Geometric Error Compensation Research Articles

Identification and compensation of position independent geometric errors of dual rotary axes for hybrid-type five-axis machine tool based on unit dual quaternions

This paper presents a novel synchronous motion trajectory based on the unit dual quaternion (UDQ) to identify the position-independent geometric errors (PIGEs) of the dual rotary axes of a hybrid five-axis machine tool using a Double ball-bar (DBB). A general irregular trajectory equipartition method is presented to deal with the asynchronous matching between DBB data sampling and trajectory points. The kinematic model is effectively simplified by redefining the PIGEs of linear/rotary axes. The installation errors of the DBB are obtained by circular/spherical fitting trajectories, which are brought into the error model for elimination. The simulation of the UDQ kinematic model combined with preset error value shows that the non-uniform variation of DBB motion will lead to the deviation of PIGEs decoupling results. A compensation strategy of major orientation errors based on the UDQ is proposed, which is verified by simulation and compensation experiments.

Evaluation and compensation of geometrical errors of X-ray computed tomography system using a laser tracking interferometer

X-ray computed tomography (X-ray CT) is a new coordinate measuring technology that can measure both the external and internal features. However, its measuring accuracy is insufficient compared with coordinate measuring machines. To improve the measurement accuracy of the X-ray CT system, it is necessary to evaluate and compensate for each error component that influences the dimensional measurement results. In this paper, we propose a method for evaluating and compensating for the geometrical errors of the X-ray CT system, which is one of the dominant error factors, using a laser tracking interferometer. A laser tracking interferometer is not required the re-alignment of the laser path, and the data can be obtained using a common coordinate system. The proposed method was applied to a CT system designed for non-destructive testing. The result clarified that the geometrical errors of the X-ray CT system were over 100 μm. Additionally, the errors in measuring the distance between the spheres were demonstrated to be reduced by compensating for the geometrical errors of the CT system.

십자형 교정체를 이용한 5축 공작기계 회전축의 기하학적 오차 추정에 관한 연구

Estimation and compensation of geometric errors for rotary axes are among methods to improve machining accuracy of five-axis machine tools. Studies have been conducted on various methodologies for estimating geometric errors for rotary axes, which are essential for improving machining accuracies of five-axis CNC machine tools. This paper presents a method for estimating geometric errors of a rotating/tilting table using a cross-shaped calibration artifact with a touch trigger probe. The proposed method includes rotary axes error estimation equations for angles of each rotary and tilt axis based on locations of probing points. Computer simulations were performed based on a MATLAB/Simulink and ADAMS cosimulation system using the probing cycle process to verify the proposed method. Computer simulation results confirmed the usefulness of the proposed method in terms of volumetric errors.

Matrix data analysis methods for applications in laser beam position measurement modules

This paper addresses the problem of selecting an optimal algorithm suitable for real-time processing of matrix sensor data in laser beam positioning applications. We compare four different algorithms and prove that the chosen one provides the same results in time by several orders of magnitude lower and with negligible memory consumption, making it suitable for use in microcontroller-based sensing modules. Full Text: PDF ReferencesS. Donati, Electro-Optical Instrumentation-Sensing and Measuring with Lasers (Prentice Hall, Upper Saddle River, NJ, 2004). DirectLink K.N. Joo, J.D. Ellis, E.S. Buice, J.W. Spronck, R.H. Munning Schmidt, "High resolution heterodyne interferometer without detectable periodic nonlinearity", Optics Expr. 18(2), 1159 (2010). CrossRef G. Budzyń, J. Rzepka, "Study on Noises Influencing the Accuracy of CNC Machine Straightness Measurements Methods Based on Beam Position Detection", J. Machine Engin. 20(3), 76 (2020). CrossRef Reference materials for PSD and CMOS sensors, , referenced 7-11-2022 CrossRef S. Das, A. Saha, "Laser Beam Position-Dependent PSD-Based Calibrated Self-Vibration Compensated Noncontact Vibration Measurement System", IEEE Trans. Instr. Meas. 68(9), 3308 (2019). CrossRef P. Zhang, J. Liu, H. Yang, L. Yu, "Position Measurement of Laser Center by Using 2-D PSD and Fixed-Axis Rotating Device", IEEE Access 7, 140319 (2019). CrossRef J. Rzepka, G. Budzyn, "Laser measurement system for machine tools", Proc. SPIE 5144, 840 (2003). CrossRef S. Xiang, H. Li, M. Deng et al., "Geometric error identification and compensation for non-orthogonal five-axis machine tools", Int. J. Adv. Manuf. Technol. 96, 2915 (2018). CrossRef N. Hagen, E. Dereniak, "Gaussian profile estimation in two dimensions", App. Opt. 47(36), 6842 (2008). CrossRef S.M. Ross, Introduction to Probability and Statistics for Engineers and Scientists (Academic Press 2014). CrossRef

