I'm asking this because I was test flying an experimental helicopter last year and we had some tracking issues due to blade mismatch, and even in a no wind hover there was a pronounced vertical vibe and not much lateral.
As I analyze this out of track condition for a hover I see the vertical lift vector at the teeter hinge being tilted and rotating with the rotor at that tilt causing a lateral oscillation of force but the vertical force staying constant. In other words even though one blade has more lift than the other, the total lift looks like it would remain the same throughout the rotation.
However, as I specifically considered our helicopter, which has blades that when tracked at one collective setting would be way out of track at a different collective setting, I thought... The blade that tracks high will not track the same amount higher when the lift coefficient is changed. This made sense to me that the total vertical lift was changing through the rotation because of cyclic pitch variation.
Example: lets say that nominal pitch at hover was 5 degrees, but due to CG it takes one degree of cyclic pitch to maintain hover. And lets say that the blades track well at 4 deg but the red blade goes higher at higher collective pitch angles. This means that as the blades are going from red 5 and blue 5 degrees pitch as they rotate the red blade is slightly high (because its above 4deg nominal) but when the red hits 4 and blue 6, the red is at its "in track" reference but the blue is BELOW track at 6 deg then when the blue hits 4 and the red 6, you get the blue at its "in track" reference but the red is ABOVE track. So if the in track reference (4 deg) makes say 500lb of lift per blade and 6 deg makes 550lb then when the red blade is at 4 deg its making 500lb but the blue is at 6 but flying lower (so maybe 530lb) than it should be and then 180 deg later the blue is at 4 deg making 500lb but the red is flying higher than it should be for 6 deg (so 570lb). You can see how the total lift would be changing cyclically causing a vertical vibe.
But then I thought: when the swashplate is tilted 1 degree and the tip path plane is matching the no feather plane (control plane), the blade angle of attack will be constant all the way around even though there is 1 degree of cyclic.
Ok I am still stumped. If a helicopter has perfectly matched blades and is in a no wind hover but out of track, is there a vertical vibe? If so please explain by showing me how the lift (vertical) vector is changing with rotation to cause a vertical vibration.