It sounds like it's sitting at a bit of an angle on the stand if it's rubbing at the bottom. If you've had it for a while it could be best to replace as they don't last forever. I got fed up with my Karlie Wonderland wheel going after 6 months - it did a similar thing, the bearings went, it leaned forwards and rubbed against the stand.
You could get another one if you're happy with it, as they are one of the cheapest. If you don't mind spending a bit more the new 12" Silent Runner is great - I love it. It's only a little bit taller than the Trixie wheel and a couple of cm deeper. I like the depth - it's not too deep but means they aren't going to rub against the sides.
It has a strong sturdy metal standard with no areas for getting trapped between the wheel and stand, which I like. It can also be cage mounted and has special plates for this but they cost £4.50 extra (ouch!).
Depends what cage you have really. The 27cm wodent wheel is good hung upside down and they seem to last a long time. I didn't like the wodent wheels freestanding, but hung upside down they are quite stable and seem to run well.
The Silent Runner only comes in orange - but I can live with that lol! It spins really well and is silent!
Silent Runner 12"
The 27cm wodent wheel is a bit more compact - slightly lower and only 7cm deep like the trixie wheel and you can choose the colour. Petplanet are out of stock but the sugarglider shop sells them as well as the Silent Runner.
11" Wodent Wheel (Senior) & Free Glider Shield
They fit together very similarly with a front and back piece and a running track. The main difference being the wodent wheel has a spindle and a small pin that holds it together - which can be a bit of a fiddle but I didn't find it too much of a fiddle. The Silent Runner doesn't have a spindle so easier in that way.
I did a review of the Silent Runner wheel if it helps at all. There are some photos at the end showing how to assemble.
https://www.youtube.com/watch?v=VFussTX5PuE
Or you could just get another Trixie wheel!