Tim did very thorough measurements with an accelerometer and notes that a major conspiring factor in his vibration issues was the resonant frequency of the entire motor/transmission assembly. The entire assembly weighs close to 200 lbs. and is only supported at either end, so the entire thing is able to flex pretty freely. With the coupling between the motor and transmission made by a 1/2" aluminum plate, there's a pretty flexible member smack dab in the middle of everything. Also, the fact the bolts into the motor were only engaged by 1.5 threads can't help either. This explains why the vibrations are so significantly reduced when the motor & flywheel are spun up without the transmission - no resonance.
In layman's terms, the transmission is able to vibrate just like a guitar string. If you hum the note 'G' next to a guitar, you'll notice the G string starts to vibrate on it's own without even plucking it while the others really don't do much. So, if the motor/flywheel vibration is the humming, then the motor and transmission are the guitar string... when you hit the right frequency, the string starts vibrating with a much greater magnitude than what's exciting it.
So, the vibration is really caused by a wide array of small factors, all conspiring to cause a large problem. We're now pursuing multiple tracks to fix each of these problems:
Sing softer: reduce the vibrations coming from the motor/flywheel assembly by shortening the distance from the motor bearing to the flywheel, eliminating the flywheel and using a small diameter lightweight racing clutch to reduce the exciting mass, and by chasing out the dozen or so tiny misalignments that could be adding up and putting things off balance and out of alignment
'Tune' that guitar string to a note higher than we can sing: stiffen the coupling between the motor and transmission to increase its resonant frequency, which may involve machining a thicker adapter plate and cutting that massive 'doughnut' down, in addition to making sure that all parts are mating flat and flush, and the bolts are fully engaged in the motor housing.
Mute: like pressing your finger gently to the guitar string, add rubber bushings to the motor mount to absorb or 'dampen' the vibrations so they want to die out rather than build up. We'll do this last since it really just masks the problem rather than solve it.
On Sunday after a team meeting to discuss all these findings, Dave, Tyler, and I measured the mating surface of the transmission. It wasn't round, flat, perpendicular nor concentric (oh boy!). We put sandpaper on the adapter plate and used it to knock down the front mating face of the transmission to get rid of that lip and make it a flat surface to mount to. In the end, it's very flat and perpendicular except around the top right bolt which is still 10 thou low.. we shimmed it with razor blades and the adapter plate sat eerily flat and perpendicular.
The adapter plate itself is not perfectly flat anymore, perhaps due to the unevenness of the mating face on the transmission, and the alignment ring is slightly undersized, so there's a good 10 thou of play in that plate. With some experimentation, the closest to concentricity we could get was 5 thou too high by pushing the plate towards the bottom of the transmission as we tightened it up. Perhaps we could knock that much off the plate's alignment ring and get it perfectly aligned. We also took precision measurements of the concentric surface on the transmission, which is slightly oval shaped (narrower horizontally than vertically, leading to greater vertical than horizontal play in the mounting plate). If we end up making a new, thicker plate, we could use these measurements to make it fit the tranny perfectly (we could also build in the 10 thou shim).
Tyler is looking for that racing clutch, which has to fit the transmission's spline. We need to consider the torque rating of the clutch... we're only dealing with 90 ft/lbs from the motor, while racing clutches are often rated very high because of the high power engines, so we may need to reduce the clamping force so we don't have too much impulse torque transferred back to the motor (then again, the rotor has so little mass, it'd be hard to get much back torque). Racing clutches also have the a shorter pedal throw, and no springs, so we need to moderate the clamping force to smooth out the clutch engagement.