BIZOMAT MAKEOS · Gears
Helical Gear Pair Geometry
What diameters, centre distance and contact ratios does this helical gear pair have?
Transverse module, pitch and tip diameters, centre distance, transverse pressure angle, virtual teeth, axial pitch and overlap ratio for a standard (unshifted) parallel-axis helical gear pair.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Normal module | mm | Normal module (the hob or cutter module). |
| Helix angle | ° | Helix angle at the pitch diameter (0 for spur gears). |
| Normal pressure angle | ° | Normal pressure angle (20° is standard). |
| Pinion teeth | teeth | Number of teeth on the pinion. |
| Gear teeth | teeth | Number of teeth on the gear. |
| Face width | mm | Face width in mesh. |
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
- The normal module: the module measured square to the tooth, equal to the module of the hob or cutter that cuts the gear.
- 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 3 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- All diameters and the centre distance scale in proportion.
- Get it right
- Do not enter the transverse module; the tool works it out from the normal module and helix angle.
What this means: Helix angle
- What it is
- The angle between the teeth and the gear axis at the pitch diameter. Both gears of an external pair have the same angle, of opposite hand.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0° to 45°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 15° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger helix angle increases the pitch diameters, centre distance and overlap ratio.
- Get it right
- 0 gives a spur gear pair, with no overlap ratio.
What this means: Normal pressure angle
- What it is
- The pressure angle of the tooth profile measured in the normal plane, set by the cutting tool.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 10° to 30°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the angle of the hob or rack cutter on the drawing.
What this means: Pinion teeth
- What it is
- The 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 20 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Raises the pinion pitch diameter and the centre distance in proportion.
- Get it right
- Count teeth on the actual pinion, not on the mating gear.
What this means: Gear teeth
- What it is
- The number of teeth on 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 45 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Raises the gear pitch diameter, centre distance and ratio.
- Get it right
- The ratio is gear teeth divided by pinion teeth.
What this means: Face width
- What it is
- The axial width over which the two gears are in mesh. It is used only for the overlap ratio.
- 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 30 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The overlap ratio rises in proportion to face width.
- Get it right
- Use the width in mesh, the narrower of the two gears.
Method and formulas
- mt = mn ÷ cos β; d = z mt; tip diameter = d + 2mn (standard addendum); a = (d₁ + d₂) ÷ 2.
- αt = atan(tan αn ÷ cos β); base diameter = d cos αt.
- Virtual teeth zv = z ÷ cos³β; axial pitch = π mn ÷ sin β; overlap ratio εβ = b sin β ÷ π mn.
- Example: mn 3, 15°, 20/45 teeth give a centre distance of 100.94 mm and an overlap ratio of 0.82385.
Limitations
- Standard, unshifted gears; profile shift changes the centre distance and tip diameters.
- Strength and contact ratio in the transverse plane need a gear rating method (ISO 6336 or AGMA 2001).
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Lay out a helical gear pair
- Check centre distance for a replacement pair
- Find axial thrust direction and overlap
Who it is for
- Gear designers
- Machinists
- Maintenance engineers
What you get
- Transverse module and pressure angle
- Pitch, tip and base diameters
- Centre distance and ratio
- Virtual number of teeth
- Axial pitch and overlap ratio
Interpreting the result
- An overlap ratio of 1 or more gives smooth, quiet running.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2195–2210. Topic reference; no source tables or recommended settings are reproduced.
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