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1
Hoang, Trung Kien, and Nguyen Minh Duc Ta. "Machining Based Geometric Error Estimation Method for 3-Axis CNC Machine." Applied Mechanics and Materials 889 (March 2019): 469–74. http://dx.doi.org/10.4028/www.scientific.net/amm.889.469.
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Computer numerical control (CNC) machine tool plays an extremely significant role in any manufacturing industry due to its automation and high accuracy. Keeping the CNC machine tool at its highest performance to meet the demand of high accuracy machining is always significant. To maintain the accuracy of a machine tool over the time, it is important to measure and compensate the geometric error, one of the main error source of machine tool, especially when the machine get old. There are totally 21 geometrical errors in a 3-axis machine tool including three translational errors and three rotational errors for each axis and three perpendicular error (Squareness) within three axes of the machine. This paper presents an economical and simple method for measuring the geometric error of a 3-axis CNC machine tool based on the machining of actual samples. Three samples for each axis will be machined following a design cutting path. The samples will then be measured using a coordinate measuring machine (CMM). The collect data will be used for estimating the geometric errors. The volumetric errors will be then computed and verified through machining of 3D geometries.
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Liu, Junfeng, Yuqian Zhao, Tao Lai, Fei Li, and Kexian Liu. "Identification of Geometrical Error on Multi-Axis Machine Tools Based on a Laser Tracker." Journal of Physics: Conference Series 2185, no. 1 (January 1, 2022): 012008. http://dx.doi.org/10.1088/1742-6596/2185/1/012008.
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Abstract 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.
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Jian, Yi, Qian Qian Li, Hong Cheng, Bin Wu Lai, and Jian Fei Zhang. "Research on Geometric Error Compensating Technique of CNC P3G Grinding Machine." Advanced Materials Research 462 (February 2012): 287–94. http://dx.doi.org/10.4028/www.scientific.net/amr.462.287.
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Kinematic accuracy is a key reason which influence workpiece's geometric error precision on traditional working process of precisely CNC（Computerized Numerical Control）P3G（polygon profile with 3 lobes） grinding machine. A systematic geometric error model has been presented for CNC P3G grinding machine， proposed multi-body system theory integrate with the structure of CNC P3G grinding machine tools, researched on the machine's space geometric errors. By means of separate geometric errors from the machine tools, build geometric mathematical error model. Then, identify 21 error parameters through method of 9 lines, analysis and calculate the total space geometric errors of the workpiece and wheel. Finally, formed a parameter-list and applied software error compensational technique ， achieved real-time control to the motions of workpiece and wheel. Experimental results shown that the geometrical error modeling technique is accurate and efficient, and the precision of CNC P3G grinding machine is highly raised 70%.
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Jiang, Chuang, Huiliang Wang, Tianhao Han, and Xing Liu. "Simulation and Compensation of Axial Geometric Errors for Cycloidal Gears Based on Form Grinding." Mathematical Problems in Engineering 2022 (April 21, 2022): 1–16. http://dx.doi.org/10.1155/2022/4804498.
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To increase quality, reduce cycloidal gear noise, and avoid unnecessary vibration and shock, a compensation of axial geometric errors method is proposed based on the cycloidal gear form grinding. In the process of machining cycloidal gears, the relative position relationship between the grinding wheel and workpiece is affected by geometric errors of the motion axes, which has serious effects on the surface accuracy of the cycloidal gears. Combined with cycloidal gear form grinding kinematic principles, a geometric error model for each axis of a four-axis computer numerical control form grinding machine is established. By changing the compensation value of the geometrical errors on six degrees of freedom, the error of the cycloid gear tooth surface machined is obtained. Based on a sensitivity analysis of geometrical errors of each axis, the corrections are determined through an optimization process that targets the minimization of the tooth flank errors. The geometric errors of each axis of the cycloid gear grinding machine are compensated, and then, the cycloid gears produced by the machine are processed. Through the processing experiment, the error data of the actual processing before and after the compensation are compared, which indicates that the machining accuracy of the cycloid gear grinding machine is obviously improved. It has an important guiding significance in improving the precision and performance of large CNC form gear grinding machines.
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Yu, Yongjian, Guoding Chen, Jishun Li, Yujun Xue, and Bitao Pang. "Prediction Method for the Radial Runout of Inner Ring in Cylindrical Roller Bearings." Mathematical Problems in Engineering 2017 (2017): 1–13. http://dx.doi.org/10.1155/2017/6584561.
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The motion error of assembled bearing depends on the geometric profile of bearing components. Therefore, it is crucial to establish the relationship between geometric error of bearing components and motion error of assembled bearing, which contributes to improving the rotational accuracy of assembled bearing in the design and machining of the bearing. The main purpose of this research is to propose an accurate method for predicting the radial runout of inner ring based on the geometrical constraint model of cylindrical roller bearings. In the geometrical constraint model, dimension and form errors in the inner raceway, the outer raceway, and rollers are considered, and the change of contact positions between the raceways and rollers caused by geometric errors of bearing components is taken into account. This method could predict the radial runout of inner ring after bearing components with geometric error are assembled. In order to testify the validity of the proposed prediction method, two particular cases in which the profiles of the inner raceway are circle and ellipse are selected, and the analysis algorithms for the radial runout of inner ring are derived. Two analytical results obtained from the analysis algorithms validate accuracy and effectiveness of the proposed prediction method.
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Conte, Javier, Jorge Santolaria, Ana Cristina Majarena, Agustin Brau, and Juan Jose Aguilar Martín. "Laser Tracker Error Modeling and Kinematic Calibration Strategy." Key Engineering Materials 615 (June 2014): 63–69. http://dx.doi.org/10.4028/www.scientific.net/kem.615.63.
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Calibration of Laser Tracker systems is based most times in the determination of its geometrical errors. Some standards as the ASME B89.4.19 [1] and the VDI 2617-10 [2] describe different tests to calculate the geometric misalignments that cause systematic errors in Laser Tracker measurements. These errors are caused not only because of geometrical misalignments and other sources of error must also be taken in count. In this work we want to state the errors in a kinematic form. Errors will be split in two different components, geometric and kinematic errors. The first ones depend on the offsets, tilts and eccentricity of the mechanical and optical components of the system. Kinematic errors are different for every position of the Laser tracker, so they will be formulated as functions of three system variables: distance (R), vertical angle (V) and horizontal angle (H) usually called d, φ and θ. The goal of this work is to set up an evaluation procedure to determine geometric and kinematic errors of Laser Trackers.
