parajared said:
and you said this
The higher available input (battery) power allowed the controller to deliver higher phase amps and hence higher torque.
and that's what got me going. In my mind's eye all these statements are wrong and that's what got me triggered.
...
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your comment a misunderstanding of phase amps and the role they play on torque.
AlanB gave a pretty good overview of how this all works, which should explain what is going on, but I'll give it another try:
The core difficulty is this statement which reveals a misunderstanding of motors and the individual roles that controllers and motors play.
parajared said:
All the motor cares about is wattage.
Although the (unloaded) speed of a motor has a direct relationship to the phase voltage and the torque has a direct relationship with phase amps, there is no place in motor equations where the voltage and current terms appear together as a product (watts) which would in turn suggest that the product is the critical value not the individual voltage and current terms. So, volts and amps 'yes', but watts 'no'.
That said, when controllers are in limiting mode, they can be viewed as dealing with power. In particular, the phase power out of a controller is always equal to the battery power in, but a controller has the ability to reduce phase voltage and increase phase amps such that the resulting phase power remains unchanged. Additionally, since motor speed is directly proportional to voltage according to motor Kv, we can likewise say that phase voltage must be proportional to speed. This means that at any given speed, the phase voltage that the controller must deliver is fixed. So knowing the input power (batteryVolts x batteryAmps) and the phase voltage the resulting phase amps are known.
So looking at controller operation when limiting without all the details:
The motor behaves according to:
So to achieve any given rpm the controller must provide:
The controller behaves according to:
Code:
(phasePower) = (batteryPower)
(phaseVolts x phaseAmps) = (batteryVolts x batteryAmps)
phaseAmps = (batteryVolts x batteryAmps) / (phaseVolts)
So at any given rpm the controller can supply this phase current:
Code:
phaseAmps = (batteryVolts x batteryAmps) / (phaseVolts)
phaseAmps = (batteryVolts x batteryAmps) / (rpm / Kv) (from above)
phaseAmps = (batteryPower x Kv) / (rpm)
The last relationship illustrates:
- Torque is dependent on the battery power not either of the battery volts and amps independently and at any given speed (rpm) different combinations of volts and amps can yield the same phase current and hence torque.
- The controller develops higher phase amps and hence more torque at lower rpm (when due to increased load) and the available phase amps (and hence torque) reduces as rpm increases (see blue lines in simulator plots).
Importantly, what we are looking at here is controller -not motor- operation. The motor role is to convert the phase amps directly into torque. It does not itself see the battery voltage or current but instead acts on the entirely different phase voltage and phase current. The controller does the magic.
For the discussion in this thread: the last equation shows that at any given speed the torque will be higher (acceleration higher) for the bike with the higher available input power (as long as the controller is limiting). Based on this I said:
The higher available input (battery) power allowed the controller to deliver higher phase amps and hence higher torque.
The twist in this case is that the OP's motor achieved higher acceleration with the higher voltage pack not because of the high voltage per se, but because the available power increased:
High voltage pack: 40Ax72V=2880W
Low voltage pack: 45Ax48V=2150W
If the higher voltage pack had been built with the same number of cells and just the S and P jiggled so the volts went up, the amps went down, and the available power remained the same, there would have been no increase in phase amps and no increase in torque.
This is why the specifics of the OP's question were important instead of dismissing the possible result out of hand as impossible because voltage doesn't control torque.
FWIW:
- The last equation above explains the common experience of increasing battery voltage and getting better torque/acceleration. This typically happens because the controller limit is not changed (e.g. they are using a 40A controller). Since this discussion is based on the premise that the controller is limiting, the battery current remains fixed at the controller limit (e.g. 40A) but the pack voltage is higher and so the available battery power is increased. Just a variation of the OP's situation with similar confusion arising about the role of battery voltage.
