Alexander F. Beck
President
George A. Jaffe
Executive Vice President

Steinmeyer GmbH
www.steinmeyer.com

Engineers working with ball screws usually use conventional life-expectancy equations for nuts with two-point contact. When it comes to four-point contact nuts, however, many manufacturers that sell them do not discuss how to calculate their operational life. But the difference between single and double-nut life calculations lies in the preload. When applied external loads are low, for example, preload determines as much as 90% of the life.

Classic L10 lifetime equations are based solely on material fatigue. But although material fatigue may be the most important, it is not necessarily the only factor in determining ball-screw life. Adverse conditions such as contamination or lack of lubricant, for example, make other factors more important.

When engineers determine the life of a ball screw, they first break down its typical duty cycle into distinct steps, each with specified (external) loads or thrusts, speeds, and travel duration. The goal is to determine how many revolutions the ball screw will make under each load. These forces, designated Fi, are converted into an equivalent load Fm* that results in the same life expectancy as the actual duty cycle.

The next equation calculates life expectancy from a ball screw's equivalent load, Fm*, and dynamic load capacity, Ca. The answer, L10, in million revolutions or inches, respectively, depends on which load capacity definition or industry standard is used.

So far, this is nothing unusual. But, what happens if the ball screw is just used for positioning with light, or even negligible thrust (i.e., Fm goes to zero), and there is still significant preload for repeatability? Plug the numbers into the equation, and life goes to infinity, which certainly cannot be true. After all, the balls carry the nut's internal load or preload, so they must affect life.

At this point, a graph will help explain the situation. The preload graph consists of two curves, each representing a force-deflection curve of one ball nut in a double nut configuration. It shows deflections increasing with greater force. It also displays how forces in the opposite nut decrease as soon as deflection causes axial displacement. Or, just imagine two springs acting against each other. As you push against one of them, it is compressed or loaded, while the other is unloaded.

Where the two curves intersect represents a state of equilibrium with zero outside thrust. The distance between the graph's X axis and the crossing lines is the preload force. Now consider an external thrust in either direction on the ball nut. The load on one nut increases, while the load on the other decreases because the ball nut moves slightly in the direction of the thrust, giving the opposite nut more room. The resulting thrust vector is the difference (or distance) between the two curves.

At some point, as the load increases, the load on one nut becomes zero.

The higher thrust vector is the important one for life calculations. (Assume the curves are linear rather than curved, which is not exactly true but a close enough approximation.) The modified load on the ball nut during step i, is then equal to preload, Fpr, (move from the crossing point horizontally to the right) plus half the outside thrust, Fi, because the horizontal line splits the outside thrust vector approximately in half.

This remains true until thrust is enough to completely unload one ball nut (approximately 2.83 times the preload), and then thrust equals the total load on the ball nut. By observing recommended guidelines this situation should never be reached, but the approximation is useful in calculating total load on the preloaded nut now designated the modified load Fi*.

This approximation is adequate because the inputs to the equation, the applied forces, are typically estimates so more accurate calculations usually aren't necessary.

As noted above, this considers only the nut carrying the higher thrust. Obviously, in double nuts more thrust is carried by one nut and it will fail first. So properly using load equations means entering outside thrust as a plus or minus value, depending on its direction, and determining which nut will be critical in the duty cycle. To do so, calculate modified loads for each step in the duty cycle, determine the equivalent modified load, Fm* by using equation 3 for each nut. Then use the higher of the two values to calculate life in equation 2.