Type in the charge you have and the tonnes you are about to add, and this shows where the
charge ends up — not just after this top-up, but after the next several. Balls do not vanish when
they wear; they become the size below. That is why a charge topped up with one size only drifts further
from your grading every month, and why it slowly fills with balls too small to be worth carrying.
Press YOUR CHARGE on the board to type it in.
How the numbers are worked out
Balls do not disappear when they wear. A 101.6 mm ball that loses steel becomes an 88.9 mm
ball. That is the whole idea here. Each size loses some weight as steel lost for good, loses some more
downward into the size below, and gains whatever comes down from the size above. Add the tonnes you
are putting in and you have the new charge.
Every step of it is from your own ball-mill-media-wear.js,
loss factor table included. Nothing is fitted and nothing is added.
One thing about this model you should know. The tonnage it wears away always comes out exactly
equal to the tonnage you say you are adding. It does not predict how fast your steel wears — it
assumes you are replacing what you lose, and works out where the charge lands. So it answers
“what will my charge look like after this top-up”, not
“how much steel will I lose this month”. For that you need your own consumption
records in grams per tonne of cement.
Total weight is conserved apart from the balls that wear past the bottom of the size ladder and
leave as scrap. That was checked: 65.800 t in, 65.800 t out when nothing reaches the bottom rung.
The smallest size in your list is the exit. Balls that wear below it leave the mill as scrap
and are counted in the scrapped tonnage. So the bottom of your list matters: stop it at 17 mm and
everything finer counts as gone, add a 15 mm and a 12 mm row and you can watch the fines pile up
before they go. Neither is more correct — it depends on where you actually screen them out.
Projecting several top-ups is that same single calculation repeated, adding the same tonnage
each time. Nothing new is introduced by repeating it.
You type your own ball sizes, in millimetres. The list opens on 110, 100, 90, 80, 70, 60, 50,
40, 30, 25, 20 and 17 mm because those are the sizes a plant actually buys, but every one of them is
editable and blank rows are ignored.
How the wear factors follow your sizes. Your loss factor table only lists eleven sizes, and
they are inch sizes — 101.6, 88.9, 76.2 mm and so on — which nobody stocks. So the two
factors are read off the shape of your own table:
D = 3.89584 × inch−0.89784 and
H = 0.73032 × inch0.94230. Those two lines were fitted to your eleven
rows and nothing else. They reproduce every row of your table to better than 0.4% for D and
0.7% for H, which is close enough that the table was almost certainly generated from formulas
like these to begin with. Where a size you type lands on one of your rows, your number is used and
the formula is ignored. Both factors are printed in the table above for every size, with a filled
dot when the value came straight from your table and a hollow one when it was read from its shape.
Does changing the size list change the answer? Barely. Running the same charge on your inch
ladder and on the commercial millimetre ladder moves the final grading by under one point, and
doubling the number of rungs moves it by about a third of a point. Sizes outside the range your table
covers — below 16 mm or above 102 mm — are flagged on screen, because those are read from
the shape of the table rather than from a row of it.
Where the loss factors came from is not recorded. Your file describes them only as a reference
table and does not name the source. They behave sensibly — size multiplied by the wear factor is
nearly constant at about 4.4, which is what a surface-to-volume wear rate should do — but that is
an observation, not a check against a published source. If you know where they came from, tell me and
I will note it here.