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In contemporary production, the computer numerical control machine tool is an essential processing apparatus. However, its geometric errors can often impact processing accuracy and stability. Therefore, an innovative geometric error identification method for CNC machine tools is proposed, which uses the polarization information in the dual-frequency laser interferometer to improve the measurement accuracy. By optimizing the polarization state of the laser system, the ability to identify the geometric error of the machine tool is improved. The findings of this study indicated that the measurement accuracy, measurement range, ease of operation, reliability, cost and applicability of the dual-frequency laser interferometer-based geometric error identification method for computer numerical control machine tools were 0.91, 0.87, 0.93, 0.77, 0.94, 0.85 and 0.97, respectively, which were better than the comprehensive performance of other methods. The study's suggested method offers a solid foundation for raising the precision and machining quality of machine tools by effectively and precisely identifying the geometric faults of CNC tools. The study's findings also establish the groundwork for future widespread use of dual-frequency laser interferometers in the detection of geometric faults in computer numerical control machine tools by offering theoretical justification for real-world uses. [ABSTRACT FROM AUTHOR]

Abstract To analyze the quantitative mapping relationship between the geometric errors of the five-axis CNC machine tool and the tooth surface deviation of spiral bevel gears, and identify the key geometric errors that affect the machining deviation of the spiral bevel gear tooth surface, a sensitivity analysis method for tooth surface machining deviation of spiral bevel gear based on screw theory and EFAST method is proposed. Firstly, the machining model of the spiral bevel gear tooth surface based on the five-axis CNC machine tool is established. Then, the geometric error transfer model of the machine tool is established based on the screw theory. Combined with the EFAST global sensitivity analysis method, the key geometric errors that affect tooth surface deviation are identified. Finally, the reliability and effectiveness tests are performed by comparing the results to the local sensitivity analysis method and simulating compensation for the key geometric errors. The result of compensation shows that the tooth surface deviation is reduced significantly according to global sensitivity analysis. The feasibility of applying sensitivity analysis to control the tooth surface deviation of spiral bevel gears has been demonstrated.

The application of single-point incremental forming has been hampered by poor geometric accuracy due to problems such as suspending sheet back and difficult forming. In this paper, hydrostatic support and ultrasonic vibration-assisted single-point incremental forming is introduced to evaluate and optimize the formability of the proposed assisted process using the geometrical accuracy of the formed sheet as a criterion for process feasibility. According to the Box-Behnken Design experimental program, experiments on hydrostatic pressure, amplitude, frequency, and tool head diameter in relation to maximum errors are conducted, and the experimental results are analyzed by ANOVA and empirical modeling. The results show that frequency and tool head diameter have significant effects on the maximum error, and the coupling effect of static pressure and tool head diameter has a significant effect on the maximum error. Using the satisfaction function to optimize the process parameters, the maximum error is smaller when the value of static pressure is 0.058 MPa, the amplitude is 0.019 mm, the frequency is 25 kHz, and the tool head diameter is 15.7 mm. The optimum parameter combination has proven to be effective through five sets of validation experiments. The methods and conclusions presented in this paper can be useful for the study of hydrostatic support and ultrasonic vibration-assisted single-point incremental forming. [ABSTRACT FROM AUTHOR]

The Linear rolling guideway (LRG) features numerous interfaces between balls and the raceway and demonstrates nonlinear contact characteristics in dynamic. However, most studies on LRG usually assume the contact behavior between the ball and the raceway is uniform, which results in a deviation from the actual conditions, especially for precision machine tools. Therefore, this study's key is to convert the preload and the ball geometry error to the ball's combined interference as initial conditions for simulation analysis. A Finite Element Model (FEM) of an LRG with a machine tool worktable was developed under the ball's combined interference, and verified by a modal vibration test. The results indicate that the simulations with the proposed approach agree well with the experimental measurements. According to the validated FEM with the pre-contact stress induced by the combined interference at the contact interface, the stochastic vibration was analyzed under varying preload levels and external loading conditions. The findings show the significant effect of preloads and ball geometry errors on response principal stress, response deformation, and displacement and stress response power spectral density (PSD) performance. This work provides a deeper understanding of preload and geometric errors for studying accuracy retention in machine tools. [ABSTRACT FROM AUTHOR]

High precision requirements in mechanical products have led machine tools to continuously improve their machining accuracy. However, the existence of geometric errors significantly affects the accuracy of machine tools. On-machine measurement (OMM) has become increasingly available for machine tools, offering an alternative method for identifying geometric errors as compared to the commonly applied traditional interferometry-based techniques. A method to identify the geometric errors based on on-machine measurement of a calibrated artefact is proposed. The mapping relation between the multiple sets of reference points on the artefact and the various types of geometric errors is elaborated on in detail. Geometric error identification experiments and the verification experiment by a laser tracer are conducted. The experiments indicate that the identification results from the proposed method and verification match well with each other, which confirms the effectiveness of the proposed identification method. Moreover, the impact of setup errors on the identification is analyzed, which suggests that the influence induced by setup errors on the identification result can be reasonably controlled. Periodic verification of machine tool geometric errors, as described in ISO 230–2, suggests continuous monitoring of machine tool accuracy and prompt detection of any degradation in accuracy. The OMM-based identification method is more easily automated and more efficient for periodic verification of machine tool accuracy. [ABSTRACT FROM AUTHOR]

