Drive torque
-Motor speed
-Critical speed
-L10 life
-All results
| Back-driving holding torque | - |
| Mechanical power at screw | - |
| Speed as fraction of critical speed | - |
| Euler buckling load | - |
| Buckling safety factor | - |
| L10 life in revolutions | - |
Method and formulas
Standard ball screw sizing relations. Steel screw: E = 206 GPa, density 7850 kg/m³.
| Quantity | Formula |
|---|---|
| Drive torque | T = F l / (2π η) |
| Back-driving torque | Tb = F l η / (2π) |
| Screw speed | n = 60 v / l |
| Power | P = F v / η |
| Critical speed | nc = (60 / 2π) (λ2 / L2) (d / 4) √(E / ρ), λ = 1.875, 3.142, 3.927, 4.730 |
| Buckling load | Pcr = π2 E I / (K L)2, I = π d4 / 64, K = 2, 1, 0.7, 0.5 |
| Life | L10 = (C / F)3 × 106 rev |
US inputs are converted to metric: 1 lbf = 4.44822 N, 1 in = 25.4 mm. Fixity order is fixed-free, simple-simple, fixed-simple, fixed-fixed.
Worked example: 5 kN on a 10 mm lead screw
With F = 5000 N, l = 10 mm, η = 0.9, v = 200 mm/s, d = 28 mm, L = 800 mm (fixed-simple) and C = 25 kN: T = 8.842 N·m, n = 1200 rpm, P = 1111 W, nc = 8251 rpm, Pcr = 195.6 kN and L10 = 125.00 million revolutions (1250.0 km of travel).
Questions
How do you calculate ball screw drive torque?
Driving torque is T = F l / (2 pi eta), where F is the axial load, l the lead and eta the screw efficiency, typically 0.85 to 0.95 for a ball screw. Add preload drag torque and bearing friction for a complete motor sizing.
Can a ball screw be back-driven?
Yes. Ball screws have low friction, so an axial load can turn the screw. The holding torque needed to stop back-driving is about T = F l eta / (2 pi). Use a brake or a self-locking drive on vertical axes.
What is ball screw critical speed?
The rotational speed at which the screw shaft whirls in its first bending mode. It depends on root diameter, unsupported length and end fixity. Keep operating speed below about 80 percent of the critical speed.
How is the buckling load found?
Euler buckling: P_cr = pi squared E I / (K L) squared, with I = pi d^4 / 64 on the root diameter. Compare the compressive load with P_cr divided by a safety factor of 3 or more.
How is ball screw life calculated?
Basic rating life in revolutions is L10 = (C / F)^3 x 10^6, where C is the basic dynamic load rating from the manufacturer and F the equivalent axial load. Travel life is revolutions times lead.
What does this calculator not cover?
Preload, varying load cycles (use an equivalent load), thermal growth, stiffness and backlash, nut and bearing support ratings, and manufacturer-specific correction factors. Confirm with the manufacturer's sizing tool.
Engineering aid for guidance. Ignores preload, load cycles, thermal growth and support bearing ratings. Verify critical designs with the screw manufacturer's data and applicable standards.