Reaction torque in a traction system

[PhysicoRaj]

Hello PF,

I am building a traction assembly for a self balancing bot project and I am having some conflict with my intuition and practical testing results. The setup consists of a motor mounted to a chassis, the shaft coupled to a wheel that rests on a surface with non-zero friction. Below image should give some idea.

Now for convenience here, the motor, or, the stator more precisely, is not mounted to any chassis, let's assume that it stays in the air just like that and is free to rotate relative to the rotor/shaft. The wheel does not slip.

I apply a torque T from the motor by applying some voltage V. This torque generated tries to rotate the wheel and the wheel rolls forward. My intuition (and also Newton's 3rd law?) tells me that when the rotor+shaft+wheels are applied with a torque the stator will experience an equal and opposite torque (reaction torque?).

Now I have go about calculating the angular acceleration of the motor body / stator (opposite in direction to angular acceleration of the wheel), if I know what torque I am generating (from the voltage applied). Assume we know every property of the system here, mass, frictions, moments of inertia etc.

But before that,

1) Is the reaction torque equal and opposite to the generated torque? In other words, can Newton's third law be directly applied to torques instead of forces?
2) If (1) is true, isn't the angular acceleration of the stator unrelated to properties of the rotor+shaft+wheels+ground part of the system?
3) If (2) is true, why do I see (by practical testing) that the angular acceleration of the stator is more when I impede the motion of the wheel on purpose? (like trying to stall).
4) If (1) is wrong (and thus (2)), how do I go about applying the laws and math to this in that case?

Thanks in advance.

 

[wrobel]

I am not sure that completely understand everything so I answer only the part I understand

Summary:: How to claculate the angular acceleration of a body that experiences reaction torque

In other words, can Newton's third law be directly applied to torques instead of forces?

yes

 

[jack action]

3) If (2) is true, why do I see (by practical testing) that the angular acceleration of the stator is more when I impede the motion of the wheel on purpose? (like trying to stall).

I'm guessing you are measuring your stator acceleration with respect to the axle? If that is the case, when the axle rolls in the opposite direction, the relative stator acceleration is less compared to when the axle is stopped.

 

[A.T.]

3) If (2) is true, why do I see (by practical testing) that the angular acceleration of the stator is more when I impede the motion of the wheel on purpose? (like trying to stall).

Are you sure the torque is the same in both cases? Usually the torque of a motor depends on the RPM.

 

[PhysicoRaj]

Are you sure the torque is the same in both cases? Usually the torque of a motor depends on the RPM.

Great point. Is your opinion then that the effect I saw in testing was due to a change in torque and if I corrected that (I know the motor parameters and the rpm at a certain time so I could modulate the voltage to keep torque constant), the stator acceleration should remain same all the time?

 

[PhysicoRaj]

I'm guessing you are measuring your stator acceleration with respect to the axle? If that is the case, when the axle rolls in the opposite direction, the relative stator acceleration is less compared to when the axle is stopped.

I am measuring the stator acceleration with respect to a frame of reference which is fixed with respect to the ground/surface. Its not relative to the axle/wheel.

Also, the stator acceleration should be more w.r.t the axle and less with a fixed reference right?

 

[hutchphd]

If I understand your rig:

1. The motor will generate a certain torque (determined by the controller).
2. That torgue and its Newtonian opposite will be applied to the stator assembly and the wheel assembly respectively.
3. The angular accelerations of each will depend on their moments of inertia and additionally, for the wheel, the external force (as torque) from the table providing linear acceleration of the whole..

 

[PhysicoRaj]

If I understand your rig:

1. The motor will generate a certain torque (determined by the controller).
2. That torgue and its Newtonian opposite will be applied to the stator assembly and the wheel assembly respectively.
3. The angular accelerations of each will depend on their moments of inertia and additionally, for the wheel, the external force (as torque) from the table providing linear acceleration of the whole..

Thanks. That is how I would like to think too. So if I were to change either the mass of the wheel or the friction it experiences, the change in torque experienced by the stator should be solely from the effect of change in RPM.

 

[A.T.]

Thanks. That is how I would like to think too. So if I were to change either the mass of the wheel or the friction it experiences, the change in torque experienced by the stator should be solely from the effect of change in RPM.

Depending on where the center of mass of the stator (and the rest of the bot attached to it) is, linear forces at the axis can also create a torque, additionally to the reaction torque: The vertical support force and if the whole thing is accelerating along the ground a horizontal force on the stator.

 

[PhysicoRaj]

Depending on where the center of mass of the stator (and the rest of the bot attached to it) is, linear forces at the axis can also create a torque, additionally to the reaction torque: The vertical support force and if the whole thing is accelerating along the ground a horizontal force on the stator.

Yes, I get that. My intention was to add up angular acceleration due to reaction torque and angular acceleration due to linear forces (like gravity on CoG and forward acceleration) creating a moment about the axle together. Can I do like this? Because Torques can be added, I guess accelerations can be added to find the net acceleration too. (Newton's 2nd law).

 

[A.T.]

Yes, I get that. My intention was to add up angular acceleration due to reaction torque and angular acceleration due to linear forces (like gravity on CoG and forward acceleration) creating a moment about the axle together. Can I do like this?

Yes, but I prefer to take the torques of the linear froces around the CoG. Gravity has no lever arm here, just the force at the axle has. You can sill add these torques to the torque moment around the axle.