Do you know where your axis slide is?

Aug. 5, 2005
Accurate axis positioning depends on whether it's measured with rotary or linear encoders.

By Dr.Ing. Jan Braasch

Edited by Jim Benes
associate editor

Axis errors rob machine tools of the necessary accuracy for the jobs to be run. Luckily, though, two common position-measuring systems prevent this from happening. However, deciding which one should be on your machine tool takes a knowledge of how both systems work and an understanding of axis errors and their effects.

Almost all machine tools incorporate recirculating ballscrews that convert rotary servomotor motion into linear slide motion. Axis-position control comes from either rotary encoders in conjunction with recirculating ballscrews or linear encoders affixed to machine slides.

A position-control loop with a rotary encoder and ballscrew, called semiclosed-loop control, includes only a servomotor with no actual position control on the slide. The position of the servomotor rotor is controlled using the pitch of the ballscrew as the measuring standard. To extrapolate the slide position with this arrangement, the mechanical system between the servomotor and slide must have a known and reproducible mechanical-transfer behavior.

A position-control loop with linear encoders — closed-loop control — includes the entire mechanical feed-drive system. With line grating on linear scales as the measuring standard, linear encoders on slides detect mechanical-transmission errors, which are compensatedby machine-control units.

As digital axes become popular, many servomotors now feature rotary encoders, which work with feedscrews for position control. With this configuration, shops must decide whether or not to add linear encoders on the slide to achieve desired axis-position accuracy.

Rotary encoder/ballscrew systems are subject to several sources of positionmeasurement problems.

Kinematic errors hinder position accuracy. They originate from ballscrew-pitch errors such as play in feed elements and from so-called pitch loss. Because ballscrew pitch is the standard for measurement in feed ballscrew/rotary-encoder systems, pitch errors directly influence measurements. Play in feed-transfer elements causes backlash. Pitch loss results from a shift of the balls during positioning of ballscrew drives with two-point preloading and causes reversal errors of 1 to 10 µ.

Most controls compensate for pitch and reversal errors. However, determining compensation values requires elaborate measurements with comparative measuring devices such as interferometers and grid encoders. In addition, reversal errors are often unstable over time and frequently require recalibration.

Strain in drive mechanisms involves forces that deform feed-drive units, thus causing shifts in axis-slide positions relative to positions measured with ballscrews and rotary encoders. They are essentially inertia forces resulting from slide accelerations, cutting forces, and guideway friction. Mean feed-drive axial rigidity is between 22.5 to 45 lb/µ (100 to 200 N/µ) with a distance between ball nut and fixed bearing of 19.7 in. (0.5 m) and a ballscrew diameter of 1.56 in. (40 mm).

Acceleration forces from a moderate 13.12 fps (4 m/sec) acceleration of a 500-kg slide mass cause deformations of 10 to 20 µ that are unrecognizable by a rotaryencoder/ballscrew system. Hence, the trend toward significantly faster acceleration rates will result in increasingly higher deformations.

Cutting forces lie in the kN range and distribute not only to the feed-drive systems, but also over entire machine structures between workpieces and tools. Linear encoders recognize and correct feed-drive-system deformations, which are relatively small as compared with those of a whole machine. With this said, critical component dimensions are normally machined at low feedrates with correspondingly low levels of feed-drivesystem deformations.

Frictional forces from guideway weight are between 1% and 2% of rollerguideway weight and between 3% and 12% of sliding-guideway weight. A weight of 1,125 lb (5,000 N) deforms feed drives from 0.25 to 6 µ.

Ballscrew friction and heat causes thermal expansion of ballscrews and is the biggest position-measurement problem for encoder/ballscrew systems. On one hand, ballscrews must be as rigid as possible for converting rotary motion of servomotors to linear feed motion, yet they must also serve as a precision measuring standard. This forces a compromise because both rigidity and thermal expansion depend on the preloading of ball nuts and fixed bearings. Both the axial rigidity and moment of friction are roughly proportional to preloading.

Because of the complex kinematics of recirculating ball nuts, they generate most of the friction in feed-drive systems. Balls endure a lot of friction from macroslip due to kinematic exigencies and, to a lesser degree, microslip from relative motion in their compressed contact areas.

Balls are not completely held in races and wobble much like tennis balls rolling down a gutter. The result is a continual pressing and pushing with occasional ball slippage. Friction among the balls intensifies because of high surface pressure from retaining devices not separating them. As in all angular-contact ball bearings, spinning friction comes from contact diameters that are not orthogonal to axes of ball rotation, so each ball therefore rotates about its contact diameter.

Recirculation systems are also problem zones for ballscrews. With every entrance into a recirculation channel, and with every exit, the rotational energy of the balls, which in rapid traverse typically rotate at 8,000 rpm, must be started and stopped, respectively.

In contrast to the preloaded thread zone, balls in the recirculation zone are not under stress. This causes them to collect in recirculation channels, which, without elaborate measures to reintroduce the balls into threads at the ends of channels, tends to congest and jam ballscrew drives.

A large portion of solid-body friction and mixed friction in ballscrew drives occurs at low speeds, while viscous friction dominates at high speeds. Typically, normal machine feedrates are far below the speeds at which the moment of friction is at its minimum. Rapid-traverse feedrates, however, are far above this minimum. Therefore, the feedrates at which a ballscrew is at optimum efficiency-seldom occur. Moment of friction is only slightly dependent on the axis load of the ball nut.

Recently,themaximum permissible speed of recirculati ballscrews has doubled, and the trend is continuing. Demand for faster accelerations mean preloading and resultant ballnut friction will both increase.

The influence of frictional heat on positioning response of feed axes becomes apparent in tests conducted in accordance with international standard ISO/DIS 230-3, which proposes uniform measurements of thermal shifts from external and internal heat sources.

Typical drive system of an NC machine tool with a linear scale on the slide (closed-loop control) and rotary encoder/ballscrew system (semiclosed-loop control).

Circular tests of a machining center without linear encoders show X-axis reversal error significantly increases after one year.

With position control via rotary encoder and spindle, the circle deviates from an ideal path at high velocity, while contour accuracy improves with linear encoders.

Moment of friction is a result of complex kinematics within a recirculating ball nut.

Moment of friction of a two-point preloaded ballscrew.


Positioning tests in accordance with ISO/DIS 230-3 on a vertical machining center illustrate the drift of axis position due to thermal growth of the screw as measured by linear encoders and a rotary encoder/ballscrew system. The ballscrew-bearing arrangement had a fixed bearing at one end of the screw and a floating bearing at the other. With this arrangement, the ballscrew freely expands away from the fixed bearing according to its temperature profile. The thermal zero point of such a feed axis is at the location of the fixed bearing, so, theoretically, if the ball nut is located at the fixed bearing, no thermal shift should occur. The machine moved to three positions on its 39.4-in. (1-m) long X axis a total of 100 times within 40 min.

When using the ballscrew/rotary-encoder system for position control, the position farthest from the fixed bearing of the ballscrew shifted by more than 110 µ within 40 min, in spite of the moderate feedrate of 32.8 fpm (10 m/min) and rapid traverse of 78.7 fpm (24 m/min). Drift quickly increases immediately after switch-on, so any change in mean feedrate in a production process immediately changes positioning accuracy. Measured positioning accuracy depends on the number of repetitions, particularly after the first few.

No drift in position values was detected when measured with linear encoders.

Dr. Braasch is director, marketing and product management at Dr. Johannes Heidenhain Co. GmbH in Traunreut, Germany.