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Gu¨ven, H. M., and R. B. Bannerot. "Derivation of Universal Error Parameters for Comprehensive Optical Analysis of Parabolic Troughs." Journal of Solar Energy Engineering 108, no. 4 (November 1, 1986): 275–81. http://dx.doi.org/10.1115/1.3268106.
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A study is presented where potential optical errors in parabolic troughs are divided into two groups: random and nonrandom. It is shown that the intercept factor is a function of both random and nonrandom errors as well as geometric parameters such as concentration ratio and rim angle. Three error parameters, universal to all collector geometries, that is, “universal” error parameters which combine random and nonrandom errors with collector geometric parameters, are derived analytically. The mathematical derivation of these universal error parameters is presented. A numerical technique, a detailed ray-trace computer routine which maps rays from elemental reflector surfaces to the absorber surface, is used to validate the existence of the universal error parameters. The universal error parameters are made up of one universal random error parameter, σ* ( =σC), and two universal nonrandom error parameters, β* ( = βC) and d* (=(dr)y/D). The use of universal error parameters for comprehensive optical analysis of troughs is also presented.
8
Wang, Xiu Shan, Yan Li, and Yong Chang Yu. "Study of the Geometrical Error Modeling of NC Lathe Based on Multi-Body System Theory." Advanced Materials Research 139-141 (October 2010): 1093–96. http://dx.doi.org/10.4028/www.scientific.net/amr.139-141.1093.
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The geometrical error modeling of the numerically controlled (NC) lathe is the key technique to kinematics design, precision analysis and error compensation. The study gives out the modeling process of the generally geometrical error model based on the multi-body system theory for the multi-axis NC machine tools. By the multi-system theory, using the low series body arrays to describe the complex mechanical system, the article has finished the geometrical error modeling of the numerically controlled lathe, analyzed the influence on the model of error of perpendicularity between the linear axes. The modeling method is highly-efficient and can not be affected by the structure of the NC machine tools. The error compensation and command correction can be implemented by the geometric errors model.
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Utami, Ratih Ayu. "Analisis Kesalahan Siswa SMP dalam Menyelesaikan Soal Bangun Ruang." MATHEdunesa 9, no. 3 (December 18, 2020): 487–94. http://dx.doi.org/10.26740/mathedunesa.v9n3.p487-494.
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This study aims to: (1) describe the location of the students' mistakes in solving geometrical problems, (2) to describe the students' mistakes in solving geometrical problems, and (3) to describe the factors that cause students' errors in solving geometric problems. This research is a qualitative study using test and interview methods and was conducted at SMP Negeri 21 Surabaya. Selection of subjects based on criteria, namely students who made many mistakes on indicators of the location and type of error, variation of errors, openness and fluency of the subject to communicate during the interview process.
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Yu, Yongjian, Guoding Chen, Jishun Li, and Yujun Xue. "Influence of Geometric Error of Rollers on Rotational Accuracy of Cylindrical Roller Bearings." Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University 37, no. 4 (August 2019): 774–84. http://dx.doi.org/10.1051/jnwpu/20193740774.
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As the rotation of roller bearings is carried out under geometrical constraint of the inner ring, outer ring and multiple rollers, the motion error of the bearing should also be resulted from geometric errors of bearing parts. Therefore, it is crucial to establish the relationship between geometric errors of bearing components and motion error of assembled bearing, which contributes to improve rotational accuracy of assembled bearing in the design and machining of the bearing. For this purpose, considering roundness error and dimension error of the inner raceway, the outer raceway and rollers, a prediction method for rotational accuracy of cylindrical roller bearings is proposed, and the correctness of the proposed prediction method is verified by experimental results. The influences of roller's geometric error distribution, roller's roundness error and the number of rollers on the runout value of inner ring are investigated. The results show that, the roller arrangement with different geometric errors has a significant impact on rotational accuracy of cylindrical roller bearings. The rotational accuracy could be improved remarkably when multiple rollers with different dimension error are distributed alternately according to the size error. Even-order roundness error of rollers has a significant effect on the rotational accuracy, and the decrease level depends on the orders of roundness errors of bearing parts and the number of rollers. But odd-order roundness error of rollers has almost no effect on the rotational accuracy. The rotational accuracy of assembled bearing would be significantly improved or decreased when even order harmonic of rollers and the number of rollers satisfy specific relationships. The greater the order of roundness error of the rollers, the more severe the influence of the roller number on rotational accuracy of assembled bearing. The rotational accuracy can not be always improved with the increase of the number of rollers.
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Mikó, Balázs, Bálint Varga, and Wojciech Zębala. "The Effect of the Feed Direction on the Micro- and Macro Accuracy of 3D Ball-end Milling of Chromium-Molybdenum Alloy Steel." Materials 12, no. 24 (December 4, 2019): 4038. http://dx.doi.org/10.3390/ma12244038.
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The machining of free form surfaces is one of the most challenging problems in the field of metal cutting technology. The produced part and machining process should satisfy the working, accuracy, and financial requirements. The accuracy can describe dimensional, geometrical, and surface roughness parameters. In the current article, three of them are investigated in the case of the ball-end milling of a convex and concave cylindrical surface form 42CrMo4 steel alloy. The effect of the tool path direction is investigated and the other cutting parameters are constant. The surface roughness and the geometric error are measured by contact methods. Based on the results, the surface roughness, dimensional error, and the geometrical error mean different aspects of the accuracy, but they are not independent from each other. The investigated input parameters have a similar effect on them. The regression analyses result a very good liner regression for geometric errors and shows the importance of surface roughness.
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Fu, Guoqiang, Yue Zheng, Sipei Zhu, Caijiang Lu, Xiaolei Deng, Luofeng Xie, and Jixiang Yang. "A four parallel laser-based simultaneous measurement method for 6-degrees-of-freedom errors of rigid body with translational motion." Review of Scientific Instruments 93, no. 8 (August 1, 2022): 085101. http://dx.doi.org/10.1063/5.0081682.
