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I am trying to run this motor.
Using the batteries stated in the title. The motor requires 12 V and I am supplying 11.98V to the motor, through a motor driver. After a while, the motor keeps slowing down and the battery voltage drops down to 5-6 V, but after I remove the battery from the motor driver it again shows 11.9V.
Is this battery capable enough to run my motors, or do I need a new one?
Assuming that the motor is in a healthy condition...
Voltage is only one aspect, you have to be sure that you battery can supply the current drawn by your motor. The maximum current, according to the link you have specified is approx 10 Ampers.
I am not sure how many batteries and in which config you are using, the description I have found is this one. It states that the maximum current that the batteries can supply is 5.2 ampers. So if you do not have any parallel connections in the battery configuration (I assume you have serial ones because of the higher voltage you have specified) you cannot supply the 10 amps required by the motor for maximum torque. Try to measure also the current, not just the voltage and see if this is the problem. You can use more then one batteries (probably 2, maybe 3) connected in parallel to each other to solve this problem.
Another source of the problem could be a short circuit with a very short duration in the driver when switching the transistors. Try to measure the current also before and after the driver stage to identify if this is the problem.
A fully charged LiPo battery cell should has a voltage of 4.2 V. Assuming that you have three cells in series, that would give 12.6 V. When you apply a big load, this voltage of course, will decrease instantly but if you measured 11.98 V in open-circuit that means the batteries were not fully charged. I guess your batteries were not charged at all.
Here is the discharge characteristic of the Samsung IRC16850, taken from this site.
A discharge current of 7 A will drain your battery flat in 20 minutes.
Furthermore a discharged battery's voltage is not the same when the load is still connected and when it is in open circuit. After disconnecting the load the battery voltage will rise, this will be the OCV (open circuit voltage).
This is a figure of a LiPo battery pack, 12 cells in series. When the load is disconnected the voltage has risen from 2.7 V to ~3.2 V in a short period of time (PB 6 voltage). This happens with your batteries too but if you reconnect the motor the voltage will drop back.
And finally, if you measure 5-6 V on your battery pack that means one cell's voltage is around 2 V and the cells are probably damaged now. The Samsung ICR18650's discharge cut-off voltage 2.75V, which means that you should not use it when the voltage is lower. Actually you should not use the cells but recharge when the voltage drops to 3 V.
If a cell is heating up it means that its internal resistance has risen. The dissipated heat will be:
$$ P = R_{internal} \times I_{discharge}^2 $$
this means that a part of the stored energy is wasted on heating the cell itself (which is very DANGEROUS as LiPo cells can easily catch fire). The effective battery capacity is lower in this case.
Without load your motor should drain 800 mA and the batteries should last 2.5 hours with that. I suggest to make some tests without any load attached to you motor, or just some light load. These batteries would be capable of supporting that, just make sure that they are fully charged. But probably you will need new cells too.
