Key Geometric Errors Research Articles

Sensitivity analysis and compensation for tooth surface deviation of spiral bevel gear machine tool

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.

Joint sensitivity analysis method of impeller aerodynamic performance to key geometric errors of five-axis machine tool

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.

Optimal proportion compensation method of key geometric errors for five-axis machine tools considering multiple-direction coupling effects

Five-axis machine tools are subject to highly coupled geometric errors that significantly affect their machining accuracy. Existing geometric error compensation methods do not consider the coupling effects between errors, resulting in insufficient error compensation efficiency and accuracy. To solve this problem, an optimal proportion compensation method for key geometric errors of five-axis machine tools was proposed, considering multiple direction coupling effects. The key geometric errors were identified using the improved Sobol method based on the volumetric error model. The coupling effects of the geometric errors were analyzed based on the overlapping terms of the key errors in multiple directions, and the coupling situation was classified into four types. The compensation sequence and proportion value in each direction were developed according to the coupling type; i.e., the key errors were compensated to the proportion value instead of the traditional compensation to zero. Taking the S-shaped specimen as an example, the experimental verification indicated that the number of geometric error items that had to be compensated by our method was reduced by 44.4 % compared to the traditional key geometric error compensation method. Additionally, the compensation accuracy was increased by 58.9 %, thus proving the effectiveness of the proposed method.

A geometric accuracy analysis and tolerance robust design approach for a vertical machining center based on the reliability theory

Abstract In the present work, an endeavor was proposed a geometric accuracy analysis and tolerance robust design approach for a vertical machining center based on reliability theory. Based on the establishment of accuracy prediction model and key geometric error traceability, combined the prediction accuracy and processing performance requirements of machine tool, the limit state equation of machining accuracy is obtained, and a calculation model of machining accuracy reliability is derived based on reliability theory. The first-order and second moment method is used to obtain an approximate solution of machining accuracy reliability. Taking key geometric errors as tolerance robust design variables, using relationships with manufacturing costs and accuracy reliability, a machine tool cost-geometric tolerance robust design model was established, which is used to realize the tolerance robust design of a vertical machining center. The results show that the method can achieve economical and rational distribution of geometric accuracy in a vertical machining center.

An approach for accuracy enhancement of five-axis machine tools based on quantitative interval sensitivity analysis

Error compensation is a common method to improve the machining accuracy of five-axis machine tools (FAMTs). Before that, in order to identify the key geometric errors that affect the machining accuracy, sensitivity analysis (SA) in entire machining region or a specified point is usually used. However, since the influence of geometric errors on form errors is different in each interval, the result of SA would be affected, which decreases the compensating accuracy. For this reason, a new approach for accuracy enhancement of FAMTs based on quantitative interval sensitivity analysis (QISA) is presented in this paper. First, based on multi-body system theory and homogeneous transform matrix, the volumetric error model of the FAMT is established. Then, the geometric error model of the FAMT is formulated. Second, development of form error model is involved in this paper to clarify the effect law of geometric error on form error. Moreover, the machining region of S-shaped test piece is divided into five intervals. Then, the QISA method is presented to calculate the sensitivity index of each geometric error and identify key geometric errors at different intervals. Finally, simulations and experiments are conducted to validate the feasibility and effectiveness of the presented method.

A method for tracing key geometric errors of vertical machining center based on global sensitivity analysis

This paper proposes a method for tracing key geometric errors of vertical machining centers based on global sensitivity analysis in order to address inconsistent dimensions associated with sensitivity coefficients, random analytical variables, and geometric errors across different positions. The kinematic chain forward solution and the volumetric error model of vertical machining centers based on a global coordinate system is constructed by means of screw theory; the identification model is constructed based on the double bar ball measurement principle. The identification model is transformed into an optimization-design problem, which is solved by a simulated annealing–genetic algorithm. The idea of orthogonal experimental design is used for reference, and 25 test points are selected for the machine tool workspace. By taking the volumetric error model as a sensitivity calculation model, and by taking geometric errors as analytical factors, multi-factor orthogonal experiments and single-factor parametric tests are designed, respectively. The F-values of the significance test results of the orthogonal experiments and the Euclidean norms, ∆P and ∆O, of the parametric test results are used as global sensitivity coefficients. The analysis results suggest that the traceability results of the key geometric errors are essentially the same across the two tests and the 13 key geometric errors of the J1VMC400B vertical machining center are traced.

