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Journal of ZheJiang University (Engineering Science)  2024, Vol. 58 Issue (4): 748-760    DOI: 10.3785/j.issn.1008-973X.2024.04.010
    
Adaptive slice method based on posterior error of hierarchical N-ary tree mapping Boolean volume contours
Hongshuai GUO1(),Shuyou ZHANG1,Guodong YI1,*(),Xiaojian LIU1,2,Jianrong TAN1
1. State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310027, China
2. Ningbo Innovation Center, Zhejiang University, Ningbo 315100, China
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Abstract  

Under the given build orientation, slice thickness affects the step effect on the surface of the fused deposition modeling part, and slice contour with its hierarchical relationship is the research basis for path planning. An adaptive slice method based on the operation of Boolean volume contours was proposed. Local contour topology was constructed on different height slice-plane of a part model and the kernel region was calculated. Contour loops were mapped to one-dimensional axis according to the intersections of connection lines between kernel points with the contour loops. The hierarchy relationship of contour loops was determined by topological mapping. N-ary tree was built by the hierarchical relationship. The Boolean operation of volume contour with feature change was mapped by the height of the N-ary tree. Adaptive slice thickness was designed according to the slice variation threshold. Volume error under any slice thickness was estimated by the posterior error of volume contour. The effectiveness of adaptive slice was verified by the volume error. According to printing examples and the comparison of different adaptive slice methods, the calculation accuracy of slice volume error obtained by contour posterior error is higher than that obtained by the method of cusp height. Volume error is reduced by controlling slice thickness on the part of volume contour features, and surface forming accuracy on the region of model features is improved with the volume error reduced.



Key wordsfused deposition modeling      adaptive slice      topological mapping      volume error      hierarchical N-ary tree      posterior error of volume contour     
Received: 01 September 2023      Published: 27 March 2024
CLC:  TP 393  
Fund:  浙江省重点研发计划项目(2021C01149);浙江省自然科学基金资助项目(LZ22E050008);宁波市自然科学基金资助项目(2021J150).
Corresponding Authors: Guodong YI     E-mail: hsg@zju.edu.cn;ygd@zju.edu.cn
Cite this article:

Hongshuai GUO,Shuyou ZHANG,Guodong YI,Xiaojian LIU,Jianrong TAN. Adaptive slice method based on posterior error of hierarchical N-ary tree mapping Boolean volume contours. Journal of ZheJiang University (Engineering Science), 2024, 58(4): 748-760.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2024.04.010     OR     https://www.zjujournals.com/eng/Y2024/V58/I4/748


层次多叉树映射布尔体廓后验误差的自适应层切

在给定构建方向下,层切厚度影响熔融沉积成型零件表面的阶梯效应,层切轮廓及其层次关系是路径规划的研究基础. 为此,提出基于布尔体廓运算的自适应层切方法,在零件模型不同高度层切面上构建局部轮廓拓扑并计算内核域,根据内核点连线与轮廓环的交点,将轮廓环数据映射到一维坐标轴,基于拓扑映射判定轮廓环层次关系. 建立层次关系多叉树,以树高映射体廓特征变化的布尔运算,根据层变阈值设计自适应层厚,通过体廓后验误差估计任意层厚的体积误差,验证自适应层切的有效性. 实例打印及不同自适应层切方法对比结果表明,采用体廓后验误差计算的层切体积误差精度比牙尖高度法的更高;通过控制体廓特征部位的层厚来减小体积误差,有助于提高模型特征部位的表面成型精度.


关键词: 熔融沉积成型,  自适应层切,  拓扑映射,  体积误差,  层次多叉树,  体廓后验误差 
Fig.1 Ordered connection of contour intersections
Fig.2 Analysis of insertion points
Fig.3 Kernel region calculation of contour loop
Fig.4 Hierarchical relationship of contour loops (${n_c} \leqslant 1$)
Fig.5 Hierarchical relationship of contour loops (nc>1)
Fig.6 Hierarchical relationships of multi-entity contour loops
Fig.7 Judgment process of hierarchical relationship and direction for contour loops
Fig.8 Data structure of N-ary tree
Fig.9 Volume error calculation by Boolean volume contour
Fig.10 Flowchart of adaptive slice
Fig.11 Test model with mesh structure
Fig.12 Extraction of arbitrary contour facet set
Fig.13 Intersection calculation of contours
Fig.14 Topology reconstruction of contour with facet index
Fig.15 Slice visualization and contour loop data of each layer
Fig.16 Hierarchical relationship judgment of contour loops
轮廓索引12345678
1?=0?100000
2?0=000?100
3+10=00000
4?000=00?10
5?0000=001
6+01000=00
7+000100=0
8+0000?100=
Tab.1 Hierarchical relationship of 10th contour loops
KeyhPCDA/mm2L/mm
0004-6-3-5None00
4107+154.19362.303
724None?31.52552.195
6102?129.89164.999
226None+15.40744.937
3101+75.72167.691
123None+18.52515.512
5108?59.89777.513
825None?23.69842.004
Tab.2 N-ary tree node information of 10th slice contour
Fig.17 Hierarchical N-ary tree based on hierarchical relationship of contour loops
Fig.18 Trend of slice change coefficient
Fig.19 Comparison between adaptive slice and uniform slice by different thresholds
Fig.20 Comparison of posterior error based on volume contour by different thresholds
Fig.21 Volume error convergence verification comparison of different methods
Fig.22 Volume error of 5000 layers calculated based on Boolean volume contour
Fig.23 Printing example of different slice methods
Fig.24 Comparison results of local amplification details with different adaptive slice thicknesses
层切方法ts/s
t = 0.50u~2.00ut = 0.50u~1.00ut = 0.25u~0.80u
相对体积误差18.34125.29430.142
B样条插值20.21927.83131.752
本研究13.48224.29532.328
Tab.3 Running time comparison of different slice algorithms
t/mm层切方法Ve/mm3$ {{{\overline V}_{\rm{e}}}} $/mm3Vew/mm3LN
IIIIIIII
u = 0.2均匀层切1.2240.9931.1421.12010.841445
0.50u~
2.00u
相对体积误差2.2131.5041.6161.77811.223382
B样条插值2.0581.6721.7911.84011.349395
本研究1.9531.3961.7131.68711.310376
0.50u~
1.00u
相对体积误差1.7391.1041.4331.42511.104398
B样条插值1.6741.0151.3391.34311.237409
本研究1.4211.0471.2571.24210.972391
0.25u~
0.80u
相对体积误差1.0970.8390.9790.9729.641503
B样条插值1.1060.8150.9160.9469.329512
本研究1.0370.8720.9840.9649.785483
Tab.4 Adaptive layering results comparison of different methods
Fig.25 Experiments measure of microscopic morphological features by metallographic electron microscopy
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