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.     

Prediction and compensation of machining geometric errors of five-axis machining centers with kinematic errors

Kinematic errors due to geometric inaccuracies in five-axis machining centers cause deviations in tool positions and orientation from commanded values, which consequently affect geometric accuracy of the machined surface. As is well known in the machine tool industry, machining of a cone frustum as specified in NAS979 standard is a widely accepted final performance test for five-axis machining centers. A critical issue with this machining test is, however, that the influence of the machine's error sources on the geometric accuracy of the machined cone frustum is not fully understood by machine tool builders and thus it is difficult to find causes of machining errors. To address this issue, this paper presents a simulator of machining geometric errors in five-axis machining by considering the effect of kinematic errors on the three-dimensional interference of the tool and the workpiece. Kinematic errors of a five-axis machining center with tilting rotary table type are first identified by a DBB method. Using an error model of the machining center with identified kinematic errors and considering location and geometry of the workpiece, machining geometric error with respect to the nominal geometry of the workpiece is predicted and evaluated. In an aim to improve geometric accuracy of the machined surface, an error compensation for tool position and orientation is also presented. Finally, as an example, the machining of a cone frustum by using a straight end mill, as described in the standard NAS979, is considered in case studies to experimentally verify the prediction and the compensation of machining geometric errors in five-axis machining.     

Influence of linear-axis error motions on simultaneous three-axis controlled motion accuracy defined in ISO 10791-6

Five-axis machine tools, which combine three linear axes and two rotary axes, are required for accuracy in machining complex shapes. In this paper, to clarify the influence of simultaneous three-axis control motion measurements as specified in ISO 10791-6, the measured results using a ball bar and R-test are compared. As the motion trajectories of the linear axes are not identical in both measurement devices, it is expected that the error motions of the linear axes cause different measurement results depending on the measurement devices. Thus, the squareness errors between the linear axes and the error motions of the linear axes are assumed as error factors that influence the measured results in this study. A mathematical model of a five-axis control machine tool that considers the error motions and squareness errors of the linear axis is constructed, and the influence of those error factors on motion accuracy is examined using an experiment and a simulation. As a result, the squareness errors and error motions of the linear axis are observed to greatly affect simultaneous three-axis controlled motion accuracy.     

Simultaneous geometric error identification of rotary axis and tool setting in an ultra-precision 5-axis machine tool using on-machine measurement

This paper presents a method to identify the position independent geometric errors of rotary axis and tool setting simultaneously using on-machine measurement. Reducing geometric errors of an ultra-precision five-axis machine tool is a key to improve machining accuracy. Five-axis machines are more complicated and less rigid than three axis machine tools, which leads to inevitable geometric errors of the rotary axis. Position deviation in the process of installing a tool on the rotary axis magnifies the machining error. Moreover, an ultra-precision machine tool, which is capable of machining part within sub-micrometer accuracy, is relatively more sensitive to the errors than a conventional machine tool. To improve machining performance, the error components must be identified and compensated. While previous approaches have only measured and identified the geometric errors on the rotary axis without considering errors induced in tool setting, this study identifies the geometric errors of the rotary axis and tool setting. The error components are calculated from a geometric error model. The model presents the error components in a function of tool position and angle of the rotary axis. An approach using on-machine measurement is proposed to measure the tool position in the range of 10 s nm. Simulation is conducted to check the sensitivity of the method to noise. The model is validated through experiments. Uncertainty analysis is also presented to validate the confidence of the error identification.     

3-RPS并联机构运动学标定方法的研究

针对六轴混联机床中因3-RPS并联机构结构参数误差引起的精度问题,分析了影响3-RPS并联机构几何精度的误差因素,给出了并联机构的误差模型;基于影响并联机构定平台运动精度较大的几何误差参数;建立了运动学标定模型.采用阻尼最小二乘法,经多次优化迭代实现了利用一组测量数据完成非线性超越矛盾标定方程组的求解.利用激光干涉仪完成了标定用数据的测量,通过3-RPS并联机构运动学逆解和各铰链的几何标定参数,得到动平台的实际位姿.通过对标定前后的Z轴定位精度的检测及实际零件加工试验,验证了3-RPS并联机构运动学标定模型和方法的正确性和有效性.     

Error analysis and compensation for the volumetric errors of a vertical machining centre using a hemispherical helix ball bar test

Machining accuracy is directly influenced by the quasi-static errors of a machine tool. Since machine errors have a direct effect upon both the surface finish and geometric shape of the finished workpiece, it is imperative to measure the machine errors and to compensate for them. A laser measurement system to identify geometric errors of a machine tool has disadvantages, such as a high cost, a long calibration time and the usage of a volumetric error synthesis model. In this study, we proposed a novel analysis of the geometric errors of a machine tool using a ball bar test without using a complicated error synthesis model. Also, a statistical analysis method was employed to derive geometric errors using a hemispherical helix ball bar test. According to the experimental result, we observed that geometric errors of the vertical machining centre were compensated by 88%.     

