A geometric error identification method for the swiveling axes of five-axis machine tools by static R-test

To address the problems of the low accuracy of geometric error identification and incomplete identification results of the linear axis detection of computer numerical control (CNC) machine tools, a new 21-item geometric error identification method based on double ball-bar measurement was proposed. The model between the double ball-bar reading and the geometric error term in each plane was obtained according to the three-plane arc trajectory measurement. The mathematical model of geometric error components of CNC machine tools is established, and the error fitting coefficients are solved through the beetle antennae search particle swarm optimization (BAS–PSO) algorithm, in which 21 geometric errors, including roll angle errors, were identified. Experiments were performed to compare the optimization effect of the BAS–PSO and PSO and BAS and genetic particle swarm optimization (GA–PSO) algorithms. Experimental results show that the PSO algorithm is trapped in the local optimum, and the BAS–PSO is superior to the other three algorithms in terms of convergence speed and stability, has higher identification accuracy, has better optimization performance, and is suitable for identifying the geometric error coefficient of CNC machine tools. The accuracy and validity of the identification results are verified by the comparison with the results of the individual geometric errors detected through laser interferometer experiments. The identification accuracy of the double ball-bar is below 2.7 µm. The proposed identification method is inexpensive, has a short processing time, is easy to operate, and possesses a reference value for the identification and compensation of the linear axes of machine tools.

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.

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

This paper proposes a novel measuring method which uses double ballbar (DBB) to inspect the kinematic errors of the rotary axes of five-axis machine tool. In this study, kinematic error mathematical model is firstly established based on the analysis of the rotary axes errors which originated from five-axis machine tools. In the simulation, working conditions considering different error origins are simulated to find the relationship between the DBB measuring patterns and the kinematic errors. In the measuring experiment, the machine rotary axes move simultaneously along a specified circular path while all the linear axes are kept stationary. The original DBB measuring data are processed to draw the measuring patterns in the polar plots which can be employed to observe and identify the kinematic errors. Rotary error compensation is implemented based on the function of external machine origin shift. Both the simulation and the experiment results show the convenience and effectiveness of the proposed measuring method as well as its operability as a calibration method of five-axis machine tools.

In the process of thermal error modeling of machine tools, the error information is not transparent and the data characteristics are not comprehensive. The Dijkstra algorithm provides an optimization for the classical algorithm, and improving the accuracy of machine tools is an important issue in advanced manufacturing technologies. In this paper we study two methods of error avoidance and error compensation. For CNC machine tools, computer real-time error compensation technology is an economical and effective basic approach. The application of the folded Dijkstra algorithm to realize the compensation technology of the full error model of geometrical machine tool including geometric error and thermal error is put forward. The practical results show the geometric error and thermal error are compensated on 3-axis and 4-axis CNC machine tools, and the accuracy of the error model and the practicality of the compensation method.

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.

Identification and compensation of position independent geometric errors of dual rotary axes for hybrid-type five-axis machine tool based on unit dual quaternions

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.

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.

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

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.

Identification of position-dependent geometric errors with non-integer exponents for Linear axis using double ball bar

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

To meet the high-precision positioning requirements for hybrid machining units, this article presents a geometric error modeling and source error identification methodology for a serial–parallel hybrid kinematic machining unit (HKMU) with five axis. A minimal kinematic error modeling of the serial–parallel HKMU is established with screw-based method after elimination of redundant errors. A set of composite error indices is formulated to describe the terminal accuracy distribution characteristics in a quantitative manner. A modified projection method is proposed to determine the actual compensable and noncompensable source errors of the HKMU by identifying such transformable source errors. Based on this, the error compensation and comparison analysis are carried out on the exemplary HKMU to numerically verify the effectiveness of the proposed modified projection method. The geometric error evaluations reveal that the parallel module has a larger impacts on the terminal accuracy of the platform of the HKMU than the serial module. The error compensation results manifest that the modified projection method can find additional compensable source errors and significantly reduce the average and maximum values of geometric errors of the HKMU. Hence, the proposed methodology can be applied to improve the accuracy of kinematic calibration of the compensable source errors and can reduce the difficulty and workload of tolerance design for noncompensable source errors of such serial–parallel hybrid mechanism.

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.