Volumetric error modelling of a stereo vision system for error correction in photogrammetric three-dimensional coordinate metrology

Optical three-dimensional coordinate measurement using stereo vision has systematic errors that affect measurement quality. This paper presents a scheme for measuring, modelling and correcting these errors. The position and orientation of a linear stage are measured with a laser interferometer while a stereo vision system tracks target points on the moving stage. With reference to the higher accuracy laser interferometer measurement, the displacement errors of the tracked points are evaluated. Regression using a neural network is used to generate a volumetric error model from the evaluated displacement errors. The regression model is shown to outperform other interpolation methods. The volumetric error model is validated by correcting the three-dimensional coordinates of the point cloud from a photogrammetry instrument that uses the stereo vision system. The corrected points from the measurement of a calibrated spherical artefact are shown to have size and form errors of less than 50 μm and 110 μm respectively. A reduction of up to 30% in the magnitude of the probing size error is observed after error correction is applied.     

A Study of High-Precision CNC Lathe Thermal Errors and Compensation

This study is addressed at the thermal deformation errors resulting from temperature rise that contribute to 40%–70% of the precision errors in machining at a turning centre, and proposes an economic, accurate, and quick measurement method. It also investigates the thermal error differentials between static idle turning and in the actual cutting environment. The temperature measurement units are intelligent IC temperature sensors with correction circuits. The A/D card extracts and transforms data and saves data in the computer files, and the displacement sensor measures the displacement deviation online during cutting. The temperatures and the deviation of thermal drifts so obtained are used to establish the relationship function using multivariable linear regression and nonlinear exponential regression models, respectively. Finally, this paper compares software compensation methods for the thermal-drift relationship. As proven by experiments, the software compensation method can limit the thermal error of a turning centre to within 5 μm. Moreover, the software compensation for the thermal error relationship using a single variable nonlinear exponent regression model can reduce the error by 40% to 60%.     

数控机床误差测量技术及其误差补偿

介绍了一种使用激光多普勒位移干涉仪对数控机床误差测量和误差补偿的方法。分轴步进体对角线测量法就是通过序列的单轴运动使机床沿着体对角线运动,这样便可以分离出数控机床的各项空间误差元素,包括直线定位误差、垂直直线度误差、水平直线度误差。然后利用测量误差自动生成补偿文件,输入数控系统,对误差进行相应的补偿。实验证明了这种测量和补偿的有效性。     

Three-point method for measuring the geometric error components of linear and rotary axes based on sequential multilateration

The linear and rotary axes are fundamental parts of multi-axis machine tools. The geometric error components of the axes must be measured for motion error compensation to improve the accuracy of the machine tools. In this paper, a simple method named the three-point method is proposed to measure the geometric error of the linear and rotary axes of the machine tools using a laser tracker. A sequential multilateration method, where uncertainty is verified through simulation, is applied to measure the 3D coordinates. Three non-collinear points fixed on the stage of each axis are selected. The coordinates of these points are simultaneously measured using a laser tracker to obtain their volumetric errors by comparing these coordinates with ideal values. Numerous equations can be established using the geometric error models of each axis. The geometric error components can be obtained by solving these equations. The validity of the proposed method is verified through a series of experiments. The results indicate that the proposed method can measure the geometric error of the axes to compensate for the errors in multi-axis machine tools.     

A linear air bearing stage with active magnetic preloads for ultraprecise straight motion

In this paper, we propose a linear motion stage designed with magnetically preloaded air bearings. The magnetic actuators for preloading air bearings were combined with permanent magnets and coils to adjust the air bearing clearance by actively controlling the magnetic force. The system was designed to achieve a simplified configuration of air bearing stage while providing ultraprecise straight motion by actively compensating for the motion errors. The porous aerostatic bearings and magnetic preload actuators were designed and analyzed numerically for a single-axis prototype linear stage driven by a coreless linear motor. A magnetic circuit model was derived for the magnetic actuators. The static stiffness and load capacity of the air bearing stage in the vertical (magnetically preloaded) direction were experimentally measured and compared with the results from the numerical analysis. Motion control laws for three degrees of freedom (i.e., vertical, pitch, and roll motions) were obtained with a high linearity and independence for each axis. The active compensation of three motion errors, the vertical, pitch and roll motion errors were performed through curve-fitting the three errors measured with combination of capacitive gap sensors and a laser interferometer. The errors were reduced from 1.09 to 0.11 μm for the vertical straightness error, from 9.42 to 0.18 arcsec for the pitch motion, and from 2.42 to 0.18 arcsec for the roll motion as level of measured repeatability.     