A new approach to thermally induced volumetric error compensation

A traditional model for thermally induced volumetric error of a three-axis machine tool requires measurement of 21 geometric error components and their variation data at different temperatures. Collecting these data is difficult and time consuming. This paper describes the development of a new model for calculating thermally induced volumetric error based on the variation of three error components only. The considered error components are the three axial positioning errors of a machine tool. They are modelled as functions of ball-screw nut temperature and travel distance to predict positioning errors when the thermal condition of the machine tool has changed due to continuous usage. It is assumed that the other 18 error components remain identical to the pre-calibrated cold start values. This assumption is justified by the fact that the machine tool’s thermal status significantly affects three axial positioning errors that dominate machining errors for a machine tool after its continuous use. To demonstrate the effectiveness of the proposed model two types of machining jobs, milling and drilling, on a three-axis horizontal CNC machining centre are simulated and the machined part profiles are predicted. The results show that the thermally induced volumetric error was reduced from 115.40 to 45.37?μm for the milled surface, and the maximum distance error between drilled holes for the drilling operation was reduced from 38.69 to ?0.14?μm after compensation.     

Assessing geometrical errors of multi-axis machines by three-dimensional length measurements

In this paper a method is presented for assessing geometrical errors of multi-axis machines based on volumetric three-dimensional length measurements. A universal machine error model is proposed since a large variety of machine configurations exists. Such models can be used for software error compensation techniques in order to improve the machine’s positioning behaviour as well as for diagnostic purposes. Length measurements are chosen for the measurement of the positioning errors of a multi-axis machine because these measurements can be executed in a short period of time in a relatively simple way combined with a high accuracy. In order to get comparable results for the geometrical errors as measured with conventional techniques, i.e., laser interferometry, the design of the measurement setup as well as the formulation of the machine error model (including parameter correlation effects) appeared to be of major importance and are subject of this paper.     

Neural network thermal error compensation of a machining center

A neural network based on Artificial Resonance Theory (ART-map) was used to predict and compensate the tool point errors of a 3-axis machining center using discrete temperature readings from the machine’s structure as inputs. A combination of kinematic error modeling, curve fitting, and the neural network were used to maintain the machine’s three-dimensional (3-D) accuracy within ±7.4 μm, regardless of the thermal state. The network model was evaluated with diagonal measurements and part machining tests. A laser ball bar was used to take the necessary measurements for training the neural network.     

Concept for the integration of geometric and servo dynamic errors for predicting volumetric errors in five-axis high-speed machine tools: an application on a XYC three-axis motion trajectory using programmed end point constraint measurements

A modelling approach for volumetric error prediction taking into account geometric and servo dynamic errors in a five-axis high-speed machine tool is proposed in this paper. Polynomial functions are used to represent and then predict the geometric errors. A simple second-order transfer function model is used to model and predict the servo dynamic error. The servo dynamic errors are added to the axis position geometric errors and propagated to the tool and workpiece using matrix transformations. The validity of the error integration concept is tested for a XYC three-axis motion trajectory. Two experimental setups are used. The first experimental test used the KGM grid encoder instrument to estimate the parameters of the servo dynamic error models of the X- and Y-axes. The second experimental test used 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. The tests involve maintaining the nominal coincidence of these two points whilst exercising the three axes. These last tests are used to estimate the geometric error parameters and also to validate the prediction performance of the integrated geometric and dynamic model. The result shows the effectiveness of the error integration concept.     

Proposition for a Volumetric Error Model Considering Backlash in Machine Tools

This paper proposes a new scheme for evaluating the machine tool volumetric error model including the backlash error. The effects of backlash errors are assessed by experiments, conducted on a three-axis vertical-type machining centre. The assessment was taken for 18 error components out of the 21 geometric errors of a machine tool. It was shown that the backlash error of a machine tool is one of the systematic errors. Some important characteristics of the backlash error were identified; that is, the backlash error is a function of position, it decreases as the feedrate increases, and its size and shape vary according to the machine structure.     

