Omega 166.088 watch with 1171/1 strap help

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Really, a chronometer rated movement would have gone into a watch with Chronometer written on the dial - usually a Constellation. Your movement, or some parts, have been changed during the life of the watch - it's not as unusual as you might think. It's not an upgrade to be honest as the parts were probably almost identical. Today, a chronometer rated ETA 2892 has some different escapement parts to a non chronometer so, it is more obvious.

As Tom says, there is scoring on the case back and, as you mentioned, it's also visible where the serial number is (for example). The central part with the big Omega shaped cutout is the rotor and this rotates to charge the watch in use. The axle and/or bush is worn and so it's flopping about and hitting things. This will add to the service cost, I'm afraid.

Regards, Chris
 
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I guess that there's no other option than that the movement is wrong, though the serial # is within the range.
 
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Possibly the ring shaped rubbing is what caused the movement to be replaced in the first place?