三坐标测量机动态误差补偿的研究

本文研究了三坐标测量机在高速测量过程中的动态误差。针对一移动桥式三坐标测量机,分析了其动态误差的产生原因,建立了动态误差的数学模型,对动态误差进行了全面的测量和补偿。实验证明动态误差具有一定的重复性,可用软件补偿,从而提高三坐标测量机快速测量的精度。     

Investigation of some dielectric properties of phosphate glasses doped with iron oxides,by a microwave technique

The effects of iron ions on dielectric properties of lithium sodium phosphate glasses were studied by non-usual, fast and non-destructive microwave techniques. The dielectric constant (ε′), insertion loss (L) and microwave absorption spectra (microwave response) of the selected glass system xFe₂O₃·(1 − x)(50P₂O₅·25Li₂O·25Na₂O), being x = 0, 3, 6, … , 15 expressed in mol.%, were investigated. The dielectric constant of the samples was investigated at 9.00 GHz using the shorted-line method (SLM) giving the minimum value of ε′ = 2.10 ± 0.02 at room temperature, and increasing further with x, following a given law. It was observed a gradual increasing slope of ε′ in the temperature range of 25 ? t ? 330 °C, at the frequency of 9.00 GHz. Insertion loss (measured at 9.00 GHz) and measurements of microwave energy attenuation, at frequencies ranging from 8.00 to 12.00 GHz were also studied as a function of iron content in the glass samples.     

面向快速探测的坐标测量机动态误差分析

坐标测量机在快速探测时，由于惯性力和驱动力的作用，引起机体变形，从而导致了动态误差的产生。分析了引起坐标测量机动态误差的原因，建立了坐标测量机的动态误差模型。采用有限元方法分析计算了快速探测过程中惯性力和驱动力产生的动态误差，验证了动态误差模型的应用，分析结果是合理的，方法是可行性的。     

Thermally induced volumetric error modeling based on thermal drift and its compensation in Z-axis

Traditional thermally induced volumetric error modeling requires 21 geometric error components at different temperatures. Taking thermal drift errors into account, 30 geometric errors are described to model volumetric error in this paper. The main sources of thermally induced volumetric error are positioning errors of each axis and thermal drift errors. An experiment on milling and boring machine is carried out, which shows that volumetric error in Z-axis is affected significantly. To compensate volumetric error of Z-axis, a model of positioning error is proposed based on nut temperature. A finite elements analysis of headstock thermal characteristic is carried out, and error chain is established, which shows the main source of thermal drift of Z-axis is ram expansion. Thermal drift compensation system of Z-axis is developed based on Invar metal and thermal error compensation module of Siemens CNC system. Therefore, the positioning error and thermal drift of Z-axis are compensated. The thermally induced volumetric error in Z-axis is reduced by 80 % after compensation.     

Application of microcomputer for assessing the probe lobing error and geometric errors of CMMs using commercial ring gauges

Performance verification and frequent reverification of working accuracy of coordinate measuring machines are currently acknowledged as essential operational processes. In this paper, an efficient microcomputer based method has been proposed for the accuracy assessment of the CMMs of CNC type based on the probing of commercially available ring gauges. The geometric inaccuracy data of the ring gauges are measured, stored, and thus can be used as a transfer standard. A computer module for measurement-path generation has been developed, with which automatic CNC measurement codes can be generated for specific CMMs. The ring gauges are measured on the CMMs, and the measured data are feedback to the PC. For the error analysis, a new error analysis module has been developed for performance checking of a measurement probe, where the direction-dependent probe lobing error can be successfully evaluated. A least-squares-based approach has been implemented, with which the scale errors and the squareness error can be evaluated simultaneously in the local measurement position. The advantages of the proposed method are:

1. The rapid assessment for the probe lobing error.
2. Simultaneous evaluation of the scale errors and the squareness error.
3. Highly integrated approach for the measurement-error evaluation processes, which are implemented via a PC.

Practical CMMs have been chosen and the accuracy assessment is performed, demonstrating the high efficiency of the developed system. The developed method can be applied to performance verification or day-to-day reverification of CMMs of CNC type.     

The calibration and error compensation techniques for an Articulated Arm CMM with two parallel rotational axes

The calibration and error compensation techniques for an Articulated Arm Coordinate Measuring Machine (AACMM) with two parallel rotational axes are proposed. An improved six-parameter D–H model is established. The reversal techniques are used to calibrate the parallelism errors, arm lengths and zero position of the AACMM. The effects of the bending and torsion deformations caused by the gravity of the arms are removed. The experiments prove that the calibration method is simple and the measurement expanded uncertainty (_2uc$2_{u_c}$) of the developed AACMM with a measuring range of (∅200–∅1000 mm) × 250 mm is less than 10 μm after error compensation.     

