Throughput |
Once the energy level has been set – and is sufficient - for a given product, in a given process, the power of the whole system must be evaluated in order to meet the quantitative requirements. Evidently, it takes more power to irradiate a couple units of products per days than several thousands per hour.
The formulae most often used to figure out the power requirements of the equipment is based on the “area method”
A/T = K F I / D
- A = Area (m2) ;
- T = Time (min);
- K = Area Processing Coefficient (function of the energy as per table below)
Energy (MeV) |
0,3 |
0,4 |
0,5 |
0,6 |
0,8 |
1,0 |
1,5 |
2,0 |
3,0 |
4,0 |
5,0 |
10,0 |
K (Mrad m2/mA min) |
3,09 |
2,26 |
1,86 |
1,64 |
1,42 |
1,31 |
1,20 |
1,16 |
1,13 |
1,13 |
1,14 |
1,17 |
- F = Fraction of electrons which are actually absorbed by the product.
- F is indeed a measure of in-efficiencies / waste caused by over scanning of the product.
- For continuous products (like films) F is often valued at 0.85 or even 0.80.
- For products on a conveyor, F can be as low as 0,7 or even 0,6 depending on the beam scanning / conveyor interface (over-scanning + spaces in between products)
- I = beam Current (mA) ; this is a major specification of the accelerator.
- D = Dose (Mrad) - note : 1Mrad = 10 kGy
Formula specific to Wires & Cables Irradiation |
As W&C are generally round in cross section, they should be treated from both sides in order to overcome the problem of “shadow” caused by the conductor. Different types of UBHS (Under Beam Handling System) allow to do this easily. Multiple passes of the product under the beam allow the dose to be integrated by the insulator, avoiding over-heating of the conductor. This may also induce a twist of the W&C by a few degrees at each pass.
This last phenomena is critical to assess the minimal energy required for an homogenous cross-linking. If the total amount of twist occurring is sufficient, one can consider that the maximum distance the electrons have to penetrate is equivalent to the wall thickness. If the product is not twisting at all, the electron must penetrate at least the half cord so the energy (worst-case scenario) can be determined using the following formula:
keV = 197p * {W(OD-W)}1/2 + 325
p = density of the compound (g/cm³)
W = insulator Wall thickness (mm)
OD = Outside Diameter (mm)
Irradiation :
Key Concept
