scholarly journals High-precision modeling of CNCs’ spatial errors based on screw theory

2022 ◽  
Vol 4 (2) ◽  
Author(s):  
Guohua Chen ◽  
Lin Zhang ◽  
Chao Wang ◽  
Hua Xiang ◽  
Guangqing Tong ◽  
...  
Keyword(s):  
Machine Tool ◽  
Evaluation Method ◽  
Screw Theory ◽  
Error Model ◽  
Error Modeling ◽  
Spatial Error Model ◽  
Cnc Machine ◽  
Spatial Error ◽  
Coordinate Vector ◽  
Tool Motion

AbstractA method for establishing machine tool’s spatial error model is put forward based on screw theory, which is different from the traditional error modeling method. By analyzing the position relationship between the ideal coordinate vector and the actual coordinate vector jointly affected by linear errors and angular errors, a single-axis screw conversion matrix error expression is brought up based on screw theory. Meanwhile, the comprehensive spatial error model of the CNC machine tool is derived by considering the influence of the workpiece motion chain and the tool motion chain on the model. Further, to compensating spatial errors of CNCs, such screw theory-based model is embedded in the error compensation system by means of integration of a few specific application examples. And in order to evaluate the compensation effects, an integrated evaluation method of quantitative spatial diagonal calculation and MATLAB simulation is proposed. Application results show that the screw theory-based spatial error model of tool has a very substantial compensation effect, which makes the position error of the machine tool decreased by about 80%.

scholarly journals Modeling Method of CNC Machine Tools’ Volume Error Considering Abbe Error

2021 ◽  
Author(s):  
GUOHUA CHEN ◽  
Lin Zhang ◽  
XIANGJIE WANG ◽  
CHAO WANG ◽  
HUA XIANG ◽  
...  
Keyword(s):  
Machine Tool ◽  
Machine Tools ◽  
Error Model ◽  
Modeling Method ◽  
Machining Accuracy ◽  
Spatial Error Model ◽  
Spatial Error ◽  
Precision Machine ◽  
Precision Machine Tools ◽  
Abbe Error

Abstract Abbe error is an important factor affecting high-precision machine tools, and the traditional modeling method does not consider Abbe error. Aiming at this problem, based on the traditional error model of machine tools and the formation mechanism of Abbe error, this paper establishes a machine tool spatial error model that considers Abbe error. Then combined with a specific machine tool, based on the measurement of 21 geometric errors of the machine tool to obtain relevant error data, through the combination of qualitative and quantitative accuracy evaluation methods, two models of traditional error model and error model considering Abbe error are analyzed. The accuracy of the machine tool is compared, and the comparison of the compensation effects of the two error models after compensation is also analyzed. The example verification shows that the machine tool spatial error model considering Abbe error is effective and feasible, and the compensation effect is better. It provides an important modeling method for improving the machining accuracy of precision machine tools.

Recursive Estimation of the Spatial Error Model

2022 ◽  
Author(s):  
Chiara Ghiringhelli ◽  
Gianfranco Piras ◽  
Giuseppe Arbia ◽  
Antonietta Mira
Keyword(s):  
Error Model ◽  
Recursive Estimation ◽  
Spatial Error Model ◽  
Spatial Error

Transportation and Urban Development

2018 ◽  
pp. 283-305
Author(s):  
Mehmet Akif Kara
Keyword(s):  
Spillover Effect ◽  
Error Model ◽  
Transportation Infrastructure ◽  
Spatial Error Model ◽  
Test Statistic ◽  
Spatial Econometric ◽  
Spatial Error ◽  
Infrastructure Investments ◽  
Regional Economic Performance ◽  
The Impact

It is noteworthy that there is a substantial literature review that examines the impact of transportation infrastructure on urban and regional economic performance. It is observed that such infrastructure investments are focused on the economic growth as well as the spillover effect in applied studies carried out in this respect. In this study, in which the effects of highway transportation infrastructure on urban output and the spillover effect of these investments are determined using the spatial econometric method, 81 cities in Turkey have been taken into consideration, and according to the results of the study, transportation infrastructure investments in Turkey have been found to contribute positively to urban output. Also, while the Moran's I test statistic reveals the spatial dependence of such investments, the Lagrange multiplier test results also determine the need to use the spatial error model. The spatial error model results reveal the existence of the positive spillover effect of transportation infrastructure investments.

