Five-axis Machine Tool Research Articles

五轴联动加工中局部轨迹优化方法

在五轴联动过程中，刀路轨迹的好坏直接影响到零件的加工效果。由于目前CNC系统普遍采用线性插补技术，刀具轨迹采用线性线段描述，这导致在节点处切向不连续，影响刀具的运动姿态，从而降低了曲面的制造精度。本文的目的是优化局部刀具轨迹，使刀具在线段连接部位平滑过渡，具体实施方法是：通过三次方B样条曲线在相邻线段构造新的控制点，这样能够满足刀具在拐角处2阶连续，保证刀具平滑过渡。实验证明，该方法可以提高五轴机床在复杂曲面上的制造精度。 In the process of the five-axis linkage, the path of the tool directly affects the machining effect of the parts. Since the linear interpolation technique is widely used in the CNC system, the tool path can be described by a linear segment, which causes the cutting direction of the nodes to be incontinuous at the nodes. The purpose of this paper is to optimize the local tool path so that the cutting tool in the line segment connecting part can transit smoothly, and the specific implementation of the method is to construct a new control point by the Cubic B-spline curve in the adjacent segment. This can meet the 2-order continuousness in the corner of the cutting tool to ensure the smooth transition of the tool. Experiments show that this method can improve the accuracy of five-axis machine tools on complex surface.

A Method to Optimize Geometric Errors of Machine Tool based on SNR Quality Loss Function and Correlation Analysis

Instead improving the accuracy of machine tool by increasing the precision of key components level blindly in the production process, the method of combination of SNR quality loss function and machine tool geometric error correlation analysis to optimize five-axis machine tool geometric errors will be adopted. Firstly, the homogeneous transformation matrix method will be used to build five-axis machine tool geometric error modeling. Secondly, the SNR quality loss function will be used for cost modeling. And then, machine tool accuracy optimal objective function will be established based on the correlation analysis. Finally, ISIGHT combined with MATLAB will be applied to optimize each error. The results show that this method is reasonable and appropriate to relax the range of tolerance values, so as to reduce the manufacturing cost of machine tools.

Verifying the accuracy of five-axis machine tool focused on kinematic ISO tests using a torus-shaped test work piece

In the aerospace industry the application of five-axis machines is increasing and becoming common practice. The determination of the accuracy of such five-axis machine however is often difficult because linear and rotary axes are used combined resulting in complex motions. Typical five-axis tests are specified in ISO10791-6 (e.g. AK4, BK4, CK4) and a modified BK4 test is used in this paper to determine the machine’s accuracy first employing five machine axes simultaneously.A new test work piece is derived that can be milled while imitating the same machine movements of the respective BK4 test. For this a torus-shape is cut in the top edge of a cylindrical work piece with a spherical radius mill enabling five-axis movements while cutting. After milling this test work piece the accuracy of the torus shape is measured using a CMM to verify the machine’s accuracy in five-axis mode.Finally the machine deviations measured during the BK4 measurement are compared with the CMM results revealing the same amplitude. A Q-value is introduced and proposed in this paper to express this amplitude of machine deviations as a single value parameter, indicating the machine’s accuracy when using five axes.

An accuracy design approach for a multi-axis NC machine tool based on reliability theory

Accuracy design constitutes an important role in machine tool designing. It is used to determine the permissible level of each error parameter of a machine tool, so that any criterion can be optimized. Geometric, thermal-induced, and cutting force-induced errors are responsible for a large number of comprehensive errors of a machine tool. These errors not only influence the machining accuracy but are also of great importance for accuracy design to be performed. The aim of this paper is the proposal of a general approach that simultaneously considered geometric, thermal-induced, and cutting force-induced errors, in order for machine tool errors to be allocated. By homogeneous transformation matrix (HTM) application, a comprehensive error model was developed for the machining accuracy of a machine tool to be acquired. In addition, a generalized radial basis function (RBF) neural network modeling method was used in order for a thermal and cutting force-induced error model to be established. Based on the comprehensive error model, the importance sampling method was applied for the reliability and sensitivity analysis of the machine tool to be conducted, and two mathematical models were presented. The first model predicted the reliability of the machine tool, whereas the second was used to identify and optimize the error parameters with larger effect on the reliability. The permissible level of each geometric error parameter can therefore be determined, whereas the reliability met the design requirement and the cost of this machining was optimized. An experiment was conducted on a five-axis machine tool, and the results confirmed the proposed approach being able to display the accuracy design of the machine tool.

