MiniHex - Revision history

Schuetz2 at 07:39, 3 March 2026

2026-03-03T07:39:11Z

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	[[Category:CRC-TR-96]]		[[Category:CRC-TR-96]]

	~~__NUMBEREDHEADINGS__~~

	{{Infobox		{{Infobox

Vettermann at 12:20, 7 December 2023

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	* MiniHexSA4_n21064m17q19		* MiniHexSA4_n21064m17q19
	\|Category = CRC-TR-96		\|Category = CRC-TR-96
	\|System-Class = AP-~~LTI~~-FOS		\|System-Class = AP-LTV-FOS
	\|nstates =		\|nstates =
	* 44902		* 44902

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	The '''MiniHex''' is used as a demonstrator in the [https://morwiki.mpi-magdeburg.mpg.de/morwiki/index.php/Category:CRC-TR-96 CRC/TR 96] Project-ID 174223256 financed by the German Research Foundation DFG.		The '''MiniHex''' is used as a demonstrator in the [https://morwiki.mpi-magdeburg.mpg.de/morwiki/index.php/Category:CRC-TR-96 CRC/TR 96] Project-ID 174223256 financed by the German Research Foundation DFG.

			==Citation==

			To cite this benchmark, use the following references:

			* For the benchmark itself and its data:

			@misc{dataCRCTR9623b,
			author = {Collaborative Research Centre Transregio 96 (CRC/TR 96)},
			title = {Model of a machine tool axis},
			howpublished = {hosted at {MORwiki} -- Model Order Reduction Wiki},
			year = 2023,
			doi = {10.5281/zenodo.10033872}
			}

			* For the background on the benchmark:

			@inbook{GalMG15,
			author = {Galant, A. and Mühl, A. and Gro{\ss}mann, K.},
			title = {Thermo-Elastic Simulation of Entire Machine Tool},
			booktitle = {Thermo-energetic Design of Machine Tools},
			editor = {Gro{\ss}mann, K.},
			publisher = {Springer International Publishing, Switzerland},
			pages = {69--84},
			year = {2015},
			doi = {10.1007/978-3-319-12625-8}
			}

	==References==		==References==

Vettermann: Add Infobox and Zenodo link

2023-10-24T14:06:57Z

Add Infobox and Zenodo link

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	__NUMBEREDHEADINGS__		__NUMBEREDHEADINGS__

			{{Infobox
			\|Title = MiniHex
			\|Benchmark ID =
			* MiniHexSA1_n44902m9q12
			* MiniHexSA2_n49590m32q35
			* MiniHexSA3_n1336m3q4
			* MiniHexSA4_n21064m17q19
			\|Category = CRC-TR-96
			\|System-Class = AP-LTI-FOS
			\|nstates =
			* 44902
			* 49590
			* 1336
			* 21064
			\|ninputs =
			* 9
			* 32
			* 3
			* 17
			\|noutputs =
			* 12
			* 35
			* 4
			* 19
			\|nparameters =
			* 6
			* 2
			* 1
			* 9
			\|components = A, B, C, E
			\|License = Creative Commons Attribution 4.0 International
			\|Creator =
			* CRC/TR 96:
			* Chair of Machine Tools Development and Adaptive Controls (Technische Universität Dresden),
			* Mathematics in Industry and Technology (Technische Universität Chemnitz)
			\|Editor = [[User:Vettermann]]
			\|Zenodo-link = https://zenodo.org/records/10033872
			}}

