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Rapid Predictions for Lower-Order Dynamics of Machine Tools Based on the Rigid Multipoint Constraints

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Abstract

This study presents a rapid predicting method for lower-order dynamic performances of machine tools. Firstly, the governing equation of motion of the component substructure is obtained drawing on the dynamic condensation from the finite element analysis. Secondly, employing the rigid multipoint constraints at the joint and interface level, the improved reduced dynamic model of component substructures is formulated, resulting in a minimum set of generalized coordinates for external nodes. Then, utilizing the screw theory, the local stiffness mapping between joint and interfaces is illustrated. This is followed by merging the component and joint substructures, resulting in the reduced dynamic model of the entire machine tool. The proposed model is hugely efficient for predicting the distributions of dynamic performances within the entire workspace and guiding the optimal functional design under the framework of virtual machine tools. Finally, a comparison study on a box-in-box type precision horizontal machine tool shows that the lower-order dynamics predicted within the proposed approach have the same trend as those obtained by a complete order finite element model. The experimental modal analysis test shows that the errors of natural frequencies between the proposed model and experiments are lower than 15.61%, demonstrating the effectiveness and accuracy of the proposed model.

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Acknowledgements

This work was funded by the EU Grant H2020-RISE-ECSASDPE (734272) and the China Scholarship Council (201908080118).

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  1. School of Engineering, The University of Warwick, Coventry, CV4 7AL, UK

    Yiwei Ma, Yanling Tian & Xianping Liu

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  1. Yiwei Ma
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Correspondence to Yiwei Ma.

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Ma, Y., Tian, Y. & Liu, X. Rapid Predictions for Lower-Order Dynamics of Machine Tools Based on the Rigid Multipoint Constraints. Int. J. Precis. Eng. Manuf. 24, 485–500 (2023). https://doi.org/10.1007/s12541-022-00761-9

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