Cranky, thanks for posting this photo for me! So as is obvious, that ring I am calling the outer ring is what I want to remove. It has teeth around the inner side that my mysterious tool must engage. It's around 32mm as you can see. Once that is removed, the inner ring that is loose can be lifted out, and then, finally, I can install the outer balls easily.

you might want to notice that the teeth on the freewheel you're struggling to regrease are worn ......
and that's a fairly old and outdated design of freewheel, too... which further reduces the chance of stumbling across an outdated "authorized repair shop-only" splined tool for low budget chinese parts.....

once again... just get a new freewheel.

i just looked thru my current collection of 50+ freewheels... the THREE that have the spline you are wanting a tool for are 2 DNPs and one insanely large Falcon.
Both brands are notorious junk brands, made in China and Taiwan.. Both brands are famous for "wobble" when New.
if you still insist on trying to locate the tool to remove that splined ring, contact Falcon.

Company Name: FALCON CYCLE-PARTS CO.,LTD.
Tel +886 4 23764633
Email sales@g-falconcycle.com
Website https://www.g-falcon.com/
10F.-2, No.270, Chung Ming S. Rd., West Dist., Taichung City 403, Taiwan (R.O.C.)

or just get a new 8 Speed freewheel, pre-packed, with the correct grease, and wearing fresh sprockets... SunRace is a brand i've used in the past... they seem to maintain better quality control than some other brands of similar price range...
oh, and i strongly advise getting a better chain (KMC and SRAM are popular, and reasonably priced), and installing it, too.. the stock chain on your bike was worn out before it was installed at the factory.

Sadly, i work on way too many Walmart bikes... i know their issues all too well.
the next thing any Walmart bike owner should do is replace the plastic-perch Brake Lever assemblies, and lousy, rust-prone, brake and shift cables and housings.

maddog, I am so disappointed! This bicycle is essentially new. Just bought it in 2024, and haven't had a chance to ride it much. How can these teeth possibly be worn?! Before I bought the bike, I did extensive research to get the best bike available within my price range. This Schwinn Traxion was highly recommended. Schwinn has been around for countless years. I would think by now they have figured out how to make a decent bike. Anyway, for now, I would like to continue using the bike as is, and perhaps some day soon, I'll take your advice and replace the freewheel. I have had no problems with this bike other than that inner ring coming loose. I just want to tighten up that ring, and put the bike back in service. So, I'll see about getting that Falcon tool you suggest. I'm happy to finally be on the same page with you all! Thank you.

They did before their first bankruptcy in 1992. They sold the company in 2001 to a foreign conglomerate.

i've had one of that exact model come thru my shop.. donated, in need of work... i sold it to a local man... he destroyed the freewheel within a month... it literally fell apart while he was riding.
What wears a Schwinn badge these days is a Taiwan Designed bike with components built in China.
You should have bought a 2001-2-3 Specialized FSR- XC and put some cash into rebuilding it... and you would have a Far better bike with Actual functioning Suspension, a hundred or so extra dollars in your bank account, and fun riding it, instead of a low end pogo stick with tires under it.

Tip: people that write flowery reviews rarely own the items they are "reviewing".

Specialized FSR-XC bikes of the 2001-2-3 vintage regularly sell for $150 to $300, depending on their need for a tune-up. I buy the frames with rear shock for $25 to $50.

as an example, here's a newer one, in great condition, for $495.. it's been modded for DH use, it appears...
https://olympic.craigslist.org/bik/d...798250859.html

Schwinn is not the brand it was 50 years ago. Just the name remains the same.
It's been through several different ownerships- Dorel Group and now PONS.
https://en.wikipedia.org/wiki/Pacific_Cycle

"In 2001, Pacific Cycle outbid Huffy Corp. in bankruptcy court for the purchase of the Schwinn/GT Corporation, obtaining control of the Schwinn and GT brands for $86 million.[6] In 2002, Schwinn was introduced to the mass-merchant channel at Walmart, Target, and Toys "R" Us.[1]


https://sheldonbrown.com/rebuild-freewheel.html

I have to say I agree with maddog - look at the difference between the width of the U shape on these two teeth - and these are on the smallest, likely least used sprocket.