To analyze the quantitative mapping relationship between the geometric errors of the five-axis CNC machine tool and the tooth surface deviation of spiral bevel gears, and identify the key geometric errors that affect the machining deviation of the spiral bevel gear tooth surface, a sensitivity analysis method for tooth surface machining deviation of spiral bevel gear based on screw theory and EFAST method is proposed. Firstly, the machining model of the spiral bevel gear tooth surface based on the five-axis CNC machine tool is established. Then, the geometric error transfer model of the machine tool is established based on the screw theory. Combined with the EFAST global sensitivity analysis method, the key geometric errors that affect tooth surface deviation are identified. Finally, the reliability and effectiveness tests are performed by comparing the results to the local sensitivity analysis method and simulating compensation for the key geometric errors. The result of compensation shows that the tooth surface deviation is reduced significantly according to global sensitivity analysis. The feasibility of applying sensitivity analysis to control the tooth surface deviation of spiral bevel gears has been demonstrated. [ABSTRACT FROM AUTHOR]

Modeling and compensating for geometric errors are important steps for improving the accuracy of three-axis machine tools. The kinematic link between the tool and the workpiece is established with a series of homogeneous transformation matrices (HTMs). The volumetric error and compensation values are then calculated based on the pre-measured geometric errors and the pre-built kinematic model. Conventionally, all 21 geometric errors are considered simultaneously in the kinematic model, necessitating a careful HTM construction process to avoid unexpected errors during the derivation of the final simplified formula for compensation. For the possible 24 configurations for three-axis machine tools, this computational process has to be done individually. To solve these time-consuming and inefficient processes, we present a unified error model capable of generating error vectors applicable to all configurations. Instead of considering all geometric errors simultaneously, the proposed method analyzes the errors in subgroups and recombines the error terms at the final step. The advantage of this approach lies in clarifying the impact of geometric errors on volumetric errors, as well as expressing error and compensation vectors for various machine tools through a unified model. The proposed unified model is theoretically demonstrated by applying it to both vertical and horizontal three-axis machine tools. Furthermore, the effectiveness of the proposed method is confirmed by conducting experimental validation on a vertical three-axis testbed. [ABSTRACT FROM AUTHOR]

ABSTRACTValidation of the TROPOspheric Monitoring Instrument (TROPOMI) SIF product is a necessity to evaluate its feasibility in various applications. A few validation works have been conducted through direct comparison with in-situ SIF retrievals or cross-comparison with similar satellite-based SIF or vegetation index (VI) products. Nevertheless, the influence of the geolocation mismatch between the validation pixel and reference data on validation results was never considered. This study, for the first time, quantifies the geolocation shift of the TROPOMI validation pixel based on a geometric location matching method and then the uncertainty caused by the geolocation mismatch. The results indicate that the geolocation shift of the TROPOMI pixel shows large temporal variations, with a standard deviation of 2.30 km and 1.91 km in the across- and along-track directions. The mean shifts are 0.17 km and 0.28 km in the across- and along-track directions respectively, indicating eastward shifts in the across-track direction and northward shifts in the along-track direction in general. More than half (42/54) of the time periods showed relative uncertainty larger than 5%, with the maximum even reaching 55.7%. Hence, the uncertainty caused by geolocation mismatch should be fully considered in the validation of satellite SIF products, especially over heterogeneous surfaces.

Large-size parts such as aircraft wing structures require a lot of hole machining for assembly between parts. As demand for hole positional accuracy, such as in determinant assembly (DA) concept, securing the positional accuracy of hole machining is becoming more important. Specifically, during the hole machining of large-size parts, significant errors occur due to thermal expansion according to temperature change of a machine tool and a workpiece. In this study, a technique for efficiently reducing the positional error of hole machining in large-size parts is proposed by compensating geometric errors and thermal errors of a machine tool and a workpiece. The thermal displacement error, representing changes in volume error due to temperature variations in the machine tool, is estimated by measuring the distance between the centers of two spheres on the master with low thermal expansion coefficient measured at the reference temperature (20 °C). The thermal expansion error, caused by variations in workpiece temperature, is estimated by assuming the temperature of the workpiece to be that of the cutting fluid just before machining. Hole machining errors are integrally compensated by considering the geometric error measured at the reference temperature and the thermal errors of the machine tool and the workpiece. In the verification experiment, the maximum error was improved by 60.2%, and it was confirmed that the tendency of the error was significantly reduced. [ABSTRACT FROM AUTHOR]

Geometric error is a crucial factor influencing the spatial accuracy of CNC machine tools. A novel methodology for modeling, measuring, and identifying geometric errors in multi-axis machine tools is proposed in this paper. Firstly, a synthetic volumetric error model is established by utilizing dual quaternions for multi-axis CNC machine tools. To characterize the relative position relationship between the tool and the workpiece, the kinematics model automatically incorporates the complex coupling between position and orientation motion in an implicit way, enabling a concise and compact representation of the kinematics. Secondly, measure path planning includes candidate measurement positions which are screened to obtain the optimal position group by using observation indices and the modified Detmax method. Thirdly, a parametric modeling method based on exponential cosine fitting is proposed for representing both angular and linear errors, and an improved sparrow search algorithm and nested parameter uncertainty optimization are established to process curve fitting–based optimization of the geometric error term. The fitting of the exponential cosine model is quantified with model uncertainty, and the nested uncertainty optimization method is employed to improve geometric error terms with a poor fitting effect. Finally, the effectiveness is demonstrated through experimental comparisons. The geometric error of a single axis has an average decreased of 69.7%, and the compensation rate of roundness driven by two-axis synchronization is an average of 68.7%. This method offers the advantage of quantifying the minimum optimal number of measurements and positions, improving the efficiency of parametric modeling. [ABSTRACT FROM AUTHOR]

