BIZOMAT 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. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Nominal major diameter
- What it is
- The nominal (major) diameter of the trapezoidal screw thread, measured over the thread crests; the first number in a designation such as Tr 32 × 6.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 2000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Pitch
- What it is
- The axial distance from one thread crest to the next, the second number in the thread designation (Tr 32 × 6 has a pitch of 6 mm).
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 50 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- For a multi-start thread enter the pitch, not the lead; the tool works out lead = starts × pitch.
What this means: Number of starts
- What it is
- The number of separate thread helices on the screw; more starts give a longer lead, and faster travel, for the same pitch.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 12. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More starts raise the lead and the efficiency, and can make the screw back-drive under load.
What this means: Axial load
- What it is
- The axial load the screw lifts, pushes or holds, acting along the screw axis through the nut.
- Units and format
- Enter a number in N: newtons. The form accepts 0.000001 N or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10000 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Torques, root stress and nut pressure are all proportional to the load.
What this means: Thread friction coefficient
- What it is
- The friction coefficient between the screw and nut thread flanks, which depends on the materials and lubrication; take it from test data or a design reference.
- Units and format
- Enter a plain number with no unit. The form accepts 0 to 1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.12 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Higher friction raises the raising torque, lowers efficiency and makes self-locking more likely.
What this means: Mean collar diameter (0 = thrust bearing)
- What it is
- The mean diameter of the sliding thrust collar face that carries the axial load; zero when a rolling thrust bearing takes it.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter 0 for a rolling thrust bearing; collar friction then drops out of both torques.
What this means: Collar friction coefficient
- What it is
- The friction coefficient at the sliding thrust collar face, used for the collar torque; ignored when the collar diameter is zero.
- Units and format
- Enter a plain number with no unit. The form accepts 0 to 1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.12 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Nut and limits
What this means: Nut length
- What it is
- The length of nut thread engaged with the screw; the tool divides it by the pitch to count the threads sharing the load.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 40 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A longer nut spreads the load over more threads and lowers the bearing pressure in proportion.
What this means: Allowable nut bearing pressure
- What it is
- The highest bearing pressure the nut thread flanks may carry for the nut material, lubrication and sliding speed, from the nut maker or a design reference.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 1000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Allowable screw root stress
- What it is
- The highest direct (tension or compression) stress you allow on the screw’s root section, from your design code or material data.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 5000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- This is checked as direct stress on the root area only; torsion and buckling of long screws are not included.
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.
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Open the Trapezoidal Lead Screw Check (Thread Size, Torque, Root Stress, Nut Pressure) calculator