A novel geometric error compensation approach for five-axis machine tools

A novel geometric error compensation approach for five-axis machine tools

COMPENSATIONOF WORKTABLEMOTIONERROR BYANACTIVELY CONTROLLEDHYDROSTATIC GUIDEWAY

The accuracy of machine tools is limited by many factors,such as geometric and thermal errors. Current error reduction approaches include e.g. volumetric compensation. However, if a machine tool has only linear axes, angular errors cannot be compensated since there is no controllable axis that could change the tool or workpiece inclination. Therefore, an actively controlled hydrostatic guideway was developed to compensate for angular and other geometric errors. This paper aims to experimentally verify the hybrid use of constant resistance and the pilot stage of an industrial proportional pressure relief valve for regulation of oil flow through hydrostatic pockets and control of these pockets as well as active compensation of machine tool geometric errors. The error reduction of the tested linear axis is presented.

Modeling of CNC machine tools’ spatial geometric error based on two-dimensional angle error

A modeling method of CNC machine tools’ spatial geometric error is proposed based on two-dimensional angle error in this paper. Different from traditional modeling method, this method takes into account the effect of additional angle errors because the machine tool’s angle errors in the system of the lower guide rail will be passed on to slip board structure to the upper guide rail system. Firstly, after analyzing the principle of two-dimensional angle error, an optimized error compensation model of CNC machine tools’ spatial geometric error contains two-dimensional angle error is established through the traditional homogeneous coordinate transformation matrix method (HTM). Further, by applying the experiment, the compensation effect of the model is verified through comparing the body diagonal errors of CNC machine tools before and after compensation. Experiment results show that the body-diagonal accuracy after compensation based on the optimized model is 87.73% higher than that before compensation, and 54.82% higher than that of the traditional model after compensation.Article HighlightsThe highlight of the study reported here is threefold: Firstly, the principle of two-dimensional angle error is analyzed. Secondly, an optimized spatial geometric error compensation model of CNC machine tool is established based on the principle of two-dimensional angle error. Thirdly, the compensation effect of the optimized compensation model is verified by comparing the bodies diagonal precision of the machine tool.

A method of geometric error identification and compensation of CNC machine tools based on volumetric diagonal error measurements

A method of geometric error identification and compensation of CNC machine tools based on volumetric diagonal error measurements

Virtual-point-based geometric error compensation model for additive manufacturing machines

PurposeThe lack of geometric and dimensional accuracy of parts produced by additive manufacturing (AM) is directly related to the machine, material and process used. This paper aims to propose a method for the analysis and compensation of machine-related geometric errors applicable to any AM machine, regardless of the manufacturing process and technology used.Design/methodology/approachFor this purpose, an error calculation model inspired by those used in computerized numerical control machines and coordinate measuring machines was developed. The error functions of the model were determined from the position deviations of a set of virtual points that are not sensitive to material and process errors. These points were obtained from the measurement of an ad hoc designed and manufactured master artefact. To validate the model, off-line compensation was applied to both the original designed artefact and an example part.FindingsThe geometric deviations in both cases were significantly smaller than those found before applying the geometric compensation. Dimensional enhancements were also achieved on the example part by using a correction parameter available in the three-dimensional printing software, whose value was adjusted from the measurement of the geometrically compensated master artefact.Research limitations/implicationsThe errors that persist in the part derive from both material and process. Compensation for these type of errors requires a detailed analysis of the influencing parameters, which will be the subject of future research.Originality/valueThe use of the virtual-point-based error model increases the quality of additively manufactured parts and can be used in any AM system.

Geometric Error Analysis and Compensation in Spherical Generating Grinding of Hemispherical Shell Resonators.

