Influence of position-dependent geometric errors of rotary axes on a machining test of cone frustum by five-axis machine tools

A machining test of cone frustum, described in NAS (National Aerospace Standard) 979, is widely accepted by machine tool builders to evaluate the machining performance of five-axis machine tools. This paper discusses the influence of various error motions of rotary axes on a five-axis machine tool on the machining geometric accuracy of cone frustum machined by this test. Position-independent geometric errors, or location errors, associated with rotary axes, such as the squareness error of a rotary axis and a linear axis, can be seen as the most fundamental errors in five-axis kinematics. More complex errors, such as the deformation caused by the gravity, the pure radial error motion of a rotary axis, the angular positioning error of a rotary axis, can be modeled as position-dependent geometric errors of a rotary axis. This paper first describes a kinematic model of a five-axis machine tool under position-independent and position-dependent geometric errors associated with rotary axes. The influence of each error on machining geometric accuracy of a cone frustum is simulated by using this model. From these simulations, we show that some critical errors associated with a rotary axis impose no or negligibly small effect on the machining error. An experimental case study is presented to demonstrate the application of R-test to measure the enlargement of a periodic radial error motion of C-axis with B-axis rotation, which is shown by present numerical simulations to be among potentially critical error factors for cone frustum machining test.     

[误差建模及精度保证方法]几何误差贡献值影响下五轴数控机床运动轴误差灵敏度分析方法

针对现有误差元素灵敏度分析与后续误差补偿关联性不强的问题,建立运动轴几何误差贡献值模型并提出运动轴几何误差灵敏度分析方法,以获得本身几何误差对机床精度有很大影响的关键运动轴。结合指数积理论和坐标系微分运动理论建立基于误差敏感矩阵的运动轴几何误差贡献值模型,各运动轴几何误差贡献值相加得到机床综合误差模型;计算各运动轴误差权重分量和误差综合权重实现运动轴误差灵敏度分析,选择误差综合权重平均值最大的运动轴为机床关键运动轴,并对关键运动轴的误差补偿方法进行分析讨论。最后,在北京精雕集团的五轴加工中心上进行仿真实验验证。研究结果表明：所建立模型和所提出分析方法是有效的,且只补偿关键运动轴的几何误差贡献值能有效地提高五轴机床加工精度。     

High accurate squareness measurement squareness method for ultra-precision machine based on error separation

Traditional measurement methods of squareness for ultra-precision motion stage have many limitations, especially the errors caused by the inaccuracy of standard specimens. On the basis of error separation, this paper presents a novel method to measure squareness with an optical square brick. The angles between the guideways and the four lines of brick section are measured based on the fact that sum of interior angle of a quadrilateral is 2π, and the squareness is obtained. A squareness measurement experiment was performed on a profilometer with a modified optical square brick. Experimental results show that the squareness accuracy between X and Y axes is not influenced by the accuracy of brick, and the measurement repeatability reaches 0.22 arcsec. Finally, a verification experiment to the proposed method was carried out with a high accurate standard specimen, and the error between the two methods is 1.06 arcsec. According to the error results and simulation analysis of the measurement system, the measurement error based on error separation is 0.06 arcsec. The proposed method is able to achieve a very high accurate squareness measurement with auxiliary components of normal accuracy, and can be applied to measure the accuracy class of sub-arcsec squareness.     

Three-point method for measuring the geometric error components of linear and rotary axes based on sequential multilateration

The linear and rotary axes are fundamental parts of multi-axis machine tools. The geometric error components of the axes must be measured for motion error compensation to improve the accuracy of the machine tools. In this paper, a simple method named the three-point method is proposed to measure the geometric error of the linear and rotary axes of the machine tools using a laser tracker. A sequential multilateration method, where uncertainty is verified through simulation, is applied to measure the 3D coordinates. Three non-collinear points fixed on the stage of each axis are selected. The coordinates of these points are simultaneously measured using a laser tracker to obtain their volumetric errors by comparing these coordinates with ideal values. Numerous equations can be established using the geometric error models of each axis. The geometric error components can be obtained by solving these equations. The validity of the proposed method is verified through a series of experiments. The results indicate that the proposed method can measure the geometric error of the axes to compensate for the errors in multi-axis machine tools.     

