Butterfly Gyroscope - Revision history

Schuetz2 at 08:41, 11 June 2025

2025-06-11T08:41:54Z

← Older revision		Revision as of 08:41, 11 June 2025
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	title = {Butterfly Gyroscope},		title = {Butterfly Gyroscope},
	howpublished = {hosted at {MORwiki} -- Model Order Reduction Wiki},		howpublished = {hosted at {MORwiki} -- Model Order Reduction Wiki},
	url = <nowiki>{~~http~~://modelreduction.org/index.php/Butterfly_Gyroscope}</nowiki>,		url = <nowiki>{https://modelreduction.org/morwiki/index.php/Butterfly_Gyroscope}</nowiki>,
	year = 2004		year = 2004
	}		}

Malhotra: infobox string

2023-11-30T09:26:47Z

infobox string

@@ Line 7: / Line 7: @@
 [[Category:MIMO]]
 [[Category:Sparse]]
 ==Description==

Mlinaric: Fixes in text, math, bib

2023-08-29T16:54:00Z

Fixes in text, math, bib

← Older revision		Revision as of 16:54, 29 August 2023
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	The butterfly is a vibrating micro-mechanical gyro that has sufficient theoretical performance characteristics to make it a promising candidate for use in inertial navigation applications.		The butterfly is a vibrating micro-mechanical gyro that has sufficient theoretical performance characteristics to make it a promising candidate for use in inertial navigation applications.
	The goal of the current project is to develop a micro unit for inertial navigation that can be commercialized in the high-end segment of the rate sensor market.		The goal of the current project is to develop a micro unit for inertial navigation that can be commercialized in the high-end segment of the rate sensor market.
	This project has reached the final stage of a three-year phase where the development and research efforts have ranged from model based signal processing, via electronics packaging to design and prototype manufacturing of the sensor element.		This project has reached the final stage of a three-year phase where the development and research efforts have ranged from model-based signal processing, via electronics packaging to design and prototype manufacturing of the sensor element.
	The project has also included the manufacturing of an [[wikipedia:Application-specific_integrated_circuit\|ASIC]], named µSIC, that has been especially designed for the sensor (see Fig. 1).		The project has also included the manufacturing of an [[wikipedia:Application-specific_integrated_circuit\|ASIC]], named µSIC, that has been especially designed for the sensor (see Fig. 1).

Line 26:		Line 26:
	The excitation electrodes are the smaller dashed areas shown in Fig. 2.		The excitation electrodes are the smaller dashed areas shown in Fig. 2.
	The detection electrodes correspond to the four larger ones.		The detection electrodes correspond to the four larger ones.
	By applying DC-biased AC-voltages to the four pairs of small electrodes, the wings are forced to vibrate in anti-phase in the wafer plane.		By applying DC-biased AC voltages to the four pairs of small electrodes, the wings are forced to vibrate in anti-phase in the wafer plane.
	This is the excitation mode.		This is the excitation mode.
	As the structure rotates about the axis of sensitivity (see Fig. 2), each of the masses will be affected by a Coriolis acceleration.		As the structure rotates about the axis of sensitivity (see Fig. 2), each of the masses will be affected by a Coriolis acceleration.
Line 32:		Line 32:
	This is the detection mode. The external angular velocity can be related to the amplitude of the detection mode, which is measured via the large electrodes.		This is the detection mode. The external angular velocity can be related to the amplitude of the detection mode, which is measured via the large electrodes.

	When planning for and making decisions on future improvements of the butterfly, it is ~~of importance~~ to improve the efficiency of the gyro simulations.		When planning for and making decisions on future improvements of the butterfly, it is important to improve the efficiency of the gyro simulations.
	Repeated analyses of the sensor structure have to be conducted with respect to a number of important issues.		Repeated analyses of the sensor structure have to be conducted with respect to a number of important issues.
	Examples of such are sensitivity to shock, linear and angular vibration sensitivity, reaction to large rates and/or acceleration, different types of excitation load cases and the effect of force-feedback.		Examples of such are sensitivity to shock, linear and angular vibration sensitivity, reaction to large rates and/or acceleration, different types of excitation load cases, and the effect of force-feedback.