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In this work is considered an elliptic problem, referred to as the Ventcel problem, involving a second-order term on the domain boundary (the Laplace--Beltrami operator). A variational formulation of the Ventcel problem is studied, leading to a finite element discretization. The focus is on the construction of high-order curved meshes for the discretization of the physical domain and on the definition of the lift operator, which is aimed at transforming a function defined on the mesh domain into a function defined on the physical one. This lift is defined in such a way as to satisfy adapted properties on the boundary relative to the trace operator. The Ventcel problem approximation is investigated both in terms of geometrical error and of finite element approximation error. Error estimates are obtained both in terms of the mesh order r > 1 and to the finite element degree k > 1, whereas such estimates usually have been considered in the isoparametric case so far, involving a single parameter k = r. The numerical experiments we led in both 2 and 3 dimensions allow us to validate the results obtained and proved on the a priori error estimates depending on the 2 parameters k and r. A numerical comparison is made between the errors using the former lift definition and the lift defined in this work establishing an improvement in the convergence rate of the error in the latter case. [ABSTRACT FROM AUTHOR]

In the stacked assembly process of the multi-stage rotor of an aeroengine, the cumulative error transmission caused by the geometric error and centroid deviation of a single blisk have a serious impact on the assembly quality and operation safety of the aeroengine rotor. Therefore, it is necessary to optimize the stacked assembly of the multi-stage rotor to improve assembly quality. In this paper, the Pareto-optimal schemes combining multi-objective optimization algorithms for stacked assembly of multi-stage rotors are proposed. First, the error propagation model for stacked assembly of multi-stage blisks based on tensor coordinate transformation is deduced. Taking blisk assembly phase as the design variable, the mathematical descriptions of geometric error and unbalance of the multi-stage rotor assembly are then established. The stacked assembly problem of the multi-stage rotor is formulated mathematically as a multi-objective optimization problem. The minimum geometric error and the minimum unbalance of multi-stage rotor are considered as optimization objectives. The Pareto-optimal assembly schemes are then solved based on the elitist non-dominated sorting genetic algorithm (NSGA-II). The simulation analysis and experimental study for the Pareto-optimal assembly schemes of multi-stage rotor are performed. Results show that compared with random stacked assembly, the geometric error is reduced by 40.6%, and the initial unbalance is reduced by 35.7%. The Pareto-optimal assembly schemes proposed in this paper can effectively improve stacked assembly quality of multi-stage aeroengine rotors. [ABSTRACT FROM AUTHOR]

Rotary axes of five-axis machine tools have highly coupled geometric errors, which are crucial factors affecting the machining accuracy. In this study, a new feature workpiece is designed, including two features of arc surface and square groove. Based on the on-machine measurement of the workpiece, five position-independent geometric errors of the two rotary axes can be identified. The cutting and measuring steps of the workpiece are described in detail, the identification principle of each error is revealed, and the uncertainty analysis is carried out. During the identification process, the machining domain and measurement domain of the same feature remain unchanged to eliminate the influence of linear axis errors on the identification results; hence, the identification accuracy is improved. In the experimental verification, the result is 90.8% consistent with the ball-bar method, which verifies the feasibility of this method. [ABSTRACT FROM AUTHOR]

As a high-performance workpiece, an impeller must ensure both dimensional accuracy and aerodynamic performance. A five-axis machine tool has various geometric errors, which seriously influence the impeller processing quality, hence it is crucial to identify the key error items and compensate them. In this study a joint sensitivity analysis method for the key geometric errors of a five-axis machine tool is proposed that focuses on the aerodynamic performance of an impeller. First, a volumetric error model and an aerodynamic performance model were built, representing the relationships between the tool center point volumetric errors and each of the geometric errors and the impeller aerodynamic performance. Then, the improved Sobol method was implemented to compute the total sensitivity index of each variable in the two models, from which two sensitivity distribution matrices were obtained. Finally, a joint sensitivity analysis was performed on these two matrices to identify the key geometric errors. Experiments were executed to ascertain the impact of compensation strategies on the impeller aerodynamic performance. The results showed that after compensating for the key errors, the total pressure ratio and isentropic efficiency loss rate of the impeller are reduced by 72.2% and 55.8% under the design parameters. The significant improvement in the aerodynamic performance of the impeller demonstrates the accuracy of key geometric error identification.

With the increasing use of GIS software's, historical planimetric data such as orthophotos and old maps represent key data sources to analyze spatio-temporal landscape evolution. However, geometric error inherent to these data are too often overlooked, possibly leading to confusing misinterpretation of measured surficial changes. The user-friendly Python tool 'PickShift', based on a Monte-Carlo approach, addresses this critical issue by quantifying the surficial uncertainty associated with any features digitized from historical planimetric data. This software provides a valuable framework for a more accurate assessment of landscape dynamics and associated uncertainties.

Abstract 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.

Abstract The ball screw pair is a precision drive component that converts rotary motion into linear motion. In practical applications, because the feed system usually has rotational torque and geometric errors, it may increase the contact load of the ball screw pair and reduce the fatigue life. In order to study the influence of different loads and geometric errors on the maximum contact load and fatigue life of ball screw pairs, the following research work was carried out. Firstly, based on the composite load and rotational torque, the ball load distribution model is established, and the accuracy of the model is verified by finite element modeling analysis. Then, the influence of different composite loads, rotation times and geometric errors (including ball size error, lead error and raceway tooth profile error) on the ball load distribution is analyzed. Finally, the influence of compound load, rotating torque and geometric error on the fatigue life of ball screw pairs is studied. The results show that the rotational torque and lead error have a great influence on the load distribution and fatigue life of the ball, and the influence of lead error on load distribution is greater than that of dimension error and tooth profile error. The fatigue life of the ball screw pair with non-uniform load distribution is shorter than that of the ball screw pair with uniform load distribution.