Rapid dynamics prediction of tool point for bi-rotary head five-axis machine tool

Receptance Coupling Substructure Analysis (RCSA), an effective approach to rapidly predict the tool point frequency response function (FRF), generally requires the response of spindle-machine assembly by experiments. This method is feasible for three-axis machine tool because the spindle and its posture are normally unchangeable. But in terms of five-axis milling, the spindle-machine assembly changes continuously. The purpose of this study is to propose new techniques to solve the constantly-changing assembly response in order that RCSA can be used for bi-rotary head five-axis machine tools. Based on receptance matrix determination in coupling direction and single degree of freedom coupling simplification, the swivel model for holder tip receptances is established for swivel motion. According to the concept of oriented frequency response function, the rotational model is derived to calculate the holder tip receptances with rotary motion. By combining the swivel model and the rotational model, the holder tip receptance of arbitrary posture can be calculated by three orthogonal postures. A five-axis machine tool with bi-rotary head is used to conduct FRF tests on different postures. Experimental results show that the models proposed can accurately predict tool point frequency response of any posture and large difference in FRFs among those postures of bi-rotary head is detected.

Measurement Accuracy Investigation of Touch Trigger Probe with Five-Axis Machine Tools

Abstract The touch trigger probe plays an important role in modern metrology because of its robust and compact design with crash protection, long life and excellent repeatability. Aside from coordinate measuring machines (CMM), touch trigger probes are used for workpiece location on a machine tool and for the accuracy assessment of the machine tools. As a result, the accuracy of the measurement is a matter of interest to the users. The touch trigger probe itself as well as the measuring surface, the machine tool, measuring environment etc. contribute to measurement inaccuracies. The paper presents the effect of surface irregularities, surface wetness due to cutting fluid and probing direction on probing accuracy on a machine tool.

Effect of the dynamic stiffness of a five-axis machine tool on the quality of sculptured surface

To achieve high quality of sculptured surface, a five-axis machine center must have excellent dynamic behavior. This article gives a new way to characterize and present the performance of machine center on milling sculptured surface which is constrained by the dynamic stiffness. First, the formation mechanism of surface quality is explained in intermittent milling process. It is mainly affected by the vibration frequency of cutting behavior. Second, the concept of dynamic stiffness of machine center is proposed and calculated based on the movement of multi-axis. To elaborate such effect, the map of dynamic stiffness on a sculptured surface, S part is obtained. The change of stiffness causes the different vibration frequency and then leads to different surface quality. Finally, experiments are conducted on S part by microscope and the waviness measurement. The results demonstrate the proposed method is very close to the true one. Presenting, measuring, and controlling the surface quality are easy for the user to understand the challenging performance of the machine center on milling sculptured surface.

Generalized cutting loads decomposition model of five-axis serial machine tools based on the screw theory

There are large volume of existing literatures focused on cutting force modeling, but so far only few research has been reported on cutting loads decomposition model to calculate cutting loads components acted on five axes of the machine, which, however, directly affect five-axis tracking accuracy. To this end, a generalized cutting loads decomposition model of five-axis serial machine tools is proposed, which provides a mathematical basis to evaluate the cutting loads components. A cutting loads decomposition model is first developed based on kinematics and virtual work analysis, then a generalized cutting loads decomposition model is established by differentiating the forward kinematics model based on the screw theory. Kinematic factors that affect the cutting load components on translational and rotary axes are also analyzed, which provides a guidance to optimize the workpiece setup location to reduce the cutting loads components acted on rotary axes. Experiments and simulations on a table-tilting five-axis machine tool verify the effectiveness of the proposed model.