	The use of model order reduction indeed decreases runtimes for repeated simulations.		The use of model order reduction indeed decreases runtimes for repeated simulations.
	Moreover, the reduction technique enables a transformation of the FE representation of the gyro into a state space equivalent formulation.		Moreover, the reduction technique enables a transformation of the FE representation of the gyro into a state space equivalent formulation.
	This will prove helpful in testing the model based Kalman signal processing algorithms that are being designed for the '''butterfly gyro'''.		This will prove helpful in testing the model-based Kalman signal processing algorithms that are being designed for the '''butterfly gyro'''.

	The structural model of the gyroscope has been done in [http://www.ansys.com/ ANSYS] using quadratic tetrahedral elements (SOLID187, see Fig. 3).		The structural model of the gyroscope has been done in [http://www.ansys.com/ ANSYS] using quadratic tetrahedral elements (SOLID187, see Fig. 3).
	The model shown is a simplified one with a coarse mesh as it is designed to test the model reduction approaches.		The model shown is a simplified one with a coarse mesh as it is designed to test the model reduction approaches.
	It includes the pure structural mechanics problem only. The load vector is composed ~~from~~ time-varying nodal forces applied at the centers of the excitation electrodes (see Fig. 2).		It includes the pure structural mechanics problem only. The load vector is composed of time-varying nodal forces applied at the centers of the excitation electrodes (see Fig. 2).
	The amplitude and frequency of each force is equal to <math>0.055 \mu N</math> and <math>2384 Hz</math>, respectively.		The amplitude and frequency of each force are equal to <math>0.055 \, \mu \text{N}</math> and <math>2384 \, \text{Hz}</math>, respectively.
	The Dirichlet boundary conditions have been applied to all ~~degree~~ of freedom of the nodes belonging to the top and bottom surfaces of the frame.		The Dirichlet boundary conditions have been applied to all degrees of freedom of the nodes belonging to the top and bottom surfaces of the frame.
	The output nodes are listed in Table 2 and correspond to the centers of the detection electrodes (see Fig. 3).		The output nodes are listed in Table 2 and correspond to the centers of the detection electrodes (see Fig. 3).
	The structural model		The structural model
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	:<math>		:<math>
	\begin{align}		\begin{align}
	M \ddot{x}(t) + E \dot{x} + K x(t) &= B u(t) \\		M \ddot{x}(t) + E \dot{x}(t) + K x(t) &= B u(t), \\
	y(t) & = C x(t)		y(t) & = C x(t),
	\end{align}		\end{align}
	</math>		</math>
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	<math>B</math> is the load vector, <math>C</math> is the output matrix.		<math>B</math> is the load vector, <math>C</math> is the output matrix.

	The statistics for the matrices is shown in Table 1.		The statistics for the matrices are shown in Table 1.

	{\| class="wikitable" style="margin: auto;"		{\| class="wikitable" style="margin: auto;"
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	:<math>		:<math>
	\begin{align}		\begin{align}
	M \ddot{x}(t) + E \dot{x}(t) + K x(t) & = B u(t) \\		M \ddot{x}(t) + E \dot{x}(t) + K x(t) & = B u(t) \\
	y(t) & = C x(t)		y(t) & = C x(t)
	\end{align}		\end{align}
	</math>		</math>
Line 151:		Line 151:
	<math>E \in \mathbb{R}^{17361 \times 17361}</math>,		<math>E \in \mathbb{R}^{17361 \times 17361}</math>,
	<math>K \in \mathbb{R}^{17361 \times 17361}</math>,		<math>K \in \mathbb{R}^{17361 \times 17361}</math>,
	<math>B \in \mathbb{R}^{17361}</math>,		<math>B \in \mathbb{R}^{17361 \times 1}</math>,
	<math>C \in \mathbb{R}^{12 \times 17361}</math>		<math>C \in \mathbb{R}^{12 \times 17361}</math>.

	==Citation==		==Citation==
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	volume = 45,		volume = 45,
	pages = {349--352},		pages = {349--352},
	series = Lecture Notes in Computational Science and Engineering,		series = {Lecture Notes in Computational Science and Engineering},
	doi = {10.1007/3-540-27909-1_18}		doi = {10.1007/3-540-27909-1_18}
	}		}