As the critical performance index of ball screws, the contact characteristics have a significant influence on the lubricant properties, tribological properties, and wear properties of ball screws, which further directly affect the service life of ball screws. The non-uniform load distribution induced by geometric errors results in imbalances among balls along the nut, negatively impacting the service life of ball screws. This study focuses on the load distribution of single-nut ball screws under low-speed working conditions. This paper proposes a self-adjustable model of load distribution that considers the flexibility of the screw and nut with respect to the determination of the non-bearing ball. A refined model for axial stiffness is proposed to systematically analyze the influence of geometric errors on stiffness variations under various loading conditions. The results confirm the ability of the proposed model to reveal the static load distribution in view of geometric errors. The greatest discrepancy observed between the theoretical predictions and the experimental data was 9.22%. The numerical simulations demonstrate variation trends in the normal contact load, the loaded-ball number, and the axial deformation of a nut with geometric errors. Furthermore, the relationship between the axial stiffness of a single-nut ball screw and the geometric error is obtained. The self-adjustable model of load distribution is helpful for studying the carrying capacity of a single-nut ball screw. The findings of the study provide a definite reference for optimization of structural design and wear life prediction.

The reasonable allocation of geometric errors of machine tools can improve their machining accuracy reliability (MAR). However, due to the complexity and high nonlinearity of limit state function (LSF) of MAR, the fitting accuracy is usually low when the traditional method is used to approximate LSF. To solve this problem, a doubly-weighted vector projection response surface (DWVPRS) method, which considers not only the approximation results of test sample points (TSPs) to LSF but the distances between TSPs and the most probable failure point (MPFP), is proposed. Using the reliability sensitivity analysis method, the key geometric errors were identified and optimized. Finally, taking a large gantry guideway grinding machine as an example to verifies the effectiveness and correctness of the DWVPRS method proposed in this paper, the results show that compared with the traditional methods, the DWVPRS method has the highest fitting accuracy to approximate LSF at the MPFP, and after the optimization of geometric accuracy, both the minimum and average reliability values of the grinding machine meet the design requirements. [ABSTRACT FROM AUTHOR]

Manipulators applied to polishing can avoid the harm of dust and noise to workers' health in manual polishing, and can significantly increase productivity. The degrees of freedom (DOF) of the existing end-effector for manipulator polishing is insufficient, and then it is difficult to adapt to complex surfaces. A passive compliant end-effector (PCEE) with 4-DOF employing pneumatic floating was designed to solve that problem in this article. According to the included angle between the floating spindle and the plunger, the supporting force functions of floating amount were constructed. Considering the characteristics of the supporting force and the operating modes comprehensively, an appropriate number of plungers was selected. Based on the equilibrium principle of spatial force system, a PCEE was designed by using the floating scheme at both ends, and then a physical model and a simplified model were provided. Eventually, the performances of 4-DOF PCEE are compared with those of the existing 2-DOF compliant end-effector (CEE). The results show that The PCEE can float with 4-DOF; when the number of plungers is 9, all performances meet the design requirements; the polishing force can adapt to the local bulges and overcome the error reflection; the 4-DOF PCEE can adaptively fit the surface to reduce its geometric error. [ABSTRACT FROM AUTHOR]

The ball screw pair is a precision drive component that converts rotary motion into linear motion. In practical applications, because the feed system usually has rotational torque and geometric errors, it may increase the contact load of the ball screw pair and reduce the fatigue life. In order to study the influence of different loads and geometric errors on the maximum contact load and fatigue life of ball screw pairs, the following research work was carried out. Firstly, based on the composite load and rotational torque, the ball load distribution model is established, and the accuracy of the model is verified by finite element modeling analysis. Then, the influence of different composite loads, rotation times and geometric errors (including ball size error, lead error and raceway tooth profile error) on the ball load distribution is analyzed. Finally, the influence of compound load, rotating torque and geometric error on the fatigue life of ball screw pairs is studied. The results show that the rotational torque and lead error have a great influence on the load distribution and fatigue life of the ball, and the influence of lead error on load distribution is greater than that of dimension error and tooth profile error. The fatigue life of the ball screw pair with non-uniform load distribution is shorter than that of the ball screw pair with uniform load distribution. [ABSTRACT FROM AUTHOR]

Tolerance design of key components is an effective method to improve the machine tools accuracy. Currently, tolerance design highly depends on the personal experience, which often subjectively determines the machine tool accuracy and also increases the manufacturing costs. To avoid the phenomenon, a machining error prediction model (MEPM) assisting tolerance design is proposed and experimental verified based on a precision vertical grinding machine (PVGM). Firstly, the mapping relationship between the tolerance parameter and geometric error of key components is obtained as the superimposed Fourier series. Subsequently, the volumetric error model including geometric errors is established by the homogeneous transform matrix and multi-body system theory. Based on a typical workpiece, a tolerance-based MEPM is obtained by integrating the ideal machining path. Finally, a grinding test on PVGM is conducted to validate the MEPM. The results show that the predicted roundness of three positions is 3.033 μm, 2.905 μm, and 2.774 μm, respectively, and the measured roundness are 3.163 μm, 2.980 μm, and 2.904 μm, respectively. The error between PVGM predicted and measured roundness is not more than 5%. The MEPM is important for assisting the tolerance design and improving the machining accuracy in the machine tools. [ABSTRACT FROM AUTHOR]

