Experiences with the master axis method for measuring spindle error motions

In this paper, the master axis method of machine tool spindle measurement is described. This method allows spindle measurements to be carried out at speed and under load. For example, a radial load representing the cutting force in a turning operation can be conveniently applied during characterization of a lathe spindle. The synchronous and asynchronous error motions have been observed to vary in both magnitude and shape with changes in load. Test results from both static and dynamic loads during testing are shown to demonstrate the utility of the method.     

Development of a measuring method for several types of programmed tool paths for NC machine tools using a laser displacement interferometer and a rotary encoder

Many circular motion measuring methods for NC machine tools have been proposed, however, the drawback common to many of these methods is the restriction on the radius size due to the short measuring range of the displacement transducers used. Moreover, most of these measurement tools are specialized, and can only perform circular test path measurements. A circularity test method using a laser displacement interferometer and a rotary encoder has been developed. The measuring method features a much longer range of motion than ordinal circular test methods such as the double ball bar (DBB) method and, therefore, the radius restriction on these measurements is greatly reduced. Moreover, this measuring system can also be used for the evaluation of positioning accuracy and other more complex test paths.

The proposed device consists primarily of a laser displacement interferometer and a rotary encoder. The holders for the interferometer head and the retroreflector are connected with a stainless steel rod. The retroreflector holder has a synthetic resin linear bearing allowing it to move relative to the interferometer head so that both optical components are always facing each other. The laser interferometer measures the change in distance between the interferometer head and the retroreflector, and the rotary encoder measures the rotation angle of the stainless steel rod.

In this paper, the background, measuring principle and apparatus structure are briefly described. The experimental setup is also presented. The apparatus was employed in several measuring experiments, including circularity tests for a vertical machining center. The results from these experiments support the validity of this measurement apparatus.     

Development and application of a system for evaluating the feed-drive errors on computer numerically controlled machine tools

This paper describes the development and application of a system for assessing the contouring characteristics of feed drives on computer numerically controlled (CNC) machine tools. The hardware comprises two linear digital displacement sensors mounted orthogonally on the work table of a CNC machine tool and operating against a precision cube, located in the spindle. Simultaneous movements of two machine axes are measured by the sensors, in conjunction with a microcomputer. Therefore, this system is capable of detecting the difference between a programmed and actual path. By using both circular and square corner programmed test paths, the system can evaluate servo-induced errors in machine tools. Application of the system to the X- and Y-axes of a machining center is undertaken, and results are shown for a range of contouring frequencies and gain settings of the axes. Comparative tests are also undertaken using a conventional double ball link bar, which is shown to be an inferior technique for characterizing the servoerrors.     

Estimation of three-dimensional volumetric errors of machining centers by a tracking interferometer

A tracking interferometer is a laser interferometer with the mechanism to steer the laser direction to automatically follow a target retroreflector. This paper experimentally investigates the performance of the tracking interferometer prototype, developed by a part of the authors, in estimating the volumetric accuracy of a machining center based on the multilateration principle. Then, the prototype's technical issues are discussed based on the measurement uncertainty analysis. This paper briefly reviews the direct algorithm to calculate the three-dimensional position of the target, as well as the indirect algorithm to estimate geometric error parameters of the machine's kinematic model. Their comparison is also presented based on the uncertainty analysis.     

Calibration of linear encoders with sub-nanometer uncertainty using an optical-zooming laser interferometer

The nonlinear errors of high-precision linear encoders were calibrated by using a nanometer-length calibrator that was based on the optical-zooming laser interferometer with an optical frequency comb. A transmission-type linear encoder and a reflection-type linear encoder were calibrated, and the cyclic nonlinear errors were evident. The magnitudes of the observed cyclic errors were 0.1 nm and 0.2 nm, respectively, and the best calibration uncertainties were 0.55 nm (k = 2). A traceable calibration service for linear encoders with the best calibration uncertainty in the sub-nanometer range has started based on this work.     

‘Open-loop’ tracking interferometer for machine tool volumetric error measurement—Two-dimensional case

The tracking interferometer, or the laser tracker, is a laser interferometer with a steering mechanism to regulate the laser beam direction to follow a retroreflector (“target”). Applying the multilateration principle, it measures the target's three-dimensional position at an arbitrary location in the workspace. Its application to the volumetric accuracy measurement for coordinate measurement machines or machine tools has been long studied. In this paper, we propose the ‘open-loop’ tracking interferometer, where the laser beam is regulated toward the command target position. This eliminates the automated tracking mechanism and thus may significantly reduce the manufacturing cost of conventional tracking interferometers. The objective of this paper is to validate this ‘open-loop’ tracking interferometer concept by investigating its measurement uncertainty both experimentally and analytically. To simplify the problem, this paper focuses on the measurement of the target's two-dimensional position by using a single-axis ‘open-loop’ tracking interferometer prototype.     

