Product-of-exponential formulas for precision enhancement of five-axis machine tools via geometric error modeling and compensation

Fu, Guoqiang; Fu, Jianzhong; Shen, Hongyao; Xu, Yanliang; Jin, Yuan

doi:10.1007/s00170-015-7035-0

Cited by 50 publications

(22 citation statements)

References 25 publications

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“…Each joint angle Q i, j ¼ (a i, j , b i, j , g i, j ) can be solved by inverse kinematics equations (10) and (11) to get P i, j . The distance e i, j from P i, j to line segment P iÀ1 P i can be calculated.…”

Section: Range Of Inverse Trigonometric Functionsmentioning

confidence: 99%

A postprocessing and path optimization based on nonlinear error for multijoint industrial robot-based 3D printing

Gao

et al. 2020

International Journal of Advanced Robotic Systems

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Multijoint industrial robots can be used for 3D printing to manufacture the complex freeform surfaces. The postprocessing is the basis of the precise printing. Due to the nonlinear motion of the rotational joint, nonlinear error is inevitable in multijoint industrial robots. In this article, the postprocessing and the path optimization based on the nonlinear errors are proposed to improve the accuracy of the multijoint industrial robots-based 3D printing. Firstly, the kinematics of the multijoint industrial robot for 3D printing is analyzed briefly based on product of exponential (POE) theory by considering the structure parameters. All possible groups of joint angles for one tool pose in the joint range are obtained in the inverse kinematics. Secondly, the nonlinear error evaluation based on the interpolation is derived according to the kinematics. The nonlinear error of one numerical control (NC) code or one tool pose is obtained. The principle of minimum nonlinear error of joint angle is proposed to select the appropriate solution of joint angle for the postprocessing. Thirdly, a path smoothing method by inserting new tool poses adaptively is proposed to reduce the nonlinear error of the whole printing path. The smooth level in the smoothing is proposed to avoid the endless insertion near the singular area. Finally, simulation and experiments are carried out to testify the effectiveness of the proposed postprocessing and path optimization method.

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Section: Range Of Inverse Trigonometric Functionsmentioning

confidence: 99%

A postprocessing and path optimization based on nonlinear error for multijoint industrial robot-based 3D printing

Gao

et al. 2020

International Journal of Advanced Robotic Systems

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“…Error modelling based on POE screw theory. In this research, error modelling is based on POE screw theory [9]. A three-axis machine tool is considered as an example, and its schematic diagram is shown in Figure 1.…”

Section: Timeliness Volumetric Error Modelingmentioning

confidence: 99%

Machining accuracy retainability prediction of machine tool based on least square support vector machine

Cheng¹,

Qi²,

Sun³

et al. 2016

Proceedings of the 2016 4th International Conference on Machinery, Materials and Information Technology Applications

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The accuracy retainability is becoming an important performance index of machine tool, and how to improve it is a tough problem faced to manufacturers and users. Generally, it needs to measure the errors termly and repeatedly during the specified period to analyze the timeliness machining accuracy retainability, which generates intricate and vast error data. In this paper, a solution to predict machining accuracy retainability is proposed based on least square support vector machine (LS-SVM). A vertical machining center that machines plane and hole continuously for half a year is selected as an illustrative example. The analysis results show that the proposed method is good at predicting the timeliness machining accuracy retainability of machine tool.

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“…(SOV). Fu et al [13,14] used the product-of-exponential theory to establish an exponential product error model for CNC machine tools and proposed a geometric error compensation method based on Jacobian of twists. In addition, Fu et al [15] applied differential motion relation to geometric error modeling, expressing the error model as the sum of the errors of the individual axes of motion.…”

Section: Introductionmentioning

confidence: 99%

A Geometric Accuracy Error Analysis Method for Turn-Milling Combined NC Machine Tool

Zhao

Luo

2020

Symmetry

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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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Product-of-exponential formulas for precision enhancement of five-axis machine tools via geometric error modeling and compensation

Cited by 50 publications

References 25 publications

A postprocessing and path optimization based on nonlinear error for multijoint industrial robot-based 3D printing

A postprocessing and path optimization based on nonlinear error for multijoint industrial robot-based 3D printing

Machining accuracy retainability prediction of machine tool based on least square support vector machine

A Geometric Accuracy Error Analysis Method for Turn-Milling Combined NC Machine Tool

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