KEVOS® MAKEOS · Mechanics
Torsional Natural Frequency of a Drive
At what frequency will this motor-and-load drive resonate in torsion, and is that safely above the control bandwidth?
Torsional stiffness of a connecting shaft and the torsional natural frequency of a single inertia on a shaft or of a motor and load joined by a shaft, compared with the servo or control bandwidth.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| System | choice | Two inertias on a free shaft, or one inertia on a shaft fixed at the other end. |
| Stiffness | choice | Calculate the stiffness from a plain shaft or enter it (couplings and gearboxes in series reduce it). |
| Torsional stiffness (entered) | N·m/rad | Overall torsional stiffness between the inertias. |
| Shear modulus | GPa | Shear modulus of the shaft. |
| Shaft outside diameter | mm | Outside diameter. |
| Shaft bore (0 = solid) | mm | Bore diameter for a hollow shaft. |
| Shaft length | mm | Twisting length of the shaft. |
| Motor inertia | kg·m² | Motor rotor inertia. |
| Load inertia | kg·m² | Load inertia referred to the same shaft. |
| Control bandwidth | Hz | Closed-loop bandwidth of the drive or controller. |
Method and formulas
- Shaft stiffness K = G J_p ÷ L, with J_p = π (d⁴ − dᵢ⁴) ÷ 32.
- Single inertia: f_n = (1 ÷ 2π) √(K ÷ J_L), as in the handbook.
- Two inertias: f_n = (1 ÷ 2π) √[K (J₁ + J₂) ÷ (J₁ J₂)].
- Example: the drive resonates at 181.15 Hz against a 50 Hz bandwidth.
Limitations
- Lumped inertias on a massless shaft; first mode only.
- Couplings, keys and gear mesh add compliance and lower the frequency.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a servo axis for torsional resonance
- Choose a coupling or shaft stiff enough for the bandwidth
- Diagnose oscillation in a motion axis
Who it is for
- Automation engineers
- Servo and controls engineers
- Machine designers
What you get
- Torsional stiffness
- Natural frequency
- Ratio to the control bandwidth
Interpreting the result
- If the resonance falls within the control bandwidth, stiffen the drive or add a notch filter.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 3412–3413. Topic reference; no source tables or recommended settings are reproduced.
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