Forgotton the name now but the newish small graters single blade I use always with parmesan and no problems. I have a grater for my Magimix but that is used only when I need tons of the stuff. Try the new grators they are very sharp and last for ever.
I suggest a hand-held microplane grater. They are available in three grades, thick to thin and even work with parmesan rind! They can be cleaned in seconds, whereas mechanical grater cannot.