BIZOMAT MAKEOS · Gears
Straight Bevel Gear Geometry
What pitch angles, cone distance and diameters does this bevel gear pair have?
Pitch cone angles, pitch and outside diameters, outer cone distance and face-width ratio of a straight bevel gear pair at any shaft angle.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Module at the outer end | mm | Transverse module at the outer (heel) end of the teeth. |
| Pinion teeth | teeth | Pinion tooth count. |
| Gear teeth | teeth | Gear tooth count. |
| Shaft angle | ° | Angle between the shafts (90° for most drives). |
| Face width | mm | Face width along the cone. |
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: Module at the outer end
- What it is
- The transverse module measured at the outer (heel) end of the teeth, where bevel gear sizes are specified.
- 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
- Diameters and cone distance scale in proportion.
- Get it right
- Use the module at the large end, not the mean module at mid-face.
What this means: Pinion teeth
- What it is
- The number of teeth on the pinion, the smaller bevel gear.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 5 teeth to 500 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.
- Get it right
- Count the pinion teeth, not the gear teeth.
What this means: Gear teeth
- What it is
- The number of teeth on the larger bevel gear.
- 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 36 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Ratio and pitch cone angles follow from both tooth counts.
What this means: Shaft angle
- What it is
- The angle between the two shaft axes where they intersect, which with the tooth counts sets the pitch cone angles.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 10° to 170°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 90° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Measure between the axes, not between the gear faces.
What this means: Face width
- What it is
- The length of the teeth measured along the pitch cone. It is used only to compare with the cone distance.
- 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 22 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Measure along the tooth, not the axial width of the blank.
Method and formulas
- tan δ₁ = sin Σ ÷ (z₂/z₁ + cos Σ); δ₂ = Σ − δ₁.
- d = m z; outer cone distance Re = d₂ ÷ (2 sin δ₂).
- Outside diameter (standard addendum = m) da = d + 2m cos δ.
- Example: 18/36 teeth at 90° give pitch angles of 26.565° and 63.435°, Re = 80.498 mm.
Limitations
- Standard straight bevel proportions with equal addendum; Gleason and other systems use unequal addenda.
- Strength needs a bevel gear rating (ISO 10300 or AGMA 2003).
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Lay out a right-angle or angled bevel drive
- Check replacement bevel gears
- Find the mounting distances
Who it is for
- Gear designers
- Machinists
- Maintenance engineers
What you get
- Pitch cone angles
- Pitch and outside diameters
- Outer cone distance
- Face width as a share of cone distance
Interpreting the result
- Face width is usually kept to a third of the cone distance or less.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2181–2190. Topic reference; no source tables or recommended settings are reproduced.
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