# DC motor theory and model

39586 Views 115 Replies 14 Participants Last post by  gor
Hello All,
You may have seen my posts on other threads about a motor model I am developing. Well, I am pretty happy with it and so let me explain.
First, the torque generated by a motor is given by the armature current times the "field" times some constant depending on the motor structure and materials.
Second, the speed of the motor is given by the armature voltage applied to the magnetics [commonly called back emf or speed-voltage] divided by the "field' times some constant again depending on the motor structure and materials.
Lastly, the really *neat* thing is that, if we use SI units, the "field" and the constants are identical... So, we use Volts, Amps, Newtons-meter and radians per second to extract a single field function [or map] which depends only on the field coil ampere-turns and which implicitly contains all the mechanical and material constants. This motor seems to have very little hysteresis in the fields, if it did some other complications would arise.
Next we need to address losses:
First, the so called copper or resistive losses are easily understood with Ohm's Law in that is the speed-voltage is the applied voltage minus the current times the resistance minus brush voltage. So we have:
Speed=(V-IR-Vb)/field, which is field*speed=V-IR-Vb or we can solve

field=(V-IR-Vb)/Speed

Second, the so called iron or magnetic torque losses can be modelled as field squared times speed times a constant. There is also torque loss due to brush friction (Tb) I prefer the form:
Torque=field*Ia*(1-field*Speed/Ia*Rm) - Tb. This is a quadratic equation that can be solved for the field:

field = (Rm/2*speed)*(Ia - SQRT(Ia^2 - 4*speed*(Torque + Tb)/Rm))

When you have dynamometer data, you can extract the loss factors by doing a leastsquares minimization of the difference between the values of the field derived from torque and speed.

I will change this section soon and update the curves:
[I have taken the published dynamometer data for the WarP 9 at 72 volts and performed a least squares fit to the RPM vs. torque data using a four-parameter model for the field plus the resistances. The results for the field map and data fit are in the first attachment.]
I then used those parameters for currents up to 1000 Amps and voltage up to 150 Volts to generate conventional torque vs. RPM curves as in the second attachment.
The third file shows my preferred display of net power generated vs RPM for various voltages and currents. Efficiencies are also shown.
The model allows for separate handling of armature and field resistances, but the dataset does not allow that separation. I hope someone can tell me the those values. I believe this motor has 13 turns per field coil.
It is not possible to get brush losses from the data either.
The model does not account for "armature reaction".
The model is implemented as an excel workbook, not friendly enough for distribution yet. I may model other common motors if you make some specific measurements.
[12/30] At "Gor's" suggestion, I have added the current lines to the torque vs rpm curves posted.
[1/3] Added nominal torque values for each current line on power vs. rpm
[1/3] Added Torque vs. RPM chart
[2/6] edit formulas

#### Attachments

• 70.2 KB Views: 326
• 38.8 KB Views: 447
• 61.6 KB Views: 415
• 52.8 KB Views: 351
1 - 20 of 116 Posts

#### Georgia Tech

· Registered
Joined
·
406 Posts
I am looking for software that takes Field pole turns, area, amrature slot count, # poles, Lam Stack length and gives back the constanse for Torque and RPM...

#### GerhardRP

· Registered
Joined
·
541 Posts
Discussion Starter · ·
I am looking for software that takes Field pole turns, area, amrature slot count, # poles, Lam Stack length and gives back the constanse for Torque and RPM...
I don't do that much. I start with measurements on a motor as built and then modify only field windings to get a modified form a DIYer could do. Also to compare motors particularly regarding magnetic losses.

#### GerhardRP

· Registered
Joined
·
541 Posts
Discussion Starter · ·
I ran across this on another thread:

"You can look at some old Zilla Data capture plots
I did with Electrabishi if it help the explanation
http://home.gci.net/~saintbernard/"

Unfortunately, on first look, I was not even close to the measurements...

Fortunately, the data includes a run at motor voltage=72, the value used on the Warfield dyno..The first attachment shows the two curves. Clearly these motors are different.

Next I evaluated the Electrabishi field map as shown in the second attachment. The solid line is my previous map multiplied by two, It appears that the Electrabishi motor has an armature with twice as many turns as the Warfield dyno'ed unit.

Can anyone shed any light on this matter? Did Netgain change the armature at some point, or is this a re-worked motor?

Gerhard

#### Attachments

• 17.9 KB Views: 254
• 31.2 KB Views: 236

#### gor

· Registered
Joined
·
416 Posts
thank you, Gerhard

2. can you add current curves to voltage curves on tq/rpm plot?
thank you

#### Attachments

• 94 KB Views: 212
• 96.1 KB Views: 214

#### GerhardRP

· Registered
Joined
·
541 Posts
Discussion Starter · ·
thank you, Gerhard

2. can you add current curves to voltage curves on tq/rpm plot?
thank you
I've added the curent curve as in your request 2. See post #1
I think the other plot would get too messy with torque added, partly because it is so closely related to current.

Gerhard

#### gor

· Registered
Joined
·
416 Posts
I've added the current curve as in your request 2. See post #1
I think the other plot would get too messy with torque added, partly because it is so closely related to current.

