Horizontal Straightness Error Research Articles

On straightness measurements of large CNC machine tools

The CNC (computerized numerically controlled) machines are widespread in use due to their high capability of precise manufacturing in industrial production. They have a wide range of designs depending on the working capacity in manufacturing. The associated form errors in large-capacity CNC machines during production shall be identified and corrected or eliminated. This study presents an investigation of one of the main form errors that may affect the manufacturing precision of these machines. This error type is a straightness error with both two kinds of horizontal and vertical errors. The study is carried out for a vertical turning center CNC machine type. The straightness errors are measured for the X axis at different latches in the Z direction and for the Z axis at three positions in the X direction with multi-displacement steps. Different algorithms are used in the determination of straightness errors. The X-axis has minimum horizontal straightness errors at latch Nr. 3 and minimum vertical straightness errors at latch Nr. 5. For the Z axis, the minimum values for horizontal and vertical straightness errors exist when the spindle is located 1200 mm away from the machining center to the right. The displacement steps have a significant impact on the determination of straightness errors.

Characterization and Correction of the Geometric Errors in Using Confocal Microscope for Extended Topography Measurement. Part I: Models, Algorithms Development and Validation

This work presents a method for characterizing and correcting the geometric errors of the movement of the lateral stage of Imaging Confocal Microscope (CM) in extended topography measurement. For an extended topography measurement, a defined number of 2D images are taken and stitched by correlation methods. Inaccuracies due to linear displacement, vertical and horizontal straightness errors, angular errors, and squareness errors based on the assumption of the rigid body kinematics are described. A mathematical model for the scale calibration of the X- and Y- coordinates is derived according to the system kinematics, the axis chain vector of CM, and the geometric error functions and their approximations by Legendre polynomials. The correction coefficients of the kinematic modelling are determined by the measured and certified data of a dot grid target standard artefact. To process the measurement data, algorithms for data partitions, fittings of cylinder centers, and determinations of coefficients are developed and validated. During which methods such as form removal, K-means clustering, linear and non-linear Least Squares are implemented. Results of the correction coefficients are presented in Part II based on the experimental studies. The mean residual reduces 29.6% after the correction of the lateral stage errors.

반전법 기반의 2축 직선 이송계의 직각도 오차 측정 기법

A new technique based on the reversal method, is suggested to measure squareness error of the two-linear axes system. The technique uses the L-type steel bar, a capacitive sensor, and three experimental installations required to measure squareness error and two horizontal straightness errors. Profile and squareness of the L-type steel bar are estimated, by using the principle of the reversal method. Also, setup errors inevitable at installation, are separated from measured data using the least square method. Multi-DOF errors of two-linear axes system are measured and analyzed, using the suggested technique. Also, the reference mirror with flatness of 30 nm is used to verify the suggested measurement technique. Difference between the two measurement methods is 3.25 arcsec, a value within measurement repeatability.

A real time error measuring device for meso-scale machine tools

This paper describes the development of a real time error measuring device for the simultaneous measurement of movement errors in straightness, yaw and roll in a linear machine stage. It was designed specifically for measuring errors in the spatial positioning of meso-scale machine tool stages. The arrangement of the optical path and design of the optical elements make it easy install the device on a linear stage. Roll, yaw and horizontal straightness error motions are sensed using the reflection of a laser beam from a plane mirror. A nonlinear measurement model was derived and simulation analysis showed this could be linearized when the measurement angle error was smaller than 0.05°. The measurement ranges of the proposed system are ±30″ for θx, ±20″ for θy and ±30μm for the z-axis. The measurement precision was verified using a laser interferometer and an electronic level and the accuracy of the angular error and straightness error measurements were found to be in the range of ±0.25″ and ±0.5μm respectively. The extended measurement uncertainties (95% confidence level) were: 0.46″ for θx error motion; 0.46″ for θy error motion; and 0.616μm for straightness.

