Today I discovered my King 10 x 22 lathe (same as Grizzly G0602) is cutting an unintentional taper. I realized I haven't checked the alignment since mounting on the new bench, so using the above method I tried to fix the issue. During the first part (Horizontal alignment) I found the alignment to be out and after some adjusting I got the average to match exactly. However in my attempts to get the Vertical alignment adjusted nothing would change. I kept getting the same averages no matter what I did. I started by adding paper shims to the tailstock and got up to 4 thicknesses without any measurable change in the readings. So I took those out and went to the headstock and started adding paper shims. I got as far as adding 8 thicknesses to each side of the headstock and still no changes.
Is there something about this lathe that prevents me from making this adjustment or am I doing something wrong? Note there is only one bolt holding the headstock down and the same on the tailstock. The bolts are dead center between the lathe bed rails.
I have a Grizzly G0602 which I understand is essentially the same as your lathe.
From the title of your thread, I assume you are checking alignment using the RDM. A few questions for you. It sounds like you checked and corrected for horizontal misalignment. For the vertical alignment check are you measuring runout in the vertical plane through the spindle? You mention the tailstock. The tailstock only comes into play when you are running between centers and checking the alignment of the tailstock to the headstock axis.
In aligning the lathe, I would check first for lathe level. Next, I would check for cross feed alignment by mounting the faceplate and sweeping the face with a dial or test indicator. Make a mark on the faceplate where the measurement will be made and make a measurement with the cross feed retracted. extend the crossfeed and rotate the faceplate so the measurement will be made at the same point. This ensures that any runout in the faceplate is compensated for. You can also skim cut the face plate to true it. My lathe has the ability to pivot the headstock slightly to angle the spindle axis to the front or rear relative to the ways. The headstock should be rotated to get the same reading. This is done first because the G602 and your King lathe have no other way to correct for cross feed misalignment except for re-machining the cross feed ways
I would them check for min/max in the horizontal and vertical plane. This is basically the alignment of the headstock, specifically the spindle axis, to the lathe bed.
This would be done with the horizontal RDM check. However, you don't want to disturb the previously aligned headstock. I would shim the base of the lathe at the tailstock to correct. Placing shims under the base to correct for taper amounts to twisting the bed and should not be used for major corrections. Although your lathe has only a single mounting bolt at the tailstock you can still shim under the four corners of the base. Remember that you are trying to induce a twist so add the shim pack equally to the left and right of the base at either the front or back.
To tilt the spindle axis up or down relative to the ways, I would check this in the vertical plane and I would shim the headstock. Vertical alignment of the spindle axis to the ways is not as critical as the horizontal alignment. It basically raises or drops the tooling slightly as you traverse the ways. The effect is small for most turning as the factor is the cosine of the angle created by the drop or rise of the tool. Unless it was a significant amount, I wouldn't bother with correcting.
Once the headstock was aligned horizontally and vertically to the ways, I would look at the tailstock. To check I would mount the test bar between centers and check the min/max readings near the headstock and the tailstock in both the horizontal and vertical planes. Adjustments would be made by shifting the tailstock to the front or rear for the horizontal adjustment and shimming the tailstock for the vertical adjustment. Note that if you add shims to the tailstock, it will have to be done equally on four corners. The tailstock axis could also be angled relative to the headstock axis. You can check this by making the measurements first with the tailstock retracted and then with it extended. You should get the same readings for both.
I hope this helps you.