Modelling of Time-varying Extrusion Systems for Fabrication of FGMs Parts by Direct Ink Writing Processes

doi:10.3969/j.issn.1004-132X.2026.02.021

Abstract

Abstract:

High-precision CFD models are time-consuming， creating challenges for the frequent gradient variations in FGMs part printing. Therefore， a time-varying extrusion system was established using a Bayesian regularization neural network as the prediction model. High-precision CFD simulation data sets were first obtained to train the neural network model， with input parameters including the target materials ratio， initial ratio in the chamber， total flow rate of the dual feed rate， and the adapted screw speed. The output parameters were labeled as delivery delay time and transition delay time. Then， the trained Bayesian regularized neural network was merged with the classical control theory approach to system description to construct the complete time-varying extrusion systems.

Key words: functionally graded materials（FGMs） part, direct ink writing process, computational fluid dynamics（CFD）, Bayesian regularized neural network, time-varying extrusion system

摘要：

高精度的计算流体力学表征模型会带来极高的时间成本，这给具有高频次复杂梯度变化的功能梯度材料零件的表征带来挑战。建立了以贝叶斯正则化神经网络为预测模型的时变挤出系统，首先通过高精度的计算流体动力学仿真模型获取数据集并用于训练神经网络模型，将材料目标比例、料腔中初始比例、双进料口流量总和以及适配的螺杆转速作为输入参数，标记交付延迟时间以及过渡延迟时间作为输出参数，再将训练后贝叶斯正则化神经网络融合经典控制理论对系统描述的方法构建完整的时变挤出系统。最后通过打印功能梯度材料样件验证了所构建的计算流体动力学仿真模型以及时变挤出系统的准确性与适用性。

关键词: 功能梯度材料零件, 直写成形工艺, 计算流体动力学, 贝叶斯正则化神经网络, 时变挤出系统

CLC Number:

TB34

WANG Shijie, DUAN Guolin. Modelling of Time-varying Extrusion Systems for Fabrication of FGMs Parts by Direct Ink Writing Processes[J]. China Mechanical Engineering, 2026, 37(2): 466-475.

王世杰, 段国林. 直写成形工艺制备的功能梯度材料零件时变挤出系统建模[J]. 中国机械工程, 2026, 37(2): 466-475.

Figures/Tables 17

Fig.1 Mixing system model

Tab.1 Mixing system structural parameters

名称	数值	名称	数值
螺杆长度/mm	60	销钉高度/mm	1
螺杆大径/mm	8	输入口直径/mm	2
螺杆小径/mm	6	挤出口直径/mm	0.5
螺距/mm	8	收缩角度/（°）	65
螺槽高度/mm	1	收缩段大径/mm	8
螺槽宽度/mm	7	成形段长度/mm	6
螺杆转速（r·min $- 1$ ）	21～45	进料口速率和（mm·s $- 1$ ）	0.4～1

Tab.1 Mixing system structural parameters

名称	数值	名称	数值
螺杆长度/mm	60	销钉高度/mm	1
螺杆大径/mm	8	输入口直径/mm	2
螺杆小径/mm	6	挤出口直径/mm	0.5
螺距/mm	8	收缩角度/（°）	65
螺槽高度/mm	1	收缩段大径/mm	8
螺槽宽度/mm	7	成形段长度/mm	6
螺杆转速（r·min $- 1$ ）	21～45	进料口速率和（mm·s $- 1$ ）	0.4～1

