A member of my quilting group has a sharpener that has a knob on top and you turn it. I can't remember the brand but maybe I can get some information from her as to brand and how it works. You may be right about my mat. It is very dry here and it may be dried out. The quilting group has a mat made of some type of plastic and it has griover all over. It seems to work for most of them but not for me. I may be holding the cutter wring. (Just letting off ideas here!)
They sharpen the bladers some how but don't know how. When I meet with them I may be able to send that information to you.
Liz