基于双倾斜度概率的流形模型3D打印层切优化方法

doi:10.3901/JME.2019.13.129

机械工程学报 ›› 2019, Vol. 55 ›› Issue (13): 129-143.doi: 10.3901/JME.2019.13.129

基于双倾斜度概率的流形模型3D打印层切优化方法

徐敬华, 任新华, 陈前勇, 张树有, 谭建荣

浙江大学流体动力与机电系统国家重点实验室杭州 310027

收稿日期:2018-08-26 修回日期:2019-01-23 出版日期:2019-07-05 发布日期:2019-07-05
通讯作者: 张树有(通信作者),男,1963年出生,博士,教授,博士研究生导师,主要研究方向为产品数字化设计、计算机图形学、制造业信息化关键技术。E-mail:zsy@zju.edu.cn
作者简介:徐敬华,男,1979年出生,副教授。主要研究方向为增材制造多尺度形态优化。E-mail:xujh@zju.edu.cn;任新华,男,1996年出生。主要研究方向为3D打印几何学。E-mail:21725106@zju.edu.cn;陈前勇,男,1993年出生,博士研究生。主要研究方向为计算机辅助设计。E-mail:11625067@zju.edu.cn;谭建荣,男,1954年出生,博士,教授,博士研究生导师。主要研究方向为产品设计理论。E-mail:egi@zju.edu.cn
基金资助:
国家自然科学基金（51775494）、浙江省科技计划（2019C01141）、浙江省公益技术应用研究（2017C31002）、浙江省高等教育课堂教学改革（kg20160014）和中央基本科研业务费专项资金（2017FZA4003）资助项目。

A Slicing Optimization Method of Manifold Model for 3D Printing Based on Dual Inclinations Probability

XU Jinghua, REN Xinhua, CHEN Qianyong, ZHANG Shuyou, TAN Jianrong

State Key Lab of Fluid Power & Mechatronic Systems, Zhejiang University, Hangzhou 310027

Received:2018-08-26 Revised:2019-01-23 Online:2019-07-05 Published:2019-07-05

摘要/Abstract

摘要： 3D打印在现代医学、高端制造领域应用广泛。现有的3D打印尚难以满足复杂形态的成形精度和效率需求。为此，本文提出了基于双倾斜度概率（Dual Inclinations Probability，DIP）的流形模型3D打印层切优化方法，DIP模型同时考虑了层切面倾斜和增厚方向倾斜的双重因素，以表征丝杠螺母运动副旋合误差、反向旋合背隙、伺服系统热效应等不确定因素。先构建流形模型的沿坐标轴的凸包围盒，通过最小体积外接圆柱获得高径比，再通过面片正交投影，获得向Oxy、Oxz和Oyz面的投影面积，以此确定3D打印最优层切方向（z向）。然后，构建关于层切面倾斜度的复合变量，建立广义卡方分布的层切倾斜度概率模型，用特定点与两面角法建立非水平面的有界面坐标方程。进一步，建立了增厚方向倾斜的倒圆锥正态概率分布模型。通过层切面梯度变化规律确定有界层切面z向最大值和最小值，运用网格面片区间分块法和层次智能筛选面片，确定与各层切平面相交的面片。提取关联的面片集合与该面片集合在有界层切面的正投影的拓扑同胚关系，通过每层截面的截交线复合环，获得3D打印流形模型的有向多连通域。根据Cavalieri原理，计算每层多面棱柱体积，以体积误差和残余高度为判定准则，对分层切片策略进行迭代优化，最终，通过DIP模型得到对不确定因素容差最大的最优鲁棒分层切片策略。以人体枢椎骨为例进行物理实验验证，打印件残余高度最大降低10.12%，阶梯效应得到抑制，证明本文方法可提高不确定因素扰动下的3D打印成形精度。

关键词: 3D打印, 不确定因素扰动, 层切面倾斜, 流形模型, 双倾斜度概率, 拓扑同胚, 增厚方向倾斜

Abstract: 3D printing is widely used in modern medicine and high-end manufacturing fields. The existing 3D printing method is still difficult to meet precision and efficiency requirements for complex shape. Therefore, a slicing optimization method of manifold model for 3D printing based on dual inclinations probability (DIP) is proposed. Both the slicing inclinations and additive inclinations are synchronously considered. Uncertainty factors such as leadscrew nut screwing error, reverse engagement back clearance and heat effect of servo system are characterized. First, the Axis-aligned Bounding Boxes of the manifold model is constructed. The height-diameter ratio is obtained by minimum bounding cylinder. The projection area in Oxy、Oxz and Oyz plane is obtained by orthogonal projection of facets to determine the optimal direction (z direction) of 3D printing. A compound variable of the inclination angle of slicing plane is derived. The probability density function and probability model of generalized chi-squared distribution are built. The bounded coordinate equations of the non-horizontal worktable are deduced by a certain point and double angle method. Further, the maximum and minimum z value of the bounded slicing planes is determined according to the gradient rule of the slicing plane. The triangular facets that intersect with different slicing planes are found out by building interval partition blocks and layered intelligent screening facet. Based on the topological homomorphism of associated facet set and its orthogonal projection on the bounded slicing plane, the directed multi-connected domains of 3D printing model is finally obtained. According to Cavalieri principle, the volume of polyhedral prism in each layer is calculated, and the strategy of slicing is optimized iteratively according to the criterion of volume error and cusp height. Finally, the optimal robust slicing strategy is determined with the greatest tolerance to uncertainties according to the DIP model. 3D printing experiments are carried out on human second cervical vertebra. The Part's maximum cusp height is reduced by 10.12%. The stair effect is suppressed. It is proved that this DIP method can improve the forming accuracy of 3D printing for uncertain error factors.