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The measurement of six-degrees-of-freedom (6-DOF) errors of rigid bodies can show the real and accurate spatial pose of those rigid bodies. It plays a major role in precision calibration, spacecraft docking, machining, assembly, etc. In this paper, a four parallel laser-based simultaneous measurement (FPL-SM) method is proposed for measuring 6-DOF errors of rigid bodies with translational motion. First, a FPL-SM device is introduced. Its four laser heads form a rectangle, which is perpendicular to the movement direction of the measured linear displacement. Second, identification formulas for all geometrical errors in rigid bodies with translational motion are presented based on the relative positions of the four lasers. Based on the readings of the four lasers, angular errors and corresponding straightness errors are calculated for the direction of motion around the other two linear motions. As the two parallel sides of the rectangle are in different planes, the straightness errors of the two planes are different. The rolling angular error in the direction is expressed as the difference between the straightness errors of the two planes divided by the distance between the two planes. Six fundamental errors for rigid bodies with translational motion are obtained by four lasers in a single setting of the device. For multiple rigid bodies with mutually perpendicular translational motion, the squareness error is calculated by fitting to the actual direction of motion. Finally, experiments were carried out on the SmartCNC_DRDT five-axis machine tool and 21 geometric errors were determined for three translational axes. Error compensation was carried out using the generated machine tool geometric error data to verify the effectiveness of the proposed FPL-SM method. In addition, geometric errors and thermal errors of the Z axis of the GTI-2740 machine tool are measured based on the FPL-SM method.
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Chen, Peng, and Huang. "A New Error Model and Compensation Strategy of Angle Encoder in Torsional Characteristic Measurement System." Sensors 19, no. 17 (August 30, 2019): 3772. http://dx.doi.org/10.3390/s19173772.
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For systems of measurement, geometric errors such as manufacturing and assembly errors could have a significant impact on the accuracy of the angle encoders of the system. In this study, an error model of angular measurement with geometric errors of a torsional characteristic measurement system was developed based on multibody system theory, the aim of which was to reveal the impact of geometric errors on angular measurement and to compensate the measurement error. According to the principle of spatial error transfer, the decomposition of geometric errors is illustrated and the error matrix of geometric errors is constructed by the Denavit–Hartenberg (DH) method. Subsequently, an error compensation function can be obtained and the impact of geometric error on angular measurement is discussed. Finally, we demonstrate by the experimental results of an ultra-autocollimator that the proposed error compensation method reduced the angular measurement error from 3.7% to 0.7%, which shows that the proposed error model can effectively predict the angular measurement error. In addition, it can be seen from the measurement results of the RV reducer that the error of the torsional characteristic measurement system decreased significantly.
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Guo, Shijie, Dongsheng Zhang, and Yang Xi. "Global Quantitative Sensitivity Analysis and Compensation of Geometric Errors of CNC Machine Tool." Mathematical Problems in Engineering 2016 (2016): 1–12. http://dx.doi.org/10.1155/2016/2834718.
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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.
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Fomin, A. A. "Limiting Product Surface and its Use in Profile Milling Design Operations." Solid State Phenomena 265 (September 2017): 672–78. http://dx.doi.org/10.4028/www.scientific.net/ssp.265.672.
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The article establishes the analytical relationships linking the geometric parameters of the shaping cutters. A mathematical model describing the geometrical errors caused by the discrete process of product profile milling with shaping cutters was developed. It was specified based on the model that the distribution of errors on the surface treated with cylindrical and shaping cutters is significantly different. It is found that the errors due to the kinematics of the cylindrical milling process, are constant at value irrespectively of the considered cross section of the cutting tooth, and the errors after the milling significantly differ in the distance function of considered transverse plane from its geometric center. The maximum error occurs in the local longitudinal planes of the product, the profile of which is located at the maximum distance from the mounting technological base of product's surface. The plane of the product, where the maximum geometrical errors are formed during the profile milling is called limiting surface. The design of technological process is performed in the product profile geometry, formed in this plane. The rule of spacious arrangement location of the limiting surface of the product according to its drawing. Using the limiting surface in the design of the operation of profile milling with shaping cutters significantly reduces the duration of the design procedure and eliminates the cost of production on experimental studies related to ensuring the geometric accuracy of products at the initial stage of their production.
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Li, Dianxin, Pingfa Feng, Jianfu Zhang, Dingwen Yu, and Zhijun Wu. "An identification method for key geometric errors of machine tool based on matrix differential and experimental test." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 228, no. 17 (March 11, 2014): 3141–55. http://dx.doi.org/10.1177/0954406214527272.
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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.
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Zou, Xicong, Xuesen Zhao, Zongwei Wang, Guo Li, Zhenjiang Hu, and Tao Sun. "Error Distribution of a 5-Axis Measuring Machine Based on Sensitivity Analysis of Geometric Errors." Mathematical Problems in Engineering 2020 (February 14, 2020): 1–15. http://dx.doi.org/10.1155/2020/8146975.
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Geometric errors are inevitably introduced into any multiaxis measuring system, and the geometric error is one of the main factors that seriously affects the measurement accuracy. The present work investigates the error distribution of the prototype of a 5-axis measuring machine based on sensitivity analysis of geometric errors. The measurement error modeling of the 5-axis measuring machine is first established via the homogeneous coordinate transformation, and the Sobol global sensitivity analysis method is then employed to quantify the influence of geometric errors on the measurement result with the sensitivity index. The result shows that most of the angular errors are the crucial geometric errors seriously affecting the measurement result. These errors are supposed to be fully considered in the accuracy design and manufacturing stages. The error levels of the crucial geometric errors were distributed and readjusted according to the sensitivity analysis result. Some practical approaches to distribute and improve the crucial geometric errors have been given in detail. The error distribution method is effective to equalize the influence of the crucial geometric errors on the measurement result as possible. The findings of this study provide significant meanings for the optimal design and accurate manufacturing of the 5-axis measuring machine, and the proposed method can be used to improve the measurement accuracy of the 5-axis measuring machine.
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PARK, SUNG-RYUNG, and SEUNG-HAN YANG. "DESIGN OF A 5-AXIS MACHINE TOOL CONSIDERING GEOMETRIC ERRORS." International Journal of Modern Physics B 24, no. 15n16 (June 30, 2010): 2484–89. http://dx.doi.org/10.1142/s0217979210065131.
