KEVOS® MAKEOS · Gears
Straight Bevel Gear Set Design (Geometry, Forces and Bending)
What are the cone angles, tooth forces and bearing loads of this straight bevel gear pair, and is the bending stress within the allowable?
Design check of a straight bevel gear pair from power and speed: pitch cone angles, pitch diameters and outer cone distance (as the bevel gear tool), face width against your limit as a share of the cone distance, the mean pitch diameter and the tangential, axial and radial forces on pinion and gear at the mean diameter, and the Lewis bending stress for bevel teeth with the face-width correction (L − b) ÷ L and the velocity factor.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Power | kW | Power through the bevel pair. |
| Pinion speed | rpm | Speed of the pinion. |
| Module at the large end | mm | Module at the outer (large) end. |
| Pinion teeth | Number of teeth on the pinion. | |
| Gear teeth | Number of teeth on the gear. | |
| Shaft angle | ° | Angle between the shafts (90° for a right-angle drive). |
| Pressure angle | ° | Pressure angle of the teeth. |
| Face width | mm | Face width along the cone. |
| Largest face width ÷ cone distance | Largest face width as a share of the outer cone distance you design to (a third is common). | |
| Lewis form factor (for the formative teeth) | Lewis form factor for the formative (equivalent spur) number of teeth. | |
| Tooth finish | choice | Manufacturing quality, which sets the velocity factor. |
| Allowable bending stress | MPa | Allowable bending stress of the pinion material (your design value). |
Method and formulas
- tan δ₁ = sin Σ ÷ (z₂ ÷ z₁ + cos Σ); δ₂ = Σ − δ₁; d = m z; outer cone distance L = d₂ ÷ (2 sin δ₂) (as the bevel gear tool).
- Mean pitch diameter d_m1 = d₁ (1 − 0.5 b ÷ L); F_t = 2T₁ ÷ d_m1; pinion axial F_a1 = F_t tan α sin δ₁ and radial F_r1 = F_t tan α cos δ₁ (the gear’s axial and radial forces swap these).
- Lewis bending σ = K_v F_to L ÷ [b m Y (L − b)], with F_to = 2T₁ ÷ d₁ at the large end.
- Example: 3 kW at 1450 rpm puts 635.67 N tangential load at the mean diameter; the bending stress is 47.393 MPa.
Limitations
- Lewis method for a first sizing; AGMA 2003 or ISO 10300 give full ratings.
- Straight bevel teeth; spiral bevels have different force directions that depend on hand and rotation.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size a bevel pair for a right-angle drive
- Find the axial and radial loads for the bearings
- Check a face width against the cone distance
Who it is for
- Design engineers
- Maintenance engineers
- Power transmission engineers
What you get
- Cone angles, diameters and cone distance
- Forces on pinion and gear at the mean diameter
- Bending stress and face-width checks
Interpreting the result
- Face width beyond about a third of the cone distance adds little strength because the inner teeth are small.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2181–2190, 2131–2160. Topic reference; no source tables or recommended settings are reproduced.
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Open the Straight Bevel Gear Set Design (Geometry, Forces and Bending) calculator
