A Brief Word on Batteries

[Carlos E Rodriguez]

2 hours ago, KingSong69 said:

@esaj

Fantastic explanation!!

I have learned from the e-bike forums to say the complicated EMF things in a one short term:

Speed is Voltage related

Torque is Amp related

:-)

what also has helped me in vaping to understand how each variable has its factor is this little tool:

http://www.sengpielaudio.com/Rechner-ohm.htm

Give in a Voltage (67volt full/or 53Volt near empty) and a needed wattage (800watt) and you will get shown the amperage which has to be delivered by the batteries:

67/800: 11,94Amps

53/800: 15,09Amps

Thats why i try to avoid high speeds, hills and hefty accelerations on half or going empty batteries...the amperage can get a lot higher to do the same thing...and may be to much for the batteries designed envelope 

http://lancet.mit.edu/motors/motors4.html

[Keith]

13 minutes ago, Carlos E Rodriguez said:

http://lancet.mit.edu/motors/motors4.html

..... and as those rather useful, and very well known, graphs show:

Speed is Voltage related (kV =RPM/Volt)

Torque is inversely speed related

 

[Chriull]

9 hours ago, Keith said:

 

Torque is inversely speed related

 

Sorry for beeing picky - torque is current related, max torque is inversely speed related. 

Edit:

With torque M = k * I and I = ( Ubatt * duty_cycle - Uback-emf) / Rcoil ...(1)

M = k * (Ubatt * duty_cycle - kv * omega) / Rcoil

the statement torque is inversely speed related is imho not wrong.

Just my above statement could be refind to:

torque is proportional to current.

But with :

Imax(v) = k * (Ubatt - kv * omega ) /Rcoil = k1 - k2 * v ...(2)

and so Mmax(v) = k3 - k4 * v

How is this relationship called, since it is neither proportional nor invers proportional? The are in a "linear context" - is there any more specific way to describe this?

 

(1) for "stable" states once dI/dt is small enough to neglect the inductance of the coils for simplicity

(2) for simplicity again assuming that a duty_cycle of 100% would be possible, since the internal resistance of the battery is not regarded, this should not matter for a first approach, Since Ubatt is here considered as "constant" i included it in the fix konstant k1.

[Mono]

 

12 hours ago, Chriull said:

There is roughly a voltage sag of 20V at full load (~45A) and this is not at a really low speed (~20 km/h).

[...]

The max current happens somewhere near the max power, so both graphs can be "combined"

I find it a little difficult to combine the graphs. Crucially though, I tend to believe the +40A current peaks are not at max power, but at startup (note also that before the peaks the current is essentially zero for a long time). That is kind-of the whole point of my what-am-I-missing question. Current going down with increasing speed and not maxing out at max power is what our theoretical model suggests and I wouldn't know how to explain the 0A current preceding the peaks and the 10A currents following the peaks otherwise. What I find strange is that the current just drops to zero at the end without any voltage drop (the voltage drops only after the current is essentially zero). That suggests indeed that the battery is not the limiting factor in the end at all, which was the suspicion to begin with. AFAICS what we observe here is an overlean due to shortage of motor power, not due to shortage of battery power. 

12 hours ago, Chriull said:

If you describe a bit more more why you think battery voltage does not inflict max speed it would be easier for us all together to refine and formulate correctly the relation.

Bottom line: I don't think that battery voltage does not inflict max speed, but I did consider voltage to be a (rather) constant factor in the equations. Why? 

On the motor side: to my understanding we do not modulate voltage to larger values than the battery provides. I understand that this part isn't that simple, but as we have conservation of energy we can look at simpler parts of the system to draw conclusions. I assume a motor is designed for a certain voltage and operating it at higher voltage will increase failure rates. 

On the battery side: to my understanding we do not (and cannot) modulate the voltage of the battery. What we modulate is the current flow by (more or less) shorting the poles. Sure, with changing current we see the voltage change in some inverse and to the most part moderate relation (larger current, smaller voltage). That is all there is to it on the battery side: we modulate current, we see to the most part insignificant voltage changes, we can compute the energy we can and have to dissipate.

Now it dawns me that your point is that you want to avoid running the wheel with half-empty battery and hence reduced "base voltage". For example, by doubling the battery capacity you want to be able to cycle between, say, 100 and 70% instead of 100 and 40%. Fair enough, it gives you an voltage boost of at most about 10% = 3.84 / 3.48 - 1. Running on full battery gives 17% more voltage than running on half-empty battery, which translates into more power and more speed. Fair enough. That wasn't my point though  (which was comparative battery demand at different speeds, not comparative battery performance at different charge levels). Since I moved from Gotway to InMotion, battery charge status has become an almost imperceptible and entirely insignificant thing. But then I also tend to never push into the wheels speed limit...

