Various types of 5-axis machine tools have been developed. In the case of a machine tool composed from linear motion, the kinematic equation can be obtained easily and intuitively. However, machine tools with more than four axes, including rotating axes, have generally performed kinematic and dynamic performance analyses using mathematical methods. In this paper, the kinematic equations of various types of machine tools are obtained, based on the Homogeneous Transformation Matrix method. The loop stiffness was then calculated as a mathematical model. A mathematical model of loop stiffness was verified by using a method to calculate the loop stiffness of a commercial program. The results of the mathematical model showed less than a 1% error with the commercial program, and this could show the validity of the mathematical model. Then, this model was applied to two types of machine tools. The minimum loop stiffness of both models is compared.

Ballscrews are important motion transfer and positioning units of industrial machinery and precision machines. Positioning accuracy of the feed drive system depends upon axial stiffness of ballscrew systems. As the nut stiffness depends upon preload and operating conditions, analytical modeling of the stiffness is performed through the contact and body deformation analysis. For accurate contact analysis, the contact angle variation between balls and grooves is incorporated in the developed model. To verify the developed mathematical stiffness model, experiments are conducted on the test-rig. Through the uncertainty analysis according to GUM (Guide to the expression of Uncertainty in Measurement), it is confirmed that the formulated stiffness model has over 85% estimation accuracy. After constructing the ballscrew DB, a quick turnaround system for the nut stiffness estimation has been developed in this research.

Linear motion (LM) ball guides have good accuracy and high efficiency. They are widely applied for precision machinery such as machine tools, semiconductor fabrication machines and robots. However, friction force incurs heat between the balls and grooves. Thermal expansion due to the heat deteriorates stiffness and accuracy of the LM ball guides. For accurate estimation of stiffness and accuracy during the linear motion, friction models of LM ball guides are required. To formulate accurate frictional models of LM ball guides according to load and preload conditions, rolling and viscous frictional analyses have been performed in this paper. Contact loads between balls and grooves are derived from Hertzian contact analysis. Contact angle variation is incorporated for the precision modeling. Viscous friction model is formulated from the shear stress of lubricant and the contact area between balls and grooves. Experiments confirm validity of the developed friction model for various external load and feedrate conditions.

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 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 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.

It is an important thing for a designer to simulate and predict the performance of a spindle and a rotary table. In addition to the general performance such as static stiffness, the error motion performance information is beneficial to the designer in many cases. However for an aerostatic bearing the fluid film physical status should be calculated in order to simulate those performances and the calculation time is another obstacle for a simple performance simulation. In this paper the investigation on experiment and simulation is performed in order to find a more effective simulation method for the rotational error motion.

The large volume multi-tasking vertical lathe was developed for machining the bearing parts for a wind power generator. Although the machined part is large in size high precision tolerances are required recently. One of the most important components to achieve this mission is the rotating table which holds and supports the part to be machined. The oil hydrostatic bearing is adopted for the thrust bearing and the rolling bearing for the radial bearing. In this article experimental performance evaluation and its analysis results are presented. The rotational accuracy of the table is assessed and the frequency domain analysis for the structural loop is performed. And in order to evaluate the structural characteristic of table the moment load experiment is performed. The rotational error motion is measured as below 10 μm for the radial and axial direction and 22,800 Nm/arcsec of moment stiffness is achieved for the rotary table.

An ultraprecision multi-axis machine tool has been designed and developed in our laboratory. The machine tool has four moving axes which are composed of three linear axes and one rotational axis. It has a gantry type structure and the Z-axis is on the X-axis and the C-axis, on which a workpiece is located, is inside the Y-axis. This paper shows control performance improving method and procedure for the ultra-precision positioning control of a hydrostatic bearing guided linear axis. Through improvements of electrical and mechanical components for the control system such as control electronics and oil pumping systems, the control disturbing noise is decreased. Also by the frequency domain analysis of control system those problem-making system components are identified and modified with analytical methods. The controller is analyzed and designed from frequency domain data and system information. In the experimental control results the nanometer order control result is successfully presented.

