Torque Required for Rotating a Cylinder

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Discussion Overview

The discussion revolves around calculating the torque required for a servomotor to rotate a vertical cylinder of a specified mass and radius at a constant RPM. Participants explore the implications of torque, moment of inertia, and the effects of gearing on motor performance, while also considering factors like friction and angular acceleration.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant queries whether the torque required can be calculated simply as the product of the cylinder's mass, gravity, and radius.
  • Another participant explains that the torque needed to maintain constant angular velocity is zero, aside from overcoming losses like friction, and introduces the concept of moment of inertia.
  • There is a discussion about the relationship between maximum torque of the servomotor, moment of inertia, and angular acceleration, with one participant expressing confusion about the implications of these relationships.
  • Participants discuss the weight and radius of the cylinder, suggesting that gearing down the motor may be necessary to ensure movement, and propose a 3:1 gear ratio as a potential solution.
  • Concerns are raised about whether the calculations are addressing the motor's capability to start moving the drum, rather than just its speed once in motion.
  • One participant requests more information about the motor's specifications, including stall torque, and suggests measuring the torque required to overcome static friction in the system.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the calculations and the adequacy of the motor's specifications for the task. There is no consensus on the best approach to ensure the motor can effectively start and maintain the rotation of the cylinder.

Contextual Notes

Participants mention neglecting friction in their calculations, which may not reflect real-world conditions. The discussion also highlights the importance of understanding the relationship between torque, moment of inertia, and angular acceleration in practical applications.

Alvaro Vargas
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Hello everyone, I am new to this forum, and here is my first question.

I need some help in a particular case regarding torques. Most of the examples given anywhere on the web and books have rotations which are affected directly by gravity like pulleys and such, but, what if I want to calculate the torque needed for a servomotor that's under a cylinder with a certain mass and radius which makes it to rotate at constant RPM about its axis, not horizontally, but vertically, kind of like a plinth.

Would (T.of.motor)= (mass.of.cylinder* gravity * radius.of.cylinder) in a practical way?
 
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Alvaro Vargas said:
Hello everyone, I am new to this forum, and here is my first question.

I need some help in a particular case regarding torques. Most of the examples given anywhere on the web and books have rotations which are affected directly by gravity like pulleys and such, but, what if I want to calculate the torque needed for a servomotor that's under a cylinder with a certain mass and radius which makes it to rotate at constant RPM about its axis, not horizontally, but vertically, kind of like a plinth.

Would (T.of.motor)= (mass.of.cylinder* gravity * radius.of.cylinder) in a practical way?

Welcome to the PF.

By "plinth", I take it that the cylinder is vertical, and you want it to rotate about its vertical axis?

In any case, the torque required to keep it rotating at a constant angular velocity is zero, except for the torque required to overcome losses like friction. The torque that is required to spin it up to speed is the same torque to overcome the losses, plus τ = I * α. Where I is the Moment of Inertia, and α is the angular acceleration. Are you familiar with Moments of Inertia? http://en.wikipedia.org/wiki/Moment_of_inertia
 
Exactly, the cylinder is vertical and I want it to rotate about its axis.

I am somewhat familiar, I=(m*r^2)/2 for a solid cylinder, but that's where my dilemma comes in, a servomotor has a pre established maximum torque, the one that I'm using is about 5.1 kg-cm, so if I have that maximum torque and the moment of inertia from the cylinder, does it mean the cylinder will just rotate with an angular acceleration= t/I?

It doesn't make too much sense to me, that would mean any cylinder could rotate regardless of the moment of inertia, just with very low angular accelerations if I is too large.
 
Alvaro Vargas said:
Exactly, the cylinder is vertical and I want it to rotate about its axis.

I am somewhat familiar, I=(m*r^2)/2 for a solid cylinder, but that's where my dilemma comes in, a servomotor has a pre established maximum torque, the one that I'm using is about 5.1 kg-cm, so if I have that maximum torque and the moment of inertia from the cylinder, does it mean the cylinder will just rotate with an angular acceleration= t/I?

It doesn't make too much sense to me, that would mean any cylinder could rotate regardless of the moment of inertia, just with very low angular accelerations if I is too large.

That sounds like a pretty small motor. How big/heavy is the cylinder?

If there is no friction or other losses, then a small motor can spin up a heavy cylinder, just pretty slowly. But for real systems, you will have bearing friction, which is usually maximum when the cylinder is not moving (similar to how the static coefficient of friction is generally larger than the dynamic one). And it will be the stall torque of the motor that will have to overcome that bearing friction. Is gearing down the motor an option?
 
The weight of the cylinder is about 30 Kg and has a 12 cm radius, I'am also neglecting friction since the drum is over a bushing, maybe that could be interchanged with a safety percentage (I don't know what percentage would be adequate for it), so, if I'm not wrong, and I hope you could redirect me, by the amount of weight I assume I would have to gear down the motor, probably to about a 3:1 ratio to ensure movement. So if I gear it down, the torque would be 5*3 Kg-cm and its maximum rated speed would be 54 RPM/3, and after it I would have to recalculate angular acceleration which would mean a little increase on how fast it starts to move?

That seems more like I'm finding how fast it is going to start moving, not if the motor is strong enough to start moving the drum, am I wrong?
 
Alvaro Vargas said:
The weight of the cylinder is about 30 Kg and has a 12 cm radius, I'am also neglecting friction since the drum is over a bushing, maybe that could be interchanged with a safety percentage (I don't know what percentage would be adequate for it), so, if I'm not wrong, and I hope you could redirect me, by the amount of weight I assume I would have to gear down the motor, probably to about a 3:1 ratio to ensure movement. So if I gear it down, the torque would be 5*3 Kg-cm and its maximum rated speed would be 54 RPM/3, and after it I would have to recalculate angular acceleration which would mean a little increase on how fast it starts to move?

That seems more like I'm finding how fast it is going to start moving, not if the motor is strong enough to start moving the drum, am I wrong?

Do you have a motor in mind? Can you post a link to its datasheet? What is its rated stall torque?

Do you have the cylinder and bearings already? You can measure the torque it takes to overcome its static friction, and compare that to the motor's datasheet numbers...
 
The datasheet is this one, it doesn't say much besides what I have described before though:

https://www.pololu.com/product/1248/specs

And I'm not using bearings, just a base that makes barely any contact with the bottom part of the drum and it will be well lubricated.
 

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