Geometric Error Measurement Research Articles

A LS-SVM method for CMM geometric error identification based on spatially integrated measurement

The measurement and identification of geometric errors are important for improving the accuracy of CMM(Coordinate Measuring Machine). Since measurement instruments cannot simultaneously identify all geometric errors, multiple installations for measurements will lead to repeated installation errors between systems, low measurement efficiency, and low identification accuracy. To obtain geometric error of CMM accuractly and conveniently, this paper proposes a method for CMM geometric error identification based on spatially integrated measurement. Specifically, the identification model is determined through the transformation of the spatial comprehensive error model. Then, the LS-SVM(least squares support vector machine) algorithm is adopted for identifying geometric errors. The validity of the proposed method is verified through simulation and experiments. Compared with the ridge regression and least squares methods, the accuracy of the proposed identification method is improved by 35.53% and 46.53%, respectively. The applicability of the proposed method is also verified by setting up another set of experiments.

An unconstrained and non-redundant identification method of geometric errors and compensation of machine tools by X-AX Laserbar

Efficient and accurate measurement and identification of geometric errors are crucial for improving the precision of CNC machine tools. The X-AX Laserbar, as a novel tool for indirect measurement, has not been extensively studied for the identification of geometric errors in machine tools. In this paper, the geometric error model for a three-axis machine tool is established to illustrate the multilateration measurement principle of the laserbar, and a non-redundant and unconstrained identification method is proposed to identify these geometric errors. This method avoids the use of redundant parameters and additional constraints by employing pose error twists to describe the geometric errors. These pose error twists are identified in a transitional coordinate system, and then the geometric errors will be identified in the machine coordinate system by deriving the relationship between the pose errors and geometric errors. The proposed method is validated with the VMC-850E three-axis machine tool. The geometric error measurement using a laserbar is completed in about 40 min, showing great efficiency. The experimental results indicate that the proposed method is capable of accurately identifying the 17 geometric errors required for error compensation. The identified geometric errors are then applied to the machine tool’s accuracy improvement through error compensation. The results show that the actual geometric errors are controlled to a low level. The proposed method can efficiently measure the geometric errors of three-axis machine tools and contribute significantly to improving their geometric 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

Analysis of Long-Distance Geometric Error Measurement and Uncertainty Based on PSD Laser Collimation Principle

Due to the limitations of traditional geometric error measurement, the measurement accuracy of long-stroke geometric errors is generally not high and the operation is complicated. In response to the above situation, in this study, a geometric error measurement system is built with a laser beam as the reference line and 2D position sensitive detector as the photoelectric conversion device. The single measurement range is 40 m, and the measurement range is further expanded through the principle of segmented splicing. Using an ultra-long guide rail as the measurement object for straightness measurement, the experimental results are similar to those of a laser interferometer. The uncertainty analysis model was obtained through the analysis of quantity characteristics, and based on this, the variance synthesis theorem and probability distribution propagation principle were studied to form two uncertainty synthesis methods. The measurement evaluation results showed that the two methods were basically consistent. The work provided a reference method for the uncertainty evaluation of position-sensitive detector measurement systems in the future.

Geometric Error Identification of Gantry-Type CNC Machine Tool Based on Multi-Station Synchronization Laser Tracers

Laser tracers are a three-dimensional coordinate measurement system that are widely used in industrial measurement. We propose a geometric error identification method based on multi-station synchronization laser tracers to enable the rapid and high-precision measurement of geometric errors for gantry-type computer numerical control (CNC) machine tools. This method also improves on the existing measurement efficiency issues in the single-base station measurement method and multi-base station time-sharing measurement method. We consider a three-axis gantry-type CNC machine tool, and the geometric error mathematical model is derived and established based on the combination of screw theory and a topological analysis of the machine kinematic chain. The four-station laser tracers position and measurement points are realized based on the multi-point positioning principle. A self-calibration algorithm is proposed for the coordinate calibration process of a laser tracer using the Levenberg–Marquardt nonlinear least squares method, and the geometric error is solved using Taylor’s first-order linearization iteration. The experimental results show that the geometric error calculated based on this modeling method is comparable to the results from the Etalon laser tracer. For a volume of 800 mm × 1000 mm × 350 mm, the maximum differences of the linear, angular, and spatial position errors were 2.0 μm, 2.7 μrad, and 12.0 μm, respectively, which verifies the accuracy of the proposed algorithm. This research proposes a modeling method for the precise measurement of errors in machine tools, and the applied nature of this study also makes it relevant both to researchers and those in the industrial sector.

