Error compensation in machine tools — a review: Part II: thermal errors

Accuracy of machined components is one of the most critical considerations for any manufacturer. Many key factors like cutting tools and machining conditions, resolution of the machine tool, the type of workpiece etc., play an important role. However, once these are decided upon, the consistent performance of the machine tool depends upon its ability to accurately position the tool tip vis-à-vis the required workpiece dimension. This task is greatly constrained by errors either built into the machine or occurring on a periodic basis on account of temperature changes or variation in cutting forces. The three major types of error are geometric, thermal and cutting-force induced errors. Geometric errors make up the major part of the inaccuracy of a machine tool, the error caused by cutting forces depending on the type of tool and workpiece and the cutting conditions adopted. This part of the paper attempts to review the work done in analysing the various sources of geometric errors that are usually encountered on machine tools and the methods of elimination or compensation employed in these machines. A brief study of cutting-force induced errors and other errors is also made towards the end of this paper.     

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.     

Computer-aided accuracy enhancement for multi-axis CNC machine tool

A computer-aided error compensation scheme has been developed to enhance the accuracy of multi-axis CNC machine tools by compensating for machine geometric and thermal errors in software way. Stationary geometric errors including the coupling effect of linkage errors between machine slides are calibrated off line. Dynamic thermal errors are predicted on line by an artificial neural network model. Because machine errors are variant with the cutting time and slide positions, a PC based compensation controller has been developed to upgrade commercial CNC controllers for real-time error compensation. The real-time compensation capability is achieved by digital I/0 communication between the compensation controller and CNC controller without the need of any hardware modification to the machine servo-drive loops. The compensation scheme implemented on a horizontal machining center has been proven to improve the machine accuracy by one order of magnitude using a laser interferometer and cutting test.     

High-precision machining by measurement and compensation of motion error

This paper describes a systematic method to model and compensate geometric errors of machine tools. In order to separate geometric errors from other errors, measured errors are analyzed in the frequency domain by using the Fourier series. Then, the frequency components corresponding to geometric errors are selected based on the repeatability of their wavelength. Finally, the components are reconstructed and forwarded for the compensation by a fine motion drive. A CNC machine tool with a fine motion mechanism on the Z-axis was developed to compensate the error components in the Z direction on the XY plane. A flat surface machining with non-rotational cutting tools was tested to validate our approach. On the plane of 45 mm×70 mm, the fluctuation of the relative displacement was reduced from 1.3 to 0.5 μm P-V. Machining experiments with a single-crystal diamond tool were also carried out and the straightness of the profile curve was reduced from 1.0 to 0.4 μm. The result of the experiments showed that the geometric errors were compensated separately from the vibration due to the bending mode of the machine column.     

Tool deflection compensation in peripheral milling of curved geometries

This paper presents compensation of surface error due to cutting force-induced tool deflections in a peripheral milling process. Previous research attempts on this topic deal with error compensation in machining of straight geometries only. This paper is concerned with peripheral milling of variable curvature geometries where the workpiece curvature changes continuously along the path of cut. In the case of curved geometries, both process geometry and the cutting forces have shown to have strong dependence on workpiece curvature and hence variation of surface error along the path of cut. This calls for a different error compensation strategy than the one which is normally used for machining straight geometries. The present work is an attempt to improve accuracy in machining of curved geometries by use of CNC tool path compensation. Mechanistic model for cutting force estimation and cantilever beam model for cutter deflection estimation are used. The results based on machining experiments performed on a variety of geometries show that the dimensional accuracy can be improved significantly in peripheral milling of curved geometries.     

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.     

Error compensation in machine tools — a review: Part I: geometric,cutting-force induced and fixture-dependent errors

Accuracy of machined components is one of the most critical considerations for any manufacturer. Many key factors like cutting tools and machining conditions, resolution of the machine tool, the type of workpiece etc., play an important role. However, once these are decided upon, the consistent performance of the machine tool depends upon its ability to accurately position the tool tip vis-à-vis the required workpiece dimension. This task is greatly constrained by errors either built into the machine or occurring on a periodic basis on account of temperature changes or variation in cutting forces. The three major types of error are geometric, thermal and cutting-force induced errors. Geometric errors make up the major part of the inaccuracy of a machine tool, the error caused by cutting forces depending on the type of tool and workpiece and the cutting conditions adopted. This part of the paper attempts to review the work done in analysing the various sources of geometric errors that are usually encountered on machine tools and the methods of elimination or compensation employed in these machines. A brief study of cutting-force induced errors and other errors is also made towards the end of this paper.     