A novel causation analysis method of machining defects for five-axis machine tools based on error spatial morphology of S-shaped test piece

In the acceptance process of newly developed five-axis machine tools (FAMTs), it is urgent for machine tool builders to understand the main causes of machining defects on S-shaped test piece. This paper proposes a novel causation analysis method based on error spatial morphology of S-shaped test piece to decouple the key geometric error parameters causing contour errors of test piece. Firstly, based on multi-body system (MBS) theory, tool axis surface error model of a FAMT is set up. In order to eliminate the effect of theoretical error on contour error of S-shaped test piece, the optimized tool path is planned based on the three-point tangential method. Then, the NC instruction is calculated, and error spatial model is established to characterize contour error of the test piece by considering tool setting position. As a basis, error spatial morphologies of test piece are drawn and the relationships between geometric error parameters and error spatial morphologies are analyzed. In order to decouple the key geometric error parameters affecting contour error of test piece, the causation analysis method of local error and global error are presented. After repairing the local and global key error parameters of the test piece obtained from these two analysis methods respectively, the local machining errors are reduced by more than 80%, and the global machining error is not beyond the tolerance. Finally, the cutting experiments of S-shaped test piece on the FAMT XKAS2525 × 60 are implemented. Error detection results of the cutting test piece are basically the same as that shown in error spatial morphologies of test piece, which verifies the correctness of error spatial model for the test piece. After compensating the global key error parameters obtained from the causation analysis method of global error in CNC system, the detection results of re-cutting test piece under the same conditions indicate the test piece has very few points that are not within the tolerance range, and detection results after compensation and global repaired results are almost similar, which verifies the feasibility and correctness of the proposed analysis method. Therefore, it is obvious that the presented method bridges between geometric characteristics of S-shaped test piece, geometric errors of machine tool, and machining defects of test piece and provides a comprehensive error analysis method in the acceptance and performance testing of FAMTs by using the S-shaped test piece. Thus, this study is of great significance for improving the accuracy evaluation method and enhancing the design accuracy of FAMTs.

A Recognition Methodology for the Key Geometric Errors of a Multi‐Axis Machine Tool Based on Accuracy Retentivity Analysis

This paper proposes a recognition methodology for key geometric errors using the feature extraction method and accuracy retentivity analysis and presents the approach of optimization compensation of the geometric error of a multiaxis machine tool. The universal kinematics relations of the multiaxis machine tool are first modelled mathematically based on screw theory. Then, the retentivity of geometric accuracy with respect to the geometric error is defined based on the mapping between the constitutive geometric errors and the time domain. The results show that the variation in the spatial error vector is nonlinear while considering the operation time of the machine tool and the position of the motion axes. Based on this aspect, key factors are extracted that simultaneously consider the correlation, similarity, and sensitivity of the geometric error terms, and the results reveal that the effect of the position‐independent geometric errors (PIGEs) on the error vectors of the position and orientation is greater than that of the position‐dependent geometric errors (PDGEs) of the linear and rotary axes. Then, the fruit fly optimization algorithm (FOA) is adopted to determine the compensation values through multiobjective tradeoffs between accuracy retentivity and fluctuation in the geometric errors. Finally, an experiment on a four‐axis horizontal boring machine tool is used to validate the effectiveness of the proposed approach. The experimental results show that the variations in the precision of each test piece are lower than 25.0%, and the maximum variance in the detection indexes between the finished test pieces is 0.002 mm when the optimized parameters are used for error compensation. This method not only recognizes the key geometric errors but also compensates for the geometric error of the machine tool based on the accuracy retentivity analysis results. The results show that the proposed methodology can effectively enhance the machining accuracy.

Geometric error analysis and compensation for multi-axis spiral bevel gears milling machine

This article proposes a method to analyze and compensate geometric errors of six-axis CNC grinding machines for spiral bevel gears. Volumetric error prediction and compensation models are realized by the forward and inverse kinematics modeling via the screw theory. Key geometric error items of motion axes and their influences on gear tooth performance are modeled and analyzed. Advantages of the proposed compensation method for geometric errors over the machine settings modification method are demonstrated. The compensation strategy has been verified on a six-axis grinding machine controlled by a Siemens CNC. The pitch error and tooth form error of machined gears before and after compensation are compared to validate the effectivity of the proposed compensation method.

A geometric error tracing method based on the Monte Carlo theory of the five-axis gantry machining center

This article proposes a tracing method to identify key geometric errors for a computer numerical control machine tool by cutting an S-shaped test piece. Adjacent part relationships and machine tool errors transform relationships are described by topology of the machining center. Global sensitivity analysis method based on quasi-Monte Carlo was used to analyze machining errors. Using this method, key geometric errors with significant influence on machining errors were obtained. Compensation of the key errors was used to experimentally improve machining errors for the S-shaped test piece. This method fundamentally determines the inherent connection and influence between geometric errors and machining errors. Key geometric errors that have great influence on machining errors can be determined quickly with this method. Thus, the proposed tracing method could provide effective guidance for the design and use of machine tools.

Key geometric error extraction of machine tool based on extended Fourier amplitude sensitivity test method

Machining accuracy is a very important index to measure the performance of NC machine tools, and how to improve the machining accuracy grabs the attention of both manufacturers and users. Since the geometric errors are intercoupling and are one of the main factors affecting machining accuracy of machine tools, in this paper, a new method for extracting key geometric errors based on the screw theory and extended Fourier amplitude sensitivity test (EFAST) method was proposed. First, screw theory was introduced, and the machining accuracy modeling of a three-axis vertical machining center (VMC) was established. Then, in order to analyze the coupling effects between geometric errors by high-dimensional nonlinear model, EFAST global sensitivity analysis method was adopted to help in extracting the main geometric errors. An illustration example on a three-axis VMC shows that the proposed method is effective and can be helpful to improve the geometric accuracy of machine tool.