Key words: additive inclination, dual inclinations probability, manifold model slicing, slicing inclination, three-dimension printing, topological homeomorphism, uncertainty disturbance

中图分类号:

TP391

徐敬华, 任新华, 陈前勇, 张树有, 谭建荣. 基于双倾斜度概率的流形模型3D打印层切优化方法[J]. 机械工程学报, 2019, 55(13): 129-143.

XU Jinghua, REN Xinhua, CHEN Qianyong, ZHANG Shuyou, TAN Jianrong. A Slicing Optimization Method of Manifold Model for 3D Printing Based on Dual Inclinations Probability[J]. Journal of Mechanical Engineering, 2019, 55(13): 129-143.

参考文献

[1] WANG X, JIANG M, ZHOU Z, et al. 3D printing of polymer matrix composites:A review and prospective[J]. Composites Part B Engineering, 2016, 110:442-458.
[2] ALLEN R J A, TRASK R S. An experimental demonstration of effective curved layer fused filament fabrication utilising a parallel deposition robot[J]. Additive Manufacturing, 2015, 8:78-87.
[3] LIM S, BUSWELL R A, VALENTINE P J, et al. Modelling curved-layered printing paths for fabricating large-scale construction components[J]. Additive Manufacturing, 2016, 12:216-230.
[4] TUMBLESTON J R, SHIRVANYANTS D, ERMOSHKIN N, et al. Additive manufacturing. Continuous liquid interface production of 3D objects[J]. Science, 2015, 347(6228):1349-1352.
[5] MARTIN J H, YAHATA B D, HUNDLEY J M, et al. 3D printing of high-strength aluminium alloys[J]. Nature, 2017, 549(7672):365-369.
[6] MINETTO R, VOLPATO N, STOLFI J, et al. An optimal algorithm for 3D triangle mesh slicing[J]. Computer-Aided Design, 2017, 92:1-10.
[7] ZHOU H F, OU Y X, HE Y H, et al. Data generation of layer slice in FDM manufacturing[M]. PARIS:Atlantis Press, 2017:105, 419-424.
[8] XULONG M A, FENG L, BO Y. Fast parallel algorithm for slicing stl based on pipeline[J]. Chinese Journal of Mechanical Engineering, 2016, 29(3):549-555.
[9] SONG Y, YANG Z, LIU Y, et al. Function representation based slicer for 3D printing[J]. Computer Aided Geometric Design, 2018, 62:276-293.
[10] ZENG L, LAI M L, QI D, et al. Efficient slicing procedure based on adaptive layer depth normal image[J]. Computer-Aided Design, 2011, 43(12):1577-1586.
[11] MA W, BUT W C, HE P. NURBS-based adaptive slicing for efficient rapid prototyping[J]. Computer-Aided Design, 2004, 36(13):1309-1325.
[12] HUANG B, SINGAMNENI S B. Curved layer adaptive slicing (CLAS) for fused deposition modelling[J]. Rapid Prototyping Journal, 2015, 21(4):354-367.
[13] HOPE R L, ROTH R N, JACOBS P A. Adaptive slicing with sloping layer surfaces[J]. Rapid Prototyping Journal, 1997, 3(3):89-98.
[14] MAO Y, WU L, YAN D M, et al. Generating hybrid interior structure for 3D printing[J]. Computer Aided Geometric Design, 2018, 62:63-72.
[15] LIND J U, BUSBEE T A, VALENTINE A D, et al. Instrumented cardiac microphysiological devices via multimaterial three-dimensional printing[J]. Nature Materials, 2017, 16(3):303-308.
[16] ZHANG Y S, YUE K, ALEMAN J, et al. 3D bioprinting for tissue and organ fabrication[J]. Annals of Biomedical Engineering, 2017, 45(1):148-163.
[17] LI L, YU F, SHI J, et al. In situ repair of bone and cartilage defects using 3D scanning and 3D printing[J]. Scientific Reports, 2017, 7(1):9416.
[18] JANG J, PARK H J, KIM S W, et al. 3D printed complex tissue construct using stem cell-laden decellularized extracellular matrix bioinks for cardiac repair[J]. Biomaterials, 2017, 112:264-274.
[19] HIRT L, REISER A, SPOLENAK R, et al. Additive manufacturing of metal structures at the micrometer scale[J]. Advanced Materials, 2017, 29(17):1604211.
[20] BHATTACHARJEE N, URRIOS A, KANG S, et al. The upcoming 3D-printing revolution in microfluidics[J]. Lab on A Chip, 2016, 16(10):1720.
[21] ZHANG S, XU J, GOU H, et al. A research review on the key technologies of intelligent design for customized products[J]. Engineering, 2017, 3(5):631-640.
[22] 徐敬华,盛红升,张树有,等. 基于邻接拓扑的流形网格模型层切多连通域构建方法[J]. 计算机辅助设计与图形学学报, 2018, 30(1):180-190. XU Jinghua, SHENG Hongsheng, ZHANG Shuyou, et al. A method of constructing layered multi-connected domains for manifold mesh model based on adjacency topology[J]. Journal of Computer-Aided Design & Computer Graphics, 2018, 30(1):180-190.
[23] 徐敬华,李俊涛,盛红升,等. 一种三维打印平台的调平系统及其测距装置与调平方法:中国, 201710461594. X[P]. 2019-01-09. XU Jinghua, LI Juntao, SHENG Hongsheng, et al. A leveling system and distance measuring equipment and leveling method of three dimensional printing device:China, 201710461594.X[P]. 2019-01-09.

基于双倾斜度概率的流形模型3D打印层切优化方法

A Slicing Optimization Method of Manifold Model for 3D Printing Based on Dual Inclinations Probability

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