[Mono]

10 hours ago, Chriull said:

How is this relationship called, since it is neither proportional nor invers proportional? The are in a "linear context" - is there any more specific way to describe this?

The technical term from maths would be affine, maybe also affine linear, and you may add with negative coefficient, but it doesn't really help if only (some) mathematicians and physicists understand what you are saying.

[Chriull]

51 minutes ago, Mono said:

 

I find it a little difficult to combine the graphs. Crucially though, I tend to believe the +40A current peak is not at max power, but at startup (note also that before the peak the current is essentially zero).

The first graph ist the power, the wheel puts on the "road(dynamometer)" - this power has to come from the battery plus the inbetween losses. The power from the battery is U*I  (1) - the voltage has the max sag at the max current peak - so the max power presumably could lie not exactly at the current peak, but somewhere very near.

51 minutes ago, Mono said:

That is kind-of the whole point of my what-am-I-missing question. Current going down with increasing speed and not maxing out at max power is what our theoretical model suggests and I wouldn't know how to explain the 10A currents following the peak otherwise.

At the first chart one sees the braking curve ( the part of the line with "negative" power) - this should be the "low current" part (~10A) of the middle voltage/current graph after the peak (non-regenerative braking)

51 minutes ago, Mono said:

What I find strange is that the current just drops to zero at the end without any voltage drop (the voltage drops only after the current is essentially zero).That suggests indeed that the battery is not the limiting factor in the end at all, which was the suspicion to begin with.

? Sorry imho i do not really get this content? Once the measurement stopped there is no speed/acceleration/torque anymore, so no current and no voltage drop anymore  (just a little lower voltage than at the beginning of the measurement in because of the burden to the battery).

The strange voltage drop inbetween the three measurements are imho contact problems or short disconnects to the measurment equipment while preparing the next dyno run.

51 minutes ago, Mono said:

AFAICS what we observe here is an overlean due to shortage of motor power, not due to shortage of battery power. 

Imho thats a nice overlean he produced, but maybe he also just stopped accelerating since he recognized he got the peak motor power and started braking the dynamometer with the wheel. The curve from "INMO V8 VITALIY" is one of the few which show the power graph almost up to max speed - could be just hard to handle the dyno without overleaning? My understanding of this graphs is, that he "walks" down the max-torque(power) vs speed limit after the absolutely max power reached - so imho he should be "throughout on the edge" to overlean.

Such an overlean happens due to shortage of motor power. But this max available motor power at this special point (the max power/torque at this speed) is a function of the available Battery voltage. So yes, it is not due to shortage of battery power - its shortage of motor power "inflicted by shortage of battery voltage"

As one sees in the comparison graph of the original and the vitaliy Inmotion V8, the vitaliy V8 reaches a higher power at higher speeds because he put stronger batteries inside. So less voltage sag and by this a higher voltage difference and higher current flowing and a higher output power is possible.

The exactly same wheel with an 90V battery pack instead of the 84V would show again more power at higher speeds... (if the electronics and the motor survive).

But finally yes - if one considers battery voltage as a constant this gives a constant max-power/torque vs speed chart which determines the motor capabilities.

But as you got "my point of view" - if the voltage sags due to the burden, the motor capabilities are limited by this. So the max-power/torque vs speed chart is nomore constant again - the limit is shifting up and down -> so a "stronger" battery can decrease the amount of this shifts. A higher voltage battery can nicely shift this limit up to give more power, etc...

 

51 minutes ago, Mono said:

Bottom line: I don't think that battery voltage does not inflict max speed, but I did consider voltage to be a (rather) constant factor in the equations. Why? 

On the motor side: to my understanding we do not modulate voltage to larger values than the battery provides. I understand that this part isn't that simple, but as we have conservation of energy we can look at simpler parts of the system to draw conclusions.

On the battery side: to my understanding we do not (and cannot) modulate the voltage of the battery.What we modulate is the current flow by (more or less) shorting the poles.

We can and do modulate the voltage. By PWMing the voltage of the battery one gets, averaged by the "inertia" of the system an average voltage of Ubattery * duty_cycle. By this and the difference to the speed-proportional back-emf generated by the motor the current is controlled.

 

51 minutes ago, Mono said:

Sure, with changing current we see the voltage change in some inverse and to the most part moderate relation (larger current, smaller voltage). That is all there is to it on the battery side: we modulate current, we see to the most part insignificant voltage changes, we can compute the energy we can and have to dissipate.

