Derivation of machine tool error models and error compensation procedure for three axes vertical machining center using rigid body kinematics

Volumetric positional accuracy constitutes a large portion of the total machine tool error during machining. In order to improve machine tool accuracy cost-effectively, machine tool geometric errors as well as thermally induced errors have to be characterized and predicted for error compensation. This paper presents the development of kinematic error models accounting for geometric and thermal errors in the Vertical Machining Center (VMC). The machine tool investigated is a Cincinnati Milacron Sabre 750 3 axes CNC Vertical Machining Center with open architecture controller. Using Rigid Body Kinematics and small angle approximation of the errors, each slide of the three axes vertical machining center is modeled using homogeneous coordinate transformation. By synthesizing the machine's parametric errors such as linear positioning errors, roll, pitch and yaw etc., an expression for the volumetric errors in the multi-axis machine tool is developed. The developed mathematical model is used to calculate and predict the resultant error vector at the tool–workpiece interface for error compensation.     

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.     

Analysis of geometric errors associated with five-axis machining centre in improving the quality of cam profile

A five-axis machine is presently one of the most versatile machine tools available and they are becoming increasingly common. To increase the accuracy capabilities of such machines, it is crucial to be able to study the geometric errors of the components and its effect on the quality of machined products. In five-axis machine tools, all linear axes are theoretically perpendicular (dot product, cos 90°=0) to each other and directed along or around the X, Y and Z of the cartesian coordinate system; but in working machines, the axes are nearly perpendicular (cos89.90°≠0) because of manufacturing error and assembly error or quasi-static error. The present paper discusses the development of a generalised error model for the effects of geometric errors of the components of the kinematic chain of a machine in the workspace and the results obtained by this model have been verified experimentally. The effect of geometric error has been studied further for cam profile generation using a five-axis machining centre and an improvement in the profile has been obtained.     

A machining test to calibrate rotary axis error motions of five-axis machine tools and its application to thermal deformation test

This paper proposes a machining test to parameterize error motions, or position-dependent geometric errors, of rotary axes in a five-axis machine tool. At the given set of angular positions of rotary axes, a square-shaped step is machined by a straight end mill. By measuring geometric errors of the finished test piece, the position and the orientation of rotary axis average lines (location errors), as well as position-dependent geometric errors of rotary axes, can be numerically identified based on the machine׳s kinematic model. Furthermore, by consequently performing the proposed machining test, one can quantitatively observe how error motions of rotary axes change due to thermal deformation induced mainly by spindle rotation. Experimental demonstration is presented.     

Construction of an error map of rotary axes on a five-axis machining center by static R-test

This paper proposes an efficient and automated scheme to calibrate error motions of rotary axes on a five-axis machining center by using the R-test. During a five-axis measurement cycle, the R-test probing system measures the three-dimensional displacement of a sphere attached to the spindle in relative to the machine table. Location errors, defined in ISO 230-7, of rotary axes are the most fundamental error factors in the five-axis kinematics. A larger class of error motions can be modeled as geometric errors that vary depending on the angular position of a rotary axis. The objective of this paper is to present an algorithm to identify not only location errors, but also such position-dependent geometric errors, or “error map,” of rotary axes. Its experimental demonstration is presented.     

Milling error prediction and compensation in machining of low-rigidity parts

The paper reports on a new integrated methodology for modelling and prediction of surface errors caused by deflection during machining of low-rigidity components. The proposed approach is based on identifying and modelling key processing characteristics that influence part deflection, predicting the workpiece deflection through an adaptive flexible theoretical force-FEA deflection model and providing an input for downstream decision making on error compensation. A new analytical flexible force model suitable for static machining error prediction of low-rigidity components is proposed. The model is based on an extended perfect plastic layer model integrated with a FE model for prediction of part deflection. At each computational step, the flexible force is calculated by taking into account the changes of the immersion angles of the engaged teeth. The material removal process at any infinitesimal segment of the milling cutter teeth is considered as oblique cutting, for which the cutting force is calculated using an orthogonal–oblique transformation. This study aims to increase the understanding of the causes of poor geometric accuracy by considering the impact of the machining forces on the deflection of thin-wall structures. The reported work is a part of an ongoing research for developing an adaptive machining planning environment for surface error modelling and prediction and selection of process and tool path parameters for rapid machining of complex low-rigidity high-accuracy parts.     