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Control over scale, dynamic, environment, and geometric errors in 5-axis machine tool are required to realize a high precision machine tool. Especially geometric errors such as translational, rotational, offset, and squareness errors are important factors which should be considered in the design stages of the machine tool. In this paper, geometric errors are evaluated for different configurations of 5-axis machine tool, namely, 1) table tilting, 2) head tilting, and 3) universal and their error synthesis models are derived. The proposed model is different from the conventional error synthesis model since it considers offset and offset errors. The volumetric error is estimated for every configuration with random geometric errors. Finally, the best configuration, the critical design parameter and error are suggested.
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Guo, Shijie, Shufeng Tang, and Dongsheng Zhang. "A Recognition Methodology for the Key Geometric Errors of a Multi-Axis Machine Tool Based on Accuracy Retentivity Analysis." Complexity 2019 (November 22, 2019): 1–21. http://dx.doi.org/10.1155/2019/8649496.
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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.
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Zhao, Zhi Su, and Xing Hua Zhang. "Geometric Curve Design Method of Fuzzy Reliability Based on Random Processing Errors." Advanced Materials Research 199-200 (February 2011): 72–77. http://dx.doi.org/10.4028/www.scientific.net/amr.199-200.72.
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In order to foresee the influence of random processing errors on geometric curve in design stage, meanwhile including success and failure process during the gradual change process in the forecast. Based on probabilistic fuzzy reliability point of view, the success or failure determination will be extended to fuzzy events. The geometric curve deign method will be also given when taking the impact of random engineering error into account. Related analysis formulae and the fuzzy criterion of success or failure of designing the curve process are established and derived. Through which, design and engineering process are integrated, the designer will be more reliably to predict the success or failure of the geometric curve design during the design stage. The processing error of lack of statistical data and the objectivity of the success or failure determination criterion will be easily solved. Economy cost and reliability design of geometrical curve design will be also considered.
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Ding, Wenzheng, Zhanqun Song, and Shuang Ding. "Investigation on Structural Mapping Laws of Sensitive Geometric Errors Oriented to Remanufacturing of Three-Axis Milling Machine Tools." Machines 10, no. 5 (May 6, 2022): 341. http://dx.doi.org/10.3390/machines10050341.
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Three-axis milling machine tools are widely used in manufacturing enterprises, and they have enormous potential demands for remanufacturing to improve their performance. During remanufacturing a three-axis milling machine tool, the structure needs to be reconstructed, so it is necessary to identify sensitive geometric errors of the remanufactured machine tool. In the traditional sensitive geometric error identification method, complex error modeling and analysis must be conducted. Therefore, professional knowledge is required, and the process of the identification is cumbersome. This paper focused on the quick identification of sensitive geometric errors for remanufacturing of three-axis milling machine tools. Firstly, sensitive geometric errors of a three-axis milling machine tool were identified based on the multi-body system theory and partial differential method. Then, mapping laws between the sensitive geometric errors and the machine tool structure were firstly presented. According to the proposed mapping laws, the sensitive geometric errors can be identified quickly and easily without complex error modeling and analysis. Finally, the simulation and experiment show that the straightness error of milling is improved up to 0.007 mm by compensating the sensitive geometric errors identified by the proposed mapping laws. The table lookup method based on the mapping laws can quickly identify the sensitive geometric errors of three-axis milling machine tools, which is beneficial for the efficiency and precision of remanufacturing of machine tools.
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Saragih, Agung-Shamsuddin, and Tae-Jo Ko. "SUM OF SINUSOIDAL PLUS NOISE MODEL TO EXTRACT COMPONENT ERROR FROM A DOUBLE BALLBAR MEASUREMENT ERROR MAP." Transactions of the Canadian Society for Mechanical Engineering 37, no. 3 (September 2013): 817–27. http://dx.doi.org/10.1139/tcsme-2013-0069.
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The double ballbar (DBB) test, which captures actual data from multiple error origins of axes interaction, was defined as sinusoid error map model plus noise. When the number of sinusoids is the same as the number of individual errors of moving axis in the test map, we can extract a single source geometric error value from the DBB error map by modeling the well-known geometric error of linear axis. We considered the “noise” as mixed errors from other sources than geometric errors. This method is applicable to both a full circle and a truncated DBB test path.
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Yin, Song, Haibo Zhou, Xia Ju, and Zhiqiang Li. "Vision-based measurement for decoupling identification of geometric errors of rotating axes for five-axis platform." Measurement Science and Technology 33, no. 4 (January 20, 2022): 045007. http://dx.doi.org/10.1088/1361-6501/ac46f1.
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Abstract In this paper, a method for identifying and decoupling geometric errors of rotation axes using vision measurement is proposed. Based on screw theory and exponential product formula, identification equations of position-dependent geometric errors (PDGEs) and position-independent geometric errors (PIGEs) of the rotation axes are established. The mapping relationships between the error twist and geometric errors are established. The error model provides the coupling mechanism of PDGEs and PIGEs. Furthermore, a progressive decoupling method is proposed to separate PDGEs and PIGEs without additional assumptions. The pose parameters, required for solving the identification equations, are obtained by visual measurement. Then, the error terms of PIGEs and PDGEs are determined. Lastly, the error calibration of the rotation axes is investigated, thus providing an average rotary table orientation error reduction of 28.1% compared to the situation before calibration.
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Liang, Gui Qiang, Jun Xian Zhang, and Fei Fei Zhao. "Geometric Error Modeling of a Vertical Machining Center." Advanced Materials Research 694-697 (May 2013): 1842–45. http://dx.doi.org/10.4028/www.scientific.net/amr.694-697.1842.
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The effect of geometric error on machining accuracy was researched by multi-body system theory, as well as homogeneous coordinate transformation method. Taking a vertical machining center as example, topological structure of the machine tool was described by lower body array. Lower body array of the machining center, motion freedom between adjacent bodies and geometric errors of the vertical machining center were analyzed. Geometric errors of the bodies in the multi-body system were expressed by homogeneous coordinate transformation. Error model for machining accuracy was deduced and geometric errors having influence on the machining accuracy were identified. The research results provide guidance for analyze of geometric errors on machining accuracy.
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Fiorentino, Antonio, G. C. Feriti, Elisabetta Ceretti, C. Giardini, C. M. G. Bort, and P. Bosetti. "Development of Tool Path Correction Algorithm in Incremental Sheet Forming." Key Engineering Materials 622-623 (September 2014): 382–89. http://dx.doi.org/10.4028/www.scientific.net/kem.622-623.382.
