Running wood through a chipper/grinder will not make shavings. It will make messy, big, wet chips/shreds and wet dust. If you have somewhere under a roof to let the stuff dry out real well (in a very  fothin layer for a few days of dry weather,r some months in a thicker layer) and then store it dry, it can be used for bedding but is not going to be absorbant or easy-to-deal-with like shavings. If you're chipping live trees you will have to dry it even longer. Otherwise, you are importing 
large quantities of humidity into the coop... think 'mold' and 'frostbite'.
If you want shavings comparable to the commercial product, you need to get into woodworking and buy a planer or joiner (the big power equipment, not like a block plane 
) and use it a whole lot. (Other power tools produce more jsut 'dust' than shavings, which won't work real well in a coop usually).
The most successful schemes I've seen for using homemade bedding involve either bagging dried fall leaves and storing them dry til you use them (not absorbant, but free), or using pine straw (only works if you have access to lotsa free fallen pine needles, obviously), or using waste paper run thru a shredder (I don't personally like shredded paper as bedding, for me it turns into a really nasty clumpy form of paper-mache, but some people seem to like it well enough). In principle you could cut, dry and store tall grass as homemade hay for use as bedding, but that is actually not at all easy to do without getting into mold. And again, it requires lots of storage, which is your whole problem in the first place.
I would suggest that, all in all, perhaps you might have more success in taking a second look at how you are USING bedding, and see if you can alter your management scheme to USE less of it. It can often be done, sometimes to a considerable degree. (I use maybe 4-5 bales of shavings per year for my 7x20 sussex pen, and it is quite clean and sanitary and good-smelling nonetheless)
Good luck, have fun,
Pat