Saak: /* Data */

2021-12-14T08:52:17Z

Data

← Older revision		Revision as of 08:52, 14 December 2021
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	Download matrices in [http://math.nist.gov/MatrixMarket/ Matrix Market] format:		Download matrices in [http://math.nist.gov/MatrixMarket/ Matrix Market] format:
	* [https://~~www~~.mpi-magdeburg.mpg.de/mpcsc/MORWIKI/Oberwolfach/ButterflyGyro-dim1e5-gyro.tar.gz ButterflyGyro-dim1e5-gyro.tar.gz] (7.4 MB)		* [https://csc.mpi-magdeburg.mpg.de/mpcsc/MORWIKI/Oberwolfach/ButterflyGyro-dim1e5-gyro.tar.gz ButterflyGyro-dim1e5-gyro.tar.gz] (7.4 MB)

	The matrix name is used as an extension of the matrix file. File <tt>*.C.names</tt> contains a list of output names written consecutively.		The matrix name is used as an extension of the matrix file. File <tt>*.C.names</tt> contains a list of output names written consecutively.

Himpe: Fix CrossRefs

2021-08-27T07:24:02Z

Fix CrossRefs

Himpe: /* Data */ Update Benchmark data file link

2018-07-17T09:23:00Z

Data: Update Benchmark data file link

← Older revision		Revision as of 09:23, 17 July 2018
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	Download matrices in [http://math.nist.gov/MatrixMarket/ Matrix Market] format:		Download matrices in [http://math.nist.gov/MatrixMarket/ Matrix Market] format:
	* [https://~~portal~~.~~uni~~-~~freiburg~~.de/~~imteksimulation~~/~~downloads~~/~~benchmark~~/~~The%20Butterfly%20Gyro%20%2835889%29/files/fileinnercontentproxy~~.~~2010~~-01-~~31.7493503105~~ gyro.tar.gz] (7.4 MB)		* [https://www.mpi-magdeburg.mpg.de/mpcsc/MORWIKI/Oberwolfach/ButterflyGyro-dim1e5-gyro.tar.gz ButterflyGyro-dim1e5-gyro.tar.gz] (7.4 MB)

	The matrix name is used as an extension of the matrix file. File <tt>*.C.names</tt> contains a list of output names written consecutively.		The matrix name is used as an extension of the matrix file. File <tt>*.C.names</tt> contains a list of output names written consecutively.

Werner: Updated BibTeX entry.

2018-04-24T08:52:59Z

Updated BibTeX entry.

← Older revision		Revision as of 08:52, 24 April 2018
Line 158:		Line 158:

	* For the benchmark itself and its data:		* For the benchmark itself and its data:
	:: Oberwolfach Benchmark Collection '''Butterfly Gyroscope'''. hosted at MORwiki - Model Order Reduction Wiki, 2004. http://modelreduction.org/index.php/Butterfly_Gyroscope		:: Oberwolfach Benchmark Collection, '''Butterfly Gyroscope'''. hosted at MORwiki - Model Order Reduction Wiki, 2004. http://modelreduction.org/index.php/Butterfly_Gyroscope

	@MISC{morwiki_gyro,		@MISC{morwiki_gyro,
	author = {Oberwolfach Benchmark Collection},		author = <nowiki>{{Oberwolfach Benchmark Collection}}</nowiki>,
	title = {Butterfly Gyroscope},		title = {Butterfly Gyroscope},
	howpublished = {hosted at {MORwiki} -- Model Order Reduction Wiki},		howpublished = {hosted at {MORwiki} -- Model Order Reduction Wiki},
	url = {<nowiki>http://modelreduction.org/index.php/Butterfly_Gyroscope</nowiki>},		url = <nowiki>{http://modelreduction.org/index.php/Butterfly_Gyroscope}</nowiki>,
	year = 2004		year = 2004
	}		}

	* For the background on the benchmark:		* For the background on the benchmark:

	@INPROCEEDINGS{morBil05,		@INPROCEEDINGS{morBil05,
	author = {D. Billger},		author = {D. Billger},
	title = {The Butterfly Gyro},		title = {The Butterfly Gyro},
	booktitle = {Dimension Reduction of Large-Scale Systems},		booktitle = {Dimension Reduction of Large-Scale Systems},
	publisher = {Springer-Verlag, Berlin/Heidelberg, Germany},		publisher = {Springer-Verlag, Berlin/Heidelberg, Germany},
	year = 2005,		year = 2005,
	volume = 45,		volume = 45,
	pages = {349--352},		pages = {349--352},
	series = Lecture Notes in Computational Science and Engineering,		series = Lecture Notes in Computational Science and Engineering,
	doi = {10.1007/3-540-27909-1_18}		doi = {10.1007/3-540-27909-1_18}
	}		}

