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Spur and Helical Gear Design Calculator

Enter the wheel torque, ratio and speed — get allowable stresses, standard centre distance and module, tooth numbers and helix angle, diameters, contact and bending checks and mesh forces.

T₂ is the wheel (output) shaft torque, n₂ its speed, Lh the service life in hours. ψₐ = 0.4 symmetric, 0.315 asymmetric, 0.25 overhung. For HB ≤ 350.
Calculate

Procedure

  1. Allowable stresses: [σ]H = (1.8·HB + 67)·K_HL, [σ]F = 1.03·HB·K_FL; for helical gears [σ]H = 0.45([σ]H₁ + [σ]H₂).
  2. Centre distance a_w = Kₐ(u + 1)·∛(T₂·10³ / (ψₐ·u²·[σ]H²)), Kₐ = 43 helical, 49.5 spur; round up to the standard series.
  3. Module m ≥ 2K_m·T₂·10³ / (d₂·b₂·[σ]F₂), not less than 0.01a_w, standard value.
  4. Helix angle 8…16°, z_Σ = 2a_w·cos β / m, z₁ ≥ 17, ratio deviation ≤ 4 %.
  5. Diameters d = m·z / cos β, d_a = d + 2m, d_f = d − 2.4m.
  6. Checks: σH ≤ [σ]H, σF ≤ [σ]F; forces Ft = 2T / d, Fr = Ft·tan 20° / cos β, Fa = Ft·tan β.

Simplified course-project method (Sheinblit textbook, based on GOST 21354-87).

FAQ

How is the centre distance calculated?
From contact strength: a_w = Kₐ(u + 1)·∛(T₂·10³ / (ψₐ·u²·[σ]H²)), rounded to a standard value.
How do I choose the module?
From bending strength and at least 0.01·a_w, rounded to a standard value.
Which helix angle should I use?
Usually 8…16°; it is refined so that the total number of teeth is an integer.
What if the contact stress check fails?
Increase the centre distance or face width, or use harder steel. Up to 5 % overload is acceptable.
Why are mesh forces needed?
They load the shafts and bearings: used for bending moment diagrams and bearing selection.