Calculating radial and axial loads for a tapered roller bearing

[voyager14]

Hi

I'm analyzing a tapered roller bearing as part of a differential. I know the shaft is providing input torque of 333.5 N-m @ 4000RPM, and I know the bore size of the bearing, 30mm. I need to find the radial and axial forces given that torque, so I can move on to finding C10, L10, rated load, and lifetime.

I've tried:
1. Diving torque by bore radius (which I realized is tangential force, which is different)
2. Using
F_r = m(ω)²r
where
ω = (RPM/60)2π
this got me
F_r = 1052N or 1.052kN

I don't know if that's correct, and I could also use help with the axial force.
Thank you.

 

[Baluncore]

If the tapered roller bearing is one of two on the input shaft to the pinion, then the pitch radius of the pinion, and the position of the two bearings will be important.

If the tapered roller bearing is one of the two that supports the differential assembly in the carrier, (axial with the axle shafts), then the pitch radius of the crown wheel will be important.

You will need to know the profile and the offset of the hypoid pinion and crown to resolve the axial forces.

 

[voyager14]

If the tapered roller bearing is one of two on the input shaft to the pinion, then the pitch radius of the pinion, and the position of the two bearings will be important.

If the tapered roller bearing is one of the two that supports the differential assembly in the carrier, (axial with the axle shafts), then the pitch radius of the crown wheel will be important.

You will need to know the profile and the offset of the hypoid pinion and crown to resolve the axial forces.

Thank you. It is one of the bearings on the input shaft to the pinion. Are there any resources you know of to help walk me through this?

 

[Baluncore]

Are there any resources you know of to help walk me through this?

I don't know of a reference, but will take a look.

Pinion bearing selection is not normally a computed parameter, it has evolved through experience. If it fails, differential manufacturers will use the next bearing up, if it never fails, try the next smaller bearing.

Radial and axial thrust may not be the critical selection parameters. The pinion bearings are always pre-loaded against each other, in order to hold the pinion in a well defined position relative to the crown wheel.

If you know the 3D position and direction vector, normal to the pinion contact area on the crown, you should be able to solve the vector problem to find the forces on the two bearings due to the input shaft torque.

 

[Baluncore]

Paywalls abound. Good intro's.
https://www.sae.org/publications/technical-papers/content/2003-01-3743/
https://www.jstor.org/stable/44730958