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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Stone, B.: Chatter and Machine Tools. Springer International, Cham (2014)
Kolluru, K., Axinte, D.: Coupled interaction of dynamic responses of tool and workpiece in thin wall milling. J. Mater. Process. Technol. 213(9), 1565–1574 (2013)
Ilanko, S., Monterrubio, L.E.: The Rayleigh-Ritz Method for Structural Analysis. ISTE, London (2014)
Ferreira, A.: MATLAB Codes for FInite Element Analysis: Solids and Structures. Springer, Berlin (2009)
Xiang, Y., Wang, C.: Exact buckling and vibration solutions for stepped rectangular plates. J. Sound Vib. 250(3), 503–517 (2002)
Mottershead, J.E., Link, M., Friswell, M.I.: The sensitivity method in finite element model updating: a tutorial. Mech. Syst. Signal Process. 25(7), 2275–2296 (2011)
Liew, K., Xiang, Y., Kitipornchai, S.: Transverse vibration of thick rectangular plates-I. Comprehensive sets of boundary conditions. Comput. Struct. 49(1), 1–29 (1993)
Cheung, Y., Zhou, D.: Vibrations of moderately thick rectangular plates in terms of a set of static Timoshenko beam functions. Comput. Struct. 78(6), 757–768 (2000)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 The Society for Experimental Mechanics, Inc.
About this paper
Cite this paper
Chan, Y.J., Tai, CY., Li, YY. (2019). Efficient Estimation of Clamped Step-Thickness Plates FRFs in Industrial Systems. In: Dervilis, N. (eds) Special Topics in Structural Dynamics, Volume 5. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-75390-4_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-75390-4_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-75389-8
Online ISBN: 978-3-319-75390-4
eBook Packages: EngineeringEngineering (R0)