Multi-DOF Incremental Optical Encoder with Laser Wavelength Compensation

This study used a reflective diffraction grating as the medium to develop a multi-DOF incremental optical encoder for motion stage. The optical encoder can measure three angular displacements, roll, yaw and pitch of the motion stage simultaneously, as well as the horizontal straightness and linear displacement, summed to five DOF errors of motion stage by only using the positive and negative first-order diffracted light. The grating diffraction theory, Doppler effect, and optical interference technique were used. Two quadrant photodetectors were used to measure the changes in three-dimensional space of diffraction direction of diffracted light, in order to construct a multi-DOF incremental optical encoder. Considering the working stability of a laser diode and preventing the influence of the zeroth-order diffracted light returning to the laser diode, an additional optical isolation system was designed and a wavelength variation monitoring module was created. The compensation for the light source wavelength variation could be 0.001 nm. The multi-DOF verification results showed that the roll error is ±0.7/60 arcsec, the standard deviation is 0.025 arcsec; the yaw error is ±0.7/30 arcsec, the standard deviation is 0.05 arcsec; the pitch error is ±0.8/90 arcsec, the standard deviation is 0.18 arcsec, the horizontal straightness error is ±0.5/250 μm, the standard deviation is 0.05 μm and the linear displacement error is ±1/20000 μm, the standard deviation is 12 nm.

Laser straightness interferometer system with rotational error compensation and simultaneous measurement of six degrees of freedom error parameters.

A laser straightness interferometer system with rotational error compensation and simultaneous measurement of six degrees of freedom error parameters is proposed. The optical configuration of the proposed system is designed and the mathematic model for simultaneously measuring six degrees of freedom parameters of the measured object including three rotational parameters of the yaw, pitch and roll errors and three linear parameters of the horizontal straightness error, vertical straightness error and straightness error's position is established. To address the influence of the rotational errors produced by the measuring reflector in laser straightness interferometer, the compensation method of the straightness error and its position is presented. An experimental setup was constructed and a series of experiments including separate comparison measurement of every parameter, compensation of straightness error and its position and simultaneous measurement of six degrees of freedom parameters of a precision linear stage were performed to demonstrate the feasibility of the proposed system. Experimental results show that the measurement data of the multiple degrees of freedom parameters obtained from the proposed system are in accordance with those obtained from the compared instruments and the presented compensation method can achieve good effect in eliminating the influence of rotational errors on the measurement of straightness error and its position.

Multi-DOF Incremental Optical Encoder with Laser Wavelength Compensation

This study used a reflective diffraction grating as the medium to develop a multi-DOF incremental optical encoder for motion stage. The optical encoder can measure three angular displacements, roll, yaw and pitch of the motion stage simultaneously, as well as the horizontal straightness and linear displacement, summed to five DOF errors of motion stage by only using the positive and negative first-order diffracted light. The grating diffraction theory, Doppler effect, and optical interference technique were used. Two quadrant photodetectors were used to measure the changes in three-dimensional space of diffraction direction of diffracted light, in order to construct a multi-DOF incremental optical encoder. Considering the working stability of a laser diode and preventing the influence of the zeroth-order diffracted light returning to the laser diode, an additional optical isolation system was designed and a wavelength variation monitoring module was created. The compensation for the light source wavelength variation could be 0.001 nm. The multi-DOF verification results showed that the roll error is ±0.7/60 arcsec, the standard deviation is 0.025 arcsec; the yaw error is ±0.7/30 arcsec, the standard deviation is 0.05 arcsec; the pitch error is ±0.8/90 arcsec, the standard deviation is 0.18 arcsec, the horizontal straightness error is ±0.5/250 μm, the standard deviation is 0.05 μm and the linear displacement error is ±1/20000 μm, the standard deviation is 12 nm.

Development of a DVD pickup-based four-degrees- of-freedom motion error measuring system for a single-axis linear moving platform

In this study, a simple and high-resolution four-degrees-of-freedom (4-DOF) motion error measuring system based on DVD pickup has been proposed. It can simultaneously measure the horizontal straightness error and three angular errors of a single-axis linear moving platform. The horizontal straightness error is measured based on the focus technique of DVD pickup and the inverse algorithm is used to solve pitch, yaw, and roll angular errors through the kinematic analysis. The grating is mounted on the moving axis of a single-axis linear moving platform and reflects incident laser beam into several diffractive rays. Photodiode IC (PDIC) of DVD pickup is set up for detecting the focus error signal (FES) of zero-order diffraction ray from grating and quadrant detectors are set up for detecting the position of ±1st-order diffraction rays from grating. The 4-DOF motion error measuring system detected the three angular errors with a related accuracy of about ±1 arc sec for a measuring range of ±100 arc sec, and detected horizontal straightness with a related accuracy of about ±2 μm for a measuring range of ±150 μm.

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.

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.