Modeling and analysis of servo dynamics errors on measuring paths of five-axis machine tools

Dynamic error is one of the major error sources for five-axis machine tools in achieving high-speed machining. It can be estimated and compensated by means of servo dynamics modeling and servo control method. This paper presents a contour error model on five-axis measuring paths where the dynamics and contour errors of the tool center point (TCP) can be estimated accurately during five-axis synchronized motions. The forward and inverse kinematics equations are derived according to the kinematic configuration of a C-type five-axis machine. To generate smooth measuring paths, the S-shape acceleration/deceleration (ACC/DEC) method is applied on planning the motion trajectory. The contour error model of the TCP is derived by substituting the commands of the measuring trajectory into the servo dynamics models. To investigate how the contour charts of the TCP are affected by the dynamic gains of five-axis servo loops, twelve combinations under different gains are studied. It is shown that, for the CK2 path, the steady-state contour error consists of an offset and a double-circular trajectory which is quite different from that of two-axis contour path. By tuning the gains of the servo loops, the dynamics mismatch among five axes can be eliminated and the contour error of the TCP (CETCP) can be reduced. To validate the contour error equations, simulations and experiments are performed to demonstrate that the proposed method improves the contouring performance of the TCP significantly when performing five-axis synchronized motions.     

Pre-compensation of contour errors in five-axis CNC machine tools

This paper presents an analytical prediction and compensation of contouring errors in five-axis machining of splined tool paths. The position commands are first fitted to piecewise quintic splines while respecting velocity, acceleration and jerk continuity at the spline joints. The transfer function of each servo drive is kept linear by compensating the disturbance effect of friction with a feed-forward block. Using the analytically represented five-axis, splined tool path, splined tracking errors and kinematic model of the five-axis machine tool, contouring errors are predicted ahead of axis control loops. The contouring errors are decoupled into three linear and two rotary drives, and the position commands are modified before they are sent to servo drives for execution. The proposed method has been experimentally demonstrated to show significant improvement in the accuracy of contouring five-axis tool paths.     

A generalized on-line estimation and control of five-axis contouring errors of CNC machine tools

Nonlinear and configuration-dependent five-axis kinematics make contouring errors difficult to estimate and control in real time. This paper proposes a generalized method for the on-line estimation and control of five-axis contouring errors. First, a generalized Jacobian function is derived based on screw theory in order to synchronize the motions of linear and rotary drives. The contouring error components contributed by all active drives are estimated through interpolated position commands and the generalized Jacobian function. The estimated axis components of contouring errors are fed back to the position commands of each closed loop servo drive with a proportional gain. The proposed contouring error estimation and control methods are general, and applicable to arbitrary five-axis tool paths and any kinematically admissible five-axis machine tools. The proposed algorithms are verified experimentally on a five-axis machine controlled by a modular research CNC system built in-house. The contouring errors are shown to be reduced by half with the proposed method, which is simple to implement in existing CNC systems.     

A new compensation method for geometry errors of five-axis machine tools

The present study aims to establish a new compensation method for geometry errors of five-axis machine tools. In the kinematic coordinate translation of five-axis machine tools, the tool orientation is determined by the motion position of machine rotation axes, whereas the tool tip position is determined by both machine linear axes and rotation axes together. Furthermore, as a nonlinear relationship exists between the workpiece coordinates and the machine axes coordinates, errors in the workpiece coordinate system are not directly related to those of the machine axes coordinate system. Consequently, the present study develops a new compensation method, the decouple method, for geometry errors of five-axis machine tools. The method proposed is based on a model that considers the tool orientation error only related to motion of machine rotation axes, and it further calculates the error compensations for rotation axes and linear axes separately, in contrast to the conventional method of calculating them simultaneously, i.e. determines the compensation of machine rotation axes first, and then calculates the compensation associated with the machine linear axes. Finally, the compensation mechanism is applied in the postprocessor of a CAM system and the effectiveness of error compensation is evaluated in real machine cutting using compensated NC code. In comparison with previous methods, the present compensation method has attributes of being simple, straightforward and without any singularity point in the model. The results indicate that the accuracy of positioning was improved by a factor of 8–10. Hence, the new compensation mechanism proposed in this study can effectively compensate geometry errors of five-axis machine tools.     

