What is the maximum rotational velocity of miniature ball-screw (diameters up to 12mm) for approximately 1000 thrust cycles, and which type/brand would that be, if the speed is limited by the ball return mechanism? The fastest I could find was 4000 rpm at 3000 N thrust, but this was from a datasheet with a big safety margin (millions of cycles).
I'm looking for either experience and data, or a general method/formula that can be used to find the maximum velocity (and load) as function of cycles or the other way round (similar to those of ball bearings). Suggestions and knowledge about faster types and brands of ballscrews than the ones I have been able to find is welcome as well.
Some more background information: Ball screws are very interesting transmissions for electrically actuated legged robotics, since they provide a high-geared rotary-to-linear transmission that is accurate, precise, energy efficient and possibly backlash-free. However, the big downside is their limited rotational speed. The maximum rotational velocity is limited by resonance and the ball return mechanism. The former limit is easy to calculate (eigenfrequency calculation), and mostly not problematic for small spindles. However, the latter is a bigger problem. The balls in a ball screw roll through the threaded spindle and have to be recirculated to the other end of the nut. The recirculation limits the rotational velocity of the ballscrews. The corresponding maximum rotational velocities are not calculate-able (for as far as I know) and are provided by manufacturers in catalogues, either directly in rpm or via a so-called $D_n$-value, where the rotational velocity in rpm is $n=D_n/d$ where d is the diameter of the ball screw. But even then, the maximum rotational velocity of ball screws is capped at 4000 rpm or lower according to datasheets (depending on brand and ball return mechanism). The highest permissible rotational velocities I found were those of Steinmeyer ballscrews, at 4000 rpm, using an end-cap-return mechanism. Note that for electrical motors (up to 200W) ideal (maximum power) velocities are higher than 4000 rpm, and even more than twice as high for many brushless motors. It appears however that ball screws can run at higher speeds than what they are specified for in reality, because the specifications hold for many millions of cycles. I can only find a single unofficial source where someone claims to have run their ball-screws up to 6000 rpm, and in missiles (one-time-use) up to 7500 rpm. I'm interested in a theory or more experimental data that backs this up.