Calculating ball screw load-life? Don't forget preload.

Can a ball screw with a reasonable amount of preload but no outside thrust last forever? Eschatological considerations aside, it's not likely. The balls still have to resist the internal, preload force.

Predicting ball screw load-life seems pretty straightforward: Compare the geometric average of loads and speeds to the dynamic load capacity. But determining equivalent loads - the critical issue, according to the folks at Steinmeyer, Inc. (Bedford, MA) - is where too many designers miss the boat.

"Almost all suppliers seem to forget about preload," contends Steinmeyer executive vice president George Jaffe. "In most applications, preload is the main factor that impacts fatigue life," he says. "Neglecting preload in load-life calculations isn't just a minor mistake. Ignore it and you risk potential disaster."

To help designers calculate preload, Steinmeyer (www.steinmeyer.com) offers both "rule of thumb" equations and a spreadsheet for greater precision. To illustrate the impact of preload, the firm examines the z-axis of a small lathe with a 32 mm diameter x 10 mm pitch ball screw using double or single nuts.

The double nut has 2x3 circuits with a 30.8 kN dynamic load capacity, a nominal preload of 10% of Cdyn (roughly 3,000 N) and 2,000 rpm speed. Rapid moves are estimated to occur 30% of the time, acceleration/deceleration 6%, and roughing 30%. Thrust is estimated at a worst-case, continuous 8,000 N; a positive load direction, because the thrust is against the chuck. Finishing occupies 40% of the lathe's time, with lighter loads and lower speeds. Dwell time is included for indexing the tool disk and loading work pieces.

Using precise equations the modified, equivalent load in the example is 3,732 N, and the resultant life is 562 million revolutions, or 24,453 hours. Using the rule of thumb equation, the numbers are 3,525 N and 667 million revolutions. Neglecting preload, however, yields quite different numbers: Mean load is 2,746 N, and life goes up to 1.4 billion revolutions, or 61,403 hours - about 2.5 times the realistic value. The rule-of-thumb equations miss the correct value by 18%, whereas omitting preload misses by 150%. 

With a 1x4 circuit single nut with 39.4 kN dynamic load capacity, preload is 3000 N, or roughly 8% of Ca. The modified, equivalent load is 4,467 N by precise calculation, 4,288 N by rule of thumb. Calculated life expectancy is 686 million revolutions (775 million with the estimated modified loads), or 29,852 hours. If preload is ignored, the mean load is 2,749 N.  Since the single nut has a higher dynamic load capacity than the double nut, the calculated life goes up to 2.94 billion revolutions, or 128,052 hours - off by a factor of 4.