Machine Tool Geometric Errors Research Articles

Portable 5-DOF measurement system using a parallel beam generation method for linear axis detection.

Geometric error detection is crucial for evaluating the accuracy of the linear axis. However, the practicality of traditional dual-beam detection systems is limited by the parallelism of beams. This study proposes a portable 5-DOF measurement system using a novel parallel beam generation method. Two orthogonal corner cube retroreflectors (CCRs) and a beam splitter (BS) are utilized to achieve two measuring beams with excellent parallelism, which is determined solely by the CCR. The theoretical parallelism of beams is analyzed and experimentally verified. Two position sensitive detectors (PSDs) and one autocollimator are used to measure two straightness errors and three angular errors, and the detection deviations are modelled and compensated. The experiment proves that dual beam that are generated on the basis of the above structure could achieve a parallelism of 5.9'' without careful adjustment. The designed 5-DOF measurement system has a straightness measurement range of ± 400 µm and an angle measurement range of ± 300''. The repeatability of the system is 2.20 µm for straightness errors, 1.58'' for yaw error, 1.82'' for pitch error and 5.04'' for roll error detection. The designed 5-DOF measurement system has the advantages of a simple structure and stable accuracy and is very practical in measuring the geometric errors of machine tools.

Efficient Method for Identifying Key Errors Based on 21-Geometric-Error Measurement of Three Linear Axes of Machine Tools

Key errors of machine tools have a significant impact on their accuracy, however accurately and quickly measuring the geometric errors of machine tools is essential for key error identification. Fortunately, a quick and direct laser measurement method and system for 21 geometric errors of three linear axes of machine tools were proposed previously, which enables the measurement of all 21 geometric errors via a one-step installation and a three-step automated measurement process. Based on this, to efficiently identify the key error factors, this paper first utilizes the 21 geometric errors obtained from the proposed measurement system to evaluate the contribution of each error to the volumetric errors of machine tools, leading to the building of a 21-geometric-error sensitivity analysis model. Then, experiments are carried out on the vertical machining tool TH5656, and all 21 geometric errors are obtained in 5 min. After this, the volumetric error distribution in the machining workspace is mapped according to the relationship between the geometric errors and the machining errors, and the key error factors affecting the manufacturing and machining accuracy of the TH5656 are ultimately determined. Thus, this new method provides a way to quickly identify key errors of the three linear axes of machine tools, and offers guidance for the machine tool configuration design, machining technology determination, and geometric error compensation.

Fast detection of geometric errors for three-axis machine tools with combined double-ball bars based on spatial circle detection

The geometric accuracy of the CNC machine tools determines the quality of the sculptured mechanical parts. Measuring and compensating the geometric errors of machine tools can effectively improve the machining accuracy. However, traditional measurement methods using a double-ball bar (DBB) can only detect the error along the rod length direction and thus require multiple measurements in three orthogonal planes of the machine tool. This work proposes a fast error detection method for the three-axis machine tools using combined double-ball bars (C-DBBs) based on the spatially circular detection (SCD) path. The test path of this method requires the simultaneous linkage of three linear axes of the machine tools and thus could identify 21 geometric errors of three-axis machine tool. Firstly, the measuring principle of the SCD method is introduced, and the mathematical model for detecting 21 geometric errors of the machine tool based on the SCD method is established. Then, the detection experiment based on the SCD method is carried out, and it is shown that 21 geometric errors of the three-axis machine tool are obtained. Finally, the verification experiment using a traditional DBB is conducted to validate the effectiveness of the proposed SCD method. The radial errors in three orthogonal planes measured by traditional DBB exhibit a good agreement with those predicted using 21 geometric errors obtained by the SCD method. Compared with the traditional DBB method, the proposed SCD method could detect 21 geometric errors of three-axis machine tools in a single measurement. This work provides an effective and efficient methodology for detecting all geometric errors of the three-axis machine tool.

