Geometric Error Identification Research Articles

Identification of two different geometric error definitions for the rotary axis of the 5-axis machine tools

Geometric errors are clearly among the critical error sources in 5-axis machine tools and directly contribute to the machining inaccuracies. According to the definition of geometric errors of the rotary axis, different understandings have been exist in published studies. It is extremely dangerous as it makes the comprehension of the geometric errors ambiguous and may make the geometric error identification and compensation less effective. This phenomenon has not been noticed so far. In this paper, two different commonly used geometric error definition and modeling methods are firstly identified and analyzed, named as “Rotary axis component shift” and “Rotary axis line shift”. The features and relationships of these two error modeling methods are analyzed. After a detailed comparison, “Rotary axis component shift” is more suitable to definite the geometric errors of rotary axis. An experiment has been conducted on a 5-axis machine tool to show the correctness of our work. The results show that the identified geometric errors of rotary axis based on the two error models are greatly different and need to be concerned.

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.

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.

Position geometric error modeling, identification and compensation for large 5-axis machining center prototype

This paper presents a position geometric error modeling, identification and compensation method for large 5-axis machining center prototype. First, regarding the prototype as a rigid multi-body system, a geometric error model has been established, which supports the identification of position geometric error associated with a translational axis by using laser interferometer, and a rotational axis by using laser tracker. Second, based on this model, an improved identification approach named as virtual rigid-body is put forward for calculating positioning error of each large translational axis. Detailed derivation of a generalized matrix equation is given. Third, analytical models based on the least-squares theory were adopted to compute error values at an arbitrary position for error compensation. Finally, the identified position geometric errors were compensated by using recursive software-based error compensation method. The results show that the position accuracy of large machining center prototype has been improved with compensation and up to the design requirements.

A calibration method for enhancing robot accuracy through integration of an extended Kalman filter algorithm and an artificial neural network

Robot position accuracy plays an important role in advanced industrial applications. In this paper, a new calibration method for enhancing robot position accuracy is proposed. In order to improve robot accuracy, the method first models and identifies its geometric parameters using an extended Kalman filtering (EKF) algorithm. Because the non-geometric error sources (such as the link deflection errors, joint compliance errors, gear backlash, and so on) are either difficult or impossible to model correctly and completely, an artificial neural network (ANN) will be applied to compensate for these un-modeled errors. The combination of model-based identification of the robot geometric errors using EKF and a compensation technique using the ANN could be an effective solution for the correction of all robot error sources. In order to demonstrate the effectiveness and correctness of the proposed method, simulated and experimental studies are carried out on serial PUMA and HH800 manipulators, respectively. The enhanced position accuracy of the robots after calibration confirms the practical effectiveness and correctness of the method.

Volumetric calibration in multi-space in large-volume machine based on measurement uncertainty analysis

Machining accuracy is a significant index to evaluate characteristics of machine tools. Error compensation has been proved as an effective method for improving machining accuracy. Error measurement and identification are the prerequisite and basis for compensation. In order to detect volumetric error and identify geometric error accurately in large machines, a new method including workspace segment and multi-lateration measurement principle using laser tracker is proposed. Firstly, a synthetic test in large-volume machine containing three steps is presented. The Monte Carlo approach is implemented for evaluating the measurement uncertainty of volumetric calibration. Uncertainty sources in the calibration process, such as laser tracker sensors, thermal drift, and machine repeatability, are introduced. In order to decrease measurement uncertainty, the measurement station is optimized. Workspace is segmented, and volumetric error is calibrated in multi-station. Total least square method is implemented to transform coordinates among different measurement systems into reference frame accurately. Finally, the accuracy of algorithms for geometric error identification is verified by comparing the test results with that measured using a laser interferometer. And the volumetric calibration accuracy is also verified through comparing X-axis positioning error tested by the laser interferometer and laser track in multi-station.

An analytical approach for crucial geometric errors identification of multi-axis machine tool based on global sensitivity analysis

Geometric errors directly affect the tool tip position, reduce machining accuracy, and are one of the most important errors of multi-axis machining tool. However, the geometric errors are intercoupling, and the measured values at different points vary and are stochastic. The identification of the most crucial geometric errors and the determination of a method to control them is a key problem to improve the machining accuracy of machine tool. To achieve this goal, a new analytical method, to identify crucial geometric errors for a multi-axis machine tool is proposed here based on multibody system (MBS) theory and global sensitivity analysis. The volumetric error modeling of multi-axis machine tool has been given by MBS theory, which describes the topological structure of multibody system simply and conveniently in a matrix. The stochastic characteristic of geometric errors is taken into consideration and Sobol global sensitivity analysis method is introduced to identify crucial geometric errors of machine tool. A vertical machining center is selected as an illustration example. The analysis results reveal that the analytical method presented in this paper can identify the crucial geometric errors and are helpful to improve the machining accuracy of multi-axis machine tool.

