# DC Series Motor Characteristic Question



## gunnarhs (Apr 24, 2012)

Frank said:


> Is there any way to use published "Speed-Torque" data for series wound motors to predict or estimate "generator" voltage (back EMF) as a function of speed? For example: at terminal speed in a race, my desired motor speed is 6K rpm, can I estimate what "Motor Volt" setting I need to ensure I can reach this? I'm trying to understand these things a bit better...
> 
> thanks


Here is a small article regarding the subject as general not sure it is what you are looking for 
http://www.precisionmicrodrives.com...-bulletins/ab-021-measuring-rpm-from-back-emf

here is an example from the text:
Motor performance-sheet
https://catalog.precisionmicrodrives.com/order-parts/product/106-002-6mm-dc-motor-12mm-type

Key data:
*Rated Voltage:* 3V
*N/L Current:* 20mA
*N/L Speed:* 23,000 RPM
*Coil resistance:* 16 Ω


Calculation
























































Now reading the Typical Performance Chart on the 106-002, at ~96 mA we can see the speed is ~12,500 RPM. 
We now have a way of calculating the back EMF and then in turn the speed of the motor from the measured current draw.


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## major (Apr 4, 2008)

gunnarhs said:


> .........<snip>........
> We now have a way of calculating the back EMF and then in turn the speed of the motor from the measured current draw.


Hi gunn,

That's interesting but not directly applicable to Frank's situation. Your referenced article deals with PM motors. Note:


> As the back EMF is generated from the rotor is moving through the magnetic field generated by the *permanent magnets*, the back EMF is directly proportional to the motor speed


 The fact that Frank has a series wound motor means that the flux is load dependent and that changes everything dealing with BEMF.

Frank,

I noticed your post and was going to reply but got busy with some battery testing and other crap. It would help me to understand why or what you think you can do with a BEMF value even if you had one  

In your example, 6000 RPM on your motor could occur with anywhere between about 25 Volts to 200 Volts depending on the load. Why would you not set motor Volts to the maximum the machine can tolerate? 

major


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## gunnarhs (Apr 24, 2012)

major said:


> Hi gunn,
> 
> That's interesting but not directly applicable to Frank's situation. Your referenced article deals with PM motors. Note: The fact that Frank has a series wound motor means that the flux is load dependent and that changes everything dealing with BEMF.


He,he I read the "generator" text instead of the headline, 
Also the graphs are more for "ideal" situation
The formulas posted are for the generator situation (regen phase) for PM of course..

But here for the series Motor

http://www.electrical4u.com/series-wound-dc-motor-or-dc-series-motor/

Here









The back EMF (E(b) decreases with load increasing the current. So it would be easier and make more sense in controlling current (torque) than Field/armature voltage (speed).
I do not know any standard speed/torque performance graphs posted for DC-series, but if the load situation is known E(b) can be estimated quite well.


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## Frank (Dec 6, 2008)

This was my thinking: If I cross the finish line at 6000 rpm and the controller is still in current limit, I could probably change the gearing (higher numerically), until it just goes out of current limit as I cross the line. In thinking about it now though, with a high voltage pack, why would the controller *ever* go out of current limit? The limiting factor would probably be the low battery cutoff voltage. I was thinking that knowledge of the theoretical bemf speed might help me somehow.

This leads to a more general question: assuming one is not traction or wheelie limited (in a motorcycle) how do you establish the ideal gear ratio in a single speed transmission situation?

I hope this makes sense...


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## major (Apr 4, 2008)

Frank said:


> This leads to a more general question: assuming one is not traction or wheelie limited (in a motorcycle) how do you establish the ideal gear ratio in a single speed transmission situation?


As the old TV game show----- The $64,000 Question 

There was some interesting discussion in my Torque is Relevant thread including some simulations. A lot of back and forth about Power vs Torque. But I still say for the best ET in the 1/4 mile: Gettin Goin Faster Sooner is critical. And that may not put the exit speed the highest. Or put peak power at the top speed. 

