KEVOS® MAKEOS · Gears
Helical Gear Helix Angle and Leads for a Fixed Centre Distance
My helical gear pair must fit a centre distance that is not the standard spur centre distance for the module and tooth numbers. What helix angle makes it fit, and what are the transverse module, pitch diameters and leads of the pinion and gear for setting up the cut?
Helix angle of a parallel-shaft helical gear pair chosen to fit a given centre distance, by the relation the handbook gives for normal diametral pitch (cos ψ = (N₁ + N₂) ÷ (2 P_n C)), in metric form cos ψ = m_n (z₁ + z₂) ÷ (2 a), with the leads L = π z m_n ÷ sin ψ, the transverse module and pitch diameters that add up to twice the centre distance, and the helix angle at the outside diameter from tan ψ = 2π R ÷ L, checked against the range of helix angles you accept.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Normal module | mm | Normal module of the cutter or hob (25.4 ÷ normal diametral pitch). |
| Teeth on the pinion | teeth | Number of teeth on the pinion. |
| Teeth on the gear | teeth | Number of teeth on the gear. |
| Centre distance | mm | Centre distance the pair must fit, measured between the shaft axes. |
| Accepted helix angles | ||
| Least helix angle you accept | ° | Smallest helix angle your design accepts, for example to keep enough overlap. |
| Largest helix angle you accept | ° | Largest helix angle your design accepts, for example from the thrust the bearings take or the cutter set-up. |
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: Normal module
- What it is
- Normal module of the cutter or hob used for both gears of the pair.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100 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
- Larger modules need a larger centre distance for the same helix angle.
- Get it right
- For inch cutters the normal module is 25.4 divided by the normal diametral pitch.
What this means: Teeth on the pinion
- What it is
- Number of teeth on the pinion, the smaller gear of the pair.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 5 teeth to 1000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 18 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More teeth reduce the helix angle at a fixed centre distance.
- Get it right
- Choose it with the gear teeth for the ratio wanted.
What this means: Teeth on the gear
- What it is
- Number of teeth on the gear, the larger gear of the pair.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 5 teeth to 5000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More teeth reduce the helix angle at a fixed centre distance.
- Get it right
- Choose it with the pinion teeth for the ratio wanted.
What this means: Centre distance
- What it is
- Centre distance the pair must fit, between the two shaft axes.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 110 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 centre distance needs a larger helix angle.
- Get it right
- Measure the housing bores or take it from the casing drawing.
Accepted helix angles
What this means: Least helix angle you accept
- What it is
- Smallest helix angle your design accepts for the pair.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0° to 89°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only moves the range check.
- Get it right
- Set it from the overlap you need for smooth running.
What this means: Largest helix angle you accept
- What it is
- Largest helix angle your design accepts for the pair.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0.1° to 89°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 45° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only moves the range check.
- Get it right
- Set it from the end thrust the bearings take or the swivel of the milling table.
Method and formulas
- cos ψ = m_n (z₁ + z₂) ÷ (2 C) — the handbook’s cos ψ = (N₁ + N₂) ÷ (2 P_n C) with P_n = 25.4 ÷ m_n.
- Transverse module m_t = m_n ÷ cos ψ; pitch diameters d = z m_t (they add up to 2C).
- Leads L₁ = π z₁ m_n ÷ sin ψ and L₂ = π z₂ m_n ÷ sin ψ (= 2π R ÷ tan ψ).
- Helix angle at the outside diameter tan ψ_a = π d_a ÷ L, with d_a = d + 2 m_n for a standard addendum.
- Example: 18 and 30 teeth of 4 mm normal module on 110 mm centres need a helix angle of 29.223°; the leads are 463.32 mm and 772.19 mm.
Limitations
- Standard (unshifted) teeth are assumed; profile shift is another way to fit a centre distance and is in the profile shift tool.
- The outside diameters assume a standard addendum equal to the normal module.
- The two gears of a parallel-shaft pair have the same helix angle and opposite hands.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Fit a helical gear pair to an existing centre distance
- Find the leads for setting up a milling machine or hobber
- Check the helix angle against what the cutter or thrust bearings allow
Who it is for
- Gear designers
- Machinists
- Gearbox repairers
What you get
- Helix angle that fits the centre distance
- Transverse module and pitch diameters
- Lead of the pinion and of the gear
- Helix angle at the outside diameters
- Check against the accepted range
Interpreting the result
- A centre distance only slightly larger than the spur centre distance gives a small helix angle with little overlap; a much larger one gives a steep helix and high end thrust.
- Set the milling machine table to the helix angle and the lead from the change gears; the helix angle at the outside diameter is larger than at the pitch diameter.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2078. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These KEVOS® Library readings explain the method this tool uses, with worked examples.
Useful alongside · KEVOS® original book
Helical gears and axial thrust
What it covers: Convert between normal and transverse module, size a helical pair to a centre distance, and calculate the axial thrust and face overlap the helix creates.
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Open the Helical Gear Helix Angle and Leads for a Fixed Centre Distance calculator