Vertical Straightness Error Research Articles

Measurement of multi-degree-of-freedom error motions of a precision linear air-bearing stage

This paper describes the measurement of straightness error motions (vertical straightness and horizontal straightness) and rotational error motions (pitch, yaw and roll) of a commercial precision linear air-bearing stage actuated by a linear motor. Each of the error motions was measured by two different methods for assurance of reliability. The stage was placed in the XY -plane and moved along the X -direction. The pitch error and yaw error, which were measured by an autocollimator and the angle measurement kit of a laser interferometer, were about 8.7 and 1.6 arc-s, respectively, over a travel of 150 mm with a moving speed of 10 mm/s. The roll error was measured by the autocollimator through scanning a flat mirror along the X -direction. The second method for roll error measurement was to scan two capacitance-type displacement probes along the flat surface placed in the XZ -plane. The two probes with their sensing axes in the Y -direction were aligned with a certain spacing along the Z -axis. The roll error can be obtained by dividing the difference of the outputs of the two probes by the spacing between the two probes. The roll error was measured to be approximately 11.8 arc-s over the 150 mm travel. The horizontal straightness error and the vertical straightness error ( Y - and Z -straightness errors) were measured by using the straightness measurement kit of the laser interferometer. The second method for straightness measurement was to scan the flat surface with a capacitance-type displacement probe. The horizontal and vertical straightness errors of the stage over the 150 mm travel were measured to be approximately 207 and 660 nm, respectively.

A four-degree-of-freedom laser measurement system (FDMS) using a single-mode fiber-coupled laser module

A simple and novel method for measuring four-degree-of-freedom geometric errors of a linear stage was put forward. A single-mode fiber-coupled laser module was used. Only a cube corner retro-reflector and a beam splitter were adopted in the moving target in order to sense the straightness errors and angular errors, respectively. In this way, the horizontal and vertical straightness errors as well as yaw and pitch errors can be measured simultaneously. Theoretic error separation has been analyzed in detail and the straightness-compensated method was given. The system based on the above method was developed. In comparison with an API five-dimensional laser measurement system, the accuracy of the measuring straightness error is about ±2.5 μm within the measuring range of ±500 μm, and the angular errors are about ±3 arcsec within the range of ±400 arcsec. In addition, there is no cable connection in the moving target, which is a great convenience for the workshop measurements.

Linear rectangular air bearing based on squeeze film generated by ultrasonic oscillation

This article reports an actively controllable linear motion air bearing that utilizes air films generated by ultrasonic oscillation. The films on eight bearing surfaces of a horn, which serves as the stator, lifted and guided a carriage consisting of four flat plates. Moreover, the oscillation that modulated the amplitude via the positioning signal varied with the thickness of the air film. Thus, this bearing regulated the position of the carriage in a vertical direction using a proportional and integral (PI) controller with a displacement sensor so that its motion error became zero. Furthermore, no pneumatic plant was needed in this bearing system. The motion straightness errors were 0.41μm peak to peak (p-p) in the vertical direction and 1.52μm p-p in the horizontal direction without compensation. Nonrepetitive motion errors were 0.34μm 2σ (two standard deviations) in the vertical direction and 0.39μm 2σ in the horizontal direction. The PI feedback control, in which a fiber optic displacement sensor measures the movement of a gauge block mounted on the carriage, decreased the vertical straightness error to 0.18μm p-p. The settling time for 0.2μm step positioning in the vertical direction was less than 0.1s. The positioning resolution was less than 20nm. Infinite stiffness under a 5.1N static load was obtained in the experiments.

Laser vector measurement technique for the determination and compensation of volumetric positioning errors. Part I: Basic theory

A new laser vector method for the measurement of the volumetric positioning errors of a computer numerically controlled machine or a precision instrument is described here. Compared with conventional laser interferometer measurement, the laser vector method measures the vector errors, namely, the displacement error, vertical straightness error, and horizontal straightness error, rather than the displacement error only. The key to the laser vector method is that the measurement direction or the laser beam direction is not parallel to the displacement direction. With four setups, all three displacement, six straightness, and three squareness errors can be determined. Once the volumetric positioning errors are measured, they can be used to compensate for the repeatable positioning errors of the machine or instrument. The basic concept, theory, and measurement errors are described. Experimental verification of the vector method is in the Part II of this article.

A 6-degree-of-freedom measurement system for the accuracy of X-Y stages

A precision 6-degree-of-freedom measurement system has been developed for simultaneous on-line measurements of six motion errors of an X-Y stage. The system employs four laser Doppler scales and two quadrant photo detectors to detect the positions and the rotations of an optical reflection device mounted on the top of the X-Y stage. Compared to the HP5528A system, the linear positioning accuracy of the developed measurement system is better than ±0.1 μm to the range of 200 mm and the vertical straightness error is within ±1.5 μm for the measuring range of ±0.1 mm. The yaw and pitch errors are about ±1 arcsec, and the roll error is about ±3 arcsec within the range of ±50 arcsec.

Evaluation of the Effective Parametric Errors in Coordinate Measuring Machines Using the Locus of Stylus on the Horizontal Plane

A new method is proposed for the evaluation of effective parametric errors in three-axis coordinate measuring machines (CMMs), using the locus of stylus of the measuring probe on an ideal horizontal plane. The CMM base, which is mostly made of granite or steel, can be used as a good reference surface for obtaining the locus of stylus of the CMM probe, after the flatness calibration has been performed. Rectangular grid measurement with electronic level has been applied for the flatness measurement, then analysed either by the least squares technique or by the minimum separation technique. The CMM probe was moved and took the reading (vertical scale coordinates) on the corresponding grid points on the precalibrated base, giving the base probing data. The discrepancy data between the flatness and the base probing data become the locus of stylus, which is to be processed to give a mean plane plus the deviation data. The mean plane is called the locus plane which is the metrological reference plane for a specific machine, the deviation data (called the error of the locus of stylus) indicate a unique error feature of the specific machine in the vertical direction. This error of the locus of stylus can be decomposed into three effective parametric error components such as vertical straightness errors of the horizontal axes, and the roll error of a horizontal axis. As the parametric errors are evaluated in the effective sense, this technique can be applied to the modern CMMs which have a software compensation scheme, which is the advantage over the conventional parametric error method. Two cases of ‘on site’ calibrations have been shown in order to demonstate the efficiency and validity of the developed method. The computer aided feature is fully achieved, so that the data acquisition, analysis, and representation are performed on line with the aid of a microcomputer (IBM/PC/XT/AT compatible).