Form error estimation in ball-end milling of sculptured surface with z-level contouring tool path

This paper presents a flexible model for estimating the form error in three-axis ball-end milling of sculptured surface with z-level contouring tool path. At an interval of feed per tooth, the whole process of sculptured surface machining is treated as a combination of sequential small inclined surface milling. For ball-end milling of the inclined surface with z-level contouring tool path, at surface generation position, an analytical model is proposed to identify the feedback effect of tool deflection on cutting edge engagement. The deflection-dependent cutting edge engagement is determined by using an iterative procedure. And ultimately, the form error is obtained from the balanced tool deflection and associated surface inclination angle. In a validation experiment, the estimated form errors are compared with both the measurements and the predictions of a rigid model. It is shown that the proposed flexible model gives significant better predictions of the form error than rigid model. Good agreement between the predicted and measured form errors is demonstrated for the ball-end milling of sculptured surface with z-level contouring tool path.     

Variable speed compensation method of errors of probes for CNC machine tools

Systematic errors of kinematic touch-trigger probes for CNC machine tools may exceed errors of the machine tool itself. As a result, the machining accuracy is strongly dependent on the probe's accuracy. Numerical correction of probes’ systematic errors can be used. However, it requires executing calculations by the CNC machine tool controller. To avoid this troublesome requirement, a new method of errors compensation is proposed. In this approach, a modification of the probe's pre-travel in a given direction is achieved by modification of measurement speed in this direction. Because all measurement speeds can be calculated offline, the controller does not have to do any calculations. The proposed method has been tested for sample kinematic probes and the error reduction was at least 10-fold.     

Error budget and uncertainty analysis of portable machines by mixed experimental and virtual techniques

This paper analyzes the error sources of portable machines, which can move along large parts to perform machining operations and defines a mixed virtual-experimental model to quantify such errors. The method combines three different aspects of particular relevance in portable machines: a process force and machine stiffness model, a geometric error model and a machine and work piece inter-referencing error model. The combination of these models helps to control and define the effects of different errors in the virtual mobile machine, before a real prototype is built. An application to a particular portable machine is presented where error values are either simulated or experimentally obtained from a conventional three-axis milling machine where typical strategies of mobile machines are implemented and tested. The research shows that portable machines can be a solution for automatic and unattended machining operations with accuracy requirements below 0.1 mm.     

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.     

在机测量线激光传感器安装位姿的全局标定

针对三轴数控机床激光测头安装位姿误差造成测量误差且不易调整和校准的问题,提出了一种在机测量线激光传感器 安装位姿标定方法。 建立了线激光在机测量系统的数学模型,通过机床运动带动线激光测头对标定基准点的空间位置进行测 量,基于手眼标定原理给出了关于测头安装位姿参数的线性求解算法,完成了对测头安装误差的全局标定。 考虑了机床定位误 差对于标定结果精度的影响,采用蒙特卡洛模拟进行了误差分析。 采用半径为 35 mm 的圆孔进行测量验证,实验结果表明,标 定后圆孔测量误差为 0. 051 6 mm,测量精度提高了约 96% ,实验结果验证了该标定方法的有效性和可行性。     

数控机床几何误差综合建模及其专家系统

利用计算机的高速计算性能和无差错性,根据机床误差运动和误差建模基本原理,提出并开发一种数控机床几何误差综合建模专家系统,实现不同类型三轴加工中心的综合误差的自动快速准确建模,并给出了实例。此建模思想和方法可以容易地推广至多轴机床、机器人以及同时包含几何误差和热误差等因素的建模。     

Critical success factors for Kaizen implementation in manufacturing industries in Mexico

To machine a noncoaxial nonaxisymmetric aspheric lens, a new parallel grinding method that employs a fixture with an adjustable gradient (AGF) is proposed. The AGF is developed for a three-axis computer numerically controlled grinding machine. The grinding method is presented according to the proposed grinding system. To ensure the machining accuracy, the main machining errors and the compensation algorithm are discussed for the grinding method using the AGF. Simulation results show that the AGF rotation errors are crucial factors affecting the profile error of the machined workpiece. Experimental results show that employing the compensation algorithm increases machining accuracy.     

Thermal error modeling of machine tool based on fuzzy c-means cluster analysis and minimal-resource allocating networks

Thermal deformation in machine tools is one of the most significant causes of machining errors. A new approach to predict the thermal error of machine tool is proposed. The temperature variables and the thermal errors are measured using the Pt-100 thermal resistances and eddy current sensors respectively. Fuzzy c-means clustering method is conducted to identify the temperatures, and the representative as an independent variable are selected meanwhile it eliminates the coupling among the variables. The learning and prediction of the thermal errors is achieved using minimal-resource allocating networks by treating the issue as functional mapping between the thermal shifts and the temperature variables. The network is made to predict the error map of a machining center. A traditional radial basis function model is introduced for comparison. The experiment result shows that the fuzzy c-means clustering method and minimal-resource allocating networks combination is a fast and accurate method for thermal error compensation in machine tools.     

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.