Geometric Error Measurement Research Articles

Geometric Error Measurement and Identification for Rotational Axes of a Five-Axis CNC Machine Tool

Geometric Error Measurement and Identification for Rotational Axes of a Five-Axis CNC Machine Tool

Optimal On-Machine Measurement of Position-Independent Geometric Errors for Rotary Axes in Five-Axis Machines with a Universal Head

This study proposes an optimal on-machine measurement method to measure position-independent geometric errors of five-axis machines, including machine tools and coordinate measuring machines, with a universal head. This measurement requires only a calibrated three-dimensional (3-D) probe and a precision sphere, which are fundamental components of on-machine measurement systems in general, to minimize measurement costs, including operator effort and operating time. Eight position-independent geometric errors are used to describe the coordinate systems of the two rotary axes through a kinematic analysis. The center of the precision sphere, which is stationary during the measurement, is measured at various angles of the rotary axes. Then, the linearized relationship between the measured positions of the precision sphere and the geometric errors is derived using an error synthesis model under rigid-body and small-value assumptions. The proposed method is tested through a simulation for validation. The geometric errors of a five-axis coordinate measuring machine with a universal head are measured with measurement uncertainty by applying the proposed method. Then, the measurement results are confirmed by comparing the measured positions of the precision sphere and calculated positions using the measured geometric errors at the other (i.e., the arbitrary, or not measured) angles of rotary axes.

转台-摆头式五轴机床几何误差测量及辨识

转台-摆头式五轴机床几何误差测量及辨识

Comparison of Direct and Indirect Methods for Five-axis Machine Tools Geometric Error Measurement

Geometrical error (GE) is a key criterion for machine tools performance evaluation. GE measurement methods can be classified as direct and indirect methods. As an indirect GE measurement method, the scale and master ball artefact (SAMBA) method can estimate the GE of linear and rotary axes by probing series of master balls and a scale bar artefact installed on the machine tool pallet. The purpose of this study is to research the performance of direct and indirect GE measurement methods (i.e. laser interferometer and SAMBA method) in linear positioning error measurement such as EXX and EYY. These errors of the X- and Y-axis are separately measured on a five-axis machine tool with the two methods. The results reveal that the SAMBA method yields similar results as the laser test in error shape and range. However, there are some minor differences which are discussed.

Measurement and identification of geometric errors of translational axis based on sensitivity analysis for ultra-precision machine tools

Identification of geometric errors of translational axis is a key step to improve the accuracy of machine tools. However, during the procedure of measurement, installation errors of instruments are inevitable and should influence the measurement results. In order to avoid this and improve the reliability and accuracy of measurement, a novel identification measurement method is proposed. The errors of positioning and straightness of translational axis are measured by a laser interferometer in four installation positions. Twelve measured results are obtained, and then are used to identify six geometric errors of translation axis, based on the homogeneous transformation matrix and the least square method. Furthermore, an optimization method based on sensitivity analysis of the identification matrix is presented to obtain the optimum installation positions of the laser interferometer, to diminish the influence of the installation errors. Finally, simulations and experiments are conducted to validate the correctness and effectiveness of proposed method. The results indicate that the optimization identification method proposed is effective and accurate.

Optimal modification of tooth flank form error considering measurement and compensation of cutter geometric errors for spiral bevel and hypoid gears

In design and manufacturing for the spiral bevel and hypoid gear, the cutter geometric errors (CGEs) is one of main factors affecting tooth flan flank form error. To get an accurate and effective modification of tooth flank form error, a novel optimization and operation approach is proposed by correlating with measurement and compensation of CGEs. Firstly, an accurate modification model with optimal machine settings is developed as a nonlinear least square problem. Where, a small number of machine settings are selected as unknown optimal design variable by sensitivity analysis method. Then, CGEs are defined and their influences on the tooth flank form error are investigated for synthesis and analysis of the accurate higher-order modification. Finally, the optimal modification with small number of machine settings is performed based on measurement of the Doppler Laser interferometer MCV2002 following ISO 230-2(1997) standard and numerical control (NC) compensation of CGEs. In additional to the optimal design parameters is set to improve computational efficiency, the Levenberg–Marquardat (L–M) algorithm with trust-region strategy is applied to solve for the new machine settings with modification variations. A numerical application to a real case is designed to identify the validity of the proposed methodology.