I noticed that too. But, the bike works well with no issues, so may as well continue riding it as is. If and when I start having any problems, that will be the time to upgrade. For now, I'm still looking for that elusive Falcon removal tool. As you all recommended, check with Falcon....well, there is no Falcon! I have not been able to find their web site. So, as of yet, haven't found that 32mm or so removal tool. I am going to try and make one out of a large hex head bolt.....that is, if I can find a bolt of the correct size!! I'll take the freewheel with me to the hardware store.

wow...
get a clue.
buy a new freewheel.
you're trying to remove a part that doesn't need to be removed, to try to remedy a problem that didn't matter, that you don't have additional shims to try and remedy the mis-perceived problem. and is common to all freewheel assemblies.
your next wrong move will be to use too thick grease in a cheap chinese freewheel, which will possibly cause the pawls to not engage, and possibly damage your crotch.

and you want to spend more money to possibly hurt yourself...?
Falcon either got bought up, went Bankrupt because they sold garbage parts, or got sued out of existence.

smh.

BTW... you may want to try a small punch and hammer to remove the cog lock ring...
and a 3/4" UNC bolt may help do what you don't need to do... or a 7/8" UNC.
and you'll need to carefully grind the head if it doesn't quite fit... grade 5 and 8 are as hard, or harder than most files.
good luck.

here... contact these folks, in China... they also use that old splined cog locknut.

https://dnpgears.webnode.page/about-us/
who knows,,, maybe they too will close their website soon! So don't Delay.. Call Today!
no telling what they will want for one of their factory-only tools.

the splines highlighted are part of the cog retaining locknut. it appears the zombie reviver has already dismantled the freewheel ratchet and is now wanting to remove that locknut/lockring... it will not achieve his goal of easing reassembly of the ratchet to the outer freewheel body.

and i completely agree that he or she should just get a new sunrace 8 SPEED freewheel... i'm not aware of a shimano EIGHT SPEED freewheel assembly, and i kinda doubt the others you mention ever made them, but someone might dig deep enough in the ratholes to find an example.
i have 2 7sp., and one 9sp. examples of the DNP and Falcon Freewheels here, as stated earlier. I scrapped about ten of them earlier this winter... i keep shimanos, suntours, a few reginas and malliards... i think have an atom somewhere too. NONE of them are 8 speed. Cassettes ended the 8 speed freewheels quickly.. their dawn was also their dusk.
i don't disassemble cheap chinese freewheels, i toss them in the scrap, mostly...
and all this is because the OP believes the cheap chinese freewheel can, somehow, be magically "better" with fresh grease, and some extra torque.

and your assumption is wrong... that's a gutted freewheel in the pic.

I'm out.. this thread has become a complete farce.

Hello, everyone,
I'm finally back! Firstly, a big thanks for all the opinions I got here. I did finally accomplish my goal of removing that ring. I bought a 1 3/32 bolt at the local hardware store, and set the bolt head into the ring. Then twisted the threaded portion of that bolt with a monkey wrench. The ring came out ever so nicely! And put new grease in the bearing races, installed the balls, etc. Been riding the bike a lot now that the weather is more cooperative. The freewheel runs nice and smoothly with no issues. I did have one other issue with the left pedal crank, but that was easily solved by removing, and reassembling, and tightening the bolt to the proper torque. I also noticed loose mounting bolts around the rear disk brake, including the disk itself. I snugged them all up with a torx wrench. Seems those bolts were never tightened up properly at the factory! I know you all mean well by suggesting I buy a new freewheel, and perhaps some day I will, but for now it is all working normally, and having a ball riding the bike.