Is the relationship between power, torque and RPM a linear relationship?

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Discussion Overview

The discussion revolves around the relationship between power, torque, and RPM in the context of a motor powering a gearbox with a specific gear ratio. Participants explore how torque is affected by gear ratios and the implications for torque at different points in a gear system.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant states that with a 20:1 gearbox, the torque should be 20 times greater while RPM decreases by the same ratio, questioning if this assumption is correct.
  • Another participant suggests that torque should be considered around the axis of the gear rather than at its outer surface, prompting clarification on the mechanics involved.
  • There is a discussion about the relationship between the torque at the 110mm shaft and the 600mm gear, with one participant proposing that the torque at the outer gear can be calculated using the ratio of their diameters.
  • One participant asserts that for a given torque, the force required to counterbalance it would differ based on where the force is applied, referencing the ratio of the gear radii.
  • Another participant confirms that the torque multiplies by the gear ratio, but later challenges the calculation of torque at the 600mm gear, stating that both gears turn at the same RPM and have the same torque.
  • A participant mentions that while the relationship between power, torque, and RPM is linear, caution is needed as motors may not produce constant torque across all speeds.
  • One participant calculates the force at the circumference of the 600mm gear based on the torque applied to the 110mm shaft, indicating the relevance of the gear's radius in this context.

Areas of Agreement / Disagreement

Participants express differing views on the application of torque calculations across gears, with some agreeing on the multiplication of torque by gear ratios while others contest the implications of torque acting around the axis versus at the surface. The discussion remains unresolved regarding the correct interpretation of torque in this context.

Contextual Notes

There are limitations in the assumptions made about torque transfer through gears, the dependence on definitions of torque application, and the potential for losses in the system that are not accounted for in the calculations.

Stephen123
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Hi I have a problem dealing with rpm power and torque.

I have a motor powering a gearbox which has a 20:1 ratio.

The power and rpm are not an issue so i have not looked at those figures but the motor produces 240Nm of torque. Since it is a 20:1 gearbox, i have assumed the torque is 20 times greater with the rpm being 20 times slower? Is this correct?

From there the power is transferred through a number of gears. Can I follow the same method above and assume the torque multiplies each time buy the gear ratio?

I.e. the gearbox output shaft is 110mm and connected to a 600mm gear, therefore is the torque at the outer surface of the gear is equal to (240nm*20)*(600/110) = 26181.8Nm of torque?

Thank you.
 
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Stephen123 said:
I.e. the gearbox shaft is connected to a 110mm shaft connected to a 600mm gear,
Did you mean "a 110mm gear is on the gearbox shaft"? It's best to post a diagram, or be more clear what gears are on the same shaft vs. meshed with their teeth.

Stephen123 said:
therefore is the torque at the outer surface of the gear
A torque not "at the outer surface of the gear" but around its axis.
 
A.T. said:
Did you mean "a 110mm gear is on the gearbox shaft"? It's best to post a diagram, or be more clear what gears are on the same shaft vs. meshed with their teeth.A torque not "at the outer surface of the gear" but around its axis.

Sorry typo, the 600mm gear is on the 110mm shaft. My thought is that if the gear was essentially a wheel, would the torque applied by the 600 diameter be a ratio of 600mm/110mm?

Therefore the torque at the 110mm shaft multiplied by the size ratio would give the torque at the outside of the 600mm?
 
Stephen123 said:
Therefore the torque at the 110mm shaft multiplied by the size ratio would give the torque at the outside of the 600mm?
For a given torque on a shaft, the required force to exactly counterbalance that torque would be different if applied on the outside of the shaft or the outside of the gear. The ratio of the required forces would indeed be the ratio of the radii. 600mm/110mm as in your example. If 600 N of force on the outside of a shaft could keep it from turning then 110 N of force on the teeth of the gear welded to the shaft could do the same thing.
 
Stephen123 said:
Hi I have a problem dealing with rpm power and torque.

I have a motor powering a gearbox which has a 20:1 ratio.

The power and rpm are not an issue so i have not looked at those figures but the motor produces 240Nm of torque. Since it is a 20:1 gearbox, i have assumed the torque is 20 times greater with the rpm being 20 times slower? Is this correct?

Yes.

From there the power is transferred through a number of gears. Can I follow the same method above and assume the torque multiplies each time buy the gear ratio?

Yes.

I.e. the gearbox output shaft is 110mm and connected to a 600mm gear, therefore is the torque at the outer surface of the gear is equal to (240nm*20)*(600/110) = 26181.8Nm of torque?

No. Both the 110mm and 600mm gear turn at the same rpm and have the same torque. As AT said, torques acts "around the axis" not at a distance from the axis.
 
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By definition:
Power = Torque X rotational speed (rotational speed is specifically Angular Velocity)
So the relationship is Linear. But very few motors will produce constant torque over all speeds so you need to be careful using that equation.
But you can say that
Gear Radius1 X RPM1 = Gear Radius2 X RPM2
and
Torque1 / Radius1 = Torque2 / radius2
and many other combinations.
 
Stephen123 said:
Sorry typo, the 600mm gear is on the 110mm shaft.
If I picture this correctly, then the shaft radius is irrelevant here. You know the torque applied to it (240Nm*20 ignoring losses), so the force at the 600mm gear's circumference is 240Nm*20/0.6m.
 
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