KEVOS® MAKEOS · Threads
Trapezoidal Lead Screw Check (Thread Size, Torque, Root Stress, Nut Pressure)
Is this trapezoidal lead screw and nut right for the load: what torque does it need, will it hold the load without backdriving, and are the root stress and nut bearing pressure acceptable?
Check of a metric trapezoidal lead screw and its nut: pitch and root diameters, lead and root area (as the Acme and trapezoidal thread tool), raising and lowering torque with collar friction, efficiency and self-locking (as the power screw torque tool), the direct stress at the root, and the bearing pressure on the nut flanks from the number of threads engaged, against your allowable stress and nut pressure.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Nominal major diameter | mm | Major (nominal) diameter of the trapezoidal thread. |
| Pitch | mm | Pitch of the thread. |
| Number of starts | Number of starts (lead = starts × pitch). | |
| Axial load | N | Axial load the screw lifts or holds. |
| Thread friction coefficient | Friction coefficient between screw and nut. | |
| Mean collar diameter (0 = thrust bearing) | mm | Mean diameter of the thrust collar; 0 if a rolling thrust bearing is used. |
| Collar friction coefficient | Friction coefficient at the collar. | |
| Nut and limits | ||
| Nut length | mm | Length of thread engagement in the nut. |
| Allowable nut bearing pressure | MPa | Allowable bearing pressure on the nut thread for the nut material and speed (bronze nuts are often 7–15 MPa for slow motion). |
| Allowable screw root stress | MPa | Allowable direct stress at the screw root. |
Method and formulas
- Pitch diameter d₂ = d − P ÷ 2; root diameter d₃ = d − 2(P ÷ 2 + clearance); lead = starts × P (as the Acme and trapezoidal thread tool).
- Raising torque = F d₂ ÷ 2 × (L + π μ d₂ sec 15°) ÷ (π d₂ − μ L sec 15°) + collar friction; self-locking if the lowering torque is positive (as the power screw torque tool).
- Root stress = F ÷ (π d₃² ÷ 4); nut pressure = F ÷ (π d₂ × P ÷ 2 × threads engaged).
- Example: lifting 10000 N needs 35.703 N·m (17.831% efficient); the root sees 52.996 MPa and the nut 8.8419 MPa.
Limitations
- Static or slow motion; wear rates at speed are governed by p × v of the nut.
- Buckling of long compression screws is not checked here.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size a lead screw for a jack, press or slide
- Choose the nut length for a bronze nut
- Check whether a screw will hold its load
Who it is for
- Design engineers
- Machine designers
- Maintenance engineers
What you get
- Pitch and root diameters, lead and root area
- Raising and lowering torque, efficiency, self-locking
- Root stress and nut bearing pressure
Interpreting the result
- A longer nut lowers the bearing pressure; a finer pitch raises self-locking margin but lowers efficiency.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 1921–1946. Topic reference; no source tables or recommended settings are reproduced.
WORKOS tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
Open the Trapezoidal Lead Screw Check (Thread Size, Torque, Root Stress, Nut Pressure) calculator
