Geometric Error Identification of a Three-Axis Machining Center

The geometric error of a three-axis vertical machining center is a critical technical indicator for evaluating its machining accuracy, and the precision of error identification plays a decisive role in the engineering effectiveness of compensation strategies. Based on the multibody system topology theory and the Denavit-Hartenberg matrix theory, this study establishes a contribution transfer model to quantify the impact of multi-axis geometric error on the positional errors at the end-effector of the three-axis vertical machining center. Experiments were performed on a VMC650 three-axis vertical machining center platform, where 21 geometric error items were precisely measured using a Renishaw XM-60 laser interferometer. An error spatial distribution function was constructed through polynomial regression analysis, and the optimal fitting coefficients of polynomial basis function combinations were solved to provide an analytical mathematical description for error prediction at arbitrary spatial positions. Based on the geometric error model, this study innovatively combines Monte Carlo sampling with principal component analysis to perform sensitivity analysis on geometric error parameters and analyze the transmission of geometric error under small disturbances, thereby effectively identifying key sensitive geometric error parameters. The research results offer theoretical guidance for structural optimization design and compensation parameter calibration of three-axis vertical machining centers, significantly enhancing their comprehensive machining accuracy.

The purpose of this study was to improve the accuracy of three-axis CNC Milling Vertical engines with a general approach by using mathematical modeling methods of machine tool geometric errors. The inaccuracy of CNC machines can be caused by geometric errors that are an important factor during the manufacturing process and during the assembly phase, and are factors for being able to build machines with high-accuracy. To improve the accuracy of the three-axis vertical milling machine, by knowing geometric errors and identifying the error position parameters in the machine tool by arranging the mathematical modeling. The geometric error in the machine tool consists of twenty-one error parameters consisting of nine linear error parameters, nine angle error parameters and three perpendicular error parameters. The mathematical modeling approach of geometric error with the calculated alignment error and angle error in the supporting components of the machine motion is linear guide way and linear motion. The purpose of using this mathematical modeling approach is the identification of geometric errors that can be helpful as reference during the design, assembly and maintenance stages to improve the accuracy of CNC machines. Mathematically modeling geometric errors in CNC machine tools can illustrate the relationship between alignment error, position and angle on a linear guide way of three-axis vertical milling machines.

In this paper, the collectivity error transformation matrix from the tip of the cutting tool to the workbench is set up for TH6350 machining center, by based on this, the numerical model of the universal geometric error of machining center is built up by applying the homogeneous coordinate transformation principle and the rigid-body hypothesis, and the geometric error of TH6350 machining center is calculated, the numerical model of geometric error is verified and analyzed by the way. The analyzed result plays a very important rule to improving designing, error compensation and practical machining of TH6350 machining center.

Workshop-suited geometric errors identification of three-axis machine tools using on-machine measurement for long term precision assurance

The article is devoted to increasing the volumetric accuracy of multi-axis machine tools. Based on the model of measurement and calculation of the volumetric geometric error of machine tools presented by the authors, a method has been developed which allows to signifi cantly improve the accuracy of the movement of the operating unit of a three-axis metal-cutting machine tool to a given point. The astatic law and the calculation of the coordinate correction according to the differential geometric model of the volumetric error are used to control the movement of the operating unit. The developed method is implemented programmatically and allows to perform the correction in the control program represented in G-code. As a result of experiments on software correction of volumetric errors according to the developed method, conducted at the State Engineering Centre of the Moscow State University of Technology “STANKIN” on a threeaxis CNC machine tool, a signifi cant reduction (up to 90 %) of geometric volumetric errors was shown. The developed method can be used to improve the accuracy of metal-cutting machine tools by creating postprocessors that calculate corrections to the coordinates set in the control system based on the results of interferometric measurements.Keywords: volumetric accuracy, interference measurements, three-axis machine tools, machine tool accuracy, geometric errors, astatic control law, mathematical modelling, differential geometry

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.

Geometric errors are one of the primary potential sources of error in a five-axis machine tool. There are two types of geometric errors: position-dependent geometric errors and position-independent geometric errors. A method is proposed to identify and measure the position-independent geometric errors of a five-axis machine tool with a tilting head by means of simultaneous multi-axis controlled movements using a double-ball bar (DBB). Techniques for identifying position-independent geometric errors have been proposed by other researchers. However, most of these are based on the assumption that position-dependent geometric errors (such as linear displacement, straightness, and angular errors) are eliminated by compensation, once the position-independent geometric errors have been identified. The approach suggested in this paper takes into account the effect of position-dependent geometric errors. The position-dependent geometric errors are first defined. Path generation for circle tests with two or three simultaneous control movements is then carried out to measure the position-independent geometric errors. Finally, simulations and experiments are conducted to confirm the validity of the proposed method. The simulation results show that the proposed method is sufficient to accurately identify position-independent geometric errors. The experimental results indicate that the technique can be used to identify the position-independent errors of a five-axis machine tool with a tilting head.

Modeling of geometric errors of linear guideway and their influence on joint kinematic error in machine tools

The geometric accuracy of a workpiece represents one of the key parameters defining its quality, and it is affected by the appropriate selection of the machine tool, control system, NC program and cutting conditions. Up-to-date control systems contain advanced compensation functions, which increase the volumetric accuracy of the machine tools. Nevertheless, these functions use correction data measurements within the machine tool’s periodic maintenance plan. This paper introduces a method for ad hoc correction data modification. This modification is based on the difference between the real and nominal workpiece geometries, which are evaluated on a coordinate-measuring machine as a standard process in high-accuracy workpiece production. Correction data are compiled in the form of a three-dimensional structured mesh, where nodes of the mesh contain such correction values that interpolations within the mesh suppress workpiece geometric deviations. The correction mesh calculations are based on the assumption that the nodes are connected by imaginary springs and that they are initially in force equilibrium. Force disbalance is introduced by workpiece geometric deviations evaluated at arbitrary points. Then the new position of force-balanced nodes is calculated. Experimental results on a three-axis machining center have verified the proposed method, where geometric accuracy of the workpiece increased more than 85% without any negative effect on surface quality. The approach presented is efficient for increasing workpiece accuracy without the need for NC program modification.

