A lot of folks have talked about what, I'll talk about how.
To measure the Total Indicated Runout TIR on the morse taper of your lather, you take a Dial Test Indicator which is a fancy measuring device that has a pin sticking out that can be pushed back and forth. You mount this gizmo on a stand such that the pin is parallel to the lathe bed, and the head of the pin is just inside the taper on your headstock, gently pressing against the inside of the taper.
You then turn the spindle by hand and observe the Dial.
Any wobble or out of roundless in the taper will make the needle swing.
The total range of that swing is the Total Indicated Runout of the taper.
Two common Dial Test Indicators are 0-4-0 or 0-15-0 which means they can measure +/- 0.004" or +/- 0.015". The 0-4-0 typically has an accuracy of 0.0001" while the 0-15-0 typically has an accuracy of 0.0005"
This TIR gives you some indication of the best accuracy you can possibly achieve with a taper mounted item in terms of wobble of the thing you are turning.
The problem with this measurement is that it does not tell you if the taper is crooked, which would make the accuracy of the taper even worse.
But for a dead center or spur center this is pretty irrelevant as the tip of the drive is so close to the taper that any error in the taper being crooked would have minimal impact.
For a taper mounted collet chuck, this would be relevent.
The other TIR measurement you can make is of the registration ring which is the metal ring that your chuck ends up pressed against when it is screwed onto the spindle.
You measure this with the pin perpendicular to the bed, touching the ring.
This measurement gives you an idea of the best case angular error when using a thread mounted chuck. It does not tell you how well centered your chuck will be on the threads, only how square it could possibly be.
This is important as you get away from the spindle. For example;
Assume 1 1/4" 8 TPI spindle thread.
The registration ring has a radius of around 7/8"
Lets assume the TIR of the registration ring is 0.0005"
So for every 7/8" away from the ring, you will get 0.0005" error plus whatever error you have in offset placement.
Assume you have a Talon Chuck which is 3" from registration ring to its jaws, and are holding a 5" long piece of wood. So the end of the wood is 8" away from the registration ring. The best you can hope for is that 0.0005 * 7/8" * 8" or 0.0035 wobble at the end.
In reality it would be worse than that because the error in the threads will always have the chuck somewhat offset from dead center adding to the above error.
This is partially why metal working lathes use 4 jaw chucks with each jaw independantly adjustable. You can correct for chuck mounting errors by tweaking the jaws to get the item perfectly centered relative to the spindle.
, but it is the gist of the meaning.