Fig.2 Rheological characteristic curves of two materials

Tab.2 Material rheological parameters

材料	稠度系数 $K$ /（ $P a ⋅ s n$ ）	量纲一流性系数 $n$
A	59.59	0.31
B	67.68	0.32

Tab.2 Material rheological parameters

材料	稠度系数 $K$ /（ $P a ⋅ s n$ ）	量纲一流性系数 $n$
A	59.59	0.31
B	67.68	0.32

Fig.3 Simulation result of CFD model

Fig.4 Bayesian regularized neural networks model

Fig.5 Training result of the Bayesian regularized neural network

Fig.6 Comparison of Bayesian regularized neural network results and CFD results

Tab.3 Input layer-hidden layer neuron weights and bias

神经元	输入层节点1	输入层节点2	输入层节点3	输入层节点4	偏置
1	0.0462	0.0087	$-$ 0.037	0.0624	0.1695
2	$-$ 0.5147	$-$ 0.2851	0.9686	0.3219	0.6197
3	0.0461	0.0086	$-$ 0.0369	0.0621	0.1688
4	$-$ 0.0463	$-$ 0.0087	0.037	$-$ 0.0625	$-$ 0.1698
5	0.0231	0.003	$-$ 0.0151	0.0231	0.0666
6	0.786	0.1731	0.5943	0.4138	$-$ 0.5373
7	0.0463	0.0087	$-$ 0.037	0.0624	0.1696
8	$-$ 0.1406	$-$ 0.2974	$-$ 0.0317	0.101	$-$ 0.1909
9	0.0457	0.0083	$-$ 0.0362	0.0606	0.1652
10	$-$ 0.0462	$-$ 0.0087	0.037	$-$ 0.0623	$-$ 0.1694

Tab.3 Input layer-hidden layer neuron weights and bias

神经元	输入层节点1	输入层节点2	输入层节点3	输入层节点4	偏置
1	0.0462	0.0087	$-$ 0.037	0.0624	0.1695
2	$-$ 0.5147	$-$ 0.2851	0.9686	0.3219	0.6197
3	0.0461	0.0086	$-$ 0.0369	0.0621	0.1688
4	$-$ 0.0463	$-$ 0.0087	0.037	$-$ 0.0625	$-$ 0.1698
5	0.0231	0.003	$-$ 0.0151	0.0231	0.0666
6	0.786	0.1731	0.5943	0.4138	$-$ 0.5373
7	0.0463	0.0087	$-$ 0.037	0.0624	0.1696
8	$-$ 0.1406	$-$ 0.2974	$-$ 0.0317	0.101	$-$ 0.1909
9	0.0457	0.0083	$-$ 0.0362	0.0606	0.1652
10	$-$ 0.0462	$-$ 0.0087	0.037	$-$ 0.0623	$-$ 0.1694

Tab.4 Hidden layer-output layer neuron weights and bias

神经元	1	2	3	4	5	6
输出节点1	0.1742	$-$ 0.6838	0.1735	$-$ 0.1745	0.0675	$-$ 0.5071
输出节点2	0.087	$-$ 0.1946	0.0866	$-$ 0.0871	0.035	$-$ 0.5838
神经元	7	8	9	10	偏置
输出节点1	0.1743	$-$ 0.0349	0.1697	$-$ 0.1741	0.7766
输出节点2	0.0871	$-$ 0.3633	0.0848	$-$ 0.0869	0.4969

Tab.4 Hidden layer-output layer neuron weights and bias

神经元	1	2	3	4	5	6
输出节点1	0.1742	$-$ 0.6838	0.1735	$-$ 0.1745	0.0675	$-$ 0.5071
输出节点2	0.087	$-$ 0.1946	0.0866	$-$ 0.0871	0.035	$-$ 0.5838
神经元	7	8	9	10	偏置
输出节点1	0.1743	$-$ 0.0349	0.1697	$-$ 0.1741	0.7766
输出节点2	0.0871	$-$ 0.3633	0.0848	$-$ 0.0869	0.4969

Fig.7 Working principle of the time-varying extrusion system

Fig.8 FGMs part 3D printer

Fig.9 FGMs extruded filament and material A system input ratio

Fig.10 The result of digital image processing of extruded filaments

Fig.11 Design of the functionally graded materials specimen

Fig.12 Response curve of time-varying extrusion system and FGMs specimen

Fig.13 Material gradient distribution results of FGMs sample

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