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The problem of obtaining sound parts by Incremental Sheet Forming is still a relevant issue, despite the numerous efforts spent in improving the toolpath planning of the deforming punch in order to compensate for the dimensional and geometrical part errors related to springback and punch movement. Usually, the toolpath generation strategy takes into account the variation of the toolpath itself for obtaining the desired final part with reduced geometrical errors. In the present paper, a correction algorithm is used to iteratively correct the part geometry on the basis of the measured parts and on the calculation of the error defined as the difference between the actual and the nominal part geometries. In practice, the part geometry is used to generate a first trial toolpath, and the form error distribution of the resulting part is used for modifying the nominal part geometry and, then, generating a new, improved toolpath. This procedure gets iterated until the error distribution becomes less than a specified value, corresponding to the desired part tolerance. The correction algorithm was implemented in software and used with the results of FEM simulations. In particular, with few iterations it was possible to reduce the geometrical error to less than 0.4 mm in the Incremental Sheet Forming process of an Al asymmetric part, with a resulting accuracy good enough for both prototyping and production processes.
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Kwintarini, Widyanti, Agung Wibowo, and Yatna Yuwana Martawirya. "Mathematical Approach for Geometric Error Modeling of Three Axis CNC Vertical Milling Machine." Applied Mechanics and Materials 842 (June 2016): 303–10. http://dx.doi.org/10.4028/www.scientific.net/amm.842.303.
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The aim of this paper overviews about to find out the errors that come from three axis CNC vertical milling machine. The errors come from, the CNC milling machine can be modelled into mathematical models and later on these error models will be used to analyse the errors in the measured data. Many errors from CNC machine tools have given significant effects toward the accuracy and repeatability of manufacturing process. There are two error sources come from CNC machine tools such as tool deflection and thermal distortions of machine tool structure. These errors later on will contribute to result in the geometrical deviations of moving axis in CNC vertical milling machine. Geometrical deviations of moving axis such as linear positioning errors, roll, pitch and yaw can be designated as volumetric errors in three axis machine tool. Geometrical deviations of moving axises happen at every axis in three axis CNC vertical milling machine. Geometrical deviations of moving axises in linear and angular movement has the amount of errors up to twenty one errors. Moreover, this geometrical errors play the major role in the total amount of errors and for that particular reason extra attention towards the geometrical deviation errors will be needed along machining process. Each of geometrical error of three axes vertical machining center is modeled using a homogeneous transformation matrix (HTM). The developed mathematical model is used to calculate geometrical errors at each axis and to predict the resultant error vector at the interface of machine tool and workpiece for error compensation.
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Tan, Kok Kiong, and Sunan Huang. "Geometrical error compensation of machines with significant random errors." ISA Transactions 44, no. 1 (January 2005): 43–53. http://dx.doi.org/10.1016/s0019-0578(07)60044-5.
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Wang, Wei, Yi Zhang, and Jian Guo Yang. "Modeling of Compound Errors for CNC Machine Tools." Advanced Materials Research 472-475 (February 2012): 1796–99. http://dx.doi.org/10.4028/www.scientific.net/amr.472-475.1796.
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In this paper, a synthesis modeling method of geometric and thermal error is presented. Through the analysis of machine error data at varying temperatures, the error distribution rule is obtained. Based on the different characteristics of geometric error and thermal error, error separation method has been carried out in the modeling. Using polynomial fitting for geometric error and linear fitting for thermal error, a synthesis mathematical model has been proposed. This error compensation method concerns the variations of geometric errors at different temperatures in the machine working, thus a comprehensive analysis is made on the error and its regularity from the overall temperature rise to the heat steady-state. Both at low and high temperatures in the machine working, the experimental validations show that the positioning errors of the machine tool are reduced effectively after applying the error compensation approach.
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Kenno, Takaaki, Ryuta Sato, Keiichi Shirase, Shigemasa Natsume, and Henny Spaan. "Identification Method of Error Motions and Geometric Errors of a Rotary Axis by R-Test." International Journal of Automation Technology 14, no. 3 (May 5, 2020): 399–408. http://dx.doi.org/10.20965/ijat.2020.p0399.
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While evaluating the accuracy of high-precision machine tools, it is critical to reduce the error factors contributing to the measured results as much as possible. This study aims to evaluate both the error motions and geometric errors of the rotary axis without considering the influence of motion error of the linear axis. In this study, only the rotary axis is moved considering two different settings of a reference sphere, and the linear axes are not moved. The motion accuracy of the rotary axis is measured using the R-test device, both the error motions and geometric errors of the rotary axis are identified from the measurement results. Moreover, the identified geometric errors are verified for correctness via measurement with an intentional angular error. The results clarify that the proposed method can identify the error motions and geometric errors of a rotary axis correctly. The method proposed in this study can thus be effective for evaluating the motion accuracy of the rotary axis and can contribute to further improvement of the accuracy of the rotary table.
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Liao, Te-Tan, Shih-Hung Chen, Kuo-Ying Chen, and Chun-Ta Chen. "SKEW RAY TRACING AND ERROR ANALYSIS OF OPTICAL LENS WITH CYLINDRICAL BOUNDARY SURFACE." Transactions of the Canadian Society for Mechanical Engineering 33, no. 2 (June 2009): 297–314. http://dx.doi.org/10.1139/tcsme-2009-0022.
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This study applies computational geometric algebra based on a 4 × 4 homogeneous transformation matrix and Snell’s law of geometrical optics to analyze skew rays and the errors of a light ray’s path as it passes through a cylindrical lens. The author addresses two important topics: (1) the determination of the direction of a reflected or refracted ray by Snell’s law and (2) the expression of the combination of two principal sources of light path error using error analysis. In topic (2), one of the sources is the translational errors Δdix, Δdiy, and Δdiz and the rotational errors Δωix, Δωiy, and Aωiz that determine the deviation of the light path at each boundary surface, while the other source is the differential changes induced in the incident point position and the unit directional vector of the refracted/reflected ray as a result of differential changes in the position and unit directional vector of the light source. The methodology presented in this study provides a comprehensive and robust approach for evaluating the error of a light ray path as it passes through a cylindrical lens.
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Feng, Xingxing, Haihua Sun, Tianqi Lv, and Yunqing Zhang. "Kinematic analysis of a PPPR spatial serial mechanism with geometric errors." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 234, no. 1 (November 4, 2018): 225–40. http://dx.doi.org/10.1177/0954406218809124.