Accuracy test of five-axis CNC machine tool with 3D probe–ball. Part I: design and modeling

The error model of CNC machine tool describes the relationship between the individual error source and its effects on the overall position errors. A practical problem in applying this technique to five-axis machine tool is that the predicted position errors cannot be justified. This paper, the first in a set of two, presents a new measurement device, the probe–ball, which can be used to measure the overall position errors of five-axis machine tools directly. To perform the accuracy test, a three-degree-of-freedom (3D) measuring probe is installed in the main spindle and a base plate is fixed on the turntable. The kinematic chain of the five-axis machine tool is then closed through connecting the central ball on the base plate with the extension bar of the probe. To generate simultaneous axes motion under the condition of closed kinematic chain, the central ball is defined as origin of the workpiece coordinate frame and the probe is driven along a path on a spherical test surface with the central ball as center. The overall position errors are measured with the 3D measuring probe. A theoretical model is derived to explain the nature of the probe–ball error measurements.     

Single setup identification of component errors for rotary axes on five-axis machine tools based on pre-layout of target points and shift of measuring reference

This paper proposes a single setup identification method of 12 component errors of rotary axes on five-axis machine tools by using a touch trigger probe and an artefact. At first, a basic idea of pre-layout of target points combined with the shift of measuring reference is proposed. Influence of setup errors of touch trigger probe and artefact on measuring results is identified quantitatively and included in error models. A single setup measuring method is then designed to identify 12 component errors of rotary axes on five-axis machine tools with a tilting head and a rotary table. The expansion of this basic idea on five-axis machine tools with other configurations is also provided. Validation and uncertainty analysis of the identified values are also provided. The measuring accuracy is guaranteed by the complete error model while the measuring efficiency is improved significantly by the single setup measuring method.     

数控机床闭环进给伺服系统运动误差的研究

机床数控系统根据插补结果发出位置控制指令对各坐标轴进行独立的位置闭环控制,驱动相应的机械传动机构,最终实现精确的轮廓进给运动.本文研究了各轴位置闭环控制特性对轮廓误差的影响,分析了两坐标轴进给运动控制系统圆弧运动时因伺服系统有限带宽引起的半径误差和运动轴性能不匹配引起的椭圆误差,并进行了仿真验证.     

Accuracy test of five-axis CNC machine tool with 3D probe-ball. Part II: errors estimation

To improve the accuracy of CNC machine tools, error sources and its effects on the overall position and orientation errors must be known. Most motional errors in the error model of five-axis machine tool can be measured with modern laser interferometer devices, but there are still some not measurable geometric errors. These not measurable errors include constant, inaccurate link errors of components such as rotary axes block, main spindle block and tool holder. After setting all measured errors in the error model, a reduced error model is defined, which describes the influence of each unknown and not measurable link error on the overall position errors of the five-axis machine tool. On the other hand, the newly developed probe-ball device can measure the overall position errors of five-axis machine tools directly. Based on the reduced model and the overall position errors, the link errors can be estimated very accurately with the least square estimation method. The error model is then fully known and can be used for advanced purposes such as error prediction and compensation.     

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.     

Accuracy enhancement of five-axis CNC machines through real-time error compensation

Although error modeling and compensation have given significant results for three-axis CNC machine tools, a few barriers have prevented this promising technique from being applied in five-axis CNC machine tools. One crucial barrier is the difficulty of measuring or identifying link errors in the rotary block of five-axis CNC machine tools. The error model is thus not fully known. To overcome this, the 3D probe-ball and spherical test method are successfully developed to measure and estimate these unknown link errors. Based on the identified error model, real-time error compensation methods for the five-axis CNC machine tool are investigated. The proposed model-based error compensation method is simple enough to implement in real time. Problems associated with the error compensation in singular position of the five-axis machine tool are also discussed. Experimental results show that the overall position accuracy of the five-axis CNC machine tool can be improved dramatically.     

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.     

A method of testing position independent geometric errors in rotary axes of a five-axis machine tool using a double ball bar

Ensuring that a five-axis machine tool is operating within tolerance is critical. However, there are few simple and fast methods to identify whether the machine is in a “usable” condition. This paper investigates the use of the double ball bar (DBB) to identify and characterise the position independent geometric errors (PIGEs) in rotary axes of a five-axis machine tool by establishing new testing paths. The proposed method consists of four tests for two rotary axes; the A-axis tests with and without an extension bar and the C-axis tests with and without an extension bar. For the tests without an extension bar, position errors embedded in the A- and C-axes are measured first. Then these position errors can be used in the tests with an extension bar, to obtain the orientation errors in the A- and C-axes based on the given geometric model. All tests are performed with only one axis moving, thus simplifying the error analysis. The proposed method is implemented on a Hermle C600U five-axis machine tool to validate the approach. The results of the DBB tests show that the new method is a good approach to obtaining the geometric errors in rotary axes, thus can be applied to practical use in assembling processes, maintenance and regular checking of multi-axis CNC machine tools.     

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.     

