Geometric Errors Of Rotary Axis Research Articles

A modified method for measuring geometric errors of rotary axes based on sensitivity analysis and error simulation

Complicated measurement for machine tools geometric errors limits the high-accuracy machining processes. This research is aimed at measuring and identifying geometric errors of rotary axes efficiently by designing and optimizing measurement method using double ballbar. First, the conical and tangential measurement patterns are designed to reduce the installation times of the double ballbar. Secondly, the effect of installation errors is reduced by analyzing the coefficient matrix to avoid error accumulation. Thirdly, measurement trajectories affected by position-independent geometric errors are simulated and eliminated. Finally, the error measurement and validation experiments were performed on a dual-turntable five-axis machine tool, and the machining precision was improved by 34.09%-48.89%. The results indicated that the scheme can effectively identify the geometric errors of rotary axes and has the advantages of high efficiency and accuracy.

Synchronous Measurement and Verification of Position-Independent Geometric Errors and Position-Dependent Geometric Errors of Rotary Axes on Five-Axis Machine Tools

Synchronous Measurement and Verification of Position-Independent Geometric Errors and Position-Dependent Geometric Errors of Rotary Axes on Five-Axis Machine Tools

Geometric error modeling and decoupling identification of rotary axis of five-axis machine tool based on spatial trajectory planning

This paper proposes a method for identification of geometric error and the improvement of measuring accuracy of rotary axes. The primary objective of this work concentrates on the decoupling identify of geometric errors of rotary axis, and the optimal selection of measurement parameters (velocity and measuring points), which can ensure measurement completeness and improve accuracy simultaneously. The proposed approach involves the construction of spatial trajectory driven four-axis motion synchronously. Subsequently, measurement parameters are optimal selected with identification matrix. In the next step, PDGEs are represented using NURBS rapidly solved. The investigations reveal that error decoupling can further enhance compensation accuracy. It was also shown that simply increasing the number of measurements does not improve identification accuracy. The result of experiment indicates that the average compensation rate of trajectory reaches 59.73 %. Therefore, the proposed method can be employed in the reliable calibration of geometric errors particular to five-axis machine tool.

A novel identification method for all geometric errors of rotary axis based on boundaryless constraint optimization method

For the redundancy in definition of position independent geometric errors(PIGEs) and position dependent geometric errors(PDGEs), it is difficult to identify all geometric errors of rotational axis simultaneously. A novel identification method using boundaryless constraint optimization method(BCOM) is established to improve PIGEs and PDGEs identification accuracy of rotary axis. For PIGEs, the two different dimension errors are identified separately based on least square method through appropriate measurement direction by double ball bar(DBB), and thus decrease condition number of identification matrix. For PDGEs, the B-spline curve is applied to fit the geometric errors and the objective function has been established. Several measurement paths are conducted and geometric errors are figured out by iterations of objective function. Furthermore, setup errors of DBB are investigated and discussed based on the sensitivity analysis. Finally, Simulations and experiments are conducted and their results demonstrate the effectiveness of the proposed method.

A new machining test to identify position-independent geometric errors of rotary axes for five-axis machine tools

A new machining test to identify position-independent geometric errors of rotary axes for five-axis machine tools

R-test-based identification method for geometric errors of rotary axes in a five-axis machine tool with a rotary table and tilting head

This paper uses an R-test method to identify the 20 geometric errors of the two rotary axes in a five-axis machine tool with a tilting head and a rotary table. The Position-Independent Geometric Errors (PIGEs) result in deviations of the actual axis from the ideal axis, leading to the overall deviation of the set points on the circular trajectory. Therefore, the actual circular trajectory can be fitted by measuring the actual coordinates of the set points, and the actual axis can be further solved to establish the solution equation of PIGEs. Further, the volumetric error model for the set points is constructed, and the unknown motion matrices associated with the linear axes in the volumetric error model are adjusted, allowing for the determination of Position-Dependent Geometric Errors (PDGEs). This method can identify geometric errors of the two rotary axes by measuring six sets of circular trajectories under three setups.

Sensitivity analysis of inverse multilateration based on tracking interferometer measurement for a bi-rotary head five-axis machine tool

This paper proposes a novel inverse multilateration that improves the accuracy by sensitivity analysis and calibration of rotary axes’ position-independent geometric errors. In recent years, the tracking interferometer measurement with inverse multilateration has been widely adopted in the assessment and compensation of the five-axis machine tool. It uses the bi-rotary head as the steering mechanism to reduce cost, which also introduces errors from rotary axes. In this paper, a sensitivity analysis for position-independent geometric errors of rotary axes is proposed to reveal the error propagation mechanism and identify the main error sources. An optimization for the number and distribution of measured points is investigated based on the result of sensitivity analysis. Monte Carlo simulations and experiments are carried out on a bi-rotary head five-axis machine tool to verify the proposed method. The results show that the accuracy and efficiency of inverse multilateration measurement have been significantly improved.