Global Quantitative Sensitivity Analysis and Compensation of Geometric Errors of CNC Machine Tool

A quantitative analysis to identify the key geometric error elements and their coupling is the prerequisite and foundation for improving the precision of machine tools. The purpose of this paper is to identify key geometric error elements and compensate for geometric errors accordingly. The geometric error model of three-axis machine tool is built on the basis of multibody system theory; and the quantitative global sensitivity analysis (GSA) model of geometric error elements is constructed by using extended Fourier amplitude sensitivity test method. The crucial geometric errors are identified; and stochastic characteristics of geometric errors are taken into consideration in the formulation of building up the compensation strategy. The validity of geometric error compensation based on sensitivity analysis is verified on a high-precision three-axis machine tool with open CNC system. The experimental results show that the average compensation rates along theX,Y, andZdirections are 59.8%, 65.5%, and 73.5%, respectively. The methods of sensitivity analysis and geometric errors compensation presented in this paper are suitable for identifying the key geometric errors and improving the precision of CNC machine tools effectively.

Sensitivity analysis of machining accuracy of multi-axis machine tool based on POE screw theory and Morris method

The geometric errors have a significant effect on the machining accuracy of multi-axis machine tool. Because of their complex inter-coupling, the process to control these geometric errors and then to improve the machining accuracy on this basis is recognized as a difficult problem. This paper proposes a method based on the product of exponential (POE) screw theory and Morris approach for volumetric machining accuracy global sensitivity analysis of a machine tool. When a five-axis machine tool is chosen as an example, there are five screws to represent the six basic error components of each axis (in an original way) according to the geometric definition of the errors and screws. This type of POE model is precise and succinct enough to express the relation of each of the components as the Morris method is based on the elementary effect (EE). The method can compare incidence of these errors and be used to describe the nonlinear relationship by less calculated amount in a global system. Based on the POE modelling, the Morris method is adopted to identify the key geometric errors which have a greater influence on the machining accuracy by global sensitivity analysis. Finally, according to the results obtained from analysis, suggestions, and guidelines are provided to adjust and modify the machine tool components to improve the machining accuracy economically.

Modeling and Analysis of Key Geometric Error for Gravity Deformation of Heavy-Duty CNC Machine Tool

Gravity has huge impact on the accuracy of heavy-duty machine tools. To investigate errors caused by gravity, it is essential to figure out the most influential factor. This paper presents a geometric error modeling for heavy-duty CNC machine tools. Regarding a machine tool as a rigid multi-body system (MBS), the geometric error model has been established by utilizing kinematics chain and homogeneous transfer matrix (HTM). By analyzing the Jacobi matrix, the influence of all the geometric error parameters has been calculated to find out the key geometric error that affect the accuracy most. It is revealed that gravity of beam and tool affect the accuracy of the machine tool most through the ANSYS simulation. It supports a theoretical basis for the further research on error compensation of the key component of a machine tool.

An identification method for key geometric errors of machine tool based on matrix differential and experimental test

This paper presents a key geometric errors identification method for machine tools based on matrix differential and experimental test. An error model for a machine tool was established by regarding the three-axis machining center as a multi-body system. The sensitivity coefficients of the machining error with respect to the geometric errors were determined using the matrix differential method, and the degree of influence of the geometric errors on the machining accuracy under ideal conditions was discussed. Using the 12-line method, 21 geometric errors of the machine tool were identified, allowing the three-dimensional volumetric error distributions of the machine tool to be mapped. Experimental results allow the degree of influence of the geometric errors on the machining accuracy under actual conditions to be confirmed. Finally, the key geometric errors affecting the machining accuracy were identified by a combination of matrix differential and experimental test. This paper provides guidance for the machine tool configuration design, machining technology determination, and geometric error compensation.

An Identification Approach for Key Geometric Error Sources of Machine Tool Based on Sensitivity Analysis

The volumetric error coupled by geometric errors of parts is the main reason affecting the machining accuracy.How to determine the influence degree on the processing precision generated by the geometric errors of parts,thus distribute the geometric errors of parts economically and reasonably,is currently a difficult problem of machine tool design.Based on the theory of multi-body system and sensitivity analysis,a new method of identifying the key geometric error sources parameters is proposed.Taking a four-axis precision horizontal machining center as example,the precision model of the machine center is built up with the theory of multi-body system,thus a mathematical model for error sensitivity analysis of four-axis computer numerical control machine tools is established with matrix differential method,finally the key geometric error sources which affect the machining precision are identified after sensitivity coefficient of error are calculated and analyzed.Calculation and example show that geometric error factors of major parts that have relatively significant influence on comprehensive spatial error of the machine tools can be identified effectively,thus important theoretical basis is provided for improving precision of machine tools reasonably and economically.