目的 针对印刷装备橡皮滚筒在高速动态工况下的振动抑制与轻量化需求,提出一种CNN-SIMP混合拓扑优化方法,通过卷积神经网络代理模型替代传统有限元迭代,实现动态响应驱动的快速优化设计。方法 以第4~6阶固有频率加权提升为优化目标,以简谐载荷作用下最大等效应力和体积分数为约束,建立橡皮滚筒动态拓扑优化模型;将优化迭代中的三维密度场周向投影为64×64的二维等效密度图,构建CNN代理模型快速预测模态频率与应力响应,并结合周期性三维有限元校核抑制误差累积。结果 优化后,滚筒质量降低了7.398%,最大等效应力降低了28.59%,最大总变形量降低了67.15%;相较于传统SIMP方法,计算效率提升了6.2倍,且优化后结构在主要传力路径与动态响应特性方面表现出良好一致性。结论 CNN-SIMP混合算法能够在保证优化结果可靠性的同时显著提高动态拓扑优化效率,实现橡皮滚筒结构轻量化与动态性能的协同优化,可为印刷装备关键旋转部件的低振动设计提供有效参考。
Abstract
To address the vibration suppression and lightweight design requirements of rubber rollers in printing equipment under high-speed dynamic operating conditions, the work aims to propose a CNN-SIMP hybrid topology optimization method, in which a convolutional neural network surrogate model is employed to replace repeated finite element iterations and thus enable rapid dynamic-response-driven design. A dynamic topology optimization model was established by maximizing the weighted enhancement of the 4th-6th natural frequencies while constraining the maximum equivalent stress under harmonic loading and the prescribed volume fraction. During the optimization process, the three-dimensional density field was circumferentially projected into a 64×64 two-dimensional equivalent density map, based on which a CNN surrogate model was constructed to rapidly predict modal frequencies and stress responses. Then, periodic three-dimensional finite element recalculations were further introduced to suppress error accumulation. The optimized roller achieved a mass reduction of 7.398%, a decrease of 28.59% in maximum equivalent stress, and a reduction of 67.15% in maximum total deformation. Compared with the conventional SIMP method, the proposed method improved computational efficiency by a factor of 6.2, while the optimized structure maintained good consistency in major load-transfer paths and dynamic response characteristics. The proposed CNN-SIMP hybrid algorithm can significantly improve the efficiency of dynamic topology optimization while ensuring the rationality of the optimization results, and it provides an effective approach for the lightweight and low-vibration design of key rotating components in printing equipment.
关键词
拓扑优化 /
固体各向同性材料惩罚法 /
卷积神经网络 /
动态响应 /
轻量化设计
Key words
topology optimization /
solid isotropic material with penalization (SIMP) /
convolutional neural network (CNN) /
dynamic response /
lightweight design
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基金
北京市自然科学基金（KZ202210015019）; 北京印刷学院校级科研支持项目（Ea202514）
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