First, here's a simple illustration just for the sake of keeping our terminology straight. (Ignore the "0.462 cm" 'dimension'. That has no relevance to anything here. This was the best illustration I could find that had the correct terms on it.)
You'll often see the 'sleeve' incorrectly identified as the 'barrel'. That's misleading. The micrometer's barrel is underneath the sleeve. The barrel is rigidly attached to the frame, and has in it the female screw thread that the spindle/thimble assembly runs in.
The sleeve, as its name implies, is merely a scale-bearing covering for the barrel. And that's the key to the zeroing adjustment; the sleeve can be forced to rotate in either direction over the barrel. That's how you get the sleeve's baseline to align with the thimble's 'zero' when the spindle is fully closed down onto the anvil.
Here's a photograph of a micrometer in need of zeroing; it's off by almost a full hundredth of a millimetre.
Down in front is the little spanner that came with the micrometer for zeroing it. On the back side of the sleeve there's a hole for the spanner's hook to engage with.
In this case, I'll need to turn the sleeve so the baseline moves upward to align with the thimble's zero. What can complicate the procedure a bit is that the sleeve's friction fit may exhibit something of a 'stick/slip' characteristic -- apply enough torque to get the sleeve to rotate, and then it may 'jump' too far, spoiling the adjustment attempt. A couple of things can be done to get around that.
First off, clamp the micrometer in a vise with some stiff cardboard in place to protect the frame from being marred by the vise jaws -- a rigidly secured micrometer is much easier to deal with than one held in one's hand. The following photo shows the arrangement, along with a method for ensuring that the faces of the anvil and spindle are perfectly clean and free of debris.
A fresh cigarette paper is probably the cleanest, most lint-free thing in the known universe. Slide one between the anvil and spindle faces before proceeding, and you'll be assured a correct zeroing. (And a follow-up blast of compressed air doesn't hurt, either.)
The little adjustment spanner is awfully short; lengthen it by clamping on a small set of Vise-Grips.
The greater effective length lent to the spanner by doing this makes it much easier to get the adjustment dead on at your first go.
And here we are.
A hassle-free, perfect zeroing job.
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