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.

 

[Doug Hunter]

This becomes a complex problem. I agree with Mfgenggear that you ought to be starting with free body diagrams. You also need to define some transfer functions between your inputs and outputs. The FBDs + TFs will define your torque (and speed) equations for you. Your system will require an independent speed control for each of the 2 pinion gear drives. The average speed of the 2 will define the speed around the pinion axis. The speed difference of the 2 will define the speed around the driven gear axis. The torques will be determined by the inertias, accelerations and resistance forces according to the transfer functions. The simplest calculations will occur under a steady-state condition assumption, but your peak torques will occur under dynamic transient conditions.

 

[3DDave]

If the gears are accurately made then the contact will be in the center of the gear tooth. If the center of the pinion tooth is 2 inches from the axis of the pinions and the load applied is 10 pounds at 10 inches from the axis of the pinions, then there will be 100 inch-pounds of torque and the load on the pinion will be 50 pounds at the center of the pinion tooth.

 

[Enrico Urru]

Thank you all for the help! @3DDave this is also my understanding of the system.

@Doug Hunter , @mfgenggear it seems it is becoming too complex for what my initial plan was. Do you have something I can refer to? at least for the FBDs and TFs? Or a software I can use to calculate the torque?

 

[mfgenggear]

Op
Yes but you will need help with FBD
Then a gear ptogram.

MITCalc Bevel Gear Calculation 1.20 Free Download

MITCalc Bevel Gear Calculation - Geometric design and strength check of bevel gear with straight and helical toothing. Application supports Imperial and Metric units, is based on ANSI/AGMA...

mitcalc-bevel-gear-calculation.soft112.com

 

[mfgenggear]

Thrust Forces Acting on Gears | KHK

When a gear pair transmits power, the force acting against the gear in the same direction as the gear shaft is called thrust.

khkgears.net

 

[mfgenggear]

AI Overview



+5

A free body diagram of a bevel gear train depicts the forces acting on each gear, including tangential, radial, and axial forces, along with the reactions at the bearings and other supports.

Here's a more detailed explanation:

• Bevel Gears:
  Bevel gears are used to connect shafts that intersect at an angle, often 90 degrees, and their tooth-bearing faces are conically shaped.
  
  
• Forces on Bevel Gears:
  The forces acting on a bevel gear mesh have three orthogonal components:
  • Tangential Force (Ft): This force is along the tangent to the pitch circle of the gear, and it's responsible for transmitting torque.
    
    
  • Radial Force (Fr): This force acts radially outwards from the gear's axis, pushing the gears apart.
    
    
  • Axial Force (Fa): This force acts along the axis of the gear, causing thrust on the bearings.
    
• Free Body Diagram:
  A free body diagram of a bevel gear train would show each gear as a separate body, with all the forces acting on it, including:
  • Applied Torque: The torque applied to the input gear.
    
    
  • Gear Mesh Forces: Tangential, radial, and axial forces from the meshing gears.
    
    
  • Bearing Reactions: Reactions from the bearings supporting the shafts.
    
• Shaft Forces:
  The free body diagram can also be used to analyze the forces on the shafts, including:
  • Shear Forces: Forces that tend to shear the shaft.
    
    
  • Bending Moments: Moments that tend to bend the shaft.
    
• Example:
  • For a simple bevel gear train with two gears, the free body diagram would show the input gear with the applied torque, the forces from the meshing gear, and the reactions at the bearings.
    
    
  • The output gear would have forces from the meshing gear and the reactions at the bearings.
    
• Importance:
  Understanding the forces acting on a bevel gear train is crucial for:
  • Gear Design: Ensuring the gears and shafts can withstand the stresses.
    
    
  • Bearing Selection: Choosing bearings with sufficient capacity to handle the axial and radial forces.
    
    
  • Strength Analysis: Determining the critical points of the shaft where stresses are highest.

 

[Doug Hunter]

There are lots of resources available, as the others shared, but I don't think that there is a simple path to an answer for your question without rolling up your sleeves and doing some real Engineering work.

 

[mfgenggear]

yes once the required torque and rpm is established. there is experience required to obtain the correct AGMA quality, material and hardness. safety factor. precision required.
gear programs will assist in obtaining these requirement. but requires a very experience engineer.

 

[dgeesaman]

Page 34 will show how to calculate reaction forces.

https://www.timken.com/wp-content/uploads/2016/10/Timken-Engineering-Manual_10424.pdf

Rating the gears themselves is a whole other animal. You looking for a PhD? Could easily become one.