The dual five-axis machining machine is state-of-the-art equipment designed for producing thin-walled aerospace parts like skins and panels. It comprises two five-axis machine tools with mirrored synchronous motions: one bi-rotary machine for milling and the other machine for follow-up support. The high absolute accuracy of the five-axis machine tools themselves and the high synchronous motion accuracy between the two machines are both crucial to ensure machining accuracy. This paper proposes an efficient method to measure and identify geometric and dynamic errors of dual five-axis machine tools. Using the R-test combined with three measurement trajectories to measure the absolute motion error of two five-axis machine tools and the synchronous motion error between the two machines. The designed trajectories include the main rotary axis linkage conditions and can fully reflect the primary motion forms of the dual five-axis machine tool. The main position-independent geometric errors and rotational axis linkage dynamic errors are identified by converting quasi-static and dynamic measurement data from three different trajectories into a unified reference coordinate system. The entire process requires only one instrument installation, effectively avoiding time-consuming repetitive installations and calibration processes while reducing the impact of installation errors on results. The effectiveness of the proposed method for measuring and identifying the geometric and dynamic errors is analyzed combined with Monte Carlo simulation. Experiments were carried out on a dual five-axis mirror milling system (MMS) with a 5000 mm X-stroke. Both simulations and experiments confirmed that the proposed method is efficient in quickly identifying key error sources of the MMS. [Display omitted] • An efficient method to measure and identify geometric and dynamic errors during synchronous motion of the MMS is proposed. • A geometric and dynamic error model is introduced for identifying key errors using error sensitivity theory. • A 3-step measurement strategy that enables rapid separation of linkage errors of the MMS is introduced. • Both simulation and experiment show the proposed method could obtain key error sources of the MMS with high efficiency. [ABSTRACT FROM AUTHOR]

The Line laser gear measuring center (LLGMC) is an innovative gear measurement equipment that offers high efficiency but low accuracy. One crucial factor that influences its measurement accuracy is the presence of geometric errors. In this study, we conducted a thorough analysis of these geometric errors and proposed a method for modeling spatial errors. Instead of directly considering the geometric errors, we replaced them with the installation errors of the gear and line laser probe. This approach simplifies and improves the error transmission relationship. Subsequently, the installation errors are converted into a unified representation of the height error of the incident light from the line laser. A spatial error model that considers nine installation errors is then further established. By numerically calculating the sensitivity of different error sources, we effectively identified the errors that have a significant impact on the accuracy of LLGMC. Moreover, accuracy distribution is carried out to ensure that LLGMC can meet the measurement accuracy requirements for gears with a tolerance class of 6. This article provides a theoretical foundation for the structural design and accuracy assurance of LLGMC during the research and development phase. [ABSTRACT FROM AUTHOR]

The sequential multilateration principle is often adopted in geometric error measurement of CNC machine tools. To identify the geometric errors, a single laser tracker is placed at different positions to measure the length between the target point and the laser tracker. However, the measurement of each laser tracker position is not simultaneous and measurement accuracy is mainly subject to positioning repeatability of the machine tool. This paper attempts to evaluate the measurement uncertainty of geometric errors caused by the positioning repeatability of the machine tool and the laser tracker spatial length measurement error based on the Monte Carlo method. Firstly, a direct identification method for geometric errors of CNC machine tools based on geometric error evaluation constraints is introduced, combined with the geometric error model of a three-axis machine tool. Moreover, uncertainty contributors caused by the repeatability of positioning of numerically controlled axes of the machine tool and the laser length measurement error are analyzed. The measurement uncertainty of the geometric error and the volumetric positioning error is evaluated with the Monte Carlo method. Finally, geometric error measurement and verification experiments are conducted. The results show that the maximum volumetric positioning error of the machine tool is 84.1 μm and the expanded uncertainty is 5.8 μm (�� = 2). The correctness of the geometric error measurement and uncertainty evaluation method proposed in this paper is verified compared with the direct geometric error measurement methods.

Abstract Assembly geometric error as a part of the machine tool system errors has a significant influence on the machining accuracy of the multi-axis machine tool. And it cannot be eliminated due to the error propagation of components in the assembly process, which is generally non-uniformly distributed in the whole working space. A comprehensive expression model for assembly geometric error is greatly helpful for machining quality control of machine tools to meet the demand for machining accuracy in practice. However, the expression ranges based on the standard quasi-static expression model for assembly geometric errors are far less than those needed in the whole working space of the multi-axis machine tool. To address this issue, a modeling methodology based on the Jacobian-Torsor model is proposed to describe the spatially distributed geometric errors. Firstly, an improved kinematic Jacobian-Torsor model is developed to describe the relative movements such as translation and rotation motion between assembly bodies, respectively. Furthermore, based on the proposed kinematic Jacobian-Torsor model, a spatial expression of geometric errors for the multi-axis machine tool is given. And simulation and experimental verification are taken with the investigation of the spatial distribution of geometric errors on five four-axis machine tools. The results validate the effectiveness of the proposed kinematic Jacobian-Torsor model in dealing with the spatial expression of assembly geometric errors.

This work proposes a rapid and robust machine-learning model to predict the volumetric error of a five-axis machine tool. For this purpose, several machine learning models – which are MultiOutput regression, Chained MultiOutput regression, Linear regression, SVM regression, XGB regression and ANN regression – have been selected, and their performances were compared to other models in the literature and to one another to find the best model for the problem at hand. The robustness of each model is investigated using three statistical metrics: namely Root Mean Square Error (RMSE), Mean Absolute Error (MAE) and Coefficient of Determination (R2). The results show that the models proposed in this paper are more effective than those in the literature, using the same data. Amongst the proposed models, the SVR Regression model has proven to be the best, considering all statistical metrics. Compared to the polynomial method in the literature with varying order levels, the method proposed here improves accuracy and predictive performance by 27%, with an RMSE of 0.03246 mm for the SVR model. Finally, based on the best model, an explicit equation has been deduced for practical applications. That prediction equation has been implemented in Excel and included in this paper. [ABSTRACT FROM AUTHOR]

