Gear Mesh Force & Helical Axial Load Calculator

Inputs

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Spur gears have no axial thrust in this model; helical gears add Fa = Ft*tan(beta).
Steady torque applied to the checked gear before service factor.
N·m
Operating pitch diameter of the checked gear.
mm
Normal pressure angle. For a spur gear, this is the same as the transverse pressure angle.
°
Helix angle at the pitch cylinder. Hidden for spur gears.
°
Multiplier for shock, duty cycle and uncertainty. Forces are based on T x SF.
Rotational speed of the checked gear for pitch-line speed and power.
rpm

Results

Default result
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Tangential force(Ft)
3,125N
Pass

3.125 kN · 702.5 lbf

Tooth load from design torque and pitch diameter.

Ft = 2*Tdesign/d.

Also computed

Radial force(Fr)1,177.5N

1.178 kN · 264.7 lbf

Fr = Ft*tan(alpha_t).

Axial force(Fa)Pass837.34N

0.8373 kN · 188.2 lbf

Helical thrust load from helix angle.

Fa = Ft*tan(beta). Spur gears return zero.

Normal force(Fn)3,442.9N

3.443 kN · 774 lbf

Vector sum of Ft, Fr and Fa.

Transverse resultant(Ftr)3,339.5N

3.339 kN · 750.7 lbf

sqrt(Ft^2 + Fr^2), useful for first-pass shaft bending.

Design torque(Td)125N·m

Applied torque multiplied by service factor.

Transverse pressure angle(alpha_t)20.647°

Method notes 3 notes
  • Forces use design torque Tdesign = T x service factor. Transmitted power is based on the entered running torque before service factor.
  • Radial force uses the transverse pressure angle. For helical gears, alpha_t = atan(tan(alpha_n)/cos(beta)); for spur gears beta = 0.
  • These are steady, frictionless mesh-force magnitudes. Tooth bending/contact stress, dynamic factor, face load distribution, backlash, lubrication and bearing span reactions are separate checks.

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