Experimental study of geometric error of CNC turning machine tools based on ISO 13041-6

The product quality of machining results is greatly influenced by the accuracy and precision of CNC lathe machine tools. Regular inspection of the geometric inaccuracy of the machine tool is necessary to verify its operational viability. This research contribution focuses on conducting experimental studies to evaluate machine tool geometric error. The aim is to explore cost-effective measurement methods as alternatives to direct measurements, which often involve laser interferometers and ball bar tests. The objective of this study is to investigate the geometric inaccuracy of a CNC turning machine by conducting experimental cutting tests in accordance with ISO 13041-6:2009. The testing will utilize conventional workpiece forms and requirements, including circularity features, flatness, circular features, and maybe combination features. Several geometric errors that can be acquired with this method include circularity errors, linear positional errors, and squareness errors. The cutting test for each workpiece feature of the given shape and specification requires the use of 5 specimens. Consequently, the mean value of the geometric error may be computed. The geometric error value is derived by the analysis of measurement data collected from a Coordinate Measuring Machine (CMM) applied to a specimen of the machined workpiece. Moreover, the evaluation of the geometric error condition of machine tools is ascertained through the comparison of the average data for each category of geometric error against the permissible standard values given in ISO 10791-2, ISO 10791-4, and ISO 13041-4. The findings of the study indicate that the implementation of the object machine study is not viable for the production of machined workpieces of satisfactory quality. This is primarily due to the presence of geometric errors in CNC turning that exceed the acceptable tolerance levels. Specifically, these errors manifest as linear positional deviations along multiple coordinates along the X-axis and Z-axis, as well as squareness deviations between the X-axis and Z-axis. The maximum value of the linear positional error along the X-axis is 55.2 μm, while the maximum value of the linear positional error along the Z-axis is 25.6 μm. Additionally, the greatest observed squareness error is 37.3 μm. The X and Z machine axes exhibit deviations beyond acceptable limits in terms of unidirectional accuracy and unidirectional repeatability, as per the established norm

Gear evaluation deviations-based crucial geometric error identification of five-axis CNC gear form grinding process

The gear form grinding accuracy is significantly affected by crucial geometric errors. The gear form grinding process is a special line contact forming method. There are exclusive evaluation standards for gear grinding accuracy. While the existing sensitivity analysis for spatial point errors cannot meet the final gear report requirements. Hence, a novel method for analysis of geometric error influence on the key gear evaluation deviations (GED) is proposed. First, the actual digital tooth surface considering geometric errors and gear form grinding mechanism was constructed according to the homogeneous transformation matrix (HTM) and multi-body system theory (MBS). Second, the GED of the digital tooth surface was gained according to the modified gear meshing equations. Third, the analytic mapping relationship between the GED and machine tool geometric errors was first established. Then, the crucial geometric errors affecting the GED were identified based on a proposed Morris method. Finally, the identification results were compared to the existing publications, and the compensation discussions of crucial errors were demonstrated to validate the advantages of the proposed method. It can be found that the compensation results of GED-oriented key errors are better than those of the traditional methods, which is beneficial to the improvement of evaluation reports.

COMPENSATIONOF WORKTABLEMOTIONERROR BYANACTIVELY CONTROLLEDHYDROSTATIC GUIDEWAY

The accuracy of machine tools is limited by many factors,such as geometric and thermal errors. Current error reduction approaches include e.g. volumetric compensation. However, if a machine tool has only linear axes, angular errors cannot be compensated since there is no controllable axis that could change the tool or workpiece inclination. Therefore, an actively controlled hydrostatic guideway was developed to compensate for angular and other geometric errors. This paper aims to experimentally verify the hybrid use of constant resistance and the pilot stage of an industrial proportional pressure relief valve for regulation of oil flow through hydrostatic pockets and control of these pockets as well as active compensation of machine tool geometric errors. The error reduction of the tested linear axis is presented.

