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

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.

Generalized actual inverse kinematic model for compensating geometric errors in five-axis machine tools

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.

Total differential methods based universal post processing algorithm considering geometric error for multi-axis NC machine tool

The simultaneous measurement and identification of position-independent geometric errors (PIGEs) and position-dependent geometric errors (PDGEs) of dual rotary axes in five-axis machine tools remain a significant challenge in precision machining. To address this issue, this study develops a geometric error measurement system for the dual rotary axes of a five-axis machine tool by integrating a scanning probe, a block, and a calibration sphere. Unlike conventional touch-trigger probes, the scanning probe acquires continuous measurement signals along the surfaces of the block and the calibration sphere, enabling the extraction of richer geometric features and providing sufficient data for the simultaneous analysis of multiple geometric error components. The proposed measurement system is implemented on a five-axis machine tool, Uni5X-400, manufactured by FALCON Machine Tools Co., Ltd., to measure the geometric information of the calibration sphere and the block and thereby identify 20 PIGEs and PDGEs associated with the dual rotary axes. A kinematic model of the measurement system is established using homogeneous coordinate transformation matrices. By applying forward and inverse kinematics, the spatial positions of the calibration sphere and block are derived, forming an explicit relationship between volumetric errors and geometric errors. The resulting error identification equations are solved using the least squares method. Experimental results demonstrate that the proposed approach can efficiently and accurately identify the geometric errors of the dual rotary axes and maintain robust reliability under real-world operating conditions, making it suitable for practical calibration and accuracy improvement of five-axis machine tools.

Cutting force is the major factor which causes machine tool geometric error, for the sake of finding the relationship between cutting force and the machine tool geometric error, this paper established a model to simulate and analysis, Mastered the situation of stress distribution of various points on the machine and the regularity of internal stress and strain distribution; designed experiments for the precise measurement, and obtained the actual data of machine geometric error. the data matches the results of the simulative analysis. the results has a certain referential value to optimize the design of machine tool, the geometric error modeling and make the realization of software compensation, etc.

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

Kinematic accuracy is a key reason which influence workpiece's geometric error precision on traditional working process of precisely CNC（Computerized Numerical Control）P3G（polygon profile with 3 lobes） grinding machine. A systematic geometric error model has been presented for CNC P3G grinding machine， proposed multi-body system theory integrate with the structure of CNC P3G grinding machine tools, researched on the machine's space geometric errors. By means of separate geometric errors from the machine tools, build geometric mathematical error model. Then, identify 21 error parameters through method of 9 lines, analysis and calculate the total space geometric errors of the workpiece and wheel. Finally, formed a parameter-list and applied software error compensational technique ， achieved real-time control to the motions of workpiece and wheel. Experimental results shown that the geometrical error modeling technique is accurate and efficient, and the precision of CNC P3G grinding machine is highly raised 70%.

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

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

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

The characteristics of geometric errors in CNC machine tools have been investigated in detail. These characteristics include position dependence, relativity, synthesis, and continuity. Tests have been designed to verify these properties, which can be used to guide the error measurement procedure. A new measurement procedure, called the relay method, has been developed. This method has high resolution and can be applied to measure geometric errors in the whole workspace. A machine has been calibrated by the relay method, and the results of error compensation show that the machine tool accuracy has been improved.

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.

This study aims to enhance the spatial precision of five-axis machining centers through a comprehensive exploration of geometric errors, encompassing modeling, efficient detection, and compensation validation. Our approach begins with the establishment of a kinematic error model covering XYZ translational axes and AC rotational axes, providing an in-depth understanding of error origins and interrelationships. Utilizing a laser tracker, we conduct direct measurements of the geometric errors associated with translational axes, and a rotational axis error detection model is developed by using a ball bar, allowing for indirect analysis of rotational axis geometric errors. The validity of both the kinematic error model and error detection is further confirmed through practical on-machine measurements.

Four-axis machine tools with two rotary axes are widely used in the machining of complex parts. However, due to an irregular kinematic relationship and non-linear kinematic function with geometric error, it is difficult to analyze the influence the geometry error of each axis has and to compensate for such a geometry error. In this study, an influence analysis method of geometric error based on the homogeneous coordinate transformation matrix and a compensation method was developed, using the Newton iterative method. Geometric errors are characterized by a homogeneous coordinate transformation matrix in the proposed method, and an error matrix is integrated into the kinematic model of the four-axis machine tool as a means of studying the influence the geometric error of each axis has on the tool path. Based on the kinematic model of the four-axis machine tool considering the geometric error, a comprehensive geometric error compensation calculation model based on the Newton iteration was then constructed for calculating the tool path as a means of compensating for the geometric error. Ultimately, the four-axis machine tool with a curve tool path for an off-axis optical lens was chosen for verification of the proposed method. The results showed that the proposed method can significantly improve the machining accuracy.