Direct cutting of a pyramid part to evaluate a five-axis machine tool with the Taguchi method

When evaluating five-axis machine tools, to develop a simple method is easy to implement for the many real unpreventable issues that occur, such as during part assembly, machining vibration, and finding a way to compare different machine tool types. A traditional verification assessment cannot overcome these issues. The implementation method for the test piece is not limited to any specific geometric cutting pattern, and these test pieces should not be limited only to a certain type of five-axis machining. In this paper, we used a pyramid test piece for the direct cutting verification comparison. By using different test piece processing and different crossed-axis five-axis machine tools, it is difficult to determine the characteristic points of machining errors, which is why we proposed a direct cutting method. From the results, we prove that the pyramid test piece is a simple one-time use method to quantify the comparison data from a single rotary axis. To calculate the cutting motion error data from the corresponding direct cutting motion, we will use mechanical advantage (MA) along with Taguchi’s method for signal-to-noise (S/N) ratio. In addition, in order to solve the interactive effect of multi-axis motion, we also proposed using Taguchi’s “variable separable model” to quantify the interaction value of each cutting motion, which solves this evaluation question.

Actual inverse kinematics for position-independent and position-dependent geometric error compensation of five-axis machine tools

This paper proposes an efficient actual inverse kinematics method to compensate the geometric errors of five-axis machine tools. The analytical expressions of corrected numerical control (NC) code are derived according to the invertibility, associative law of multiplication, and block calculation of homogenous transformation matrix (HTM). No additional analysis and models are needed for the compensated expressions, appropriate conversion with the geometric error model based on HTM is sufficient. It is simple, convenient and universal for geometric error compensation. The corrected NC code can be obtained through algebraic operation, without time-consuming iteration, differential, or pseudo-inverse algorithm. Then compensation accuracy and efficiency of the method are simulated. And the results indicate higher efficiency compared to existing method. At last, the method is verified by cutting experiment on a five-axis machine tool. Both simulation and experiment results can validate the feasibility of the method. The proposed method significantly improves the computation efficiency and is considered more suitable for real-time compensation.

A formulation of tooth deformation and its error compensation for worm gear transmission mechanisms

Milling head and rotary table are the key components in five-axis CNC machine tools. However, tracking and positioning precision of these rotary axes based on worm gear mechanisms are affected by the backlash, friction, elastic deformation, and other nonlinearities. Therefore, finding out a simple and universal principle to predict the tooth deformation in an initial design is quite significant. A novel deformation calculation and compensation method with finite element analysis and circular plate theory is proposed for the worm gear transmissions. When the relationship (form factor) between the solutions of circular plate theory and finite element analysis is derived, deformation calculation with finite element analysis can be replaced by multiplying the solution of circular plate theory and the form factor. Analysis and calculation results show that the presented method can provide a reference for the compensation control of the positioning errors.

Table-Based Volumetric Error Compensation of Large Five-Axis Machine Tools

This paper presents a geometric error compensation method for large five-axis machine tools. Compared to smaller machine tools, the longer axis travels and bigger structures of a large machine tool make them more susceptible to complicated, position-dependent geometric errors. The compensation method presented in this paper uses tool tip measurements recorded throughout the axis space to construct an explicit model of a machine tool's geometric errors from which a corresponding set of compensation tables are constructed. The measurements are taken using a laser tracker, permitting rapid error data gathering at most locations in the axis space. Two position-dependent geometric error models are considered in this paper. The first model utilizes a six degree-of-freedom kinematic error description at each axis. The second model is motivated by the structure of table compensation solutions and describes geometric errors as small perturbations to the axis commands. The parameters of both models are identified from the measurement data using a maximum likelihood estimator. Compensation tables are generated by projecting the error model onto the compensation space created by the compensation tables available in the machine tool controller. The first model provides a more intuitive accounting of simple geometric errors than the second; however, it also increases the complexity of projecting the errors onto compensation tables. Experimental results on a commercial five-axis machine tool are presented and analyzed. Despite significant differences in the machine tool error descriptions, both methods produce similar results, within the repeatability of the machine tool. Reasons for this result are discussed. Analysis of the models and compensation tables reveals significant complicated, and unexpected kinematic behavior in the experimental machine tool. A particular strength of the proposed methodology is the simultaneous generation of a complete set of compensation tables that accurately captures complicated kinematic errors independent of whether they arise from expected and unexpected sources.

