How to calculate the maximum axial and radial force of the gearbox

1. Main influencing factors
Bearing selection and arrangement
The ability of the reduction gearbox to withstand axial and radial forces mainly depends on the type of bearings used (such as deep groove ball bearings, tapered roller bearings, thrust bearings, etc.) and their arrangement structure.
Shaft diameter and support distance (cantilever length)
A thicker, shorter shaft can withstand greater forces. Long cantilevers are prone to produce excessive bending moments, affecting the bearing capacity.
Gear force
The force direction and magnitude of planetary gear trains, spur gears or helical gears are different. Helical gears will produce axial force.
Box rigidity and lubrication conditions
Insufficient rigidity can lead to deformation and stress concentration.
Practical application life and safety factor requirements
If the operation needs to be performed for a long time, the allowable load needs to be reduced and the safety factor needs to be increased.

2. Estimation methods of radial force and axial force
1. Radial force (Fr) estimation formula (taking gear as an example):
Fr = 2 * T / d
Fr: Radial force (N)
T: output or input shaft torque (Nm)
d: Gear pitch diameter (m) (for planetary reducer, it is the PCD of the three position holes on the output shaft)
**Note: ** If it is a multi-tooth load or planetary gear, you need to multiply the force distribution coefficient or make corrections based on the actual number of teeth.

2. Axial force (Fa) estimation formula (mainly used for helical gears):
Fa = Ft * tan⁡(β)
Ft: Tooth force (related to torque)
β: Gear helix angle (only for helical teeth)

3. Calculation of actual design allowable value
When designing a reduction gearbox, the rated allowable axial force and radial force are defined based on the data sheet provided by the bearing manufacturer. The common steps are as follows:

Check the selected bearing model, which corresponds to:
Radial basic rated load (Cr)
Axial load capacity (usually needs to be multiplied by a factor)
Confirm the position of the load application point (the length of the cantilever will amplify the load)
Calculate or simulate actual working conditions
Add a safety factor (usually 1.5 to 2

Example (hypothesis)
Assuming that the maximum output torque of the reducer output shaft is T=200 Nm and the output gear pitch diameter is d=80 mm, the radial force is:

Fr=2 * 200 / 0.08=5000 N
If it is a helical gear, the helix angle β=20 degrees, then:

Fa=5000 * tan⁡(20∘)≈1820 N
Then it is necessary to confirm whether the bearing can withstand the load in these two directions.

📌 Recommendations
If you are using a planetary reducer, you can ask the manufacturer for a "maximum allowable axial/radial force" chart (usually related to shaft speed and load position).
If you design it yourself, please make detailed calculations for the bearings and structure and consider the safety factor.