Bevel Gear Dimensions
Compute pitch cone angle γ, equivalent teeth Zv, cone distance A and tip diameter Da for straight bevel gears (shaft angle Σ, default 90°).
Inputs
Formula
Fundamentals
Bevel gears transmit motion between intersecting shafts; teeth lie on a frustum and are common in differentials and right-angle drives.
At shaft angle $\Sigma$, single-stage ratio $i=Z_2/Z_1$; pitch-cone angles satisfy $\tan\delta_1=Z_1/Z_2$, $\tan\delta_2=Z_2/Z_1$ (for $\Sigma=90^\circ$).
History
Bevel gears developed with steam engines and the auto industry in the 19th c.; Gleason's manufacturing methods made right-angle drives in car differentials efficient and reliable.
Engineering applications
Used in car differentials, helicopter main reducers, indexing heads and construction-machinery steering where two intersecting shafts must drive each other.
Glossary
| Pitch angle $\delta$ | Angle between pitch-cone generator and shaft axis. |
| Shaft angle $\Sigma$ | Angle between the two shaft axes, usually $90^\circ$. |
| Back cone | Auxiliary cone normal to pitch generator, used to flatten the tooth form. |
How to use
- Fill in Pinion teeth Z₁, Gear teeth Z₂, Outer module m, Shaft angle Σ in the Inputs section (watch the unit on each field).
- Click Calculate; the tool evaluates the formula shown above.
- Read Pitch cone angle γ₁, Pitch cone angle γ₂, Equivalent teeth Zv₁, Cone distance A, Tip diameter Da₁ in the results area.
Formula · Worked Example · Knowledge
Formula
Worked Example
Key Points
- Shaft angle Σ is usually 90°; equal teeth give equal pitch angles.
- Cone distance $A=m\sqrt{z_1^2+z_2^2}/2$ sets blank size.
- Low pinion teeth risk undercut; use profile shift.
Parameters
Inputs
| Parameter | Symbol | Unit | Default |
|---|---|---|---|
| Pinion teeth Z₁ | Z1 | 20 | |
| Gear teeth Z₂ | Z2 | 30 | |
| Outer module m (mm) | m | mm | 3 |
| Shaft angle Σ (°) | sigma | ° | 90 |
Outputs
| Result | Symbol | Unit |
|---|---|---|
| Pitch cone angle γ₁ | gamma1 | ° |
| Pitch cone angle γ₂ | gamma2 | ° |
| Equivalent teeth Zv₁ | Zv1 | |
| Cone distance A | A | mm |
| Tip diameter Da₁ | Da1 | mm |
Applications
- Common engineering use cases