Ball Screws
OK, going to run down the specs for ball screws, and what you can expect to pay for different solutions...
First, there are two ways that the ball screws can be manufactured, they can be rolled or ground. The cheapest of these is rolled, which is when a plain bar of steel is pushed through dies that literally press it into a given shape. The alternative is to grind them, this gives higher accuracy and tolerances but is more difficult, and costs more.
In terms of performance, there are two main criteria to consider, accuracy and axial clearance. Accuracy is the deviation from ideal condition as the nut moves it's way up the screw, whereas axial clearance is backlash - the potential for loose movement of the nut on the screw. Accuracy is listed as a C number, from C0 to C10 as defined by JIS B 1192 (ISO 3408) standard. Rolled ball screws can be found from C6 to C10, but the most common is C7, defined as a flat accuracy of at most +/-52 microns per 300mm movement. For accuracies of C6 and below, deviation is specified for given length ranges, for instance C5 is 27 microns of culminative error and 20 microns of fluctuation for screws between 400mm and 500mm of length. See tables here from TKH (second page) or here from hiwin (page 15). C5 is probably the most common ground screw size, although they can be found from C0 to C7. In terms of pure price, you should expect to pay at least twice as much for a C5 ground screw as compared to a rolled C7 screw, and much more again if you want C3 or better.
For axial clearance, or axial play / backlash, different manufacturers specify this in different ways. For instance, in the above linked Hiwin document "axial play" is specified based on the accuracy C number between C0 and C6, e.g. 5 microns and 25 microns respectively. They don't specify C7 at all, and advise that if zero backlash is needed then "preload should be added" (buy two nuts?!). Other manufacturers give a preload or P number, such as on page 6 of this document by TBI. Preload is then the tightness of the balls inside the nut (...), with P0 being no preload and having axial play values given on page 7 (e.g. 50 microns max for D4 to D14mm rolled screws). P1 is no preload, and no axial play, above that P2 to P4 have increasing preload, which will increase the stiffness of the nut but will also add friction, heat, and reduce lifespan. Preloaded, i.e. P1 and above, is not available for rolled screws because their accuracy is not sufficient. Therefore, if you want to buy a ball screw without any backlash all, you'll need to buy ground - this is common across manufacturers. To give an example of price, TBI are relatively affordable, and I was recently quoted for C7 P0 rolled 250mm long 1002 sized (D10mm, 2mm lead) as US$122, or the same size but C5 P1 at US$274 (email quote from Panstar Motion on Aliexpress). Another example of axial play specification is from TKH, page 15-19 in the document linked in previous paragraph, who provide classification G0 for zero backlash, then GT, then G1, G2 and G3. Why? No idea! But G3 is the most loose, with 0 to 50 microns of play. In other cases, a typically more expensive solution is for manufacturers to supply single nuts, which are actually made from two nuts with preload between them.
Typically all the above specs will be visible in the product part number, somewhere, although since backlash specifications vary between manufacturers you'll need to know what to look for, but the C number accuracy should jump out. Also, the size and lead will be easily visible, with the part number typically having a format something like manufacturer - product line - size - details including length. So for instance:
TBI SFKR1002DFC7-250-P0
TBI manufacturer, SFK range, 10mm diameter, 2mm lead, you can see a C7 accuracy and a P0 backlash, 250 is length. Or:
THK NNB BNK1404-3RRG2+
THK BNK range, D14mm, 4mm lead, G2 axial clearance, 430mm length, C7 accuracy. Of course part numbers vary between manufacturers, check documentation for details!
A third criteria for accuracy is called the K number, for stiffness, with a unit of N/um - that is, axial force required to create 1 micron of movement. You'll generally need to go deeper into the manufacturers documentation to find this, it probably wont be there in the part number.
One final detail to consider is the maximum speed - different to critical velocity, this is rated as a DN value and depends to the pickup of the balls within the nut and the return mechanism. DN is simply the maximum RPM x screw nominal diameter (mm, I dont know if there is a version of DN in freedom units!!), and is generally rated for a series of ballscrews. Again, design rather than size dependant, although DN values dont always apply as well to the smallest and largest sizes in a range. DN values of 50,000 to 150,000 are standard. Since this is effectively rating the speed of the balls, larger diameter screws will have lower maximum RPM values. So example, DN of 70,000 on a 12mm nominal diameter screw = 5,833rpm, or for a 38mm nominal diameter we get just 1,842rpm. Potential problems with gantry speed can be solved by using higher lead screws and gearing down the motor to achieve required accuracy.
I've been talking about high end details on professional ball screws so far, however super cheap screws can be bought these days from China, albeit in limited sizes. Typically SFU1204, 1605, 2005 and 2505. Accuracy and axial play are not generally stated, but I've seen people measuring 30 to 70 microns backlash (1 to 3 thou), which is OK for some applications, but woefully inadequate for others. Accuracy is more difficult to measure, and not something that I can comment on - however, since they don't comply with any standards, there really is no way to guarantee the specifications you are going to receive. And of course there are many different manufacturers, or at least sellers, with no way to sort through them. Motion tends to be not particularly smooth, leaning towards crunchy at times, as you might expect, but again sufficient in many cases. Oh and they might arrive slightly bent... All together, I'm not too sure about how useful these are compared with lead screws. The main use case is probably to reduce cost in systems where the screws are going to be run hard, at high speed with high loads, but accuracy is not critical and the increased friction of lead screws would be unacceptable. You dont get the main benefits of quality lead screws, that is known tolerances on accuracy, potentially zero backlash, and extremely smooth movement, but you do get all the drawbacks. That is, sensitivity to misalignment, and they have to be kept totally clean of dust and chips. Lead screws dont care about such things, can be preloaded to completely remove backlash, but will have higher friction.
If you do buy one of these cheap screws and want to improve performance, some people have found that cleaning out the old grease can help, as there are probably particulates etc in it - not assembled in clean rooms then. However, unless you know what you are doing, you should not attempt to disassemble a ball screw! Putting them back together again is rarely easy. If you need to remove the nut, e.g. for maintenance, then make sure to slide it over a rod sized to the root diameter of the screw. This will stop the balls falling out, and make re-assembly considerably easier. You may be able to do this to replace the grease, if you are careful, but I have never tried. Generally replacing grease on ball screws is done by injecting into the lubrication hole on the nut, so try to make this easy to access during design phase!
