How to use this calculator
- Choose gear type. Select spur for no axial thrust, or helical when the gear has a helix angle.
- Enter torque and pitch diameter. Use the torque and operating pitch diameter for the gear being checked.
- Enter pressure and helix angle. Use the normal pressure angle and, for helical gears, the pitch-cylinder helix angle.
- Add service factor. Use a duty or shock multiplier when sizing shafts, bearings or housings from the mesh load.
- Read the force components. Use Ft, Fr and Fa as input loads for shaft bending, thrust bearings and gear-tooth strength checks.
How it works
Gear mesh force starts with the tangential tooth load. The applied torque is
multiplied by the service factor, then divided by the pitch radius:
Ft = 2 x Tdesign / d
where Tdesign = T x SF and d is the operating pitch
diameter.
The radial separating force is the tangent-force component along the transverse
pressure angle:
Fr = Ft x tan(alpha_t). For helical gears, the normal pressure
angle is converted with alpha_t = atan(tan(alpha_n) / cos(beta)).
Helical thrust is Fa = Ft x tan(beta); for spur gears
beta = 0, so Fa = 0.
The normal force is the vector magnitude:
Fn = sqrt(Ft^2 + Fr^2 + Fa^2). The transverse resultant shown by
the calculator, sqrt(Ft^2 + Fr^2), is a convenient first-pass load
for shaft bending before bearing-span reactions are resolved. Use the
overhung load calculator to split a
gear, pulley or sprocket force into bearing reactions and peak shaft bending
moment.
Worked example
Verified against the live calculator
For a helical gear carrying 100 N*m at 1200 rpm, with
80 mm pitch diameter, 20 degrees normal pressure angle,
15 degrees helix angle and 1.25 service factor, the
design torque is 125 N*m.
The calculator gives Ft = 3125 N, alpha_t = 20.647 degrees,
Fr = 1178 N and Fa = 837 N. The normal force is
3443 N, the transverse resultant is 3339 N, pitch-line
speed is 5.03 m/s, and running power before service factor is
12.57 kW.
Frequently asked questions
How do you calculate tangential gear tooth force?
Tangential gear force is Ft = 2T/d, where T is torque and d is pitch diameter. This calculator applies the entered service factor first, so the force uses Tdesign = T x SF.
How do you calculate radial gear force?
Radial separating force is Fr = Ft x tan(alpha_t). For a spur gear alpha_t is the pressure angle. For a helical gear, alpha_t = atan(tan(alpha_n)/cos(beta)).
How do you calculate axial force on a helical gear?
Helical gear thrust force is Fa = Ft x tan(beta), where beta is the helix angle at the pitch cylinder. Spur gears use beta = 0 in this calculator, so axial force is zero.
Which pitch diameter should I enter?
Use the operating pitch diameter of the gear being checked. If the mesh has profile shift or a changed center distance, use the working pitch diameter rather than only the catalog reference diameter.
Can I use this for bearing loads?
Yes as a load-input step. Ft, Fr and Fa give the gear forces; the bearing reactions still depend on gear location, bearing spacing, shaft layout, load direction, thrust arrangement and any other loads on the shaft.
Does this rate gear tooth strength?
No. It calculates mesh forces only. Tooth bending stress, pitting/contact stress, dynamic factor, face load distribution, material, heat treat and lubrication need an AGMA/ISO gear rating method or manufacturer data.
Method & assumptions
- External spur or parallel-shaft helical gear mesh with forces reported as magnitudes.
- Friction, sliding losses and dynamic mesh amplification are not included.
- The helix-angle sign and rotation direction determine thrust direction; this calculator reports thrust magnitude only.
- Use the resulting forces with the actual gear location and bearing spacing to compute bearing reactions.
- Gear tooth bending strength and contact stress require an AGMA/ISO strength rating or manufacturer data.