This close-up of the ball contact in a profile projector shows a gothic arch. It consists of at least two radii slightly larger than the ball used, but offset so the raceway touches the ball on both sides. Such thread profiles allow independent control of track conformity and contact angle, and are also suitable for four-point contact.

Alexander F. Beck
President
George A. Jaffe
Executive Vice President
Steinmeyer Inc.
www.steinmeyer.com

Ball screws are preloaded using different methods, resulting in either two or four-point contact of load balls. And all preload methods, whether by using oversized balls, shifting pitch, or using a double nut, serve the same purpose -- eliminating backlash. Preload also defines the contact between balls and races. But what are the differences, and how should one make the choice between the various methods?

Balls running between flat surfaces have small contact patches with each other and cannot transmit high loads. Thus ball-screw tracks usually have a curvature perpendicular to the balls' direction of movement. Track conformity, the dimensional relationship between ball and track, is expressed as the ratio of track radius to ball diameter. Therefore, track conformity of 0.5 means the ball fits exactly into the track curvature. Although this is desirable for optimum load bearing, track conformity of 0.5 is usually accompanied by excessive sliding between ball and track (sometimes referred to as differential slip) and cannot be used. Moreover, normal manufacturing tolerances of the ball-track shape make the contact patch move to any high spot, resulting in unpredictable contact angles. So, the closer track conformity is to 0.5, the more precise the track shape has to be. Optimum track conformity for ball screws is between 0.52 to 0.56, and the optimum contact angle is 45°.

If the ball screw's thread profile is a semicircular arc with constant curvature, balls will only run on one side of the track. That's because the balls must be smaller than the arc forming the track. This means it is impossible to preload such ball screws with oversized balls. Doing so would produce track conformity of 0.5 and all its disadvantages. Hence, ball screws with thread profiles consisting of semicircular arcs and constant curvatures can only be preloaded using an offset between nut and shaft raceways. These offsets must be established either by a double-nut configuration, or by grinding them into the nut threads.

More options are available when offsets are built directly into thread profiles. The so-called gothic-arch profile, for example, consists of at least two radii with offset centers. This lets a ball touch both sides of the raceway at the same time. In this case, track conformity is greater than 0.5, minimizing friction, and using a contact angle immune to dramatic changes due to manufacturing tolerances. When using such thread profiles, it's possible to use four-point contact preload with oversized balls, or two-point contact through some sort of offset preload.

The simplest way to establish offset for preloading is by using a split nut. It is comprised of two nut halves, each having some play, and preloaded against each other. The result is two-point ball contact.

The same effect comes with a nut made from a single piece with ID threads ground so there's a small offset in the middle of the nut, resulting in the same two-point contact. There is no way to adjust this offset, so it takes trial and error to generate the desired preload value. To increase or decrease preload, balls are exchanged for larger or smaller ones. Such nuts are generally referred to as pitch-shift nuts. Although they are not split-type ball screws, they transmit loads exactly the same way as double nuts do. Thus it is misleading to call them single nuts. They perform much like double nuts and require separate ball circles for both thrust directions. The only difference is that they eliminate the potentially troublesome issue of joining two separate nuts. However, Steinmeyer solved this double nut connection dilemma with its patented Unilock system. (Is that a single or a double nut? Machine Design, March 20, 2003).

Steinmeyer's newest UltraSpeed nuts establish two-point contact with an offset. But because they use dual-start threads, offset is between the two threads. Each thread of the nut forms a closed ball circuit, so there are two two-point-contact circuits running at opposite sides of their respective shaft ball tracks.

UltraSpeed nuts are also available without offset and preloaded solely by oversized balls. These nuts have four-point contact, and because both threads are used, they have twice the number of load turns compared to conventional nuts. This gives them significantly higher load capacities and better stiffness.

From a performance point of view, it doesn't matter how offset is established as long as manufacturing and assembly tolerances ensure proper load distribution among balls, and the nut body is stiff enough to transmit thrust without compromising load distribution. But there is an important difference between two and four-point contact in the way balls move and transmit loads.

Balls and races form a contact patch that grows in size as loads increase, so balls will not roll without some degree of slip. This (differential) slip affects how balls move because it generates friction forces on the ball. With ideal four-point contact, this slip increases friction and heating, and may cause additional wear. In two-point contact however, these slip-induced forces spin the balls around their contact lines. This spin generates forces that try to push the ball sideways out of its track. These side forces are direction sensitive. So in one direction of rotation, balls try to climb closer to the screw's OD, and in the opposite direction, they move down towards the screw's minor diameter. Both cases increase preload.

When reversing, balls pass through the middle of their (geometrically correct) ball track, so preload drops to the initial value. This causes the nut's drag torque to drop during reversal. There is also some loss in the nut's axial travel each time the balls move from one side of their geometrically correct track to the other. In other words, the ball nut has some hysteresis, or "lost motion." This should not be confused with play because the balls are continuously under load. This lost motion, generally on the order of only a few microns, adds to the lost motion of other mechanical components and can be compensated the usual way -- by adding a few microns of feed each time motion reverses. However, as the nut's inherent hysteresis builds over moves of 1/8th of a turn, smaller turns may combine with a reversal and become overcompensated.

Besides this typical behavior of "double" nuts (i.e., nuts with two-point contact), there are other aspects that differentiate nut types. For example, single nuts have ball circuits that carry load in both directions, and are generally more compact and less expensive. Due to additional contact patches, they are also somewhat less efficient than double nuts and exhibit more wear.

So use caution when calculating fatigue life of single nuts because preload is taken into account differently. Single nuts must have a higher load capacity if they are to have the same life as a double nut. As a general rule, for a comparable life, single nuts need at least one more turn of load balls compared to double nuts.

### Two-point contact

Four point contact stems from oversized balls and no offset between nut and shaft raceways. All balls carry loads in both directions. Thus nuts with four-point contact are more compact with more friction.

• Suitable for short screws (lengths less than 20 times the diameter of the screw).
• Has higher torque fluctuations.
• Preloads drop faster when ball and tracks wear.
• Somewhat higher friction and heating, reducing efficiency.
• Compact and cost efficient.
• No thrust limitations relative to preload.