Development of magnetically preloaded air bearings for a linear slide: active compensation of three degrees of freedom motion errors

This article describes a linear air-bearing stage that uses active control to compensate for its motion errors. The active control is based on preloads generated by magnetic actuators, which were designed to generate nominal preloads for the air bearings using permanent magnets to maintain the desired stiffness while changing the air-bearing clearance by varying the magnetic flux generated by the current in electromagnetic coils. A single-axis linear stage with a linear motor and 240 mm of travel range was built to verify this design concept and used to test its performance. The motion of the table in three directions was controlled with four magnetic actuators driven by current amplifiers and a DSP (Digital Signal Processor)-based digital controller. The motion errors were measured using a laser interferometer combined with a two-probe method, and had 0.085 microm of repeatability for the straightness error. As a result of feed-forward active compensation, the errors were reduced from 1.09 to 0.11 microm for the vertical motion, from 9.42 to 0.18 arcsec for the pitch motion, and from 2.42 to 0.18 arcsec for the roll motion.     

Development of a three-degree-of-freedom laser linear encoder for error measurement of a high precision stage

In this study, a laser linear encoder with three degrees of freedom (3-DOFs) based on diffraction and interference was developed to measure the linear displacement and two angular errors of a linear moving stage. Parts of the linear motion errors induced from the two angular errors can be calculated by this prototype 3-DOF laser encoder. It was an effective method for online error calculation and compensation to improve precision stage performance. This new function was superior to other laser encoders. The verification results showed that the resolution is 20 nm. It detected displacements relative to an external grating scale with accuracy of about +/-150 nm for a measuring range of +/-1 mm, and detected the angular errors with related accuracy of about +/-1 arc sec for a measuring range of +/-100 arc sec.     

基于开放式数控系统的几何误差补偿研究

首先将21项几何误差产生的综合效应分解到各个轴,实现几何误差补偿模型。介绍了在一台开放式数控系统上实施软件误差补偿过程,软件误差补偿原理仅与机床本体的几何误差有关,而与基本指令无关。补偿嵌入算法简便易行,执行时间短,不影响系统的实时性。通过实际测量计算验证了补偿嵌入算法的有效性和实用性,对于提高国产数控系统几何误差补偿水平具有重要的工程价值。     

扫描隧道显微镜微位移工作台的神经网络PID控制方法研究

提出了一种基于神经网络理论的微位移工作台控制方案。该工作台以压电陶瓷作为微位移驱动元件,对伺服电机大位移进行位移补偿。分析了压电陶瓷微位移驱动器的原理,建立了工作台的数学模型。神经网络PID控制器对工作台进行闭环控制,利用BP网络的自学习和自适应能力,实时调整网络加权值,改变PID控制器的控制系数,减小工作台的位移误差。采用专用的压电陶瓷驱动电源对工作台的位移进行了实验,相对于常规PID控制器,微位移为11.41 μm时的响应时间从1.5 s缩短到1 s,稳态位移误差从3.13％减小到1.05％,工作台的稳定性和定位精度得以提高,改善了扫描隧道显微镜的工作性能。     

数控机床热变形误差研究及补偿应用

热变形误差是影响机床加工精度的重要因素之一,通过误差补偿的方法可以提高机床的加工精度。研究了通过实时补偿热变形误差提高数控机床加工精度的方法,阐述了热误差的基本原理,介绍了热误差的测量方法。采用模糊聚类的方法来布置测温点,利用多元线形回归方法建立了机床热变形与温升之间的数学模型。在PLC补偿系统的作用下,在加工过程中对XH718数控机床进行实时补偿。实验结果表明补偿效果很好。     

基于Volterra级数的转子故障诊断研究 

基于Volterra级数的转子故障诊断研究
唐浩;屈梁生;温广瑞
西安交通大学机械制造系统工程国家重点实验室,西安,710049
在简要介绍了Volterra级数基本理论的同时,应用遗传算法对Volterra级数的核进行了辨识,并取得了良好的辨识效果。与传统的基于信号处理的诊断方法不同,该方法将基于系统模型的Volterra级数非线性故障诊断方法应用于转子轴承系统的故障诊断,研究了转子在正常状态和碰摩状态下的起车过程中Volterra级数核的变化。实验结果验证了该方法的可行性与有效性。
This paper briefly introduced the basic theory of
Volterra series.Then,it identified the Volterra kernels by using genetic algorithm(GA) and achieved a satisfactory identification result.Being different from the traditional diagnosis schemes based on signal processing approach,the Volterra series method based on system modeling was employed in the area of fault diagnosis for rotor-bearing system.We
investigated the changes of Volterra kernels under normal state and rubbing state during run-up stages.Finally,experimental results certify its feasibility and effectiveness.
Volterra;nonlinear;genetic algorithm;fault diagnosis     