A three-point method based on sequential multilateration is applied to measuring the geometric error components (GECs) of three-axis machine tools (MTs). To meet the accuracy requirement of geometric error mapping, a sequential multilateration scheme is developed for high-accuracy point measurement by introducing four additional targets into the measuring system, and the uncertainty of point measurement is verified by simulation. Three independent targets fixed on the MT’s spindle assembly move along with each axis step by step and their coordinates at each step can be determined by the distance data acquired by laser tracker at all steps based on sequential multilateration. Then the volumetric errors of the three target points can be obtained by comparing the actual coordinates and the corresponding desired coordinates, and nine equations can be established by substituting volumetric errors into the error model of linear axis, so that the six GECs of each axis can be obtained by solving these equations. The three squareness errors can be determined by computing the angles between the average lines of the three axes which are achieved by linear curve fitting. Experiments are conducted to measure these 21 GECs, and the volumetric errors in the three-axis MT’s workspace, which are determined by these measured GECs based on the error model of three-axis MT, are compensated. Finally, the positioning errors of the MT with compensation and without compensation are evaluated by laser interferometer, respectively, the experimental results of which demonstrate that the positioning errors are significantly reduced by the error compensation.

A precision multi-degree-of-freedom measuring (MDFM) system has been developed and implemented for the simultaneous measurement of straightness, pitch, yaw, and roll errors of the moving axes of a CMM. The system is based on the principles of laser alignment and autocollimator. Its measurement principles and the influence of laser beam drifts on its measurement quality have been investigated and some improvement schemes have been implemented. Through the measurements of actual as well as artificially created geometric errors of the CMM, it has been found that the system’s accuracy of measuring straightness error components is better than 1 μm and its accuracy for angular error measurements is better than 0.5 arcsec.

Virtual manufacturing systems can provide useful means for products to be manufactured without the need of physical testing on the shop floor. As a result, the time and cost of part production can be decreased. There are different error sources in machine tools such as tool deflection, geometrical deviations of moving axis and thermal distortions of machine tool structures. Some of these errors can be decreased by controlling the machining process and environmental parameters. However other errors like tool deflection and geometrical errors which have a big portion of the total error, need more attention. This paper presents a virtual machining system in order to enforce dimensional, geometrical and tool deflection errors in three-axis milling operations. The system receives 21 dimensional and geometrical errors of a machine tool and machining codes of a specific part as input. The output of the system is the modified codes which will produce actual machined part in the virtual environment.

CNC machine tools play an extremely important role in the equipment manufacturing industry. Because a machine tool has multiple geometric errors which are highly coupled, the error identification process is difficult. Most direct and indirect measurement methods do not consider the dynamic errors in the actual cutting process. This study aims to optimize the error identification process of three-axis CNC machine tools, and proposes an efficient identification and separation method for the dynamic error and the quasi-static error based on feature workpiece cutting. In this study, a stepped feature workpiece that can reflect geometric errors is designed, and the mapping relationship between the geometric error components and the features is established. After the feature workpiece is cut, it performs two tests of on-machine measurement and CMM calibration sequentially. It can realize the identification and separation of 7 geometric errors and corresponding dynamic errors based on the two sets of test data. This method takes the actual cutting workpiece as the error source and can identify and separate the dynamic error and the quasi-static error simultaneously. Thus, the measurement efficiency of this method is higher than direct measurements. The geometric error identification result is highly consistent with the laser interferometer measurement, which proves the method in this study is feasible, efficient, and accurate.

The CNC machine tool is the passive executor of machining code. It cannot predict the machining accuracy during machining. If the error is found to be out of tolerance after processing, it will not only scrap the parts, but also greatly affect the processing efficiency. This phenomenon is very prominent when machining sculptured surface parts with five-axis machine tools. Therefore, this paper proposes a Digital Twin (DT) modeling method of five-axis machine tools for predicting Continuous Trajectory Contour Error (CTCE) caused by tracking errors and geometric errors. The DT consists of three parts: the Setpoints Trajectory (ST) model, the Actual Trajectory (AT) model considering tracking errors and geometric errors and the CTCE model. For a specific machine tool, according to the basic geometric information of the machine tool (tool length, kinematic chain information, etc.) and 41 geometric errors, the DT can be established. Inputting the Setpoints Positions (SPs) and the Linear Encoder Detection Positions (LEDPs), the DT can be used to predict the Tool-Tip Position Trajectory (TTPT) contour error and the Tool Orientation Trajectory (TOT) contour error. In order to verify the proposed method experimentally, the KMC400S U five-axis machine tool is selected to establish its DT by which the contour error of the S-shaped trajectory are predicted offline. Then, the DMU50 five-axis machine tool is selected to establish its DT to predict the contour error of the circular trajectory in real time. Combined with the deep motion mechanism, this paper proposes a DT modeling method for the vertical application scene of parts machining accuracy prediction, which is of great significance to developing the DT application theory and ensuring the machining accuracy of parts.

Geometric error measuring, modeling, and compensation for CNC machine tools: A review