KEVOS® MAKEOS · Mechanics
Composite Rotor Inertia and Energy (Up to Three Shapes, Offsets, Stored and Released Energy)
For a rotor built up from rings, tori, cones, shells or tubes, what is its total moment of inertia, how much energy does it store at speed, and is the energy given up for my allowed slow-down enough for the duty?
Inertia and energy of a rotating assembly of up to three bodies: the moment of inertia of each body about its own axis or a diameter, moved to the rotation axis by its offset (as the more mass moments of inertia tool), the total inertia and radius of gyration, the kinetic energy at speed and the energy released for the allowed speed drop, against the energy each cycle of the duty needs.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Body 1 | ||
| Body and axis | choice | Shape of body 1 and the axis its inertia is taken about. |
| Mass (0 = unused) | kg | Mass of body 1 (0 to leave it out). |
| Dimension A | mm | Dimension A of body 1 (see the shape). |
| Dimension B | mm | Dimension B of body 1. |
| Dimension C | mm | Dimension C of body 1. |
| Offset of its axis from the rotation axis | mm | Distance between body 1’s axis and the rotation axis (parallel axis). |
| Body 2 | ||
| Body and axis | choice | Shape of body 2. |
| Mass (0 = unused) | kg | Mass of body 2. |
| Dimension A | mm | Dimension A of body 2. |
| Dimension B | mm | Dimension B of body 2. |
| Dimension C | mm | Dimension C of body 2. |
| Offset of its axis from the rotation axis | mm | Offset of body 2. |
| Body 3 | ||
| Body and axis | choice | Shape of body 3. |
| Mass (0 = unused) | kg | Mass of body 3. |
| Dimension A | mm | Dimension A of body 3. |
| Dimension B | mm | Dimension B of body 3. |
| Dimension C | mm | Dimension C of body 3. |
| Offset of its axis from the rotation axis | mm | Offset of body 3. |
| Duty | ||
| Speed | rpm | Running speed. |
| Allowed speed drop | % | How far the rotor may slow while giving up energy. |
| Energy needed per cycle | J | Energy the duty takes from the rotor each cycle. |
Method and formulas
- Inertia of each shape about its axis (as the more mass moments of inertia tool), plus m × offset² (parallel axis).
- Total J and radius of gyration √(J ÷ m).
- Stored energy = ½ J ω²; released for a drop from ω₁ to ω₂ = ½ J (ω₁² − ω₂²).
- Example: J = 0.42263 kg·m² stores 5,213.9 J and gives up 990.65 J for a 10% drop.
Limitations
- Rigid bodies of uniform density; hubs, spokes and bolts add inertia not counted.
- Energy drawn faster than the motor can replace it.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Find the inertia of a built-up flywheel or rotor
- Check a rotor stores enough energy for a punch or shear
- Size a motor start from the total inertia
Who it is for
- Design engineers
- Machine designers
- Engineering students
What you get
- Inertia of each body and in total
- Stored energy and energy released
- Against the duty
Interpreting the result
- Mass at large radius dominates: a thin rim or torus gives far more inertia per kilogram than a solid disc.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 228–240, 182–186. Topic reference; no source tables or recommended settings are reproduced.
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