The optimal design of a measurement system to measure the geometric errors of linear axes

In this paper, a measurement system consisting of an L-type reference mirror and five capacitive sensors is analyzed and optimized to measure the geometric errors of linear axes more accurately. The positions of the reference coordinate system and capacitive sensors are optimized to minimize the standard uncertainty of estimated geometric errors, which is due to the standard uncertainty of the component—the L-type reference mirror and the capacitive sensors. Primarily, the flatness of the L-type reference mirror and the linearity of the capacitive sensors cause the component uncertainties. The capacitive sensors fixed on the linear axis are moved, and the L-type reference mirror is fixed on the base of the machine tool to eliminate Abbe's error, which is proportional to the command position of a linear axis. Five geometric errors of a linear axis are measured with a single setup and single measurement, simply. Finally, the optimized measurement system is applied to measure the geometric errors of linear axes X and Y of a three-axis machine tool. And the standard uncertainties of the measured geometric errors are calculated based on the specifications of the L-type reference mirror and the capacitive sensors.     

转台-摆头式五轴机床几何误差测量及辨识

为降低转动轴几何误差对转台-摆头式五轴机床精度的影响,提出了基于球杆仪的位置无关几何误差测量和辨识方法。基于多体系统理论及齐次坐标变换方法建立了转台-摆头式五轴机床位置无关几何误差模型,依据旋转轴不同运动状态下的几何误差影响因素建立基于圆轨迹的四种测量模式,并实现10项位置无关几何误差的辨识。利用所建立的几何误差模型进行数值模拟,确定转动轴的10项位置无关几何误差对测量轨迹的影响。最后,采用误差补偿的形式实验验证所提出的测量及辨识方法的有效性,将位置无关几何误差补偿前后的测量轨迹进行比较。误差补偿后10项位置无关几何误差的平均补偿率为70.4%,最大补偿率达到88.4%,实验结果表明所提出的建模和辨识方法可用于转台-摆头式五轴机床转动轴精度检测,同时可为机床精度评价及几何精度提升提供依据。     

Product of exponential model for geometric error integration of multi-axis machine tools

This paper proposes a product of exponential (POE) model to integrate the geometric errors of multi-axis machine tools. Firstly, three twists are established to represent the six basic error components of each axis in an original way according to the geometric definition of the errors and twists. The three twists represent the basic errors in x, y, and z directions, respectively. One error POE model is established to integrate the three twists. This error POE formula is homogeneous and can express the geometric meaning of the basic errors, which is precise enough to improve the accuracy of the geometric error model. Secondly, squareness errors are taken into account using POE method to make the POE model of geometric errors more systematic. Two methods are proposed to obtain the POE models of squareness errors according to their geometric properties: The first method bases on the geometric definition of errors to obtain the twists directly; the other method uses the adjoint matrix through coordinate system transformation. Moreover, the topological structure of the machine tools is introduced into the POE method to make the POE model more reasonable and accurate. It can organize the obtained 14 twists and eight POE models of the three-axis machine tools. According to the order of these POE models multiplications, the integrated POE model of geometric errors is established. Finally, the experiments have been conducted on an MV-5A three-axis vertical machining center to verify the model. The results show that the integrated POE model is effective and precise enough. The error field of machine tool is obtained according to the error model, which is significant for the error prediction and compensation.     

Kinematic error separation on five-axis NC machine tool based on telescoping double ball bar

The theory and algorithm of the homogeneous transformation matrix (HTM) method are applied in establishing the kinematic error model of five-axis machining tool with two-axis turntable. Based on this model, a new method for the kinematic error separation in five-axis numerical control (NC) machining tool is proposed. In this study, three types of simultaneous three-axis control motions are designed for each rotary axis to identify the deviations. In the measurement, two translational axes and one rotary axis are simultaneously controlled to keep a constant distance between the tool and the worktable. Telescoping double ball bar is used to measure the relative distance between the spindle and the worktable in the motion of NC machining tool. Finally, the value measured by telescoping double ball bar is substituted into the model to obtain kinematic error of NC machining tool. Comparison has confirmed that the proposed method is high precision and can be applied to effectively and conveniently measure the five-axis machining tool.     

