• International Journal of Precision Engineering and Manufacturing
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• 제4권2호
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• pp.64-70
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• 2003

A new method using a transfer function is introduced in the present paper for analyzing the motion errors of hydrostatic bearing tables. The relationship between film reaction force in a single-side hydrostatic pad and the form error of guide rail is derived at various spatial frequencies by finite element analysis, and it is expressed as a transfer function. This transfer function clarifies so called 'the averaging effect of an oil film' quantitively. It is found that the amplitude of film force is reduced as the spatial frequency increases or the relative width of the pocket is reduced. The motion errors of a multi pad type table are estimated using a transfer function, the form errors of a guide rail and the geometric relationship between the pads. The method is named as the Transfer Function Method (TFM). The motion errors calculated by the TFM show good agreement with the motion errors calculated by the Multi Pad Method considering the entire table as an analysis object. From the results, it is confirmed that the proposed TFM is very effective to analyze the motion errors of hydrostatic tables.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2005년도 춘계학술대회 논문집
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• pp.769-772
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• 2005

Five DOF motion errors of a hydrostatic bearing table driven by the coreless type linear motor were compensated utilizing the active controlled capillaries in this study. Horizontal linear motion and yaw error were simultaneously compensated using two active controlled capillaries and vertical linear motion, pitch and yaw error were also simultaneously compensated using three active controlled capillaries. By the compensation, horizontal linear motion accuracy and yaw were improved from 0.16 ${\mu}m$ and 1.96 arcsec to 0.02 ${\mu}m$ and 0.03 arcsec. Vertical linear motion accuracy, pitch and roll were also largely improved from 0.18 ${\mu}m$, 2.26 arcsec and 0.14 arcsec upto 0.03 ${\mu}m$, 0.07 arcsec and 0.02 arcsec. The compensated motion errors were within the range of measuring repeatability which was ${\pm}0.02\;{\mu}m$ in the linear motion and ${\pm}0.05$ arcsec in the angular motion. From these results, it is found that the motion error compensation method utilizing the active controlled capillaries are very effective to improve the five motion accuracies of the hydrostatic bearing tables.

• 한국정밀공학회지
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• 제19권1호
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• pp.65-70
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• 2002

An analysis method for calculating motion accuarcy of double sides hydrostatic table is proposed in this paper. In this method, profiles of each rails are assumed as periodic function, therefore it is represented as the sum of spacial frequencies. Bearing clearance at any position rail is depended on the variation of linear, angular motion error of table and the form errors of both sides of a rail. Finite element method is applied to calculate pressure distributions in bearing clearance. In order to simplify the analyzing process, double sides table model is converted into equivalent single side table model. Results calculated by the proposed modeling method agree well with the results directly caculated by double sides modeling method, and also agree well with experimental results. From the theoretical and experimental analysis, it is verified that the proposed analysis method is very effective to analyze the motion accuracy of double sides hydrostatic table.

• 한국정밀공학회지
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• 제14권8호
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• pp.130-136
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• 1997

For compensating the error motion of hydrostatic guideways, we introduce a way that the clearance of table is actively controlled corresponding to the amount of error with the variable capillary. The structure and the theoretical design method of active controlled capillary using piezo actuator, named ACC, are proposed in this paper. Basic characteristics such as the maximum controllable range, micro step response and available dynamic bandwidth are tested for confirmation of structural suitability of ACC, and these characteristics are also tested on the table mounted with ACC for verifying the availability. The experimental result showed that by the use of ACC, the error motion within 2.7 .mu. m of a hydrostatic guideway can be compensated with the resolution of 2.7nm, 1/100 contollable range, and the frequency bandwidth of 5.5 Hz. From these results, it is confirmed that the ACC is very effective to improve the motion accuracy of high or ultra precision hydrostatic guideways.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2004년도 추계학술대회 논문집
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• pp.672-676
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• 2004