The voltage we see in all the logs and charts is the voltage measured at the battery before it is PWMed and averaged. (2)

 

51 minutes ago, Mono said:

Now it dawns me that your point is that you want to avoid running the wheel with half-empty battery and hence reduced "base voltage". For example, by doubling the battery capacity you want to be able to cycle between, say, 100 and 70% instead of 100 and 40%. Fair enough, it gives you an voltage boost of at most about 10% = 3.84 / 3.48 - 1. Running on full battery gives 17% more voltage than running on half-empty battery, which translates into more power and more speed. Fair enough. That wasn't my point though  (which was comparative battery demand at different speeds, not comparative battery performance at different charge levels). Since I moved from Gotway to InMotion, battery charge status has become an almost imperceptible and entirely insignificant thing. But then I also tend to never push into the wheels speed limit...

Yes, imho it's just the difference of the starting assumption if Ubat is constant or not and the from this following implications. (Btw, since most/all wheels have a current/power limiting to protect the electronics and wiring the comparative battery demand is quite "constant" from low speeds on to somehwere in the "medium" speed range. Just once the max-torque vs speed limit is reached the possible current (battery demand) is limited by the motor...)

A new interesting point to analyse came up while i wrote this - the seeming discrepancy between (1) and (2). Since the supplied Power Pbatt=Ubatt * Ibatt from the logs seem to correspond with the delivered motor power (minus the losses), the motor gets an averaged voltage of Ubatt * duty_cycle the motor has to get a higher current than Ibatt? .... with this insight/cognition i think i dismiss myself from further discussions regarding this point - that should be way beyond my possible knowledge...... or i had some mental hickups with one of the prior points?

[Mono]

I still cannot conclusively align the graphs  (It's probably not even possible in principle, as there is little indication of time in the wattage graphs). Assuming the current peak is close to the power peak as you suggest, then we don't actually see an overlean, but "just" normal wheel behaviour under acceleration and (possibly?) braking. Why? Because after the peak we see recovered voltage and around 8-12A current, i.e. a rather decent operating condition delivering 600-800W or so. In this case, how can we conclude that we see the limit power of the wheel? How do we know how close to the limit we have come without going over it?

1 hour ago, Chriull said:

But finally yes - if one considers battery voltage as a constant this gives a constant max-power/torque vs speed chart which determines the motor capabilities.

not sure I can follow the "constant". AFAICS are neither max-power, nor max-torque, nor power divided by torque (i.e. speed) constant when plotted against speed. BTW, it should be rather simple to factor in a voltage sag in the ideal power vs speed graph.

[Chriull]

1 hour ago, Mono said:

I still cannot conclusively align the graphs  (It's probably not even possible in principle, as there is little indication of time in the wattage graphs).

Yes the time is missing to easily align the graphs - one would have to calculate the supplied power graph from the u and i graph and try to find some correspondance with the power over speed graph... 

Quote

Assuming the current peak is close to the power peak as you suggest, then we don't actually see an overlean, but "just" normal wheel behaviour under acceleration and (possibly?) braking. Why? Because after the peak we see recovered voltage and around 8-12A current, i.e. a rather decent operating condition delivering 600-800W or so.

Imho its a nice example of quite often happening accidents, where people state the wheel unexpectedly cut-off. The accelerate (high load/burden) and wonder why the wheel "cuts out" already at 24 km/h (from this graph) while it should go 30 km/h and there was no tilt-back or beeping as warning! Imho the last bit along the "limit" is where the wheel feels soft and cannot balance anymore and  if one does not manage to balance oneself one falls...

An "overlean" in controlled enviroment like a dynamometer imho just means that the wheel cannot hold its position anymore and tilts forward while one presses it forward to accelerate. But i never attended or made such a measurement - so it could also be, as written some posts before, that he just stopped the test once the max was reached to not torture the wheel any longer?

Maybe @EcoDrift can give us some hints regarding this?

Quote

In this case, how can we conclude that we see the limit power of the wheel? How do we know how close to the limit we have come without going over it?

 

Quote

not sure I can follow the "constant". AFAICS are neither max-power, nor max-torque, nor power divided by torque (i.e. speed) constant when plotted against speed. BTW, it should be rather simple to factor in a voltage sag in the ideal power vs speed graph.

I meant the whole max-torque and max power (sorry for the divide sign used as seperator) over speed limit curve is as "whole graph" constant:

(maybe i should have posted such a graphic earlier so it gets clear what i meant?...)

So this line between "Stall Torque" and "No Load speed" is "constant" or better fixed for a constant Ubatt. If Ubatt decreases (i.e. a voltage sag) the whole line shifts parallel downwards (lower stall torque and lower no load speed). For higher Ubatt it shifts parallel upwards.

Every point between 0,0 - (Stall Torque,0)-(0,No Load speed)-(0,0) is a valid possible operating point of the motor (in motor mode - for braking there should be other diagramms for regenerative/non-regenerative braking with negative torques).

so as you asked above "How do we know how close to the limit we have come without going over it": There is no possibility for the motor to operate "above" this line.