In this paper, a kinematic separation calibration method of 6R series manipulator is proposed, and its absolute accuracy is improved by a binocular camera and standard sphere. First, a geometric error mapping model for the robotic arm was established, and the error parameters were divided into position parameters and attitude parameters for calibration purposes. Second, in the process of solving error parameters using numerical algorithms, it is easy to encounter matrix ill-conditioned problems. The spectral correction iteration method is introduced to improve the calculation accuracy. Third, three standard balls are installed at the end of the robotic arm as markers, and the center coordinates are measured using a binocular camera to obtain the actual end pose parameters. To verify the effectiveness of the proposed method, a simulation model verification was designed, and the results showed that the separation calibration method was the best. Finally, the IRB-1200 robot was successfully calibrated using the proposed method; the average robot position and angle error after calibration was significantly decreased. The position accuracy was improved by 66.9%, and the attitude accuracy was improved by 86.2%. [ABSTRACT FROM AUTHOR]

To solve the problem of geometric error measurement for five-axis ultra-precision machine tools in interpolated five-axis motion, a measurement method based on the double ballbar (DBB) is proposed in this paper. The method proposed in this research can measure the geometric errors of five-axis ultra-precision machine tool through only one-time installation, and the new method is less limited by the layout of machine tools. The motion trajectory is designed, and the length of the DBB remains constant during the measurement process to achieve the measurement of the geometric errors. Furthermore, the measured results are compared with the theoretical results of the error model. It is found that the trend and the amplitude of the measurement results are in agreement with the theoretical results. It is proved that the method can measure the geometric errors of five-axis ultra-precision machine tool effectively. [ABSTRACT FROM AUTHOR]

This study implemented the measurement results and administrative information obtained from the hole plate into the Digital Calibration Certificate (DCC). The DCC comprises three parts: Norms and Standards, Hierarchical Structure, and XML as Exchange Format. DCCs play a significant role in the field of metrology and statistics by ensuring data interoperability, correctness, and traceability during the conversion and transmission process. The hole plate is a length standard used for two-dimensional geometric error measurements. We evaluated the accuracy of the high-precision coordinate measuring machine (CMM) in measuring a hole plate and compared the measurement error results obtained from the hole plate with those of the laser interferometer, autocollimator, and angle square. The results show that the maximum difference in linear error is −0.30 μm, the maximum difference in angle error is −0.78″, and the maximum difference in squareness error is 4.54″. The XML is designed for machine-readability and is modeled and edited using the XMLSpy 2022 software, which is based on information published by PTB. The administrative management and measurement results tasks are presented in PDF format, which is designed for human-readability and ease of use. Overall, we implemented the measurement results and information obtained from the hole plate into the DCC. [ABSTRACT FROM AUTHOR]

The machining error of heavy-duty vertical lathes is significantly affected by geometric errors. Thus, this paper investigates the measurement and modeling of heavy-duty vertical lathes for error tracing. Specifically, the heavy-duty vertical lathe geometric error is measured by a laser interferometer, its error value is identified, and the polynomial model of the error value is established using a polynomial high-order fitting method. After that, based on the multi-body system theory, the heavy-duty vertical lathe bed and cutting tool topology is created to describe the pose relationship of each component of the heavy-duty vertical lathe. Then, the geometric error model of the heavy-duty vertical lathe is established using a homogeneous transformation matrix, and the virtual machined rotary surface model is constructed by combining the cutting tool trajectory and the eccentric installation of the workpiece. Each geometric error is input into the virtual model to compare its effect on the machining error of the workpiece. Among the 19 errors traced, the X-direction positioning error of the horizontal slide, the X-direction straightness error of the vertical slide, the X-direction straightness error of the workbench spindle, the X-direction installation eccentricity error of the workpiece, the rotation angle error of the horizontal slide around the Y-axis, and the rotation angle error of the workbench spindle around the Y-axis are the key errors heavily impacting the machining error of the heavy-duty vertical lathe. According to the influence of each key error term, the mapping relationship between the error term and the machining error of the workpiece is established to complete the error tracing. [ABSTRACT FROM AUTHOR]

Assembly geometric error as a part of the machine tool system errors has a significant influence on the machining accuracy of the multi-axis machine tool. And it cannot be eliminated due to the error propagation of components in the assembly process, which is generally non-uniformly distributed in the whole working space. A comprehensive expression model for assembly geometric error is greatly helpful for machining quality control of machine tools to meet the demand for machining accuracy in practice. However, the expression ranges based on the standard quasi-static expression model for assembly geometric errors are far less than those needed in the whole working space of the multi-axis machine tool. To address this issue, a modeling methodology based on the Jacobian-Torsor model is proposed to describe the spatially distributed geometric errors. Firstly, an improved kinematic Jacobian-Torsor model is developed to describe the relative movements such as translation and rotation motion between assembly bodies, respectively. Furthermore, based on the proposed kinematic Jacobian-Torsor model, a spatial expression of geometric errors for the multi-axis machine tool is given. And simulation and experimental verification are taken with the investigation of the spatial distribution of geometric errors on five four-axis machine tools. The results validate the effectiveness of the proposed kinematic Jacobian-Torsor model in dealing with the spatial expression of assembly geometric errors. [ABSTRACT FROM AUTHOR]

