Optimizing natural frequencies in compliant mechanisms through geometric scaling

IF 4.5 1区 工程技术 Q1 ENGINEERING, MECHANICAL Mechanism and Machine Theory Pub Date : 2024-11-01 DOI:10.1016/j.mechmachtheory.2024.105822
Vivien Platl, Lena Zentner
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Abstract

This work contributes to the dynamic analysis and optimization of compliant mechanisms in terms of their natural frequencies. The previously established analytical method based on Bernoulli beams and the transfer matrix method, which underlies the existing calculation tool CaTEf, is extended to enable the scaling of any specified geometric parameter or parameter set within a given mechanism to achieve a desired natural frequency. By introducing a scaling parameter, precise adjustments of selected geometric parameters are ensured while accounting for inherent dependencies. Minor discrepancies are revealed in parameter studies when comparing results obtained with our proposed analytical method to those from the Finite Element Method (FEM) regarding the resulting scaled values. Following validation, the analytical method is seamlessly integrated into CaTEf and verified against experimental data, demonstrating strong agreement. This work results in a highly efficient analytical method for optimizing compliant mechanisms in terms of their dynamic behavior, especially natural frequencies, while significantly reducing modeling and calculation time.

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通过几何缩放优化顺变机构的固有频率
这项工作有助于根据自然频率对顺变机构进行动态分析和优化。之前建立的基于伯努利梁和传递矩阵法的分析方法是现有计算工具 CaTEf 的基础,通过扩展该方法,可对给定机构中的任何指定几何参数或参数集进行缩放,以实现所需的固有频率。通过引入比例参数,可确保对所选几何参数进行精确调整,同时考虑固有的依赖关系。在参数研究中,当比较我们提出的分析方法和有限元法(FEM)得出的结果时,会发现两者的缩放值存在微小差异。经过验证后,分析方法被无缝集成到 CaTEf 中,并与实验数据进行了验证,结果表明两者非常吻合。这项工作产生了一种高效的分析方法,用于优化顺从机构的动态行为,特别是自然频率,同时显著减少建模和计算时间。
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来源期刊
Mechanism and Machine Theory
Mechanism and Machine Theory 工程技术-工程:机械
CiteScore
9.90
自引率
23.10%
发文量
450
审稿时长
20 days
期刊介绍: Mechanism and Machine Theory provides a medium of communication between engineers and scientists engaged in research and development within the fields of knowledge embraced by IFToMM, the International Federation for the Promotion of Mechanism and Machine Science, therefore affiliated with IFToMM as its official research journal. The main topics are: Design Theory and Methodology; Haptics and Human-Machine-Interfaces; Robotics, Mechatronics and Micro-Machines; Mechanisms, Mechanical Transmissions and Machines; Kinematics, Dynamics, and Control of Mechanical Systems; Applications to Bioengineering and Molecular Chemistry
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