The geometric accuracy of a hemispherical shell resonator (HSR) affects the assembly accuracy and final performance of a hemispherical resonant gyroscope in many ways. During the precision grinding of a resonator, the tool-setting error and wear error affect the form and positional accuracy of the inner and outer spherical surfaces. In this study, a compensation method for generating grinding of the HSR is proposed to address this problem. The geometric errors of the inner and outer spherical surfaces are systemically analyzed and a geometric model of the tool setting and wheel wear is established for generating grinding of the HSR. According to this model, a mapping relationship between the wheel pose and size, form, and positional error of the HSR was proposed. Experiments regarding machining, on-machine measurements, and error compensation were performed using the mapping relationship. The results demonstrate that the proposed method can reduce the radius error of the inner and outer spherical surfaces from 10 μm to 1 μm, sphericity from 5 μm to 1.5 μm, and concentricity from 15 μm to 3 μm following grinding. The form and positional errors are simultaneously improved, verifying the effectiveness of the proposed method.

Mist-edge-fog-cloud computing system for geometric and thermal error prediction and compensation of worm gear machine tools based on ONT-GCN spatial–temporal model

The geometric precision of worm gears (WGs) determines the service performance and life of precision machine tools, indexing turntables and other equipment. The machining accuracy of worm gear machine tools (WGMTs) is the core to guarantee the geometric precision of WGs, and is greatly affected by the thermal and geometric errors. To improve the machining accuracy of WGMTs, the thermal and geometric errors should be controlled and compensated. But the control system has a poor real-time performance, and the synchronous control of the geometric and thermal errors cannot be currently achieved, and the thermal error model has a low prediction accuracy and low robustness. To make up for the above gap, a mist-edge-fog-cloud computing system is designed for the error prediction and compensation to relieve the bandwidth pressure of the industrial Internet. Moreover, a sensor network composed of multiple sensors is constructed to obtain the thermal information, and then the ordered neuron temporal-graph convolutional network (ONT-GCN) is proposed based on the ordered neuron-long short term memory network (ON-LSTMN) and graph convolutional network (GCN) for the first time to conduct the spatial and temporal modeling of the thermal error data. The interaction among multiple sensors is explicitly considered, and the dependence of the temporal information of the thermal error data on and spatial information of sensors is taken into account. Besides, to realize the error control, the mapping relationship between the tooth surface error and geometric-thermal errors is established. The error mapping model converts 51 geometric errors and 4 thermal errors into the spatial errors of the hob. Moreover, the sensitivity of errors is analyzed, and then the key error items that affect the geometric precision of the tooth surface are identified and compensated. The results show that the ONT-GCN is superior to traditional time-series modeling methods and that the mist-edge-fog-cloud computing system can effectively shorten the executing time compared with other system frameworks, and can improve the machining accuracy of WGMTs.

Influence Analysis of Geometric Error and Compensation Method for Four-Axis Machining Tools with Two Rotary Axes

Four-axis machine tools with two rotary axes are widely used in the machining of complex parts. However, due to an irregular kinematic relationship and non-linear kinematic function with geometric error, it is difficult to analyze the influence the geometry error of each axis has and to compensate for such a geometry error. In this study, an influence analysis method of geometric error based on the homogeneous coordinate transformation matrix and a compensation method was developed, using the Newton iterative method. Geometric errors are characterized by a homogeneous coordinate transformation matrix in the proposed method, and an error matrix is integrated into the kinematic model of the four-axis machine tool as a means of studying the influence the geometric error of each axis has on the tool path. Based on the kinematic model of the four-axis machine tool considering the geometric error, a comprehensive geometric error compensation calculation model based on the Newton iteration was then constructed for calculating the tool path as a means of compensating for the geometric error. Ultimately, the four-axis machine tool with a curve tool path for an off-axis optical lens was chosen for verification of the proposed method. The results showed that the proposed method can significantly improve the machining accuracy.