In this paper, measuring system of 5 DOF motion errors are proposed using two capacitive type sensor, a straight edge and a laser interfoerometer. Yawing error and pitching error are measured using the laser interferometer, and rolling error is measured by the reversal method using a capacitive type sensor. Linear motion errors of horizontal and vertical direction are measured using the sequential two point method. In this case, influence of angular motion errors is compensated using the previously measured angular motion errors. In the horizontal direction, measuring accuracy is within 0.05 $\mu$m and 0.27 arcsec, and in the vertical direction, it is within 0.15 $\mu$m and 0.5 arcsec. From these results, it is confirmed that the proposed measureing system is very effective to the measurement of 5 DOF motion errors in the ultra precision feed tables.

• 한국정밀공학회지
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• 제22권11호
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• pp.135-141
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• 2005

Measurement of five DOF motion errors in a ultra precision feed table was attempted in this study. Yaw and pitch error were measured by using a laser interferometer and roll error was measured by using the reversal method. Linear motion errors in the vertical and horizontal directions were measured by using the sequential two point method. In this case, influence of angular motion errors was compensated by using the previously measured ones by the laser interferometer and the reversal method. The capacitive type sensors and an optical straight edge were used in the reversal method and the sequential two point method. Influence of thermal deformation on sensor jig was investgated and minimized by the periodic measurement according to the variation of room temperature. Deviation of gain between sensors was also compensated using the step response data. 5 DOF motion errors of a hydrostatic table driven by the linear motor werer tested using the measurement method. In the horizontal direction, measuring accuracies for the linear and angular motion were within ${\pm}0.02\;{\mu}m$ and ${\pm}0.04$ arcsec, respectively. In the vertical direction, they were within ${\pm}0.02{\mu}m$ and ${\pm}0.05$ arcsec. From these results, it was found that the introduced measurement method was very effective to measure 5 DOF motion errors of the ultra precision feed tables.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2012년도 춘계학술대회 논문집
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• pp.427-428
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• 2012

• 한국정밀공학회지
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• 제21권7호
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• pp.185-194
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• 2004

In order to analyze the motion errors of the aerostatic stage, it is necessary to consider the influence of the moment variation occurred inside the pads. In this paper, a motion error analysis method utilizing the transfer functions on the reaction force and moment is proposed, and general characteristics of the transfer functions are discussed. Calculated motion errors by the proposed method show good agreement with the ones calculated by Multi fad Method, which is considered the entire table as an analysis object. Also, by the introduction of the transfer function of motion errors, which represent the relationship between the spatial frequency components of the rail form error and motion errors, motional characteristics of the porous aerostatic stage can be generalized. In detail, the influence of the spatial frequencies is analyzed qualitatively, and the patterns of the insensitive frequencies which almost do not affect the linear motion error or angular motion error according to the rail length ratio and the number of the pad are verified. The relationship between the moment variation occurred inside the pads and the motion errors is also verified together.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 1995년도 추계학술대회 논문집
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• pp.466-469
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• 1995

This paper presents a design and performance of the 6 D.O.F linear motion table with a magnetic bearing suspension. The linear positioning of the table with a 150mm stroke is driven by a brushless DC Linear motor and the other attitudes of the stage are controlled by the analog PD controller with magnetic bearing actuators. Each magnetic bearing unit which consists of 3 electromagnets, 3 capacitance probes and 3 backup bearings affords controlled forces by detecting the air gap between the probes and guideways. An integral type capacitance probe amplifier is equipped on the upper plate of the table so that the probe line to the probe amplifier can be shorter therefore the problems due to the stray capacitance and noise can be reduced. Form the pitch-yaw errormeasured by the autocollimator, the vertical and horizont straightness errors of the table are derived that they are maintained below 1.mu. m over 100mm stroke. The positioning accuracy of the linear motion is maintained below 2 .mu. m and the repeatability error is below 1 .mu. m

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2010년도 춘계학술대회 논문집
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• pp.125-126
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• 2010