Dual quaternion-based kinematic modeling for decoupling identification of geometric errors of rotary axes in five-axis platforms

Identification of the geometric errors of rotary axes is important for deciding the machining accuracy of five-axis platforms. In this paper, a programmable identification method is proposed to decouple the position-dependent and position-independent geometric errors (PDGEs and PIGEs) of the rotation axis. First, the kinematics model of the five-axis platform is developed by dual quaternions theory, and then the physical significance of left multiplication and right multiplication of PDGEs error model is analyzed. The motion difference between the base coordinate system and its local coordinate system is compared by simulation analysis. The geometric relationship between rotation direction and motion elements is established based on the error model, which is used to design an optimization algorithm for identifying the orientation errors of PIGEs. Additionally, the effect of linear axis PIGEs is eliminated by equivalent replacement, and a sample regression model is developed to identify the offset errors of PIGEs. The PDGEs are separated considering the Motion First principle. Finally, the proposed model and identification method were verified on a five-axis dispensing platform.

One-step measurement method of five-axis machine tools using a laser tracer

To improve the motion accuracy of five-axis machine tools, it is important to develop a simple methodology to calibrate all geometric errors. This paper proposes a one-step measurement method to calibrate the five-axis machine tool using a laser tracer. First, a simplified geometric error definition of the five-axis machine tool is presented, which is sufficient and necessary to determine the tool error relative to the workpiece. Subsequently, a one-step measurement method using a laser tracer is proposed, and joint movements of five motion axes are adopted to simultaneously identify all geometric errors. Besides, a measurement path generating method is presented to save the trouble of manually planning the complex measurement path. Compared with the traditional two-step measurement method, the proposed method only needs four laser tracer positions and two reflector offsets, simplifying the measurement procedure and enhancing the measurement accuracy of geometric errors of rotary axes.

Equivalent geometric errors of rotary axes and novel algorithm for geometric errors compensation in a nonorthogonal five-axis machine tool

The indirect identification of the geometric errors (GEs) in the rotary axis of a machine tool yields six equivalent GEs (EGEs) that are position-dependent; through an analytical proof, this study demonstrates that these errors also represent four position-independent GEs of the axis. Moreover, a novel algorithm using ball bar measurements to calculate the EGEs of a nutating rotary B-axis and a rotary C-axis is presented herein. This paper also presents a new analytical solution for the actual inverse kinematics of a nonorthogonal five-axis machine tool; this solution is used for GE compensation. The presented algorithms are implemented in a self-developed software that alters the nominal numerical control code in order to eliminate GEs. The compensation accuracy and efficiency are tested using a simulation system. The results demonstrate that the proposed compensation algorithm eliminates all identified GEs. Lastly, a cutting test executed on a machine confirms that the proposed algorithms considerably improve machining accuracy.

Separation and compensation of geometric errors of rotary axis in 5-axis ultra-precision machine tool by empirical mode decomposition method

In machining of a microstructure on a free form surface, a five-axis ultra-precision machine tool has a great advantage in its flexibility and efficiency compared to a conventional machine tool. However, rotary axes in the five-axis machine tools are sensitive to geometric errors due to their complicated structures. Therefore, the geometric errors of the rotary axes must be identified and compensated. Due to the nonlinear coupling and inevitable mutual influence between position independent geometric errors (PIGEs) and position dependent geometric errors (PDGEs), it is difficult to separate and compensate PIGEs and PDGEs accurately and effectively through conventional modeling and compensation methods, and there is no unified standard to judge whether the results are accurate. This paper first proposed an empirical mode detection (EMD) method to identify PIGEs and PDGEs of the rotary axis of a five-axis ultra-precision machine tool directly and simultaneously without any objective function, which solves the problem of mutual influence between mixed errors that cannot be avoided by conventional methods. The geometric errors are regarded as the mixed signals related with the rotation angle of the rotary axis, which are brought into the EMD procedure to calculate the error components. Cutting experiments were carried out on an Al6061 workpiece, and the results were analyzed to verify the proposed method.

