基于平面光栅的加工中心几何误差辨识研究

本文运用齐次坐标变换原理和刚体假设，利用加工中心刀尖点到工件的封闭特性，推导出了包含21项几何误差的数学模型，基于平面光栅测量辨识出全部几何误差，同时还介绍了平面光栅的结构，工作原理和特点等。建立误差的模型和辨识误差的方法具有通用性，可以推广到其它多轴数控机床误差建模和误差辨识的分析之中。     

Identification of two different geometric error definitions for the rotary axis of the 5-axis machine tools

Geometric errors are clearly among the critical error sources in 5-axis machine tools and directly contribute to the machining inaccuracies. According to the definition of geometric errors of the rotary axis, different understandings have been exist in published studies. It is extremely dangerous as it makes the comprehension of the geometric errors ambiguous and may make the geometric error identification and compensation less effective. This phenomenon has not been noticed so far. In this paper, two different commonly used geometric error definition and modeling methods are firstly identified and analyzed, named as “Rotary axis component shift” and “Rotary axis line shift”. The features and relationships of these two error modeling methods are analyzed. After a detailed comparison, “Rotary axis component shift” is more suitable to definite the geometric errors of rotary axis. An experiment has been conducted on a 5-axis machine tool to show the correctness of our work. The results show that the identified geometric errors of rotary axis based on the two error models are greatly different and need to be concerned.     

基于Sobol’法的机床关键几何误差元素辨识方法研究

针对机床几何误差元素多、误差测量与辨识过程繁琐等问题,利用Sobol’全局灵敏度分析方法对空间误差模型中的几何误差元素进行灵敏度分析,筛选出影响较大的几何误差元素,从而降低误差测量与辨识过程的复杂度,简化空间误差模型。以螺旋理论为建模基础,建立机床空间误差模型;对所有几何误差元素进行Sobol序列抽样并通过蒙特卡洛估计法求解灵敏度,计算各误差元素的一阶灵敏度值及全局灵敏度值,从21个误差项中筛选出对机床空间误差影响较大的12项;将简化模型与完备模型进行对比,空间误差元素简化率为48%,其预测精度大于80%,说明了误差元素筛选的有效性,为机床空间误差建模、误差元素辨识以及空间误差补偿工作的简化提供参考。     

Identification and compensation of geometric errors of rotary axes on five-axis machine by on-machine measurement

The geometric errors of rotary axes are the fundamental errors of a five-axis machine tool. They directly affect the machining accuracy, and require periodical measurement, identification and compensation. In this paper, a precise calibration and compensation method for the geometric errors of rotary axes on a five-axis machine tool is proposed. The automated measurement is realized by using an on-the-machine touch-trigger technology and an artifact. A calibration algorithm is proposed to calibrate geometric errors of rotary axes based on the relative displacement of the measured reference point. The geometric errors are individually separated and the coupling effect of the geometric errors of two rotary axes can be avoided. The geometry error of the artifact as well as its setup error has little influence on geometric error calibration results. Then a geometric error compensation algorithm is developed by modifying the numeric control (NC) source file. All the geometric errors of the rotary errors are compensated to improve the machining accuracy. The algorithm can be conveniently integrated into the post process. At last, an experiment on a five-axis machine tool with table A-axis and head B-axis structure validates the feasibility of the proposed method.     

高精密数控机床的非线性误差分析、控制及补偿

误差控制及补偿是提高数控机床精度的重要手段,因此误差模型的建立与分析显得至关重要.本文详细阐述了数控机床几何误差、热误差、切削力误差和控制误差的基本概念、起因、建模及参数辨识,综述了误差研究现状,并对今后的研究方向进行了展望.对减小误差的控制策略和误差综合软件补偿两个方面进行了探讨.为提高数控机床的加工精度提出了可行的思路.     