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The present study focuses on the kinematic analysis of a PPPR spatial serial mechanism with a large number of geometric errors. The study is implemented in three steps: (1) development of a map between the end-effector position error and geometric source errors within the serial mechanism kinematic chains using homogeneous transformation matrix; (2) selection of geometric errors which have significant effects on end-effector positioning accuracy by sensitivity analysis; (3) kinematic analysis of the serial mechanism within which the geometric errors are modelled as interval variables. The computational algorithms are presented for positioning accuracy analysis and workspace analysis in consideration of geometric errors. The analysis results show that the key factors which have significant effects on end-effector position error can be identified efficiently, and the uncertain workspace can also be calculated efficiently.
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Wang, Wei Qing, and Huan Qin Wu. "Sensitivity Analysis of Geometric Errors for Five-Axis CNC Machine Tool Based on Multi-Body System Theory." Applied Mechanics and Materials 271-272 (December 2012): 493–97. http://dx.doi.org/10.4028/www.scientific.net/amm.271-272.493.
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Abstract: In order to determine that the effect of geometric error to the machining accuracy is an important premise for the error compensation, a sensitivity analysis method of geometric error is presented based on multi-body system theory in this paper. An accuracy model of five-axis machine tool is established based on multi-body system theory, and with 37 geometric errors obtained through experimental verification, key error sources affecting the machining accuracy are finally identified by sensitivity analysis. The analysis result shows that the presented method can identify the important geometric errors having large influence on volumetric error of machine tool and is of help to improve the accuracy of machine tool economically.
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Choudhuri, S. A., and E. C. De Meter. "Tolerance Analysis of Machining Fixture Locators." Journal of Manufacturing Science and Engineering 121, no. 2 (May 1, 1999): 273–81. http://dx.doi.org/10.1115/1.2831216.
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The geometric variability of locators within a machining fixture is a known source of datum establishment error and machined feature geometric error. A locator tolerance is used to specify the range of permissible locator variation. Currently there are no models that relate a locator tolerance scheme to the worst case geometric errors that may result due to datum establishment error. This paper presents a methodology for modeling and analyzing the impact of a locator tolerance scheme on the potential datum related, geometric errors of linear, machined features. This paper also provides a simulation study in which locator tolerance analysis is applied to reveal some important insights into the relationship between machined feature geometric error, locator design, and locator tolerance scheme.
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Liu, Xiaojian, Yang Wang, Lemiao Qiu, Chenrui Wu, Peng Zhang, and Shuyou Zhang. "An improved geometric error analysis method considering the variety of sensitivities over working space." Advances in Mechanical Engineering 10, no. 8 (August 2018): 168781401879238. http://dx.doi.org/10.1177/1687814018792389.
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Machine tool accuracy analysis has become increasingly important since accuracy as the major parameter of a machine is to a large extent determined by geometric accuracy design. In order to improve the comprehensiveness and veracity of geometric accuracy design, this article proposes an improved geometric error analysis method considering the variety of sensitivities over working space. A multi-rigid-body model which includes cutting tool’s wear-out error and workpiece’s clamping error is established to represent the position relationship of machine tool’s working components. The expression of geometric error is converted from matrix form to screw form through the screw mapping theory, so that rotational error can be expressed and calculated directly like the translational error. Considering motion errors along axes over the whole working space instead of at a fixed position, an improved sensitivity analysis algorithm is conducted to identify, among 38 components of errors increased the variety with tool wear and clamping errors, which of them have a significant impact on four different types of machine errors. Finally, the proposed method was implemented and validated on a horizontal boring machine, and the sensitivity analysis results over working space would offer vital evidence for the machine’s geometric accuracy design.
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Wan, Peng, Jun Jie Guo, and Hai Tao Li. "Study on the Method of Error Identification and Compensation for Gear Measuring Center." Advanced Materials Research 482-484 (February 2012): 1821–28. http://dx.doi.org/10.4028/www.scientific.net/amr.482-484.1821.
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Gear Measuring Center(GMC) is commonly used to test error of the tooth surface of the gear, whose geometric accuracy directly impacts on the accuracy of measurement. How to quickly and accurately detect space geometric error of the measuring machine and compensate becomes the essential means of high-precision measurements. According to the problem above, in the paper, three-beams laser detection technology is proposed. The detection of the geometric errors of the linear axis was achieved. The accurate measurement for the position and attitude of the plane mirror on measurement seat was achieved based on laser telemetry principle. The positioning error, the pitching angle errors, the deflection angle errors and the straightness errors were separated. And then based on multi-body system theory, by using of homogeneous coordinate transformation, the error compensation model of 4-axis measuring machine which includes three shifting pairs and one revolute pair was established, and the algorithm was given in the paper. The theoretical foundation for real-time compensation of 4-axis GMC was established. The geometric errors of GMC can be improved by the method of the error detection and compensation. The method plays a very important role in high-precision measurements.
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Li, Pengzhong, Ruihan Zhao, and Liang Luo. "A Geometric Accuracy Error Analysis Method for Turn-Milling Combined NC Machine Tool." Symmetry 12, no. 10 (September 30, 2020): 1622. http://dx.doi.org/10.3390/sym12101622.
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Turn-Milling Combined NC machine tool is different from traditional machine tools in structure and process realization. As an important means in the design stage, the analysis method of geometric accuracy error is also different from the traditional method. The actual errors and the error compensation values are a pair of "symmetry" data sets which are connected by the movement of machine tools. The authors try to make them more consistent through this work. The geometric error terms were firstly determined by topological structure analysis, then based on homogeneous coordinate transformation and multibody system theory, the geometric error model was established. With the interval theory, the function rule of sensitivity of geometric error sources to spatial errors was analyzed in detail, and the global maximum interval sensitivity of nine geometric error sources was extracted, providing a theoretical basis for error compensation and precision distribution. The geometric error sensitivity analysis method proposed in this paper can accurately evaluate the influence weights of each error term on the machining accuracy, and identify the important sensitive error terms with great influence on the machining accuracy from many error terms.
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Song, Zhanqun, Shuang Ding, Zhiwei Chen, Zhongwang Lu, and Zhouzhou Wang. "High-Efficient Calculation Method for Sensitive PDGEs of Five-Axis Reconfigurable Machine Tool." Machines 9, no. 5 (April 25, 2021): 84. http://dx.doi.org/10.3390/machines9050084.
