Total ballbar dynamic tests for five-axis CNC machine tools

The linear and rotary axes of a five-axis machine tool are driven simultaneously to generate a specified tool position and orientation in workpiece coordinates. It is crucial that these servo-controlled axes are of balanced dynamics to achieve high tracking accuracy. In this paper, ballbar circular tests for all possible combinations of linear and rotary axes of a five-axis machine tool are investigated and total ballbar dynamic tests are proposed. Through the relational arrangement of the test sequence, the total ballbar dynamic tests can be employed to identify dynamic differences between linear and rotary axes. More importantly, the velocity gains of the position control loops of all servo-controlled linear and rotary axes can be tuned synchronously to eliminate gain mismatch errors. Experimental results have proved the effectiveness of the new methods.     

Ballbar dynamic tests for rotary axes of five-axis CNC machine tools

This paper proposes a new ball bar test method for the inspection of dynamic errors of rotary axes in five-axis CNC machine tools. The test circle is defined in a workpiece coordinate system and the ball bar test is performed by simultaneously driving of linear–rotary axis couple. The effects of the center position and the radius on the setting values, rotational range and measurement sensitivity of the rotary axis were investigated. The proposed ball bar test is performed in two steps: the circular positioning and the circular tracking with a continuous feed. Axial dynamic errors are obtained by subtracting the measured tracking errors from the positioning errors. A ball bar test system (BBTS) was developed to plan the tool path and the tool orientation, to communicate with the five-axis CNC controller and to process the measured data. Error patterns were simulated regarding the gain mismatch, backlash and tracking direction to help a fast diagnosis of the error sources. Simulations and experimental results prove the effectiveness of the new test method.     

Modeling and improvement of dynamic contour errors for five-axis machine tools under synchronous measuring paths

In this paper, a contour error model of the tool center point (TCP) for a five-axis machine tool is proposed to estimate dynamic contour errors on three types of measuring paths. A servo tuning approach to achieve five-axis dynamic matching is utilized to improve contouring performance of the cutting trajectory. The TCP control function is developed to generate measuring trajectories where five axes are controlled simultaneously to keep the TCP at a fixed point. The interpolation method of the rotary axes with S-shape acceleration/deceleration (ACC/DEC) is applied to plan smooth five-axis velocity profiles. The contour error model for five axes is derived by substituting five-axis motion commands into servo dynamics models. The steady state contour error (SSCE) model is demonstrated to illustrate three particular dynamic behaviors: the single-circle with amplitude modulation, double-circle effect and offset behavior. Furthermore, the model is also utilized to investigate the behaviors of dynamic contour errors change in 3D space. The factors that affect dynamic contour errors, including the initial setup position, feedrate and five-axis servo gains, are analyzed. With the developed servo tuning process under the measuring paths (CK1, CK2 and CK4), the contour errors caused by servo mismatch are reduced remarkably. Finally, experiments are conducted on a desktop five-axis engraving machine to verify the proposed methodology can improve dynamic contouring accuracy of the TCP significantly.     

Geometric error measurement and identification for rotary table of multi-axis machine tool using double ballbar

In this paper, comprehensive geometric errors, including linkage errors and volumetric errors, of a rotary table are measured totally by employing a double ballbar and obtained by a two-step identification procedure. The derivations of the center of the ball installed on the table are measured in the error sensitive directions with newly developed serial of two axes controlled circular paths. Hence, there are nine results measured from three mounting positions of the ball at the same rotation angle. These results are used to form the identification model based on the homogeneous transformation. Moreover, a sensitivity analysis method is applied to select the optimum installation parameters of the ballbar to diminish the influence of the inaccuracy of the measurement parameters. As the mounting position errors of the socket on the table are inevitable during the installation of the balls, a new correction procedure is developed as well. Finally, an experiment is conducted on the four-axis machining center. The comparison results between the predicted errors and the measured results are shown to verify the proposed 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.     

Validation of volumetric error compensation for a five-axis machine using surface mismatch producing tests and on-machine touch probing

In order to validate volumetric error compensation methods for five-axis machine tools, the machining of test parts has been proposed. For such tests, a coordinate measuring machine (CMM) or other external measurement, outside of the machine tool, is required to measure the accuracy of the machined part. In this paper, a series of machining tests are proposed to validate a compensation strategy and compare the machining accuracy before and after the compensation using only on-machine measurements. The basis of the tests is to machine slots, each completed using two different rotary axes indexations of the CNC machine tool. Using directional derivatives of the volumetric errors, it is possible to verify that a surface mismatch is produced between the two halves of the same slot in the presence of specific machine geometric errors. The mismatch at the both sides of the slot, which materializes the machine volumetric errors is measured using touch probing by the erroneous machine itself and with high accuracy since the measurement of both slot halves can be conducted using a single set of rotary axes indexation and in a volumetric region of a few millimetres. The effect of a compensation strategy is then validated by comparing the surface mismatch value for compensated and uncompensated slots.     

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.     

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.     

