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Damaged Stepper Motor by Exceeding Current Rating

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Hello fellow engineers! I've looked around on the web to find an answer to this question but haven't had any luck. I'm hoping someone here might know the answer. 

I have a stepper motor in my setup that I noticed is losing steps and not able to run as it should. I noticed after the fact that I was running it at 2A as opposed to the rated 1A. I know that running a stepper motor at a current higher than the rated current can damage it, but what exactly is getting damaged? I'd like to be able to measure the damage to prove that's the root cause of what happened. For example, can I use a multimeter to check the electrical properties and identify a problem? I have noticed that the winding resistance is measured at ~2.9 ohms on one winding and ~2.5 ohms on the other whereas another motor I have of the same type is measuring ~2.9 ohms on each. Of course the motor phase resistance in the datasheet is listed as 2.8 ohms so nothing matches exactly. 

I have another similar motor that was also exposed to the higher current for a shorter period of time and now it's acting a little off as well. I'd like to be able to check it to see if it was damaged as well.

Thanks in advance for any help!

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It is difficult to say for certain, but normally in motors of any sort, the windings overheat and the varnish breaks-down (either burns off or melts) resulting in localised short circuits, identifiable by reduced resistance.

...I could be wrong, but your figures seem to back this up!

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