Simplified machine tool - Revision history

Schuetz2 at 07:37, 3 March 2026

2026-03-03T07:37:01Z

← Older revision		Revision as of 07:37, 3 March 2026
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	}}		}}

	~~__NUMBEREDHEADINGS__~~

	==Motivation==		==Motivation==

Saak at 12:33, 25 October 2023

2023-10-25T12:33:36Z

← Older revision		Revision as of 12:33, 25 October 2023
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	~~{{preliminary}} <!-- Do not remove -->~~

	[[Category:benchmark]]		[[Category:benchmark]]
	[[Category:Sparse]]		[[Category:Sparse]]

Vettermann: add citation

2023-10-20T09:25:48Z

add citation

← Older revision		Revision as of 09:25, 20 October 2023
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	* simplifiedMachineToolFineSA3_n11956m8q8		* simplifiedMachineToolFineSA3_n11956m8q8
	* simplifiedMachineToolFineSA4_n12812m5q5		* simplifiedMachineToolFineSA4_n12812m5q5
	\|Category = ~~CRC_TR_96~~		\|Category = CRC-TR-96
	\|System-Class = LTI-FOS		\|System-Class = LTI-FOS
	\|nstates =		\|nstates =
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	\|Creator =		\|Creator =
	* CRC/TR 96:		* CRC/TR 96:
	* Sauerzapf~~, Stefan~~		* Stefan Sauerzapf
	* Naumann~~, Andreas~~		* Andreas Naumann
	* [[User:Vettermann]]		* [[User:Vettermann]]
	* [[User:Saak]]		* [[User:Saak]]
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	==Data==		==Data==

	The system matrices can be downloaded ~~under the following link~~ [https://~~tuc~~.~~cloud~~/~~index~~.~~php~~/~~s/apdEG37gj8EaRDY simplified_machine_tool.tar~~.gz]. There is a set of matrices for each subassembly. The numbering of the subassemblies is shown in Fig. 1. The model is available in two versions: a fine discretization with <math> n=166\,817 </math> degrees of freedom and a coarse discretization with an overall system dimension of <math> n=45\,260 </math>. The dimensions of the subassemblies of both models can be seen in the following table:		The system matrices can be downloaded from [https://doi.org/10.5281/zenodo.10017861 zenodo]. There is a set of matrices for each subassembly. The numbering of the subassemblies is shown in Fig. 1. The model is available in two versions: a fine discretization with <math> n=166\,817 </math> degrees of freedom and a coarse discretization with an overall system dimension of <math> n=45\,260 </math>. The dimensions of the subassemblies of both models can be seen in the following table:

	{\| class="wikitable" style="margin: auto;"		{\| class="wikitable" style="margin: auto;"
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	The '''simplified machine tool''' model was developed 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 '''simplified machine tool''' model was developed 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{dataSauNVetal23,
			author = {S. Sauerzapf and A. Naumann and J. Vettermann and J. Saak},
			title = {Matrices for a simplified machine tool model},
			howpublished = {hosted at {MORwiki} -- Model Order Reduction Wiki},
			year = 2023,
			doi = {10.5281/zenodo.10017861}
			}

			* For the background on the benchmark:

			@inproceedings{SauVNetal20,
			author = {Sauerzapf, S. and Vettermann, J. and Naumann, A. and Saak, J. and Beitelschmidt, M. and Benner, P.},
			title = {Simulation of the thermal behavior of machine tools for efficient machine development and
			online correction of the {Tool} {Center} {Point} ({TCP})-displacement},
			booktitle = {Conference Proceedings on Thermal Issues, Aachen, 26-27 February},
			organization = {euspen},
			pages = {135--138},
			year = {2020},
			url = {https://www.euspen.eu/knowledge-base/TI20125.pdf }
			}

	==References==		==References==
Line 218:		Line 245:
	<references>		<references>
	<ref name="euspen2020">		<ref name="euspen2020">
	S. Sauerzapf, J. Vettermann, A. Naumann, J. Saak, M. Beitelschmidt and P. Benner, "<span class="plainlinks">[https://www.euspen.eu/knowledge-base/TI20125.pdf Simulation of the thermal behavior of machine tools for efficient machine development and online correction of the Tool Center Point (TCP)-displacement]</span>", Conference		S. Sauerzapf, J. Vettermann, A. Naumann, J. Saak, M. Beitelschmidt and P. Benner, "<span class="plainlinks">[https://www.euspen.eu/knowledge-base/TI20125.pdf Simulation of the thermal behavior of machine tools for efficient machine development and online correction of the Tool Center Point (TCP)-displacement]</span>", Conference Proceedings on Thermal Issues, Aachen, 26-27 February, pp. 135–138, euspen, 2020.
	Proceedings on Thermal Issues, Aachen, 26-27 February, pp. 135–138, euspen, 2020.
	</ref>		</ref>
	</references>		</references>

