Here are a couple of links of my posts from 2008 & 2009 that might shed more lights on X, Y and Z axis spins:
The following link talks a bit more about Z-axis spin (aka bullet spin):
In the old Operation Doubles
web site, Kathy Krajco talks about the altered axis of rotation for a twist serve. She does not give a name to the Z-axis component of spin but she does talk about how the resultant spin axis is different for a twist serve than it is for a regular topspin-slice serve.
For most shots that we discuss in tennis (with topspin, underspin & sidespin), the actual axis of rotation of the spinning will be perpendicular to the flight of the ball. However, due to the presence of a Z-axis spin, the actual rotation of the ball on a twist serve is no longer perpendicular to the flight of the ball -- it is offset somewhat from the perpendicular.
Here is an archive of the late Kathy Krajco's old OD web site page. Unfortunately, some of her excellent gif
s showing the spins may no longer work: