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Two rotating axes of the five-axis machine tools complicate the kinematics, which increases the difficulty of trajectory planning of five-axis CNC machining. In the process of machining a free-form surface with a ball-end cutter, the tool is required to follow the tool tip path of the surface and the restriction of tool orientation is only constrained within a certain range. This paper proposes a planning algorithm based on differential vector optimization for generating a smooth trajectory of each axis for five-axis machining. Firstly, the kinematic model of the five-axis CNC machine tool and the Jacobian matrix are built. Secondly, the optimization objectives combined with the smoothness optimization requirements and the limits of the tool axis vector are established. Then, the trajectory of the moving axis is generated by integrating the optimized differential vector. At last, a waveform surface machining process is simulated in the VERICUT software with the trajectory generated by the proposed optimization method. To prove the feasibility and superiority of the method, the real part machining experiment is conducted in an A-C type five-axis CNC machine. The experiments verify the smoothness and optimal of the proposed path planning method.

In order to fulfill the demands of increasingly complex processes, laser additive manufacturing processes are combined with five-axis linkage technology. The tool axis vector is critical to the accuracy of part shaping. However, due to the machine performance limitation, the previous methods of tool axis planning may cause the laser deposition head to decelerate and wait for the rotary table, leading to an abnormal bulge at the position. Therefore, this paper proposed a tool axis vector optimization method based on automatically smoothing the C-axis rotary angle. First, the adjustment range of the C-axis angle is calculated by forward and negative kinematics, to ensure that the molten pool is still formed at the planned position after adjustment. Then, the positions with large changes in C-axis angle are detected and locally optimized to ensure that the optimized result allows the laser deposition head to maintain a constant speed when linked with other axes. Finally, global optimization is performed using curve smoothing to deal with the corner regions left by the local optimization to make the machine motion smoother. The printing results of S-shaped and elbow parts show a significant improvement in print quality with less wear and tear on the machine, thus demonstrating the effectiveness and feasibility of the method.

The position-dependent geometric errors (PDGEs) of the rotary axes have a critical influence on the accuracy of the five-axis machine tool. It is necessary to measure, identify, and further compensate the PDGEs to improve the accuracy of the five-axis machine tool. The present study presents a method to identify the PDGEs of the rotary axes using the double ball bar (DBB). The presented method requires eight measurement patterns based on four different installation positions of the DBB. All 12 PDGEs of the rotary axes can be identified, especially the angular positioning error that cannot be identified in most of the other presented methods. Experimental verification is carried out, and the measurement uncertainty and the limitations of the presented method are analyzed. Compared with some other reported studies, the advantage of the presented method is that it can identify all PDGEs of the rotary axis and requires less measurement patterns.

For the machining accuracy of five-axis machine tools, it must be emphasized that not only the PIGEs but also the PDGEs of rotary axes influence the machining accuracy. However, until now there is no any commercial measurement system available for identifying the PDGEs in the rotary axes of five-axis machine tools. As a result, this study proposes a robust, efficient, and automatic measurement method to identify and compensate the position-dependent geometric errors (PDGEs) of rotary axes on five-axis machine tools. The proposed measurement method has established an on-machine measurement for the PDGEs of rotary axes by using a touch-trigger probe and three spheres installed on the spindle as well as the tilting rotary table, respectively. For each rotary axis, only a single measuring pattern is implemented to measure the PDGEs with a single setup, which delineates the advantages of efficient and automated identifying procedures in each periodical measurement. By implementing the proposed measurement method, 12 PDGEs can be numerically identified based on the measurement algorithm, which is built through a kinematic error model as well as a least square method. Finally, the proposed measurement method is experimentally conducted on a commercial five-axis machine tool. Moreover, after consequently performing the proposed measurement method, the PDGEs of the rotary axes were quantitatively compensated by the commercial controller to validate its feasibility. The experimental results have clearly delineated that the linear errors and angular errors are reduced from at most 37.81 μm and 10.23 mdeg to 0.9 μm and 0.26 mdeg, respectively. Consequently, the experimental results have demonstrated that the proposed measurement method is efficient and precise.

As a foundation to enhance the machining accuracy of five-axis machine tools, a robust, efficient, and precise method to measure the location errors of rotary axes on five-axis machine tools has been proposed in this study. This precise identification and calibration methodology for on-machine measurement of location errors of rotary axes is achieved by using a touch-trigger probe and a precise sphere installed on a tilting rotary table. Compared to commercially available devices, such as the double ball bar and R-test, the proposed measurement method has the advantages of efficient and automated calibration procedures in each periodical measurement. This proposed calibration algorithm builds a kinematic error model and measurement equations by using a forward and inverse kinematic approach and estimates the location errors by applying the least squares method. Moreover, the proposed calibration algorithm defines the location errors of the two rotary axes so they can be estimated and separated individually to avoid coupling effects. All the location errors of the rotary axes measured using the proposed measurement method were identified after compensation to improve the accuracy of the five-axis machine tool. A simulation was implemented to inspect the influence of uncertainties on the identified location errors of the rotary axes. Finally, an experimental demonstration on a five-axis machine tool with a tilting rotary table validates the feasibility of the proposed measurement method.