• This study used a mass inertial unit (IMU) and a laser interferometer as measurement tools, and effectively fused their measurement errors using an unscented Kalman filter method. • By integrating the measurement errors of IMU and laser interferometer, the true error value of the approximate machine tool can be obtained. • By using the error prediction method of data fusion, relatively high accuracy error prediction results and error decoupling results can be obtained. The Mass Inertial Unit (IMU), as a positioning measurement instrument, is unstable when used to measure the positioning error of machine tools. Through a large number of numerical simulations, it is found that the error measurement results of IMU conform to normal distribution, and the real error value of the machine tool can be approximately obtained by fusing the errors measured by IMU and laser interferometer. After experimental comparison, it was found that the error after fusion decreased compared to the residual measured using IMU alone. On this basis, this article proposes an error prediction method based on IMU and laser interferometer error fusion. By dividing the measurement space into spatial cubes and conducting error measurement and fusion on the nodes of each cube, the error measurement curve can be predicted based on the distance between each node and the origin. Prediction can be achieved separately through IMU without laser interferometer, which can greatly improve measurement efficiency and have high prediction accuracy. After experimental verification, this method can predict the upper, lower, and full branches of multi axis motion through IMU, and can decouple the error of the machine tool based on different motion branches. [ABSTRACT FROM AUTHOR]

[Display omitted] • This study evaluates the geometric accuracy of 3D-printed hole in Ti-6Al-4 V plate suitable for bioimplants and also focuses on the hole diameter precision and surface roughness. • As specimen 8 having the parameter of laser power 195 W, the scanning speed 900 mm/sec and the hatch distance 70 µm exhibited minimal average geometric errors across top surface roughness, internal hole curve surface roughness, external and internal circular hole shapes. • These results are very important for designing processes to ensure high-quality 3D-printed titanium alloy specimens. This study examines the quality of circular-hole 3D-printed objects using laser powder bed fusion (L-PBF) on Ti-6Al-4V titanium alloy that typically used for orthopedic implants. Meanwhile measuring surface roughness and hole dimension deviations in AM specimens is very challenging. Thus, the specimens were printed with varying process parameters, followed by an L9 orthogonal array experiment, where parameters included laser power (LP) at 175, 185, and 195 W; scanning speed (SS) at 600, 900, and 1200 mm/s; and hatch distance (HD) at 70, 90, and 110 µm. Thus the, minimum surface roughness values are Ra 2.4 µm for the top surface and Ra 16.06 µm for the inside hole curve. Whereas the smallest hole deviations are 0.1102 mm for external and 0.2094 mm for internal diameters. Therefore, this analysis include FESEM, EDX, XRD, profilometry and stereomicroscopy. Where the best settings are LP 195 W, SS 900 mm/s, and HD 70 µm, producing well-fused, uniform α-phase Ti-6Al-4V specimens that are suitable for biomedical applications. [ABSTRACT FROM AUTHOR]

Abstract In order to improve the low output accuracy caused by the elastic deformations of the branch chains, a finite element-based dynamic accuracy analysis method for parallel mechanisms is proposed in this paper. First, taking a 5-prismatic-spherical-spherical (PSS)/universal-prismatic-universal (UPU) parallel mechanism as an example, the error model is established by a closed vector chain method, while its influence on the dynamic accuracy of the parallel mechanism is analyzed through numerical simulation. According to the structural and error characteristics of the parallel mechanism, a vector calibration algorithm is proposed to reduce the position and pose errors along the whole motion trajectory. Then, considering the elastic deformation of the rod, the rigid-flexible coupling dynamic equations of each component are established by combining the finite element method with the Lagrange method. The elastodynamic model of the whole machine is obtained based on the constraint condition of each moving part, and the correctness of the model is verified by simulation. Moreover, the effect of component flexibility on the dimensionless root mean square error of the displacement, velocity and acceleration of the moving platform is investigated by using a Newmark method, and the mapping relationship of these dimensionless root mean square errors to dynamic accuracy is further studied. The research work provides a theoretical basis for the design of the parameter size of the prototype.

This paper proposes a new geometric error compensation algorithm for the five-axis machine tools. Firstly, the general machining error model of five-axis machine tool is established based on multi-body theory (MBS) and homogeneous transmission matrix (HTM). Secondly, considering deviation of tool setting point, the initial NC code of each axis is calculated. Thirdly, based on the initial NC code, a geometric error compensation is developed by the present improved particle swarm optimization (IPSO) to seek the optimal NC code. In this model, the tool pose and the volume error are regarded as particles and optimal object, respectively. According to the objective function, the optimal particles are selected in a given interval to reduce the volume error of machine tool. Finally, an experiment is implemented by the S-shaped test to verify the effectiveness of this method. Compared with linear interpolation (LI) compensation, the comprehensive machining accuracy based on PSO method has improved by 17.5%, and the maximum machining error has reduced by 0.0058 mm. [ABSTRACT FROM AUTHOR]

Error compensation is an effective method to guarantee the machining accuracy of machine tools. This paper proposes a method for geometric error identification and compensation of CNC machine tools based on volumetric diagonal error measurements. A geometric error model for CNC machine tools was established. Thereafter, the error measurement principle of the laser tracker was established. Based on this characteristic, error identification equations used to describe the position-dependent geometric errors were derived based on polynomials. A regularisation method was then selected to identify geometric error parameters. The identified geometric errors could be substituted in the space compensation module for error compensation. This paper takes a horizontal three-axis machining centre as an example to illustrate the proposed method. Results of the experiment reveal that the error identification and compensation method is convenient and effective in reducing volumetric diagonal errors. Moreover, the final volumetric diagonal positioning error with compensation was controlled at approximately 20 μm. [ABSTRACT FROM AUTHOR]