Geometric Error Measurement of Rotary Axes on Five-Axis Machine Tools: A Review

Geometric Error Measurement of Rotary Axes on Five-Axis Machine Tools: A Review

Geometric error measurement uncertainty analysis of rotary axis based on Monte Carlo method

Ballbar is widely used for geometric error measurement of the rotary axis, and the uncertainty analysis is of great significance to ensure the reliability of error identification. This study analyzes the measurement uncertainty based on the Monte Carlo method. First, this study clarifies the uncertainty mechanisms caused by tool setting error, translational axis motion error, and ballbar installation error, and proposes a measurement model comprehensively considering the uncertainty sources. In this study, the same ballbar measurement experiments were carried out 10 times in three measurement modes, and the standard deviation of the ballbar length change under different rotation angles was analyzed to ensure that the uncertainty of the geometric error can be effectively analyzed. Furthermore, the uncertainty of each error at different angles of the rotary axis is evaluated based on the measurement model. The results show that the translational axis motion error and tool setting error are important sources of uncertainty. The measurement uncertainty of the angle positioning error is the largest in A- and C-axis, and its standard uncertainty reaches 9.38″ and 2.81″. After optimizing the sine and cosine terms in the identification model, the standard uncertainties of the angular positioning errors are reduced to 6.43″ and 2.26″, and also the estimated errors are close to the actual values, which verifies the validity of the uncertainty analysis method.

A geometric error measurement method for five-axis ultra-precision machine tools

A geometric error measurement method for five-axis ultra-precision machine tools

Uncertainty evaluation of multilateration-based geometric error measurement considering the repeatibility of positioning of the machine tool

Uncertainty evaluation of multilateration-based geometric error measurement considering the repeatibility of positioning of the machine tool

A Novel Measurement Method for Determining Geometric Errors of Rotary Tables by Using LaserTRACER and Reflectors

In this paper, a novel and robust measurement method is proposed for obtaining the geometric errors of rotary tables by using LaserTRACER and the reflectors mounted on the reflector standard fixture. For the machining accuracy, the six-degree-of-freedom (6-DOF) geometric errors of the rotary axes interactively influence the manufacturing quality of the precise workpieces. Therefore, this paper mainly aims to develop a measurement method for identifying the 6-DOF geometric errors of rotary tables without using the external linear axis. Furthermore, the set-up errors of the reflector standard fixture are also considered and identified to reduce the influence of the 6-DOF geometric error measurements. For each rotary table geometric error measurement, the positions of the LaserTRACER as well as the relative distance between the reflectors and the LaserTRACER are measured and obtained for determining the 6-DOF geometric errors of the rotary tables. In addition, the homogeneous transformation matrix (HTM), multilateration method, and least squares method are used for building the mathematical measurement algorithm. Moreover, the experimental verifications are implemented to demonstrate the accuracy of the proposed measurement method. Conclusively, the experiment and simulation verification results clearly delineate that the maximal relative differences in the linear errors and the angular errors of the 6-DOF geometric errors are, at most, 3.25% and 2.30%, respectively.

Least squares based geometric error measurement for sparse view CT: a 2D simulation study

X-ray computed tomography (CT) is considered as one of the most common techniques in non-destructive testing and is also an essential and important method in the field of dimensional measurement. For high-precision measurement task scenarios, geometric errors due to the instability of the CT motion equipment cannot be ignored and need to be accurately measured and corrected. In-situ testing of large objects such as geotechnical materials, mechanical assemblies, metal weldments and concrete specimens also requires high-precision CT imaging of their interiors to obtain information of interest. The rotation of the scanning parts for these large in-situ tests and sparse-view scanning mode also makes it difficult to measure geometric errors. This paper therefore proposes a method for simultaneous measurement of geometric errors based on a priori information for in-situ testing characteristics. This method is capable of measuring geometric errors in sparse view projections with a length accuracy of 0.1 mm and an angular accuracy of radians in 0.5 seconds per angle, as the simulation results show. The reconstruction results show that this level of geometric error measurement accuracy provides a dimensional measurement accuracy of 0.01 mm for the internal structure. The data for the simulation experiments in this paper are generated from real concrete data by noisy simulation.

NEW DEVICE FOR RAPID MEASUREMENT OF MACHINE TOOL GEOMETRIC ERRORS

Control systems of modern machine tools are equipped with a number of functions for volumetric accuracy enhancement. These functions can compensate for all the geometric errors of the axes, which are characterized by 21 errors for a 3-axis machine tool. Compensation data are stored in compensation tables and the control system calculates actual compensation based on these tables and actual machine tool position. Geometric errors are measured within the machine tool maintenance plan and it presents a time-consuming process. Measurement is mainly based on interferometric devices, where the precise setup of laser source and detector is challenging. This article introduces an original system for automatic interferometer set up to speed up the measurement of geometric errors. The system is designed for the interferometer Renishaw XM-60, which simultaneously measures all 6 degrees of freedom. The developed control software identifies interferometer position and transforms the measured data into a machine coordinate system. Numerical simulation verified the proposed solution.

