S-shaped Test Research Articles

Feasibility of 8-Shaped Motion Test for Five-Axis Machining Center

ISO 10791-7, which specifies the machining accuracy test standard for machining centers, and ISO 10791-6, which specifies the interpolation motion test standard, were revised in 2014 to include five-axis machining centers (5-axis MCs). In addition, cone frustum test, which has been used as the National Aerospace Standard (NAS), was revised and introduced in these ISO standards. However, prior to the establishment of these standards, an aircraft manufacturing company in China proposed S-shaped machining test to measure the accuracy of the test piece of an aircraft. This was adopted as an informative annex of ISO 10791-7 in 2020. Furthermore, in 2019, China proposed a method related to S-shaped machining test and a method of 8-shaped interpolation motion test. Since the S-shaped test requires high acceleration and deceleration in some sections, the test results depend on the performance of the computer-aided manufacturing (CAM) software; therefore, it is not efficient in determining the accuracy of the machine tools. In contrast, in the 8-shaped motion test, the tip of the spindle moves based on a sine curve; consequently, high acceleration/deceleration does not occur. Since the tip of the cutting tool is fixed, a device called R-test is used to measure the position of the center of reference ball using three displacement sensors. In this study, we have discussed the feasibility and problems of the 8-shaped motion test. First, the motion of the machine in the figure “8” motion test is clarified. Next, the definition of the parameters necessary to create the NC programs is outlined. In addition, we have proposed a method in which suitable conditions are set for simultaneous 5-axis feed on a 5-axis MC. Finally, the results of an actual test are applied to the 5-axis MC to confirm that no major problems exist.

Kinematics and geometric features of the s-cone test piece: identifying the performance of five-axis machine tools using a new test piece.

The design of machine parts of different sizes and shapes has become relevant in the manufacturing industry which requires five-axis machine tools of high dynamic performance; different machining test pieces have been used to test and reflect the machine tool's performance. The S-shaped is still under development and consideration of which a new test piece better than the S-shaped part has been recommended to be put forward making the NAS979 the only standardized test piece; however, it has some limitations. Hence, this study proposes a new test piece to objectively satisfy the demand for machine tools with higher dynamic performance, which shows much improvement over the standard NAS979 and is the best alternative to the S-shaped test piece, and it combines the geometric and kinematic features of both test pieces. Geometrically, it has non-uniform surface continuity, variable twist angle, and variable curvature; and the cutting tool moves in close and opened angles along the tool path; there is sudden rise and fall of axes' velocity, acceleration, and jerk with much impact during machining which makes the S-cone test piece be machined by only five-axis machine tools with high dynamic performance, and has a better dynamic performance identification effect than the S-shaped test piece based on the trajectory test. Detailed work on the validation of the machine tool's dynamic performance using the S-cone part will be captured next part of this study.

A normal section plane method for profile error analysis of five-axis machine tools based on the ideal tool flank milling surface

The existing studies on profile error analysis and machining accuracy measurement do not consider the impact of the theoretical errors on the machine tool accuracy measurement. Therefore, this study proposes an estimation method of the surface profile error based on the normal section plane, using the theoretical flank milled surface for comparison. This effectively improves the accuracy of profile error estimation. The theoretical flank milled surface is the surface machined by flank milling under ideal conditions. Hence, compared to the traditional analysis method based on the designed three-dimensional model of S-shaped test pieces, the calculated profile error of this method does not include theoretical errors, thereby eliminating the impact of theoretical errors on machine tool accuracy measurement and evaluation. First, an improved method for continuous parameterized dual spline interpolation was proposed. It simplifies the solution of the singular problem of the coefficient matrix of the spline basis function and obtains a continuous ideal machining tool axis trajectory surface with complete geometric characteristics. Next, a method for constructing the theoretical flank milled surface machined with a cylindrical milling tool using equidistant mapping characteristics was proposed; then, the differential transformation relationship at the cutting contact point of the curved surface under the influence of tool path errors was established. Furthermore, the normal section plane method based on the differentiation of the cutting contact point was proposed. The problem of solving the distance from a point to a surface is converted to the problem of solving the distance from a point to a curve in the normal section plane. This improves the accuracy of profile error estimation. The effectiveness of the method was verified by comparing the analysis results of the profile errors of a typical cylindrical surface with the point to surface and the point to curve methods.

Elasto-geometrical error modeling and compensation of a five-axis parallel machining robot

Parallel manipulators have the potentials of high efficiency and high precision in the field of machining and manufacturing. However, accuracy improvement of the parallel manipulator is still an essential and challenging issue, encountering two important problems. Firstly, the ignorance of elastic deformation caused by gravity or deviations of static stiffness model restricts further improvement of accuracy. To solve this problem, an elasto-geometrical error modeling method is proposed. The comprehensive effects of structural errors, elastic deformation under gravity and compliance parameter errors on pose deviations are disclosed. On this basis, the identification equation of actual structural errors and compliance parameter errors can be established. Secondly, the ill-conditioned identification matrix and the identification equation with anisotropic residual error can lead to inaccurate identification results. To solve this problem, a weighted regularization method is proposed. The identification equation with isotropic residual error is built, and accurate identification can be realized with the regularization method. Based on the proposed methods, the error compensation experiment is conducted on the prototype of a five-axis parallel machining robot using a laser tracker. Experiment results show that the accuracy of the machining robot is significantly improved after compensation. An M1_160 test piece and an S-shaped test piece are machined and measured to further validate the effectiveness of the proposed methods. The elasto-geometrical error modeling method and the weighted regularization method can be applied to other parallel manipulators’ accuracy improvement.

Behavior of Speed and Acceleration in the S-Shaped Test

Behavior of Speed and Acceleration in the S-Shaped Test

Tool diameter optimization in S-shaped test piece machining

S-shaped test piece is used to assess the performance of five-axis numerical control machine tools. Compared to traditional test method and test pieces, it performs better and was agreed to be included in the draft international standard at the 79th ISO/TC39SC2 meeting. However, the lack of theoretical research is the barrier to apply for standard and to be widely used. Therefore, this paper aims to study one of the theoretical research that how to choose the suitable tool diameter. We proposed a new research method based on software AdvantEdge, Vector Method for error calculation, Microelement Model of cutting force and deformation model of cantilever beam. The simulation results show that the 20 ≤ diameter < 30 is the proper choices and the 20 is the best choice, which is consistent with the empirical consequence. This method not only provides the theoretical support for the S-shaped test piece, but also can be applied to other parts with complex curved surfaces.

A novel approach to calculating the dynamic error reflected on an S-shaped test piece

This paper proposes a novel approach to calculating the dynamic error distribution reflected on an S-shaped test piece. First, a numerical model of an S-shaped test piece is established, and the distribution characteristics for the twist angle and curvature are analysed. Second, a delay continuous method (DCM), which can transform the discrete input into a delayed step input, is presented to express the single-axis dynamic error affected by the input quantitatively in the form of a mathematical expression. Based on the sinusoidal input, the feasibility of the DCM is verified by comparing the experimental results of a Simulink simulation model and a mathematical expression derived by the DCM. Third, according to a new three-point tangential (NTPT) positioning algorithm and the DCM, this article makes the first attempt to investigate the quantitative calculation method of the influence of the dynamic performance of a servo feed system for five-axis numerical control (NC) machine tools on the dynamic error distribution for S-shaped test pieces after processing. Parameter p, representing the dynamic characteristic of the servo feed system, is varied to compare the difference of the dynamic error distribution law on S-shaped test pieces. The calculation results show that the parameter p can be adjusted to reduce the dynamic error of the final machined test pieces. It is important to improve the dynamic performance of servo feed systems for five-axis NC machine tools and enhance the machining quality of test pieces. In addition, compared with the calculation results of the dynamic error distribution for an NAS979 test piece, the S-shaped test piece can reflect the dynamic performance of the servo feed system for five-axis NC machine tools more accurately and effectively. Finally, the effectiveness of the proposed calculation method is verified through processing experiments on a five-axis NC machine tool.

A novel method for evaluating the validity of dynamic accuracy test pieces for five-axis machine tools

The detection method for direct machining the standard test pieces, which is commonly employed to exhibit the machining precision of five-axis machine tools, can truly reflect the dynamic accuracy of five-axis machine tools in the actual machining process. Existing theories on explaining the phenomenon that the ability of S-shaped test pieces to detect dynamic accuracy for five-axis machine tools are stronger than those of NAS979 test pieces mostly used the qualitative research methods, and they cannot be quantitatively used to reveal the mathematical relationship between machine tools and test pieces. Therefore, this article makes the first attempt to investigate the quantitative evaluation method for the validity of dynamic accuracy test pieces. The dynamic error function of the servo feed system in the frequency domain was derived first by establishing the mechanical system model and control system model. The method of dipole cancellation was used to acquire a simplified transfer function for the dynamic error affected by the input. Based on the zero-order hold property of the discrete input signals, the expression of dynamic error affected by input in the time domain, which intuitively shows the mathematical relationship among the machine tool performances, the test piece characteristics and the dynamic error of the servo feed system, was obtained. Then, the novel evaluation methods of the linear combinatorial value and the combinatorial linear combinatorial value were proposed. A series of comparative analyses between an S-shaped test piece and an NAS979 test piece were carried out based on the proposed new evaluation methods. A machining experiment conducted on a five-axis machine tool is used to verify the evaluation results.

An approach for accuracy enhancement of five-axis machine tools based on quantitative interval sensitivity analysis

Error compensation is a common method to improve the machining accuracy of five-axis machine tools (FAMTs). Before that, in order to identify the key geometric errors that affect the machining accuracy, sensitivity analysis (SA) in entire machining region or a specified point is usually used. However, since the influence of geometric errors on form errors is different in each interval, the result of SA would be affected, which decreases the compensating accuracy. For this reason, a new approach for accuracy enhancement of FAMTs based on quantitative interval sensitivity analysis (QISA) is presented in this paper. First, based on multi-body system theory and homogeneous transform matrix, the volumetric error model of the FAMT is established. Then, the geometric error model of the FAMT is formulated. Second, development of form error model is involved in this paper to clarify the effect law of geometric error on form error. Moreover, the machining region of S-shaped test piece is divided into five intervals. Then, the QISA method is presented to calculate the sensitivity index of each geometric error and identify key geometric errors at different intervals. Finally, simulations and experiments are conducted to validate the feasibility and effectiveness of the presented method.

Geometric deviation reduction method for interpolated toolpath in five-axis flank milling of the S-shaped test piece

Geometric deviation, defined as the distance between the designed surface and the machined surface, is an important component of machining errors in five-axis flank milling of the S-shaped test piece. Since the interpolated toolpath in practical machining process is the approximation of the theoretical toolpath, the geometric deviation caused by the interpolated toolpath appears. To overcome this problem, a novel geometric deviation reduction method is suggested in this study. First, the features of the S-shaped test piece are analyzed. Second, the theoretical toolpath is generated according to the designed surface and the cutter location data is obtained by discretizing the theoretical toolpath. The linear interpolation of the cutter location data is carried out to obtain the interpolated toolpath. Then, the geometric deviation is modeled by calculating the Hausdorff distance between the tool axis trajectory surface based on the interpolated toolpath and the offset surface of the designed surface. Finally, the geometric deviation is reduced by optimizing the cutter location data without inserting more cutter location points. The machining experiment is conducted to verify the effectiveness of the proposed method. The experimental results agree with the simulation results, and both of them indicate the geometric deviation on the machined surface reduces after optimization.

Effect of CAD/CAM Post Process on S-Shaped Machining Test for Five-Axis Machining Center

ISO 10791-7, the test standard for machining centers, was revised in 2014 to add the test method for five-axis machining centers. However, an S-shaped test was additionally proposed as an accuracy test of aircraft parts from China immediately before the establishment of the test standard. In an ISO meeting, various problems such as creating three-dimensional models and evaluation items have been indicated for the proposed test method. By revising these problems, the standard was finally completed and will be introduced as an informative annex soon. However, it is still an inappropriate test method from the viewpoint of performance inspection for machine tools. In this research, the S-shaped test method draft proposed in September 2016 is tested using two types of five-axis machining centers and commercial CAM software. Consequently, a hidden problem is revealed, that is, an abrupt movement that affected the final result is added to the machine because the rotation direction of the rotary axes is not ideal. This is attributed to the performance of the CAM software’s post processor that converts from CL data to NC program. This study provides some insights into avoiding the problem and obtaining better test results.

An optimized single-point offset method for reducing the theoretical error of S-shaped test piece

The S-shaped test piece is utilized to comprehensively detect the machining accuracy of multi-axis machine tools. However, due to the existence of the influence of theoretical error for S-shaped test piece on the acceptance of multi-axis machine tools, therefore, a new methodology to reduce the theoretical error is proposed in this study. Firstly, the uniform double cubic B-spline surface model is applied to a surface representation. By utilizing this model, a model of the S-shaped test piece is established. Furthermore, the distribution of the twist angle at the selected three section lines is obtained. Meanwhile, the influence of twist angle on the theoretical error of S-shaped test pieces is analyzed. Then, the single-point offset (SPO) method is analyzed, which has some drawbacks. In order to significantly reduce the theoretical error of S-shaped test piece, the optimized single-point offset (OSPO) method is proposed. Moreover, the tool path of the S-shaped test piece is generated by CAD/CAM software based on the OSPO method. Finally, in order to verify the feasibility of the presented method, a machining and measurement experiment is carried out on the gantry-type five-axis milling machine tool (XKAS2525) and coordinate measuring machine (CMM) based on the S-shaped test piece, respectively. Experiment results show that the average theoretical error of S-shaped test pieces based on the OSPO method is reduced by about 50.1% than that on the SPO method. In addition, the vast majority of theoretical errors based on the OSPO method are approximately less than 5 μm, which can be negligible. It is therefore reasonable to conclude that, compared with the SPO method, the proposed method in this paper can avoid the influence of theoretical error on the acceptance of multi-axis machine tools intuitively and efficiently.

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.

The Calculation of Roughness Uncertainty by Fitting B-Spline Filter Assessment Middle Lines

The roughness and uncertainty are important parameters of surface morphology. The least square middle line method is often used to estimate the roughness and its uncertainty. However, the roughness and its uncertainty obtained by the least square middle line method are inaccurate. This paper proposes a method to calculate exactly the roughness and its uncertainty by piecewise fitting the smooth B-spline filter assessment middle lines. A B-spline smoothing filter is selected to determine the assessment middle line of roughness. The B-spline filter can not only give the accurate roughness, but also obtain the smooth assessment middle line. The model of roughness uncertainty is proposed by piecewise fitting B-spline filter middle lines as the quadratic curves. The S-shaped test part is used to verify the model of roughness uncertainty.

Machining deformation prediction of thin-walled workpieces in five-axis flank milling

Five-axis flank milling is the main processing method for manufacturing aerospace thin-walled workpieces. The sidewalls of such workpieces are prone to deformation during the milling process because of their low rigidity, which severely affects machining accuracy. Based on this fact, this paper proposes a novel model to predict surface form errors caused by milling force. This study describes an efficient cutter-workpiece engagement (CWE) extraction method for the computation of cutting forces and identification of machining geometry changes during the five-axis flank milling process. The paper then focuses on the establishment of an iterative scheme for machining deformation calculation. This procedure is carried out by considering the coupling effect between cutting forces and tool/workpiece (T/W) deformations, in which the radial cutting depth and the tool axis vector are taken as feedback variables for the iterative computation. Subsequently, the reliability of the proposed model is validated by a 3-mm S-shaped test piece machining with a high-speed steel end mill. The work shows that the surface deformation error comes from the joint effect of the instantaneous milling force and the local stiffness of the workpiece. The relative error rate of the simulation model is 18.8%, which shows good prediction accuracy compared with existing methods.

Influence of NC Program Quality and Geometric Errors of Rotary Axes on S-Shaped Machining Test Accuracy

An S-shaped machining test is proposed for the ISO 10791-7 standard to verify the performance of five-axis machining centers. However, investigation of the factor that has the most influence on the geometrical accuracy of finished S-shaped workpieces has not been undertaken. Determination of the influence of NC program tolerance and geometric errors concerning the rotary axes on the accuracy of the finished S-shaped workpiece forms the main objective of the study. Actual cutting experiments as well as simulations were performed during the proposed investigation. Our results clarify that NC-program tolerance has a significant influence on the end quality of the machined surface. Although geometric errors pertaining to rotary axes also have a significant influence on machined-surface quality, it is difficult to evaluate the influence of each individual error, because all geometric errors make glitches at the same point on the machined surface. The proposed S-shaped machining test can be used to provide a complete demonstration of available machining techniques.

Dynamic accuracy evaluation for five-axis machine tools using S trajectory deviation based on R-test measurement

Abstract This paper presents a new S trajectory kinematic measurement method to evaluate the dynamic accuracy of five-axis machine tools based on R-test measurements. The S trajectory is obtained by scaling the machining path of the S-shaped test piece to the measuring stroke of the R-test. A geometric and dynamic accuracy simulation model is established to analyze the influence of various error factors on the S trajectory test and compare with the conical kinematic test described in ISO10791.6 quantitatively. The simulation results shown that the S trajectory test is more sensitive to most geometric errors and dynamic errors than the conical test. Particularly, to reflect the dynamic error factors such as poor rigidity of machine tools, servo mismatch, reverse error and nonlinear error, the S trajectory test has obvious advantages. Meanwhile, compared with the actual S-shaped piece machining, which is under development for inclusion in ISO 10791.7, the proposed non-cutting kinematic test method can simply reflect the dynamic accuracy of five axis machine tools itself without the interference of other factors and does not require additional workpiece and testing equipment. The proposed method is verified through experiments on a five-axis machine tool.

Theoretical error compensation when measuring an S-shaped test piece

S-shaped test piece aims to assess the performance of five-axis numerical control (NC) machine tools. When the draft international standard (DIS) was introduced at the 79th ISO/TC39SC2 meeting, it was agreed that this test piece would be included. The S-shaped test piece, however, has undeveloped surfaces, which contribute to theoretical error. Because the test piece is used to assess the performance of machine tools and to conduct error tracing, theoretical error should not be included in the detection results obtained by the coordinate measuring machine (CMM). Therefore, the S-shaped test piece, excluding the influences of theoretical error, is crucial to research. This paper calculates the theoretical error of the S-shaped test piece when processed with the single-point offset (SPO) position method and proposes pre-compensation (PRC) and post-compensation (POC) methods to eliminate the influences of theoretical error. We conducted a theoretical analysis to compare three methods, the two compensation methods and the one uncompensated method, and verified the results through actual experiments. Research from principle and practice demonstrates that both the PRC and POC methods compensated for theoretical error up to 0.01 mm and that PRC is more accurate when considering the difference of approximately ±0.0015 mm.

A geometric error tracing method based on the Monte Carlo theory of the five-axis gantry machining center

This article proposes a tracing method to identify key geometric errors for a computer numerical control machine tool by cutting an S-shaped test piece. Adjacent part relationships and machine tool errors transform relationships are described by topology of the machining center. Global sensitivity analysis method based on quasi-Monte Carlo was used to analyze machining errors. Using this method, key geometric errors with significant influence on machining errors were obtained. Compensation of the key errors was used to experimentally improve machining errors for the S-shaped test piece. This method fundamentally determines the inherent connection and influence between geometric errors and machining errors. Key geometric errors that have great influence on machining errors can be determined quickly with this method. Thus, the proposed tracing method could provide effective guidance for the design and use of machine tools.

An improved positioning method for flank milling of S-shaped test piece

Accuracy detection for five-axis numerical control (NC) machine tools that can truly reflect their practical machining precision is of crucial importance. Standard test pieces are commonly employed for this purpose. However, poor accuracy detection performance is obtained when the test pieces used here are applied to five-axis NC machine tools. This paper introduces a new S-shaped test piece that is exclusively designed for the precision detection of five-axis NC machine tools. The S-shaped test piece integrates numerous characteristics associated with aviation parts and has been widely adopted by machine tool makers. This article presents a numerical model of the latest S-shaped test piece and shows that its side surfaces represent typical undevelopable ruled surfaces. The curvature changes along the ruled lines inevitably produce a theoretical error. Thus, machining methods seek to reduce the theoretical error as much as possible. Based on basic summaries of five existing positioning algorithms, a novel algorithm is proposed to position the tool head using three points, wherein two are tangential to the top and bottom boundary curves, respectively, and the third is tangential to the midpoint of the ruled line. The proposed positioning algorithm together with five existing positioning algorithms is applied to the S-shaped test piece, and a numerical error performance analysis is conducted. The results indicate that the machined surface reduces the theoretical error by at least 96% compared to all the existing numerical positioning algorithms except for Redonnet’s algorithm. Compared with Redonnet’s algorithm, the accuracy of the proposed algorithm is equivalent, although the proposed algorithm reduces the calculation time by 62.7%, and is not sensitive to the initial values. Hence, the computational process demonstrates that the proposed method is efficient, robust, and universal. Finally, simulation results were confirmed through an actual machining experiment.