An identification method for key geometric errors of machine tool based on matrix differential and experimental test

This paper presents a key geometric errors identification method for machine tools based on matrix differential and experimental test. An error model for a machine tool was established by regarding the three-axis machining center as a multi-body system. The sensitivity coefficients of the machining error with respect to the geometric errors were determined using the matrix differential method, and the degree of influence of the geometric errors on the machining accuracy under ideal conditions was discussed. Using the 12-line method, 21 geometric errors of the machine tool were identified, allowing the three-dimensional volumetric error distributions of the machine tool to be mapped. Experimental results allow the degree of influence of the geometric errors on the machining accuracy under actual conditions to be confirmed. Finally, the key geometric errors affecting the machining accuracy were identified by a combination of matrix differential and experimental test. This paper provides guidance for the machine tool configuration design, machining technology determination, and geometric error compensation.

Modeling, identification and compensation for geometric errors of laser annealing table

In order to improve the process precision of an XY laser annealing table, a geometric error modeling, and an identification and compensation method were proposed. Based on multi-body system theory, a geometric error model for the laser annealing table was established. It supports the identification of 7 geometric errors affecting the annealing accuracy. An original identification method was presented to recognize these geometric errors. Positioning errors of 5 lines in the workspace were measured by a laser interferometer, and the 7 geometric errors were identified by the proposed algorithm. Finally, a software-based error compensation method was adopted, and a compensation mechanism was developed in a postprocessor based on LabVIEW. The identified geometric errors can be compensated by converting ideal NC codes to actual NC codes. A validation experiment has been conducted on the laser annealing table, and the results indicate that positioning errors of two validation lines decreased from ±37 μm and ±33 μm to ±5 μm and ±4.5 μm, respectively. The geometric error modeling, identification and compensation method presented in this work can be straightforwardly extended to any configurations of 2-dimensional worktable.

Research on Geometric Error Tracing of NC Machine Tools

Geometric accuracy is an important performance criterion for NC machine tools, and the 9-line method based on laser measuring technology is widely used for error tracing. Three kinds of application problems of the traditional 9-line method are analyzed, and a new geometric error identification model is established by modifying the traditional method. The new model can improve the stability of identification results effectively, and make it possible that the manufacturing and assembly errors of the joints can be traced. Moreover, since the traditional 9-line method has principle errors in roll angle's identification, an experiment-based method is proposed to eliminate the principle errors. The effectiveness of these approaches are verified by both computational and experimental results.

An Improvement Geometric Error Identification Method of CNC Machine Tool Based on Double Ball Bar

The double ball bar is widely used because it can quickly, easily and cost-effectively detect and evaluate the accuracy of CNC machine tools. But since the error recognition algorithm based on the double ball bar ignores the quadratic item, its recognition accuracy would be reduced. In this paper, an improved CNC verticality error and position error identification formula, combined with the machine tool error model to deduce a new error recognition model of double ball bar measurement is proposed. It can be drawn that the accuracy of the model are better than the existing methods because it keeps the second item in the derivation process of the model.

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.

A general strategy for geometric error identification of multi-axis machine tools based on point measurement

Geometric error component identification is needed to realize the geometric error compensation which can significantly enhance the accuracy of multi-axis machine tools. Laser tracker has been applied to geometric error identification of machine tools increasingly due to its high capability in 3D metrology. A general method, based on point measurement using a laser tracker is developed for identifying the geometric error components of multi-axis machine tools in this study. By using this method, all the component errors and location errors of each axis (including the linear axis and rotary axis) of the multi-axis machine tools can be measured. Three pre-described targets are fixed on the stage of the under-test axis which moves step by step. The coordinates of the three targets at every step are determined by a laser tracker based on the sequential multilateration method. The volumetric errors of these three target points at each step can be obtained by comparing the measured values of the target points’ coordinates with the ideal values. Then, nine equations can be established by inversely applying the geometric error model of the axis under test, which can explicitly describe the relationship between the geometric error components and volumetric error components, and then the component errors of this axis can be obtained by solving these equations. The location errors of the axis under test can be determined through the curve fitting. In brief, all the geometric error components of a single axis of multi-axis machine tools can be measured by the proposed method. The validity of the proposed method is verified through a series of experiments, and the experimental results indicate that the proposed method is capable of identifying all the geometric error components of multi-axis machine tools of arbitrary configuration.

Geometric Error Identification of a Three-Axis Machining Center

Geometric errors of a machining center can cause great influence on machining accuracy, and these geometric errors should be identified and compensated in the actual working conditions. Taking a three-axis vertical machining center as example, 21 geometric errors of the machine tool were solved. By using the 12-line method based on a laser interferometer, identification principle of the positioning errors, straightness errors, pitch errors, yaw errors, roll errors and squareness errors are presented, and all of the 21 geometric errors of the machining center were identified. Geometric errors having great influence effect on machining accuracy can be identified. The research results provide guidance for analyze of geometric errors of machining center.