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.

A pressure rise is generated while air bearing stages are moving in high vacuum environment. This study analyzed this pressure rise phenomenon theoretically and verified it experimentally using two different kinds of stages - linear and rotary air bearing stages. Results indicate that the pressure rise was caused by additional leakage resulting from stage velocity, along with adsorption and outgassing of gas molecules from the guide rail surface. Though tilting of the stage due to acceleration and deceleration reached several micrometers, it had a negligible effect on pressure rise because the tilting time was very short. Therefore, a rotary air bearing stage showed much less pressure rise than a linear stage because the rotary stage theoretically has nothing to do with the above causes. Additional leakage caused by stage velocity was inevitable if the stage had movements, but pressure rise caused by adsorption and outgassing could be suppressed by improving the surface quality to reduce real surface area, and by coating the guide rail surface with titanium nitride (TiN) which has less adhesion probability of gas molecules. The results also indicate that the pressure rise increased when the air bearing stage operated under high vacuum conditions.

Recently, mastering processes for high density optical disc such as Blu-ray disc rely on electron beams, which are operable in only vacuum. In the mastering process, one of the most important tasks is to design precision stages for providing precise positioning of the works with respect to the source in a high vacuum environment. In this paper, we have developed a precision rotation table usable in the electron beam mastering. The rotation table adopted air bearings for a high positioning repeatability and velocity stability. The air leakage from the air bearings has been minimized by employing the differential exhaust scheme using three steps of air drain. The design parameters such as diameters of exhaust lines, seal lengths, and pumping speeds were decided according to the optimization method using genetic algorithm. The performance on the vacuum level of the rotation table was evaluated experimentally and theoretically. The results indicate that a vacuum level of 10?⁴ ㎩ is achieved with operation of air bearings in a vacuum chamber, which is sufficient for the electron beam mastering.

This paper presents the optimal design of an exhaust system of a vacuum-compatible air bearing using a genetic algorithm. To use the air bearings in vacuum conditions, the differential exhaust method is adopted to minimize the air leakage, which prevents air from leaking into a vacuum chamber by recovering air through several successive seal stages in advance. Therefore, the design of the differential exhaust system is very important because several design parameters such as the number of seals, diameter and length of an exhaust tube, pumping speed and ultimate pressure of a vacuum pump, seal length and gap(bearing clearance) influence on the air leakage, that is, chamber's degree of vacuum. In this paper, we used a genetic algorithm to optimize the design parameters of the exhaust system of a vacuum-compatible air bearing under the several constraint conditions. The results indicate that chamber's degree of vacuum after optimization improved dramatically compared to the initial design, and that the distribution of the spatial design parameters, such as exhaust tube diameter and seal length, was well achieved, and that technical limit of the pumping speed was well determined.

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.

This paper describes a theoretical analysis and experimental verification on the performances of a vacuum-compatible air bearing, which is designed with a cascaded exhaust scheme to minimize the air leakage in a vacuum environment. The design of the vacuum-compatible air bearing equipped with the differential exhaust system requires great care because several design parameters, such as the number of exhaust stages, diameter of exhaust tube, pumping speed of a vacuum pump, and bearing clearance greatly influence the air leakage and thus degree of vacuum. In this study, a performance analysis method was proposed to estimate the performances of the air bearing, such as load capacity, stiffness, and air leakage. Results indicate that the load capacity and stiffness of the air bearing was improved as its boundary pressure, which was determined by the 1^st exhaust method, was lowered, and the dominant factors on the chamber's degree of vacuum were the number of exhaust stages, exhaust tube diameter and bearing clearance. A vacuum chamber and air bearing stage using porous pad were fabricated to verify the theoretical analysis. The results demonstrate that chamber pressure up to an order of 10^-3 Pa was achieved with the air bearing stage operating inside the chamber, and this analysis method was valid by comparing predicted values with experimental data, for the mass flow rates from the porous pad, and pressures at each exhaust port and chamber, respectively.

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㎛.