A novel elasto-geometric model is introduced that simultaneously estimates joint compliances and geometric error parameters by employing the loaded double ball bar apparatus. The model parameters are estimated from tests at different force levels by distinguishing between errors that change with the applied force (compliance effect) from those that do not (geometric effects). At lower forces, the geometric errors are dominant while at higher forces compliance errors dominate. Using all data to build a single global geometry and compliance set of parameters (global constant compliance model), the radial volumetric variations due to geometric errors and compliance are estimated at 0.019 mm and 0.046 mm, respectively, making compliance dominant by more than three times. The impact of dominant and non-dominant equivalent global compliance CXXX, CYYY, CXYX, CCXY, CCYY, and CCCY on the loaded circular test readings at the highest force level of 742 N are predicted to be around 0.045, 0.034, 0.00058, 0.0022, 0.0014, and 0.0045 mm peak-to-peak, respectively. The impact of loaded geometric parameters EXX1, EYY1, EYX2, EXY2, EC(0Y)X, EXt0, and EYt0 on the loaded circular test readings is predicted to be around 0.019, 0.014, 0.0074, 0.012, 0.00017, 0.0076, and 0.0012 mm peak-to-peak, respectively. The dominant global compliances are CXXX and CYYY at 0.0619 and 0.0461 μ m / N , respectively. [ABSTRACT FROM AUTHOR]

For a 2UPR-RPU over-constrained parallel manipulator, some geometric errors result in internal forces and deformations, which limit the improvement of the pose accuracy of the moving platform and shorten the service life of the manipulator. Analysis of these geometric errors is important for restricting them. In this study, an evaluation model is established to analyse the influence of geometric errors on the limbs' comprehensive deformations for this manipulator. Firstly, the nominal inverse and actual forward kinematics are analysed according to the vector theory and the local product of the exponential formula. Secondly, the evaluation model of the limbs' comprehensive deformations is established based on kinematics. Thirdly, 41 geometric errors causing internal forces and deformations are identified and the results are verified through simulations based on the evaluation model. Next, two global sensitivity indices are proposed and a sensitivity analysis is conducted using the Monte Carlo method throughout the reachable workspace of the manipulator. The results of the sensitivity analysis indicate that 10 geometric errors have no effects on the average angular comprehensive deformation and that the identified geometric errors have greater effects on the average linear comprehensive deformation. Therefore, the distribution of the global sensitivity index of the average linear comprehensive deformation is more meaningful for accuracy synthesis. Finally, simulations are performed to verify the results of sensitivity analysis. [ABSTRACT FROM AUTHOR]

Volumetric and geometric errors should be periodically checked to ensure that the accuracy of machine tools remains within the tolerable range. However, existing methods require complex devices, and are thus unsuitable for cost-effective interim error checks. We present a simple, rapid and cost-effective method for interim error checks. The measurement paths are constructed using a virtual polyhedron; volumetric errors are checked by calculating the coordinates of the vertices using the measured side lengths. The tool is sequentially moved to each vertex, and the side lengths are measured using a double ball-bar. As the virtual polyhedron is composed of virtual regular tetrahedrons, the relationships between the coordinates of the vertices and side lengths are unique. Linear scale and squareness errors are measured using an error synthesis model with a least-squares approach. The method was applied to a real machine tool, and performance was verified by confirming that the maximum L2 norm of volumetric error is improved from 57.6 to 32.8 μm after compensating for the measured geometric errors. Thus, the validity of the proposed method was confirmed by an improvement of 43% in volumetric error. The measurement results were confirmed by the circular tests of ISO 230-4; the peak-to-valley radial deviation improved from 16.0 to 11.2 μm after compensation, and the proposed method contributed to a 30% improvement in the radial deviation. [ABSTRACT FROM AUTHOR]

The ball screw (BS) has become an indispensable key functional component in many fields, such as precision manufacturing equipment and intelligent manufacturing production lines. Inevitable geometric errors and non-constant operating conditions affect the accuracy decay of the BS component. In this paper, a numerical analysis method of this accuracy decay with geometric parameters errors, under non-constant operating conditions, is established. The accuracy degradation of the BS, under a single non-constant operation condition or multiple non-constant operating conditions, is analyzed, using a proposed numerical analysis method. The average value of the relative error between numerical analysis and theoretical model results was 5.52%, 5.66%, and 5.40%, under the three operating conditions of non-constant rotation rate (RR), non-constant contact load (CL), and non-constant rotation rate and contact load (RR + CL), respectively. And the maximum relative error value was 11.11%, 11.11%, and 10.98%. In addition, the numerical analysis method of BS accuracy degradation was compared to experimental tests. The average value of the relative error between numerical analysis outcome and experimental tests was 7.07%, 6.08%, 6.56%, and the maximum relative error value was 11.11%, 14.29%, and 13.04% under the three operating conditions of RR, CL, and RR + CL, respectively. [ABSTRACT FROM AUTHOR]

In order to improve both the accuracy and efficiency of grinding slide, this paper designs a novel grinder with dual-lead-dual-head. Since the geometric error is one of the major contributors causing machine inaccuracies, the sensitivity analysis is performed to identify the critical geometric error terms, and an application to accuracy self-test is also given. The volumetric model of the grinder with 38 geometric errors is built using the homogeneous transformation matrix (HTM) and multi-body system (MBS) theory. An improved Sobol method with quasi-Monte-Carlo algorithm is utilized to perform the global sensitivity analysis (GSA) in the entire workspace. The particular sensitivity analysis is further carried out on the basis of the machining characteristics of a typical slide. All sensitivity analysis results are validated through the error compensation simulations. Besides that, some discussions are given to determine the total critical errors of the grinder considering both entire workspace and particular machining requirements. Finally, the pitch and yaw errors between the dual-grinding-head are investigated, and based on the sensitivity analysis results, a quick accuracy self-test approach is proposed to reduce the measurement load in practice. [ABSTRACT FROM AUTHOR]