基于PMAC快速PID整定与精度补偿研究

数控系统中动态性能与定位精度决定了加工质量及效率,为满足磨床数控系统控制要求及加工精度,研究快速整定PID方法及提高定位精度补偿方式,基于PMAC运动控制器搭建五轴数控工具磨床的全闭环伺服系统。针对伺服系统动态性能差、跟随误差较大等问题,阐述了基于PMAC的前馈-PID陷波滤波器伺服算法,提出了快速PID整定方法。针对定位精度差的问题,论述了定位补偿原理及方式,使用激光干涉仪进行目标点测量后制作螺距补偿和反向间隙补偿表。结果表明,PID整定方法得当,五轴磨床的动态响应性能良好,跟随误差大幅度减小;定位补偿措施合理,定位精度和重复定位精度大幅度提高,达到设计要求的3μm以内。     

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.     

五轴数控机床转动轴与平动轴联动的轮廓误差仿真分析

以主轴头两摆的五轴联动数控机床为研究对象,对转动轴与平动轴联动加工不同空间位置圆弧时的轮廓误差进行了分析。采用D-H(Denavit-Hartenberg)法对按不同圆弧路径加工时各轴的进给指令计算公式进行了推导,并将指令输入到动态仿真工具Simulink构建的进给系统仿真模型中,比较刀具理想位置与实际位置的偏差,从而得到轮廓误差曲线。通过仿真曲线分析了轮廓误差的分布特性,得到了各参数对轮廓误差影响的对应关系,利用这种关系检测机床,达到提高机床性能的目的,同时为机床的调整与维修提供一种便捷手段。     

Feed optimization for five-axis CNC machine tools with drive constraints

Real time control of five-axis machine tools requires smooth generation of feed, acceleration and jerk in CNC systems without violating the physical limits of the drives. This paper presents a feed scheduling algorithm for CNC systems to minimize the machining time for five-axis contour machining of sculptured surfaces. The variation of the feed along the five-axis tool-path is expressed in a cubic B-spline form. The velocity, acceleration and jerk limits of the five axes are considered in finding the most optimal feed along the tool-path in order to ensure smooth and linear operation of the servo drives with minimal tracking error. The time optimal feed motion is obtained by iteratively modulating the feed control points of the B-spline to maximize the feed along the tool-path without violating the programmed feed and the drives’ physical limits. Long tool-paths are handled efficiently by applying a moving window technique. The improvement in the productivity and linear operation of the five drives is demonstrated with five-axis simulations and experiments on a CNC machine tool.     

Double ballbar test for the rotary axes of five-axis CNC machine tools

In this paper a new method that uses the double ballbar to inspect motion errors of the rotary axes of five-axis CNC machine tools is presented. The new method uses a particular circular test path that only causes the two rotary axes to move simultaneously and keeps the other three linear axes stationary. Therefore, only motion errors of the two rotary axes will be measured during the ballbar test. The theoretical trace patterns of various error origins, including servo mismatch and backlash, are established. Consequently, the error origins in the rotary block can be diagnosed by examining whether similar patterns appear in the motion error trace. The method developed was verified by practical tests, and the servo mismatch of the rotary axes was successfully detected.     

数控机床动态轨迹误差仿真与优化研究

在介绍数控机床加工轨迹运动控制原理的基础上,对数控机床动态轨迹误差进行了仿真研究,得出数控机床动态轨迹误差与拟加工曲线的曲率和机床进给速度相关的结论。在待加工的工件几何曲线曲率已定情况下,提出了变进给速度的数控机床动态轨迹误差优化策略,仿真结果表明:该控制策略能够有效地减少机床动态轨迹误差量,提高相关轨迹曲线的加工精度。     

Measurement and verification of position-independent geometric errors of a five-axis machine tool using a double ball-bar

In this study, position-independent geometric errors, including offset errors and squareness errors of rotary axes of a five-axis machine tool are measured using a double ball-bar and are verified through compensation. In addition, standard uncertainties of measurement results are calculated to establish their confidence intervals. This requires two measurement paths for each rotary axis, which are involving control of single rotary axis during measurement. So, the measurement paths simplify the measurement process, and reduce measurement cost including less operator effort and measurement time. Set-up errors, which are inevitable during the installation of the balls, are modeled as constants. Their effects on the measurement results are investigated to improve the accuracy of the measurement result. A novel fixture consisting of flexure hinges and two pairs of bolts is used to minimize set-up error by adjusting the ball's position located at the tool nose. Simulation is performed to check the validation of measurement and to analyze the standard uncertainties of the measurement results. Finally, the position-independent geometric errors of the five-axis machine tool (involving a rotary axis and a trunnion axis) are measured using proposed method.