Simple and simultaneous measurement of five-degrees-of-freedom error motions of high-speed microspindle: Error analysis

We have developed a simple and low-cost optical measurement system for the simultaneous measurement of the five-degrees-of-freedom error motions of high-speed microspindles. We demonstrated the usefulness of the system by using it to measure actual spindle rotation errors, and analyzed the major error factors. First, the measurement error due to the form error of the lens was analyzed by ray tracing. Second, we analyzed the measurement error due to a displacement of an irradiation laser point on a 3 mm diameter ball lens. Furthermore, we investigated the effect of the centrifugal force and the crosstalk problem of multiple laser beams. The results indicated that a form error of the rod lens significantly affected the measurement accuracy and that a change in the laser beam irradiation point of the ball lens due to a radial displacement had no significant effect on the measurement accuracy. Finally, we confirmed that, owing to the centrifugal force, the measurement accuracy decreased as the speed of rotation increased, and that there was no crosstalk that the reflected and transmitted laser beams in the X direction were detected by the photodiode in the Y direction for displacements within −10 to 10 μm.     

评定三坐标测量机的动态误差

对三坐标测量机的动态误差作出整体分析。分析影响坐标测量机动态误差的主要因素。指出由于附加惯性力的影响产生的各部件绕气浮导轨联结处的偏转和各运动部件本身的弯曲变形是造成动态误差的主要原因。提出由动态偏转角误差推导测头动态位移误差的方法。用激光干涉仪和电感测微仪对三坐标测量机的动态偏转角误差进行了测量。理论和实验结果证明,在高速测量过程中,由于附加惯性力的影响,除了各部件绕气浮导轨联结处产生较大偏转外     

A long-stroke 3D contact scanning probe for micro/nano coordinate measuring machine

This paper presents a long-stroke contact scanning probe with high precision and low stiffness for micro/nano coordinate measuring machines (micro/nano CMMs). The displacements of the probe tip in 3D are detected by two plane mirrors supported by an elastic mechanism, which is comprised of a tungsten stylus, a floating plate and two orthogonal Z-shaped leaf springs fixed to the outer case. A Michelson interferometer is used to detect the vertical displacement of the mirror mounted on the center of the floating plate. An autocollimator based two dimensional angle sensor is used to detect the tilt of the other plane mirror located at the end of the arm of the floating plate. The stiffness and the dynamic properties are investigated by simulation. The optimal structural parameters of the probe are obtained based on the force-motion model and the constrained conditions of stiffness, measurement range and horizontal size. The results of the performance tests show that the probe has a contact force gradient within 0.5 mN/μm, a measuring range of (±20 μm), (±20 μm), and 20 μm, respectively, in X, Y and Z directions, and a measurement standard deviation of 30 nm. The feasibility of the probe has preliminarily been verified by testing the curved surface of a convex lens.     

Thermal error compensation of a 5-axis machine tool using indigenous temperature sensors and CNC integrated Python code validated with a machined test piece

Achieving high workpiece accuracy is the long-term goal of machine tool designers. There are many causes for workpiece inaccuracy, with thermal errors being the most common. Indirect compensation (using prediction models for thermal errors) is a promising strategy to reduce thermal errors without increasing machine tool costs. The modelling approach uses transfer functions to deal with this issue; it is an established dynamic method with a physical basis, and its modelling and calculation speed are suitable for real-time applications. This research presents compensation for the main internal and external heat sources affecting the 5-axis machine tool structure including spindle rotation, three linear axes movements, rotary C axis and time-varying environmental temperature influence, save for the cutting process. A mathematical model using transfer functions is implemented directly into the control system of a milling centre to compensate for thermal errors in real time using Python programming language. The inputs of the compensation algorithm are indigenous temperature sensors used primarily for diagnostic purposes in the machine. Therefore, no additional temperature sensors are necessary. This achieved a significant reduction in thermal errors in three machine directions X, Y and Z during verification testing lasting over 60 h. Moreover, a thermal test piece was machined to verify the industrial applicability of the introduced approach. The results of the transfer function model compared with the machine tool's multiple linear regression compensation model are discussed.     

Column-by-column compositional mapping by Z-contrast imaging

A phenomenological method is developed to determine the composition of materials, with atomic column resolution, by analysis of integrated intensities of aberration-corrected Z-contrast scanning transmission electron microscopy images. The method is exemplified for InAs_xP_1−x alloys using epitaxial thin films with calibrated compositions as standards. Using this approach we have determined the composition of the two-dimensional wetting layer formed between self-assembled InAs quantum wires on InP(0 0 1) substrates.     

