WORKED SIZING EXAMPLE · 7 MIN READ
10 mm vs 20 mm ball-screw lead:
speed, torque and power
The short answer
At the same 666.7 mm/s peak linear speed, a 10 mm lead requires about 4,000 rpm and 0.254 N·m, while a 20 mm lead requires about 2,000 rpm and 0.507 N·m. In this first-pass model, peak axial force and peak power stay the same.
01 · INPUTS
Start with one motion task
The comparison changes only the screw lead. All other motion and calculation assumptions stay fixed so the effect of lead is visible.
The 1.5× factor is included in the displayed preliminary peak torque and power. Preload drag, seal drag, gearbox effects, and rotating-inertia torque are not included at this stage.
02 · MOTION PROFILE
Both leads must produce the same linear motion
With symmetric acceleration and deceleration, the requested acceleration time leaves a 0.4 s constant-speed segment. The peak linear speed is:
v = S / (T − tₐ) = 400 / (0.8 − 0.2) = 666.7 mm/sThe corresponding acceleration is 3.333 m/s². For this horizontal example, the peak axial force combines guide friction and acceleration force:
F = μmg + ma = 0.05 × 25 × 9.81 + 25 × 3.333 = 95.6 N03 · LEAD COMPARISON
Lead trades rotational speed for torque
Screw speed is inversely proportional to lead. The linear-load torque required to generate the same axial force is proportional to lead.
n = 60v / LM = FL / (2πη) × safety factor| Calculated result | 10 mm lead | 20 mm lead |
|---|---|---|
| Peak linear speed | 666.7 mm/s | 666.7 mm/s |
| Screw speed | 4,000 rpm | 2,000 rpm |
| Peak axial force | 95.6 N | 95.6 N |
| Preliminary peak torque | 0.254 N·m | 0.507 N·m |
| Preliminary peak power | 106 W | 106 W |
| Immediate observation | Lower torque, higher rpm | Lower rpm, higher torque |
The calculator flags 4,000 rpm for further review because it exceeds its basic 3,000 rpm screening threshold. That threshold is only an early warning: the actual permissible speed must be calculated from the candidate screw geometry, support arrangement, support span, and DN limit.
04 · POWER
Why the preliminary power estimate stays the same
Doubling lead halves screw rpm and doubles the corresponding linear-load torque. Because rotational power is proportional to torque multiplied by angular speed, those two changes offset each other in the simplified model.
P = Fv / η × safety factor ≈ 95.6 × 0.6667 / 0.90 × 1.5 = 106 WThis does not mean the same motor will perform identically with both leads. The motor torque–speed curve, reflected load inertia, screw inertia, coupling inertia, drive voltage, duty cycle, and efficiency at the operating point can change the final result.
05 · CATALOG REVIEW
Lead alone cannot determine the final choice
A useful comparison narrows the search; it does not select a finished assembly. Before choosing a screw and motor, verify these items using the actual supplier data.
Use thread root diameter, unsupported span, and end-support arrangement. Compare the operating rpm with the permissible value.
Check the candidate nut’s ball-center diameter and published DN limit. Use the lower limit from critical speed and DN.
Confirm that available peak and continuous torque cover the duty point at the required motor speed and drive voltage.
Include reflected moving mass, screw inertia, coupling inertia, motor rotor inertia, and any transmission components.
Check maximum compressive load, permissible tensile/compressive load, static rating, shock, and vibration conditions.
Use the candidate dynamic load rating, equivalent axial load, load factor, travel, dwell time, and target service life.
Compare both leads with your own inputs
The calculator runs locally in your browser and does not require an account.
06 · QUESTIONS
Common questions about screw lead
Does doubling lead always halve screw speed?
For the same linear speed, yes: screw rpm is inversely proportional to lead. A change in the requested motion profile will also change the required rpm.
Why does the 20 mm lead need more torque?
For the same axial force and efficiency, torque is proportional to lead. Doubling lead doubles the linear-load portion of the required torque.
Should I automatically choose the 20 mm lead?
No. It is the lower-speed option in this example, but the final choice still depends on critical speed, DN, motor torque at 2,000 rpm, inertia ratio, positioning requirements, life, stiffness, preload, and supplier limits.
REFERENCES
Primary engineering references
- Oriental Motor — Motor Sizing Calculations
- Thomson — Precision Metric Ball Screws, Engineering Guidelines
- THK — Permissible Rotational Speed
- THK — Studying the Service Life
This worked example is for preliminary sizing and education. It does not replace the candidate manufacturer’s catalog, application engineering review, complete duty-cycle analysis, or machine safety assessment.