A new methodology for identifying location errors in 5-axis machine tools using a single ballbar set-up

Ballbar testing of rotary axes in 5-axis machine tools can be time-consuming and requires high levels of operator expertise; especially in the set-up process. Faster tests reduce down-time and encourage frequent updates to compensation parameters to reflect the current state of the machine. A virtual machine tool (VMT) is developed to emulate the machine tool, its geometric errors and the testing procedures. This was used to develop a new single set-up testing method to identify all rotary axis locations errors, whilst remaining robust in the presence of set-up error and linear axis squareness errors. New testing and data processing techniques remove the requirement for fine-adjustment of the tool-cup and permit full automation of necessary toolpaths, including transitions. Using the VMT, error identification residuals were found to be 2.7 % or less. Experiments and statistical analysis then showed that all errors can be measured using a single set-up, and values are sufficiently close to the values measured using conventional multi-set-up procedures to be used in error compensation. This method will significantly reduce set-up durations and removes the need for any modified testing hardware.     

嵌入式时栅角位移传感器短周期误差分析与补偿

为提高嵌入式时栅角位移传感器测量精度,从传感信号形成机理出发,对短周期误差成因进行了详细分析。通过对绕组等效分析和激励信号分析,确定了短周期误差的主要特性为一次和二次误差,一次误差来源为零点残余误差和直流分量误差,二次误差来源为激励信号正交误差。针对短周期误差补偿,提出了基于超限学习机的误差补偿方法,通过对测量值与真实值样本的训练得到模型最优参数,根据模型参数建立短周期误差模型,利用所得误差模型实现对短周期误差的补偿。实验结果表明,短周期误差分析结果与传感器实际误差特性一致,采用该补偿方法传感器短周期误差大幅度降低,降低了约96%。对比和重复性实验表明,该方法与谐波补偿法相比精度提高了约1倍,误差补偿效果更优,同时方法具有良好的测量稳定性,对提高嵌入式时栅角位移传感器的测量精度具有重要的理论和现实意义。     

A general strategy for geometric error identification of multi-axis machine tools based on point measurement

Geometric error component identification is needed to realize the geometric error compensation which can significantly enhance the accuracy of multi-axis machine tools. Laser tracker has been applied to geometric error identification of machine tools increasingly due to its high capability in 3D metrology. A general method, based on point measurement using a laser tracker is developed for identifying the geometric error components of multi-axis machine tools in this study. By using this method, all the component errors and location errors of each axis (including the linear axis and rotary axis) of the multi-axis machine tools can be measured. Three pre-described targets are fixed on the stage of the under-test axis which moves step by step. The coordinates of the three targets at every step are determined by a laser tracker based on the sequential multilateration method. The volumetric errors of these three target points at each step can be obtained by comparing the measured values of the target points’ coordinates with the ideal values. Then, nine equations can be established by inversely applying the geometric error model of the axis under test, which can explicitly describe the relationship between the geometric error components and volumetric error components, and then the component errors of this axis can be obtained by solving these equations. The location errors of the axis under test can be determined through the curve fitting. In brief, all the geometric error components of a single axis of multi-axis machine tools can be measured by the proposed method. The validity of the proposed method is verified through a series of experiments, and the experimental results indicate that the proposed method is capable of identifying all the geometric error components of multi-axis machine tools of arbitrary configuration.     

阶梯轴类零件激光在机测量误差补偿研究

轴类零件主要用来传递转矩和承受载荷,常通过数控车床加工而成其精度要求高,可用激光位移传感器对其轮廓信息进行采集,但由于机床存在位置及运动误差等,使得在机测量精度较低。因此为提高测量精度,提出面向阶梯轴类零件激光测量的实时误差补偿算法,并分别对补偿前后台阶测量点云进行模型重构,对比分析其测量误差。对比分析结果验证了补偿算法的有效性。台阶面测量表明,经几何关系修正后,其平面测量误差与三坐标测量结果差值为0.002 mm,证明测量拟合精度高。     

Form-truing error compensation of diamond grinding wheel in CNC envelope grinding of free-form surface