Gerhard
thank you, Gerhard
so, on chart: WarP 9 Power vs RPM.pdf (61.0 KB) - if we put torque on the right-side vertical scale, torque curves will be about the same as current curves (1000A, 800A, 600A)?
may be add like: "1000A, 500Nm"?

(if plot it just to try and see if it worth it (or just to make sure where they are) - sometimes it's confusing how they all related) : ))))
preatty interesting - thanks again
something like on pictures attached, but how torque and power will look like on one chart (combined)...
http://www.uqm.com/propulsion_specs.php
http://www.uqm.com/pdfs/hitor%20spec%20sheet%209.22.09.pdfhttp://www.uqm.com/pdfs/PowerPhase 100.pdf

#### Attachments

• 71.6 KB Views: 218
• 68.4 KB Views: 197

#### GerhardRP

· Registered
Joined
·
541 Posts
Discussion Starter · ·
thank you, Gerhard
so, on chart: WarP 9 Power vs RPM.pdf (61.0 KB) - if we put torque on the right-side vertical scale, torque curves will be about the same as current curves (1000A, 800A, 600A)?
may be add like: "1000A, 500Nm"?
I have noted the nominal torque value for each current line in power vs. RPM.

(if plot it just to try and see if it worth it (or just to make sure where they are) - sometimes it's confusing how they all related) : ))))
pretty interesting - thanks again
something like on pictures attached, but how torque and power will look like on one chart (combined)...
Torque and power are linearly related... Power = Torque x Speed. Lines of constant torque vs. RPM are straight lines from the origin.
The charts you show are efficiency maps...cool. Do you have a link to the source for those curves.
Gerhard

#### gor

· Registered
Joined
·
416 Posts
p.s.well, one version could be bit messy - just to make sure all curves are where you think it should be - while other wersions - clean and easy to read
(and that's how we can see what layouts works better than the other ....)

thanks 4 update, Gerhard - looks pretty good - informative and intuitive - beautifull

that's the beauty
G., with and w/o efficiency curve, pleeeese

#### gor

· Registered
Joined
·
416 Posts
Gerhard, how Tq, Power and RPM curves would look on current and voltage(xy) scale?

#### GerhardRP

· Registered
Joined
·
541 Posts
Discussion Starter · ·
Added Torque vs. RPM chart to Post #1.
Gerhard

#### gor

· Registered
Joined
·
416 Posts
Added Torque vs. RPM chart to Post #1.
Gerhard
gorgeous
reminds hydraulic motors charts
now we have everything- from any point of view : ))))
Gerhard, can you put rpm on Volts(x) Amps axis?
would be great - plain simple: volts increasing(x) - Rpm goes... amps incr/decr -rpm (and torque) curve goes such and such...

#### Attachments

• 69.1 KB Views: 186
• 83.2 KB Views: 186

#### maxvtol

· Registered
Joined
·
118 Posts
Is there any chart comparable to what the Thunderstruck AC50 has, similar to a conventional ICE chart? I've included a chart below from the source here . I've included battery amps and efficiency.

I've never seen a Warp 9 or ADC motor chart that shows efficiency below 2158 rpm, so what is the efficiency of a DC motor at lower rpms, is it still in the 85%+ range? And I assume the efficiencies in a DC chart don't include the controller, so how can you compare?

My thinking is that if a DC motor has a higher efficiency from 0 to 2500rpm where the AC motor is low, this may compensate for the regen of the AC motor, ie from 0 to 15 or 20mph where the acceleration and the amps are the highest the DC is more efficient. Both AC and DC seem to be very efficient in the mid range.

The Wh/mile in the EVAlbum for the AC motors don't seem to be dramatically better than the DC motors. Other than the brush maintenance, I think I'm finding the DC a better solution for my EV project.

#### Attachments

• 73 KB Views: 180

#### major

· Registered
Joined
·
7,793 Posts
Is there any chart comparable to what the Thunderstruck AC50 has, similar to a conventional ICE chart? I've included a chart below from the source here . I've included battery amps and efficiency.

I've never seen a Warp 9 or ADC motor chart that shows efficiency below 2158 rpm, so what is the efficiency of a DC motor at lower rpms, is it still in the 85%+ range? And I assume the efficiencies in a DC chart don't include the controller, so how can you compare?

My thinking is that if a DC motor has a higher efficiency from 0 to 2500rpm where the AC motor is low, this may compensate for the regen of the AC motor, ie from 0 to 15 or 20mph where the acceleration and the amps are the highest the DC is more efficient. Both AC and DC seem to be very efficient in the mid range.

The Wh/mile in the EVAlbum for the AC motors don't seem to be dramatically better than the DC motors. Other than the brush maintenance, I think I'm finding the DC a better solution for my EV project.
Hi max,

Here is another one. If you study it you can see that low speed efficiency takes a dive at maximum torque output. And the curve you show is just that, max output. I suspect you would see a marked increase in motor/control efficiency if you just went to 90% torque at the lower RPM. But all motors, AC and DC are going to be 0% efficient at 0 RPM. So the DC motor efficiency will taper off as speed decreases also. You are hard pressed to find accurate information on this.

