Lead Screw Torque, Efficiency & Self-Locking Calculator

How Flank Angle α Impacts Torque Across Buttress (7°), Acme (29°), and Trapezoidal (30°) Screws

When unwrapping one helix revolution of a power screw into a right-angled inclined plane of base π dm and vertical rise equal to the lead L = n · P, the normal force on a sloped thread flank increases by 1 / cos α, where α is the load-bearing flank half-angle. As documented in Machinery's Handbook (31st Ed., Industrial Press) and Shigley's mechanical design equations, this wedges the thread slightly into the nut, raising the effective coefficient of friction to μ′ = μ / cos α:
• Square Thread (α = 0°): cos 0° = 1.0000 (highest efficiency, difficult to machine or compensate for wear).
• ASME B1.9 7°/45° Buttress Thread (α = 7.0°): cos 7° = 0.9925 (μ′ = 1.0075μ — matches square-thread efficiency while retaining the root shear strength of a wide trapezoidal base for unidirectional hydraulic presses and vise screws).
• ASME B1.5 29° Acme Thread (α = 14.5°): cos 14.5° = 0.9681 (μ′ = 1.0329μ — easy to cut with split nuts on lathe leadscrews).
• DIN 103 30° Metric Trapezoidal Thread (α = 15.0°): cos 15° = 0.9659 (μ′ = 1.0353μ).

When Is a Leadscrew Self-Locking vs. Overhauling (Back-Driving)?

A power screw is statically self-locking when the thread friction angle φ′ = arctan(μ / cos α) exceeds the helix lead angle λ = arctan(L / (π dm)). Equivalently, when μ / cos α > tan λ, the thread lowering torque TL,thread = (F dm / 2)(μ′ − tan λ) / (1 + μ′ tan λ) is positive, meaning you must apply positive torque to lower the load. The calculator's status uses the net lowering torque (thread plus collar), so a thrust collar can hold a load that the thread alone would overhaul. Because self-locking requires φ′ > λ, the theoretical thread efficiency of any self-locking screw can never exceed 50% (and typically sits between 20% and 38%). With μ = 0.15 on this Tr 24×5 screw, n = 2 reaches about 48%, n = 3 about 57% and n = 4 about 63% thread efficiency. The n = 2 screw is still self-locking, with a margin of only 0.41° (φ′ = 8.83° > λ = 8.42°).

At n = 3 (λ = 12.52°) the thread alone overhauls: its lowering torque is TL,thread = −5.55 N·m, so the load back-drives. With a plain thrust collar (μc = 0.08, dc = 36 mm, 8 kN) the collar adds +11.52 N·m of resistance and the net lowering torque becomes +5.97 N·m, so the screw holds only via collar friction (HOLDS ONLY VIA COLLAR — BRAKE REQUIRED). That hold depends on collar friction, which changes with wear and lubrication, so it is not a reliable brake. At n = 4 the net lowering torque is −0.06 N·m (NO HOLD WITHOUT BRAKE) and the screw back-drives. Fit a motor holding brake whenever the load must stay in place.

Worked Examples: Single-Start Tr 24×5 Lifting Jack vs. 4-Start Fast Actuator

Worked Example 1 (Tr 24×5 vs Buttress 24×5 at 8 kN): For a single-start Tr 24 × 5 screw (dm = 21.5 mm, λ = 4.23°) with greased bronze nut (μ = 0.15) and plain thrust washer (μc = 0.08, dc = 36 mm), the engine computes thread torque 19.95 N·m plus collar torque 11.52 N·m for a total raise torque of 31.47 N·m (ηth = 31.9%, ηtot = 20.2%). Switching to a 7° load-flank Buttress profile lowers raise torque to 31.10 N·m.

Worked Example 2 (4-Start High-Lead Tr 24×20P5 Actuator with Rolling Thrust Bearing): Increasing to 4 starts (Lead L = 20.0 mm, λ = 16.49°) with a PTFE nut (μ = 0.10, φ′ = 5.91°) and ball thrust bearing (μc = 0.02) boosts thread efficiency to 71.8% (total 66.4%) at TR = 38.34 N·m, but because λ (16.49°) > φ′ (5.91°), the lowering torque is negative (-13.19 N·m)—the actuator back-drives! Verify root torsional stress in the shaft torsional shear stress calculator.

Trapezoidal metric screws follow ISO 2904 for dimensions and ISO 2903 for tolerances (International Organization for Standardization (ISO)), inch Acme profiles follow ASME Codes & Standards, and unit conversions follow NIST Special Publication 811. The friction coefficient μ moves the raise torque, the lowering torque and the self-locking status more than any other input, and the typical values in Table 2 have no cited source. Measure the torque on the actual nut and collar before you choose a holding brake or a self-locking margin.

Check the thrust collar as a separate element. Its torque is set by the collar friction μ_c and the mean collar diameter d_c, and it changes with wear and lubrication, so a collar that holds the load today may not hold it after a few cycles. Treat collar friction as a convenience, not as the brake.

Next step: Look up thread pitch diameters and 3-wire readings in the 29° Acme calculator, DIN 103 trapezoidal calculator, and 7°/45° Buttress thread calculator.