  ### Author Topic: How resistance and inductance affect the behavior of DC motor  (Read 1813 times)

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#### fishandchips

• Regular Contributor
• • Posts: 178
• Country:  ##### How resistance and inductance affect the behavior of DC motor
« on: April 18, 2017, 10:16:31 pm »
Just curious, how the resistance and inductance of a DC motor affect its behavior?

#### Benta

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• Country:  ##### Re: How resistance and inductance affect the behavior of DC motor
« Reply #1 on: April 19, 2017, 12:51:11 am »
Ideally, a DC motor should have zero resistance. Any resistance is pure heat loss, whether it's the armature windings or the brushes.
The reactance is not very interesting when supplying the motor with pure DC, but will have an impact when using PWM control.
More important, though, are parasitic losses, specially iron loss. I've seen motors that wouldn't even start when PWMd at 20 kHz. Most RC model motors are PWMd at 1...3 kHz, no higher, for this reason.

#### MrAl

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•  • Posts: 467 ##### Re: How resistance and inductance affect the behavior of DC motor
« Reply #2 on: April 19, 2017, 12:52:33 am »
Just curious, how the resistance and inductance of a DC motor affect its behavior?

Hi there,

The resistance sets the max current through the armature, along with the back emf.
The inductance limits the current over time, so that when we apply a voltage to the motor it takes time for the motor to reach full current even though it may happen quickly.
Since the torque is depending on the current, the torque builds up as a function of the inductance also.  This means that the motor gets more and more torque as time progresses.  That in turn means that the rotational inertia and friction gets driven by a gradually increasing torque, and that slows the progress of getting the motor up to speed also.
So the inductance acts similar to the rotational inertia in that it prevents the motor from getting up to max speed in zero time, but takes some finite time to get there.  Once the motor gets up to normal operating speed, the current into the motor is limited by the resistance, and the resistance and the friction limit the final speed once the inductance and rotational inertia effects settle down.

An analogy would be two low pass filters connected one after the other.  The first low pass filter is made from the resistance and inductance, the second is made from the rotational inertia and friction.  When we first apply the voltage to the motor/filter, the output of this analogous filter takes time to build up to maximum.

There is also some feedback which is usually called the "back emf" which acts to subtract from the applied voltage thus limiting the maximum speed as well.

« Last Edit: April 19, 2017, 12:54:57 am by MrAl »

#### Benta

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•   • Posts: 2030
• Country:  ##### Re: How resistance and inductance affect the behavior of DC motor
« Reply #3 on: April 19, 2017, 01:33:17 am »
Just curious, how the resistance and inductance of a DC motor affect its behavior?

Hi there,

The resistance sets the max current through the armature, along with the back emf.
The inductance limits the current over time, so that when we apply a voltage to the motor it takes time for the motor to reach full current even though it may happen quickly.
Since the torque is depending on the current, the torque builds up as a function of the inductance also.  This means that the motor gets more and more torque as time progresses.  That in turn means that the rotational inertia and friction gets driven by a gradually increasing torque, and that slows the progress of getting the motor up to speed also.
So the inductance acts similar to the rotational inertia in that it prevents the motor from getting up to max speed in zero time, but takes some finite time to get there.  Once the motor gets up to normal operating speed, the current into the motor is limited by the resistance, and the resistance and the friction limit the final speed once the inductance and rotational inertia effects settle down.

An analogy would be two low pass filters connected one after the other.  The first low pass filter is made from the resistance and inductance, the second is made from the rotational inertia and friction.  When we first apply the voltage to the motor/filter, the output of this analogous filter takes time to build up to maximum.

There is also some feedback which is usually called the "back emf" which acts to subtract from the applied voltage thus limiting the maximum speed as well.

Some things are a bit off here.

