Apparently the Quadraflex uses a flat stretch belt, while the WW's use cogged belts.
 
All the tristar parts site I could see on the internet offered brushes with dual brush rows.  None had beater bars.  Interesting that the bars are no longer used.
 
http://www.tristarvacuumscanada.com/
 
might have more information.

You should be able to find a brushroll w/ beater bars on it.  I am curious as to which model you have.  Eureka built the power nozzles for the vacuum cleaner at one time and the beater bar agitators are still avail.  You may have a generic brushroll right now.
 
The HOOVER and Wessel-Werk power nozzles clean well.  The W-W is going to be alittle bit quieter and have the cogged belt.  This nozzle would be easy to fit, but very expensive.  I would say to stick w/ what you have.   After reading your posts, it looks like you are trying to find the "perfect" or "best" vacuum cleaner.  You are not going to find it.

Interesting wrt John Kaido's Miele comments.
  
I've found the smaller of Miele's power nozzles (the 217) is indeed harder to push than their larger 236. But only if the Miele's motor speed is turned all the way up.  Apparently the small brush opening causes greater concentration of "suction" and creates drag.  Ironically, the smaller brush has much softer bristles, so it is not as thorough on rugs as its bigger brother.
Neither Miele power brush has beater bars, though.  
 
Simplicity's site (found via Carmine's link leading to Simplicity's site)  offers the link to the business week article for those who wish to read it:
 
http://www.businessweek.com/innovate/content/apr2006/id20060427_567693.htm

I got a 2-speed red CXL Tristar w/Interstate built PN but it had a beater bar on the brush roll when I got the vac; the bristles were worn, so I got a cheap generic brush roll w/ball bearings.  But I should've bought a Eureka VibraGroomer roller since I know the Eureka roller can fit the Tristar PN & the Tri-Star is an UNBEATABLE vac when the PN has a beater bar, so sometimes I use my old Kenmore PN (got it from someone[geared belt]) thanx to its 2 rows of bristles + beater bar (but the height selector part broke) & has terific edge cleaning but no light.  Is that clip available @ any vac shop or do I have to go 2 Sears to get that clip its part of the selector that raises/lowers the front wheels.
 
Does anyone recommend "retro-fitting" beater bars on brush rolls?  I thought about that so the Tri-star can clean better b/c my shag (old) & hi pile (new) carpets need beating action of a beater bar + deep down grooming to remove old dirt the Electrolux left behind.  I'm not sure if the Tri-Star PN has "windtunnel" design like the Hoover WT & turbo brush, but its the BEST PN I own; however, I hate changing the "rubber band" belt every few months or when the brush stalls b/c it has no reset switch like the Lux & Sears PN.  What does the slide switch on top of the Tri-star PN have to do with carpet pile b/c the nozzle does NOT raise or lower when I slide the selector, or does it change airflow in the nozzle?

Isn't it a shame that Hoover doesn't have beater bars anymore?  The delux Eureka PN has a STEEL agitator with steel beater bars NOT PLASTIC!  I think uprights & PN's should have metal brush rolls with metal beater bars & replaceable brush strips b/c plastic & wood get nicked over time & can ruin carpets.