Hello Steve:
I believe you are describing a sycamore tree. The bark peels away naturally leaving at least for a period of time an olive green colored smooth bark. the bark comes off in plates or patches. the spiked ball is actually the seed of the sycamore. The leaves once the tree is mature should be about the size of a small dinner plate. Extension has a web site for selecting trees at: http://urbanext.illinois.edu/treeselector/ that may be helpful for you.
You can take a few leaves and seed ball to a local garden center or retail nursery to confirm the kind of tree you have if you need to.
Respectfully, Richard Hentschel