Influence of Tool Length and Profile Errors on the Inaccuracy of Cubic-Machining Test Results

A cubic-machining test has been proposed to evaluate the geometric errors of rotary axes in five-axis machine tools using a 3 × 3 zone area in the same plane with different tool postures. However, as only the height deviation among the machining zones is detected by evaluating the test results, the machining test results are expected to be affected by some error parameters of tool sides, such as tool length and profile errors, and there is no research investigation on how the tool side error influences the cubic-machining test accuracy. In this study, machining inaccuracies caused by tool length and tool profile errors were investigated. The machining error caused by tool length error was formulated, and an intentional tool length error was introduced in the simulations and actual machining tests. As a result, the formulated and simulated influence of tool length error agreed with the actual machining results. Moreover, it was confirmed that the difference between the simulation result and the actual machining result can be explained by the influence of the tool profile error. This indicates that the accuracy of the cubic-machining test is directly affected by tool side errors.

A general identification method for position-dependent geometric errors of rotary axis with single-axis driven

Position-dependent geometric errors (PDGEs) of rotary axis affect the accuracy of the multi-axis machine tool. However, many PDGE identification methods were not general enough and not applicable when the structure of the machine tool was limited or changed. In this paper, a general PDGE identification method with single-axis driven was proposed. Firstly, the comprehensive length change model of the double-ball bar (DBB) was established. The simplification was conducted through the constraint condition to obtain the identification matrix. Then, the effect of the installation errors of the DBB was analyzed and eliminated. Simulations were carried out to validate the correctness of the proposed method when considering the installation errors. Next 10 measurement patterns were determined according to the structure limitation of the small-size 5-axis machine tool. Totally 364 combinations with full rank identification matrix are available. Finally, the prediction experiments and analysis for standard deviation were conducted to further validate the effectiveness of the proposed method. It turned out that the small condition number of the identification matrix can more likely achieve high accuracy. And an improved combination using 5 patterns was proposed with the same accuracy achieved compared to that using a total of 10 patterns.

A novel methodology for predicting and identifying geometric errors of rotary axis in five-axis machine tools

The geometric errors of rotary axes are crucial error sources of a five-axis machine tool. They directly affect the machining accuracy, and therefore become one of the most important items for accuracy design. In this paper, a prediction and identification method for the geometric errors of rotary axes on a five-axis machine tool is proposed. The prediction is realized by calculating the mapping relationship between tolerances and geometric errors of rotary axes, which is based on exploring rotary axes’ motion regulation and Fourier series fitting. Then in order to figure out the practical geometric errors of rotary axes, the identifying model is established based on homogeneous transform matrix (HTM). Double ball-bar (DBB) is adopted to test error motions of rotary axes. Finally, a demonstration experiment has been conducted for verifying the effectiveness and precision of the proposed prediction model. The experimental results show that the predicting model is able to reflect the motion principle of rotary axes’ kinematic errors. The SSE, which expresses residual sum of squares between estimated value and identified point, of ez(c),δx(c),ey(c),δz(c),ex(c), and δy(c), are 7.7716 × 10−11, 1.2064 × 10−4, 2.7838 × 10−10, 2.9639 × 10−7, 1.8966 × 10−10, and 2.7838 × 10−10, respectively. And R2, who represent fitting equation’s coefficient of determination, of abovementioned geometric errors, are 0.8978, 0.9876, 0.9978, 0.9453, 0.9985, and 0.9978, respectively. The computing results show that two kinds of curves are basically coincide, and the proposed method is proven to be feasibility.

Simultaneous geometric error identification of rotary axis and tool setting in an ultra-precision 5-axis machine tool using on-machine measurement

This paper presents a method to identify the position independent geometric errors of rotary axis and tool setting simultaneously using on-machine measurement. Reducing geometric errors of an ultra-precision five-axis machine tool is a key to improve machining accuracy. Five-axis machines are more complicated and less rigid than three axis machine tools, which leads to inevitable geometric errors of the rotary axis. Position deviation in the process of installing a tool on the rotary axis magnifies the machining error. Moreover, an ultra-precision machine tool, which is capable of machining part within sub-micrometer accuracy, is relatively more sensitive to the errors than a conventional machine tool. To improve machining performance, the error components must be identified and compensated. While previous approaches have only measured and identified the geometric errors on the rotary axis without considering errors induced in tool setting, this study identifies the geometric errors of the rotary axis and tool setting. The error components are calculated from a geometric error model. The model presents the error components in a function of tool position and angle of the rotary axis. An approach using on-machine measurement is proposed to measure the tool position in the range of 10 s nm. Simulation is conducted to check the sensitivity of the method to noise. The model is validated through experiments. Uncertainty analysis is also presented to validate the confidence of the error identification.

Identification and compensation of position-dependent geometric errors of rotary axes on five-axis machine tools by using a touch-trigger probe and three spheres

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.

