Pick the screw, lead, load and speed. Get the motor torque, linear speed, efficiency, whether it holds the load by itself, the critical speed and buckling limit, and steps per millimetre for a stepper.
Screw type
Standard size
Ø mm
lead mm
μ
Steel screw, bronze nut, greased: 0.10 – 0.15. Plastic (POM) nut: 0.08 – 0.12. Dry: up to 0.2.
N
RPM
mm
End bearings
steps
×
Screw turns, nut travels
How it is calculated
Ph is the lead (travel per turn = pitch × starts), d₂ the pitch or ball-circle diameter, dr the root diameter, F the axial load, μ the friction. Critical speed and buckling use the common catalogue formulas with their usual safety factors (0.8 on speed, 0.5 on load) already included.
Lead angle λ = atan(Ph / (π · d₂))
Friction angle ρ' = atan(μ / cos(α/2)) α = 30° trapezoidal, 29° ACME, ball ≈ 0.005
Efficiency η = tan λ / tan(λ + ρ') turning the screw to push the load
Back-drive η' = tan(λ − ρ') / tan λ the load turns the screw; self-locking if λ ≤ ρ'
Drive torque T = F · Ph / (2π · η) (N·mm)
Linear speed v = n · Ph (mm/min)
Critical speed n_c = f · dr / L² · 10⁷ f: 3.4 fixed–free, 9.7 supported–supported, 15.1 fixed–supported, 21.9 fixed–fixed
Buckling load P_k = m · dr⁴ / L² · 10⁴ m: 1.3, 5.1, 10.2, 20.3 for the same four cases
Steps per mm = steps per rev · microsteps / Ph
Trapezoidal sizes follow ISO 2904 (Tr d × P), ACME follows ASME B1.5. Ball screw root diameters are estimated; use the maker's catalogue for the final check, and also check the DN value (d · n) against the maker's limit, usually 50 000 – 70 000 for ball screws.