立式加工中心空间几何误差辨识解析及定位误差补偿研究

为大幅提升立式加工中心加工精度,满足当代数控机床对高精度的需求,针对立式加工中心3个运动轴,深入分析了其轴向运动空间几何误差,提出了可有效辨识运动轴轴向运动空间6项几何误差的辨识方法.建立了空间6项几何误差辨识模型,并针对关联轴联动垂直度误差进行了有效分析,建立了垂直度误差辨识解析模型.同时,针对3个独立运动轴轴向定位...     

Measurement and compensation of error motions of a diamond turning machine

This paper describes the measurement and compensation of error motions of a diamond turning machine for nanofabrication of large sinusoidal metrology grids. The diamond turning machine has a T-base design, which consists of a spindle with its rotation axis along the Z-direction and a cross-slide with its movement direction along the X-direction. A fast-tool-servo (FTS) unit is mounted on the X-slide to generate sinusoidal microstructures on a flat workpiece surface mounted on the spindle. The error motions of the X-slide and the spindle, which introduce Z-directional profile errors (out-of-flatness) on the grid surface, are measured and compensated. The out-of-straightness of the X-slide is measured to be approximately 60 nm over a travel of 80 mm by using the reversal method. It is also confirmed that the out-of-straightness of the X-slide has a 10-nm periodic component with a period of 11 mm corresponding to the diameter of the needles used in the roller bearing of the X-slide. The angular motion of the spindle is measured to be approximately 0.3″ by using an autocollimator, which can cause a 73-nm out-of-flatness over a workpiece 100 mm in diameter. The axial motion of the spindle is measured to be approximately 5 nm, which is the smallest error motion. The out-of-flatness of the workpiece is reduced from 0.27 to 0.12 μm through compensating for the error motions by utilizing the FTS unit based on the measurement results of error motions.     

Axis geometrical errors analysis through a performance test to evaluate kinematic error in a five axis tilting-rotary table machine tool

Geometrical work piece errors in milling process are commonly generated by different error sources. Axis geometrical errors, such as the straightness error for linear axis and the offset location error of the origin of rotary axis, introduce kinematic error in the tool path. Direct measurement of kinematic error requires special devices such as laser interferometers, grid plate encoders or double ball bars, which impose production stop and specialized staff. These problems could be analyzed using indirect measurements obtained by means of a cutting performance test that is already a standard for three axis machine tools. Because of the different architectures of five-axis milling machines these tests are hardly standardizable, therefore this paper proposes a devised easy-to-use and time efficient cutting performance test to identify and quantify axis geometrical errors for a five axis tilting-rotary table machine tool. This test can be performed as a periodical checkup or, in case of production, as a re-start test. The main goal of this study is to develop a kinematic analytical model capable of correlating the work-piece geometrical errors to the axis geometrical errors of the machine tool. The model has been implemented on a multi-body software in order to simulate the axes motion sequence of the performance test and validated to decouple the kinematic error into the geometrical axis errors. The developed models have demonstrated to be capable of correcting a generic five axis tool path by predicting the tool-path error displacement. The overall validation of this approach has been carried out by comparing the simulated and experimentally measured profile of the NAS 979 standard five axis contouring cone frustum profile.     

基于激光干涉仪的数控机床运动误差识别与补偿

提出了数控机床运动误差的软件补偿方法。采用刚体运动假设和齐次坐标变换建立了多轴机床空间运动误差的通用模型。该模型把刀具相对于工件的空间误差表示为机床各结构件之间运动误差的位置函数。给出了全部运动误差参数的激光干扰仪识别方法，提出了一种新的roll误差测量措施，在立式加工中心上进行了运动误差的补偿实验，结果证明所提出的运动误差软件联动补偿效果显著。     

A new methodology for identifying location errors in 5-axis machine tools using a single ballbar set-up

Ballbar testing of rotary axes in 5-axis machine tools can be time-consuming and requires high levels of operator expertise; especially in the set-up process. Faster tests reduce down-time and encourage frequent updates to compensation parameters to reflect the current state of the machine. A virtual machine tool (VMT) is developed to emulate the machine tool, its geometric errors and the testing procedures. This was used to develop a new single set-up testing method to identify all rotary axis locations errors, whilst remaining robust in the presence of set-up error and linear axis squareness errors. New testing and data processing techniques remove the requirement for fine-adjustment of the tool-cup and permit full automation of necessary toolpaths, including transitions. Using the VMT, error identification residuals were found to be 2.7 % or less. Experiments and statistical analysis then showed that all errors can be measured using a single set-up, and values are sufficiently close to the values measured using conventional multi-set-up procedures to be used in error compensation. This method will significantly reduce set-up durations and removes the need for any modified testing hardware.     