Rotary axes of five-axis machine tools have highly coupled geometric errors, which are crucial factors affecting the machining accuracy. In this study, a new feature workpiece is designed, including two features of arc surface and square groove. Based on the on-machine measurement of the workpiece, five position-independent geometric errors of the two rotary axes can be identified. The cutting and measuring steps of the workpiece are described in detail, the identification principle of each error is revealed, and the uncertainty analysis is carried out. During the identification process, the machining domain and measurement domain of the same feature remain unchanged to eliminate the influence of linear axis errors on the identification results; hence, the identification accuracy is improved. In the experimental verification, the result is 90.8% consistent with the ball-bar method, which verifies the feasibility of this method.

By studying the structure and functional characteristics of five-axis linkage CNC machine tool, design five-axis CNC machine tool with X, Y, Z linear motion axes, B and C rotation axes. The virtual simulation system of miniature five-axis machine tool is built based on the VERICT, and an impeller part was simulated and processed as an example. Check whether the state of each moving axis in the machine tool movement is correct, and judge the rationality of the structure design of the machine tool based on the error information such as interference and collision in the processing. It is proved by simulation that the machine can realize five-axis linkage machining within the design range and meet the design requirements.

Rotation axes have been proven to be the greatest factor leading to machine tool errors, which seriously affect the machining accuracy. Therefore, it is imperative to identify the geometric errors of the rotation axes. This research focuses on how to identify the critical geometric errors of the rotation axes, so that the coupling effect of geometric errors which seriously affects the identification of geometric errors of the rotation axes can be examined. To achieve this goal, this paper proposes a global quantitative sensitivity analysis method based on homogeneous transformation matrix (HTM) theory and Sobol sensitivity analysis method. The size and randomness of geometric errors are taken into consideration and the specific indexing angles of the rotation axes are introduced to identify the critical geometric errors of the five-axis machine tool. Based on this analysis method, each geometric error components and the coupling effect between different error sources are evaluated under different indexing angles. The variation of the coupling effect of each error components within the traverse of the rotation axes is explored. The geometric error measurement experiment is established and the results are compared with the simulation results. The simulation results and experimental results reveal that the critical geometric errors that affect the machining accuracy and the variation of the geometric errors coupling effect, which provides useful guidance for the manufacturers and users of five-axis machine tools.

The geometric error of the rotation axis of a multi-axis machine tool is highly sensitive among the geometric errors of the machine tool. Therefore, establishing an evaluation system for geometric errors of rotation axes is important for improving the machining accuracy of workpieces. First, a model for predicting the geometric error of the rotation axis was established based on the multi-body system theory, and then the mapping relationship between the geometric error of the rotation axis and each region with curvature changes in the S-shaped sample was identified. Next, based on the average value in seven different regions with curvature changes in the S-shaped sample, the weights of the mapping regions were calculated. Subsequently, the weights of the 12 geometric errors of the rotation axis (εx(A), εy(A), εz(A), δx(A), δy(A), δz(A), εx(C), εy(C), εz(C), δx(C), δy(C), and δz(C)), and the weights of two rotation axes were identified to establish a comprehensive evaluation system for the geometric errors of rotation axes. Finally, an S-shaped specimen was machined and subjected to on-machine measurement experiments on a five-axis CNC machine, and two rotary axes were evaluated using the established evaluation system. The results show that the maximum average difference between the actual and theoretical values for the S-shaped samples is within reasonable limits. Further, the comprehensive performance of the machine’s rotation axes was evaluated step by step based on the theoretically calculated weight values.

Abstract To solve the problem of geometric error measurement for five-axis ultra-precision machine tools in interpolated five-axis motion, a measurement method based on the double ballbar (DBB) is proposed in this paper. The method proposed in this research can measure the geometric errors of five-axis ultra-precision machine tool through only one-time installation, and the new method is less limited by the layout of machine tools. The motion trajectory is designed, and the length of the DBB remains constant during the measurement process to achieve the measurement of the geometric errors. Furthermore, the measured results are compared with the theoretical results of the error model. It is found that the trend and the amplitude of the measurement results are in agreement with the theoretical results. It is proved that the method can measure the geometric errors of five-axis ultra-precision machine tool effectively.