Find a good simulation program and develop sound models for the motor/controller and battery and start iterating. Validate your calculations with track experience. It takes some time, and practice, and you'll find some surprises. I think it was Shawn who tells the story of changing his ratio opposite of everybody's advice and improving his ET.


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## gunnarhs (Apr 24, 2012)

Frank said:


> This was my thinking: If I cross the finish line at 6000 rpm and the controller is still in current limit, I could probably change the gearing (higher numerically), until it just goes out of current limit as I cross the line. In thinking about it now though, with a high voltage pack, why would the controller *ever* go out of current limit? The limiting factor would probably be the low battery cutoff voltage. I was thinking that knowledge of the theoretical bemf speed might help me somehow.
> 
> This leads to a more general question: assuming one is not traction or wheelie limited (in a motorcycle) how do you establish the ideal gear ratio in a single speed transmission situation?
> 
> I hope this makes sense...


 1. You need to find out the max power your battery pack can deliver for the race-time, this will be the benchmark for your performance. 
Power = Voltage X Current
2. Then you will choose a (series) motor which can deliver this max power for the racetime at least which is usable for the batterypack and fits into the vehicle.
3. Controller should be chosen a bit bigger than max-power of motor.
Again power should be the limiting factor (P = Voltage X Current).
4. Single speed Ratio can be chosen for the median speed interval to start with (for a short track it is average speed for a long track the most common speed. Again Consider
Max - power for shorter race (and nominal power for a long race) 
Power = Torque * Speed (angular) = Force * Speed (Linear).
Wheel Torque = ratio * Motor Torque
Motor speed = ratio* Wheel speed.


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## Frank (Dec 6, 2008)

Thanks for the replies. I'll be reading that thread major. The motorcycle in question has been chassis limited up to now. I can now launch fairly hard w/o having to climb all over the thing while experiencing wheelspin at inopportune moments going down the track. I had my best pass ever two weekends ago, after which I discovered that I had my low battery voltage limit set too high. Sunday's weather is (so far) supposed to be good, although the season is winding down and high temp is predicted at only 58*F.

gunnarhs: I already have the machine running. The motor is the weak link in the power train (ADC 6.7" 4-brush motor, IIRC it's the version with 51 comm bars.) It has a Z1K and 72s2p 100c LiPo cells. I've run it at 900A/180V motor limits although I have no idea what voltage the motor experienced. (I also have doubts the motor ever saw 900A as the LBV limit was artificially limiting output.) The brushes and comm look pretty good so far. It's only 1/8-mile track so that is an advantage. I'm not sure how much more the motor can take but will try the full 1000A output if things work out this weekend.


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## gunnarhs (Apr 24, 2012)

Frank said:


> Thanks for the replies. gunnarhs: I already have the machine running. The motor is the weak link in the power train (ADC 6.7" 4-brush motor, IIRC it's the version with 51 comm bars.) It has a Z1K and 72s2p 100c LiPo cells. I've run it at 900A/180V motor limits although I have no idea what voltage the motor experienced. (I also have doubts the motor ever saw 900A as the LBV limit was artificially limiting output.) The brushes and comm look pretty good so far. It's only 1/8-mile track so that is an advantage. I'm not sure how much more the motor can take but will try the full 1000A output if things work out this weekend.


