Breaking crash analysis

[zlymex]

9 hours ago, Chriull said:

Imho thats real (theoretical) efficiency over speed for BLDC motors. (derived from the max torque over speed diagramm)

The efficiency formula is:
Efficiency=Torque*Speed/(Current*Voltage)
This is simply the same as efficiency=output_power/input_power.

But, if the 'Current' is the armature current and 'Voltage' is the supply voltage:
Efficiency=Torque*Speed/(Armature_Current*Supply_Voltage)
this will be wrong. And the conclusion of 'efficiency is roughly speed divided by max speed' seems based on this wrong formula.

For a given and constant torque, the armature current is also fixed, because it is proportional to the torque. And the supply voltage usually regarded as constant for the argument, then the wrong equation is simplified as
Efficiency = c * speed
where c is a constant.
This is how the curve of efficiency calculated/plotted, that appears to be very linear with speed when the speed is not very high.

The correct formula should either be:
Efficiency=Torque*Speed/(Armature_Current*Armature_Voltage), for the motor, or
Efficiency=Torque*Speed/(Supply_Current*Supply_Voltage), for the EUC as a whole(including the controller).

It could be argue that the Supply_Voltage is the Armature_Voltage.
If that is the case, it/they will not be constant.
When the speed decreases, so will be the back-EMF, and the Armature_Voltage is not very much different than the counter-EMF, because back-EMF is proportional with speed, 
Armature_Voltage - back-EMF = Ra * Ia, which is small and constant.
where Ra is the armature resistance, and Ia is the armature current.

Because of Efficiency=Torque*Speed/(Armature_Current*Armature_Voltage), and
the Efficiency is proportional to Speed/Armature_Voltage when Torque is constant, when the speed decreases, the Armature_Voltage will also decreases, thus the Efficiency will not be decreases with speed proportionally.

It's pity that Gotway and Wheellog only give Armature_Current and Supply_Voltage, and the product of these two is not any power(not the motor input power, not the battery output power). I installed a current sensor to the EUC to measure the supply current, thus I can calculate the supply power and the efficiency of the EUC as a whole. 

The efficiency of the EUC is always smaller than the efficiency of the motor.
Therefore, for a given condition, if I measure the efficiency of the EUC to be 40%, then the efficiency of the motor must be greater than 40%.

9 hours ago, Chriull said:

The other two charts you linked, show something different. The first is efficiency over torque for a fixed speed.

But, there are curves of different speed. Take Torgue=5 for example, the blue curve indicates 75% efficiency at low speed(10krpm), which is much larger than theoretical prediction of 25%(=10krpm/40krpm*100%). And the efficiency at 20krpm and at 30krpm are about the same(around 82%). These contradict the theoretical curve.

[zlymex]

10 hours ago, Chriull said:

If you take a look at the following link (unfortionately in german - but not too much written anyway ):

http://www.pedelecforum.de/forum/index.php?threads/nabenmotor-von-www-at.97/page-6#post-1612

you'll see that the efficiency over speed curves with current limiter ("mit Strombegrenzung") already look much more like your curves...

(P_aufgenommen: "consumed Power, P_abgegeben: "submitted/delivered" power, P_verlust: "lost/dissipated" power, Wirkungsgrad: efficiency)

And these are theoretical (computed) graphs.

Yes, the real EUC employs a current limit. But the theoretical curve of torque-speed and power-speed does not. If it does, the curves will be look like this:

The torque-speed curve is now consist of two line segments, and the power-speed curve is now a line segment plus a partial parabolic curve.
Therefore, the theoretical curve of efficiency-speed does not employs a current limit.

Even if under the current limit(so is the torque limit), the efficiency will be not less than the situation where there is no current limit, because there are sayings that efficiency become smaller at large torque.

My conclusion, the efficiency-speed curve below is wrong at low to medium speed part.

[Chriull]

6 hours ago, zlymex said:

 

...For a given and constant torque, the armature current is also fixed, because it is proportional to the torque....

When the speed decreases, so will be the back-EMF, and the Armature_Voltage is not very much different than the counter-EMF, because back-EMF is proportional with speed, 
Armature_Voltage - back-EMF = Ra * Ia, which is small and constant.
where Ra is the armature resistance, and Ia is the armature current.

That's all good and right - just this diagramm is not for a constant torque but for the maximum torque at each rotational speed. (As you answered this to my previous post saying " Imho thats real (theoretical) efficiency over speed for BLDC motors. (derived from the max torque over speed diagramm) )

So Ra*Ia is not constant and does not have to be small. Especially not for low rotational speeds were maximum torque is very high and so the Ia. Which causes the efficiency to be so low in this diagramm for low speeds.

So this diagramm is still true but is based on other assumptions!

Quote

But, there are curves of different speed. Take Torgue=5 for example, the blue curve indicates 75% efficiency at low speed(10krpm), which is much larger than theoretical prediction of 25%(=10krpm/40krpm*100%). And the efficiency at 20krpm and at 30krpm are about the same(around 82%). These contradict the theoretical curve.

No - as said above its not condratictional but based on different assumptions. The blue curve is of course true for 5 mMm at 10 krpm.

The much lower efficiency value of the "theoretical curve" comes from calculating the efficiency with the maximum possible torque at this 10 krpm which leads to much higher armature currents and by this to much higher losses.

The reason i linked this graphs was just to show an maximal efficiency at high load condition and that the efficiency gets lower at low and at high speeds.

6 hours ago, zlymex said:

Therefore, the theoretical curve of efficiency-speed does not employs a current limit.

Exactly. 

If you reread my post saying: "If you take a look at the following link (unfortionately in german - but not too much written anyway  ):

http://www.pedelecforum.de/forum/index.php?threads/nabenmotor-von-www-at.97/page-6#post-1612

you'll see that the efficiency over speed curves with current limiter ("mit Strombegrenzung") already look much more like your curves.."

and follow the link you'll see that there is another chart which shows this theoretical curve with current limiting.

[Mono]

@Chriull, nice find these

http://www.pedelecforum.de/forum/index.php?threads/nabenmotor-von-www-at.97/page-6#post-1612

From there it should be comparatively simple to produce efficiency graphs for any given (max) current, right?