Gear Mesh Force Calculator

Inputs

Gear type

Spur gears have no axial thrust in this model; helical gears add Fa = Ft*tan(beta).

Applied torque (T)

Steady torque applied to the checked gear before service factor.

N·m

Pitch diameter (d)

Operating pitch diameter of the checked gear.

Normal pressure angle (alpha_n)

Normal pressure angle. For a spur gear, this is the same as the transverse pressure angle.

Helix angle (beta)

Helix angle at the pitch cylinder. Hidden for spur gears.

Service factor (SF)

Multiplier for shock, duty cycle and uncertainty. Forces are based on T x SF.

Gear speed (n)

Rotational speed of the checked gear for pitch-line speed and power.

rpm

Default result

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)837.34N

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.