Hi looking at your specs if I understand you right you have a 
At least 46 kWh Battery Pack (144 X 100Ah cells at 3,2 V), which should put out 4-5C for such a short time (almost 200 kW). Controller does this easy too (assuming the ZK1-HV-version). Even if batteries would sag to under 3V you still would have enough Voltage for the motor. 
Assuming every component is OK it is more a question how to configure the controller. The quick and easy thing is to measure voltage and current battery side and the current motor side. Be sure that there is no setting in the controller that limits the current motor side less than 1000A.
When starting Motor current could be up to 3,5 times higher than battery current. When finishing the race battery current should be near motor current -> Voltage would be quite similar too.
For example
1) Start: Battery Voltage 230V, battery current 200A Motor current 700 A (about 50 kW)
2) Accel: Battery Voltage 200V, battery current 700A Motor current 1000 A (about 150 kW)
3) Finish: Battery Voltage 200V battery current 500A Motor current 500 A (about 100 kW)

I must admit that I have no drag racing and no motorcycle experience so my numbers may be out of way but the tendency should be that the optimal end speed would be when motor voltage/current gets near battery voltage/current without the battery - voltage sagging more than 20% (meaning motor reaching max speed). 
So by watching these three parameters for series motor this should be sufficient (I assume you have RPM ending by 6000)

What is your gear-ratio by the way?

PS: 
For series motor I would generally use lower gear ratio as it has high torque and it is shaky at high speed.
For high speed AC-motor (Siemens 1PV5135-4WS14) I would use Back-EMF calculation and higher ratio (up to 10 for car) with higher speed (meaning using speed to make torque) if I was using single ratio setup (I do not though).
For PM which has less high speed I would increase (armature) voltage a bit (not more than 20%) the same for SepExDC but keep the ratio for car at about 7) if I was using single ratio setup (we did)
For efficiency/range I would always use at least a two speed gear setup regardless of motor (try to keep the motor in optimal point and use a smaller motor which limits of course my max speed). But that is irrelevant here.


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## Frank (Dec 6, 2008)

Hi gunnarhs,

I wasn't clear when I listed the cell specs; they are 100C cells at ~4.4AH each, let's call it 9AH. I'm currently charging (sorry - bad pun) to 4.05 vpc so it's about 290 V off the charger. On a constant-power basis, if the motor sees 900A at 150V, battery current is about 550A (assuming they sag down to 250V.) I don't think the motor is seeing that: the Wallace Racing Calculator says my performance is obtained at ~ 65HP. Assuming typical lousy efficiencies, battery HP might be about 100 or 75kW; 300A at 250V.

Gear ratio is 65/14 and rear tire diameter is 26" I think. Thanks for your thoughts!

...still reading the "torque/relevant" thread...


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## Frank (Dec 6, 2008)

Frank said:


> ...still reading the "torque/relevant" thread...


Well, that was... a bit painful. Fortunately, most of the material was endless repeats of the same old positions, so I did a lot of skimming. I don't know if I should thank you or curse you, major. 

There is an analogous discussion in paved land-speed racing. Some are proponents of the "drag strip" launch i.e. launch hard, go through the gears hard. Others are "soft" starters i.e. get the clutch out easy, then go. 

p.s.: torque is relevant, lol.


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## major (Apr 4, 2008)

I hope it didn't hurt too much, Frank  Speed comes in many different flavors. And it makes a difference which flavor your tastes favor. You'll want to gear differently shooting for the standing mile, flying mile, average speed, exit (trap) speed, Elapsed Time, etc. 

Back to the topic: The DC series motor characteristic is uniquely appropriate for the drag race where you strive for the quickest ET in the 1/8 or 1/4 mile. And that characteristic is significantly different from what has been used in drag racing (namely the ICE) so there are few who really understand how to apply it (choose the proper gear ratio).


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## Frank (Dec 6, 2008)

Jeff, do you follow the NEDRA list? Here's the question I posted over there:

Here is something I don't understand: the various Wallace Racing Calculators indicate between 62-70 rwhp based on 60' time, ET and speed. Let's call it 60kW for arguments sake. At 900A that's only 66 volts at the motor! Even with *very* bad efficiencies the numbers don't add up. Maybe these calculators don't work for lighter weights? Does anyone know of a different calculator? I know how to do the math, just don't want to program it! What am I missing??

One of the reasons for my original question in this thread (is it possible to calculate BEMF from published data) was so I might validate this kind of information.

