I have a 3D printer where presumably a smoothing cap just fell off the X axis controller section of the mainboard. Didn't make a lick of difference in anything operationally. Still works great.
Checks out, most boards are made with very conservative amounts of decoupling capacitance because it’s way easier than dealing with random failures due to not enough capacitance
I've understood that capacitors can be used for timing, or smoothing a voltage after a power regulator (I think).
How/what does adding capacitance help with?
Voltage spikes from line inductance, voltage drop-outs from line resistance. Basically you have little reservoirs of charge scattered all around the board (current flow isn't instantaneous in a real circuit).
It helps to always think of current draw in a compete loop, out the "top" of the capacitor, through your IC, and back into the ground side (this isn't necessarily what's happening physically). Shorter loop means less inductance, shorter traces less resistance.
Smoothing is part of the story: but the important question is what is causing the roughness? Switch mode power supplies have inherent output ripple that can be filtered, but that’s distinct from transient variations in the load. Decoupling capacitors are used to provide a low impedance path at high frequencies i.e. fighting inductance.
It could be there to control emissions. You’d need to analyze the circuit to determine its purpose.
Very possible! I actually have a 100MHz scope and sdrs that tune from 9khz to 2ghz, could be an interesting distraction on the weekend to see if that axis is any noisier than the others.