Inputs
Example data table
| Scenario | Drive | Speed | Gear | Mass | Key input | Typical result |
|---|---|---|---|---|---|---|
| Indexing table | Rotary | 60 rpm | 5:1 | 5 kg | Jload 1.0e-4 kg·m² | Peak torque rises during acceleration |
| Belt axis | Belt | 200 mm/s | 1:1 | 8 kg | Radius 20 mm, μ 0.1 | RMS torque depends on dwell holding |
| Slide with screw | Lead screw | 150 mm/s | 2:1 | 10 kg | Lead 5 mm/rev, 40% eff | Torque increases strongly with low screw efficiency |
Formula used
- Angular speed: ω = rpm · 2π / 60
- Motor speed with reduction: ωm = ωL · N
- Reflected inertia: Jref = JL / N²
- Total motor-side inertia: JT = Jm + Jref
- Acceleration torque: Tacc = JT · α, with α = ωm/tacc
- Load torque at motor: Tload,m = Tload,L / (N · η)
- Belt torque from force: Tload,L = F · r
- Screw torque from force: Tload,L = F · lead / (2π · ηs)
- RMS torque: TRMS = √(Σ(T²·t)/Σt)
- Recommended torque: Trec = safety · T
How to use this calculator
- Select a drive type that matches your mechanism.
- Enter gear ratio and efficiency for your transmission.
- Fill in the motion profile: speed and timing segments.
- Provide mass, incline, friction, and any external force.
- Add pulley radius or lead screw parameters if needed.
- Enter motor inertia and load inertia, or estimate it.
- Click Calculate torque to view RMS and peak results.
- Download CSV or PDF for documentation and sharing.
FAQs
1) What is the difference between RMS and peak torque?
Peak torque is the highest momentary requirement, usually during acceleration or braking. RMS torque is the heating-equivalent average over the whole cycle. Size continuous capability from RMS, and check peak capability against the maximum value.
2) Why does low efficiency increase required torque?
Losses convert some motor power into heat in gears, belts, or screws. The motor must supply extra torque so the load still receives the needed torque. A small drop in efficiency can produce a noticeable torque increase.
3) How should I choose a safety factor?
Use a factor that covers uncertainty in friction, payload variation, and modeling error. Many designs start near 1.3. Increase it for harsh environments, wear, or unknown duty cycles, and reduce it only with verified measurements.
4) What does inertia ratio mean for servo sizing?
It compares reflected load inertia to motor inertia. High ratios can reduce responsiveness, increase settling time, and stress the control loop. More reduction, a stiffer mechanism, or a larger motor inertia can improve stability.
5) When should I use belt versus lead screw calculations?
Use belt when linear motion is produced by a pulley radius. Use lead screw when translation is produced by screw lead. Screw efficiency matters a lot, especially for sliding screws, so include a realistic value for accurate torque estimates.
6) Does this include gravity for vertical axes?
Yes. Set the incline angle to 90 degrees for upward motion against gravity. If your axis can be back-driven, consider holding torque during dwell. If you use a brake or counterbalance, adjust the model accordingly.
7) Why can the deceleration torque be negative?
During braking, the required inertia torque reverses direction. The motor may need to absorb energy, often through regeneration or a resistor. Peak value is taken by magnitude, because the amplifier must handle both motoring and braking demands.
8) What inputs most strongly affect the torque result?
Acceleration time, gear ratio, efficiency, and reflected inertia are usually dominant. For linear axes, mass and incline angle add large steady forces. For screws, efficiency and lead are critical. Use measured friction when possible for best accuracy.