BIZOMAT MAKEOS · Mechanics
Single-Plane Balance Correction Check (Unbalance, Correction Mass, Residual, Grade)
From the known out-of-balance masses on this disc-shaped rotor, what correction mass do I add and where, and will the residual after rounding the mass and placing it be within the balance grade?
Single-plane balancing of a narrow rotor: the resultant unbalance and its angle from the known masses, the correction mass at your correction radius and its angle opposite, and the centrifugal force of the unbalance (as the plane balancing tool); the permissible residual unbalance for the rotor’s mass, speed and balance grade (as the balance grade tool); and the residual left when the correction mass is rounded to your weight steps and placed with an angle error.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Known unbalance masses (mass 0 = unused) | ||
| Mass 1 | g | Known unbalance mass 1 (or the trial-run equivalent). |
| Radius 1 | mm | Radius of mass 1. |
| Angle 1 | ° | Angle of mass 1. |
| Mass 2 | g | Mass 2. |
| Radius 2 | mm | Radius of mass 2. |
| Angle 2 | ° | Angle of mass 2. |
| Mass 3 | g | Mass 3. |
| Radius 3 | mm | Radius of mass 3. |
| Angle 3 | ° | Angle of mass 3. |
| Mass 4 | g | Mass 4 (0 if unused). |
| Radius 4 | mm | Radius of mass 4. |
| Angle 4 | ° | Angle of mass 4. |
| Correction | ||
| Correction radius | mm | Radius at which the correction mass is fitted. |
| Weight step available | g | Smallest step of the balance weights you have. |
| Angle placement error | ° | Likely error in placing the weight at the correct angle. |
| Rotor | ||
| Rotor mass | kg | Mass of the rotor. |
| Maximum service speed | rpm | Highest speed the rotor runs at. |
| Balance quality grade | choice | Balance quality grade required. |
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.
Known unbalance masses (mass 0 = unused)
What this means: Mass 1
- What it is
- A known unbalance mass on the rotor, or the equivalent mass found from a trial run, at the radius and angle given next to it.
- 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 50 g as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter 0 for an unused mass; the tool multiplies mass by radius, so a zero in either removes it.
What this means: Radius 1
- What it is
- The distance from the rotation axis to the centre of unbalance mass 1.
- 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 unbalance mass 1, measured from a reference mark on the rotor.
- 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
- Measure all angles from the same mark and in the same direction.
What this means: Mass 2
- What it is
- A known unbalance mass on the rotor, or the equivalent mass found from a trial run, at the radius and angle given next to it.
- 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.
- Get it right
- Enter 0 for an unused mass; the tool multiplies mass by radius, so a zero in either removes it.
What this means: Radius 2
- What it is
- The distance from the rotation axis to the centre of unbalance mass 2.
- 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 80 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 unbalance mass 2, measured from a reference mark on the rotor.
- 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 90° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Measure all angles from the same mark and in the same direction.
What this means: Mass 3
- What it is
- A known unbalance mass on the rotor, or the equivalent mass found from a trial run, at the radius and angle given next to it.
- 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 20 g as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter 0 for an unused mass; the tool multiplies mass by radius, so a zero in either removes it.
What this means: Radius 3
- What it is
- The distance from the rotation axis to the centre of unbalance mass 3.
- 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 120 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 unbalance mass 3, measured from a reference mark on the rotor.
- 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 200° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Measure all angles from the same mark and in the same direction.
What this means: Mass 4
- What it is
- A known unbalance mass on the rotor, or the equivalent mass found from a trial run, at the radius and angle given next to it.
- 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.
- Get it right
- Enter 0 for an unused mass; the tool multiplies mass by radius, so a zero in either removes it.
What this means: Radius 4
- What it is
- The distance from the rotation axis to the centre of unbalance mass 4.
- 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 4
- What it is
- The angular position of unbalance mass 4, measured from a reference mark on the rotor.
- 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
- Measure all angles from the same mark and in the same direction.
Correction
What this means: Correction radius
- What it is
- The radius from the rotation axis at which you will fit the correction weight.
- 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
- A larger correction radius needs a proportionally smaller correction mass.
What this means: Weight step available
- What it is
- The smallest increment of correction weight you can fit, such as the step between available washers or clip-on weights.
- Units and format
- Enter a number in g: grams. The form accepts 0.001 g to 100000 g. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 g as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The correction mass is rounded to this step, which adds to the residual unbalance.
What this means: Angle placement error
- What it is
- The likely error in fitting the correction weight at the calculated angle.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0° to 180°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger placement error leaves a larger residual unbalance.
Rotor
What this means: Rotor mass
- What it is
- The total mass of the rotor being balanced, used for the permissible residual unbalance.
- Units and format
- Enter a number in kg: kilograms. The form accepts 0.000001 kg to 1000000 kg. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Permissible residual unbalance rises in proportion to rotor mass.
What this means: Maximum service speed
- What it is
- The highest speed the rotor runs at in service, used for the unbalance force and the permissible residual.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0.000001 rpm to 1000000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1500 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Permissible residual unbalance falls in inverse proportion to speed.
What this means: Balance quality grade
- What it is
- The balance quality grade the rotor must meet, from the balance quality standard for the rotor type or from the customer specification.
- Units and format
- Choose one of 7 options from the list: G 0.4; G 1; G 2.5; G 6.3; G 16; G 40; G 100.
- Example
- The form opens with “G 6.3” selected as a worked example. Choose the option that matches your case.
Method and formulas
- Unbalance U = |Σ mᵢ rᵢ ∠aᵢ|; correction mass = U ÷ r_c at the opposite angle; force = U ω² (as the plane balancing tool).
- Permissible residual U_per = G × 1000 ÷ ω × rotor mass (g·mm) (as the balance grade tool).
- Residual = |U − m_rounded r_c ∠(angle error)| by the law of cosines.
- Example: add 32 g at 209.91° and 100 mm; the residual 116.02 g·mm is within 802.14 g·mm.
Limitations
- Single plane for narrow rotors; long rotors need two-plane balancing.
- Known masses or a trial-weight result; measurement error is not included.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Balance a fan, pulley or flywheel in one plane
- Check that the weights available can reach the grade
- Show the effect of placement error
Who it is for
- Maintenance technicians
- Vibration analysts
- Machinists
What you get
- Resultant unbalance and correction mass and angle
- Permissible residual for the grade
- Residual after rounding and placement error
Interpreting the result
- Angle error matters more than mass rounding: 10° error leaves about 17% of the original unbalance.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 191–196. Topic reference; no source tables or recommended settings are reproduced.
- ISO 21940-11:2016 Mechanical vibration — Rotor balancing — Part 11: Procedures and tolerances for rotors with rigid behaviour
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 in one plane
In Whirling Shafts by the Numbers
What it covers: Balancing a narrow rotor in one plane: adding unbalances as vectors, sizing and placing a correction weight, the residual left by weight steps and angle errors, and trial-weight field balancing.
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