• Journal of the Korean Society for Precision Engineering
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• v.19 no.6
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• pp.77-85
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• 2002

An analysis method which calculates corrective machining information for improving the motion accuracy of linear motion guide Is proposed in this paper. The method is composed of two algorithms. One is the algorithm fur prediction of the motion errors from rail form error. The other is the algorithm for prediction of rail form error from the motion errors of table. Transfer function is utilized in each algorithm, which represents the ratio of bearing reaction force variation to unit magnitude of spatial frequencies of raid from error. As the corrective machining information is acquired from the measured motion errors of table, the method has a merit not to measure rail form error directly. Validity of the method is verified both theoretically and experimentally. By applying the method, linear motion error of test equipment is reduced from 5.97$\mu$m to 0.58$\mu$m, and reduced from 32.78arcsec to 6.21 arcsec in case of angular motion error. From the results, it is confirmed that the method is very effective to improve the motion accuracy of linear motion guide.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2000.05a
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• pp.692-695
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• 2000

This paper is concerned with Accuracy Design of LM Guide System in Machine Tools. Elastic deformation of bearing is calculated by Hertz contact theory and motion error of LM block is analyzed. A new algorithm using block stiffness is proposed fur the analysis of motion accuracy of the table. The best advantage of this algorithm is fast analysis speed because it isn't necessary iteration processes for satisfying equilibrium equation of the table. Motion errors of the table analyzed under artificial form error of rail theoretically and experimentally. Only one of two rails is bent by putting a thickness gauge into horizontal direction. This form error of rail is measured by gap sensor against the other rail. Then, motion errors of the table are predicted by proposed new algorithm theoretically and measured by laser interferometer. Measurements are carried out by changing the preload and thickness. The results show that the table motion errors are reduced from 1/2 to 1/60 times than form error of rail according to its height and width. And the effect of preloading is almost negligible.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2000.05a
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• pp.658-662
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• 2000

In order to achieve systematical method for improving motion accuracy of hydrostatic table, an algorithm using finite element method is proposed in this paper. Quantification of averaging effect of oil film on motion error is performed theoretically by analysis on the relationship between spacial frequency of rail form error and motion error of table. Influences of film stiffness and pocket size on the motion error of table are also analyzed theoretically Validity of the algorithm is verified experimentally from the test on the motion error of table with three types of rail which have different form profile. Experimental results show that the algorithm is very effective to analyze theoretically the motion error of hydrostatic table.

• Journal of the Korean Society for Precision Engineering
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• v.19 no.5
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• pp.139-148
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• 2002

Motion errors of linear motion guideway are analyzed theoretically in this paper. For the analysis, an new algorithm predicting motion errors of bearing and guideway is proposed using the Hertz's elastic deformation theory. Accuracy averaging effect can be calculated quantitatively by analyzing relationship between motion errors of guideway and spatial frequency of rail form error. Influences of design parameters on the motion errors including the number of balls, preload, ball diameter, bearing length and the number of bearings are analyzed. As it is difficult to measure the rail form error, experimental results are compared with results analyzed by the equivalent analysis method which evaluate the motion errors of guideway using the measured errors of bearing. From the experimental results, it is confirmed that the proposed analysis method it effective lo analyze the motion errors of linear motion bearing and guideway.

• Journal of the Korean Society for Precision Engineering
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• v.17 no.12
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• pp.137-144
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• 2000

In order to achieve systematical method for improving motion accuracy of hydrostatic table, an algorithm using finite element method is proposed in this paper. Quantification of averaging effect of oil film on motion error is performed theoretically by analysis on the relationship between spacial frequency of rail form error and motion error of table. Influences of film stiffness and pocket size on the motion error of table are also analyzed theoretically. Validity of the algorithm is verified experimentally from the test on the motion error of table with three types of rail which have different form profile. Experimental results show that the algorithm is very effective to analyze theoretically the motion error of hydrostatic table.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2000.11a
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• pp.179-183
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• 2000

This paper is concerned with achieving the high motion accuracy of linear motion bearing guide according to estimate accuracy average effect of bearing. Accuracy average effect can be obtained b analysis the relationship between motion error of the table and spatial frequency of the rail form error. And influences of ball diameter, ball number, and clock length on block motion error and block number on the table motion error are analyzed theoretically. In addition to, a simple experiment is performed in order to verify theoretical result.

• Journal of the Korean Society for Precision Engineering
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• v.19 no.5
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• pp.56-63
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• 2002

A new model utilizing a transfer function is introduced in the present paper for analizing motion errors of hydrostatic tables. Relationship between film reaction force in a single hydrostatic pad and form error of a guide rail is derived at various spacial frequencies by finite element analysis, and it is expressed as a transfer function. This transfer function clarifies so called averaging effect of the oil film quantitively. For example, it is found that the amplitide of the film reaction farce is reduced as the spacial frequency increases or relative width of the pocket is reduced. Motion errors of a multiple pad table is estimated from transfer function, geomatric relationship between each pads and form errors of a guide rail, which is named as Transfer Function Method(TFM). Calculated motion errors by TFM show good agreement with motion errors calculated by Multi Pad Method, which is considered 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.

• International Journal of Precision Engineering and Manufacturing
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• v.4 no.2
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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.

• 연구논문집
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• s.34
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• pp.101-112
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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 occurredinside the pads. In this paper, a motion error anaysis 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 Pad 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 quantatively, 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.

• Journal of the Korean Society for Precision Engineering
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• v.21 no.7
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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.