if you want to polish big flat surfaces
pay to have it done if this is a one shot thing.
if you want to do some pieces or want to say you did it then I suggest:
go to mscdirect.com
buy a cheap surface plate, import ok, but bigger width and length than your parts. Thickness isn't an issue, thin is ok, thick just costs more.
(might find one on craigslist too) or a perfectly flat piece of steel works to but it must be surface ground and known to be flat.
buy some 1000, 1500 and 2000 grit paper.
with a clean surface plate, lay the grit paper, face up.
place your metal part on the paper and work it in a figure 8 motion.
It is is going very slowly, go down in grit. It all depends on what the finish is you are starting with. Start with 1000 and look to see is it is getting better or worse.
Realize you are removing the peaks of the metal and working down to the valleys. If you have deep spots you may have to go down to 500 paper to get it flat before the polishing begins.
If 2000 grit paper is still not the desired finish, go back to mscdirect and get small small tubes of diamond polish. Green is coarse, yellow then white. mix some oil or wd 40 with the paste so it is slippery enough to continue the figure 8. (the working motion of the figure 8 is critical in keeping it flat.)
As you work thru this process you will find that polishing will reveal deep scratches, so you may have to work back and forth, getting enough grit to work out the deep scratches and back thru the polishing steps.
Most importantly, you must be clean between steps. If your metal or work area has grit from the last step, it will damage your work. So clean your metal between steps, clean the plate, the area and especially your hands.
If you work towards the diamond polish, you can accomplish a mirror finsh without scratches.
you can shop at graingers or other industrial suppliers, I have no connection to msc, just used them for many years with good service and price.
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