Error analysis and optimization of a 3-degree of freedom translational Parallel Kinematic Machine

In this paper, error modeling and analysis of a typical 3-degree of freedom translational Parallel Kinematic Machine is presented. This mechanism provides translational motion along the Cartesian X-, Y- and Z-axes. It consists of three limbs each having an arm and forearm with prismatic-revolute-revolute-revolute joints. The moving or tool platform maintains same orientation in the entire workspace due to its joint arrangement. From inverse kinematics, the joint angles for a given position of tool platform necessary for the error modeling and analysis are obtained. Error modeling is done based on the differentiation of the inverse kinematic equations. Variation of pose errors along X, Y and Z directions for a set of dimensions of the parallel kinematic machine is presented. A non-dimensional performance index, namely, global error transformation index is used to study the influence of dimensions and its corresponding global maximum pose error is reported. An attempt is made to find the optimal dimensions of the Parallel Kinematic Machine using Genetic Algorithms in MATLAB. The methodology presented and the results obtained are useful for predicting the performance capability of the Parallel Kinematic Machine under study.     

Concept for the integration of geometric and servo dynamic errors for predicting volumetric errors in five-axis high-speed machine tools: an application on a XYC three-axis motion trajectory using programmed end point constraint measurements

A modelling approach for volumetric error prediction taking into account geometric and servo dynamic errors in a five-axis high-speed machine tool is proposed in this paper. Polynomial functions are used to represent and then predict the geometric errors. A simple second-order transfer function model is used to model and predict the servo dynamic error. The servo dynamic errors are added to the axis position geometric errors and propagated to the tool and workpiece using matrix transformations. The validity of the error integration concept is tested for a XYC three-axis motion trajectory. Two experimental setups are used. The first experimental test used the KGM grid encoder instrument to estimate the parameters of the servo dynamic error models of the X- and Y-axes. The second experimental test used a programmed end point constraint procedure with measurement of the 3D volumetric positioning errors between a point on the tool holder and another fixed to the machine table. The tests involve maintaining the nominal coincidence of these two points whilst exercising the three axes. These last tests are used to estimate the geometric error parameters and also to validate the prediction performance of the integrated geometric and dynamic model. The result shows the effectiveness of the error integration concept.     

Measurement of multi-degree-of-freedom error motions of a precision linear air-bearing stage

This paper describes the measurement of straightness error motions (vertical straightness and horizontal straightness) and rotational error motions (pitch, yaw and roll) of a commercial precision linear air-bearing stage actuated by a linear motor. Each of the error motions was measured by two different methods for assurance of reliability. The stage was placed in the XY-plane and moved along the X-direction. The pitch error and yaw error, which were measured by an autocollimator and the angle measurement kit of a laser interferometer, were about 8.7 and 1.6 arc-s, respectively, over a travel of 150 mm with a moving speed of 10 mm/s. The roll error was measured by the autocollimator through scanning a flat mirror along the X-direction. The second method for roll error measurement was to scan two capacitance-type displacement probes along the flat surface placed in the XZ-plane. The two probes with their sensing axes in the Y-direction were aligned with a certain spacing along the Z-axis. The roll error can be obtained by dividing the difference of the outputs of the two probes by the spacing between the two probes. The roll error was measured to be approximately 11.8 arc-s over the 150 mm travel. The horizontal straightness error and the vertical straightness error (Y- and Z-straightness errors) were measured by using the straightness measurement kit of the laser interferometer. The second method for straightness measurement was to scan the flat surface with a capacitance-type displacement probe. The horizontal and vertical straightness errors of the stage over the 150 mm travel were measured to be approximately 207 and 660 nm, respectively.     

Development of high-precision micro-coordinate measuring machine: Multi-probe measurement system for measuring yaw and straightness motion error of XY linear stage

Today, with the development of microsystem technologies, demands for three-dimensional (3D) metrologies for microsystem components have increased. High-accuracy micro-coordinate measuring machines (micro-CMMs) have been developed to satisfy these demands. A high-precision micro-CMM (M-CMM) is currently under development at the National Metrology Institute of Japan in the National Institute of Advanced Industrial Science and Technology (AIST), in collaboration with the University of Tokyo. The moving volume of the M-CMM is 160 mm × 160 mm × 100 mm (XYZ), and our aim is to achieve 50-nm measurement uncertainty with a measuring volume of 30 mm × 30 mm × 10 mm (XYZ). The M-CMM configuration comprises three main parts: a cross XY-axis, a separate Z-axis, and a changeable probe unit. We have designed a multi-probe measurement system to evaluate the motion accuracy of each stage of the M-CMM. In the measurement system, one autocollimator measures the yaw error of the moving stage, while two laser interferometers simultaneously probe the surface of a reference bar mirror that is fixed on top of an XY linear stage. The straightness motion error and the reference bar mirror profile are reconstructed by the application of simultaneous linear equations and least-squares methods. In this paper, we have discussed the simulation results of the uncertainty value of the multi-probe measurement method using different intervals and standard deviations of the laser interferometers. We also conducted pre-experiments of the multi-probe measurement method for evaluating the motion errors of the XY linear stage based on a stepper motor system. The results from the pre-experiment verify that the multi-probe measurement method performs the yaw and straightness motion error measurement extremely well. Comparisons with the simulation results demonstrate that the multi-probe measurement method can also measure the reference bar mirror profile with a small standard deviation of 10 nm.     