Kinematic and geometric error compensation of a coordinate measuring machine

In this paper, kinematic modelling of a Coordinate Measuring Machine (CMM) is carried out and the methodology followed in modelling is explained in detail. The model is simplified by certain assumptions which may result in over-simplification of the model. Consequently, the model is investigated and enhanced by adding the relevant and suitable geometric error terms. Different approaches are employed to evaluate the model coefficients. In the first approach, a commercial ring gauge is measured in a structured lattice in the work volume of the CMM. Resulting errors in these measurements are used in conjunction with some statistical methods to arrive at sets of model coefficients values. The second approach is based on measurement of the individual 21 error terms in the CMM by means of laser interferometry. These measurements are used to evaluate another set of model coefficients. A compensation strategy is proposed and tested using the model and the sets of coefficients obtained. Volumetric Performance of the CMM is evaluated according to ASME standards, before and after compensation. Improvement in the CMM volumetric performance is demonstrated and compared.     

An error control approach to tool path adjustment conforming to the deformation of thin-walled workpiece

Producing an accurate part mainly depends on the position and orientation of the cutting tool with respect to the workpiece which is mainly influenced by the rigid body motion of the workpiece and the elastic deformation of workpiece-fixture-cutter system. For the purpose of minimizing the machining error, a new modification strategy of the nominal tool path is not that directly compensate the control commands of the machine tools, but that modify the cutter location source file (CLSF) from the computer aided manufacturing (CAM) system by means of the proposed modification model on the basis of the prediction deviation, namely, the deviation of the cutting tool relative to the workpiece in computer numerical control (CNC) machining operation. Therefore, it is not only simpler, but also easier implemented by common manufacturing engineer. The effectiveness of the proposed strategy is verified by a machining example.     

Analysis of setting errors in precision ballscrew machining and the automatic adjustable center

Generally, in machining precision machine elements such as ballscrews, machining errors could occur for various reasons. In this research, the influence of improper setting errors in ballscrew machining, such as misalignment between centers, runout of spindle, and unsuitable contact conditions between the center and the center hole, was analyzed. From the analysis, among the setting errors, the misalignment between centers was found to be an important one. An automatic adjustable center for 2D arbitrary positioning was designed and manufactured to eliminate the alignment error in machining workpieces supported by two centers. This adjustment system could be practically applied to reduce machining errors.     

Accuracy enhancement of five-axis machine tool based on differential motion matrix: Geometric error modeling,identification and compensation

This paper presents the precision enhancement of five-axis machine tools according to differential motion matrix, including geometric error modeling, identification and compensation. Differential motion matrix describes the relationship between transforming differential changes of coordinate frames. Firstly, differential motion matrix of each axis relative to tool is established based on homogenous transformation matrix of tool relative to each axis. Secondly, the influences of errors of each axis on accuracy of tool are calculated with error vector of each axis. The sum of these influences is integration of error components of machine tool in coordinate system of tool. It endows the error modeling clear physical meaning. Moreover, integrated error components are transformed to coordinate frame of working table for integrated error transformation matrix of machine tools. Thirdly, constructed Jacobian is established using differential motion matrix of each axis without extra calculation to compensate the integrated error components of tool. It makes compensation easy and convenient with reuse of intermediate. Fourthly, six-circle method of ballbar is developed based on differential motion matrix to identify all ten error components of each rotary axis. Finally, the experiments are carried out on SmartCNC500 five-axis machine tool to testify the effectiveness of proposed accuracy enhancement with differential motion matrix.     

轴类零件形位误差在机床上的测量技术研究

本文论述了采用误差分离技术在机床上测量轴类零件形位误差的原理，方法、给出了该方法的数据处理流程图和测量装置的组成简图，并对系统的测量准确度进行了分析。     

基于误差预测的机床精度分析与设计

数字化精度分析是当前确保机床设计精度的重要手段。精度建模与精度分析等重要手段主要针对机床几何精度、运动精度及工件表面成形运动精度。对于复杂成形运动机床,目前精度设计标准与工件加工精度之间尚无准确对应关系。为此,提出了基于误差预测的机床精度设计方案,该方案分为两阶段数字化精度分析。第一阶段通过技术系统实现工件到工艺系统各部件精度分配与检测,在规定的精度下达到机床输出精度。第二阶段通过机床系统完成机床输出到机床各组成部件精度分配与检查。文中以YK3610滚齿机为例,详细分析了两系统误差模型及应用方法,并通过试验验证机床的实际切割精度可达5-4-4等级,因此该方法为复杂成形运动机床精度的设计提供了依据。     

