FBD of two translating rollers connected by a belt

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    Belt Fbd
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Discussion Overview

The discussion revolves around the dynamics of a mechanism consisting of two rollers connected by a belt, focusing on the relationship between forces and acceleration. Participants explore the forces acting on the rollers, the role of the belt, and the implications for angular acceleration in a simplified model.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about the forces acting on the rollers and questions whether the tension in the belt is relevant to the forces applied.
  • Another participant suggests that if equal forces are applied to both rollers, the belt may be unnecessary, indicating a potential misunderstanding of the system's mechanics.
  • A participant clarifies that both rollers are pulled by the same force and that there is a static link between them, questioning the implications of this setup on tension in the belt.
  • Concerns are raised about the relationship between angular acceleration and the belt connection, with one participant noting that connecting the rollers with gears reduces angular acceleration.
  • There is mention of a potential sign error in the equations relating to the forces and moments acting on the rollers, indicating a need for careful analysis of the system's dynamics.
  • Assumptions are made that both rollers have equal angular acceleration due to their identical diameters and linear acceleration, suggesting a simplification in the analysis.

Areas of Agreement / Disagreement

Participants express differing views on the necessity of the belt and the implications of the forces acting on the rollers. There is no consensus on the correct interpretation of the forces and tensions involved, and the discussion remains unresolved regarding the relationship between angular acceleration and the belt connection.

Contextual Notes

Participants highlight potential inconsistencies in the equations used to describe the system, particularly regarding the treatment of tension and forces. The discussion also reflects varying assumptions about the mechanical connections and the nature of the forces acting on the rollers.

ramadhankd
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Hey, I'm trying to create a mechanism consisting of multiple rollers connected with belt, moving in the same linear direction with acceleration a, but I got stuck in finding the relationship between the forces and acceleration. I even got confused in building the FBD of only two rollers. The picture below is the FBD of two rollers connected with a belt that I made. As can be seen the equation is quite inconsistent. Can anyone tell me what's wrong?
Thanks
1575120327766.png
 

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  • 1575120020044.png
    1575120020044.png
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@ramadhankd
Nice drawing.
I am unclear as to how you are accelerating the rollers.
From the diagram, are you pulling on each roller with equal forces of F ( pulling force 2F )?
Or is it that the tension in the belt is drawing along the roller at the left?
In the first case, the belt is superfluous.
In the second case, there should be no F pulling the roller on the left.

Do you have a mechanical link between the roller centres, or just freewheeling under the belt.
 
256bits said:
@ramadhankd
Nice drawing.
I am unclear as to how you are accelerating the rollers.
From the diagram, are you pulling on each roller with equal forces of F ( pulling force 2F )?
Or is it that the tension in the belt is drawing along the roller at the left?
In the first case, the belt is superfluous.
In the second case, there should be no F pulling the roller on the left.

Do you have a mechanical link between the roller centres, or just freewheeling under the belt.

The rollers are both pulled by the same force F. There is indeed a link connecting them, yet this link is static so no kinematic analysis is needed to be done. You said that the belt is superfluous, meaning that the tension is zero? I try to solve It and what I found is that T1=T2, with no actual relation to determine T. The model I attached above is a simplification of the actual model. The actual model is like this.

I simplify the model as two rollers connected with the belt to know how the angular acceleration is affected by the belt. Shall It have lower angular acceleration, same, or more than when they aren't connected by the belt? I'm curious because when I try to connect the rollers using gear mechanism (yes, the rollers are going to move in an alternate rolling direction), the angular acceleration is reduced. I attached my analysis for this case just in case you need to review It.
1575180531864.png

I try to solve it using the same approach, yet the equations involved are just too much It got me confused. Thus, I try to simplify the mechanism using the two rollers model. My aim is only to know the value of angular acceleration (thus affecting the angular velocity and displacement, of the Blue (big) wheel should It able to be accelerated by the red (small) wheel, while both are contacting the ground. I design this for a roller mop, where more angular acceleration means more angular velocity and displacement, thus yielding more mopping action and better efficiency.
 

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ramadhankd said:
The rollers are both pulled by the same force F
Your analysis seems to indicate that the total moment of inertia for a two cylinder system is reliant upon whether the cylinders rotate in the same direction, or in opposite direction.
Is there a sign error someplace.
 
The sign error is the equation that states ma=F+(T1+T2)-fr and ma=F-(T1+T2)-fr. There is inconsistency at the (T1+T2) variable. It's like having y=x and y=-x and try to solve for x using the two function.
My assumptions are that both move in equal angular acceleration since the diameter are the same, and of course, the same linear acceleration.
Both rollers are identical so there's no need to calculate their relation to each other.
 

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