	==Motivation==		==Motivation==
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	:<math>		:<math>
	\begin{align}		\begin{align}
	E_k\dot{T}_k&=(~~A_{0_k}~~-\sum_{i=1}^{l_k}\kappa_{ext_i}(t)E^~~\Gamma_{k_i}~~)T_k+B_k u_k(t),\quad k=1,\dots,4\\		E_k\dot{T}_k&=(A_k-\sum_{i=1}^{l_k}\kappa_{ext_i}(t)A^i_k)T_k+B_k u_k(t),\quad k=1,\dots,4\\
	y_k(t)&=C_k T_k,\\		y_k(t)&=C_k T_k,\\
	\end{align}		\end{align}
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	\| <math> E_k \in \mathbb{R}^{n\times n} </math> \|\| - FE mass matrix		\| <math> E_k \in \mathbb{R}^{n\times n} </math> \|\| - FE mass matrix
	\|-		\|-
	\| <math> ~~A_{0_k}~~ \in \mathbb{R}^{n\times n} </math> \|\| - basic stiffness matrix (discrete Laplacian)		\| <math> A_k \in \mathbb{R}^{n\times n} </math> \|\| - basic stiffness matrix (discrete Laplacian)
	\|-		\|-
	\| <math> l \in \mathbb{R} </math> \|\| - number of boundary conditions with the ambience (Robin boundary conditions (RBC))		\| <math> l \in \mathbb{R} </math> \|\| - number of boundary conditions with the ambience (Robin boundary conditions (RBC))
	\|-		\|-
	\| <math> E^~~{\Gamma}_k~~ \in \mathbb{R}^{n\times n} </math> \|\| - boundary mass matrix (part of stiffness matrix arising from RBC)		\| <math> A^i_k \in \mathbb{R}^{n\times n} </math> \|\| - boundary mass matrix (part of stiffness matrix arising from RBC)
	\|-		\|-
	\| <math> T_k \in \mathbb{R}^n </math> \|\| - state vector (discrete temperature)		\| <math> T_k \in \mathbb{R}^n </math> \|\| - state vector (discrete temperature)
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	==Data==		==Data==

	The system matrices ~~are given in the [http://math.nist.gov/MatrixMarket/ Matrix Market] format and~~ can be ~~found in~~ [https://~~tuc.cloud/index~~.~~php~~/s/~~PNZkXoxGL56nmQc MiniHex.tar.gz~~]. There is a set of matrices for each subassembly. The numbering of the subassemblies is as follows:		The system matrices can be downloaded from [https://zenodo.org/records/10033872 Zenodo]. There is a set of matrices for each subassembly and input data to simulate a work process. The numbering of the subassemblies is as follows:
	1 - belt housing with motor, 2 - spindle, 3 - spindle nut and 4 - feed tube.		1 - belt housing with motor, 2 - spindle, 3 - spindle nut and 4 - feed tube.
	Further the archive contains some MATLAB files with the description and computation of the 18 contacts between the		Further the archive contains some MATLAB files with the description and computation of the 18 contacts between the subassemblies as well as the computation of the temperature-dependent heat transfer coefficients. The overall system dimension is <math> n=116892 </math> with <math> n_1=44902 </math> , <math> n_2=49590 </math>, <math> n_3=1336 </math> and <math> n_4=21064 </math>.
	subassemblies as well as the computation of the temperature-dependent heat transfer coefficients. The overall system dimension is <math> n=116892 </math> with <math> n_1=44902 </math> , <math> n_2=49590 </math>, <math> n_3=1336 </math> and <math> n_4=21064 </math>.

	==Origin==		==Origin==

Vettermann at 07:38, 2 June 2023

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← Older revision		Revision as of 07:38, 2 June 2023
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	<references>		<references>
	<ref name="galant2016">		<ref name="galant2016">
	A. Galant, S. Schroeder, B. Kauschinger and M. Beitelschmidt, "Erstellung und Abgleich eines strukturbasierten thermischen Modells der kugelgewindegetriebenen Vorschubachsen eines Hexapoden", in Thermo-Energetische Gestaltung von Werkzeugmaschinen, <span class="plainlinks">[https://d-nb.info/~~1082556157Tagungsband~~ 4. Kolloquium zum SFB/TR 96]</span>, C. Brecher, ed., RWTH Aachen, Aachen, 2016, pp. 15–32.		A. Galant, S. Schroeder, B. Kauschinger and M. Beitelschmidt, "Erstellung und Abgleich eines strukturbasierten thermischen Modells der kugelgewindegetriebenen Vorschubachsen eines Hexapoden", in Thermo-Energetische Gestaltung von Werkzeugmaschinen, <span class="plainlinks">[https://d-nb.info/1082556157 Tagungsband 4. Kolloquium zum SFB/TR 96]</span>, C. Brecher, ed., RWTH Aachen, Aachen, 2016, pp. 15–32.
	</ref>		</ref>

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← Older revision		Revision as of 07:23, 2 June 2023
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	<!-- </figure> -->		<!-- </figure> -->

