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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2022, Vol. 56 Issue (2): 398-407    DOI: 10.3785/j.issn.1008-973X.2022.02.021
    
Comprehensive error modeling and compensation of a large gantry automatic fiber placement machine
Jian-bo WU(),Jun LI,Cheng-gan ZHENG,Liang CHENG*()
Key Laboratory of Advanced Manufacturing Technology of Zhejiang Province, Zhejiang University, Hangzhou 310027, China
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Abstract  

A comprehensive error modeling and compensation method of gravity deformation and geometric error was proposed, in order to improve the accuracy of a large gantry automatic fiber placement (AFP) machine. Finite element method (FEM) was used for static analysis of the gantry AFP machine, and the gravity deformation model was established by workspace meshing method. A geometric error model based on homogeneous transformation matrix (HTM) and Chebyshev polynomial was established, in which the geometric error parameters were identified by combining the measurement data of gravity deformation removal and Powell algorithm. The gravity deformation model and the geometric error model were combined, and a G-code correction strategy based on comprehensive error compensation was proposed. A comprehensive error compensation experiment was performed on the gantry AFP machine, and results showed that before compensation, the error of the gantry AFP machine was large, which cannot fully meet the requirement of placement accuracy. After compensation, the position error and posture error were greatly reduced, the posture error was reduced by over 80%, and the position error was reduced by more than 90%, which met the requirement of placement accuracy, and proved the effectiveness of the proposed comprehensive error modeling and compensation method.

Key words： gantry automatic fiber placement (AFP) machine      gravity deformation      workspace meshing      geometric error      error identification      comprehensive error compensation     
Received: 26 August 2021      Published: 03 March 2022
CLC:  TH 161  
Corresponding Authors: Liang CHENG     E-mail: wujianbo1011@zju.edu.cn;chengliang@zju.edu.cn
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Jian-bo WU
Jun LI
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Liang CHENG
Cite this article:

Jian-bo WU,Jun LI,Cheng-gan ZHENG,Liang CHENG. Comprehensive error modeling and compensation of a large gantry automatic fiber placement machine. Journal of ZheJiang University (Engineering Science), 2022, 56(2): 398-407.

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https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2022.02.021     OR     https://www.zjujournals.com/eng/Y2022/V56/I2/398


大型龙门铺丝机综合误差建模及补偿

为了提高大型龙门自动铺丝(AFP)机的精度，提出重力变形与几何误差综合建模与补偿方法. 采用有限元法对龙门铺丝机进行静力学分析，通过工作空间网格化方法建立重力变形模型；基于齐次变换矩阵与切比雪夫多项式建立几何误差模型，结合剔除重力变形的测量数据与Powell算法实现对几何误差参数的辨识；综合重力变形模型和几何误差模型，提出基于综合误差补偿的G代码修正策略. 在龙门铺丝机上开展综合误差补偿对比实验，结果表明，补偿前龙门铺丝机误差较大，不能完全满足铺放精度需求，而经过补偿后位置误差和姿态误差均大幅度降低，其中姿态误差减小80%以上，而位置误差减小90%以上，满足铺放精度需求，证明了所提出的综合误差建模和补偿方法的有效性.


关键词： 龙门自动铺丝(AFP)机,  重力变形,  工作空间网格化,  几何误差,  误差辨识,  综合误差补偿 
Fig.1 Large gantry AFP machine
Fig.2 Finite element simulation of gantry AFP machine
Fig.3 Coordinate changes before and after gravity deformation
Fig.4 Meshing of joint space
Fig.5 Gravity deformation of sample points in joint space
Fig.6 Definition of coordinate system for gantry AFP machine
坐标系 几何误差元素
$\{ {O_{{\rm{Base}}} }\} \to \{ {O_{\rm{R}}}\}$ ${x_{\rm{R}}}$、 ${y_{\rm{R}}}$、 ${z_{\rm{R}}}$、 ${\alpha _{\rm{R}}}$、 ${\beta _{\rm{R}}}$、 ${\gamma _{\rm{R}}}$
$\{ {O_X}\} \to \{ {O_Y}\} $ ${S_{xy}}$
$\{ {O_Y}\} \to \{ {O_Z}\} $ $ {S_{xz}} $、 ${S_{yz}}$
$\{ {O_Z}\} \to \{ {O_B}\} $ ${\eta _{xB}}$、 ${\eta _{zB}}$
$\{ {O_B}\} \to \{ {O_A}\} $ ${x_A}$、 ${y_A}$、 ${z_A}$、 ${\eta _{yA}}$、 ${\eta _{zA}}$
$\{ {O_A}\} \to \{ {O_C}\} $ ${\eta _{xC}}$、 ${\eta _{yC}}$
$\{ {O_C}\} \to \{ {O_{\rm{T}}}\}$ ${x_{\rm{T}}}$、 ${y_{\rm{T}}}$、 ${z_{\rm{T}}}$
Tab.1 Position-independent geometric error element
Fig.7 Geometric error calibration experiment
Fig.8 Verification of end geometric error element identification
Fig.9 Iterative calculation of axis joint compensation
Fig.10 Schematic diagram of comparison experiment of comprehensive error compensation
Fig.11 Comparison of end position and pose error before and after compensation
?PX/mm ?PY/mm ?PZ/mm ?θX/rad ?θY/rad ?θZ/rad
补偿前最大值 4.900 7.340 0.390 ?6.51×10?3 2.15×10?3 ?5.14×10?3
补偿前平均值 4.860 7.230 0.310 ?6.02×10?3 1.88×10?3 ?3.26×10?3
补偿后最大值 ?0.092 ?0.532 0.046 ?7.02×10?4 ?5.45×10?4 ?6.79×10?5
补偿后平均值 ?0.053 ?0.480 0.003 ?4.11×10?4 ?3.00×10?4 ?4.94×10?4
平均值减小 98.9% 93.4% 99.0% 93.1% 84.0% 84.8%
Tab.2 Statistical data of position and pose error before and after compensation
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