# Series Motors 101



## Tesseract (Sep 27, 2008)

I have specific data for the field windings but was told the armature resistance is typically half that of the field....

WarP 9 = 3.29mΩ
WarP 11 = 7.80mΩ
TransWarP = 7.80mΩ


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## gerd1022 (Jun 9, 2008)

thanks... my excel sheet is growing. I'll be able to post some info tonight


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## Tesseract (Sep 27, 2008)

gerd1022 said:


> thanks... my excel sheet is growing. I'll be able to post some info tonight


That's one helluva night... do you live near the arctic circle??? 

One thing I am curious about, since this is series motors 101, is the trade-offs from advancing the brush timing besides the obvious ones like forget reversing and really forget regen.

That is, which is better for EV's: a neutrally-timed motor wound for a higher voltage (eg - the ES-31B from D&D) or a lower voltage (higher ampacity) motor with advanced brush timing to tolerate the higher voltage???


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## gerd1022 (Jun 9, 2008)

Tesseract said:


> That's one helluva night... do you live near the arctic circle???


ouch... haha. sorry ive been a bit busy

anyway, ill so what i did was first i decided to use the data from the Warp 9, which seems to be probably the most common motor for EVs and the data for 72 volts is available online.

So i used the equations 

T= (1/(K_t*K_f))*(V/(w+R/(K_t*K_f)))^2

T = K_t*i^2

In the above equations, T = torque, K_t is a constant, K_f is a constant, V is the applied voltage, w (lowercase omega) is the angular speed, R is the resistance, and i is the current.

First i used the data from the warp site to plot a Torque vs current graph, then a Torque vs speed graph. These graphs are attached. I then did a curve fit for the T vs i graph and found an approximate K_t. 

Once i knew K_t, i could plot the theoretical torque speed equation on the measured torque speed graph. The only unknown was K_f, so i played around with the value until the theoretical and measured were as close as possible.

Once i had the equation for 72 volts, i could change the voltage and see where the curve went. Since PWM essentially changes the voltage applied to the motor, this was the equivalent of stepping on your throttle. 

Next i did a pretty rough load curve for my 78 Triumph spitfire of about 1000 kg, taking aerodynamics, rolling resistance and gearing into account. I could then overlay the load curves for different gearing over my motor curves. The intersection of the two curves told me what voltage and amperage i would be operating at the achieve each speed in each gearing.

This graph can also be seen attached. An example of how to read it, in third gear, if i want to go 50 mph, i have to apply 72V to the motor and i will be pulling about 120 amps. 

Note, the axes on the two torque speed graphs are N-m and radians/sec, in order to convert to actual car speed, you have to divide the motor speed by the gearing reduction and multiply by the tire radius. 




> One thing I am curious about, since this is series motors 101, is the trade-offs from advancing the brush timing besides the obvious ones like forget reversing and really forget regen.
> 
> That is, which is better for EV's: a neutrally-timed motor wound for a higher voltage (eg - the ES-31B from D&D) or a lower voltage (higher ampacity) motor with advanced brush timing to tolerate the higher voltage???


thats a very good question, i would tend to think a motor rewound for 144 volts might be better, as advancing the brushes seems like a kind of half assed approach to the problem, however, i remember from my motor class that since rewinding changes the resistance and the motor constants, it usually leads to worse performance at lower voltages than the "intended" voltage.


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## tomofreno (Mar 3, 2009)

This is very interesting! Have you done any further work to determine accuracy? I would like to estimate vehicle range with the WarP9 motor. In order to do that I need to know the motor efficiency at a given vehicle speed, so I need to know input and output power. The manufacturer's curves would give this information, but as you say they are only available for certain motor voltages. 

The required HP (accounting for drive train efficiency) to move the vehicle at a given speed will tell me the power out. But I need the motor voltage and current required to deliver the required motor torque to estimate input power. The ratio of the two powers will estimate the efficiency at a given vehicle speed. 

It looks like your last graph is motor torque vs motor rpm, with required torque to move the vehicle in 3 different gears. So you determine the voltage required to supply the required torque from this graph, then use the other graph of motor torque vs motor current to determine the required motor current. The product of this current and voltage give me the input power I want to determine. Correct?


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## tomofreno (Mar 3, 2009)

In your torque-current graph you show a fitted equation of the form ax +bx*x. But the torque equation has no linear term, it only depends on current squared, so I don't see how you obtained an estimate of kt from this. The WarP9 data is fairly linear with only a very weak quadratic dependence, so impossible to get a good fit with only a current squared term. I'm not sure how to proceed.


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## gerd1022 (Jun 9, 2008)

its been awhile since i looked at that... but i think if you look at the torque current curve, you can see the manufacturers specs ( i think i called them the "Measured Values"), and the quadratic curve fit that excel put on. 

The last pink line is the line that i made using the equation T = K*I^2. I used the excel curvefit as a starting point to estimate my K, then fiddled with it till it looked good. Not the most scientific approach, but it was pretty much all I could do.


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