Research on shaving processing of spiroid face gear

To reduce tooth surface errors and improve the quality of tooth surface morphology for the spiroid face gear manufactured roughly by die-casting, a method of shaving processing for this type of gears was developed. According to the differential geometry and the meshing theory of spatial crossed axes gears, the kinematics of the shaving processing for the spiroid face gear was analyzed, while the cutting velocity of both contact tooth surfaces was derived to illustrate the feasibility of gear shaving. With the designed tooth geometry of the shaving cutter, the simulation of generation of tooth surfaces for the spiroid face gear was developed. Machining experiments for such type gears were performed on a five-axis computer numerical control machine tool (CNC machine) with the axially grooved shaving cutters. The geometric error measurement of the shaved spiroid face gears was determined by D40 CNC gear measuring center. The research results are of sound great significance to improve the engagement and lubrication for the spiroid face gears.

Design and experimental verification of novel six-degree-of freedom geometric error measurement system for linear stage

In this study, a novel and simple measurement system for simultaneously measuring the geometric errors in six-degree-of-freedom (6-DOF) for a moving linear stage of a machine tool is designed and validated. Compared to laser interferometer and laser Doppler systems, this new measurement system is less expensive and capable of multiple functions. The proposed measurement system comprises an optics module, composed of two reflectors and two cubic beam splitters; a sensing module, composed of three two-dimensional position sensitive detectors (PSDs); and a helium-neon (He-Ne) laser. Using skew-ray tracing and a first-order Taylor series expansion, the 6-DOF geometric errors of the moving linear stage, which include translation and rotation errors, are analyzed. A laboratory prototype system is built to verify the effectiveness and accuracy of the proposed measurement system. The experimental results show that the displacement uncertainty and the angular uncertainty of the proposed measurement system are less than 1.2µm and 0.4″, respectively. Compared with the Renishaw laser interferometer XL-80 laser system, the translational accuracy and the rotational accuracy of the proposed measurement system are less than ±1µm and ±0.2″, respectively, when the linear stage travels 6mm.

Total measurement of geometric errors of a three-axis machine tool by developing a hybrid technique

A hybrid measurement technique using a five-DOF measuring system and laser interferometer is suggested for all geometric errors of a three-axis machine tool. All geometric errors are defined in a single coordinate system, by eliminating the effect of Abbe’s offsets, for accurate measurement. The five-DOF measurement comprises five capacitive sensors and an L-type reference mirror. The system measures three PIGEs (position independent geometric errors) and five PDGEs (position dependent geometric errors) for each axis. The 18 geometric errors of the machine tool are measured using the results from two experiments (XY and YZ-planes), and the homogeneous transform is used to identify the geometric errors in a single coordinate system, eliminating the effects of installation errors such as mirror misalignment. A laser interferometer is used to measure three PDGEs (one linear displacement error and two straightness errors) for each axis. The two straightness errors are used to estimate the optimal Abbe’s offsets (for the X, Y and Zaxes) between the two measuring coordinate systems, and the linear displacement of each axis is calculated, minimizing the effect of Abbe’s offsets. Through this analytical approach, all geometric errors are expressed for a single coordinate system. The suggested measurement technique can therefore be used to investigate all geometric errors of a three-axis machining tool.

System for simultaneously measuring 6DOF geometric motion errors using a polarization maintaining fiber-coupled dual-frequency laser.

A novel method for simultaneously measuring six degree-of-freedom (6DOF) geometric motion errors is proposed in this paper, and the corresponding measurement instrument is developed. Simultaneous measurement of 6DOF geometric motion errors using a polarization maintaining fiber-coupled dual-frequency laser is accomplished for the first time to the best of the authors' knowledge. Dual-frequency laser beams that are orthogonally linear polarized were adopted as the measuring datum. Positioning error measurement was achieved by heterodyne interferometry, and other 5DOF geometric motion errors were obtained by fiber collimation measurement. A series of experiments was performed to verify the effectiveness of the developed instrument. The experimental results showed that the stability and accuracy of the positioning error measurement are 31.1 nm and 0.5 μm, respectively. For the straightness error measurements, the stability and resolution are 60 and 40 nm, respectively, and the maximum deviation of repeatability is ± 0.15 μm in the x direction and ± 0.1 μm in the y direction. For pitch and yaw measurements, the stabilities are 0.03″ and 0.04″, the maximum deviations of repeatability are ± 0.18″ and ± 0.24″, and the accuracies are 0.4″ and 0.35″, respectively. The stability and resolution of roll measurement are 0.29″ and 0.2″, respectively, and the accuracy is 0.6″.

Research on geometric error measurement system of machining center BV75 based on laser interferometer

This paper measures the twenty one geometric errors of numerical control machining center with parameter identification through laser interferometer, the main contents illustrate the measurement system, measurement model and some testing results combined with specific experimental conditions, at the same time provide particular reference value on numerical control machine tool(NC machine tool) geometric precision detection.