Thoughts?


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## major (Apr 4, 2008)

Frank said:


> Jeff, do you follow the NEDRA list? Here's the question I posted over there:
> 
> Here is something I don't understand: the various Wallace Racing Calculators indicate between 62-70 rwhp based on 60' time, ET and speed. Let's call it 60kW for arguments sake. At 900A that's only 66 volts at the motor! Even with *very* bad efficiencies the numbers don't add up. Maybe these calculators don't work for lighter weights? Does anyone know of a different calculator? I know how to do the math, just don't want to program it! What am I missing??
> 
> ...


Let's take a look at what is actually happening during your pass. Can post the Zilla data from the 900A run? What is the actual motor voltage? And for a 6.6" 4 brush motor, efficiency will suck at 900A and low voltage. At launch it is zero percent efficient  

I never understood those calculators for HP. How can you have 62-70 rwhp at zero RPM on the rear wheel? So is it average power for the distance, or peak? Does it assume some type of standard clutch for launch? Dumping numbers from an electric pass into an ICE calculator is bound to indicate funny results, IMO.

What always holds true is F = ma. That is what the fellow was using to calculate the race performance in the torque-relevant thread. But I doubt you have the torque curve for the motor. And from what I read, it may no longer be in running shape  Otherwise, you could have run some simple tests to determine the torque/amp.

BTW, I do follow the NEDRA list on email. Bill D used to do the calcs using a spreadsheet with each row being a 0.001 second increment during the pass. Just a piecewise integration of the F=ma but he tells of good correlation to Killacycle track times. I bet he'd help you.


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## GerhardRP (Nov 17, 2009)

major said:


> <snip> But I still say for the best ET in the 1/4 mile: Gettin Goin Faster Sooner is critical. And that may not put the exit speed the highest. Or put peak power at the top speed.
> <snip>


I have said [but I don't know if anyone listened] that you should set your gears so that at maximum torque output of the motor, you barely have traction...be just under wheel spin. That will use the most of your motor.
I second Major's request for a Zilla data dump.


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## major (Apr 4, 2008)

Frank said:


> Jeff, do you follow the NEDRA list? Here's the question I posted over there:
> 
> Here is something I don't understand: the various Wallace Racing Calculators indicate between 62-70 rwhp based on 60' time, ET and speed. Let's call it 60kW for arguments sake. At 900A that's only 66 volts at the motor! Even with *very* bad efficiencies the numbers don't add up.


Did you see John Metric's comment? 


> I found that calculator for a single gear EV gives roughly half the actual peak rear wheel horsepower number. Very roughly.


Does that make you feel any better?


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## Frank (Dec 6, 2008)

... Just another piece of information. Mike W.'s post that their Junior's motor voltage only rises to 40V at 3750 rpm is very interesting. It tells me how important understanding the speed limits of these motors is. If I'm geared for, say, 7500 at 120 mph and the motor can safely turn 9000 then I'm giving up potential acceleration force. Potential meaning only if it can be used. If 120 is unrealistic there's more to be had there as well. My comment about only 60 some-odd volts at the motor only shows my ignorance/assumptions about what I thought was happening, lol.


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## GerhardRP (Nov 17, 2009)

Hi Frank,
You might try reading my old motor theory thread http://www.diyelectriccar.com/forums/showthread.php/dc-motor-theory-and-model-39931.html
If you can get zilla dumps [even just the octal form] I might be able to analyse your system. What would be best is a series of runs with different motor current limits, say 200,400,600, 800 amps. Then for good measure, do a coast-down.
Gerhard
PS. I did find a performance graph if your motor is X91-4001. It says "calculated" meaning, I think, extrapolated from an 86V measurement.


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## kennybobby (Aug 10, 2012)

Frank said:


> Is there any way to use published "Speed-Torque" data for series wound motors to predict or estimate "generator" voltage (back EMF) as a function of speed?
> ...


