Enter the wheel shaft torque, the gear ratio, the wheel speed and the service life — the calculator picks the outer pitch diameter of the wheel from the Ra40 series, the face width, the outer module and the tooth numbers, finds the cone angles, diameters and mesh forces, and checks contact and bending strength.
How a closed bevel gear is designed
- Allowable stresses are as for a spur gear:
[σ]H = (1.8·HB + 67)·K_HL, [σ]F = 1.03·HB·K_FL; for straight teeth the smaller [σ]H is taken. - Outer pitch diameter of the wheel
d_e2 = 165·∛(T₂·10³·K_Hβ·u / (K_d·[σ]H²)), K_Hβ = 1, K_d = 1; rounded to the nearest number of the Ra40 series. - Cone angles: tan δ₂ = u, δ₁ = 90° − δ₂; outer cone distance
R_e = d_e2 / (2·sin δ₂). - Face width b = 0.285·R_e, rounded by the Ra40 series.
- Outer transverse module
m_te ≥ 14·T₂·10³·K_Fβ / (K_F·d_e2·b·[σ]F2), K_F = 0.85; not rounded to a standard value but at least 1.5 mm. - Tooth numbers z₂ = d_e2 / m_te, z₁ = z₂ / u, z₁ ≥ 18; the ratio deviation is at most 4 %. Profile shifts x₁ = −x₂ come from the table by z₁ and u.
- Diameters of tips and roots follow from the outer module and the cone angles; mean diameters d_m = d_e·(1 − 0.5·b / R_e).
- Mesh forces: F_t = 2T₁·10³ / d_m1; the pinion radial force F_r1 = F_t·tan 20°·cos δ₁ equals the wheel axial force F_a2, and the pinion axial force F_a1 = F_t·tan 20°·sin δ₁ equals the wheel radial force F_r2.
- Checks of contact stress σH and tooth bending σF.
The result feeds the shaft and bearing calculations and the coupling selection; the whole cycle is in the gearbox course wizard.
FAQ
How does a bevel gear differ from a spur gear?
The shaft axes intersect (most often at 90°) and the wheels are truncated cones. Besides the tangential and radial forces the mesh produces an axial force, so the shaft bearings are loaded differently than in a spur gear.
Why is it called the outer transverse module?
A bevel tooth changes size along its length. The module m_te is defined at the outer end, while forces and stresses are computed at the mean section with m_m = m_te·d_m / d_e.
How are the pitch cone angles found?
For an orthogonal gear tan δ₂ = u, δ₁ = 90° − δ₂. After the tooth numbers are chosen the angles are refined with the actual ratio u_f = z₂ / z₁.
Why at least 18 teeth on the pinion?
With fewer teeth the noise grows and the tooth root may be undercut. Such pinions use a profile shift; the coefficient x₁ is taken from the table.
What if contact stress exceeds the allowable?
First widen the face b, then enlarge the outer pitch diameter d_e2, or choose a harder material and recompute the allowable stresses.