A new multigrid based method for characteristic diagram based correction of thermo-elastic deformations in machine tools

• Autorzy: Naumann Christian , Putz Matthias

Identyfikatory

DOI

10.5604/01.3001.0013.6229

• Języki publikacji: EN

Abstrakty

EN

It is a well-known problem of milling machines, that waste heat from motors, friction effects on guides, environmental variations and the milling process itself greatly affect positioning accuracy and thus production quality. An economic and energy-efficient method of correcting this thermo-elastic positioning error is to gather sensor data (temperatures, axis positions, etc.) from the machine tool and the process and to use that information to predict and correct the resulting tool center point displacement using high dimensional characteristic diagrams. The computation of these characteristic diagrams leads to very large sparse linear systems of equations which require a vast memory and computation time to solve. This is particularly problematic for complex machines and varying production conditions which require characteristic diagrams with many input variables. To solve this issue, a new multigrid based method for the computation of characteristic diagrams will be presented, tested and compared to the previously used smoothed grid regression method.

Słowa kluczowe

EN

thermal effects; algorithm; machine tool; measurement

• Wydawca: Wydawnictwo Wrocławskiej Rady FSNT NOT
• Czasopismo: Journal of Machine Engineering
• Rocznik: 2019
• Tom: Vol. 19, No. 4
• Strony: 42--57
• Opis fizyczny: Bibliogr. 26 poz., rys.

Twórcy

autor

Naumann Christian

• Fraunhofer Institute for Machine Tools and Forming Technology IWU, Chemnitz, Germany

autor

Putz Matthias

• Fraunhofer Institute for Machine Tools and Forming Technology IWU, Chemnitz, Germany

Bibliografia

• [1] BONSE R., McKEOWN P., WECK M., 1995, Reduction and compensation of thermal errors in machine tools, Annals of the CIRP, 44/2, 589–598.
• [2] BRIAN J., 1990, International status on thermal error research, Annals of the CIRP, 39/2, 645–656.
• [3] GROSSMANN K., et al., 2015, Thermo-Energetic Design of Machine Tools, Springer, 1–11.
• [4] JEDRZEJEWSKI J., MODRZYCKI W., 1992, A New Approach to Modelling Thermal Behaviour of a Machine Tool under Service Conditions, CIRP Annals, 41/1, 455–458.
• [5] ESS M., 2012, Simulation and Compensation of Thermal Errors of Machine Tools, Dissertation ETH Zurich.
• [6] MORIWAKI T., SHAMOTO E., 1998, Analysis of Thermal Deformation of an Ultraprecision Air Spindle System, CIRP Annals, 41/1, 315–319.
• [7] BRECHER C., HIRSCH P., WECK M., 2004, Compensation of thermo-elastic machine tool deformation based on control internal data, CIRP Annals Manufacturing Technology, 53/1, 299–304.
• [8] NAUMANN C., PRIBER U., 2012, Modellierung des Thermo-Elastischen Verhaltens von Werkzeugmaschinen mittels Hochdimensionaler Kennfelder, Proceedings Workshop Computational Intelligence, Dortmund, Germany.
• [9] IHLENFELDT S., NAUMANN C., PRIBER U., RIEDEL I., 2015, Characteristic Diagram Based Correction Algorithms for the Thermo-elastic Deformation of Machine Tools, Proceedings 48th CIRP CMS, Naples.
• [10] BRECHER C., KLATTE M., WENZEL C., 2015, Application of Machine Integrated Deformation Sensors, Proceedings of the 11th International LAMDAMAP Conference, Huddersfield. UK, 8–17.
• [11] DENKENA B., et al., 2011. Effiziente Fluidtechnik für Werkzeugmaschinen, Wt Werkstattstechnik online, 101/5, 347–352.
• [12] DROSSEL W.G., VOIGT I., 2016. Wärmespeicher in Werkzeugmaschinen, VDI-Z, 158/12, 42–44.
• [13] DROSSEL W.G., LAUER M., SCHNEIDER D., VOIGT I., 2016, Development and examination of switchable heat pipes, Applied thermal engineering, 99, 857–865.
• [14] GIM T., et al., 2001, Ball screw as thermal error compensator, Proceedings of the 16th ASPE Annual Meeting.
• [15] MARCKS P., UHLMANN E., 2008, Compensation of Thermal Deformations at Machine Tools using Adaptronic CRP-Structures, Proceedings 41st CIRP Conference on Manufacturing Systems, Springer, 183–186.
• [16] HERZOG R., et al., 2015, Correction Algorithms and High-Dimensional Characteristic Diagrams, Thermo-energetic Design of Machine Tools, Lecture Notes in Production Engineering, Springer, 159–174.
• [17] LI Y., et al., 2014, Thermal error modelling of the spindle based on multiple variables for the precision machine tool, International Journal of Advanced Manufacturing Technology, 72, 1415–1427.
• [18] NAUMANN C., IHLENFELDT S., PUTZ M., 2018, On the Selection and Assessment of Input Variables for the Characteristic Diagram Based Correction of Thermo-Elastic Deformations in Machine Tools, Journal of Machine Engineering, 18/4, 25–38.
• [19] NAUMANN C., et al., 2017. Optimized Grid Structures for the Characteristic Diagram Based Estimation of Thermo-elastic Tool Center Point Displacements in Machine Tools, Journal of Machine Engineering, 17/3, 36–50.
• [20] PRIBER U., 2003. Smoothed Grid Regression, Proceedings Workshop Fuzzy Systems, Dortmund, Germany, 13, 159–172.
• [21] DAVIS T.A., RAJAMANICKAM S., SID-LAKHDAR W.M., 2016, A survey of direct methods for sparse linear systems, Technical Report, Texas A&M University.
• [22] VORST H.A., 2002, Efficient and reliable iterative methods for linear systems, Journal of Computational and Applied Mathematics, 149, 251–265.
• [23] HACKBUSCH W., 1985, Multigrid Methods and Applications, Springer.
• [24] PENG J., et al., 2017, BPX-Like Preconditioned Conjugate Gradient Solvers for Poisson Problem and Their CUDA Implementations, Advances in Intelligent Systems and Computing, 454, 633–643.
• [25] GLÄNZEL J., IHLENFELDT S., NAUMANN C., PUTZ M., 2016, Decoupling of fluid and thermo-elastic simulations of machine tools using characteristic diagrams, Proceedings CIRP ICME 2016, Ischia, Italy.
• [26] ZHANG S., 2010, On the Full C1-Qk Finite Element Spaces on Rectangles and Cuboids, Advances in Applied Mathematics and Mechanics, 2/6, 701–721.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).