A linear model for the machine tool assembly error prediction considering roller guide error and gravity-induced deformation

2020 ◽  
Vol 234 (15) ◽  
pp. 2939-2950 ◽  
Author(s):  
Gaiyun He ◽  
Panpan Shi ◽  
Longzhen Guo ◽  
Bohui Ding
Keyword(s):  
Machine Tool ◽  
Error Model ◽  
Error Modeling ◽  
Propagation Model ◽  
Joint Surface ◽  
Analytical Relationship ◽  
Error Prediction ◽  
Linear Superposition ◽  
Roller Guide ◽  
Assembly Error

In assembly, error prediction and control according to the error state of the machine parts are the key links to ensuring the accuracy of the entire machine tool. In this study, an assembly error modeling method considering the error of the roller guide and gravity-induced deformation is proposed. First, based on the Hertz contact theory, a nonlinear error propagation model for the roller guide to the moving part is proposed. With this model, the analytical relationship between the straightness error of the guide rail and the errors of the moving part can be established. Then, after the linearization of the guide error model, a machine assembly error model considering the guide error is proposed. This model expresses the linear relationship between the error of the rolling joint surface and the error of the machine tool after the final assembly. Additionally, considering the influence of gravity deformation of structural parts, the gravity deformation is extracted by the finite element analysis method and added to the model by linear superposition. As a result, the model corresponds more with the practical assembly process. Finally, an assembly error prediction method of the precision horizontal machining center is presented, and a case is studied to demonstrate the validity of the proposed model and method.

Spatial Error Model

2008 ◽  
pp. 1101-1101
Author(s):  
Shashi Shekhar ◽  
Hui Xiong
Keyword(s):  
Error Model ◽  
Spatial Error Model ◽  
Spatial Error

Tracking Error Modeling of the Theodolite Based on GRNN Method

2011 ◽  
Vol 121-126 ◽  
pp. 4870-4874
Author(s):  
Miao Li ◽  
Hui Bin Gao
Keyword(s):  
Evaluation Method ◽  
Tracking Error ◽  
High Accuracy ◽  
Error Model ◽  
Error Modeling ◽  
General Regression Neural Network ◽  
Engineering Practice ◽  
Tracking Accuracy ◽  
Model Based ◽  
General Regression

To meet the requirement of high tracking accuracy as well as develop more reasonable evaluation method, in this paper, the General Regression Neural Network (GRNN) has been applied to build the tracking error model of the theodolite. First, we analyze the nonlinear factors in the theodolite. Second, we discuss the principle of GRNN, including its structure, the function as well as its priors. Third, we build the tracking error model based on GRNN and verify the model through the different parameters. The result indicated that the network model based on GRNN has high accuracy and good generalization ability. It could instead the real system to a certain extent. The research in this paper has important value to the engineering practice.

Modified Jacobian-Torsor Based Error Modeling and Quantitative Sensitivity Analysis for Single Axis Assembly of Machine Tool

2017 ◽  
Author(s):  
Zhengchun Du ◽  
Jian Wu ◽  
Jianguo Yang
Keyword(s):  
Sensitivity Analysis ◽  
Machine Tool ◽  
Error Modeling ◽  
Small Displacement ◽  
Cnc Machine ◽  
Statistical Solution ◽  
Mechanical Parts ◽  
Comprehensive Method ◽  
Precision Design ◽  
Final Error

The influence of component errors on the final error is a key aspect of error modeling of CNC machine tool. Nevertheless, the mechanism by which the errors in mechanical parts accumulate to result in the component errors and then impact the final error of CNC machine, has not been identified; the identification of this mechanism is highly relevant to precision design of CNC machine. In this study, error modeling based on the Jacobian-torsor theory is founded to determine the mechanism by which fundamental errors in mechanical parts influence the comprehensive error of single-axis assembly. Firstly, the constraints of small displacement torsors (SDTs) for typical features and the statistical solution are proposed to perfect the modified Jacobian-torsor model theoretically. Next, the modified Jacobian-torsor model is applied to the error modeling of a single-axis assembly in a three-axis machine center. Furthermore, the comprehensive errors of the single-axis assembly are evaluated by Monte Carlo simulation based on the synthesized error model. The accuracy and efficiency of the modified Jacobian-torsor model are verified through a comparison between the simulation results and the measured data from a batch of similar vertical machine centers. Based on the modified Jacobian-torsor model, the application of quantitative sensitivity analysis of single-axis assembly is investigated, along with an analysis of the analysis of key error sources to the synthetical error ranges of the single-axis assembly. This model is providing a comprehensive method for the better understanding of the key error source of the machine tool and has the potential to enable error allocation and precision improvement of the assembly and the whole machine tool in future.

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