Thermal Error Measurement and Real Time Compensation System for the CNC Machine Tools Incorporating the Spindle Thermal Error and the Feed Axis Thermal Error

Thermally induced errors have been significant factors affecting machine tool accuracy. In this paper, the thermal spindle error and thermal feed axis error have been considered, and a measurement/compensation system for thermal error is introduced. Several modelling techniques for thermal errors are also implemented for the thermal error prediction; i.e. multiple linear regression, neural network, and the system identification methods, etc. The performances of the thermal error modelling techniques are evaluated and compared, showing that the system identification method is the optimum model having the least deviation. The thermal error model for the feed axis is composed of geometric terms and thermal terms. The volumetric errors are calculated, combining the spindle thermal error and feed axis thermal error. In order to compensate for the thermal error in real-time, the coordinates of the CNC controller are modified in the PMC program. After real-time compensation, the machine tool accuracy improved about 4–5 times. ID="A1" Correspondence and offprint requests to: Dr H. J. Pahk, School of Mechanical and Aerospace Engineering, Seoul National University, San 56–1, Shinlim-Dong, Kwanak-Ku, Seoul 151–742, Korea. E-mail: hjpahk@plaza.snu.ac.kr     

Leap motion controller three dimensional verification and polynomial correction

We propose a leap motion controller (LMC) dimensional verification based on ISO 10360-2:2009 with a coordinated measuring machine (CMM) as the reference framework. A pointer device comprising a thin aluminum cylinder was used to simulate a human finger. This was mounted on the spindle of the CMM to mark known positions over the LMC workspace. Polynomial tendency line corrections were applied to reduce the error in the LMC and CMM framework alignment. One dimension verification results were less than 0.1 mm in the X and Z axes, whereas the Y axis produced unsuitable results. The mean error was 9.6 mm in three-dimensional (3D) verification. Our findings demonstrate the difference between manufacturer quoted accuracy (0.01 mm) to that practically obtainable when the pointer was placed in a known position. LMC needs to add tracking models and position error compensation in applications requiring high accuracy, such as industrial processes or surgical procedure simulations.     

数控成形砂轮磨齿机床几何误差分析与函数补偿法

以QCYK7332A数控成形砂轮磨齿机为例,对机床误差进行了分析。应用多体系统理论以及齐次坐标变换建立了几何误差模型,得到了此模型下砂轮尖的6个自由度误差表达式,并在此基础上以机床B轴为例,说明了运动轴误差转化到磨具上,从而引起所加工齿轮的齿距、齿形、压力角等误差。为了减小误差,提出了函数补偿法,并以测量机床的X轴角度误差为例,说明机床误差预测以及实时误差补偿的过程,为提高数控成形砂轮磨齿机精度、减小机床的几何误差提供了理论依据。     

A comprehensive error compensation system for correcting geometric, thermal, and cutting force-induced errors

A comprehensive error compensation system has been developed to correct geometric, thermal, and cutting force-induced errors on a turning centre. The basic approach to error compensation is proposed in this paper. The implementation of error compensation control and of hardware configuration of the system are also presented. A total of 11 geometric and thermal error components and 10 cutting force-induced error components can be compensated for using this system. Performance evaluations have been carried out using actual cutting tests. Experimental results show that the diameter accuracy of the part has been improved more than 5 times and taper accuracy of the part has been improved about 5 times.     

三坐标测量机动态误差的建模方法

为了提高三坐标测量机的测量速度,缩短测量周期,分析了影响给定的三坐标测量机动态误差的因素。对三坐标测量机的具体和了分析,用电感测微仪进行了动态偏转角的测量,并推导出由动态偏转误差得到测头处的动态位移误差的方法。同时,对由导轨的直线度造成的误差进行了讨论。指出动态误差主要是由各构件绕气浮导轨连接处的偏转和各运动构件本身的弯曲变形造成挫理论上可以证明,在气浮导轨力矩刚度和横梁弯曲刚度已知的情况下,只要