	The mobile demonstrator-machine '''MiniHex''' consists of six struts of variable length, which are driven by ball screws, each with a servo-motor <ref name="grossmann2015"/>. Following one of the feedaxes is considered. It is divided into four stationary		The mobile demonstrator-machine '''[https://tu-dresden.de/ing/maschinenwesen/imd/lwm/forschung/werkzeugmaschinen-versuchsfeld/hexapod-minihex MiniHex]''' consists of six struts of variable length, which are driven by ball screws, each with a servo-motor <ref name="grossmann2015"/>. Following one of the feedaxes is considered. It is divided into four stationary
	subassemblies: belt housing with motor, spindle, spindle nut and feed tube. The thermal finite element (FE) model was generated in ANSYS and afterwards the FE system matrices were exported for post-proceessing, such as MOR, to MATLAB.		subassemblies: belt housing with motor, spindle, spindle nut and feed tube. The thermal finite element (FE) model was generated in ANSYS and afterwards the FE system matrices were exported for post-proceessing, such as MOR, to MATLAB.
	The evolution of the temperature field is modelled with the heat equation		The evolution of the temperature field is modelled with the heat equation

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caption

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	<!-- <figure id="fig:MiniHex"> -->		<!-- <figure id="fig:MiniHex"> -->
	[[File:MiniHex.png\|480px\|thumb\|right\|<caption>Thermal FE-modeling with segmented spindle surface to enter position-dependent heat flows <ref name="galant2015"/></caption>]]		[[File:MiniHex.png\|480px\|thumb\|right\|<caption>Figure 1: Thermal FE-modeling with segmented spindle surface to enter position-dependent heat flows <ref name="galant2015"/></caption>]]
	<!-- </figure> -->		<!-- </figure> -->

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	heat transfer coefficients. Thus the average temperatures of all contact areas are needed as outputs <math> y(t) </math>. Further, the temperatures in certain nodes of interest complete the output <math> y(t) </math>.		heat transfer coefficients. Thus the average temperatures of all contact areas are needed as outputs <math> y(t) </math>. Further, the temperatures in certain nodes of interest complete the output <math> y(t) </math>.
	For more information concerning MOR for systems with moving loads see e.g. <ref name="lang2014"/> and the references therein.		For more information concerning MOR for systems with moving loads see e.g. <ref name="lang2014"/> and the references therein.



	==Data==		==Data==

	The system matrices are given in the [http://math.nist.gov/MatrixMarket/ Matrix Market] format and can be found in [~~[Media~~:~~MiniHex~~.~~tar~~.~~gz\|~~MiniHex.tar.gz]]. There is a set of matrices for each subassembly. The numbering of the subassemblies is as follows:		The system matrices are given in the [http://math.nist.gov/MatrixMarket/ Matrix Market] format and can be found in [https://tuc.cloud/index.php/s/PNZkXoxGL56nmQc MiniHex.tar.gz]. There is a set of matrices for each subassembly. The numbering of the subassemblies is as follows:
	1 - belt housing with motor, 2 - spindle, 3 - spindle nut and 4 - feed tube.		1 - belt housing with motor, 2 - spindle, 3 - spindle nut and 4 - feed tube.
	Further the archive contains some MATLAB files with the description and computation of the 18 contacts between the		Further the archive contains some MATLAB files with the description and computation of the 18 contacts between the
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	<references>		<references>
	<ref name="galant2016">		<ref name="galant2016">
	A. Galant, S. Schroeder, B. Kauschinger and M. Beitelschmidt, "Erstellung und Abgleich eines strukturbasierten thermischen Modells der kugelgewindegetriebenen Vorschubachsen eines Hexapoden", in Thermo-Energetische Gestaltung von Werkzeugmaschinen, ~~Tagungsband~~ 4. Kolloquium zum SFB/TR 96, C. Brecher, ed., RWTH Aachen, Aachen, 2016, pp. 15–32.		A. Galant, S. Schroeder, B. Kauschinger and M. Beitelschmidt, "Erstellung und Abgleich eines strukturbasierten thermischen Modells der kugelgewindegetriebenen Vorschubachsen eines Hexapoden", in Thermo-Energetische Gestaltung von Werkzeugmaschinen, <span class="plainlinks">[https://d-nb.info/1082556157Tagungsband 4. Kolloquium zum SFB/TR 96]</span>, C. Brecher, ed., RWTH Aachen, Aachen, 2016, pp. 15–32.
	</ref>		</ref>

	<ref name="galant2015">		<ref name="galant2015">
	A. Galant, A. Mühl and K. Großmann, "Thermo-Elastic Simulation of Entire Machine Tool", in Thermo-energetic Design of Machine Tools, K. Großmann, ed., Springer International Publishing, Switzerland, 2015, pp. 69–84.		A. Galant, A. Mühl and K. Großmann, "Thermo-Elastic Simulation of Entire Machine Tool", in <span class="plainlinks">[https://doi.org/10.1007/978-3-319-12625-8 Thermo-energetic Design of Machine Tools]</span>, K. Großmann, ed., Springer International Publishing, Switzerland, 2015, pp. 69–84.
	</ref>		</ref>