If you use SI units (Nm/A for KT, V/(rad/s) for KEMF), then KT = KEMF for DC motors and permanent-magnet synchronous. For english units Kb=1.356*Kt (ft-lbs).

For the motor chart above at 50 ft-lbs (260 Amps), i calculate about 0.26 V/rad/sec, or 27.2 V per 1000 RPM. This is your 'generator' voltage.

So for the 144-.03xI curve, the motor voltage was 136.2 - 3.7(27.2) = 35.5 volts. 144 applied minus IR drop minus Vbemf.

Mechanical power ~35 hp, Electrical input power 144v x 260A ~50 hp.


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## major (Apr 4, 2008)

kennybobby said:


> If you use SI units (Nm/A for KT, V/(rad/s) for KEMF), then KT = KEMF for DC motors and permanent-magnet synchronous. For english units Kb=1.356*Kt (ft-lbs).
> 
> For the motor chart above at 50 ft-lbs (260 Amps), i calculate about 0.26 V/rad/sec, or 27.2 V per 1000 RPM. This is your 'generator' voltage.
> 
> ...


Hey kenbob,

Your Kt, Kv method isn't typically applied to series wound motors because the flux is not constant as in PMDC motors. Those K constants include the motor flux. So, in other words, series motors have a load dependent torque/amp and RPM/volt constant. Some linear approximation can be applied to the series motor once it is into saturation.

I do fail to see what or how your calculation of 35.5 motor voltage relates to that curve  

Regards,

major


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## kennybobby (Aug 10, 2012)

i was only calculating the motor voltage for comparison to the OP's information. From a practical standpoint most folks probably wouldn't be talking motor voltage but rather pack supply voltage.



Frank said:


> ... Just another piece of information. Mike W.'s post that their Junior's *motor voltage only rises to 40V at 3750 rpm* is very interesting. ... ... My comment about only 60 some-odd volts at the motor only shows my ignorance/assumptions about what I thought was happening, lol.


But the motor voltage is less than the supply due to IR drop and back emf.


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## major (Apr 4, 2008)

kennybobby said:


> But the motor voltage is less than the supply due to IR drop and back emf.


I do not understand. Motor voltage can be measured at the motor terminals. The generated voltage (some call BEMF) is the motor voltage minus the IR drop inside the motor (armature current times the winding resistance plus the voltage drop in the brushes). In most cases motor voltage is equal to supply voltage minus a fraction of a volt drop in the cables from the supply to the motor. In the EV case, the supply is the motor controller. Motor voltage is typically assumed equal to the controller output voltage which is battery voltage times the PWM duty cycle.

All of this and I still see nothing of 35.5V or thereabouts.


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## GerhardRP (Nov 17, 2009)

major said:


> I do not understand. Motor voltage can be measured at the motor terminals. The generated voltage (some call BEMF) is the motor voltage minus the IR drop inside the motor (armature current times the winding resistance plus the voltage drop in the brushes). In most cases motor voltage is equal to supply voltage minus a fraction of a volt drop in the cables from the supply to the motor. In the EV case, the supply is the motor controller. Motor voltage is typically assumed equal to the controller output voltage which is battery voltage times the PWM duty cycle.
> 
> All of this and I still see nothing of 35.5V or thereabouts.


I am always bemused by the often expressed effort to reduce the BEMF as if it were some sort of loss. The motor voltage is the sum of Ohmic loss, brush voltage and the BEMF. The power converted by the motor is the BEMF times the current. BEMF is the good guy in this equation.


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## Frank (Dec 6, 2008)

Thanks for everyone's input. I would like to supply a data dump but the racing season is over, the drag strip is closed and the motor is hurt (I may be looking for an upgrade anyway).

I believe the motor is a K99-4007 which is electrically identical to K91-4003. I don't think it's the same as the x91-4001 but don't know for sure.  Based on weight, it is not however.

Gerhard, I'll have a look at that thread.


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