Use of a Virtual Polyhedron for Interim Checking of the Volumetric and Geometric Errors of Machine Tools

Use of a Virtual Polyhedron for Interim Checking of the Volumetric and Geometric Errors of Machine Tools

A four parallel laser-based simultaneous measurement method for 6-degrees-of-freedom errors of rigid body with translational motion.

The measurement of six-degrees-of-freedom (6-DOF) errors of rigid bodies can show the real and accurate spatial pose of those rigid bodies. It plays a major role in precision calibration, spacecraft docking, machining, assembly, etc. In this paper, a four parallel laser-based simultaneous measurement (FPL-SM) method is proposed for measuring 6-DOF errors of rigid bodies with translational motion. First, a FPL-SM device is introduced. Its four laser heads form a rectangle, which is perpendicular to the movement direction of the measured linear displacement. Second, identification formulas for all geometrical errors in rigid bodies with translational motion are presented based on the relative positions of the four lasers. Based on the readings of the four lasers, angular errors and corresponding straightness errors are calculated for the direction of motion around the other two linear motions. As the two parallel sides of the rectangle are in different planes, the straightness errors of the two planes are different. The rolling angular error in the direction is expressed as the difference between the straightness errors of the two planes divided by the distance between the two planes. Six fundamental errors for rigid bodies with translational motion are obtained by four lasers in a single setting of the device. For multiple rigid bodies with mutually perpendicular translational motion, the squareness error is calculated by fitting to the actual direction of motion. Finally, experiments were carried out on the SmartCNC_DRDT five-axis machine tool and 21 geometric errors were determined for three translational axes. Error compensation was carried out using the generated machine tool geometric error data to verify the effectiveness of the proposed FPL-SM method. In addition, geometric errors and thermal errors of the Z axis of the GTI-2740 machine tool are measured based on the FPL-SM method.

Accuracy Improvement of a Laser Diode-Based System for Measuring the Geometric Errors of Machine Tools

Active methods are proposed to improve the measurement accuracy of a compact laser diode-based (LD-based) system, which is designed to measure the geometric errors of machine tools. The LD has some advantages, such as a small size, low cost and high efficiency. However, the laser spot of the LD is elliptical and the stability in the output power of the LD is low, which limits the accuracy of the measurement system, where the LD is used as the laser source. An active shaping method is proposed to shape the elliptical laser spot of the LD without adding additional optical elements. In addition, the laser beam drifts, including the linear drift and angular drift, are compensated in real-time by a proposed improved active error compensator, which consists of two drift feedback units and a Backpropagation Neural Networks-based PID controller, during the long-distance measurement. A series of experiments were conducted to verify the effectiveness of the proposed methods and the capability of the constructed LD-based system.

Modelling and compensation of machine geometric errors for the surface texturing process

Bio-inspired surface textures have been widely used in various industries because of their unique functionality. The geometric accuracy of the texturing equipment and its effect on the texture geometry are essential for the functional performance of the textured surfaces. This paper presents a surface texture error model that predicts the surface texture topography considering the geometric errors of the machine tool. An error compensation method is proposed to improve the accuracy of the texture by considering the characteristics of the synchronised tool's linear motion and spindle rotation simultaneously. Micro ball-end mill surface texturing experiments are carried out to validate the developed geometric error compensation model considering machine tool geometric errors. The surface topographies before and after the error compensation are examined and compared. The results prove the effectiveness of the proposed error compensation method in enhancing the geometric accuracy of the texture topography.

Research on geometric error modelling and decoupling of machine tool based on NURBS projection curve

As a geometric measuring instrument of machine tool, double ball bar (DBB) instrument can effectively identify the geometric error of machine tool. In the existing literature, DBB mostly uses the two-dimensional circle as the identification trajectory to identify the geometric error continuously, and the most efficient way of single recognition is still in two-dimensional plane. Aiming at the low efficiency of DBB spatial geometric error recognition, the recognition range of DBB is extended from two-dimensional plane to spatial hemisphere. A method of space recognition and decoupling based on NURBS projection curve is proposed in this paper. The error decoupling of feed axis and rotation axis is realized in an experiment. The identification method has the characteristics of high efficiency, no secondary assembly and avoiding interference. It can decouple all the five-axis in hemispherical space at one time and get the effective solution.