	<ref name="grossmann2015">		<ref name="grossmann2015">
	K. Großmann, ed., "Thermo-energetic Design of Machine Tools", Springer International Publishing, Switzerland, 2015, pp. 9-10.		K. Großmann, ed., "<span class="plainlinks">[https://doi.org/10.1007/978-3-319-12625-8 Thermo-energetic Design of Machine Tools]</span>", Springer International Publishing, Switzerland, 2015, pp. 9-10.
	</ref>		</ref>

Vettermann: minor edit

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	==Description==		==Description==

			<!-- <figure id="fig:MiniHex"> -->
			[[File:MiniHex.png\|480px\|thumb\|right\|<caption>Thermal FE-modeling with segmented spindle surface to enter position-dependent heat flows <ref name="galant2015"/></caption>]]
			<!-- </figure> -->

	The mobile demonstrator-machine '''MiniHex''' consists of six struts of variable length, which are driven by ball screws, each with a servo-motor <ref name="grossmann2015"/>. Following one of the feedaxes is considered. It is divided into four stationary		The mobile demonstrator-machine '''MiniHex''' consists of six struts of variable length, which are driven by ball screws, each with a servo-motor <ref name="grossmann2015"/>. Following one of the feedaxes is considered. It is divided into four stationary
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	are divided into smaller parts and the average temperature of these parts is used for computing the input <math> u(t) </math>. To be more precise, the spindle is divided into 32 parts and the feed tube into 17 parts <ref name="galant2016"/>.		are divided into smaller parts and the average temperature of these parts is used for computing the input <math> u(t) </math>. To be more precise, the spindle is divided into 32 parts and the feed tube into 17 parts <ref name="galant2016"/>.
	In the simulation the calculated average temperature of an area in the current time step serves as input temperature of this area in the next time step and is also used for calculating the thermally dependent		In the simulation the calculated average temperature of an area in the current time step serves as input temperature of this area in the next time step and is also used for calculating the thermally dependent
	heat transfer coefficients. Thus the average temperatures of all contact areas are needed as outputs <math> y(t) </math>. Further, the ~~temperature~~ in certain nodes of interest complete the output <math> y(t) </math>.		heat transfer coefficients. Thus the average temperatures of all contact areas are needed as outputs <math> y(t) </math>. Further, the temperatures in certain nodes of interest complete the output <math> y(t) </math>.
	For more information concerning MOR for systems with moving loads see e.g. <ref name="lang2014"/> and the references therein.		For more information concerning MOR for systems with moving loads see e.g. <ref name="lang2014"/> and the references therein.

	~~<!-- <figure id="fig:MiniHex"> -->~~
	~~[[File:MiniHex.png\|thermal FE modelling with segmented spindle surface to enter position-dependent heat flows <ref name="galant2015"/>]]~~
	~~<!-- </figure> -->~~

	==Data==		==Data==
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	==Origin==		==Origin==

	The '''MiniHex''' is used as a demonstrator in the CRC/TR 96 financed by the German Research Foundation DFG.		The '''MiniHex''' is used as a demonstrator in the [https://morwiki.mpi-magdeburg.mpg.de/morwiki/index.php/Category:CRC-TR-96 CRC/TR 96] Project-ID 174223256 financed by the German Research Foundation DFG.

	==References==		==References==
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	<ref name="lang2014">		<ref name="lang2014">
	N. Lang, J. Saak and P. Benner, "Model Order Reduction for Systems with Moving Loads", at-Automatisierungstechnik, 8/2014, pp. 512–522.		N. Lang, J. Saak and P. Benner, "<span class="plainlinks">[https://doi.org/10.1515/auto-2014-1095 Model Order Reduction for Systems with Moving Loads]</span>", at-Automatisierungstechnik, 8/2014, pp. 512–522.
	</ref>		</ref>
	</references>		</references>

Vettermann: numbered headings

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numbered headings

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	[[Category:MIMO]]		[[Category:MIMO]]
	[[Category:CRC-TR-96]]		[[Category:CRC-TR-96]]

			__NUMBEREDHEADINGS__


	==Motivation==		==Motivation==