OK, done? Good. If you hadn't already guessed, I didn't mean the thing that occasionally cleans my clothes when I remember to do things like that; I was actually referring to the tiny metal discs with the hole in them that you put between the head of a screw and the thing the screw is attached to (fig. 1). It's sort of common knowledge that you use washers when you want to be extra-sure a screw will stay in place, but I'll be damned if I can tell you why that is exactly.
|Fig. 1: A bunch of washers somebody inexplicably decided to take a picture of (thx Wikipedia)|
Unsurprisingly, washers are not rocket science (I mean, except for the fact that they're probably used in rocket construction). Basically, your standard flat washers (not the split-ring lock washers, which I'll come to) perform two basic functions: increasing friction and redistributing load. The friction-increasing feature is particularly useful if the surface you're screwing into isn't particularly flat; sticking a washer between the screw and the surface means the underside of the screw head will have a nice flat metal surface to bear down onto; since frictional force is proportional to surface area, that makes the screw much less likely to loosen. See the diagram below for an illustration of this.
|Screws attached to an uneven surface without (A) and with (B) a washer to give the screw head as much contact area as possible.|
The second function (load redistribution) will be familiar to anyone who's ever tried to tightly screw a bolt into some kind of soft material like wood; after a certain point, the pressure exerted on the wood by the screw head exceeds the strength of the wood and further tightening just causes the screw head to get buried in the wood. So basically there's a "critical screw tightness" that you can't exceed for any given material, and for materials that are softer than metal it often isn't tight enough for things that need to be load-bearing.
Remember when I said "pressure" up there? That was the giveaway; pressure equals force per area. In this case, it's the force applied by the screw head on the material during tightening, divided by the area of the screw head. So to keep from going over that critical pressure, you can either decrease the force (not tighten the screw as much, which is as previously discussed not helpful) or increase the area of the screw head. By now you've probably put together that sticking a nice, fat washer between the screw and the wood increases the effective area of the screw head by quite a bit, and will let you get screws and bolts into soft materials much more tightly than you normally could. See below:
|Screws attached to soft material, ruining the hole by overtightening (A) or using a washer to spread the force out and keep that from happening (B)|
So that's what regular old washers do, and if I'd given it much thought I probably could've worked that out for myself. Split-ring "lock" washers, though, are a whole other story and much more complicated/interesting.
You'll see lock washers used between screws that absolutely need to stay in place no matter what; holding bits of your car together, for example. That's because lots of things, including but not limited to vibration, thread damage, thermal expansion/contraction, and corrosion can cause a screw to slowly loosen over time. The lock washer counteracts this, by applying a continuous spring force pushing the screw head and the material apart. That way, if the screw manages to loosen a little bit for whatever reason, it'll just be shoved outward a tiny little bit by the lock washer but stay "tight," rather than being able to move around freely and possibly damage/loosen itself some more.
There are other kinds of washers that are mostly application-specific (plumbing washers, for example, are supposed to be leak-tight) but those are the two main ones you'll see a lot in everyday life. And now we know why.
Thanks to the wonderful straightdope.com, which has been doing basically the same thing as this blog for much longer and better, for the explanation on this one.