How important is the minimum layer height on a 3d printer?
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As with any manufacturing process, you'll need to learn to "use the right tool for the job". It depends on the requirements of the part. To answer your question, I would suggest using a larger layer height for the sheer fact of reducing print time on larger objects.

However, it depends on the part and how small the details are on the part. If your part has sharp edges that are required for the proper functionality of the part, then you'll want to use a smaller layer height. Or if your part fits into another part, you'll probably want to use a smaller layer height.

Another variable might be whether or not post-processing is necessary. Is this part going to be purposefully printed larger/rougher with the idea to use a Dremel later to smooth everything out? If yes, then use a larger layer height.