High-Efficient Calculation Method for Sensitive PDGEs of Five-Axis Reconfigurable Machine Tool

Sensitive geometric errors of a machine tool have significant influence on machining accuracy, and it is important to identify them. Complex modeling and analysis must be carried out to identify the sensitive geometric errors of a five-axis machine tool by using the traditional method. Once the configuration structure of the machine tools is reconstructed, repetitive error modeling and analysis are required, and the identification cycle of sensitive geometric errors is long. Therefore, this paper proposes a high-efficient calculation method for sensitive position-dependent geometric error (PDGEs) identification of a five-axis reconfigurable machine tool. According to the results of sensitive geometric errors of the RTTTR-type and TTTRR-type five-axis machine tools, the mapping expressions between sensitive PDGEs and the configuration structure of machine tools was established. In this method, sensitive PDGEs can be calculated directly according to the mapping expression, which eliminates the process of error modeling and analysis. Taking a RTTTR-type five-axis machine tool as an example, the sensitive PDGEs were calculated according to the presented mapping expressions without error modeling and analysis. A series of analysis points in the machining area were selected to compare the machining errors before and after sensitive PDGE compensation. The results show that this calculation method is accurate.

A mapping model between the workpiece geometric tolerance and the end pose error of CNC machine tool considering structure distortion of cutting process system

Aiming at the problem that the geometric accuracy design index of machine tools is difficult to be determined reasonably in the geometric precision design process of CNC machine tools, this paper presents a mapping model between geometric tolerance of the workpiece and end pose error (positional and orientational error of the tool relative to the workpiece) of the machine tool considering structure distortion of cutting process system. Only considering the factors of the machine tool geometric errors, this paper first establishes the relationship between the geometric tolerance requirements of the workpiece and relative pose error at the end of machine tools, and completes the estimation of the machine tools end pose error. Then this paper analyzes the elastic deformations of the cutting process system caused by the cutting force. These elastic deformations produce machining errors. Based on the above analysis, the estimated variation range of the end pose error can be adjusted by the emulation of the geometric tolerance of the workpiece and used as the geometric accuracy design index of machine tools. This paper takes the international standard small size contour processing test piece as an example to explain the application process of the proposed model.

Efficient uncertainty estimation of indirectly measured geometric errors of five-axis machine tools via Monte-Carlo validated GUM framework

Whether using a machine tool as a machining or a measuring system, its accuracy has a key role in ensuring product quality. As a result, conducting periodic geometric calibration of a machine tool to quantify and to compensate for the machine's geometric errors is highly desirable. The measured geometric errors must be accompanied by uncertainty estimates, reflecting the lack of exact knowledge of the value of measurands. Indirect calibration approaches, as opposed to direct ones, have gained considerable attention recently because they can be automated and take considerably less time to conduct. However, the uncertainty of the indirectly measured error parameters is more challenging to estimate because of the complexity of the used mathematical models and the large number of machine error parameters identified simultaneously. The use of uncalibrated artifacts also adds to the wariness towards such approaches. In this paper, two different approaches are used to evaluate the uncertainty of machine geometric errors identified by the scale and master ball artefact (SAMBA), an indirect approach relying on the on-machine probing of uncalibrated and calibrated artifacts. First, a simulator of an adaptive Monte Carlo method (MCM) determines the uncertainty of machine tool geometric errors. A multivariate sample generator draws at random the input vectors from a joint probability distribution function (PDF) obtained through experimental replications over 15 days. Supplement 2 to the Guide to the expression of uncertainty in measurement (GUM) specifies the conditions where an adaptive MCM validates the GUM uncertainty framework (GUF). Adhering to the instructions given by this standard, the validity of GUF, a much faster uncertainty evaluation method, is examined. Results show that the adaptive MCM procedure, which takes 24 h to run, validates the alternative GUF approach, which takes a computation time of only 10 min. A maximum disagreement of 1% between the geometric errors from experimental replications and their estimates identified by the adaptive MCM implies that the marginal means of the estimated output joint PDF in the adaptive MCM well represent the average of the output quantities. High dependencies of the linear terms (slopes) of the linear positioning errors of prismatic axes X, Y, and Z on the SAMBA scale bar length cause high correlations between these errors with correlation coefficients up to 0.965. The largest standard uncertainty estimated for the angular geometric errors is 1.26 μrad (associated with the out-of-squareness error of axis Z relative to axis X, EB0Z) and that for the translational geometric errors is 1.03 μm (associated with the distance between the spindle axis and axis B along axis X, EX0S). Axis X is estimated to have the largest standard uncertainty (6.1 μm/m) of the linear terms (slopes) of the linear positioning errors among the machine's prismatic joints.