Uncertainty analysis of a laser calibration system for evaluating the positioning accuracy of a numerically controlled axis of coordinate measuring machines and machine tools

This paper presents an uncertainty analysis of a Positional Error Calibrator based on a laser interferometer system. This laser calibration system is capable of evaluating the positioning accuracy of a numerically controlled axis of machine tools and coordinate measuring machines (CMM) under dynamic conditions. In order to assess the measurement uncertainty of this calibrator, an analysis of the uncertainty components that make up the uncertainty budget of this calibrator has been carried out. These uncertainty components can be classified into three categories as follows: (1) uncertainties intrinsic to the laser system; (2) uncertainties due to environmental effects; (3) measuring uncertainties due to the installation. The procedure for evaluating the uncertainty of this calibrator follows GUM (“Guide to the Expression of Uncertainty in Measurement”). This uncertainty analysis was carried out when this calibrator was used to assess the positional errors of the “X” axis of a moving bridge type CMM.     

快速调整激光干涉仪光线准直系统的设计

使用激光干涉仪能够很好地解决数控机床定位精度差的问题,然而调整激光器的方向,使激光束与所测机床轴的移动方向平行是一项很重要而且麻烦的工作。为快速准确调整激光器方向,在对激光干涉仪工作原理深入研究的基础上,分析了激光束偏心的原因,构建了以PLC为控制核心,驱动两台电机控制干涉仪平移与旋转运动,实现快速调整激光干涉仪激光束准直。实验结果表明,此设计节省了大量人力、时间的开支,能够控制干涉仪快速对准,具有工业应用推广价值。     

Impact of measurement procedure when error mapping and compensating a small CNC machine using a multilateration laser interferometer

This paper deals with the accuracy of compensation of machine tools using a tracking interferometer using the multilateration method. The measurement strategy and thermal drift compensation of the measurements are studied. It shows that most effects of temperature are accurately compensated by the laser tracking interferometer software. However, thermal drifts of accessories are not taken into account, and are therefore not corrected. To validate the robustness of procedures, the geometrical errors of the same machine tool were measured by five measurement strategies using the same equipment. Each strategy is devised and carried out independently by a different person from several institutions. For each strategy, the geometrical compensations were applied to a set of nominal tool path points. The difference, between the nominal points and the compensated or uncompensated points was calculated. This criterion was used to discuss the procedures employed by the participants.     

Dynamic characteristics of spindle with water-lubricated hydrostatic bearings for ultra-precision machine tools

A key component of ultra-precision machine tools is the spindle. The motivation for this study was to improve machining accuracies in precision cutting and grinding by pursuing improvements in the spindle characteristics by designing a sophisticated spindle with water-lubricated hydrostatic bearings. The static bearing stiffness of the developed spindle was investigated in previous studies. In addition to the static bearing stiffness, the dynamic characteristics regarding bearing stiffness also affect significantly on the machining results. In this study, dynamic characteristics of the developed spindle with water-lubricated hydrostatic bearings were investigated via simulations and experiments. Not only bearing dynamics but also rotor dynamics were considered in this study.In the simulation studies, the spindle dynamic characteristics were analysed based on the transfer matrix method. A spindle rotor supported with hydrostatic bearings was represented by discrete sections of the rotor. The mathematical model of transverse linear vibrations of the spindle rotor was derived with distributed parameters for these discretized rotor sections. As a result of the analysis on the amplitude-frequency characteristic, radial displacements of the rotor due to bearing displacement and bending deformation were defined. Then, the frequency characteristics were represented with Nyquist plots. Resonant frequencies and amplitudes formation in the transverse vibration of the rotor were determined. The influence of rotor bending deformations on spindle compliance was assessed. Furthermore, the study examined the influences of the supply pressure of the lubricating fluid, radial clearance and journal diameter of the hydrostatic bearings on the amplitude of the rotor vibration, and the resonance frequency of the system.Furthermore, the dynamic characteristics of the spindle were examined experimentally. The simulation results were in good agreement with the actual spindle dynamics obtained experimentally. The influence of the structural parameters of the rotor and the operating parameters of the bearings on the spindle dynamic characteristics was also determined. It was verified that the amplitude of the vibration of the rotor overhang part was dominantly affected not by bearing stiffness but by bending stiffness of the bearing journal of the front bearing and the length of the rotor overhang.Then it was verified that the resultant displacement of the rotor in the radial direction due to the influence of the bearing characteristics and the structural effect of the rotor is significantly small. Practical recommendations to improve the spindle design in terms of the dynamic characteristics of the spindle with water-lubricated hydrostatic bearings were also derived.