Geometric error measurement of facing head and machining verification on large horizontal boring and milling machine tool

Geometric error measurement of facing head and machining verification on large horizontal boring and milling machine tool

Synchronous measurement and verification of position-independent geometric errors and position-dependent geometric errors in C-axis on mill-turn machine tools

Synchronous measurement and verification of position-independent geometric errors and position-dependent geometric errors in C-axis on mill-turn machine tools

Accuracy improvement of linear stages using on-machine geometric error measurement system and error transformation model.

In order to improve the accuracy of linear stages, a compact, portable and easy installation of a six-degree-of-freedom (6DOF) geometric error measurement system, in which two mirrors with special position and orientation are innovatively regarded as the sensitive elements of the roll error, is proposed. A set of combined focus lenses is integrated into the 6DOF measurement system to improve the resolution of the roll error. The accuracy of a linear stage is evaluated by the positional errors at the functional point, which is located at the working volume of a linear stage. An error transformation model based on the Abbe principle and the Bryan principle is established to estimate the positional errors at the functional point according to those at the measurement point. A series of experiments are carried out to verify the capable of the designed system and the effectiveness of the established model.

Modeling method of CNC tooling volumetric error under consideration of Abb\xe9 error

The Abbé error is a key factor for high-precision CNC machine tools. Unluckily, it is not taken into account in traditional machine tool volumetric error models. In this respect, based on the traditional machine tool volumetric error models, a new machine tool volumetric error model containing Abbé error is performed by analyzing the mechanism of Abbé error formation tool volumetric and based on 21-item geometric error measurement data, Abbé arm, and angle functional relationship. Moreover, integrated qualitative and quantitative simulation method for evaluation of machine tool space precision are correspondingly presented. Finally, an example was utilized to further verify the value of our model by means of analysis and comparison of the tooling precision prior to and after performance of compensation, and its validity and feasibility were proved. This study provides an important modeling method for high-precision machine tools and has very important theoretical significance and practical value.

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.

Influencing factors of rotary table geometric error measurement using four-station laser tracers

The laser tracer multi-station measurement method has outstanding performance in computerized numerical control (CNC) rotary table geometric error measurement and separation. However, external factors, such as layout, selected distance between the target mirror and measurement coordinate system, uncertainty of the length measurement, selection of measuring radii for the rotary table, and installation deviation from the target mirror center to the rotary table surface, have negative effects on the results. In this research, the position dilution of precision in the global positioning system measurement process is introduced to evaluate the influence of the laser tracers’ positions on measurement errors. The optimal measurement layout of the laser tracer is used to select the distance between the target mirror and XY plane of the laser tracer measurement coordinate system for the simulation. Then, the influence of the length measurement uncertainty on the laser tracer self-calibration and point measurement results used for calibration is examined based on the Monte Carlo simulation method. Different measurement radii in the rotary table are selected, and four-station laser tracers are used to perform the virtual measurement and evaluate the maximum uncertainty in the X, Y, and Z directions to further determine the best measurement radii of the CNC rotary table. Finally, the effects of the deviation of the target mirror installation center on the geometric error items of the CNC rotary table are quantitatively examined through a simulation. The analysis of the influencing factors in the geometric error measurement and separation process of the CNC rotary table can help further understand how the final results are formed, so as to control the influencing factors during the measurement process and finally optimize them in practice.

Comprehensive measurement model of geometric errors for three linear axes of computer numerical control machine tools

The geometric error measurement of computer numerical control (CNC) machine tools is developing towards automation and high precision. This not only improves the measurement efficiency, but also reduces the error caused by the long measurement time. This paper proposes a high-efficiency, automatic method of measuring 21 geometric errors of the three linear axes of CNC machine tools and establishes a comprehensive measurement model. The measurement system and model are applicable to linear axis geometric error measurement for all CNC machine tools. The measurement model was developed using rigid body kinematics theory and combined with the ray-tracing method. It mainly analyses the error crosstalk, system errors caused by optical components, laser beam drift, and non-parallelism errors between the measuring beams. ZEMAX was used to verify the model accuracy. Further, repeatability and comparison experiments were conducted to confirm the reliability and accuracy of the measurement system and model.

Modeling, identification, and measurement of geometric errors for a rotary axis of a machine tool using a new R-test

Modeling, identification, and measurement of geometric errors for a rotary axis of a machine tool using a new R-test