A unified approach for circularity and spatial straightness evaluation using semi-definite programming

This paper demonstrates that a modern optimization method known as semi-definite programming (SDP) can serve as a unified tool for circularity and spatial straightness evaluation. Based on the minimum zone criterion (MZC), the problems of circularity and spatial straightness evaluation are formulated as differentiable constrained optimization problems firstly, and then reformulated as SDP problems. Within the SDP framework, both of the two aforementioned problems can be solved efficiently using recently developed interior-point algorithms, which are available in many efficient software packages. The effectiveness and efficiency of the novel approach are illustrated by examples and numerical simulations.     

焊接机器人工艺方案技术攻关与实施

某型号航空零件在焊接中存在单件产品质量、夹具定位精度、焊接机器人运行精度等均不稳定的现象。在确保工厂效益的前提下,通过改进焊接机器人夹具、优化机器人运行程序,使焊缝质量得到保证,不再需要补焊和返工,企业产能大幅提高。     

一种快速选配机床挂轮的方法

通过计算器简单、快速的计算，可快速选配机床挂轮。     

Tool path generation and error control method for multi-axis NC machining of spatial cam

In this paper, based on the homogeneous coordinate transformation and conjugate surface theory, a tool path generation method is developed for generating spatial cam in order to establish the interface between the design and manufacture of this class of product. The mathematical error (chordal deviation) between the design and manufacture surface has been analysed and used as a basis for selecting the tool path control point. Moreover, the developed tool path generation method is verified through a cutting simulation software with solid model. It is also verified through the trial cut with model materials on a five-axis numerical controlled machine. The results show that the mathematical error of the cam surface can be controlled within given tolerance by the proposed method.     

A novel spindle inclination error identification and compensation method in ultra-precision raster milling

In the ultra-precision raster milling (UPRM) process, the existence of spindle inclination error can directly affect the dimensional accuracy of machined components. This study developed a novel spindle inclination error identification and compensation method based on the groove cutting in UPRM. In this method, the tilt angle of the intersection curve of two toruses (ICTT) generated from two neighboring rotary cuts in UPRM was measured to identify the spindle inclination error. A mathematical model was developed to simulate the ICTT profile and present the relationship between the tilt angle of ICTTs and the spindle inclination error by solving the differential of the ICTT function, by which the spindle inclination error can be solved under the given cutting parameters and the tilt angle of ICTTs. The effects of cutting parameters on the tilt angle of ICTTs were explored. An error compensation procedure was designed and a group of groove cutting experiments was conducted to identify and compensate the spindle inclination error. The theoretical and experimental results show that the proposed method can compensate for the spindle inclination error effectively and accurately.     

A new method and device for motion accuracy measurement of NC machine tools. Part 2: device error identification and trajectory measurement of general planar motions

This paper describes in two parts a new method and device for measuring motion accuracy of NC machine tools. In the first part, the measurement principle and the characteristics of the prototype device have been presented and discussed. In the second part, an efficient and practical approach to identifying the errors of the proposed device after assembly is developed and evaluated. The approach ensures realising the aim of the investigation, i.e. to measure the most items of the motion accuracy, especially, to measure and assess the trajectory accuracy of a general planar motion of NC machine tools. The result of the identification experiment by using the prototype device on a machining centre for the prototype device is presented and it well verifies the validity and practicality of the approach. Some measurement results for the general planar motions of the machining centre are also shown, which sufficiently demonstrate the desirable capability of the proposed method and device.     

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.     

Measurement of spindle thermal errors in machine tool using hemispherical ball bar test

The assurance of top-quality products in machining processes requires improved machine tool accuracy. Among the various errors related to machine tools, thermal errors of a spindle have a significant effect on machining accuracy and directly influence both the surface finish and the geometric shape of the finished workpiece. Accordingly, the current paper proposes a new measurement method for spindle thermal errors in a machine tool based on the use of a ball bar system instead of the conventional capacitance sensor system. The novel measurement method is more efficient and easier to use compared to conventional measurement systems. Furthermore, a single ball bar system is sufficient for the simultaneous measurement of both geometric and thermal errors.