Functional accuracy investigation of work-holding rotary axes in five-axis CNC machine tools

Rotary axes error motions of five-axis CNC machine tools affect dimensional, geometrical and form accuracy of machined features according to structural design and sensitive direction considerations. Work carrying kinematic chains mostly use one rotary axis in radial Fixed Sensitive Direction (radial FSD) setup. The application keeps workpiece axis coaxial with the axis of rotation, preparing more flexibility for machining of complicated features. In spite of conspicuous advantages, in case of poor geometrical quality of machined features, lack of knowledge about error patterns makes the error source isolation process more difficult. This paper investigates the consequences of cycling error motions of radial FSD work-holding rotary axes, in order to prepare intuitive knowledge about possible error patterns. A virtual cutting module equipped with an error-mapping model is generated to simulate the cutting process in vicinity of different error motion scenarios. As a novel approach, comparison of measured deviations with available error patterns facilitates the error source isolation. Experimental results conducted on airfoil cutting process verified the effectiveness of the presented method.

High Efficiency Machining for Integral Shaping from Simplicity Materials Using Five-Axis Machine Tools

In the integrally shaping process from a simple material shape to an objective shape, it is necessary to reduce the time required for the machining process in order to improve cost savings and the effectiveness of mass production. For the purpose of achieving high efficiency in the integral shaping from simplicity materials, we have focused on a rough cutting process that requires the most time in the manufacturing process. The purpose of this research is to propose a method for realizing high-speed rough machining using five-axis machine tools with a voxel model, and confirm the high efficiency of the rough cutting. In this research, we use five-axis controlled machine tools for material machining, and suggest two machining methods for the rough cutting process using the voxel model. The first method derives the tool posture where the cutting removal quantity becomes the maximum; this method also carries out a rough cutting process via 3+2 axis controlled machining. The other method carries a complete convex shape that includes the required shape, and simultaneously machines via five-axis machining based on the complete convex shape. This paper demonstrates the 3+2 axis control machining method that uses the voxel model to perform the rough machining process with high efficiency, and the simultaneous five-axis control machining method that uses a complete convex shape model for rough machining. We confirm the results with a computer simulation and actual machining experiments.

Online adaptive measurement and adjustment for flexible part during high precision drilling process

Shape of flexible part is easy to be out of tolerances due to deformations in the clamping and machining process. These deformations are generated randomly and hard to be predicted. Surface normal drilling and countersinking of flexible part is commonly necessary in aircraft assembly process. An online high precision surface normal measurement and cutter orientation compensation method is developed for adaptively drilling of flexible part in this paper. During the process of normal measurement and adjustment, the distance from tool nose to drilling point is accurately measured and adjusted synchronously, which is critical for countersinking. To accurately measure the current normal of the deformed workpiece, two 2D laser displacement sensors are applied to measure the surface profiles of the workpiece and sample two sets of geometrical points each time. Two crossed spatial curves are respectively fitted by the two sets of geometrical points, and the surface normal at the intersection point of the crossed curves is computed. After the deviation between the measured normal and tool orientation is calculated, an online compensation method is used to eliminate the deviation and meet the perpendicularity requirement of the cutter axis to the workpiece surface, and the distance from tool nose to drilling point is measured and adjusted to the setting value synchronously. The compensation method is based on the kinematic transformation of a five-axis machine tool and is implemented by NC compensation. Simulations and experiments are conducted to validate the feasibility and effectiveness of the online adaptive measurement and adjustment method.

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

This paper proposes a new method to identify the 12 geometric error components of the swiveling axes of five-axis machine tools by static R-test. First, the geometric error modeling of a five-axis machine tool including the error sources of the C-A swiveling head is briefly introduced based on the MBS method. With the assistance of an auxiliary fixture, the measuring strategy of the swiveling axes that consists of six inspection modes by static R-test is proposed. Then, a geometric error identification algorithm for the C- and A-axis is respectively proposed based on the least square method. Numerical simulation is conducted and the results show that the accuracy of the identification algorithm can reach 89 %. An optimization method for the auxiliary fixture is proposed by minimizing the condition number of the identification matrixes to further improve the identification accuracy. Finally, numerical simulation shows that the identification accuracy can be increased to 97 % after optimization. The theoretical analysis and numerical simulation results indicate that the proposed swiveling axes geometric error identification method is both efficient and effective.

