Using some simple mathematics and dimensions we can do some cylindrical cell electrode estimation.
Knowing the outer and inner diameter of the spiral along with it’s thickness we can calculate the length of the material to create it.
D is the inner diameter of the cylindrical can.
The inner diameter is that of the mandrel around which we wind the spiral.
Outer Jelly Roll Diameter
The outer jelly roll diameter will be the inside diameter of the can. Note: although the cells are nominally 18mm, 21mm or 46mm in diameter the actual cell sizes can vary quite a bit.
|Outer Diameter [mm]||18||21||46|
|Typical Can Thickness [mm]||0.22 to 0.28||0.22 to 0.34||0.5 to 0.6|
|Inner Diameter [mm]||17.44 to 17.56||20.32 to 20.56||44.8 to 45|
The inner spiral diameter is set by the mandrel upon which the cell is wound and by the requirement to be able to weld the bottom tab to the inside of the cell can.
This diameter is also set by the minimum bent radius for the coated electrodes without cracking.
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For an 18650 cell this is typically a 2mm diameter mandrel.
Cell Electrodes and Spiral
The anode and the cathode are coated with active material on both sides of the electrodes. Represented here by the 3 lines.
From this schematic you can see that 2 separators are required.
Also, if you follow the spiral around you can see that in the centre the cathode (red) only needs to be coated on one side.
The outside spiral run of the anode (black) also only needs coating on one side.
Anode and Cathode Thickness
The anode and cathode thicknesses will be determined by the chemistry and a number of parameters.
A power cell will typically have thinner active coatings and a higher surface area for a given cell volume.
An energy cell will have thicker coatings, thereby increasing the energy density of the cell.
- Double sided coating thickness 126µm
- Copper electrode thickness 10µm
- Double sided coating thickness 125µm
- Aluminium electrode thickness 20µm
- Separator thickness 16µm
- Total layer thickness = 126µm + 125µm + 2x 16µm = 283µm
Note: this is a very much an estimation, please use it as such.
Tesla particularly uses Cylindrical cells in their Electric Vehicles. As per recent announcement Tesla is moving to 4680 from 21700 and the older 18650. Rivian and Lucid Motors are also using cylindrical cells 21700 in their vehicle models (R1T, R1S and AIR Dream, Air GT respectively). BMW along with CATL have announced that its NEUE KLASSE type models will use the 46mm diameter geometry cylindrical cells too.
Cylindrical Cell Electrode Estimation: An alternative geometric approach.
Here we present a simple method for estimating electrode length in a cylindrical cell. The method is equally applicable to other formats since we make an estimation of the total active electrode area. Results require knowledge of one electrode Active Material (AM) chemistry, electrode porosity and thickness and cell capacity. We assume that 100% of the active material is utilised and contributes to the cell capacity. This is optimistic and will likely lead to an underestimate of the length.