In Phase II we developed an efficient, self-calibrating identification method to estimate the temperature state of a machine tool as well as the resulting TCP displacement, using as few temperature sensors as possible.
This model-driven approach requires uncertain and, in general, time-dependent parameters such as heat exchange coefficients between machine bed and the environment to be permanently adjusted.
To this end, we developed and implemented a data assimilation method to simultaneously estimate parameters and temperature states.
In order to meet the requirement of using only a small number of temperature sensors while, at the same time, improving the estimation precision, we developed optimal experimental design methods.
Robust optimization methods were used to obtain good reconstruction results independently of the operating point.
The methods were verified using measurements obtained from the machine bed integrator.
In order to reduce the computational effort, we compared several model order reduction techniques in the context of sensor placement.
It is the goal of the project in phase III to master spatially as well as temporally bly varying parameters and heat sources.
These occur, e.g., from the usage of lubricating coolants and due to the deployment of shavings during processing.
To achieve this goal, we will need to develop tailored estimators to quantify the uncertainties and, on the other hand, devise modern mathematical methods such as space/time tensor methods in order to guarantee the real time capabilities of the digital machine image.
Moreover, we will take into account displacement and strain measurements in the TCP estimation in addition to temperature measurements, which constitutes a significant extension to the data assimilation and optimal sensor placement methods.
@INBOOK{NaumannRiedelHerzog:2025:1,
AUTHOR = {Naumann, Andreas and Riedel, Ilka and Herzog, Roland},
PUBLISHER = {Springer Fachmedien Wiesbaden},
BOOKTITLE = {Thermo-energetische Gestaltung von Werkzeugmaschinen},
DATE = {2025},
DOI = {10.1007/978-3-658-45180-6_12},
PAGES = {189--197},
TITLE = {Datenassimilation und optimale Sensorplatzierung},
}
Holger Rudolph, Stefan Sauerzapf, Xaver Thiem,
Andreas Naumann and Michael Beitelschmidt
Strukturmodelle von Werkzeugmaschinen
Thermo-energetische Gestaltung von Werkzeugmaschinen, p.19-45, 2025
@INBOOK{RudolphSauerzapfThiemNaumannBeitelschmidt:2025:1,
AUTHOR = {Rudolph, Holger and Sauerzapf, Stefan and Thiem, Xaver and Naumann, Andreas and Beitelschmidt, Michael},
EDITOR = {Brecher, Christian},
PUBLISHER = {Springer Fachmedien Wiesbaden},
BOOKTITLE = {Thermo-energetische Gestaltung von Werkzeugmaschinen},
DATE = {2025},
DOI = {10.1007/978-3-658-45180-6_2},
PAGES = {19--45},
TITLE = {Strukturmodelle von Werkzeugmaschinen},
}
@ARTICLE{BuengerHerzogNaumannStoll:2024:1,
AUTHOR = {Bünger, Alexandra and Herzog, Roland and Naumann, Andreas and Stoll, Martin},
PUBLISHER = {Informa UK Limited},
DATE = {2024-10},
DOI = {10.1080/15502287.2024.2408291},
EPRINT = {2306.12736},
EPRINTTYPE = {arXiv},
JOURNALTITLE = {International Journal for Computational Methods in Engineering Science and Mechanics},
NUMBER = {6},
PAGES = {475--488},
TITLE = {Uncertainty propagation of initial conditions in thermal models},
VOLUME = {25},
}
Christian Naumann,
Andreas Naumann, Nico Bertaggia, Alexander Geist, Janine Glänzel,
Roland Herzog, Daniel Zontar, Christian Brecher and Martin Dix
Hybrid thermal error compensation combining integrated deformation sensor and regression analysis based models for complex machine tool designs
3rd International Conference on Thermal Issues in Machine Tools (ICTIMT2023), p.28-40, 2023
@INPROCEEDINGS{NaumannNaumannBertaggiaGeistGlaenzelHerzogZontarBrecherDix:2023:1,
AUTHOR = {Naumann, Christian and Naumann, Andreas and Bertaggia, Nico and Geist, Alexander and Glänzel, Janine and Herzog, Roland and Zontar, Daniel and Brecher, Christian and Dix, Martin},
PUBLISHER = {Springer International Publishing},
BOOKTITLE = {3rd International Conference on Thermal Issues in Machine Tools (ICTIMT2023)},
DATE = {2023},
DOI = {10.1007/978-3-031-34486-2_3},
PAGES = {28--40},
SERIES = {Lecture Notes in Production Engineering},
TITLE = {Hybrid thermal error compensation combining integrated deformation sensor and regression analysis based models for complex machine tool designs},
}
