Enter Design Inputs
Example Data Table
| Case | Load (N) | Lead (mm/rev) | Mean Dia (mm) | Screw μ | Collar Dia (mm) | Collar μ | Speed (rpm) |
|---|---|---|---|---|---|---|---|
| Compact axis | 6000 | 5 | 20 | 0.003 | 28 | 0.015 | 900 |
| General motion | 12000 | 10 | 32 | 0.004 | 45 | 0.020 | 1200 |
| High load lift | 24000 | 8 | 40 | 0.005 | 55 | 0.025 | 750 |
Formula Used
Lead angle: λ = arctan(Lead / (π × Mean Diameter))
Ideal lifting torque: Tideal = F × Lead / (2π)
Thread raising torque: Tthread = F × dm / 2 × ((μ + tanλ) / (1 − μtanλ))
Collar torque: Tcollar = F × μc × dc / 2
Total raising torque: Ttotal = Tthread + Tcollar
Overall efficiency: η = Tideal / Ttotal × 100
These equations estimate mechanical efficiency from helix geometry and friction. They are useful for actuator sizing, energy checks, and comparing alternate lead selections.
How to Use This Calculator
- Enter the axial load carried by the screw.
- Provide screw lead and mean diameter values.
- Enter screw and collar friction coefficients.
- Add rotational speed and travel distance if needed.
- Click Calculate Efficiency to show results above the form.
- Review torque, efficiency, power loss, travel speed, and backdrivability.
- Export the results using the CSV or PDF buttons.
Frequently Asked Questions
1. What does ball screw efficiency mean?
It shows how much input torque becomes useful linear work. Higher efficiency means lower friction losses, lower heat generation, and less drive power for the same load.
2. Why is collar friction included?
Support bearings, thrust collars, and adjacent surfaces can add meaningful torque loss. Including collar friction gives a more practical system estimate than thread friction alone.
3. Is this useful for motor sizing?
Yes. The total input torque and input power outputs help estimate motor requirements. You should still include acceleration, shock loading, safety margin, and duty-cycle thermal limits.
4. What friction coefficient should I use?
Use supplier data when possible. Ball screws usually have low rolling friction, while seals, preload, lubrication condition, and support bearings can raise the effective value.
5. What does backdrivable indicate?
It indicates whether the load can drive the screw in reverse. If lowering torque becomes negative at the thread, the screw is considered backdrivable under this simplified model.
6. Does lead affect efficiency?
Yes. A larger lead increases the lead angle, which often raises theoretical efficiency. However, it also changes speed, torque demand, positioning resolution, and potential backdriving behavior.
7. Can I use this for trapezoidal screws?
Only as a rough first estimate. Trapezoidal and Acme screws need flank-angle adjustments, higher sliding friction assumptions, and sometimes different formulas for accurate predictions.
8. Why do output and input power differ?
The difference is the estimated friction loss. That lost power appears mainly as heat in the thread contacts, support components, lubrication film, and surrounding hardware.