A ballbar test for measurement and identification the comprehensive error of tilt table

This paper proposes a comprehensive geometric error measurement and identification method for a tilt table equipped in a five-axis machine tool with two turntables using the double ballbar. Three positional errors of the socket, caused by both the volumetric error and linkage error of the tilt table, are measured in the sensitive directions with simple circular paths. A mathematics model is applied to map the relationship between the night results that are from three installation positions of the socket and all the errors of the tilt table. Firstly, all the measured results are applied to establish the average axis that is just with the linkage error of the tilt table using the newly developed circular fitting method, rather than solving the large-scale linear equations. Then, the linkage error is treated as the trend item in the measured results for it keeps constant during the rotation of the tilt table. Hence, the volumetric error is identified by the remaining part of the measured results, which are obtained by subtracting the part caused by the linkage error, using the pseudo invert matrix method. Meanwhile, an error model is established to analyze the influence of the installation errors of the socket and the tool cup. Two simple correction procedures, using a low-cost electron clamp and an easily operated circular path, are developed to eliminate these two installation errors before the ballbar test. Finally, a verification experiment, by comparing the predicted value from the identified errors with the measured results by the ballbar, is carried out to validate the effectiveness and correctness of the proposed method.

CNC machine tool work offset error compensation method

Machine tool accuracy and repeatability is one of the most important considerations for manufacturing parts with the required quality for consistent performance in their assemblies. One of the most challenging areas has been the ability to quickly identify and evaluate the quasi-static and dynamic machine errors and apply the corresponding error models to compensate. Because there are many challenges associated with some methods, including the cost in design, analysis and control of precision machine tools, the compensation method has been the most effective approach to control part quality. However, error compensation by measurement of geometric errors is greatly affected by the error modeling and error measurement methods, which could require significant machine downtime to implement. This paper presents the development of a global offset compensation method utilizing the measurements of the machined part(s). The global offset for a machine tool is estimated through a model while utilizing the computed deviation between the measured and nominal dimensions of the part. Furthermore, the paper presents several other compensation concepts supporting the global offset method. The strengths and limitations of all compensation methods are also discussed.

Identification of geometric errors of rotary axes on 5-axis machine tools by on-machine measurement

Geometric error is among the most important fundamental elements that significantly affect the machining accuracy of multi-axis machine tools. This paper developed an efficient, accurate, and automatic geometric error measurement and identification method for rotary axis of a five-axis machine tool based on on-machine measurement by using a touch-trigger probe with a test piece. Before on-machine measurement, the test piece is installed and pre-machined to a designated geometry. Then, the coordinates of the reference points on the test piece are indirectly measured at different rotary axis positions. The geometric errors of each rotary axis then can be identified individually and the calculation algorithm is easy to establish and solve. Due to the special features of this method, neither the geometric inaccuracy of the test piece nor its installation error on the workbench affects the geometric error measurement and identification results. Geometric errors of a five-axis machine tool with double table rotary axes are measured as an example to validate the efficiency and effectiveness.

A Modified Sequential Multilateration Scheme and its Application in Geometric Error Measurement of Rotary Axis

Geometric error compensation becomes an essential technology for improving the accuracy of multi-axes machine tools. Laser tracker has been has been considered as an enabling instrument which can be used to measure the geometric error of machine tools due to its high accurate and feasible measurement capability. This paper presents a modified sequential multilateration method for measuring the geometric errors of rotary axes of the machine tools. The method is developed based on a single laser tracker and three targets fixing on the rotary stage. The coordinates of the three targets are measured based on the modified sequential multilateration method using a single laser tracker when the rotary stage is rotated. Then geometric error components are identified based on established geometric error model which takes the positioning error of the targets as input. The validity of the proposed method is verified through both computer simulation and experiments conducted on a multi-axis machine tool.

Using a double ball bar to measure 10 position-dependent geometric errors for rotary axes on five-axis machine tools

To improve the accuracy of five-axis machine tools, the measurement and compensation of position-dependent geometric errors (PDGEs) for rotary axes are of great importance. A double ball bar-based measuring method is proposed to precisely calibrate PDGEs. For each rotary axis, five measuring patterns are designed, in which the ball bar is sensitive to one direction throughout the measuring process. In the measurement, the ball bar functions as a high-precision displacement sensor with a single degree of freedom. Based on the ball bar readings, analytical solutions for 10 PDGEs, except for two angular position errors, are simply deduced. Simulations are conducted to analyze the influence of PDGEs and setup errors on measuring patterns. The advantages of the proposed method are discussed by comparison with three other measuring schemes. Finally, experimental verification of this approach is conducted on a five-axis machine tool. The results confirm that the method provides precision results of PDGEs for rotary axes.

