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考慮輸出剛度不確定性的柔順機(jī)構(gòu)拓?fù)鋬?yōu)化設(shè)計
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國家自然科學(xué)基金項(xiàng)目(52065019、52165002,、51665011),、江西省自然科學(xué)基金項(xiàng)目(20202BAB204015、20202ACBL214013)和江西省研究生創(chuàng)新專項(xiàng)資金項(xiàng)目(YC2021-S463)


Topological Design of Compliant Mechanisms Considering Uncertainties of Output Stiffness
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    摘要:

    為了降低機(jī)構(gòu)性能對輸出剛度不確定因素的敏感程度,,提出一種考慮輸出剛度不確定性的柔順機(jī)構(gòu)拓?fù)鋬?yōu)化設(shè)計方法,。采用區(qū)間模型描述輸出剛度的不確定性,利用多項(xiàng)式混沌展開式(Polynomial chaos expansion, PCE)和Smolyak稀疏網(wǎng)格積分法計算隨機(jī)響應(yīng)統(tǒng)計矩,,以機(jī)構(gòu)輸出位移的期望值最大化和標(biāo)準(zhǔn)差最小化為目標(biāo)函數(shù),,以機(jī)構(gòu)結(jié)構(gòu)體積為約束,建立考慮輸出剛度不確定性的柔順機(jī)構(gòu)穩(wěn)健性拓?fù)鋬?yōu)化模型,,采用移動漸近線優(yōu)化算法更新設(shè)計變量,。夾持器和咬合機(jī)構(gòu)數(shù)值算例驗(yàn)證提出設(shè)計方法的有效性,與確定性拓?fù)鋬?yōu)化結(jié)果比較,,穩(wěn)健性拓?fù)鋬?yōu)化設(shè)計獲得的柔順機(jī)構(gòu)構(gòu)型有所不同,,機(jī)構(gòu)的輸出位移標(biāo)準(zhǔn)差減小,,有效地降低機(jī)構(gòu)對輸出剛度不確定性的敏感程度。隨著加權(quán)系數(shù)增大,,獲得的柔順機(jī)構(gòu)輸出位移標(biāo)準(zhǔn)差和期望值減小,。隨著不確定輸出剛度幅值增大,獲得的柔順機(jī)構(gòu)輸出位移標(biāo)準(zhǔn)差增大,,并且輸出位移期望值有所減小,。

    Abstract:

    To reduce the sensitivity of the performance to the uncertainties of the output stiffness, a method for topology optimization of compliant mechanisms considering uncertainties of the output stiffness was proposed. The interval model was employed to describe uncertainties of the output stiffness. The polynomial chaos expansion and Smolyak sparse grid method were applied to calculate the statistical moments of the structural responses. Maximization of the expected value of the output displacement and minimization of the standard deviation of that were developed as the objective function, and the structure volume was used as the constraint. The model for robust topology optimization of compliant mechanisms considering uncertainties of the output stiffness was established. The design variables were updated by the method of moving asymptotes. Numerical examples such as compliant gripper and crunching mechanism were presented to demonstrate the validity of the proposed method. Compared with the results of deterministic topology optimization, the optimal configurations of compliant mechanisms obtained by robust topology optimization were different, and the standard deviation of the output displacement was decreased. Thus, the sensitivity of the mechanical performance to the uncertainties of the output stiffness can be reduced effectively. As the weighting coefficient was increased, the expected value and standard deviation of the output displacement of the mechanism were decreased. As the amplitude was increased, the standard deviation of the output displacement was increased, and the expected value of the output displacement was decreased.

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占金青,李翼豐,朱本亮,劉敏.考慮輸出剛度不確定性的柔順機(jī)構(gòu)拓?fù)鋬?yōu)化設(shè)計[J].農(nóng)業(yè)機(jī)械學(xué)報,2023,54(1):412-418. ZHAN Jinqing, LI Yifeng, ZHU Benliang, LIU Min. Topological Design of Compliant Mechanisms Considering Uncertainties of Output Stiffness[J]. Transactions of the Chinese Society for Agricultural Machinery,2023,54(1):412-418.

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  • 收稿日期:2022-09-18
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  • 在線發(fā)布日期: 2023-01-10
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