I certainly don't fit into that genius category. But you haven't stated nearly enough information. If you expect accurate answers you have to provide enough information to prevent guessing about what you mean. Ok it's been leveled, but to what degree of accuracy? Carpenters level, digital level or more properly with what would normally be referred to as a machinists master level of roughly .0002" over 10" for accuracy or better. There's a definite and very logical reason a level of that accuracy is required. Because of the distance the cutting tool tip is above the lathe ways, it works to directly magnify any errors in the lathe bed itself. Visualise it as slowly rolling the tool tip into or away from the work piece as the carriage tavels along the lathe bed and follows any twist in the bed. .0001" inaccuracy or twist in the lathe bed will roll the tool tip in or out of the cut a whole lot more than the .0001" the bed has. It can be done without an expensive level, but it will also take a whole lot more time. And bed leveling is sort of misnamed, so mostly for that reason it's somewhat misunderstood by too many. It's just the fastest and easiest method of getting both ways so there in the same plane. In other words flat, hopefully parallel and true to each other. Then what's the bench built from your going to mount the lathe to and what the floor that bench is sitting on is even constructed of? Any wood at all in either of those two areas and it simply can't and won't stay leveled to the accuracy it's been set to for more than an hr. or two with the slightest change in humidity and maybe a bit less so with any temperature changes. My 450 lb bench top lathe is bolted to a pair of steel mechanics roll away cabinets with the castors removed that are themselves firmly bolted together at multiple points. Loaded with lathe & mill tooling, that steel support base itself weighs roughly 1,000-1,200 lbs plus the weight of the lathe. I then built 1" thick steel plates that are screw adjustable to level my lathe bed, and it still moves around because I unfortunately do have a wooden floor construction for my shop. Then what size of lathe? Plus exactly how are you adjusting the lathe ways so that they are in fact level? Most seem to assume perfectly level bed ways will or should produce a properly parallel turned shaft. It can't and doesn't, and the smaller the lathe the less true that is. Depending on the quality and accuracy the lathe was built to and the unavoidable but standard deflection of the lathe parts themselves under the cutting loads it was designed to do, some very minor but important compensation needs to be applied to then gently tweak the lathe bed so it will in fact turn parallel. Since the head stock end for obvious reasons is the most rigid I leave it alone once it's known to be level and adjust the tail stock end only until it does turn parallel with a known to be correct centered tail stock Morse Taper. But the best and largest machine tools ever made will ALL deflect an easily measurable amount under the cutting loads there capable of. That's a fact of physics and reality. Anyone thinking those massive machines can't or don't deflect just means they don't understand what really happens. So that minor tweaking is still part of the process. There's no such natural or man made product yet that is completely rigid, it's physically impossible to do so. But bed leveling to turn parallel is only part of it, if the tail stock isn't also correct it can't drill or ream holes without them being tapered. So how accurate is it centered to the head stocks spindle after the bed is leveled? Then how accurate is it's quill alignment in both up/down, left/right? Have you checked those alignments with an indicator yet?
That as you call it bar bell test is more accurately called a two collar test, and it can be used to do that minor bed tweaking. Most seem to prefer aluminum for it's ease of cutting for a test bar. Myself I think steel more accurately reflects what the lathe is capable of under real world cutting conditions. "However", there are definite requirements, one being that the cutting tool tip needs to be razor sharp so the minimum of cutting tool pressure is applied to the test bar your cutting. Standard carbide tips simply require too much pressure so your test bar will deflect instead of cut cleanly to end up with meaningful test cut results. Some properly ground and then honed High Speed Steel would be the much better choice. Google for a PDF of the South Bend How to run a Lathe book for some preferred HSS tool grinds.That 12L14 would work fine, but again it depends on it's starting diameter that you haven't mentioned. Due to what's called Youngs Modulus (Google it) roughly the maximum bar extension out past the chuck jaws should be no more than 3 times it's diameter. So checking a bar over even 6" between the two collars would require a starting diameter of at the minimum of 2". Anything less will give meaningless test results. Once that's known to be correct, I then adjust my tail stock to be centered to the head stocks center of rotation. At that point I use a 2" x 12" long steel bar between centers to do a final parallelism check so there's no unknown effects from a lathe chuck.
I'm not saying this to be insulting to anyone, I'm being factual. I'd estimate 90%++++ of the information given on the more hobby level forums is either incomplete and on up to even being completely wrong about properly checking & tuning any machine tool to perform it's best. One I've seen far too much being mentioned is moving or shimming the head stock. That would be the very last thing I'd ever do and certainly not until I've run some actual and PROPER tests that proved beyond doubt it was in fact out of alignment and by exactly how much. Very few seem to understand that some of the best lathes made have both there head and tail stock Morse Tapers and spindle or quill C/L's purposely misaligned at the factory to be pointed roughly .001" high and the same amount towards the operator over approximately 12". That's built in to help compensate for both predicted work piece weight and cutting tool loads. A side benefit of that misalignment is the machine then starts to wear towards a bit better accuracy instead of immediately away from being accurate. It also helps to produce very slighly concave faced parts so mating part faces don't rock as they would with convex facing cuts. And properly leveling any lathes bed is only a first initial starting point to where the other 90% of the work & test checks need to be done. Google for an online PDF of the book written by a Dr. Georg Schlesinger titled Testing Machine Tools. PRINT the whole thing off and then study it enough times until you fully grasp the concepts of why the tests are being done in the way they are, as well as how and why it's being done in the way they are. None of this is quite as intuitive as some seem to think. Schlesinger literally wrote the book about this, and the vast majority of the best machine tools including the most modern cnc's made today still use the same test methods or slightly modified versions to suit the machine tools exact requirements. My last lathe purchase came with a test certificate of it's accuracy that I verified myself the factory results were in fact true. I don't EVER blindly trust anything in writting that's shop related unless I check it myself. And that includes almost everything I've bought with Starret, Mitutoyo brands on them. Every test and diagram of what was being tested in this lathes certificate were 100% for sure taken directly from that Schlesinger book. Correctly using it's information can help to tune a lathe to actually produce better and more accurate parts than the factory built it to do IF your willing to invest in the correct test equipment and spend the time & effort it takes to do so. I've test checked and adjusted my lathe using the methods from within that book to turn parallel between centers to less than .0002" in 12". Unfortunately for me it won't stay that way for more than a few hrs at most. But I've proved Schlesinger's methods do work just as well today as when that book was first printed.
The less you spend on any machine tool then the less accuracy you should expect to find. Some of these off shore lathes are more than crude and poorly designed / built. So if you did decide to run those Schlesinger tests? You'd better be prepared for a whole lot of disappointment and frustration. There still well worth doing because you can't hope to make adjustments, possible additions or modifications, re-machine, grind, or hand scrape to be vastly better without already knowing what is or isn't already correct. Your also not going to fully understand even the basics of this overnight. Fwiw I've been trying to educate myself about machine tool alignment for over 40 years and I've still got lots to learn.