@INPROCEEDINGS{NaumannSaakSauerzapfVettermannBeitelschmidtHerzog:2022:1,
AUTHOR = {Naumann, Andreas and Saak, Jens and Sauerzapf, Stefan and Vettermann, Julia and Beitelschmidt, Michael and Herzog, Roland},
EDITOR = {Shen, Tielong and Gao, Rui and Hirano, Yutaka},
PUBLISHER = {Linköping University Electronic Press},
BOOKTITLE = {Proceedings of Asian Modelica Conference 2022},
DATE = {2022-11},
DOI = {10.3384/ecp19381},
TITLE = {Advanced open source data formats for geometrically and physically coupled systems},
}
@ARTICLE{HerzogNaumann:2021:1,
AUTHOR = {Herzog, Roland and Naumann, Andreas},
PUBLISHER = {Wiley},
DATE = {2021-12},
DOI = {10.1002/pamm.202100089},
JOURNALTITLE = {Proceedings in Applied Mathematics and Mechanics},
NUMBER = {1},
TITLE = {Optimal sensor placement for stochastic sources in machine tools},
VOLUME = {21},
}
@ARTICLE{SauerzapfNaumannBeitelschmidt:2021:1,
AUTHOR = {Sauerzapf, Stefan and Naumann, Andreas and Beitelschmidt, Michael},
PUBLISHER = {Wiley},
DATE = {2021-12},
DOI = {10.1002/pamm.202100035},
JOURNALTITLE = {Proceedings in Applied Mathematics and Mechanics},
NUMBER = {1},
TITLE = {Building models for coupled thermo elastic problems in different software architectures using a new model exchange format},
VOLUME = {21},
}
@ARTICLE{BrecherHerzogSpierlingNaumannTzanetos:2021:1,
AUTHOR = {Brecher, Christian and Herzog, Roland and Spierling, Robert and Naumann, Andreas and Tzanetos, Filippos},
PUBLISHER = {MM Publishing},
DATE = {2021-04-21},
DOI = {10.17973/MMSJ.2021_7_2021069},
EVENTTITLE = {2nd International Conference on Thermal Issues in Machine Tools (ICTIMT)},
JOURNALTITLE = {MM Science Journal},
NUMBER = {3},
PAGES = {4628--4635},
TITLE = {Optimal positioning methods of integral deformation sensors --- expert knowledge versus mathematical optimization},
VOLUME = {2021},
}
Julia Vettermann, Stefan Sauerzapf,
Andreas Naumann, Jens Saak, Peter Benner, Michael Beitelschmidt and
Roland Herzog
Model order reduction methods for coupled machine tool models
@ARTICLE{VettermannSauerzapfNaumannSaakBennerBeitelschmidtHerzog:2021:1,
AUTHOR = {Vettermann, Julia and Sauerzapf, Stefan and Naumann, Andreas and Saak, Jens and Benner, Peter and Beitelschmidt, Michael and Herzog, Roland},
PUBLISHER = {MM Publishing},
DATE = {2021-04-20},
DOI = {10.17973/MMSJ.2021_7_2021072},
EVENTTITLE = {2nd International Conference on Thermal Issues in Machine Tools (ICTIMT)},
JOURNALTITLE = {MM Science Journal},
NUMBER = {3},
PAGES = {4652--4659},
TITLE = {Model order reduction methods for coupled machine tool models},
VOLUME = {2021},
}
@ARTICLE{NaumannHerzog:2021:1,
AUTHOR = {Naumann, Andreas and Herzog, Roland},
PUBLISHER = {Wiley},
DATE = {2021-01},
DOI = {10.1002/pamm.202000255},
JOURNALTITLE = {Proceedings in Applied Mathematics and Mechanics},
NUMBER = {1},
TITLE = {Optimal sensor placement for thermo-elastic coupled machine models},
VOLUME = {20},
}
@INPROCEEDINGS{BrecherHerzogSpierlingTzanetosNaumann:2020:1,
AUTHOR = {Brecher, Christian and Herzog, Roland and Spierling, Robert and Tzanetos, Filippos and Naumann, Andreas},
LOCATION = {Aachen, Germany},
URL = {https://www.euspen.eu/knowledge-base/TI20137.pdf},
BOOKTITLE = {Conference Proceedings on Thermal Issues 2020},
DATE = {2020-02-26},
EVENTTITLE = {euspen Special Interest Group Meeting on Thermal Issues},
PAGES = {26--29},
TITLE = {Evaluation of optimal positioning methods of integral deformation sensors for the correction of thermal errors in machine tools},
}
Stefan Sauerzapf, Julia Vettermann,
Andreas Naumann, Jens Saak, Michael Beitelschmidt and Peter Benner
Simulation of the thermal behavior of machine tools for efficient machine development and online correction of the tool center point (TCP)-displacement
Conference Proceedings on Thermal Issues 2020, p.135-138, 2020
@INPROCEEDINGS{SauerzapfVettermannNaumannSaakBeitelschmidtBenner:2020:1,
AUTHOR = {Sauerzapf, Stefan and Vettermann, Julia and Naumann, Andreas and Saak, Jens and Beitelschmidt, Michael and Benner, Peter},
LOCATION = {Aachen, Germany},
URL = {https://www.euspen.eu/knowledge-base/TI20125.pdf},
BOOKTITLE = {Conference Proceedings on Thermal Issues 2020},
DATE = {2020-02-26},
EVENTTITLE = {euspen Special Interest Group Meeting on Thermal Issues},
PAGES = {135--138},
TITLE = {Simulation of the thermal behavior of machine tools for efficient machine development and online correction of the tool center point (TCP)-displacement},
}
