Prediction of Forming Quality and Synergistic Optimization of Process Parameters of Dielectric Layers Fabricated by Piezoelectric Valve Based Non-normal Printing

ZHANG Zijian; GUO Yibo; LIU Qingtao; XUE Zenghui; WANG Qing; YIN Enhuai

doi:10.3969/j.issn.1674-6457.2026.10.025

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Journal of Netshape Forming Engineering ›› 2026, Vol. 18 ›› Issue (10) : 255-265. DOI: 10.3969/j.issn.1674-6457.2026.10.025

Advanced Manufacturing Technology and Equipment

Prediction of Forming Quality and Synergistic Optimization of Process Parameters of Dielectric Layers Fabricated by Piezoelectric Valve Based Non-normal Printing

ZHANG Zijian¹, GUO Yibo¹, LIU Qingtao¹, XUE Zenghui², WANG Qing², YIN Enhuai^2,3,*

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Abstract

To address the problems of increased surface roughness and non-uniform thickness distribution of dielectric layers during non-normal printing of piezoelectric valve based jetting on inclined substrates, the work aims to propose a synergistic process parameter optimization method for dielectric layer forming quality to improve surface quality and thickness uniformity. Substrate inclination angle, delay time, number of printed layers, line spacing, and printing speed were selected as the investigated factors, while surface roughness and thickness uniformity were taken as the evaluation indices. Significant affecting factors were first identified through an orthogonal experimental design. On this basis, dual-response regression models were established through the Box-Behnken design within Response Surface Methodology (RSM). The Pareto-optimal solution set was then obtained with the Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D), and the non-dominated solutions were further ranked by the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) to determine the optimal process parameter combination for the best overall performance. Delay time, substrate inclination angle, and number of printed layers were identified as the significant factors affecting the surface roughness and thickness uniformity of dielectric layers fabricated by non-normal printing. The developed models showed high fitting accuracy, with coefficients of determination (R²) of 0.991 5 and 0.998 8 for the surface roughness model and thickness uniformity model, respectively. The optimized parameter combination was determined to be a substrate inclination angle of 16.69°, a delay time of 11.32 ms, and one printed layer, under which the surface roughness and thickness uniformity were 1.110 7 μm and 1.641 9%, respectively. Experimental validation yielded average values of 1.182 6 μm and 1.763 0%, with relative errors of 6.47% and 7.38%, respectively, both below 10%. In addition, process window analysis was conducted to identify the feasible parameter region satisfying the dual-response requirements. The multi-objective optimization method based on RSM-MOEA/D-TOPSIS can effectively achieve synergistic optimization of the forming quality of dielectric layers in piezoelectric valve based non-normal printing, providing a theoretical basis and process reference for the high-quality fabrication of dielectric layers in complex curved electronic devices.

Key words

non-normal printing / piezoelectric valve printing / response surface methodology / multi-objective optimization / multi-objective evolutionary algorithm based on decomposition (MOEA/D)

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ZHANG Zijian, GUO Yibo, LIU Qingtao, XUE Zenghui, WANG Qing, YIN Enhuai. Prediction of Forming Quality and Synergistic Optimization of Process Parameters of Dielectric Layers Fabricated by Piezoelectric Valve Based Non-normal Printing[J]. Journal of Netshape Forming Engineering. 2026, 18(10): 255-265 https://doi.org/10.3969/j.issn.1674-6457.2026.10.025

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