基于多体系统理论的车铣中心空间误差模型分析

数控机床的误差建模是进行机床运动设计、精度分析和误差补偿的关键技术,也是保证机床加工精度的重要环节.本文利用多体系统理论来构建超精密数控机床的几何误差模型,该模型简便、明确,不受机床结构和运动复杂程度的限制,为计算机床误差、实现误差补偿和修正控制指令提供了理论依据.在机床实际应用中,可以利用由精密机床误差建模所推导出的几何位置误差来修正理想加工指令,控制机床的实际运动,从而实现几何误差补偿,提高机床加工精度.     

Integrated post-processor for 5-axis machine tools with geometric errors compensation

Geometric errors of 5-axis machine tools introduce great deviation in real workpiece manufacture and on-machine measurement like touch-trigger probe measurement. Compensation of those errors by toolpath modification is an effective and distinguished method considering the machine calibration costs and productivity. Development of kinematic transformation model is involved in this paper to clarify the negative influences caused by those errors at first. The deviation of the designed toolpath and the real implemented toolpath in workpiece coordinate system is calculated by this model. An iterative compensation algorithm is then developed through NC code modification. The differential relationship between the NC code and the corresponding real toolpath can be expressed by Jacobi matrix. The optimal linear approximation of the compensated NC code is calculated by utilizing the Newton method. Iteratively applying this approximation progress until the deviation between the nominal and real toolpath satisfies the given tolerance. The variations of the geometric errors at different positions are also taken into account. To this end, the nominal toolpath and the geometric errors of the specific 5-axis machine tool are considered as the input. The new compensated NC code is generated as the output. The methodology can be directly utilized as the post-processor. Experimental results demonstrate the sensibility and effectiveness of the compensation method established in this study.     

Enhanced virtual machining for sculptured surfaces by integrating machine tool error models into NC machining simulation

Sculptured surface machining is a time-consuming and costly process. It requires simultaneously controlled motion of the machine axes. However, positioning inaccuracies or errors exist in machine tools. The combination of error motions of the machine axes will result in a complicated pattern of part geometry errors. In order to quantitatively predict these part geometry errors, a new application framework ‘enhanced virtual machining’ is developed. It integrates machine tool error models into NC machining simulation. The ideal cutter path in the NC program for surface machining is discretized into sub-paths. For each interpolated cutter location, the machine geometric errors are predicted from the machine tool error model. Both the solid modeling approach and the surface modeling approach are used to translate machine geometric errors into part geometry errors for sculptured surface machining. The solid modeling approach obtains the final part geometry by subtracting the tool swept volume from the stock geometric model. The surface modeling approach approximates the actual cutter contact points by calculating the cutting tool motion and geometry. The simulation results show that the machine tool error model can be effectively integrated into sculptured surface machining to predict part geometry errors before the real cutting begins.     

基于岭回归的数控机床温度布点优化及其热误差建模

提出一种基于岭回归分析的数控机床温度布点优化方法.数控机床热误差建模一般采用多元线性回归方法,在多元线性回归模型中,隐含着要求解释变量之间无强相关性的假定.然而在实际的建模中,各自变量与因变量之间的相互关系并不与简单相关系数所反映的情况完全吻合.通过岭迹对温度变量进行优化选择,实现了温度测点优化布置,并选用适当的岭参数k建立了数控机床热误差的多元线性回归优化模型,提高了热误差模型的精确性和鲁棒性.     

立式加工中心空间误差验证及补偿

为提高某立式加工中心整机加工精度,借助旋量理论建立完备立式加工中心空间误差模型,在此基础上实现机床空间误差有效补偿.以旋量理论为基础推导并建立机床刀具运动链与工件运动链运动学正解,分析机床21项几何误差原理,在考虑21项几何误差的基础上建立该立式加工中心完备空间误差模型;利用九线法完成各项几何误差辨识;基于旋量运动学正解求解机床运动学逆解后得出运动轴实际运动路径,并通过体对角线实验对比补偿前后的效果.结果表明:所提补偿方法补偿效果显著,验证了机床空间误差模型的准确性,实现了提高机床加工精度的目的.     