Vettermann at 12:49, 19 October 2023

2023-10-19T12:49:51Z

← Older revision		Revision as of 12:49, 19 October 2023
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	* [[User:Vettermann]]		* [[User:Vettermann]]
	* [[User:Saak]]		* [[User:Saak]]
	\|Editor = [[User:~~Saak~~]]		\|Editor = [[User:Vettermann]]
	\|Zenodo-link = https://doi.org/10.5281/zenodo.10017861		\|Zenodo-link = https://doi.org/10.5281/zenodo.10017861
	}}		}}

Vettermann: add Infobox

2023-10-19T12:36:37Z

add Infobox

@@ Line 8: / Line 8: @@
 [[Category:MIMO]]
 [[Category:CRC-TR-96]]
 __NUMBEREDHEADINGS__
@@ Line 100: / Line 149: @@
 ==Data==
-The system matrices can be downloaded under the following link [https://tuc.cloud/index.php/s/apdEG37gj8EaRDY MAX_stand.tar.gz]. There is a set of matrices for each subassembly. The numbering of the subassemblies is shown in Fig. 1. The model is available in two versions: a fine discretization with <math> n=166\,817 </math> degrees of freedom and a coarse discretization with an overall system dimension of <math> n=45\,260 </math>. The dimensions of the subassemblies of both models can be seen in the following table:
+The system matrices can be downloaded under the following link [https://tuc.cloud/index.php/s/apdEG37gj8EaRDY simplified_machine_tool.tar.gz]. There is a set of matrices for each subassembly. The numbering of the subassemblies is shown in Fig. 1. The model is available in two versions: a fine discretization with <math> n=166\,817 </math> degrees of freedom and a coarse discretization with an overall system dimension of <math> n=45\,260 </math>. The dimensions of the subassemblies of both models can be seen in the following table:
 {| class="wikitable" style="margin: auto;"

Vettermann: Created page with "{{preliminary}} Category:benchmark Category:Sparse Category:linear Category:first differential order Category:ODE Category:MIMO..."

2023-09-01T15:07:31Z

Created page with "{{preliminary}}  Category:benchmark Category:Sparse Category:linear Category:first differential order Category:ODE Category:MIMO..."

New page

{{preliminary}} 

[[Category:benchmark]]
[[Category:Sparse]]
[[Category:linear]]
[[Category:first differential order]]
[[Category:ODE]]
[[Category:MIMO]]
[[Category:CRC-TR-96]]

__NUMBEREDHEADINGS__

==Motivation==

Due to the increasing interest in manufacturing accuracy without an additional energy demand for cooling, knowledge about the thermo-elastic behavior of entire machine tools becomes crucial. Methods to correct the thermally induced position error between the tool-center-point (TCP) and the workpiece in real-time are needed. Therefore, reduced-order models that enable a fast simulation of entire machine tools are applied in the design and production process.

==Description==
<figure id="fig:plot1">
[[File:DMU_Dummy_subassemblies.png|480px|thumb|right|<caption>Subassemblies of the simplified machine tool.</caption>]]
</figure>

The '''simplified machine tool''' benchmark is a linear time-invariant thermal model used for investigation and demonstration purposes in the [https://morwiki.mpi-magdeburg.mpg.de/morwiki/index.php/Category:CRC-TR-96 CRC/TR 96]. For more information on first numerical experiments, see <ref name="euspen2020"/>. It is divided into four stationary subassemblies (SA): machine bed, X-slide, Z-slide, Y-slide, see Fig. 1. The thermal finite element (FE) model was generated in ANSYS and afterwards the FE system matrices were exported for post-processing, such as MOR, to MATLAB. The interaction between the subassemblies is modeled by contact boundary conditions. In this case an input-output coupling was used, i.e., the model is block diagonal and thus the subassemly models can be reduced separately for structure preserving MOR. The evolution of the temperature field is modeled by the heat equation

