Lathe is cutting a taper

Metal

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So my dad has a grizzly lathe I was turning down a shaft on yesterday

The thing cuts fine, a little bit of squeaking and intermittent cutting at the beginning, but it doesn't cut straight.
One end of the shaft ended at 7.35 or so, the other at 7.55 (about 12" of shaft, so its waaay off)

For the life of me I can't imagine how that could be so, the only thing I can think of is the head and center are inline with one another, but not inline with the bed. I suppose it could maybe be the dead center being off as well (I will try and indicate it) but I had no signs that the 1" shaft was being bent by two hundreths or more, and the center holes I drilled seemed good.

Any idea how to look at and adjust this?
 
Have you confirmed the head and tailstock are aligned? If not, I would start by checking this alignment. The tailstock should have adjustment and could have moved over time.

There are many videos on lathe alignment. An example is MrPete222 aka Tubalcain.

 
I'll check the tailstock like I said, assuming it is straight, what is the next step?
 
3 major things could cause taper, bed twist, tailstock alignment, & headstock alignment. I would check in that order. Usually leveling the lathe first (not level to the world, for bed twist) then aligning the tailstock first should do it. But if for some reason the headstock is out of alignment I would align that first & then the tailstock. But you first have to check bed twist.
 
Do you know if the lathe _ever_ cut straight? Depending on the model, some of the less-expensive Chinese lathes are well known for needing a lot of adjustment before they perform well. The tailstock often is the worst in this regard. My 7X12 certainly fell into this category.
 
If the headstock and tailstock are aligned, the lathe is level and it is still cutting a taper, then you may have to tweak the level to add a slight twist to offset for what may be wear in the lathe bed.

Keith Rucker had to use a slight twist in his LaBlond lathe restoration to offset wear in the lathe bed.

https://www.youtube.com/watch?v=5bWpgElMm8c&t=1377s
A recent thread on how to get metal stock for machining talked about the drive rods in printers/scanners having good tolerance so can be used as a poor-mans test bar. Another source is the shafts of shock absorbers and hydraulic cylinders.

A decent piece of metal for a poor-mans test bar will be useful to diagnose the root cause of remaining problems.
 
I have a feeling it's push over from tool bit pressure I bet a follow rest would prove it. I'm not saying the head can't be off but I'm betting its either he didn't use the tailstock between center and chuck or its the material flexing during the cut. If you want to Ck use the centers and drive dog method. Tapers can be from the tailstock or head stock.
 
One simple inspection you can make while checking alignment of your tailstock, is to examine the bottom of the tailstock, where it slides along the bed. If your ways have wear, often you will find equivalent wear on the bottom of the tailstock. Wear usually causes the tailstock to dip down and to the left - causing the lathe to cut a taper if positioned out along the ways in the areas where the tailstock most resides during turning operations.

Aligning centers with the tailstock up against the headstock only tells you you are aligned at the headstock. Move the tailstock back, with bed wear, taper can be a problem. So checking for worn contact surfaces on the bottom of the tailstock will either eliminate bed wear, or be a possible indictor wear is a problem.

If you can feel a notch, or ridge, on the bottom of the tailstock, with your fingernail, figure wear is a major culprit contributing to cutting unwanted tapers. If so, it is possible to shim back up to factory height.

Glenn
 
3 major things could cause taper, bed twist, tailstock alignment, & headstock alignment. I would check in that order. Usually leveling the level first (not level to the world, for bed twist) then aligning the tailstock first should do it. But if for some reason the headstock is out of alignment I would align that first & then the tailstock. But you first have to check bed twist.

Metal, I would listen to darkzero's advice. Get the ways leveled (an entire discussion all by itself) and align the tailstock, then go from there.

And when you do your 2 Collar test, listen to @Silverbullet and minimize deflection by taking light passes (0.002-0.003" deep) with a sharp HSS tool. This is Machinist 101; basic, but you have to do it right.
 
Said machine has an adjustable tail stock? If so check this first as it is the easiest thing to change, many have index lines but unless it is a very highend machine I would not trust them.

Every part is a test bar unless you always finish the part in one pass, skim the length then measure the ends and center then adjust the tail stock accordingly, do so until it reaches a taper that is within your idea of what it should be. This is the so called 2 collar test in place on the part being turned, it doesn't get any better then that. If a long thin part it will also tell you how much the part is bending away from the tool in the center which is more difficult to easily overcome.
If a NC lathe just program the taper out, this is by far the easiest way (-:
 
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