How this calculation works
A power screw exchanges rotary motion for axial movement, but friction changes the torque needed to raise a load. This page calculates thread-only raising torque, mechanical efficiency and the signed lowering condition for an ideal square thread.
tanλ = lead/(πdm); Traise = Wdm(μ+tanλ)/[2(1−μtanλ)]; η = W lead/(2πTraise)A worked example
A 1000 N load with 20 mm mean diameter, 4 mm lead and friction coefficient 0.15 requires about 2.1572 N m of raising torque. Ideal useful work per turn is four joules. The resulting efficiency is about 29.51 percent.
Good to know
The model assumes square thread geometry and constant Coulomb friction. It does not include collar torque, buckling, thread strength, lubrication change or back-driving protection. A theoretical self-locking result is not a safety device specification.
Reference: Penn State — power screw mechanics (opens in a new tab) ↗
What this model answers
A power screw exchanges rotary motion for axial movement, but friction changes the torque needed to raise a load.
This page calculates thread-only raising torque, mechanical efficiency and the signed lowering condition for an ideal square thread.
The Lead screw speed and command pulse calculator converts lead and rotation into travel. Raising torque additionally requires axial load and thread friction.
Keep the input conventions consistent
Lead is axial travel per revolution, which equals pitch multiplied by thread starts.
Use mean thread diameter, not the outside diameter by default. The friction coefficient applies to the thread contact; collar and thrust-bearing friction are deliberately absent.
Read the result carefully
The lowering result uses a sign convention: positive torque means effort is needed to lower, while a negative value means the load tends to overhaul and requires restraint.
The equality between friction coefficient and tangent of lead angle is the neutral theoretical boundary.
A screw can require positive lifting torque while its lowering behavior depends on the friction and lead-angle relationship. Do not infer a holding device from efficiency alone. The ideal square-thread comparison omits collar friction and other losses that may materially change torque in an assembled mechanism.
Work through the numbers
A 1000 N load with 20 mm mean diameter, 4 mm lead and friction coefficient 0.15 requires about 2.1572 N m of raising torque.
Ideal useful work per turn is four joules. The resulting efficiency is about 29.51 percent.
Where the calculation stops
The model assumes square thread geometry and constant Coulomb friction.
It does not include collar torque, buckling, thread strength, lubrication change or back-driving protection. A theoretical self-locking result is not a safety device specification.
A few questions, answered
Can I substitute a metric V thread without adjustment?
No. Thread flank geometry changes the effective friction relationship; this page implements a square thread only.
What should I change in the comparison?
Remove thread friction to inspect the ideal one-hundred-percent efficiency limit.