Estimation and compensation of angular misalignment at robot end brush roller-workpiece contact interface via elastic contact force perception

When the non-standard customized brush roller tool is used for robotic grinding of large-scale components, the clamping and positioning error of the brush roller at the end of the robot is extremely easy to cause misalignment at the brush roller-workpiece contact interface, which will affect the machining accuracy and surface quality. In order to ensure the parallel contact between the brush roller and the workpiece surface during the machining process, a calculation model of the angular misalignment at the brush roller-workpiece contact interface is proposed based on the elastic contact force perception, and then the accurate positioning of the robot end brush roller is realized by a fast compensation method. Firstly, according to the geometric force relationship between the brush roller and the workpiece, as well as the determined brush roller material property parameters, the estimation model of angular misalignment is established. Secondly, both the axial force and normal torque at the time of initial contact detected by the force-controlled sensor are regarded as the input parameters in the model. Furthermore, the calculated brush roller-workpiece contact offset is used as the geometric error compensation amount, and the brush roller is deflected to achieve error compensation by the robot RAPID program control command. The finite element simulation results are compared with the theoretical calculation values, and the average relative error is 15.1%. The experiment on robotic grinding and brushing of high-speed rail body indicates that the compensated angle can be reduced to 0.024° from an average of 0.179° before compensation, coupled with uniform material removal depth. The proposed method can significantly improve the contour accuracy of large-scale components.

Piecewise modeling and compensation of geometric errors in five-axis machine tools by local product of exponentials formula

Piecewise modeling and compensation of geometric errors in five-axis machine tools by local product of exponentials formula

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.

Simulation and Compensation of Axial Geometric Errors for Cycloidal Gears Based on Form Grinding

To increase quality, reduce cycloidal gear noise, and avoid unnecessary vibration and shock, a compensation of axial geometric errors method is proposed based on the cycloidal gear form grinding. In the process of machining cycloidal gears, the relative position relationship between the grinding wheel and workpiece is affected by geometric errors of the motion axes, which has serious effects on the surface accuracy of the cycloidal gears. Combined with cycloidal gear form grinding kinematic principles, a geometric error model for each axis of a four-axis computer numerical control form grinding machine is established. By changing the compensation value of the geometrical errors on six degrees of freedom, the error of the cycloid gear tooth surface machined is obtained. Based on a sensitivity analysis of geometrical errors of each axis, the corrections are determined through an optimization process that targets the minimization of the tooth flank errors. The geometric errors of each axis of the cycloid gear grinding machine are compensated, and then, the cycloid gears produced by the machine are processed. Through the processing experiment, the error data of the actual processing before and after the compensation are compared, which indicates that the machining accuracy of the cycloid gear grinding machine is obviously improved. It has an important guiding significance in improving the precision and performance of large CNC form gear grinding machines.

Research on geometric error modeling and compensation method of CNC precision cylindrical grinding machine based on differential motion theory and Jacobian matrix

Research on geometric error modeling and compensation method of CNC precision cylindrical grinding machine based on differential motion theory and Jacobian matrix

Identification of Geometrical Error on Multi-Axis Machine Tools Based on a Laser Tracker

The geometrical errors are affected by many factors for a multi-axis machine tool, such as materials, manufacturing, assembly, measurement, control, and environmental. The geometric error will eventually be reflected in the accuracy of the workpiece; therefore, for each part of the machine tool, the measurement of geometric error is essential. Most geometrical errors are measured separately for each axis. The single geometrical error measurement method is time-consuming. The multiple geometric error measurement methods have some limitations based on different instruments. Laser tracker based on GPS (Global Positioning System) positioning principle can measure the dimensional coordinate. Thus, the laser tracker measured geometric errors in high efficiency, high precision, wide range. This paper introduces the method of measuring the multi-axis machine geometrical error by using a laser tracker with a 1280mm×1280mm×240mm range and compares the measurement result from the traditional method. The results show the laser tracker method has high measurement accuracy, and rapid measurement and compensation of geometrical errors are achievable on a large-stroke machine tools.

Modeling and Compensation of Machine Geometric Errors for Surface Texturing Process

Modeling and Compensation of Machine Geometric Errors for Surface Texturing Process

Modelling and compensation of machine geometric errors for the surface texturing process

Bio-inspired surface textures have been widely used in various industries because of their unique functionality. The geometric accuracy of the texturing equipment and its effect on the texture geometry are essential for the functional performance of the textured surfaces. This paper presents a surface texture error model that predicts the surface texture topography considering the geometric errors of the machine tool. An error compensation method is proposed to improve the accuracy of the texture by considering the characteristics of the synchronised tool's linear motion and spindle rotation simultaneously. Micro ball-end mill surface texturing experiments are carried out to validate the developed geometric error compensation model considering machine tool geometric errors. The surface topographies before and after the error compensation are examined and compared. The results prove the effectiveness of the proposed error compensation method in enhancing the geometric accuracy of the texture topography.