Based purely on the description of the sound, I would suggest you are probably looking for something which is rubbing against a panel of some sort. All good ideas here, but transmissions etc tend to whine and shriek rather than 'grate'.
The first thing I would do is crawl around underneath and look for signs of rotating parts with insufficient clearance to body (bearing in mind this may change when there's weight in the car). Are the rear wheels rubbing against the body or wings for example?
The fact that it's a steady noise when driving is perhaps your biggest clue - if it doesn't rise and fall with engine speed and sounds the same in all gears then begin your search from propshaft rearwards.
Then it's a process of elimination, work your way through the suggestions starting with easiest first until you can satisfy yourself that each is or is not the cause. For example take the starter off completely, bump start the car and if the noise is still there then it's not the starter. I've forgotten who said it but it's certainly true that sounds are transmitted through the structure and you can't always tell where they are coming from.
The first thing I would do is crawl around underneath and look for signs of rotating parts with insufficient clearance to body (bearing in mind this may change when there's weight in the car). Are the rear wheels rubbing against the body or wings for example?
The fact that it's a steady noise when driving is perhaps your biggest clue - if it doesn't rise and fall with engine speed and sounds the same in all gears then begin your search from propshaft rearwards.
Then it's a process of elimination, work your way through the suggestions starting with easiest first until you can satisfy yourself that each is or is not the cause. For example take the starter off completely, bump start the car and if the noise is still there then it's not the starter. I've forgotten who said it but it's certainly true that sounds are transmitted through the structure and you can't always tell where they are coming from.