The problem with 6 parallel strings of 3 is that the strings will not have exactly the same characteristics; which means that they may not all draw the same current. This could result in one or more drawing excessive current if you use a 3A constant-current type of charger.
This is true, but as the schematic shows, the batteries are not only connected as strings of three but also in parallel. This means that the only option you have is to balance charge at three levels of six parallel batteries.
Unless you go for fast charging, forced charging etc, and in the process reduce the life of the battery, the charging regime for LiIon batteries is very simple: charge to 4V and discharge to 3V. You can juggle with the figures to get different trade offs. And that is all there is to it. Of course you are wise to limit the current to a level specified on the battery data sheet. This is an area where parallel charging does have a disadvantage: you cannot, in theory, fast charge, because you cannot guarantee that the batteries will current share at all times. In practice it is not normally a problem because the internal resistance of the batteries tends to even the charging currents out.
And once a bank of parallel bank capacitors have settled into their environment there should not be any problems.
As a consequence, you can charge LiIon batteries in parallel quite successfully, although as I keep saying, it is far superior to charge each battery individually.
In the case of the six batteries in parallel at a first stab I guess that a maximum charging current of 6A would be OK for 18650 LiIon batteries.
In terms of safety:
(1) Keep away while charging and discharging or if the battery is hot.
(2) Never put your eyes near a hot or charging or discharging battery. In fact, never put your eyes near any battery at any time.
(3) Legislate for an explosion- make sure that if a battery explodes it does the minimum of damage and that the damage is acceptable.
This applies to any battery type and any charging method. It also applies equally to, so called, protected batteries.
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