The Geometric Errors Identification of New Methods in Four-Axis Machining Center Axis

A method for fast measuring and identify the six geometric errors of each rotary axes in Four- axis machining center was invented. The method adopted the ball-bar to measure the X, Y, Z direction deviations of the centre block installed on the rotary table in the different rotation angle. And deduced the geometric error identification model in rotary axes based homogeneous transformation, and then identify the axis of the six basic geometric errors. in order to reduce the influence of the inaccuracy of the ball-bar and the reference point position, this paper put forward new method based on the analysis of the sensitivity matrix method, used to guide rational distribution points, so as to improve the error identification accuracy.

Geometric error measurement and compensation for the rotary table of five-axis machine tool with double ballbar

This paper proposes a novel measuring method for geometric error identification of the rotary table on five-axis machine tools by using double ballbar (DBB) as the measuring instrument. This measuring method greatly simplifies the measurement setup, for only a DBB system and a height-adjustable fixture are needed to evaluate simultaneously five errors including one axial error, two radial errors, and two tilt errors caused by the rotary table. Two DBB-measuring paths are designed in different horizontal planes so as to decouple the linear and angular errors. The theoretical measuring patterns caused by different errors are simulated on the basis of the error model. Finally, the proposed method is applied to a vertical five-axis machining center for error measurement and compensation. The experimental results show that this measuring method is quite convenient and effective to identify geometric errors caused by the rotary table on five-axis machine tools.

A Geometric Error Identification and Simulation Method Based on Laser Tracker for Large-Scale Multi-Axis NC Machine Tools

To evaluate the profile error of manufacture mainly caused by geometric error of machine tool, this paper proposes a geometric error identification and profile error simulation method. The identify method measures each axis of machine tool based on laser tracker, then using the least square method to fit the axis, as a result the coordinate system of each axis can be built. The geometric error of machine tool can be gained by analysis of the coordinate system. Building the kinematics model of large-scale multi-axis NC machine tool considered the geometric error, then using MATLAB and UG second development to achieve simulation of profile error.

Geometric Error Identification and Compensation for Rotation Axes of Five-Axis Machine Tools

In NC machining, the precision of the final parts is affected by many factors, including geometric deviation of machine tool components and structures, deformation of process system caused by cutting force and cutting heat, servo delay, tool wear and so on. Among which geometric error of machine tool is one of the most important factors. This study focused on geometric error identification and compensation of rotation axes of five-axis machine tools. A new method was proposed to identify the 6 geometric error parameters of each rotation axes of five-axis machine tools based on a ball-bar system. Regarding the machine tool as a rigid multi-body system (MBS), a geometric error model was established based on homogeneous transfer matrix (HTM). Finally, the geometric errors were compensated by correcting NC codes by the prototype software system developed in this study. An experiment and an application were conducted and the results show that the proposed method is effective to improve the machining accuracy.

A New Method for Identifying Geometric Errors Inherent to Revolving Axle of Multi-Axis Machine Tool

Geometric errors identification of revolving axle of multi-axis machine tool has encountered a great difficulty in geometric errors compensation. This paper describes a new method to identify geometric errors inherent to revolving axle of multi-axis machine tool based on a ball-bar system. Under RTCP (Rotation Around Tool Center Point) or RPCP (Rotation Around Part Center Point) function, the displacement errors of revolving axle in X, Y and Z direction can be obtained by the ball-bar system respectively at every measurement angle. With the corresponding identification algorithm proposed in this paper, the whole six geometric errors of revolving axle can be identified. This new method is suitable for any type of multi-axis machine tool and without structural constraints. To confirm the validity of the proposed method, an experiment has been conducted on a five-axis machine tool, and the results show that this method is effective and applicable.

Integrated geometric error modeling, identification and compensation of CNC machine tools

This paper presents an integrated geometric error modeling, identification and compensation method for machine tools. Regarding a machine tool as a rigid multi-body system (MBS), a geometric error model has been established. It supports the identification of the 21 translational geometric error parameters associated with linear-motion axes based on a laser interferometer, and 6 angular geometric error parameters for each rotation axis based on a ball-bar. Based on this model, a new identification method is proposed to recognize these geometric errors. Finally, the identified geometric errors are compensated by correcting corresponding NC codes. In order to validate our method, a prototype software system has been developed, which can be used for conducting tests on any type of CNC machine tool with not more than five axes. An experiment has been conducted on a five-axis machine center with rotary table and tilting head; the results show that the integrated geometric error modeling, identification and compensation method is effective and applicable in multi-axis machine tools.