BIZOMAT MAKEOS · Threads
Thread Helix Angle and Screw Efficiency
What is the helix angle of this thread, how efficient is it, and will it self-lock?
Lead, helix (lead) angle, efficiency raising a load and self-locking check for a power or fastening screw with a given flank angle and friction coefficient.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Pitch diameter | mm | Pitch (mean) diameter of the thread. |
| Pitch | mm | Pitch: axial distance between adjacent threads. |
| Number of starts | starts | Number of starts; lead = starts × pitch. |
| Thread form | choice | Thread profile; the half-angle is used for the friction wedge effect. |
| Coefficient of friction | Thread friction coefficient for the materials and lubrication (about 0.1–0.2 for lubricated steel on bronze). |
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: Pitch diameter
- What it is
- The pitch (mean) diameter of the screw thread, roughly midway between the major and minor diameters, where the helix angle is measured.
- 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 20 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger pitch diameter lowers the helix angle, which usually lowers efficiency and makes self-locking more likely.
- Get it right
- Use the pitch diameter, not the outside diameter of the screw.
What this means: Pitch
- What it is
- The axial distance between adjacent thread crests. With the number of starts it gives the lead.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 200 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.
- Effect on the result
- A longer pitch raises the lead and helix angle.
- Get it right
- On a multi-start screw the pitch is not the lead; enter the crest-to-crest distance.
What this means: Number of starts
- What it is
- The number of separate thread helices on the screw. Lead, the travel per turn, equals starts times pitch.
- Units and format
- Enter a number in starts: a number of thread starts. The form accepts 1 starts to 20 starts. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 starts 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 helix angle, which usually raises efficiency and makes self-locking less likely.
- Get it right
- Count the thread ends visible at the end of the screw.
What this means: Thread form
- What it is
- The thread profile, which sets the flank half-angle used for the friction wedge effect: square, Acme, trapezoidal or V.
- Units and format
- Choose one of 4 options from the list: Square (0° flank); Acme (29° included); Trapezoidal (30° included); V-thread (60° included).
- Example
- The form opens with “Acme (29° included)” selected as a worked example. Choose the option that matches your case.
- Get it right
- The options list the included angle; the tool uses half of it.
What this means: Coefficient of friction
- What it is
- The coefficient of friction between the screw and nut threads for the materials and lubrication in service, from supplier data or tests.
- 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 0.15 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Higher friction lowers efficiency and makes the screw more likely to self-lock.
- Get it right
- Friction at start-up is higher than when running; use the condition you are checking.
Method and formulas
- Lead L = starts × P; tan λ = L ÷ π d₂.
- Normal flank angle αₙ = atan(tan α cos λ).
- Efficiency η = tan λ (cos αₙ − μ tan λ) ÷ (cos αₙ tan λ + μ).
- Self-locking when μ ≥ cos αₙ tan λ.
- Example: 20 mm pitch diameter with 4 mm pitch has a 3.6426° helix angle and 28.838% efficiency.
Limitations
- Collar or thrust-bearing friction is not included and lowers overall efficiency.
- Vibration can back-drive a nominally self-locking screw.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check whether a jack or lead screw will back-drive
- Compare single and multi-start screws
- Find the helix angle for tool clearance
Who it is for
- Design engineers
- Maintenance engineers
- Automation engineers
What you get
- Lead and helix angle
- Efficiency raising a load
- Self-locking or back-driving
Interpreting the result
- If the screw must hold a load safely, use a brake; do not rely on self-locking under vibration.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 1921–1928, 2061–2062. Topic reference; no source tables or recommended settings are reproduced.
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