Estimating Dynamic Cutting Forces of Machine Tools from Measured Vibrations using Sparse Regression with Nonlinear Function Basis
##plugins.themes.bootstrap3.article.main##
##plugins.themes.bootstrap3.article.sidebar##
Abstract
Estimating relationships between system inputs and outputs can provide insight to system characteristics. Furthermore, with an established input-output relationship and measured output, one can estimate the corresponding input to the system. Traditionally, the relationship between input and output can be represented with transfer functions or frequency response functions. However, those functions need to be built on physical parameters, which are hard to obtain in practical systems. Also, the reverse problem of solving for the input with a known/measured output is often more difficult to solve than the forward problem. This paper aims to explore the data-driven input-output relationship between system inputs and outputs for system diagnostics, prognostics, performance prediction, and control. A data-driven relationship can provide a new way for system input estimation or output prediction. In this paper, a sparse linear regression model with nonlinear function basis is proposed for input estimation with measured outputs. The proposed method explicitly creates a nonlinear function basis for the regression relationship. A threshold-based sparse linear regression is designed to ensure sparsity. The method is tested with experimental data from a spindle testbed that simulates cutting forces within machine tools. The results show that the proposed approach can predict the input force based on the measured vibration response with high accuracy. The current model is also compared with neural networks, which is another nonlinear regression method.
How to Cite
##plugins.themes.bootstrap3.article.details##
Frequency response function, sparse linear regression, nonlinear function basis, spindle, Manufacturing
Cao, H. R., Zhang, X. W., & Chen, X. F. (2017). The Concept and Progress of Intelligent Spindles: A Review. International Journal of Machine Tools & Manufacture, vol. 112, pp. 21-52.
Grossi, N., Sallese, L., Scippa, A., & Campatelli, G. (2017). Improved Experimental-Analytical Approach to Compute Speed-Varying Tool-Tip FRF. Precision Engineering, vol. 48, pp. 114-122.
Postel, M., Aslan, D., Wegener, K., & Altintas, Y. (2019). Monitoring of Vibrations and Cutting Forces with Spindle Mounted Vibration Sensors. CIRP Annals-Manufacturing Technology, vol. 68, issue 1, pp. 413-416.
Qu, Y., Vogl, G. W., & Wang, Z. (2021). A Deep Neural Network Model for Learning Runtime Frequency Response Function Using Sensor Measurements. Proceedings of the ASME 2021 16th International Manufacturing Science and Engineering Conference. June 21-25, Cincinnati, OH.
Raissi, M., Perdikaris, P., Karniadakis, G.E., (2019). Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations, Journal of Computational Physics, vol. 378, pp. 686-707, ISSN 0021-9991.
https://doi.org/10.1016/j.jcp.2018.10.045
Schmid, P. (2010). Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics, vol. 656, pp. 5-28.
doi:10.1017/S0022112010001217
Williams, M.O., Kevrekidis, I.G. & Rowley, C.W. A Data–Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition. J Nonlinear Science, 25, 1307–1346 (2015).
https://doi.org/10.1007/s00332-015-9258-5
This work is licensed under a Creative Commons Attribution 3.0 Unported License.
The Prognostic and Health Management Society advocates open-access to scientific data and uses a Creative Commons license for publishing and distributing any papers. A Creative Commons license does not relinquish the author’s copyright; rather it allows them to share some of their rights with any member of the public under certain conditions whilst enjoying full legal protection. By submitting an article to the International Conference of the Prognostics and Health Management Society, the authors agree to be bound by the associated terms and conditions including the following:
As the author, you retain the copyright to your Work. By submitting your Work, you are granting anybody the right to copy, distribute and transmit your Work and to adapt your Work with proper attribution under the terms of the Creative Commons Attribution 3.0 United States license. You assign rights to the Prognostics and Health Management Society to publish and disseminate your Work through electronic and print media if it is accepted for publication. A license note citing the Creative Commons Attribution 3.0 United States License as shown below needs to be placed in the footnote on the first page of the article.
First Author et al. This is an open-access article distributed under the terms of the Creative Commons Attribution 3.0 United States License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.