Nested XY air bearing stages include linear electric motor drives and laser interferometer position feedback system. Base is granite. Arrangement is often used in inspection operations.

The components that make up your high-accuracy positioning system — base and bearings, position-measuring system, motor-and-drive system, and controller — must work together as well as possible. In Part 1 ( PTD) we covered system base and bearings. Here, we cover position measurement. Part 3 will cover stage, drive, and encoder design; the drive amplifier; and controllers.

Position-measuring system

Generally, you can classify controllers as “open-loop” or “closed-loop.” With open-loop controllers (generally used with step motors) every impulse that the controller emits causes a certain slide displacement. However, there is no means to determine how large the displacement has been. For example, 500 pulses may have been emitted, but due to stiction, ball-screw tolerance, hysteresis, winding errors, and so forth, the table may have moved for only 498 pulses. A major disadvantage is that no positioning error correction occurs.

In a closed-loop system, or servo system, a position encoder provides feedback to the controller. The controller continues to send motor control signals until the exact desired position of the slide has been reached.

Figure 1 shows a slide with no position feedback in the upper illustration, followed by the three common methods for measuring slide position:
• Position encoder mounted on the motor or ball-screw shaft.
• Linear encoder mounted on the slide.
• Laser interferometer with mirrors mounted on the slide.

In the first method, slide position is measured indirectly — the position encoder mounts on the drive shaft. Tolerance, wear, and compliance in mechanical components between the slide and the position encoder lead to deviations between desired and true slide positions. Combined with the ball screw, slide accuracy at best is limited by ball-screw accuracy. Typical accuracies are ±5 to ±10 mm/300-mm travel.

Most linear measuring systems consist of an accurate glass scale and a photoelectric measuring head. Either the scale or the head attaches directly to the moving slide and measures slide position directly. Nor errors are introduced by ballscrew inaccuracies. Typical accuracies for the scale itself are ±1 to ±5 mm/m. This is also the accuracy of the slide itself at the measuring-head location.

The stage load (whose position accuracy is what we are really interested in) is always some distance from the measurement scale, measured in a direction perpendicular to the direction of movement, because most encoders are located under the slide, but the load is on top. This is even more pronounced with stacked stages. During a move, if the slide tilts somewhat because of deviations in straightness of the bearing ways, reversal errors, and so forth, a deviation relative to the position of the load vs. the encoder is created.

Dr. Ernst Abbé of Zeiss first described this error. Abbé error occurs when the measuring point of interest is displaced from the true measuring scale location, and when angular errors exist in the positioning system.* Abbé error makes the indicated position either shorter or longer than the true position, depending on the angular offset.

Abbé error =
(Offset distance) ×
(Tangent of offset angle)

If the angle is measured in radians then the equation is simply
Abbé error =(Angle) × (Offset)

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