Sculptured surface-oriented machining error synthesis modeling for five-axis machine tool accuracy design optimization

Customer-oriented design is very important for machine tool manufacturers to win competition in the market. Mechanical parts with complicated sculptured surface are widely utilized in mechanical systems such as automobiles, aircrafts and wind turbines, and they are often machined by five-axis machine tools with high precision requirements. However, traditional machine tool design has not accounted for the varied machining errors in producing complex sculptured surface, which leads to inferior performance. To address this challenge, a novel machining error synthesis model is proposed in this paper for accuracy optimization in designing general five-axis machine tools used for making various sculptured surfaces. The new synthesis model is constructed by integrating a generic machine tool volumetric error model and two new surface machining error production models, and it bridges between the surface machining profile error and the machine tool accuracy. The synthesis model is then applied as a constraint in machine tool accuracy design optimization. A cost-tolerance function is formulated to construct the objective function, and a heuristic algorithm is developed to implement the optimization. These modeling and optimization methods are validated by one case study.

Squareness error modeling for multi-axis machine tools via synthesizing the motion of the axes

This paper presents one novel model of squareness errors using the D-H matrix to improve the accuracy of integrated geometric errors of the machine tools. It considers the motion of the axis and reflects the geometric meaning of the squareness errors. Firstly, analysis of the existing squareness error models is proposed. It helps to find the improvements of the modeling. Secondly, squareness error modeling is represented by integrating the kinematic property of the axes. The influences of squareness errors are to change the translational direction of translational axes and to deflect the axial line of rotary axes. The squareness error model of translational axes is expressed as the translational homogeneous matrix along the real movement direction. And, the model of rotary axes is expressed as the rotational homogeneous matrix around the real axial line. The unit vector of the real direction is established based on the geometric definition of squareness errors. The models are available for different axes with the property of the axes. Finally, experiments are conducted on one SmartCNC500 five-axis machine tool. The virtual large squareness errors of translational axes and C-axis are simulated by the motion of axes. The positions of the target are measured by laser tracker when moving the axes. The comparisons of measured points and calculated points with the proposed model and one existing model are proposed. The results show that the novel models are precise.

The tool following function-based identification approach for all geometric errors of rotary axes using ballbar

This paper proposes a tool following function-based identification approach (TFFIA) for geometric errors of two rotary axes for one five-axis machine tool. It is comprehensive to identify all geometric errors of rotary errors. Firstly, synthetic error formulas of ballbar originate from the geometric error model of machine tools in order to consider the influences of 21 errors of three translational axes. It makes the approach more reasonable and precise. Secondly, the structures of three measurement patterns of TFFIA are described. Thirdly, in each pattern, errors of rotary axes affecting the accuracy of the sensitive direction are identified. As the result, the identification equations of all 20 errors coincide with the geometric properties of errors. Moreover, the impacts of setup errors of ballbar are eliminated with least square method to improve the precise of TFFIA. According to the structures of three patterns, only three installation of workpiece ball of ballbar are needed in the whole identification of two rotary axes to obtain the required ballbar readings. It greatly shortens the measurement time. Twenty geometric errors of two rotary axes are calculated with identification equations and ballbar readings. Finally, TFFIA is applied to a SmartCNC500 five-axis vertical machining center. The corresponding comparisons are proposed to verify the effectiveness and accuracy of TFFIA.

Accuracy evaluation of rotary axes of five-axis machine tools with a single setup of a double ball bar

A double ball bar (DBB) is used extensively to evaluate the geometric and dynamic performance of three-axis machine tools by means of the XY, YZ and XZ planar circular tests. However, research using a DBB to test the rotary axes of five-axis machine tools simply, quickly and effectively is scarce. In this paper, a method having two steps to identify the imprecision of the rotary axes caused by the position-independent geometric errors (PIGEs) is presented for a tilting rotary type five-axis machine tool using a DBB. The first step is designed to evaluate two rotary axes with one setup. Its advantage of fast diagnosis effectively reduces the machine down time, and thus can be employed as a quick testing approach of the machine tool. However, if some of the diagnosed errors fall outside their tolerances, a more accurate but slower check needs to be carried out due to the limitation of the first step. The second step aims to test the two rotary axes separately, each in two sub-steps. By means of varying the position of the pivot, the A- and C-axes can be tested individually. Both steps are performed with only one axis moving, thus simplifying the error analysis. Implementation of the proposed methods was carried out on a Hermle C600U five-axis machine tool. To show the validity of the method, the identified PIGEs are compensated for in each step, which suggests that the first step can be used as a fast and preliminary indication of a five-axis machine tool’s performance, whilst the second can be carried out if a more thorough evaluation is needed.