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The heterodyne He-Ne laser interferometer is the most widely used sensing unit to measure the position error. It measures the positioning error from the displacement of a moving reflector in terms of the wave length. But, the wave length is affected by the variation of atmospheric temperature. Temperature variation of 1℃ results in the measuring error of 1 ppm. In this paper, for measuring more accurately the position error of the ultra precision stage, the refractive index compensation method is introduced. The wave length of the laser interferometer is compensated using the simultaneously measured room temperature variations in the method. In order to investigate the limit of compensation, the stationary test against two fixed reflectors mounted on the zerodur® plate is performed firstly. From the experiment, it is confirmed that the measuring error of the laser interferometer can be improved from 0.34㎛ to 0.11㎛ by the application of the method. Secondly, for the verification of the compensating effect, it is applied to estimate the positioning accuracy of an ultra precision aero static stage. Two times of the refractive index compensation are performed to acquire the positioning error of the stage from the initially measured data, that is, to the initially measured positioning error and to the measured positioning error profile after the NC compensation. Although the positioning error of an aerostatic stage cannot be clarified perfectly, it is known that by the compensation method, the measuring error by the laser interferometer can be improved to within 0.1㎛.
This paper describes the design and evaluation procedure of an ultra-precision rotary table for freeform generating machined tools. Design of the thrust and journal hydrostatic bearings and experimental evaluation of the table were performed. To get the compact size and less lost motion direct drive servomotor with ultra precision encoder. From the considered design, following performance were confirmed by experiment. The total stiffness of the prototype rotary table was 483.6 N/㎛ and 97.6 N/㎛ for axial and radial direction, respectively. Rotational accuracy of the table was investigated by capacitive sensor and reversal measurement technique, and 0.10 ㎛ radial direction and 0.05 ㎛ axial direction of the rotational accuracy were confirmed. The micro resolution of the table was also investigated with displacement of capacitive sensor, and 0.5/10000° of micro resolution was confirmed. Index accuracy of the table was evaluated by the autocollimator and polygon mirror, and the ±0.39 arcsec accuracy and ±0.16 arcsec repeatability of the table were confirmed. Those are under the general requirements of ultra precision rotary tables for freeform generating machined tools.
The error motion of a machine tool spindle directly affects the surface errors of machined parts. The error motions of the spindle are not desired errors in the three linear direction motions and two rotating motions. Those are usually due to the imperfect of bearings, stiffness of spindle, assembly errors, external force or unbalance of rotors. The error motions of the spindle have been needed to be decreased to desired goal of spindle’s performance. The level of error motion is needed to be estimated during the design and assembly process of the spindle. In this paper, the estimation method for the five degree of freedom (5 D.O.F) error motions of the spindle is suggested. To estimate the error motions of the spindle, waviness of shaft and bearings, external force model was used as input data. And, the estimation models are considering geometric relationship and force equilibrium of the five degree of the freedom. To calculate error motions of the spindle, not only imperfection of the shaft, bearings, such as rolling element bearing, hydrostatic bearing, and aerostatic bearing, but also driving elements such as worm, pulley, and direct driving motor systems, were considered.
The volumetric errors of CNC machining centers are determined by 21 errors, including 3 linear errors, 6 straightness errors, 3 perpendicular errors, 9 angular errors and non-rigid body errors of the machine tool. It is very time consuming and hard to measure all of these errors in which laser interferometer and other parts are used directly. Hence, as many as 21 separate setups and measurements are needed for the linear, straightness, angular and perpendicular errors. In case of the 5-axis machining centers, two more rotary tables are used. It can make 35 error sources of the movement. Therefore, the measured errors of multi movements of the 5-axis tables are very complicated, even if the relative measured errors are measured. This paper describes the methods, those analyze the error sources of the machining centers. Those are based on shifted diagonal measurements method (SDM), R-test and Double ball bar. In case, the angular errors of machine are small enough comparing with others, twelve errors including three linear position errors, six straightness errors and three perpendicular errors can be calculated by using SDM. To confirm the proposed method, SDM was applied to measuring 3 axes of machine tools and compared with directly measurement of each errors. In addition, the methods for measuring relative errors of multi-axis analysis methods using R-test and Double Ball Bar are introduced in this paper.
The error motion of a machine tool spindle directly affects the surface errors of machined parts. Those are usually due to the imperfectness of bearings, stiffness of spindle, assembly errors, external force or unbalance of rotors. The error motions of the spindle have been needed to be decreased to desired goal of spindles performance. The level of error motion is needed to be estimated during the design and assembly process of the spindle. In this paper, the estimation method for the five degree of freedom (5 D.O.F) error motions for rotary units such as a spindle and rotary table are suggested. To estimate the error motions of the rotary unit, waviness of bearings and external force model were used as input data. The estimation model considers geometric relationship and force equilibrium of the five degree of the freedom motions.
This paper describes a three-probe system that can be used to measure the parallelism and straightness of a pair of rails simultaneously. The parallelism is measured using a modified reversal method, while the straightness is measured using a sequential two-point method. The measurement algorithms were analyzed numerically using a pair of functionally defined rails to validate the three-probe system. Tests were also performed on a pair of straightedge rails with a length of 250 mm and a maximum straightness deviation of 0.05 ㎛, as certified by the supplier. The experimental results demonstrated that the parallelism-measurement algorithm had a cancellation effect on the probe stage motion error. They also confirmed that the proposed system could measure the slope of a pair of ra ils about 0.06 μrad, Therefore, by combining this technique with a sequential differential method to measure the straightness of the rails simultaneously, the surface profiles could be determined accurately and eliminate the stage error. The measured straightness deviation of each straight edge was less than 0.05 ㎛, consistent with the certified value.