has a 4" steel disc brake on it that is not balanced, so even with the lower RPM, it is a larger problem.
The spindle should be balanced as a unit, thus it would include the disc brake.
no harmonics
Yes it does, the spindle has a natural frequency ( all things do even the human body) and a critical speed, and whether you get vibration or worst yet resonance can be
dependant on the dampening effects of the mounting, bearing, machine frame, runout, etc, and could be influenced by repetative driving forces and transmissions.
Usualy you deisgn the part or system to not operate near a harmonic, in some analysis it is looked at to the 16th mode and design
changes made to move the natural freqeuncy away from a resaonant point for a given or fixed rpm. In the analysis, the harmonics of the system are used
and it is important to go through the resonant points / modes in a timely fashion such that resonance cannot occur.
You can have a spindle balanced to satisfy some spec, ( there are ISO and ASME spec quidelines for rotating machinery ). As you have become aware, as soom as you
add a different component the balance changes, runout changes, leveling plays into this, the natural frequency has changed. As a component in the makeup, a good
example is the addition of say a set screw / screws, or weight additive attachment can be used, or even a movable balance plate can be used to advantage, but ,
like all things it becomes a matter of degree and what your trying to do ( your unlikely to be removing material to accomplish it).
The 4 jaw chuck can be balanced, but then as soon as you put something into it there goes everything to poop again.
From a practical viewpoint, lets use consider what we do instinctively on say a lathe. If the lathe starts to get some vibration while we are trying to turn
something mounted off center, we slow it down and take cuts to make things symetrical and at some some point we crank up the speed and do more finishing to the piece.
Instinctively we deal with balance, runout, and vibration.
Now if you were to do some study on a part relative to it's natural frequency and as compared to degree of out of balance / loading conditions you could probably
relate back to some calcualted speed and balanced adjustments. Not something you would want to invest into if not in a large production quantity.
Time spent trying to follow a procedure may not pay when an additional roughing cut may be quicker.
I guess my viewpoints are more from a design point of view but the topic is of interest.
Back to the sidelines......
RICH