Life of a ball screw is determined by material fatigue and wear from surface erosion of balls and races. While surface erosion is hard to predict, fatigue can be calculated. The equations that I will use here are the ones from the ISO 3408 standard, which is widely used.
First, you need to determine the average load the ball screw will “see” during operation. Since we are dealing with fatigue effects here, the magnitude of the load matters as well as the number of revolutions made with this load. Keep in mind that balls will be loading and unloading any given spot in the race as they pass over it, so even constant ball screw loads will cause an alternating load on that spot.
The average load is calculated with the equations below. Fm is also called “equivalent” load, because it would cause the same (or equivalent) fatigue to the ball screw as the actual duty. For simplicity, the number of revolutions is expressed as (q*n), where q could be the time, or percentage of time, and n is the speed in revolutions per minute. Of course, you could replace this product (q*n) with number of revolutions. One other important factor is preload which is often ignored by some manufacturers. If you are using a ball screw with zero backlash (whether it is single or double nut) then the equivalent load has to include preload (which if you think about it is a constant load on the ball screw). I will deal with how to address preload in the life equation in a separate post as well as how to calculate equivalent load for a single nut and a double nut (yes it is handled differently). The second equation can be used to calculate the average speed nm, which would be useful to convert the resulting ball screw life (which is in revolutions) into hours, for example.
Once you have that, find the dynamic load capacity of your ball screw in the manufacturer’s documentation, making sure that it uses the right standard (1 million revolutions), and the proper measurements of course. If the capacity of your screw is given in lbf, then it’s a good idea to check if the manufacturer used the ANSI definition of dynamic capacity (1 million inches of travel). You would then not only need to convert the lbf into N or whatever you are using, but also make a conversion for the different definition of the load capacity. I will deal with that in another post.
Finally, you may calculate the theoretical life expectancy L10 of your ball screw using the following formula:
L10 is expressed in million revolutions.