Prediction of machining accuracy based on geometric error estimation of tool rotation profile in five-axis multi-layer flank milling process

In five-axis multi-layer flank milling process, the geometric error of tool rotation profile caused by radial dimension error and setup error has great influence on the machining accuracy. In this work, a new comprehensive error prediction model considering the inter-layer interference caused by tool rotation profile error is established, which incorporates a pre-existing prediction model dealing with a variety of errors such as geometric errors of machine tool, workpiece locating errors, and spindle thermal deflection errors. First, a series of tool contact points on the tool swept surface in each single layer without overlapping with others are calculated. Second, the position of the tool contact points on the overlapped layers is updated based on the detection and calculation of inter-layer interferences. Third, all evaluated tool contact points on the final machined surface are available for completing the accuracy prediction of the machined surface. A machining experiment has been carried out to validate this prediction model and the results show the model is effective.

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.

Research on the application of multiplication dimension reduction method in global sensitivity analysis of CNC machine tools

Three-axis computer numerical control (CNC) milling machines have a wide range of application in practical processing. The error transfer principle of machine tools is an important factor to improve the precision of machine tools. Based on multibody system theory and homogeneous transformation matrix theory, a geometrical error model of three-axis CNC milling machines is proposed in this paper. In addition, the global sensitivity analysis of machine tool errors was carried out to identify important errors. The analysis model has two layers of higher dimensional integration; hence, in the aim of solving this issue, a multiplication dimension reduction method was used in this paper. By this means, a one-dimensional integration model was obtained, and sensitivity analysis of machine tool geometric errors was realized. The present work provides a good theoretical basis for the optimization design and error compensation of machine tools.

A novel causation analysis method of machining defects for five-axis machine tools based on error spatial morphology of S-shaped test piece

In the acceptance process of newly developed five-axis machine tools (FAMTs), it is urgent for machine tool builders to understand the main causes of machining defects on S-shaped test piece. This paper proposes a novel causation analysis method based on error spatial morphology of S-shaped test piece to decouple the key geometric error parameters causing contour errors of test piece. Firstly, based on multi-body system (MBS) theory, tool axis surface error model of a FAMT is set up. In order to eliminate the effect of theoretical error on contour error of S-shaped test piece, the optimized tool path is planned based on the three-point tangential method. Then, the NC instruction is calculated, and error spatial model is established to characterize contour error of the test piece by considering tool setting position. As a basis, error spatial morphologies of test piece are drawn and the relationships between geometric error parameters and error spatial morphologies are analyzed. In order to decouple the key geometric error parameters affecting contour error of test piece, the causation analysis method of local error and global error are presented. After repairing the local and global key error parameters of the test piece obtained from these two analysis methods respectively, the local machining errors are reduced by more than 80%, and the global machining error is not beyond the tolerance. Finally, the cutting experiments of S-shaped test piece on the FAMT XKAS2525 × 60 are implemented. Error detection results of the cutting test piece are basically the same as that shown in error spatial morphologies of test piece, which verifies the correctness of error spatial model for the test piece. After compensating the global key error parameters obtained from the causation analysis method of global error in CNC system, the detection results of re-cutting test piece under the same conditions indicate the test piece has very few points that are not within the tolerance range, and detection results after compensation and global repaired results are almost similar, which verifies the feasibility and correctness of the proposed analysis method. Therefore, it is obvious that the presented method bridges between geometric characteristics of S-shaped test piece, geometric errors of machine tool, and machining defects of test piece and provides a comprehensive error analysis method in the acceptance and performance testing of FAMTs by using the S-shaped test piece. Thus, this study is of great significance for improving the accuracy evaluation method and enhancing the design accuracy of FAMTs.