:<math>
\begin{align}
c_p\rho\frac{\partial T}{\partial t}&=\lambda \Delta T, & &\text{ on } \Omega_k , \text{ } k=1,\dots,4, \\
\lambda\frac{\partial T}{\partial n}&=f, & &\text{ on } \Gamma_{c_k} \subset\partial\Omega_k , \text{ } k=1,\dots,4, \\
\lambda\frac{\partial T}{\partial n}&=\alpha_{ext}(T_{ext}-T), & &\text{ on } \Gamma_{ext_k} \subset\partial\Omega_k , \text{ } k=1,\dots,4, \\
T(0)&=T_0, & &\text{ at } t=0
\end{align}
</math>

with

:<math>
\begin{align}
f=q_{fric}+\kappa_c(T_{c_i}-T_{c_k}), \quad i,k=1,\dots,4, \quad i\neq k,
\end{align}
</math>

and

:{| style="text-align:left"
| <math> k </math> || - number of the subassembly, <math> k=1,\dots, 4 </math>
|-
| <math> T </math> || - temperature
|-
| <math> c_p </math> || - specific heat capacity
|-
| <math> \rho </math> || - density
|-
| <math> \lambda </math> || - heat conductivity
|-
| <math> \Omega_k </math> || - domain of the k-th subassembly
|-
| <math> \Gamma_{c_k} </math> || - contact boundary of the k-th subassembly (partly time varying, moves with the position of the z-slide (considered as heat flow))
|-
| <math> \kappa_{ext} </math> || - heat transfer coefficient between a subassembly and the ambient air
|-
| <math> T_{ext} </math> || - external temperature
|-
| <math> \Gamma_{ext_k} </math> || - contact boundary with the ambience
|-
| <math> q_{fric} </math> || - friction driven heat flow induced by the movement
|-
| <math> \kappa_c </math> || - heat transfer coefficient between two subassemblies
|-
| <math> T_{c_k} </math> || - temperature of the contact area of subassembly k.
|-
|}

The finite element discretization of the heat conduction models leads to the four systems

:<math>
\begin{align}
E_k\dot{T}_k&=A_kT_k + B_k u_k(t),\quad k=1,\dots,4\\
y_k(t)&=C_k T_k,\\
\end{align}
</math>

with

:{| style="text-align:left"
| <math> E_k \in \mathbb{R}^{n\times n} </math> || - capacity matrix
|-
| <math> A_k \in \mathbb{R}^{n\times n} </math> || - conductivity matrix
|-
| <math> T_k \in \mathbb{R}^n </math> || - discrete temperature
|-
| <math> B_k \in \mathbb{R}^{n \times m} </math> || - input map
|-
| <math> u_k \in \mathbb{R}^m </math> || - input vector
|-
| <math> y_k \in \mathbb{R}^p </math> || - output vector
|-
| <math> C_k \in \mathbb{R}^{p \times n} </math> || - output map.
|-
|}

==Data==

The system matrices can be downloaded under the following link [https://tuc.cloud/index.php/s/apdEG37gj8EaRDY MAX_stand.tar.gz]. There is a set of matrices for each subassembly. The numbering of the subassemblies is shown in Fig. 1. The model is available in two versions: a fine discretization with <math> n=166\,817 </math> degrees of freedom and a coarse discretization with an overall system dimension of <math> n=45\,260 </math>. The dimensions of the subassemblies of both models can be seen in the following table:

{| class="wikitable" style="margin: auto;"
|+ style="caption-side:bottom;"|
|-
|Model
|Subassembly <math>k</math>
|<math>n_k</math>
|<math>m_k</math>
|<math>p_k</math>
|-style="background-color:#FFFFFF;"
|fine
|1
|<math>106\,641</math>
|<math>6</math>
|<math>5</math>
|-style="background-color:#FFFFFF;"
|
|2
|<math>35\,408</math>
|<math>8</math>
|<math>8</math>
|-style="background-color:#FFFFFF;"
|
|3
|<math>11\,956</math>
|<math>8</math>
|<math>8</math>
|-style="background-color:#FFFFFF;"
|
|4
|<math>12\,812</math>
|<math>5</math>
|<math>5</math>
|-style="background-color:#FFFFFF;"
|coarse
|1
|<math>28\,183</math>
|<math>6</math>
|<math>5</math>
|-style="background-color:#FFFFFF;"
|
|2
|<math>10\,080</math>
|<math>8</math>
|<math>8</math>
|-style="background-color:#FFFFFF;"
|
|3
|<math>3\,721</math>
|<math>8</math>
|<math>8</math>
|-style="background-color:#FFFFFF;"
|
|4
|<math>3\,276</math>
|<math>5</math>
|<math>5</math>
|-
|}

==Origin==

The '''simplified machine tool''' model was developed 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>
<ref name="euspen2020">
S. Sauerzapf, J. Vettermann, A. Naumann, J. Saak, M. Beitelschmidt and P. Benner, "<span class="plainlinks">[https://www.euspen.eu/knowledge-base/TI20125.pdf Simulation of the thermal behavior of machine tools for efficient machine development and online correction of the Tool Center Point (TCP)-displacement]</span>", Conference
Proceedings on Thermal Issues, Aachen, 26-27 February, pp. 135–138, euspen, 2020.
</ref>
</references>

==Contact==

''[[User:Saak]]''