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Sensitive geometric errors of a machine tool have significant influence on machining accuracy, and it is important to identify them. Complex modeling and analysis must be carried out to identify the sensitive geometric errors of a five-axis machine tool by using the traditional method. Once the configuration structure of the machine tools is reconstructed, repetitive error modeling and analysis are required, and the identification cycle of sensitive geometric errors is long. Therefore, this paper proposes a high-efficient calculation method for sensitive position-dependent geometric error (PDGEs) identification of a five-axis reconfigurable machine tool. According to the results of sensitive geometric errors of the RTTTR-type and TTTRR-type five-axis machine tools, the mapping expressions between sensitive PDGEs and the configuration structure of machine tools was established. In this method, sensitive PDGEs can be calculated directly according to the mapping expression, which eliminates the process of error modeling and analysis. Taking a RTTTR-type five-axis machine tool as an example, the sensitive PDGEs were calculated according to the presented mapping expressions without error modeling and analysis. A series of analysis points in the machining area were selected to compare the machining errors before and after sensitive PDGE compensation. The results show that this calculation method is accurate.
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Liang, Gui Qiang, Ai Rong Zhang, and Ting Ting Guo. "The Effect of Geometric Error on Machining Accuracy for Machining Center." Advanced Materials Research 690-693 (May 2013): 3244–48. http://dx.doi.org/10.4028/www.scientific.net/amr.690-693.3244.
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In order to improve machining accuracy of machining center, the effect of geometric error on machining accuracy was researched by multi-body system theory. Taking a vertical machining center as example, topological structure of the machining center was described by lower body array. Geometric errors of the bodies in the multi-body system were expressed by homogeneous coordinate transformation. Error model for machining accuracy was deduced and geometric errors having great influence on the machining accuracy were identified. The research results show that, straightness errors and linear displacement errors in three directions have direct influence on machining accuracy, and the effect on machining accuracy caused by angle errors are related to the dimensions of the machining center and travel distance of the three axes. The research results provide guidance for analysis on sensitivity of geometric errors.
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Ma, Dong, Jiakun Li, Qibo Feng, Qixin He, Yaowen Ding, and Jianying Cui. "Simultaneous Measurement Method and Error Analysis of Six Degrees of Freedom Motion Errors of a Rotary Axis Based on Polyhedral Prism." Applied Sciences 11, no. 9 (April 27, 2021): 3960. http://dx.doi.org/10.3390/app11093960.
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A novel method is proposed for measuring the six degrees-of-freedom (DOF) geometric motion errors of a rotary axis based on a polyhedral prism. An error-sensitive unit which consists of a polyhedral prism and a planar reflector, is designed to carry out measurement of all six DOF errors, including the angular positioning error, the tilt motion error around the Y axis, the tilt motion error around the X axis, the radial motion error along the X and Y axes, and the axial motion error along the Z axis. The mathematical error model, including the six DOF geometric motion errors of the rotary axis, the installation errors between the polyhedral prism and the rotary axis, the manufacturing errors of the polyhedral prism, and the position errors of the sensors, are established. The effectiveness of the proposed method and the compensation model was simulated and experimentally verified.
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Cheng, Qiang, Dong Sheng Xuan, Jie Sun, and Zhi Feng Liu. "Geometric Errors Sensitivity Analysis of Precision Vertical Machining Center Based on Multi-Body System Theory." Applied Mechanics and Materials 108 (October 2011): 61–66. http://dx.doi.org/10.4028/www.scientific.net/amm.108.61.
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Parts of geometric error coupled into space error is the main reason that affects machining accuracy of machine tools; therefore, how to determine the effect of geometric error to the machining accuracy and then assigning geometry precision of parts economically is a difficult problem in machine tool designing process. Therefore, based on multi-body system theory, a sensitivity analysis method of geometric error is put forward in this paper. Let’s take precision vertical machining center for an example. Firstly, an accuracy model of machining center is established based on multi-body system theory, and with 21 geometric errors obtained through experimental verification, key error sources affecting the machining accuracy are finally identified by sensitivity analysis. The example analysis shows that the proposed method can effectively identify the main geometric errors of parts that have great influence on volumetric error of machine tool, and thus provides important theoretical basis to improve the accuracy of machine tool economically.
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Базров, Борис, and Boris Bazrov. "Problems in estimate of parts geometrical accuracy." Science intensive technologies in mechanical engineering 2018, no. 4 (April 19, 2018): 8–12. http://dx.doi.org/10.12737/article_5aacd85793bdc2.44830790.
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The paper reports the analysis of the method for parts geometrical accuracy definition which includes the following stages: part surfaces measurement, a representation of measurement results and their relative position, a definition without errors count and a definition of surface errors. There are shown drawbacks of stages enumerated such as a neglect of measurement base surface errors, an ambiguity of measurement base positions regarding surfaces under control, use of bases of error account and criteria for errors estimate irrespective of surface operation functions.
A multi-gradation of the method for the estimate of a part error resulting in the accumulation of total error is shown.
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Fan, Jinwei, Peitong Wang, and Zhuang Li. "A novel geometric error identification and prediction approach." MATEC Web of Conferences 363 (2022): 01007. http://dx.doi.org/10.1051/matecconf/202236301007.
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This paper proposed an integrated geometric error identification and prediction method to solve the uncertainty problem of the PDGEs of rotary axis. First, based on homogeneous transform matrix (HTM) and multi-body system (MBS) theory, The transfer matrix only considering the C-axes rotated is derived to the position error model. Then a geometric errors identification of rotary axis is introduced by measuring the error increment in three directions. Meanwhile the geometric errors of C-axis are described as truncated Fourier polynomials caused by fitting discrete values. Thus, The geometric error identification is converted into the function coefficient. Finally, the proposed new prediction and identification model of PDGEs in the global frame are verified through simulation and experiments with double ball-bar tests.
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He, G. Y., C. X. Hu, and X. Liu. "Evaluation Modeling and Optimal Adjustment of Position Error Based on Localization Sensitivity Analysis." Materials Science Forum 697-698 (September 2011): 258–61. http://dx.doi.org/10.4028/www.scientific.net/msf.697-698.258.