基于球杆仪的PRS-XY型混联数控机床关键结构参数误差快速检测技术

对PRS-XY型混联数控机床的关键结构参数误差的快速检测技术进行了研究.提出了影响机床运动精度的关键结构参数,并建立了误差计算模型,进而提出了能够反映机床运动性能的球杆仪测试方案.通过仿真计算,得到了关键结构参数误差对检测结果的影响,并通过实验进行了验证.最终建立了PRS-XY型混联数控机床关键参数误差与检测相关结果的对应关系,为快速误差诊断提供了依据.     

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.     

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.     

On-machine measurement of location errors on five-axis machine tools by machining tests and a laser displacement sensor

This paper proposes an on-machine measurement (OMM) of all location errors on five-axis machine tools. Five machining patterns are successively performed on a cubic workpiece. The basic idea is to use a set of large rotations of rotary axes to prolong the moving distance of linear axes when squareness errors of linear axes are identified. Then, a set of small rotations of rotary axes are used to decouple the squareness errors of linear and rotary axes. Based on this, the long and deep slots in previous machining tests are improved to be a set of short and shallow ones. These miniaturized slots reduce the material removal and minimize the influence of cutting force and thermal deformation on the measuring results. Then the cutting tool is substituted by a laser displacement sensor (LDS) to measure the mismatch between the finished surfaces of the corresponding slots. All the measured surfaces are located on the bottom of the slots to fit the LDS characteristic of one dimensional measurement. Three gestures of the rotary table and tilting head are used to implement the single-setup OMM and the influence of location errors on the measuring results is compensated. Validation of the identified values is also provided by a set of simple tests using different measuring instruments. The efficiency and accuracy of location errors measurement method on five-axis machine tools are improved.     

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.     

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.     

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.     

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.     

Error map construction for rotary axes on five-axis machine tools by on-the-machine measurement using a touch-trigger probe

Position-dependent geometric errors, or “error map,” of a rotary axis represent how position and orientation of the axis of rotation change with its rotation. This paper proposes a scheme to calibrate the error map of rotary axes by on-the-machine measurement of test pieces by using a contact-type touch-trigger probe installed on the machine's spindle. The present scheme enables more efficient and automated error calibration, which is crucial to implement periodic check of rotary axes error map or periodic update of its numerical compensation for five-axis machine tools. The uncertainty analysis of the error calibration is also presented with a particular interest in the influence of error motions of linear axes. The experimental demonstration is presented.     

Single setup estimation of a five-axis machine tool eight link errors by programmed end point constraint and on the fly measurement with Capball sensor

Five-axis machine tools can be programmed to keep a constant nominal tool end point position while exercising all five axes simultaneously. This kinematic capability allows the use of a 3D proximity sensing head mounted at the spindle to track the position changes of a precision steel ball mounted on the machine table effectively measuring the 3D Cartesian volumetric errors of the machine. The new sensing head uses capacitive sensors to gather data on the fly during a synchronized five-axis motion which lasts less than 2 min. Because the measured volumetric errors are strongly affected by the link geometric errors, they can be used to estimate the link errors through an iterative procedure based on an identification Jacobian matrix. The paper presents the new sensor, the identification model and the experimental validation. The approach allows all eight link errors i.e. the three squarenesses of linear axes and the four orientations and center lines offset of the rotary axes to be estimated with the proposed single setup test. The estimation approach is performed on a horizontal five-axis machine tool. Then, using the estimated link errors, the volumetric errors are predicted for axes combinations different from those used for the identification process. The estimated machine model correctly predicts 52–84% of the volumetric errors for the tested trajectories.     

基于空间样条曲线的数控五轴机床误差辨识研究

在划分球杆仪空间误差辨识区域的基础上,基于NUBRS空间样条曲线生成辨识轨迹。分析球杆仪空间辨识原理,并依据此原理建立适用于NUBRS空间曲线的误差辨识模型,该模型包含18个误差因素。依据五轴机床多体运动学的分析结果,提出了一种空间误差辨识方法。通过激光干涉仪的测量及误差补偿,在消除9项空间位移误差的基础上,使用生成的NURBS曲线对剩余9项角度误差因素进行辨识。经实验验证,在进行NUBRS曲线修正后,该方法可有效辨识出3个坐标系中的18项误差因素。     

Analysis of circular trajectory equivalent to cone-frustum milling in five-axis machining centers using motion simulator

The present paper describes the effect of the half apex angle of the cone-frustum on the motion trajectory under simultaneous five-axis motion and the effect of the sensitive direction of the ball bar when the motion trajectory is measured along the three-dimensional circular conical path. In the present paper, simulation of the measurement by means of a ball bar instrument is mainly conducted using a motion simulator developed previously. In particular, a precise mathematical model was developed to express the pitch errors of the axes of rotation of the five-axis machining center having a tilting rotary table driven by worm gears. In the experiment and simulation, primarily the center position and half apex angle of the cone-frustum were varied. In addition, two sensitive directions of the ball bar were investigated. The motion simulator incorporating the pitch error model can express the detailed trajectories obtained by the ball bar, even if the half apex angle and center position of the cone-frustum and the sensitive direction of the ball bar were changed. Then, the influence of the frictional force of the linear axes of motion, and the backlash and pitch error of the axes of rotation on the circular trajectories were analyzed. In particular, for the case of a half apex angle of 45°, the trajectory due to the errors of the axis of rotation is strongly affected by the sensitive direction of the ball bar.