axial position given in the same row. Zero leaves the row out.
- Units and format
- Enter a number in g: grams. The form accepts 0 g to 10000000 g. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 g as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Radius 2
- What it is
- The distance from the rotor axis to the centre of gravity of the matching mass.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Angle 2
- What it is
- The angular position of the matching mass, measured from one reference line on the rotor in a consistent direction.
- Units and format
- Enter a number in °: degrees of angle. The form accepts -360° to 360°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 120° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Axial position 2
- What it is
- The distance along the axis from correction plane A to the plane of the matching mass, positive towards plane B and negative for a mass lying beyond plane A.
- Units and format
- Enter a number in mm: millimetres. The form accepts -100000 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 300 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Mass 3
- What it is
- An unbalanced mass somewhere along the rotor, with its radius, angle and axial position given in the same row. Zero leaves the row out.
- Units and format
- Enter a number in g: grams. The form accepts 0 g to 10000000 g. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 g as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Radius 3
- What it is
- The distance from the rotor axis to the centre of gravity of the matching mass.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Angle 3
- What it is
- The angular position of the matching mass, measured from one reference line on the rotor in a consistent direction.
- Units and format
- Enter a number in °: degrees of angle. The form accepts -360° to 360°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Axial position 3
- What it is
- The distance along the axis from correction plane A to the plane of the matching mass, positive towards plane B and negative for a mass lying beyond plane A.
- Units and format
- Enter a number in mm: millimetres. The form accepts -100000 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Correction radii
What this means: Correction radius in plane A
- What it is
- The radius at which the centre of gravity of the correction mass in plane A will sit.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The plane A correction mass is inversely proportional to this radius.
What this means: Correction radius in plane B
- What it is
- The radius at which the centre of gravity of the correction mass in plane B will sit.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The plane B correction mass is inversely proportional to this radius.
Method and formulas
- Moments about plane A: U_B = −Σ (mᵢ rᵢ ∠θᵢ) zᵢ ÷ L.
- Forces: U_A = −Σ (mᵢ rᵢ ∠θᵢ) − U_B.
- Correction mass = |U| ÷ correction radius in each plane.
- Example: corrections of 27.042 g in plane A and 19.526 g in plane B.
Limitations
- Rigid rotor below its first critical speed.
- Measured unbalance from a balancing machine is more reliable than calculated item masses.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Work out corrections for a long rotor or roll
- Balance a fixture with offset masses at different heights
- Check bearing loads from couple unbalance
Who it is for
- Maintenance engineers
- Machine designers
- Balancing technicians
What you get
- Correction mass and angle in plane A
- Correction mass and angle in plane B
- Static and couple unbalance
Interpreting the result
- If the correction in one plane is tiny, a single-plane correction may be enough.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 191–195. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Balancing long rotors in two planes
In Whirling Shafts by the Numbers
What it covers: Why a long rotor needs corrections in two planes: resolving unbalances by moments, checking each plane against its grade, weighing hammer sets, and why a static balance left a couple behind.
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