As for every speed v with the corresponding rotational speed omega we have an

Uback_emf = kv * omega

and by this a maximal possible current

Imax= (Ubatt - Uback_emf) / Rcoil (1)

Which leads to a maximal possible torque of Mmax = k * Imax

And the max possible Power Pmax = Mmax * omega

In our case, since i linked power over speed curves the red maximum power is the limit for this dynamometer tests - so i was wrong to draw the yellow straight lines as limit into the power over speed graphs from the dynamometer. Correctly it would need these maximum power curve as limit! So now i also know, why the measured power over speed graphs are not limited by straight lines as the torque over speed graph but curves  - so many thanks for this discussion to fine tune my understandings of EUC!

As one sees nicely at all of this dynamometer test results

this wheels followed nicely a curve looking like the max power over speed curve! (just not the IPS Zero 340 which seems to somehow cut power...)

So he nicely managed to follow this max power line - would imho need quite superhuman abilities to produce such graphs on the dynamometer by hand without reaching the limit!

And looking again at the (original) INMO V8 measured power graph, it could be that he maybe missed the peak power by not accelerating strong enough in the beginning?

(1) asuming again a "stable" state once dI/dt is small enough to neglect the inductance of the coils for simplicity

[Carlos E Rodriguez]

@mono.  I dont understand your arguments. Please I do not mean disrespect but it sounds you are arguing with us and @esaj @Chriull  with opinions and we are showing you the very technical details. Maybe I misunderstand but we do know what we are talking about and we use the Engineering explanations and examples.  Somehow I feel you keep quedstioning the proven science of magnetism and inductance and power and induction.  It really bothers me but maybe I am mistaken in my interpretation.

 

[Mono]

3 hours ago, Chriull said:

So this line between "Stall Torque" and "No Load speed" is "constant" or better fixed for a constant Ubatt. If Ubatt decreases (i.e. a voltage sag) the whole line shifts parallel downwards (lower stall torque and lower no load speed). For higher Ubatt it shifts parallel upwards.

Right, yet voltage sags appear with high currents, which is only in the left part of this graph at the low speeds. So it is rather not the case that voltage sags actually observed in practice will shift the entire line equally. Battery charge status on the other hand may well do exactly that. Just FTR, I gave the formula for this line in two of my previous posts of this thread (I know, it was quite low hanging fruits) and posted the picture several times in this forum, should probably have done again as well, as it is quite informative. 

[Mono]

47 minutes ago, Carlos E Rodriguez said:

we do know what we are talking about and we use the Engineering explanations and examples

LOL, relax, though, how about you showing me your Diploma and I showing you mine? Just kidding ...

BTW, http://lancet.mit.edu/motors/motors4.html was a nice find. 

[Chriull]

5 minutes ago, Mono said:

Right, yet voltage sags appear with high currents, which is only in the left part of this graph at the low speeds. So it is rather not the case that voltage sags actually observed in practice will shift the entire line equally.

Yes. Or just in the range of the speed range high accelerations/loads happen.

But as one sees inthe comparison of the original Inmotion V8 and Inmotion V8 Vitaliy there is also quite some difference in the right part of the graph (after Pmax reached) 

Also from the charts KING 16-840 and KING 16-340 (4p vs 2p and different capacity cells) a big difference can be seen in the right part of the graph.

Also unfortionately these comparable graphs are not all continuing in direction to no-load speed but most a cut-off early. Would be nice to see the graphs of the wheels with different battery configurations coming together again...( how much, when, ...)

Especially since some current/power limiting functions are implemented in the firmwares to protect the mb/mosfets/wires from too high low speed currents there should be some more "equity" between the left and right part of the graphs.

Imho rumours were from something about 1.8kW Limit for the KS16 A/B/C and a gotway representative informed us of a "high speed - no delay" 120A current "cut-off".

5 minutes ago, Mono said:

Battery charge status on the other hand may well do exactly that.

Defenitely between 4,2 to ~3,2V per cell is a huge range and (quite) direct proportional to the maxtorque change...

[Mono]

 

18 hours ago, Chriull said:

But as one sees inthe comparison of the original Inmotion V8 and Inmotion V8 Vitaliy there is also quite some difference in the right part of the graph (after Pmax reached) 

Right, but unfortunately it is hard to say to what extend the difference must be attributed to the battery modification. I have by far not enough information that I could conclude this with some confidence. 

17 hours ago, Chriull said:

Defenitely between 4,2 to ~3,2V per cell is a huge range and (quite) direct proportional to the maxtorque change...

Not sure I would call 25% huge, and the realistic range is probably even a little bit smaller (I believe I have never seen values below 3.45V, but I always only measure from the outside of the wheel). Maybe more importantly: this range is a given and entirely independent of whether we operate based on 67V or 84V or 100V.

[Mono]

Funny, as we were talking about the relevance of voltage, here it is: