KEVOS® MAKEOS · Gears
Helical Gear Set Design (Geometry, Forces and Bending)
What are the sizes, tooth forces and bearing thrust of this helical gear pair, and is the tooth bending stress within the allowable?
Design check of a parallel-axis helical gear pair from power and speed: transverse module, pitch diameters, centre distance, transverse pressure angle, virtual teeth and overlap ratio (as the helical gear tool), the tangential, axial and separating forces the bearings must carry, pitch-line velocity and the Lewis bending stress in the normal plane with the velocity factor (as the Lewis bending tool), using the form factor for the virtual number of teeth.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Power | kW | Power through the gear pair. |
| Pinion speed | rpm | Speed of the pinion. |
| Normal module | mm | Normal module (the hob or cutter module). |
| Helix angle | ° | Helix angle at the pitch diameter. |
| Normal pressure angle | ° | Normal pressure angle. |
| Pinion teeth | Number of teeth on the pinion. | |
| Gear teeth | Number of teeth on the gear. | |
| Face width | mm | Face width in mesh. |
| Lewis form factor at the virtual teeth | Lewis form factor read for the pinion’s virtual number of teeth (z ÷ cos³β), shown in the results. | |
| Tooth finish | choice | Manufacturing quality, which sets the velocity factor. |
| Allowable bending stress | MPa | Allowable bending stress of the pinion material (your design value). |
| Least overlap ratio wanted | Least overlap (face contact) ratio you want for smooth running (often at least 1). |
Method and formulas
- m_t = m_n ÷ cos β; d = z m_t; a = (d₁ + d₂) ÷ 2; tan α_t = tan α_n ÷ cos β; virtual teeth z_v = z ÷ cos³β; overlap ratio ε_β = b sin β ÷ (π m_n).
- T₁ = P ÷ ω₁; tangential force F_t = 2T₁ ÷ d₁; axial F_a = F_t tan β; separating F_r = F_t tan α_t.
- Lewis bending σ = K_v F_t ÷ (b m_n Y) with K_v from the pitch-line velocity (as the Lewis bending tool).
- Example: 7.5 kW at 1450 rpm gives a 1,590.3 N tangential force and 426.13 N of thrust; the bending stress is 73.895 MPa.
Limitations
- Lewis method for a first sizing; full ratings use AGMA or ISO 6336 factors and pitting resistance.
- Form factor must be read for the virtual number of teeth.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size a helical gear pair for a reducer
- Find the thrust load for bearing selection
- Compare helix angles for smoothness against thrust
Who it is for
- Design engineers
- Maintenance engineers
- Power transmission engineers
What you get
- Gear geometry and centre distance
- Tangential, axial and separating forces
- Bending stress and overlap checks
Interpreting the result
- A larger helix angle runs smoother but raises the thrust the bearings must take.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2195–2210, 2131–2160. Topic reference; no source tables or recommended settings are reproduced.
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Open the Helical Gear Set Design (Geometry, Forces and Bending) calculator
