Back to basics -
1. Check that your headstock and tailstock are aligned. There is no way to adjust the tailstock, but you can align the headstock. Put the spur-type drive center in the headstock, and the cone live center in the tail stock. Extend the tailstock quill as far as it will go, and then back off by turning the handle one turn. Slide the tailstock up to the headstock, and closely inspect how the two points align. Note that alignment involves two dimensions. Fixing a misalignment in the vertical plane is difficult (theoretically , shims could be inserted under the headstock if the headstock is low, but if the theadstock is hign, there probably is no simple fix that I would want to attempt). So I would consider vertical misalignment to be a manufacturing defect and contact PSI Customer Service about a warranty replacement. However, that's a rare situation fairly unlikely. A more probable situation is that they won't align in the horizontal plane. That's very easily fixable - there are four socket-head screws attaching the headstock to the bed ways, and the lathe was supplied with a hex wrench that matches those screws. Loosen the screws, and twist the headstock until the headstock and tailstock drive points are aligned in the horizontal plane, and then tighten the screws. To be cautions, check the alignment again - and again.
2. The other possible problem is that there is too much backlash in the tailstock. Loosen the tailstock clamp, and then grab the tailstock and wiggle it to see if it can rotate about an imaginary vertical axis. The tailstock is aligned to the bedways by means of a machined rectangular protrusion on the bottom that fits between the bedways. Many lathe owners have observed that the protrusion is very slightly too narrow, and as a result, the tailstock can rotate just a bit. On my 12" Turncrafter, I get about 0.6 degrees of rotation - yeah, that's pretty small, but its enough to cause the horizontal plane alignment to shift a millimeter or so on the horizontal plane. There is no simple fix for this problem - you simply have to be aware of it and account for it in using your lathe. There are two times when this can be a problem:
When drilling: on the lathe - the fix for this problem is really simple. Mount the blank in a scroll chuck in the headstock, spin the lathe, and use a skew to cut a small dimple exactly on the center of rotation where you intend to drill. Then, with the drill bit in a jacobs chuck mounted in the tailstock, slide the tailstock up to just before the bit touches the blank, and wiggle it until the bit is centered on that dimple - THEN lock down the tailstock and drill the hole.
When turning pens using a pen mandrel - the fix here is very similar to the drilling situation, except that you should align the tip of the cone center to the end of the mandrel. The problem, however, is that if the mandrel is bent, the rotational axis of the tailstock won't be aligned with the rotational axis of the headstock, and that causes the rattling you have experienced. You can minimize the problem by turning one blank at a time even though the mandrel is long enough to turn two blanks simultaneously - making the mandrel shorter reduces the alignment error. Also, in my experience, if you have aligned the headstock and tailstock as described above, and if then observe how that alignment can shift as a result of tailstock wiggle, you can pretty much eyeball where the tailstock needs to be within that 'wiggle range' so that the tailstock axis is aligned with the headstock axis. It won't be perfect, but it will be close enough, and will compensate to some degree for a slight bend in the mandrel shaft. Obviously, replacing the mandrel shaft is will fix the problem - temporarily, until it becomes bent again. I'm sure that someone will point out that a better solution is to throw away the mandrel and turn pen blanks between centers, but I'll let them speak for themselves.