First, torque is demanded from the mechanical load and not defined by the motor. The motor will try to deliver this torque, and will pull current accordingly. A more appropriate term might be "available torque", meaning it's there on demand.
Second, yes, inductance has an effect, but it's probably an order of magnitude lower than mechanical inertia.
Third, back EMF, which you dismiss as a feedback-related side show, is the key operating parameter for a DC motor. The back EMF is directly proportional to rpm, and only when supply voltage and back EMF are the same (minus losses) is the motor in equilibrium and will run steadily at a certain speed.

An ideal motor (zero resistance, inductance and other losses) will run at a constant speed at constant voltage no matter how much torque is demanded from the mechanical load - and will pull current accordingly, actually meaning zero current at zero load (which is utopical, of course).

« Last Edit: April 19, 2017, 07:32:28 am by Benta »

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#### MrAl

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•  • Posts: 467 ##### Re: How resistance and inductance affect the behavior of DC motor
« Reply #4 on: April 19, 2017, 11:43:09 pm »
Just curious, how the resistance and inductance of a DC motor affect its behavior?

Hi there,

The resistance sets the max current through the armature, along with the back emf.
The inductance limits the current over time, so that when we apply a voltage to the motor it takes time for the motor to reach full current even though it may happen quickly.
Since the torque is depending on the current, the torque builds up as a function of the inductance also.  This means that the motor gets more and more torque as time progresses.  That in turn means that the rotational inertia and friction gets driven by a gradually increasing torque, and that slows the progress of getting the motor up to speed also.
So the inductance acts similar to the rotational inertia in that it prevents the motor from getting up to max speed in zero time, but takes some finite time to get there.  Once the motor gets up to normal operating speed, the current into the motor is limited by the resistance, and the resistance and the friction limit the final speed once the inductance and rotational inertia effects settle down.

An analogy would be two low pass filters connected one after the other.  The first low pass filter is made from the resistance and inductance, the second is made from the rotational inertia and friction.  When we first apply the voltage to the motor/filter, the output of this analogous filter takes time to build up to maximum.

There is also some feedback which is usually called the "back emf" which acts to subtract from the applied voltage thus limiting the maximum speed as well.

Some things are a bit off here.

First, torque is demanded from the mechanical load and not defined by the motor. The motor will try to deliver this torque, and will pull current accordingly. A more appropriate term might be "available torque", meaning it's there on demand.
Second, yes, inductance has an effect, but it's probably an order of magnitude lower than mechanical inertia.
Third, back EMF, which you dismiss as a feedback-related side show, is the key operating parameter for a DC motor. The back EMF is directly proportional to rpm, and only when supply voltage and back EMF are the same (minus losses) is the motor in equilibrium and will run steadily at a certain speed.

An ideal motor (zero resistance, inductance and other losses) will run at a constant speed at constant voltage no matter how much torque is demanded from the mechanical load - and will pull current accordingly, actually meaning zero current at zero load (which is utopical, of course).

Hello,

Things are a bit off in your reply.  You are interpreting the intent incorrectly.

First, one of the questions was about inductance, so the answer included inductance.  It doesnt matter how high or how low when it comes to deciding whether to reply about inductance or not.  If you want to add to the discussion then you should do so without implying that there was some kind of mistake.  We cant say everything in one reply.  Does the inductance play a lesser role than rotational inertia?  Only on one aspect of the motor and that is with respect to the speed.  The direct electrical effects are much more significant.  You chose to reply only to the effect it has on the speed as compared to the effect on the speed the inductance has.

Second, who is 'dismissing' the back emf?  That was specifically addressed in the reply so nobody was 'dismissing' the back emf here.  The back emf feedback is a large controlling factor.

My advice to you is as follows:
1.  First, read the reply more carefully.  Try to understand what is being said.
2.  Study the electrical effects of the inductance as well as the effect it has on shaft speed.
3.  Torque is developed from the motor current.  The load responds to that force.

