Bicycle Mechanics - how vital is an axle spacer? Will a slightly off-center axle go out of wack fast?

I have a rear wheel with AWC 3 speed hub. I had to remove the wheel from the frame to get a broken spoke fixed. The wheel was fixed and I put the bike back together again just fine. I rode it around for a day and when I got home I found a tiny black ring the thickness of a dime on the floor where I had taken it apart. The black ring was perfectly round and had no threading of any kind on it. I put it where I thought I wouldn't lose it, thinking I would re-assemble it when I had more time, but of course I lost the darn thing. Now I don't know if it's my imagination or not, but it seems that the wheel now has a slight tendency to work itself a little crooked in the dropouts after a good long ride. I thought I was screwing down the nuts pretty tight, but could a dime's thickness of washer make it unbalanced enough to notice??? I typically have a heavily laden pannier bag on the drive side of the bike, so might it just as easily be the off balance weight causing this impression?

If the tiny spacer is important enough to warrant replacement, I'm not absolutely certain which side of the hub it's supposed to go on! When I eyeball my chainline it looks pretty straight, and I know that my sprocket remains oriented the same way it was at the factory. The wheel just seems to work its way towards the LEFT chainstay ever so gradually. Do I just need to reset it in the dropouts again and it's all in my head?

I went to my local bike shop today asking for a thin spacer but they said just identifying the hub wasn't enough, that I need to take it in. I didn't tell them the whole story because I didn't want them to think I'm nuts. (Also there were two crazy expensive racing bikes ahead of me in the queue and I was maybe a little embarrased to explain the whole oddly complex 3-speed question) What do you all think?

I wouldn't worry about the spacer.

The slipping left dropout is a different issue. Make sure the mating surfaces of the axle-locknuts, both dropout faces and axle-nuts are clean and free of any dirt or grease. When you tighten the nut, how tight are you turning it? What size wrench? Do you have a torque number?

Are the nuts basic nuts with a separate washer? Or do they have built-in flanges? Are those serrated? Or do you have nuts with captured washers that spin?

Post some photos of the hub and dropouts, perhaps something is bent weird.

a washer can be important. Please refer to this link:

http://www.users.globalnet.co.uk/~hadland/awc.pdf

which you will note happily gives the tech info, diagrams,
and parts list for your hub. Try real hard to remember
what your washer looked like. If it was the slotted anti-
rotation washer, you will indeed experience problems
with maintaining hub position in the dropouts -- particularly
in a coaster brake hub such as yours where the brake
exerts a great deal of torquing force on the hub shell.

Take a good look at what you have and try to match it
up against the exploded diagram. Concentrate, breathe,
collect yourself, and fix your bicycle. Good luck and godspeed.

Mike Larmer

No, it wasn't the anti-rotation washer. I made extra sure not to mess up that one. I took a good look at this diagram, and I think what I lost was #45 HMW 146. It was just a plain washer. As far as tightening the nuts goes, I used an adjustable wrench and pushed down on it with my weight till it seemed to be on super tight. I don't have a digital camera handy, but there was indeed some grit there that might have made it lose traction.