Measurement and compensation of geometric errors of three-axis machine tool by using laser tracker based on a sequential multilateration scheme

A three-point method based on sequential multilateration is applied to measuring the geometric error components (GECs) of three-axis machine tools (MTs). To meet the accuracy requirement of geometric error mapping, a sequential multilateration scheme is developed for high-accuracy point measurement by introducing four additional targets into the measuring system, and the uncertainty of point measurement is verified by simulation. Three independent targets fixed on the MT’s spindle assembly move along with each axis step by step and their coordinates at each step can be determined by the distance data acquired by laser tracker at all steps based on sequential multilateration. Then the volumetric errors of the three target points can be obtained by comparing the actual coordinates and the corresponding desired coordinates, and nine equations can be established by substituting volumetric errors into the error model of linear axis, so that the six GECs of each axis can be obtained by solving these equations. The three squareness errors can be determined by computing the angles between the average lines of the three axes which are achieved by linear curve fitting. Experiments are conducted to measure these 21 GECs, and the volumetric errors in the three-axis MT’s workspace, which are determined by these measured GECs based on the error model of three-axis MT, are compensated. Finally, the positioning errors of the MT with compensation and without compensation are evaluated by laser interferometer, respectively, the experimental results of which demonstrate that the positioning errors are significantly reduced by the error compensation.

Volumetric Verification of Multiaxis Machine Tool Using Laser Tracker

This paper aims to present a method of volumetric verification in machine tools with linear and rotary axes using a laser tracker. Beyond a method for a particular machine, it presents a methodology that can be used in any machine type. Along this paper, the schema and kinematic model of a machine with three axes of movement, two linear and one rotational axes, including the measurement system and the nominal rotation matrix of the rotational axis are presented. Using this, the machine tool volumetric error is obtained and nonlinear optimization techniques are employed to improve the accuracy of the machine tool. The verification provides a mathematical, not physical, compensation, in less time than other methods of verification by means of the indirect measurement of geometric errors of the machine from the linear and rotary axes. This paper presents an extensive study about the appropriateness and drawbacks of the regression function employed depending on the types of movement of the axes of any machine. In the same way, strengths and weaknesses of measurement methods and optimization techniques depending on the space available to place the measurement system are presented. These studies provide the most appropriate strategies to verify each machine tool taking into consideration its configuration and its available work space.

Geometric error measurement and identification for rotary table of multi-axis machine tool using double ballbar

In this paper, comprehensive geometric errors, including linkage errors and volumetric errors, of a rotary table are measured totally by employing a double ballbar and obtained by a two-step identification procedure. The derivations of the center of the ball installed on the table are measured in the error sensitive directions with newly developed serial of two axes controlled circular paths. Hence, there are nine results measured from three mounting positions of the ball at the same rotation angle. These results are used to form the identification model based on the homogeneous transformation. Moreover, a sensitivity analysis method is applied to select the optimum installation parameters of the ballbar to diminish the influence of the inaccuracy of the measurement parameters. As the mounting position errors of the socket on the table are inevitable during the installation of the balls, a new correction procedure is developed as well. Finally, an experiment is conducted on the four-axis machining center. The comparison results between the predicted errors and the measured results are shown to verify the proposed method.

Measurement and verification of position-independent geometric errors of a five-axis machine tool using a double ball-bar

In this study, position-independent geometric errors, including offset errors and squareness errors of rotary axes of a five-axis machine tool are measured using a double ball-bar and are verified through compensation. In addition, standard uncertainties of measurement results are calculated to establish their confidence intervals. This requires two measurement paths for each rotary axis, which are involving control of single rotary axis during measurement. So, the measurement paths simplify the measurement process, and reduce measurement cost including less operator effort and measurement time. Set-up errors, which are inevitable during the installation of the balls, are modeled as constants. Their effects on the measurement results are investigated to improve the accuracy of the measurement result. A novel fixture consisting of flexure hinges and two pairs of bolts is used to minimize set-up error by adjusting the ball's position located at the tool nose. Simulation is performed to check the validation of measurement and to analyze the standard uncertainties of the measurement results. Finally, the position-independent geometric errors of the five-axis machine tool (involving a rotary axis and a trunnion axis) are measured using proposed method.