Dynamic and geometric error assessment of an XYC axis subset on five-axis high-speed machine tools using programmed end point constraint measurements

This paper presents a technique for assessing the volumetric errors on a five-axis machine tool for motion involving two linear axes and one rotary axis at selected feed rates using data from two sources. The first source of data is obtained through a programmed end point constraint procedure with measurement of the 3D volumetric positioning errors between a point on the tool holder and another fixed to the machine table reference frame. The tests involve maintaining the nominal coincidence of these two points whilst exercising the three axes. The second source of data is the position feedback signal from the encoder provided by the machine controller. Tests were carried out at low and high feed rates to evaluate the effect of geometric and dynamic errors. Polynomial functions are used to represent and then predict the geometric errors. The predicted geometric errors are then added to the dynamic errors provided by the servo errors from position feedback signals and propagated to the tool centre point and are compared with the measured volumetric errors. It shows that the influence of the geometric errors are dominant at low feed, whereas the effects of the servo errors of the linear axes become dominant as the feed increases, reaching 80% of the total error at a feed of 10,000 mm/min.     

Position error reduction of tool center point in multi-tasking machine tools through compensating influence of geometric deviations identified by ball bar measurements

A method to compensate the influence of geometric deviations on tool center point (TCP) for a multi-tasking machine tool is proposed in this paper. Some methods to compensate geometric deviations of a rotary axis in five-axis machining centers have been proposed. However, due to the special topological structure of multi-tasking machine tools, the identification and compensation methods for geometric deviations are different from those of the five-axis machining centers, which have been seldom researched until now. In this paper, the main attention is paid to analyze the eccentricities of the trajectories measured by a ball bar under simultaneous three-axis motions and to reduce the influence of the identified geometric deviations on the position error of TCP by the compensation method. It is divided into two sequential subtasks. At first, the geometric deviations are identified by using the eccentricities of measured trajectories. A simple and practical measuring procedure is proposed to identify geometric deviations of rotary axes existing in a multi-tasking machine tool. For the second step, a method is proposed by modifying the original NC code according to the kinematic chain model of the targeted machine tool to compensate the influence of the existing geometric deviations on TCP. An experiment is conducted on a multi-tasking machine tool with a swivel tool spindle head in the horizontal position. The repeatability of the measured eccentricities based on three experimental results is also investigated to reduce the influence of measuring error on the identified results. As a result, the corresponding values of geometric deviations after the compensation are less than 2.2 arcseconds or 2.4 μm. It is concluded that the influence of geometric deviations on TCP is compensated effectively, and the position error of TCP is reduced significantly.     

Applying bidirectional kinematics to assembly error analysis for five-axis machine tools with general orthogonal configuration

Since a five-axis machine tool has two more rotary axes and two more degrees of freedom than a three-axis machine tool, it can manufacture a complex surface more efficiently. However, there are more error terms due to the extra axes. Error sources for machine tools include structural error, dynamic error, and static error. The static error, which includes thermal and geometric errors, is the main source of machining inaccuracy in machine tools. Although a large number of studies have been made on geometric errors, the influence of individual error term on volumetric error is seldom discussed. This paper analyzes assembly error that belongs to the category of static error, and the analytic method can be applied to general orthogonal configurations. By adopting the machine tool form-shaping function, the effect of assembly errors on volumetric errors has been investigated. And the error terms that cannot be compensated by driving single control axis have been recognized and explored for general orthogonal configurations.     

