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Erschienen in:
2019 | OriginalPaper | Buchkapitel
5. Efficient Estimation of Clamped Step-Thickness Plates FRFs in Industrial Systems
verfasst von : Yum Ji Chan, Chung-Yu Tai, Yuan-You Li
Erschienen in: Special Topics in Structural Dynamics, Volume 5
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Abstract
Frequency response functions (FRFs) of thin workpieces, which are typically clamped step-thickness cantilever plates, are needed at every stage in order to avoid chatter (cutting-related instability). Due to variability of machining procedure, FRF estimation is proposed to be carried out at the embedded computer at machine tool, which has limited computing power. A combination of Reissner-Mindlin plate theory and Rayleigh-Ritz method are used to form small system matrices to estimate FRFs. Mode shapes of uniform-thickness Timoshenko beams are taken as the admissible functions. Example shows that a system with approximately 500 DOFs, which is much smaller than a full finite-element model with 10,000’s of DOFs, can estimate the first four natural frequencies with a similar error level during every step of cut. Additionally, experimental natural frequencies are used to estimate the contact stiffness at the vice. As a result, the change in those natural frequencies during machining are determined accurately.