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Sensitivity analysis is to evaluate how sensitive the surface deviation of a workpiece is to a geometric error of locator. With this thinking, the relationship between geometric error of locators and the position error of holes group is presented. The fixture system errors model and evaluation model of position errors are established. Furthermore with both models, a method of optimizing the position errors by adjusting the locators’ position is presented, which can get to accuracy localization. At last, a simulation study is used to verify the method.
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Liu, Yi Lei, Dong Gao, and Gang Wei Cui. "Volumetric Error Model of Large CNC Machine Tool and Verification Based on Particle Swarm Optimization." Key Engineering Materials 579-580 (September 2013): 76–79. http://dx.doi.org/10.4028/www.scientific.net/kem.579-580.76.
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Volumetric error has large effect on machine tool accuracy; improving CNC machine tool accuracy through error compensation has received significant attention recently. This paper intends to represent volumetric error measurement based on laser tracker. The volumetric error is modeled by homogenous transformation matrix with each coordinate corresponding to each motion axis. Based on parts of spatial points volumetric error, the geometric errors which affect volumetric positioning error are verified through particle swarm optimization with the L2 parameters as the target function. The chebyshev orthogonal polynomials are applied to approximate geometric errors.
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He, Zhen Ya, Jian Zhong Fu, and Xin Hua Yao. "Error Modeling and Identification Technology for Circular Path of NC Machine Tools." Applied Mechanics and Materials 278-280 (January 2013): 345–49. http://dx.doi.org/10.4028/www.scientific.net/amm.278-280.345.
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An error mapping modeling and identification technology for the circular path test of NC machine tools is proposed. First, geometric error modeling of the NC machine tool was established and the theory of the laser measurement method was introduced. Then through further analyzing the influence of the geometric errors to circular path deviations, the error items were identified, such as the displacement errors, backlashes and squareness errors. Finally measurement and compensation experiment of circular path was conducted. The experimental results show that the geometric error modeling is feasible, and the measurement method can be set up easily and rapidly, even can be used to measure smaller radius circular path under a high feed rate condition. After compensation, the accuracy of the circular path of the machine tool is improved by 50.88%.
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Li, Xin, Zhi Xiong Zhang, Jian Zhong Shang, and Yu Jun Cao. "Research on Angular Variation for Aeroplane-Assembly Base on State Space Model." Applied Mechanics and Materials 278-280 (January 2013): 149–54. http://dx.doi.org/10.4028/www.scientific.net/amm.278-280.149.
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Abstract. Variation modeling is one of the most significant tools for assembly variation analysis. Considering dimension and geometric errors, and part situation errors, the error source that affects assembly accuracy is classified into two types: error of geometric location and orientation, error of geometric form. And unify these different types of error or deviation by the concept of Virtual Fixture. So a rigid assembly state space model is developed for stream of variation analysis in multi-station assembly processes. And an aeroplane-cabin-assembly process is analyzed in this model. The developed methodology outperforms the current simulation based techniques in computation efficiency, the model is validated using Monte Carlo series Simulations.
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Lee, Kwang Il, A. G. Nanda Kumar, and Seung Han Yang. "A Novel Measurement System to Evaluate the Six Geometric Errors of Rotary Table." Advanced Materials Research 314-316 (August 2011): 1691–94. http://dx.doi.org/10.4028/www.scientific.net/amr.314-316.1691.
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In this paper, the novel measurement system for estimating the six geometric error of rotary table has been proposed. This system configuration comprising four components namely laser diode, beam splitter, position sensitive detector (PSD) and deflecting mirror. The advantage of this approach is that all six geometric error of rotary table can be evaluated by just measuring four set of points from this system configuration. To estimate the geometric errors, a linear relationship is established mathematically between measurement points and geometric errors. The line equation and plane equation along with homogeneous transformation matrix are used to define the linear relationship. The mathematical model is simulated to verify the validity of the system; the result shows the proposed system is suitable to measure the geometric errors of rotary table.
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Hsu, Chi-Hua, Jr-Rung Chen, Fan-Hsi Hsu, and Yu-Ta Chen. "A Novel Measurement Method for Determining Geometric Errors of Rotary Tables by Using LaserTRACER and Reflectors." Applied Sciences 13, no. 4 (February 13, 2023): 2419. http://dx.doi.org/10.3390/app13042419.
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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.
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Nguyen, Hoai-Nhan, Phu-Nguyen Le, and Hee-Jun Kang. "A new calibration method for enhancing robot position accuracy by combining a robot model–based identification approach and an artificial neural network–based error compensation technique." Advances in Mechanical Engineering 11, no. 1 (January 2019): 168781401882293. http://dx.doi.org/10.1177/1687814018822935.
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Robot position accuracy plays a very important role in advanced industrial applications. This article proposes a new method for enhancing robot position accuracy. In order to increase robot accuracy, the proposed method models and identifies determinable error sources, for instance, geometric errors and joint deflection errors. Because non-geometric error sources such as link compliance, gear backlash, and others are difficult to model correctly and completely, an artificial neural network is used for compensating for the robot position errors, which are caused by these non-geometric error sources. The proposed method is used for experimental calibration of an industrial Hyundai HH800 robot designed for carrying heavy loads. The robot position accuracy after calibration demonstrates the effectiveness and correctness of the method.
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Lin, Zixin, Wenjie Tian, Dawei Zhang, Weiguo Gao, and Lina Wang. "A mapping model between the workpiece geometric tolerance and the end pose error of CNC machine tool considering structure distortion of cutting process system." Advances in Mechanical Engineering 13, no. 3 (March 2021): 168781402110047. http://dx.doi.org/10.1177/16878140211004771.
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Aiming at the problem that the geometric accuracy design index of machine tools is difficult to be determined reasonably in the geometric precision design process of CNC machine tools, this paper presents a mapping model between geometric tolerance of the workpiece and end pose error (positional and orientational error of the tool relative to the workpiece) of the machine tool considering structure distortion of cutting process system. Only considering the factors of the machine tool geometric errors, this paper first establishes the relationship between the geometric tolerance requirements of the workpiece and relative pose error at the end of machine tools, and completes the estimation of the machine tools end pose error. Then this paper analyzes the elastic deformations of the cutting process system caused by the cutting force. These elastic deformations produce machining errors. Based on the above analysis, the estimated variation range of the end pose error can be adjusted by the emulation of the geometric tolerance of the workpiece and used as the geometric accuracy design index of machine tools. This paper takes the international standard small size contour processing test piece as an example to explain the application process of the proposed model.