Machine tool calibration: Geometric test uncertainty depends on machine tool performance

In order to show a sufficient geometric performance, every machine tool has to be calibrated geometrically before it may come into operation. The geometric machine errors have to be identified. They can afterwards be compensated either mechanically or numerically in the machine control.Machine tools are usually calibrated geometrically by performing a sequence of different measurements to identify single errors such as squareness errors between linear axes, straightness errors, positioning errors etc.The uncertainty of such measurements is of course affected by the uncertainty of the measuring device under the given environmental conditions. Methods to describe such influences are widely known and applied.Other effects having an impact on the error parameters to be determined (e.g. squareness errors) are dependent on the performance of the machine tool under test. Neglected geometric errors, hysteresis and thermal drift affect the measurement result. Such effects may be much more important contributors to the overall test uncertainty than the measurement uncertainty of the measuring device.In this paper the problem of error interdependencies leading to a worse test uncertainty is explained. The occurrence of such effects is shown with exemplary measuring results. A method for estimating the overall test uncertainty even for complex measurements is introduced. The dependence of the test uncertainty on the geometric machine performance is explained.     

可配置型五坐标B样条插补控制器的研制

针对采用五轴联动数控机床的线性插补功能进行数控加工存在的不足,提出了一种B样条插补控制策略用于五轴联动数控机床以实现复杂曲面零部件的高速高精数控加工。参考开放式、模块化体系结构控制器(OMAC)标准,开发了具有B样条插补功能的五轴联动数控机床运动控制器。该控制器将控制任务按照实时性要求进行划分。人机交互、代码解析及参数映射关系构造等过程离线完成,插补运算、离散逻辑控制及逆运动学变换等过程由实时线程执行,保证了数控系统的硬实时性。为简化NC程序的编制过程,控制器设计为接收工件坐标系下的加工信息。通过开发适应各种形式数控机床的逆运动学变换模块,并将机床参数设计为可用户定制,使得控制器具有良好的通用性。在控制器内部建立NC程序文件中位置曲线和方位曲线间的参数映射关系,使得机床平动轴与转动轴间的运动规划符合实际加工要求,并可保证加工精度。实际加工实验中,在采用B样条插补算法的NC程序量降低为线性插补NC程序量15%倍时,其插补误差为线性插补误差的45%,控制器插补精度为0.68,表明该B样条插补控制器可以满足五坐标数控加工的要求。     

Mapping and compensation of geometric errors of a machine tool at different constant ambient temperatures

Thermo-mechanical effects due to changes in the ambient temperature on the shop floor and internal heat sources caused by the manufacturing process significantly contribute to the geometric deviations of a machine tool and therefore, the geometric deviations of the manufactured workpiece. Minimizing these thermally induced geometric deviations is worthwhile since the requested tolerances of machined workpieces become continually smaller nowadays. To investigate the overall deformations of a machine tool structure due to variations in ambient temperature the geometric errors of a five-axis machine tool at different ambient temperatures by means of a portable climate simulation chamber are systematically mapped. While positioning and squareness errors of the linear axes are significantly influenced by the ambient temperature, straightness as well as rotational errors were less sensitive to temperature effects. For the investigated machine tool errors of the two rotational axes are negligible due to an active cooling of these axes. Through numerical error compensation of the linear axes, the geometric errors of the investigated machine tool can be reduced up to 80%. Finally, an outlook how a temperature-dependent compensation could be derived from previously measured compensation fields at discrete temperatures and afterwards applied on-the-fly during manufacturing is given.     

Geometric error modeling and compensation for large-scale grinding machine tools with multi-axes

Synthesis modeling of a geometric error-based traditional method for large-scale grinding machine tools with six axes is too complicated to perform in a real-time compensator with a built-in position control system, and it is difficult to obtain all of the error elements corresponding to the model. This paper proposed a novel strategy in which a machine may be considered as translation axes and rotary axes, and geometric errors of the translation axes and rotary axis are modeled and the geometric error models of the machine are very simple for real-time error compensation. The volumetric errors of the translation axes are measured using spatial circular curve ball bar test, and every element of the rotary axis is also obtained by a series of considerate ball bar tests. According to the characteristics of a position controller used in the machine, a synthesis error compensation system based on the NUM numerical control system was developed. Error compensation experiments were carried out, and the results show that the accuracy of the machine is improved significantly.