Torque calculation for bevel gear mechanism

[Enrico Urru]

I am trying to determine the torque required by the two pinion bevel gears to move the bigger bevel gear (when the pinion gears rotate in the same direction), like in a differential mechanism. The driven bevel gear has a load on its end. Being the driven bevel gear horizontal it exerts the highest torque on the pinion gears. I would like to know if my calculations are correct. Assume pressure angle on gear teeth phi=20°, Rd=radius driven, Rp= radius driven, Td= torque drive, Tp= torque pinion, L = distance from center weight to face of driven gear, F=force of the load. I uploaded a picture of the set up.

The torque of the driven gear on the pinion is Td = F*L*cos(phi),
and the torque on the pinion to balance the driven gear with the weight is Tp=(Rd/Rp)*Td

 

[Doug Hunter]

Your situation is unclear to me. What is the frame of reference for your statement "when the pinion gears rotate in the same direction"? From any given global frame of reference, the 2 pinion gears cannot rotate in the same direction without breaking the bigger gear. They functionally have to turn in opposite directions in any single global frame of reference.

 

[Enrico Urru]

I hope this picture can clarify. Imagine the gears are supported on each end by a bearing on the holes on the frame. The t link in the middle helps supporting the structure and has bearings inside, also the two pinion gears can rotate indipendently from each other. When the pinion gears rotate, as the arrows show, will rotate the driven gear around the pinion axis. Does this help?

 

[Doug Hunter]

Thank you for the clarification. If your goal is to spin the block weight around the pinion axis, then you don't need the gears at all. If your goal is to spin the block weight around the pinion axis with a speed reduction, then your system as drawn simply won't work that way. If your goal is to spin the block weight around the driven gear axis, then your system can work as drawn, but the pinion gears will turn in opposite directions and it matters if you are driving one or both. Which is your goal/intent?

In the end, my recommendation is that you need to find a Mechanical Engineer in your organization (or listen to the one you have) or hire one. I am available if you want to contact me at my website below. There are other good ones here as well.

 

[Doug Hunter]

Also, regarding automotive differentials, there is more to the mechanism that allows the 2 "pinions" to turn in the same direction. This video illustrates the concept well:

 

[Enrico Urru]

Thank you!
I'm trying to build a differential wrist mechanism used in robotic arms.
My intention is to spin the driven gear around it's own axis and around the pinion gears axis. I assume that if the driven gear has a weight on it then it will require more torque to rotate around the pinion axis than its own axis.
See this video show what my goal is

I am trying to determine the torque requirements to chose the right components

 

[mfgenggear]

I am trying to determine the torque required by the two pinion bevel gears to move the bigger bevel gear (when the pinion gears rotate in the same direction), like in a differential mechanism. The driven bevel gear has a load on its end. Being the driven bevel gear horizontal it exerts the highest torque on the pinion gears. I would like to know if my calculations are correct. Assume pressure angle on gear teeth phi=20°, Rd=radius driven, Rp= radius driven, Td= torque drive, Tp= torque pinion, L = distance from center weight to face of driven gear, F=force of the load. I uploaded a picture of the set up.

The torque of the driven gear on the pinion is Td = F*L*cos(phi),
and the torque on the pinion to balance the driven gear with the weight is Tp=(Rd/Rp)*Td

Gears are designed by the torque, rpm and precision. Torque rpm and precision is based on load and function. Which requires a free body diagram.