Chien-Hong Liu

Precision modeling of form errors for cylindricity evaluation using genetic algorithms

A heuristic approach is proposed in this paper to model form errors for cylindricity evaluation using genetic algorithms (GAs). The proposed GAs method shows good flexibility and excellent performance in evaluating the engineering surfaces via measurement data involved with randomness and uncertainty. The numerical-oriented genetic operator is used as a basic representation for error modeling in the paper. The theoretical basis for the proposed Gas-based cylindricity evaluation algorithms is first presented. The performance of the method under various combinations of parameters and the precision improvement on the evaluation of cylindricity are carefully analyzed. One numerical example is presented to illustrate the effectiveness of the proposed method and to compare the Gas-based modeling results with those obtained by the least-squares method. Numerical results indicate that the proposed GAs method does provide better accuracy on cylindricity evaluation. The method can also be extended for solving difficult form error minimization and profile evaluation problems of various geometric parts in engineering metrology.

The min-max problem for evaluating the form error of a circle

There have been many studies to evaluate the form error of a circle. Most of them, such as the optimum methods and limacon model, employed the approximate solution to obtain the desired results. In this paper, three mathematical models depending on the method used to select the exact control points are constructed to evaluate the analytic solution of the minimum circumscribed circle, the maximum inscribed circle and the minimum zone circle by directly resolving the simultaneous linear algebraic equations. These new and simple mathematical methods are verified to be useful for determining the exact solution.

A study on analyzing the problem of the spherical form error

Abstract Many methods to evaluate the form error of a sphere have been studied over the years. Most of these, such as the optimum methods, employed the approximate local solution to obtain the desired results. In this paper, three mathematical models are constructed to evaluate the solutions of the minimum circumscribed sphere, the maximum inscribed sphere, and the minimum zone sphere by directly resolving the simultaneous linear algebraic equations. Examples are given to verify that the model is admissible and reliable. These simple mathematical methods are verified to be useful for determining the exact solution.

Verification and evaluation method for volumetric and positional errors of CNC machine tools

This paper provides a testing device and an automatic sampling technique for fast checking of volumetric errors of CNC machine tools. With the proposed automatic sampling technique, the verification work is carried out automatically and reliably. Furthermore, the analyzed result obtained via the traditional least-squares method is not the minimum zone solution, and may overestimate the volumetric error. Thus, genetic algorithms (GAs) are employed to obtain the minimum zone solution in this paper. Experimental test results show that the proposed method is superior to the least-squares method.

Evaluation of straightness and flatness using a hybrid approach—genetic algorithms and the geometric characterization method

Abstract A heuristic approach is presented in this paper for efficient evaluation of exact straightness and flatness values using a hybrid approach combining genetic algorithms (GAs) with the geometric characterization method. The procedure of the hybrid approach begins with the evolution of GAs, and then the geometric characterization method, based on minimum zone criteria, is inserted into the process to improve the speed of convergence of the GAs. Numerical results indicate that the hybrid approach provides better accuracy and efficiency.

The application of the double-readheads planar encoder system for error calibration of computer numerical control machine tools

Abstract THis paper presents a useful measuring method for rapidly verifying geometric errors using a double-readheads planar encoder system. The system is capable of comparing the displacement measurements between two parallel lines simultaneously when the machine axes are moved. With the calculated model and the various specified test paths, the proposed measuring method provides rapid performance, simplicity of set-up, low cost and pre-process verification of computer numerical control (CNC) machine tools. Complete set-ups and procedures for geometric error verification are clearly presented. Also, the proposed system tested the dynamic performance of the CNC machine tools. It is an integrated system that can complete both dynamic performance and the geometric verification of CNC machine tools.

Automatic straightness measurement of a linear guide using a real-time straightness self-compensating scanning stage

Abstract In this paper a method is developed for straightness measurement of a linear guide by using a straightness self-compensating stage with an optical straightness measuring system, an eddy current sensor, and a cross-roller type compensation stage. Both the compensation stage and the optical straightness system were set up on a scanning stage to measure the straightness error of the scanning stage. The measured straightness error was fed back to the control system to compensate directly in real time. Thus, straightness of a linear guide without the added straightness error of the scanning stage could be measured. The Hewlett Packard laser straightness calibration system was used to verify the real-time compensated results. Straightness error of the scanning stage was compensated from the worst straightness error of 20 μm/150 mm to 0.9 μm/150 mm. The eddy current sensor measured straightness of the linear guide and the measured result matched the result obtained by the coordinate measuring machine.

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

Abstract 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.

Development of a middle-range six-degrees-of-freedom system

Abstract This paper describes the successful development of a middle-range six-degrees-of-freedom stage, using the features of a flexible structure. The system includes two parts: a middle-range positioning X—Y stage and a four-degrees-of-freedom stage. The flexible structure of the four-degrees-of-freedom stage is built from two kinds of flexible bodies: circular hinges and a new two-degrees-of-freedom flexible body. The four-degrees-of-freedom stage was designed to compensate movement errors including linear displacement, pitch, and roll errors. The linear displacement reaches 20 mm along the X-axis, 20 mm along the Y-axis, and 5 μm along the Z-axis. The rotation angle around the X-axis (θ x ), Y-axis (θ y ), and Z-axis (θ z ) were all 10 arcsec. A novel six-degrees-of-freedom measuring system was also designed. Precision feedback control is demonstrated in a series of experiments performed using the proposed measurement system.

High-resolution three-degrees-of-freedom motion errors measuring system for a single-axis linear moving platform:

Abstract In this study, a high-resolution three-degrees-of-freedom (3-DOF) motion error measuring system based on interference is described. It can simultaneously measure the linear displacement and two angular errors of a single-axis linear moving platform. The displacement is measured using a polarization interference technique and the two angular errors are also measured based on the geometry optical theorem. The verification results show that the resolution is about 20 nm. The 3-DOF measurement system detected displacements relative to a measurement mirror move with an accuracy of about ±8 μm for a measuring range of ± 50 mm, and detected the angular errors with a related accuracy of about ± 2 arc sec for a measuring range of ± 100 arc sec.