立式加工中心关键几何误差判定与量化验证

针对现阶段机床空间误差模型不完整且传统灵敏度分析存在局限性,导致其关键几何误差溯源不准确,以及关键几何误差判定结果难以量化验证的问题,以某立式加工中心为研究对象,提出一种机床关键几何误差判定与量化验证方法。以旋量理论为基础,研究某立式加工中心空间误差建模,以输出机床完整空间误差模型;在此基础上,以基于传统局部灵敏度分析为基础,利用误差贡献度因子判定机床关键几何误差;借助数值模拟实验对判定结果进行量化验证。结果表明：相较于传统灵敏度分析结果,利用误差贡献度因子判定关键几何误差的结果更准确;基于误差贡献度因子的判定结果,不仅能量化几何误差相对机床空间误差的影响程度,同时可为机床部件制造精度设计提供理论参考。     

四轴联动加工中心几何误差软件补偿技术研究

以多体系统理论为基础,通过分析位移变换矩阵和位置变换矩阵,建立了四轴联动加工中心的几何误差模型.基于Windows平台开发了误差补偿软件,可以对测量数据进行机床几何误差的软件补偿,有效地提高了在线检测精度.软件系统在MAKINO立式加工中心上进行了实验验证,补偿效果明显.     

基于敏感度分析的机床关键几何误差元素辨识与评定

为了正确识别和判定机床关键几何误差元素对机床精度设计的影响,以PCV-620立式加工中心为研究对象,采用多体系统理论建立机床空间误差模型,从而得到机床几何误差元素与机床精度之间的关联函数。对空间误差模型进行灵敏度分析,获得机床各运动方向的局部灵敏度系数,完成机床关键几何误差元素的初步辨识。以局部灵敏度系数为基础,提出一种与局部灵敏度系数和工作空间中任意位置处的几何误差元素值相关的全局灵敏度系数计算方法,将其作为机床关键几何误差元素的辨识和评定标准,分析得到PCV-620立式加工中心的关键几何误差元素包含3项定位误差、3项垂直度误差和5项直线度误差。     

Evaluation of servo,geometric and dynamic error sources on five-axis high-speed machine tool

Many sources of errors exist in the manufacturing process of complex shapes. Some approximations occur at each step from the design geometry to the machined part.The aim of the paper is to present a method to evaluate the effect of high-speed and high dynamic load on volumetric errors at the tool center point.The interpolator output signals and the machine encoder signals are recorded and compared to evaluate the contouring errors resulting from each axis follow-up error. The machine encoder signals are also compared to the actual tool center point position as recorded with a non-contact measuring instrument called CapBall to evaluate the total geometric errors. The novelty of the work lies in the method that is proposed to decompose the geometric errors into two categories: the quasi-static geometric errors independent from the speed of the trajectory and the dynamic geometric errors, dependent on the programmed feed rate and resulting from the machine structure deflection during the acceleration of its axes.The evolution of the respective contributions for contouring errors, quasi-static geometric errors and dynamic geometric errors is experimentally evaluated and a relation between programmed feed rate and dynamic errors is highlighted.     

Prediction and identification of rotary axes error of non-orthogonal five-axis machine tool

This paper proposes an efficient and automated scheme to predict and identify the position and motion errors of rotary axes on a non-orthogonal five-axis machining centre using the double ball bar (DBB) system. Based on the Denavit-Hartenberg theory, a motion deviations model for the tilting rotary axis B and rotary C of a non-orthogonal five-axis NC machine tool is established, which considers tilting rotary axis B and rotary C static deviations and dynamic deviations that total 24. After analysing the mathematical expression of the motion deviations model, the QC20 double ball bar (DBB) from the Renishaw Company is used to measure and identify the motion errors of rotary axes B and C, and a measurement scheme is designed. With the measured results, the 24 geometric deviations of rotary axes B and C can be identified intuitively and efficiently. This method provides a reference for the error identification of the non-orthogonal five-axis NC machine tool.     