Identification of integrated geometric errors of rotary axis and setup position errors for 5-axis machine tools based on machining test

As a fundamental error source, geometric errors of 5-axis machine tools have a negative influence on a machine tool’s motion accuracy. Large numbers of efficient and robust geometric error measurement and compensation methods have been developed by existing researches to improve the performance of the machine tools during the automatic machining of the workpiece. However, influence of the geometric errors on workpiece clamping is hard to measure and evaluate in most of the clamping processes since manual operations are involved. It is important to identify both geometric errors and setup position errors to control the entire machining process, standing from the perspective of a manufacturer. In this study, a position-dependent geometric error and setup position error identification method is investigated based on machining test. A kinematic model for a 5-axis machine tool with tilting rotary table is constructed while considering both geometric errors of the two rotary axes and setup position errors. Machining patterns and calculation algorithm are designed to analytically calibrate these errors. Experimental demonstration is conducted to validate the feasibility of the proposed measurement method.

Identification and compensation of geometric errors of rotary axes in five-axis machine tools through constructing equivalent rotary axis (ERA)

This paper proposes a volumetric accuracy enhancement method of rotary axes in five-axis machine tools through constructing equivalent rotary axis (ERA). The influences of translational axes, setup errors of table ball and tool ball are simultaneously considered. A new concept named ERA, originated from the definition of axis of rotation, is proposed to globally describe the instantaneous position and orientation of rotary axes. Based on this concept, only six parameters are needed to describe the influences of geometric errors rather than ten parameters required by the existing concept of PDGEs and PIGEs. At the same time, the coupled relationship between the compensated motion commands of rotary axes and geometric error components is eliminated, and the geometric error compensation is realized by formulating analytical expressions. The typical characteristics of the proposed method lie in the following three aspects. First, the axis twists in the identification method naturally follow the constraint of rotary axis, and thus the normalization and iteration procedure required by existing literatures are avoided. Second, compact form of geometric error compensation is established and explicit equations are given to generate the compensated motion commands. Specially, the inverse kinematic model of five-axis machine tools can be well integrated into the proposed method. Third, besides machine tools with non-orthogonal rotary axes, the proposed method can also be easily applied to five-axis machine tools with non-orthogonal rotary axes just by modifying the ERA parameters. Simulation results and blade machining tests verify the effectiveness of the proposed method, and more than 70% machining precision improvement is observed.

Continuous measurements with single setup for position-dependent geometric errors of rotary axes on five-axis machine tools by a laser displacement sensor

This study proposes a continuous measurement method of 12 position-dependent geometric errors for rotary axes on five-axis machine tools with a tilting rotary table. Firstly, an algorithm for calculating the three-dimensional position deviations of the standard sphere is presented. The target points on the sphere surface are pre-distributed for the measurements. Then, the single setup continuous measurement method implemented by the standard spheres and a laser displacement sensor is designed. Before performing the measurements, the installation error of the laser displacement sensor is controlled in an acceptance range by an adjustment device with simple procedures. To expand this measurement idea, the application of this continuous measurement method on five-axis machine tools with one rotary axis on the spindle and another one on the worktable is illustrated. The standard uncertainties and the range of the uncertainty contributors are also provided. Finally, an experiment is performed to validate the identification accuracy and efficiency of the proposed method.

Identification of position independent geometric errors of rotary axes for five-axis machine tools with structural restrictions

Abstract Some of five-axis machine tools, which are widely used for micro-machining, have structural restrictions, such as the center line of tilting rotary axis being close to the surface of worktable or beneath the worktable. In this paper, simultaneous motions of both rotary and translational axes are combined with double ball bar to establish a measurement and one installation-based method for identifying the position independent geometric errors (PIGEs) of rotary axes for this kind of five-axis machine tools. Due to the existence of structural restrictions, the tool ball usually cannot be placed in the center line of the tilting rotary axis, and thus, actual spatial motion of ball bar is considered in the proposed identification procedure. For each rotary axis, two test configurations, i.e. the one along the radial direction of rotary axis and the other along the axial direction, are proposed to carry out the designed measurement and identification. Especially, to well avoid the potential negative problems induced by structural restrictions, rotary and translational axes are simultaneously controlled to carry out the measurement, and in the identification procedure, eccentricities together with angle shift and setup errors are comprehensively involved. Based on this basic consideration, spatial plane, on which the actual trajectory of table ball lies, is accurately constructed to integrate the actual movement of ball bar into the PIGEs identification procedure. Novel fitting strategies are developed to mathematically model both the actual trajectory and the spatial plane of table ball’s motion, which are then adopted to formulate the expressions for identifying location and orientation errors. Both simulation and experimental verifications show that the proposed method is effective and helpful for checking and improving the status of five-axis machine tools.