五轴数控旋风铣削机床加工螺纹的误差补偿研究

基于小误差运动假设,分析了五轴旋风铣削机床误差运动和补偿运动间的相互关系,建立了考虑工件热胀冷缩时进行其空间5个误差量计算的数学模型,为五轴旋风铣床用于螺纹精加工时的误差实时插补提供了理论基础,也是建立考虑工件热变时通用五轴旋风铣床误差实时插补数学模型及以旋风铣削精加工质量为目标函数、约束于多变量的数学模型的第一步.     

基于BP神经网络的磨床力误差补偿方法

为建立磨削加工参数与磨削力导致的力变形误差之间的关系模型,提出基于神经网络的力误差建模和实时补偿方法.建立经遗传算法优化的BP神经网络以表征磨削参数与磨削力的关系;运用有限元方法对零件进行力学分析,建立磨削力与力变形量的关系模型;建立加工参数与切削力误差映射模型,预测误差补偿量,进行实时补偿.实验结果表明:该切削力误差...     

Error compensation in flexible end milling of tubular geometries

There are many machining situations where slender tools are used to machine thin walled tubular workpieces. Such instances are more common in machining of aircraft structural parts. In these cases, cutting force induced tool as well as workpiece deflections are quite common which result into surface error on machined components. This paper presents a methodology to compensate such tool and workpiece induced surface errors in machining of thin walled geometries by modifying tool paths. The accuracy with which deflections can be predicted strongly depends on correctness of the cutting force model used. Traditionally employed mechanistic cutting force models overestimate tool and workpiece deflections in this case as the change of process geometry due to deflections is not accounted in modeling. Therefore, a cutting force model accounting for change in process geometry due to static deflections of tool and workpiece is adopted in this work. Such a force model is used in predicting tool and workpiece deflection induced surface errors on machined components and then compensating the same by modifying tool path. The paper also studies effectiveness of error compensation scheme for both synclastic and anti-clastic configurations of tubular geometries.     

五轴联动后处理中非线性误差控制的研究

文中分析了非线性误差的产生原因及有效估算方法.通过机床的运动学分析,建立了BV100五轴联动机床的运动变换数学模型;结合线性插补原理,提出了该类机床的非线性运动误差的估算及补偿模型;通过VB语言,开发了具有非线性误差补偿功能的专用后置处理器,并通过某叶轮的切削加工实验验证了该后置处理器的正确性和实用性.     

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。     

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.     

Precompensation of machine dynamics for cutting force estimation based on disturbance observer

Complex machine-structure dynamics of a movable stage affects observer-based cutting force estimation. A dynamic compensation approach based on the concept of machine-in-the-loop learning is proposed to enhance the accuracy of cutting force estimation based on a disturbance-observer. Machine dynamics induced estimation errors are pre-compensated by modifying a digital filter representing an inverse disturbance transfer function. The order and parameters of the filter are self-optimized to enhance the estimation accuracy during iterative pre-milling tests with various rotational spindle speeds. The experimental results show that the proposed self-optimized filter achieves accurate wide-band cutting force estimation in milling process.     

Accuracy improvement of miniaturized machine tool: Geometric error modeling and compensation

A novel capacitance–sensor based multi-degree-of-freedom (DOF) measurement system has been developed for measuring geometric errors of a miniaturized machine tool (mMT) overcoming the size limitations. In the present work five geometric error components of a three-axis mMT are measured simultaneously along each axis and the squareness errors are determined by the slopes of straightness error profiles. Least-squares fitting method is used to represent the analytical models of geometric errors. A kinematic chain consisting of various structural members of mMT is introduced to establish the positional relationships among its coordinate frames. Based on this kinematic chain a general volumetric error model has been developed to synthesize all geometric error components of a miniaturized machine tool. Then, a recursive compensation method is proposed to achieve error compensation efficiently. Test results show that the positioning accuracy of miniaturized machine tool has been improved with compensation.     

Tool path accuracy enhancement through geometrical error compensation

Kinematic and geometric errors of CNC machine tools, introduce large deviations in the real path traveled by the cutting tool. Tool path deviation reduces geometrical and dimensional accuracy of the machined features of the component. Tool path modification is an effective strategy to increase accuracy of the machined features. An improved error estimation model based on kinematic transformation concepts has been developed and used to calculate the volumetric overall error. These calculations are applicable for each arbitrary target positions of the machine's work space. Also a NC Program editor software has been developed in order to manage the calculations, modifications and to generate the new compensated NC program. The compensation procedure includes: fragmentation of nominal tool path to small linear elements, translating nominal position of elements to real positions using the Kinematics error model, finding compensated positions using the error compensation algorithm, converting newly generated elements to new tool paths using the packing algorithms and finally editing old NC program using NC code generator algorithm. Experimental tests showed 4-8 times accuracy improvement for linear, and S-pline tool paths deviations.     

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.     

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.     

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.