Question about motor torque

[lebevti]

When a motor runs at constant speed, why is there is a nonzero torque? Shouldn't the torque be zero, since the rotational speed is constant and thus the acceleration is zero?

Compare it to Force=mass*acceleration
A block moving at constant speed undergoes no force, right? It is just moving on inertia.

Doesn't the same thing apply to torque?
Some relevant equations:

Torque = Force*radius
Torque= (moment of inertia) *(rotational acceleration dw/dt)

so back to the motor, which has a torque-speed characteristic...a motor runs at constant speed (w) under mechanical load, and the mechanical power is P=torque*w
But since the rotational speed is constant, why is the torque nonzero?

can someone tell me the flaw in my thinking, or have I turned the physics world upside down?

 

[JimB]

a motor runs at constant speed (w) under mechanical load, and the mechanical power is P=torque*w

You have just answered your own question.

There is a LOAD on the motor output shaft.

To move that load needs POWER, and as you just said P=torque*w

Now. if you wanted to accelerate that load from its constant rotational speed, you would need some extra torque.
Just how much extra torque depends on ho fast you want it to accelerate and the effective moment of inertia presented by the load.

JimB

 

[cowboybob]

Unless I'm missing some element of the question (Ideal motor?), the motor's rotor is the minimum load., therefore torque ≠ 0.

 

[MrAl]

Hi,

Yes there is usually always at least a little friction that has to be overcome, even with nothing connected to the motor shaft. The bearings are not perfect, and there is also some air resistance for the armature to overcome. This torque of course could be much smaller than a normal shaft load would be in a real life application.

 

[lebevti]

You have just answered your own question.

There is a LOAD on the motor output shaft.

To move that load needs POWER, and as you just said P=torque*w

Now. if you wanted to accelerate that load from its constant rotational speed, you would need some extra torque.
Just how much extra torque depends on ho fast you want it to accelerate and the effective moment of inertia presented by the load.

JimB

ok but this is my question: if the rotational velocity is constant, whether load or no-load, there IS NO acceleration... hence wouldn't the torque be zero? (Torque = moment of inertia * acceleration)

what am I missing here?

 

[MrAl]

Hi,


What you are missing is very simple. You seem to be assuming that torque is ONLY required to overcome INERTIA. Torque is ALSO required to overcome FRICTION.
In other words, what you are explaining yourself is only that which happens when only the inertia is considered in a system and the friction is ignored.

What you are considering is the torque that has to overcome the inertia only. To get acceleration the motor has to push harder because the inertia acts against change.
But after the motor comes up to speed and the speed remains constant, there is still friction in the system that requires constant push from the motor.

The friction and the inertia enter into the equation as two different constants. If you decrease the friction to zero then you dont need torque to keep the motor running, but that's not considered possible in the real world.

You can think of it as a brick flying through space vs sliding across a glass surface. The brick flying through space requires acceleration to get to speed, but after that no more force is required. The brick sliding on the surface however even after it comes up to speed needs constant force to keep it going because it is rubbing on the glass surface (even though the glass is smooth there is still some friction present).

So the bottom line is that there are at least two things that require torque from the motor:
1. Inertia
2. Friction

The inertia is something that requires an application of torque for a limited amount of time assuming the motor reaches some constant speed, but the friction is something that requires constant torque even after reaching the final speed.

Another way to think about it is like this...
Say you have a 'perfect' motor with no friction, but still has some rotational inertia. You start the motor up, it comes up to speed slowly, then reaches the final target speed, lets say 100 rotations per second. With no friction, the rotational inertia will keep the motor spinning indefinitely. This mean you can drop the motor current to zero (and thus have zero torque) and still have the motor keep turning.
But now you lightly touch a finger to the shaft of the motor, which causes friction between your finger and the shaft. What happens? Obviously the motor experiences friction now, which would tend to slow it down unless more current was delivered to the motor to keep it running at 100 rps as before, and this is because the current develops more torque in the motor. Thus the motor again runs as 100rps, but only with the addition of MORE torque.
Also, remove that extra current and that takes away that additional torque, which would then cause the motor to slow down, so it becomes clear that more torque is needed to overcome the friction. Since the friction is constant it requires constant torque to keep the motor up to speed.

A simplified model of the motor with no inertia and no inductance:

w=Ia*R*Km/(F*R+K)
where
w is the speed,
Ia is the armature current,
R is the armature resistance,
Km and K are motor constants,
F is the friction.

Since F is in the denominator, as F is increased it takes more and more current (Ia) to keep the motor at the same speed (w).

 

[lebevti]

ok thanks, that helps out, makes sense

 

[MrAl]

Hi,

I did a quick plot of speed with constant torque and with later the torque being reduced to zero, both with and without friction in the system. The torque was applied at t=0 seconds and reduced to zero at t=3 seconds.

The result with no friction in the system was the speed would ramp up and it would continue to ramp up forever but then when the torque was reduced to zero at t=3 seconds the speed leveled off and remained constant.

The result with friction however was much different, with two things most noticeable:
1. The speed did not ramp up as a straight line it did with no friction, but ramped up as a curved line, which means the speed would taper off to some constant value even with the constant torque applied instead of increasing indefinitely.
2. When the torque is reduced to zero at t=3 seconds, the speed immediately begins to decrease and eventually falls to zero.

So the main differences are that with no friction the speed ramps up indefinitely until the torque is reduced to zero and then it levels off and remains a constant (straight horizontal line), while with friction the speed ramps up as a curve and would eventually reach some finite final value until the torque is reduced to zero at which time the speed would fall and eventually reach zero.

This kind of behavior is usually what we see in nature. The friction in a mechanical system (or resistance in a circuit) is the main limiting factor.