Below:
(1) Safety advice.
(2) Charge rate
Safety circuit: A "safety circuit" is a small PCB with electronics that is integrated as part of each cell and which protects the battery, the equipment and you from the more excessive behaviours of LiIon batteries. Without a safety circuit a LiIon cell is a small bonfire waiting to happen.
LiIOn 18650 cells really really really should have a safety circuit per cell. Genuine Panasonic cells are usually NOT supplied with safety circuits - as it is assumed a battery integrator will add them.
Non-Panasonic cells often will not have a safety circuit.
Pack Integration:
Charging individual LiIon cells is a reasonably straightforward task.
Integrating and then charging multiple Lithium Ion cells in series or parallel (let alone series parallel) is a challenging task which is far easier to do wrong than right.
Done wrong it can shorten cell life and can lead to spectacular expensive and dangerous destruction of the battery.
There are ICs available which can be used to reasonably safely charge LiIon battery packs. Failure to properly manage charging of multiple cells is about the battery equivalent of driving drunk, or blindfolded.
Brand: If you buy shoes, clothes, handbags or jewellery, brand may matter but often branding and high price benefit the manufacturer far more than you.
With LiIon cells, it is possible to but low price unknown brand cells that are of good quality and whose datasheets and claimed specifications are legitimate.
However, many LiIon cells that not made by major manufacturers are of low quality, datasheets may be copied from other makers or not available and actual performance is often inferior to what is claimed.
Genuine Panasonic cells are usually of good quality and datasheets are available and reliable and specifications are meaningful. Pansonic are not the only trustable brand, but are about as good as any. Even major manufacturers have had problems with LiIon batteries. This tells you something about what is liable to be experienced with products from unknown manufacturers and whose spec sheets are unavailable or untrustable.
The cells you provided a link to claim to be Panasonic NCR18650As.
If they don't say Panasonic on them then they almost certainly aren't.
The picture in the ad did not show a Panasonic logo and the cells do not look like cells in Panasonic literature. (That said, here are a number for sale on ebay that look similar, that do claim to be genuine and that do not appear to have Panasonic labelling. For example, the person selling these in a group buy very specifically claims them to be genuine Panasonic cells.)
If they DO say Panasonic on them they MAY not be.
They do say that they are made in Japan. Generally, Japanese manufacture is a sign of reasonable quality. In many cases low quality cells which are not made in japan claim to be Japanese made.
Panasonic NCR18650 data here
Panasonic NCR18650 data sheet here
Panasonic LiIon safety precautions
So, finally -
Charging rate
IF these are genuine Panasonic NCR18650A cells
then the recommended charge rate is 0.7C or 2 amps per cell or per series string.
If these are not genuine Panasonic cells
then the maximum charge rate is in the data sheet
and the data sheet may or may not be available
and the datasheet if available may be believable.
Or not.
In such cases 0.7C or 2A max per series string is probably "safe enough" but this is not certain.
Clone cell capacity may be as low as 2000 mAh.
0.7C x 2000 Mah = 1.4A.
2A for a 2000 mAh cell is 1C.
This is often"safe enough" for a clone cell.
YMMV *
"*" Your mileage may vary. ~~~= Don't try this at home.
Comparative results from different brands
The table below is reported on a Mountainbike Forums pag by a user whose competence is unknown, but who seems capable enough. All such results need to be treated with due care but also can be useful. mAh capacity results for cells tested showed a genuine Panasonic protected cell having highest capacity and an unprotected Panasonic cell as having slightly less (by about 2%). This result is somewha surprising and needs to be considered with care - but may be due to different cell batches or statistical differences between cells.
From this useful discussion page
Q&A:
So its meen that I can charge my 3S3P battery pack with 24v max 6AH Charger?
A cell requires up to 2A x 4.2V = 8.4W.
Your charger is rated at 24 x 6 A = 288 Watt.
So using a boost or buck converter that will charge about 288/8.4 =~ 288/9 = 30+ cells. BUT you will need to use a converter to do this.
If you connect to battery with a linear requlator you have 6A max or up to 3 strings in parallel and not more than 5S so 5 x 3 = 15 cells max.
.
3S3P = 9 cells.
You say 21 cells.
Do you means 3S7P = 21 cells?
BUT
3S = 14.6V max, 9V min.
4S = 16.8V - 12V
5S = 21V - 15V
6S = 25.2V - 18V
7S = 29.4V - 21V
A 24 VDC charger will charge up to 5S without a boost converter.
If you want 24V nominal you need 6S or 7S or maybe 5S.
How do you intend to do speed control?
What IC or controller do you intend to use?
Just connecting 24 V to cells will not work - as I think and hope you know. .
You need a specialist LiIon charger IC. Digikey sells a number that would be suitable.
I meen 7S3P - 7X3.7=25.9V
For Lithium Ion = LiIon cells
Vmax = 4.1V or 4.2V fully charged
Vmin = ~= 3.0C. Slightly lower is possible but there is almost no energy left and you risk cell damage.
7 x 3.0V = 21V min.
7 x 4.2 = 29.4V max.
So IF you charge 7 cells in series you need about 30V DC.
IF you want to charge 3P strings at full capacity you need 3 x 2A = 6A.
You can charge slower.
Your 24V supply is not high enough to charge all 7S cells directly.
You need a boost converte or a higher voltage supply.
21 cells requires about 21 x 2A x 4.2V max ~= 180 Watts - although less can be OK.
Your 24C, 6A supply can provide 24 x 6 = 144 Watts.
If you use a boost converter to 30V if overall efficiency is 80% then you need 180/80% =
225 Watts OR your 14 Watt supply at 24V will deliver 144 x 80% = 115 Watts at 30V.
115W into 7S3P at 4.2V cell = 115/21/4.2 = 1.3A = 65% of maximum allowed. This is acceptable - charging will take less than 50% more time than best allowable.
But you still require a charge controller IC.
.
Best Answer
Ask yourself this, can I remove the battery from the laptop and still have it run fine if it is plugged in? I am assuming this is a yes. This would mean that the load is being met by the supply from your battery charger. So, so long as you have the same continuous current capacity from your battery pack that you do from your charger you should be set.
If we assume that that rate is less than 5amps, (you have a pig of a laptop if it is that much) then you are golden as almost all genuine 18650 cells can source at least that much. Many source up to 15-30amps even.
You are also asking if it is safe to have too high of a discharge capability of your cells: No, not really. If you draw only 5amps out of a cell that can source 30, that is fine. The cells will always run a cooler than if you were taxing it more. So that is good.
If you want a bit more help, I would recommend the sanyo ncr 18650 ga cell. It can source up to 10amps continuously. You only need <5amps so it will run nice and cool. It also has one of the highest capacities of all the 18650 cells available these days so your battery will last nice and long between charges.