Which is better, AC or DC? It wouldn't surprise me if they were about the same. And how often and how long do you operate the motor at low RPM and high loads? And low RPM, even at high torque, is not going to command high power. So losses due to a few efficiency points difference may equate to a small amount of power for a short time, meaning not much energy wasted.

AC vs DC? Your choice. Low speed efficiency at maximum output may be a poor metric on which to base your choice, especially with the lack of good data on the available motor/controller products.

Regards,

major

#### Attachments

• 48.6 KB Views: 173

#### maxvtol

· Registered
Joined
·
118 Posts
Thanks major,
Here is another one. If you study it you can see that low speed efficiency takes a dive at maximum torque output.
That's still a AC motor curve. I was hoping for DC efficiency at low rpm. But if the efficiency curves vs rpm are similar, that answers my question. I just wonder why you can't seem to find a chart with efficiency at the lower rpms for a DC motor.

And how often and how long do you operate the motor at low RPM and high loads? And low RPM, even at high torque, is not going to command high power. So losses due to a few efficiency points difference may equate to a small amount of power for a short time, meaning not much energy wasted.
So for a 100 v pack and acceleration pulling 300 amps, wouldn't that pull out 30kw from the batteries for the accel period? The charts I've seen have more current drawn on startup for city driving (which mine will be mostly), so over 20+ stops/starts for my typical trip, the "area under the curve" for watts vs time could be significant for the acceleration. So if somehow the DC was more efficient during acceleration, even a small increase could make some difference, say enough to be as efficient as an AC with regen? That's what I was hoping to find out.

#### major

· Registered
Joined
·
7,793 Posts
So for a 100 v pack and acceleration pulling 300 amps, wouldn't that pull out 30kw from the batteries for the accel period? The charts I've seen have more current drawn on startup for city driving (which mine will be mostly), so over 20+ stops/starts for my typical trip, the "area under the curve" for watts vs time could be significant for the acceleration. So if somehow the DC was more efficient during acceleration, even a small increase could make some difference, say enough to be as efficient as an AC with regen? That's what I was hoping to find out.
Hi max,

You may be looking at motor current, which will be high at high torque regardless of RPM. But battery current will be lower than motor current at lower RPM because the motor voltage is lower than battery voltage. The controller is acting similar to a transformer giving you current multiplication at reduced voltage output. Motor performance curves alone will not show this.

If the mission for your EV has this much low speed (mph) and high torque (fast acceleration) requirement, maybe you need to consider a multi-ratio transmission. Also, that many stops may mean that you can benefit from regeneration more than most. Regeneration is not going to show up as efficiency on any of the curves you're looking at. And probably not in these Whr/mile figures posted for existing EVs. It is probably unwise to count on regeneration for any significant increase in available range using lead-acid batteries. I'm unsure about Lithium batteries as I've never tried it. But I can tell you regeneration is a nice feature. I like it.

Regards,

major

#### GerhardRP

· Registered
Joined
·
541 Posts
Discussion Starter · ·
Hi max,
<snip>
AC vs DC? Your choice. Low speed efficiency at maximum output may be a poor metric on which to base your choice, especially with the lack of good data on the available motor/controller products.
I am modelling the Warp 9 motor, but unfortunately at low RPM the losses are dominated by copper losses and I don't trust the resistances I estimated from Netgain's dyno curves. If you know accurate numbers for the armature and field resistances, I will draw a good low RPM high current efficiency map.
Thanks,
Gerhard

#### major

· Registered
Joined
·
7,793 Posts
.........Warp 9 motor.......... If you know accurate numbers for the armature and field resistances.......
Sorry, don't have those numbers. I had one of these motors here for a few months, but don't have a Wheatstone bridge. Even then you still have the pesky problem of brush voltage drop.

Regards,

major

#### maxvtol

· Registered
Joined
·
118 Posts
Motor performance curves alone will not show this.
Thanks major,
With my mechanical engineering background, I guess I'm just trying to compare AC and DC with apples and oranges data, and need to brush up on my electrical basics.

I love the idea of regen, but my little donor car (still ICE at the moment) is so much fun to drive, I think I'm going to have to go DC to keep the performance and stay within budget. I was just trying to justify DC in my mind, when like you said there's probably not that much difference.

#### maxvtol

· Registered
Joined
·
118 Posts
You may be looking at motor current, which will be high at high torque regardless of RPM. But battery current will be lower than motor current at lower RPM because the motor voltage is lower than battery voltage. The controller is acting similar to a transformer giving you current multiplication at reduced voltage output. Motor performance curves alone will not show this.
OK, just jumped on my e-bike and under hard acceleration, the amps on the battery maxes out (like I thought on my earlier question), but of course at steady speed is very low at low rpm like you say.

I guess my earlier question should have been does a DC motor/system accelerate more efficiently than an AC motor/system. I guess my error was trying to look at steady state chart data to try to figure this out.

1 - 20 of 116 Posts