Dengfeng Xu

Modeling of Axial Magnetic Force and Stiffness of Ring-Shaped Permanent-Magnet Passive Vibration Isolator and Its Vibration Isolating Experiment

Magnetic suspension vibration isolators have attracted more and more attention in the field of semiconductor industry and high precision equipments. A novel ring-shaped permanent-magnet passive vibration isolator is mainly reported in this paper. An analytical expression of axial magnetic force of the isolator is derived and validated by the finite element analysis and experiment. It proves that the analytical expression is efficient. An analytical expression of the axial stiffness of the isolator is deduced by derivative of the axial magnetic force with respect to the axial relative displacement of the inner ring. Furthermore, the parametric study of the axial magnetic force and stiffness are carried out. As a ring-shaped permanent-magnet passive vibration isolator case study, the isolator was constructed by four couples of the ring-shaped permanent magnets. The vibration isolation performance of the isolator was subsequently calculated and tested. The experimental results have shown a good agreement with the calculated ones. It demonstrates that the proposed isolator can realize low-frequency vibration isolation.

Modeling and analysis of a negative stiffness magnetic suspension vibration isolator with experimental investigations

This paper presents a negative stiffness magnetic suspension vibration isolator (NSMSVI) using magnetic spring and rubber ligaments. The positive stiffness is obtained by repulsive magnetic spring while the negative stiffness is gained by rubber ligaments. In order to study the vibration isolation performance of the NSMSVI, an analytical expression of the vertical stretch force of the rubber ligament is constructed. Experiments are carried out, which demonstrates that the analytical expression is effective. Then an analytical expression of the vertical stiffness of the rubber ligament is deduced by the derivative of the stretch force of the rubber ligament with respect to the displacement of the inner magnetic ring. Furthermore, the parametric study of the magnetic spring and rubber ligament are carried out. As a case study, the size dimensions of the magnetic spring and rubber ligament are determined. Finally, an NSMSVI table was built to verify the vibration isolation performance of the NSMSVI. The transmissibility curves of the NSMSVI are subsequently calculated and tested by instruments. The experimental results reveal that there is a good consistency between the measured transmissibility and the calculated ones, which proves that the proposed NSMSVI is effective and can realize low-frequency vibration isolation.

A Holistic Self-Calibration Algorithm for

Self-calibration technology is an important approach with the utilization of an artifact plate with mark positions that are not precisely known to calibrate the precision metrology system. In this paper, we study the self-calibration of xy precision metrology systems and present a holistic self-calibration algorithm based on the least squares method. The proposed strategy utilizes three traditional measurement views of an artifact plate on the xy metrology stage and provides relevant symmetry, transitivity, and redundancy. The misalignment errors of all measurement views, particularly errors of the translation view, are totally determined by detailed mathematical manipulations. Consequently, a least-squares-based robust estimation law is synthesized to calculate the stage error even under the existence of random measurement noise. Computer simulation validates that the proposed method can accurately realize the stage error when there is no random measurement noise. Furthermore, the calculation accuracy of the proposed scheme under various random measurement noises is studied, and the results verify that the proposed algorithm can effectively attenuate the effects of random measurement noise. The proposed strategy, in fact, provides a well-understood solution to the xy self-calibration problem for engineers in practical applications.

xy

As previous self-calibration technologies are mostly limited to 1-D or 2-D metrology systems, a holistic and explicit self-calibration strategy is proposed for 3-D precision metrology stages in this paper. With different alignments of a rigid cubic artifact on the uncalibrated 3-D stage, four measurement views are constructed to provide the symmetry, transitivity, and redundancy of the 3-D stage error. The first-order components of the stage error, i.e., the nonorthogonality and the scale difference, are determined through the first three measurement views with mathematical processing. The residual components of the stage error are then determined through a least square-based calculation law. Additionally, the misalignment error and the artifact error are all identified through rigorous algebraic manipulation, which may be useful as foundation for synthesis of other self-calibration algorithms. Computer simulation is carried out, and the results validate that the proposed scheme can achieve good calibration accuracy even under the existence of various random measurement noises. Experimental results are also presented to provide a preliminary illustration and validation of the proposed approach in practical applications.

Precision Metrology Systems

Precision rotary metrology stages need calibration technology to determine the stage error for improvement of angle measurement accuracy. In this paper, we study the calibration of precision rotary metrology stages, and present an on-axis angle self-calibration approach different from previous perspectives. Without resorting to specially designed angle comparators or added read-heads, the proposed scheme fully utilizes different measurement views of a newly designed artifact plate on the uncalibrated rotary stage. The measurement deviation of each mark line from its nominal angle position, is rigidly modeled as the combination of stage error, artifact error, misalignment error and random measurement noise. Based on the circle closure principle and mathematical definition of the axis orientation, the misalignment error of each measurement view can be directly determined by rigid algebraic processing. A least-square based calculation law is finally synthesized to determine the stage error. Computer simulation validates that the proposed method can realize the stage error accurately even there exist various random measurement noises. Finally, a practical description on how to measure the angular marks of different measurement views is provided. The proposed strategy essentially provides a novel on-axis angle self-calibration principle with accuracy, simplicity and robustness orientation to meet industrial requirements.

A Holistic Self-Calibration Approach for Determination of Three-Dimensional Stage Error

Precision rotary metrology stages need calibration technology to determine the stage error for the compensation and improvement of angle measurement accuracy. Departing from previous perspectives, we present an on-axis angle self-calibration approach for rotary metrology stages with the utilization of an angular artifact plate. Specifically, the artifact plate with angular mark lines, whose accuracy is not precisely known, is first presented as the assistant tool. Then, the artifact plate is placed in the uncalibrated rotary metrology stage with different alignments to construct independent measurement views. The measurement deviation of each mark line from its nominal angle position is rigidly modeled as a combination of stage error, artifact error, misalignment error and random measurement noise. Based on the circle closure principle and the mathematical definition of axis orientation, the misalignment error of each measurement view can be directly determined by algebraic processing. With the comparison of the different measurement views, transitivity and redundancy can be obtained, and a least-squares calculation law is synthesized to determine the stage error and to meet the challenge of random measurement noise. The designed artifact plate is developed for the explanation of a standard angle self-calibration procedure, and a practical description of how to measure the angular marks of different measurement views is also provided in detail. Computer simulation finally validates that the proposed method can realize the stage error accurately even when there exist various random measurement noises. The proposed strategy essentially provides a novel on-axis angle self-calibration approach with accuracy, simplicity and robustness orientation to meet industrial requirements.

A novel on-axis self-calibration approach for precision rotary metrology stages

As previous self-calibration technologies are mostly limited to X, XY, XYZ, and angular metrology stages, we study the self-calibration of precision XYθz metrology stages and present an on-axis self-calibration strategy. Specifically, a designed artifact plate with grid mark lines and angular mark lines whose accuracy is not precisely known, is presented as the assistant tool. And four measurement views of the designed artifact plate on the uncalibrated XYθz stage are fully utilized to provide the symmetry, transitivity and redundance of the XYθz systematic measurement error (i.e., stage error). In addition, circle closure principle is employed for the angular stage error component. Resultantly, a least-square based calculation law is proposed for the final determination of the stage error. Computer simulation is conducted and the calculation results validate that the proposed scheme can accurately realize the stage error even under the existence of various random measurement noises. As an integration of XY self-calibration and angular self-calibration, the proposed scheme solve the XYθz self-calibration problem, and possesses special merits such as simplifying the mathematical processing for calculation of misalignment errors.