Identification of inherent position-independent geometric errors for three-axis machine tools using a double ballbar with an extension fixture

This paper presents a double ballbar method with an extension fixture to identify the position-independent geometric errors of three-axis machine tools with respect to their entire workspace by conducting face- and body-diagonal length tests. To extend the length of the double ballbar to the required nominal length in the face- and body-diagonal directions, an extension fixture is designed and manufactured using a fused-deposition-modeling 3D printer to ensure that it is lightweight. Inherent position-independent geometric errors can be calculated from measured lengths by using homogeneous transformation matrices, which are multiplied under the assumption of small values, to determine the volumetric error produced by a machine tool. The relationships between the position-independent geometric errors, roll-pitch-yaw errors, and measured lengths can be derived according to the definition of the straightness errors, based on the end-point of the reference straight line. Finally, the position-independent geometric errors, with analysis of measurement uncertainties, can be identified by substituting the values of the roll-pitch-yaw errors, measured by a multi-axis calibrator, into the derived relations. The results can then be validated by re-measuring the face- and body-diagonal lengths with error compensation. The main advantage of the proposed approach is that it can be used to identify the inherent position-independent geometric errors of machine tool workspaces. This could contribute to reducing volumetric errors in machine-tool workspaces by allowing compensation for measurement errors, thus making machine tools more effective.

A Recognition Methodology for the Key Geometric Errors of a Multi‐Axis Machine Tool Based on Accuracy Retentivity Analysis

This paper proposes a recognition methodology for key geometric errors using the feature extraction method and accuracy retentivity analysis and presents the approach of optimization compensation of the geometric error of a multiaxis machine tool. The universal kinematics relations of the multiaxis machine tool are first modelled mathematically based on screw theory. Then, the retentivity of geometric accuracy with respect to the geometric error is defined based on the mapping between the constitutive geometric errors and the time domain. The results show that the variation in the spatial error vector is nonlinear while considering the operation time of the machine tool and the position of the motion axes. Based on this aspect, key factors are extracted that simultaneously consider the correlation, similarity, and sensitivity of the geometric error terms, and the results reveal that the effect of the position‐independent geometric errors (PIGEs) on the error vectors of the position and orientation is greater than that of the position‐dependent geometric errors (PDGEs) of the linear and rotary axes. Then, the fruit fly optimization algorithm (FOA) is adopted to determine the compensation values through multiobjective tradeoffs between accuracy retentivity and fluctuation in the geometric errors. Finally, an experiment on a four‐axis horizontal boring machine tool is used to validate the effectiveness of the proposed approach. The experimental results show that the variations in the precision of each test piece are lower than 25.0%, and the maximum variance in the detection indexes between the finished test pieces is 0.002 mm when the optimized parameters are used for error compensation. This method not only recognizes the key geometric errors but also compensates for the geometric error of the machine tool based on the accuracy retentivity analysis results. The results show that the proposed methodology can effectively enhance the machining accuracy.