KEVOS® 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. |
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.
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