In computer numerical control (CNC) grinding of free-form surface, an ideal arc profile of trued diamond grinding wheel is generally employed to plan 3D tool paths, whereas its form-truing errors greatly influence the ground form accuracy. A form-truing error compensation approach is proposed by using an approached wheel arc profile to replace the previously designed ideal one. The objective is to directly compensate the trued wheel arc-profile errors. It may avoid the time consumption of traditional approach that compensates the measured coordinate point errors of workpiece to an iterative grinding operation. First, the 3D tool path surface was constructed to plan the 3D tool paths. Second, the CNC arc truing of grinding wheel was conducted to analyze the form-truing error distribution relative to the applied wheel arc profile. Then, the form-truing error compensation was carried out in CNC envelope grinding. Finally, the iterative closest point (ICP) algorithm was used to match the measured coordinate points of workpiece to ideal free-form surface. It is shown that the 3D tool path surface constructed is practicable to plan arbitrary 3D tool paths for the form-truing error compensation. The ICP matching may be used to investigate 3D ground form error distribution. It is confirmed that the form-truing error compensation can directly improve the 3D ground form accuracy. It may decrease the 3D ground form error by about 20% when the 2D form-truing error is reduced by about 58% using the same truing conditions for CNC grinding.     

[误差建模及精度保证方法]双五轴数控铣削机床旋转轴误差辨识方法

为了快速、系统地辨识双五轴数控铣削机床旋转轴几何误差,提出了一种基于R-test的误差测量辨识方法。根据R-test误差模型研究误差测量值与各项误差参数的关系,辨识旋转轴各个几何误差项以得到旋转轴的安装误差和运动误差;利用最小二乘法原理平面圆拟合和直线拟合的方法分别辨识出2项位移误差和2项垂直度误差;基于多体系统理论及齐次坐标变换方法建立刀具坐标系与工件坐标系的齐次坐标变换模型,并辨识出3项移动误差和3项转动误差;最后,根据所得辨识值对X向和Y向位移误差进行补偿。实验结果表明,补偿后X向和Y向位移误差明显减小,误差补偿结果验证了测量、辨识的准确性和有效性。     

An integrated error compensation method based on on-machine measurement for thin web parts machining

Thin webs are widely used in the aerospace industry for the advantages of compact structure, light weight and high strength-to-weight ratio. Due to its low rigidity, serious machining error may occur, therefore, Finite Element method and mechanism analysis are usually utilized to modeling its deformation. However, they are very time-consuming and only suitable for elastic deformation error. In this study, an integrated error compensation method is proposed based on on-machine measurement (OMM) inspection and error compensation. The OMM inspection is firstly applied to measure the comprehensive machining errors. The Hampel filtering is then used to eliminate outliers, followed by the triangulation-based cubic interpolation as well as a machine learning algorithm which are used to establish the compensation model. At last, the real time compensation of high-density cutting points is realized by developing the compensation system based on External Machine Zero Point Shift (EMZPS) function of machine tool. Three sets of machining experiment of a typical thin web part are conducted to validate the feasibility and efficiency of the proposed method. Experiment results revealed that after compensation, the comprehensive machining errors were controlled under different machining conditions and 58.1%, 68.4% and 62.6% of the machining error ranges were decreased, respectively. This method demonstrates immense potential for further applications in efficiency and accuracy improvement of thin-walled surface parts.     

A real time machining error compensation method based on dynamic features for cutting force induced elastic deformation in flank milling

During the machining process, cutting forces cause deformation of thin-walled parts and cutting tools because of their low rigidity. Such deformation can lead to undercut and may result in defective parts. Since there are various unexpected factors that affect cutting forces during the machining process, the error compensation of cutting force induced deformation is deemed to be a very difficult issue. In order to address this challenge, this article proposes a novel real time deformation error compensation method based on dynamic features. A dynamic feature model is established for the evaluation of feature rigidity as well as the association between geometric information and real time cutting force information. Then the deformations are calculated based on the dynamic feature model. Eventually, the machining error compensation for elastic deformation is realized based on Function Blocks. A thin-walled feature is used as an example to validate the proposed approach. Machining experiment results show that the errors of calculated deformation with the monitored deformation is less than 10%, and the thickness errors were between ?0.05 mm and +0.06 mm, which can well satisfy the accuracy requirement of structural parts by NC (Numerical Control) machining.     

Development of 2-axis hybrid positioning system for precision contouring on micro-milling operation

A 2-axis hybrid positioning system was developed for precision contouring on micro-milling operation. The system was developed to overcome the micro-positioning limitations of conventional linear stage positioning system on machine tools. A 2-axis flexure hinge type piezoelectric stage was added on a standard milling machine to obtain better machining results. The control method used for the hybrid system was active error compensation type, where errors from linear stages are cancelled by the piezoelectric stage motion. Positioning experiments showed an improvement of machine accuracy which was confirmed by the machining results. A micro-pillar was fabricated for the validation of long-range and high-precision contouring capability. The system was successfully implemented on micro-milling machining to achieve high-precision machining results.