Problem with the reaction forces in the gearbox

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Discussion Overview

The discussion revolves around the calculation of reaction forces in a gearbox, specifically focusing on the Y direction reactions at the bearings of an intermediate shaft. Participants are attempting to reconcile their numerical results with provided solutions, exploring the methods used to derive tangential forces and the application of moment equilibrium.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant presents their calculated reaction forces, noting discrepancies with the provided solution values.
  • Another participant questions the method of obtaining tangential forces, seeking clarification on the calculations involved.
  • A participant details their calculations for tangential forces based on motor torque and gear ratios, asserting their correctness.
  • One participant identifies potential errors in the equations of moments about the bearings, suggesting a need to revise distances and directions of forces.
  • Concerns are raised about the understanding of free body diagrams and the implications of energy flow in the system.
  • A later reply mentions the use of online software to verify reaction calculations, contingent on the correctness of initial assumptions regarding force directions.

Areas of Agreement / Disagreement

Participants express differing views on the correctness of the moment equilibrium equations and the interpretation of force directions. There is no consensus on the resolution of the discrepancies in calculated reaction forces.

Contextual Notes

Participants highlight the importance of accurately distinguishing between the directions of tangential forces and the need to consider contact pressure angles in their calculations. There is an acknowledgment of the complexity involved in calculating reaction forces on multiple planes.

Who May Find This Useful

This discussion may be useful for individuals interested in mechanical engineering, particularly those dealing with gearbox design and analysis, as well as students learning about reaction forces and free body diagrams.

Amaelle
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Homework Statement
Look at the image
Relevant Equations
Monet equilibrium
Conservation of energy
Gears ratio
Greetings, I have tried to find the reactions of the bearings on the Y direction in the intermediate shaft. but I couldn´t find the numerical results of the solutions

1649427759575.png

1649427835373.jpeg

here is my attempt:
1649428064327.jpeg

in order to find the forces I did the moment equilibruim around the point A and B
1649428643557.png


With FT1 FT2 and FT3 the tangential forces applied by the gears on the intermediate shaft and RyA and RyB are the reaction forces I´m trying to find.

as you could see my reaction forces are
RAy= 3831,63 N
Rby=-1402,92
the solution says
Ray=-3687N
Rby=278,52N
I don´t know what´s wrong with my approach!

thank you!
 
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The last picture is barely visible.
How are you obtaining the value of each tangential force on the gears?
 
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thank you!
  • for Ft1 :we started by calculating the torque of the motor
Cm =power motor/Wmotor=194,26Nm
then Ft1 =Cm/r1
with r1=(z1*m/2) m is the modulus of the gear
we got FT1=6167 N.

  • For Ft3:
  • we calculated w6 the velocity of the load 2 with the gears ratio we got w6=18,75 rad/s
  • C6=Power load1/w6=985N.m
  • by the gear ratio we could get C4=518,47N
  • FT3=C4/r4=7014N
  • For FT7
  • w7=34,89 rad/s (by gear ratio)
  • C load 2=power load 2/w7 =343,94N
  • C8 =C load 2* z5/z6 =3275,6N,m
  • FT7=C8/r8=3275,6 N
In order to have the reactions RyA and RyB I just made the torque equilibruim around A and B
 
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Amaelle,
Here are your errors:
The calculated values of the tangential forces are all correct.
The equations of moments about bearings A and B are not.

Revise the distances between each force and the bearings.
You need to make a distinction regarding the direction of tangential forces on the intermediate gears and shaft.
Consider the flow of energy, it moves downstream: the input driven gear "feels" different than the output driving gears.
The function of the reaction forces is to keep the shaft in its spatial position regarding the forces on the gears.

It seems that you have a persistent difficult with Free body diagrams and the direction of the forces.
I recommend you to re-visit that chapter, since you seem to be very strong in everything else you have done in this and other threads.

Also, are you supposed to calculate the reaction forces on both planes?
I ask because the solution values that you show seem to be accounting for the contact pressure angle (thrust force on plane z-x), rather than being reasonable for the power force on plane z-y.
 
Last edited:
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Lnewqban said:
Amaelle,
Here are your errors:
The calculated values of the tangential forces are all correct.
The equations of moments about bearings A and B are not.

Revise the distances between each force and the bearings.
You need to make a distinction regarding the direction of tangential forces on the intermediate gears and shaft.
Consider the flow of energy, it moves downstream: the input driven gear "feels" different than the output driving gears.
The function of the reaction forces is to keep the shaft in its spatial position regarding the forces on the gears.

It seems that you have a persistent difficult with Free body diagrams and the direction of the forces.
I recommend you to re-visit that chapter, since you seem to be very strong in everything else you have done in this and other threads.

Also, are you supposed to calculate the reaction forces on both planes?
I ask because the solution values that you show seem to be accounting for the contact pressure angle (thrust force on plane z-x), rather than being reasonable for the power force on plane z-y.
thanks a million! you mean that my feeybody diagram is wrong? if so this might explain why my results are wrong?
Could you tell what are the wrong directions?
yes the exercice ask about the the reactions on the the other plane by I can solve them once i fix this first!
thanks a million!
 
1649615179592.png

I used an online software to calculate the reactions and I got the same results if my initially supposed directions are correct.
(ignore the fact that I inverted the bearings here as I´m not calculating forces in the x directions right now)
 

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