Power-Screw Torque, Efficiency, and Self-Locking
The torque to raise or lower a load on a lead screw, and whether it self-locks.
Example
You enter
- Axial load F (lbf) 1000
- Mean thread diameter dm (in) 1
- Lead l = pitch x starts (in) 0.2
- Thread friction coefficient 0.15
- Collar friction coefficient 0.15
- Collar mean diameter dc (in, 0 = thrust bearing) 1.5
- Thread form acme
You get
- Torque to raise the load 222.9 in-lbf
- Torque to lower the load 157.7
- Efficiency 14.3
Details, formula, and sources
Shigley Ch. 8: T_raise = (F dm/2)(l + pi mu dm sec_a)/(pi dm - mu l sec_a) + F muc dc/2, T_lower with (pi mu dm sec_a - l)/(pi dm + mu l sec_a), sec_a = 1/cos of the thread half-angle (square 0, Acme 14.5, Unified 30 deg); efficiency = F l/(2 pi T_raise); self-locking when pi mu dm sec_a > l. 1,000 lbf on a 1 in mean-dia, 0.2 in lead Acme screw (mu 0.15, 1.5 in collar at 0.15) needs 223 in-lbf to raise, 158 to lower, runs 14.3% efficient, and self-locks - drop the collar for a thrust bearing and efficiency nearly doubles to 29%, a collar penalty thread geometry alone cannot show. Sizes a jack, clamp, vise, or lead-screw drive. Column buckling, thread stress, and wear are separate. A design aid; Shigley and the maker govern.
sec_a = 1/cos(alpha) (square 0, Acme 14.5, Unified 30 deg); T_raise = (F dm/2)(l + pi mu dm sec_a)/(pi dm - mu l sec_a) + F muc dc/2; T_lower with (pi mu dm sec_a - l)/(pi dm + mu l sec_a); efficiency = F l/(2 pi T_raise); self-locking if pi mu dm sec_a > l.
The power-screw raising and lowering torque with the thread half-angle correction and the collar-friction term (Shigley, Mechanical Engineering Design, Ch. 8 -- power screws), by name.
The power-screw torque equations are standard published machine-design results; the load, thread geometry, and friction coefficients are the user's inputs.
Estimate. AHJ and licensed professional govern.
Field names used by the API: axial_load_lbf, mean_diameter_in, lead_in, thread_friction, collar_friction, collar_diameter_in, thread_form, raise_torque_in_lbf, lower_torque_in_lbf, efficiency_pct
- Torque equations T_raise/T_lower with sec_a = 1/cos(thread half-angle) and the collar term F muc dc/2Shigley Ch. 8
- Self-locking self-locking when pi mu dm sec_a > l (positive lowering thread torque)Shigley Ch. 8
- Scope single screw; buckling, thread stress, and wear are separate; half-angle taken directlyscope of this tile