A general approach for error modeling of machine tools

This paper presents a general and systematic approach for geometric error modeling of machine tools due to the geometric errors arising from manufacturing and assembly. The approach can be implemented in three steps: (1) development of a linear map between the pose error twist and source errors within machine tool kinematic chains using homogeneous transformation matrix method; (2) formulation of a linear map between the pose error twist and the error intensities of a machine tool; (3) combination of these two models for error separation. The merit of this approach lies in that it enables the source errors affecting the compensatable and uncompensatable pose accuracy of the machine tool to be explicitly separated, thereby providing designers and/or field engineers with an informative guideline for the accuracy improvement by suitable measures, i.e. component tolerancing in design, manufacturing and assembly processes, and error compensation. Two typical multi-axis machine tools are taken as examples to illustrate the generality and effectiveness of this approach.     

机床误差正交光栅检测及补偿的研究

文章提出了多轴机床空间误差的平面正交光栅检测和补偿方法.建立了包含21项几何误差的数控机床误差模型,给出了应用神经网络进行空间误差识别和补偿的技术.通过试验对比,验证了该方法的可行性.     

Geometric and force errors compensation in a 3-axis CNC milling machine

This paper proposes a new off line error compensation model by taking into accounting of geometric and cutting force induced errors in a 3-axis CNC milling machine. Geometric error of a 3-axis milling machine composes of 21 components, which can be measured by laser interferometer within the working volume. Geometric error estimation determined by back-propagation neural network is proposed and used separately in the geometric error compensation model. Likewise, cutting force induced error estimation by back-propagation neural network determined based on a flat end mill behavior observation is proposed and used separately in the cutting force induced error compensation model. Various experiments over a wide range of cutting conditions are carried out to investigate cutting force and machine error relation. Finally, the combination of geometric and cutting force induced errors is modeled by the combined back-propagation neural network. This unique model is used to compensate both geometric and cutting force induced errors simultaneously by a single model. Experimental tests have been carried out in order to validate the performance of geometric and cutting force induced errors compensation model.     

机床空间精度预测与NC代码补偿研究

以某立式加工中心为研究载体,提出一种空间精度补偿技术。以旋量理论为基础,在充分考虑机床切削点空间位置的基础上,建立包含全部几何误差的立式加工中心空间精度模型,同时输出空间精度显示预测模型。针对传统空间精度补偿不充分的局限性,将空间精度补偿思路转换为NC代码最优化问题,基于遗传算法求解该最优化问题,通过实验验证优化结果的有效性。结果表明：基于旋量理论的机床空间精度建模包含21项几何误差,空间精度预测结果较为准确;基于NC代码最优化的空间精度补偿技术使得机床空间定位精度最大补偿率为90.94%,验证了所提方法的有效性。     

Adaptive Monte Carlo applied to uncertainty estimation in five axis machine tool link errors identification with thermal disturbance

Knowledge of a machine tool axis to axis geometric location errors allows compensation and corrective actions to be taken to enhance its volumetric accuracy. Several procedures exist, involving either lengthy individual test for each geometric error or faster single tests to identify all errors at once.This study focuses on the closed kinematic chain method which uses a single setup test to identify the eight link errors of a five axis machine tool. The identification is based on volumetric error measurements for different poses with a non-contact Cartesian measuring instrument called CapBall, developed in house.In order to evaluate the uncertainty on each identified error, a multi-output Monte Carlo approach is implemented. Uncertainty sources in the measurement and identification chain – such as sensors output, machine drift and frame transformation uncertainties – can be included in the model and propagated to the identified errors. The estimated uncertainties are finally compared to experimental results to assess the method. It also reveals that the effect of the drift, a disturbance, must be simulated as a function of time in the Monte Carlo approach.Results shows that the machine drift is an important uncertainty source for the machine tested.