BIZOMAT MAKEOS · Mechanics
Counterbalancing Masses in One Plane
What counterweight, at what angle, balances these masses rotating in one plane?
Resultant unbalance of up to four masses at given radii and angles in a single plane of rotation, the counterweight mass and angle at a chosen radius that balances them, and the unbalance force at speed before correction.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Masses (mass 0 = unused) | ||
| Mass 1 | g | Mass of the first unbalanced item. |
| Radius 1 | mm | Radius of its centre of gravity from the axis. |
| Angle 1 | ° | Angular position measured from a reference line. |
| Mass 2 | g | Second mass. |
| Radius 2 | mm | Its radius. |
| Angle 2 | ° | Its angle. |
| Mass 3 | g | Third mass. |
| Radius 3 | mm | Its radius. |
| Angle 3 | ° | Its angle. |
| Mass 4 | g | Fourth mass (0 if unused). |
| Radius 4 | mm | Its radius. |
| Angle 4 | ° | Its angle. |
| Correction | ||
| Counterweight radius | mm | Radius at which the counterweight’s centre of gravity will sit. |
| Running speed | rpm | Speed for the unbalance force before correction. |
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.
Masses (mass 0 = unused)
What this means: Mass 1
- What it is
- An unbalanced mass on the rotor, such as a boss, keyway or attached part, whose centre of gravity lies at the radius and angle 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 50 g as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Its unbalance is mass × radius, so it rises in proportion to the mass.
- Get it right
- Use only the eccentric mass; material that is symmetrical about the axis causes no unbalance.
What this means: Radius 1
- What it is
- The distance from the axis of rotation 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.
- Get it right
- Measure to the centre of gravity of the mass, not to its outer edge.
What this means: Angle 1
- What it is
- The angular position of the matching mass around the axis, 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
- Measure all angles from the same reference line and in the same direction; the counterweight angle is reported on the same basis.
What this means: Mass 2
- What it is
- An unbalanced mass on the rotor, such as a boss, keyway or attached part, whose centre of gravity lies at the radius and angle 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 axis of rotation 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 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 the matching mass around the axis, 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 90° 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 on the rotor, such as a boss, keyway or attached part, whose centre of gravity lies at the radius and angle 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 20 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 axis of rotation 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 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 the matching mass around the axis, 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 200° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Mass 4
- What it is
- An unbalanced mass on the rotor, such as a boss, keyway or attached part, whose centre of gravity lies at the radius and angle 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 4
- What it is
- The distance from the axis of rotation 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 4
- What it is
- The angular position of the matching mass around the axis, 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.
Correction
What this means: Counterweight radius
- What it is
- The radius at which the centre of gravity of the counterweight will sit; the counterweight mass is found for this radius and placed opposite the resultant unbalance.
- 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 counterweight mass is inversely proportional to its radius.
What this means: Running speed
- What it is
- The running speed used to show the force the existing unbalance produces before correction. It does not change the counterweight.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0 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
- The unbalance force rises with the square of speed.
Method and formulas
- Resultant unbalance U = Σ mᵢ rᵢ ∠θᵢ (vector sum of mass × radius).
- Counterweight: m_c = |U| ÷ r_c, placed 180° from the resultant.
- Unbalance force = |U| ω².
- Example: the three masses need 31.666 g at 100 mm, at 209.91°.
Limitations
- All masses in one plane; masses in different planes need two-plane balancing.
- Mass × radius uses each item’s own centre of gravity.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Balance a lathe fixture or faceplate set-up
- Find the counterweight for an offset rotating part
- Estimate bearing load from unbalance at speed
Who it is for
- Machinists
- Toolmakers
- Maintenance engineers
What you get
- Counterweight mass and angle
- Resultant unbalance
- Unbalance force at speed
Interpreting the result
- Check the result by static balancing on parallels or a balancing stand.
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
Unbalance and balancing in place
In Vibration Monitoring by the Numbers
What it covers: How unbalance makes a 1× vibration, the force on the bearings, balance quality grades, single-plane balancing with a trial weight and vectors, splitting a correction, and a trial weight left on.
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