This can be an interesting discussion if you, as they say, just chill out a little :-)

#### rstofer

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• Country:  ##### Re: How resistance and inductance affect the behavior of DC motor
« Reply #5 on: April 20, 2017, 02:16:55 am »
I remember taking a class in motors, rotors and dynamos in college and the part I recall is where the math got deep.  I still have the book but none of the knowledge.

Mathworks has a pretty good discussion on modeling DC motors.  Matworks has a pretty good discussion on just about everything!

https://www.mathworks.com/help/physmod/elec/ref/dcmotor.html

An example of the overall importance of inductance:

Quote

Armature inductance
Inductance of the conducting portion of the motor. If you do not have information about this inductance, set the value of this parameter to a small, nonzero number. The default value is 1.2e-05 H.

More simply, as pointed out above, inductance isn't a factor of significance right up until PWM shows up.

Here is another Mathworks video re: DC motor control:

https://www.mathworks.com/videos/speed-control-of-a-dc-motor-using-pwm-68962.html

https://www.precisionmicrodrives.com/tech-blog/2015/08/03/dc-motor-speed-voltage-and-torque-relationships
« Last Edit: April 20, 2017, 02:21:53 am by rstofer »

#### Zero999 ##### Re: How resistance and inductance affect the behavior of DC motor
« Reply #6 on: April 20, 2017, 02:28:33 am »
Quote

Armature inductance
Inductance of the conducting portion of the motor. If you do not have information about this inductance, set the value of this parameter to a small, nonzero number. The default value is 1.2e-05 H.

More simply, as pointed out above, inductance isn't a factor of significance right up until PWM shows up.
Yes, in a DC motor armature, the inductance is akin to the leakage inductance in a transformer, which will be small.

#### MrAl

• Frequent Contributor
•  • Posts: 467 ##### Re: How resistance and inductance affect the behavior of DC motor
« Reply #7 on: April 20, 2017, 09:35:51 pm »
Hello again,

Yes, the inductance has an effect but it does depend on the application as mentioned.
In some apps inductance will hardly have an effect, because the main point is the speed of rotation and the torque.  But what we usually like to do is know ALL of the effects and then dismiss any that may not be needed at the time of analysis, not before that.

So what this boils down to is that the there is some inductance, and that inductance may or may not have an effect on the overall system in the given application.

An application that will not feel the significance of the inductance is when the motor is running constantly.  The effects of the inductance go away after a short time period, so if it is running constantly the inductance will no longer play a part.
Conversely, connect a large DC motor to a DC power supply with jumper leads and let it run for several seconds, then disconnect the motor and watch the spark fly :-)  The spark is due to the inductance mostly.
What this means is that we could make a boost converter out of a motor although it may not be the best :-)

As has been said a PWM application may feel the presence of the inductance much more than a regular constant run motor application, but to take the point home, where we really see a big impact is in a stepper motor application where a good drive circuit takes into account the inductance as one of the key points of the design, by making the voltage source as high as possible.  This aids in the speed of response by a large factor and that is much more important in a stepper.

So in conclusion we see applications where L is important and applications where L is not important, but knowing how to deal with it means that gives us the ability to decide when it is important and when it is not, and when it is we know how to handle it.  If we ignore it ALL the time, we will eventually run into a problem when it becomes important because we wont know it was important :-)

As in many design settings a good idea is to look at the defining equations as rstofer pointed out.  That's the best route to take i believe, maybe the only one that will work in every case.

Just as a quick reference, the inductance enters into the denominator of the motor equation:
K/(s*L+R)

where we also see the resistance R.  This is the main torque developer and is powered by the applied voltage minus the back emf.  We can see that is similar to a low pass filter, and we know that a low pass filter takes time to react to a step change in input.  For the motor that means the torque is delayed by some amount, and that means the force applied to the shaft is delayed by some amount.  The amount of delay however is only part of the story, the physical effect, and while the delay is caused by the inductance the purely electrical effect is separate and may appear external to the motor in the leads of the motor as a current and voltage.
« Last Edit: April 20, 2017, 09:44:49 pm by MrAl »

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