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No it shouldn't be that loud.

We have built several custom open gearboxes times in the past few years - One time it was being put together - it seemed a little hard but the students persevered - and then it screamed when first run! - well it was put together with 14 tooth pinions where the gear centers were set up for 12 tooth pinions - once fixed - it purred.
We also find that if using 2 parallel plates with spacers for the gearbox that before you tighten the bolts through the spacers, feel how the gears turn, get them right before socking it down. Ideally we want to control the center distances by a couple thousandths or so - but there is typically more slop in the bolting up process - things you can get away with in FIRST.
If it is too loud - screeching - then I would guess the center distance between the gears you are using is too tight, If too loose, it will not be as loud - just lots of backlash, and premature wear.