	==References==		==References==

Himpe at 10:17, 6 April 2018

2018-04-06T10:17:44Z

← Older revision		Revision as of 10:17, 6 April 2018
Line 1:		Line 1:
	~~{{preliminary}} <!-- Do not remove -->~~

	[[Category:benchmark]]		[[Category:benchmark]]
	[[Category:Oberwolfach]]		[[Category:Oberwolfach]]

Hund: /* Citation */

2018-04-06T08:39:12Z

Citation

← Older revision		Revision as of 08:39, 6 April 2018
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	* For the background on the benchmark:		* For the background on the benchmark:

	@INPROCEEDINGS{~~morLieBRetal04~~,		@INPROCEEDINGS{morBil05,
	~~title~~ = {~~MEMS Compact Modeling Meets Model Order Reduction: Examples of the Application of Arnoldi Methods to Microsystem Devices~~},		author = {D. Billger},
	~~author~~ = {~~J. Lienemann, D. Billger, E.B. Rudnyi, A. Greiner, and J.G. Korvink~~},		title = {The Butterfly Gyro},
	booktitle = {~~Technical Proceedings~~ of ~~the 2004 Nanotechnology Conference and Trade Show~~}		booktitle = {Dimension Reduction of Large-Scale Systems},
	year = ~~2004~~,		publisher = {Springer-Verlag, Berlin/Heidelberg, Germany},
	~~month~~ = ~~{March}~~,		year = 2005,
	pages = {~~303~~--~~306~~},		volume = 45,
	~~month~~ = ~~{June},~~		pages = {349--352},
	~~publisher = {Nano~~ Science and ~~Technology Institute, Boston}~~,		series = Lecture Notes in Computational Science and Engineering,
	~~isbn~~ = {0-~~9728422~~-8-4}		doi = {10.1007/3-540-27909-1_18}
	}		}

	==References==		==References==

Hund at 08:22, 6 April 2018

2018-04-06T08:22:14Z

← Older revision		Revision as of 08:22, 6 April 2018
Line 170:		Line 170:
	}		}

			* For the background on the benchmark:

			@INPROCEEDINGS{morLieBRetal04,
			title = {MEMS Compact Modeling Meets Model Order Reduction: Examples of the Application of Arnoldi Methods to Microsystem Devices},
			author = {J. Lienemann, D. Billger, E.B. Rudnyi, A. Greiner, and J.G. Korvink},
			booktitle = {Technical Proceedings of the 2004 Nanotechnology Conference and Trade Show}
			year = 2004,
			month = {March},
			pages = {303--306},
			month = {June},
			publisher = {Nano Science and Technology Institute, Boston},
			isbn = {0-9728422-8-4}
			}
	==References==		==References==

← Older revision		Revision as of 07:24, 27 August 2021
Line 17:		Line 17:
	The goal of the current project is to develop a micro unit for inertial navigation that can be commercialized in the high-end segment of the rate sensor market.		The goal of the current project is to develop a micro unit for inertial navigation that can be commercialized in the high-end segment of the rate sensor market.
	This project has reached the final stage of a three-year phase where the development and research efforts have ranged from model based signal processing, via electronics packaging to design and prototype manufacturing of the sensor element.		This project has reached the final stage of a three-year phase where the development and research efforts have ranged from model based signal processing, via electronics packaging to design and prototype manufacturing of the sensor element.
	The project has also included the manufacturing of an [[wikipedia:Application-specific_integrated_circuit\|ASIC]], named µSIC, that has been especially designed for the sensor (see ~~<xr id="fig1"/>~~).		The project has also included the manufacturing of an [[wikipedia:Application-specific_integrated_circuit\|ASIC]], named µSIC, that has been especially designed for the sensor (see Fig. 1).

	The gyro chip consists of a three-layer silicon wafer stack, in which the middle layer contains the sensor element.		The gyro chip consists of a three-layer silicon wafer stack, in which the middle layer contains the sensor element.
	The sensor consists of two wing pairs that are connected to a common frame by a set of beam elements (see ~~<xr id="fig2"/>~~ and ~~<xr id="fig3"/>~~);		The sensor consists of two wing pairs that are connected to a common frame by a set of beam elements (see Fig. 2 and Fig. 3);
	this is the reason the gyro is called the butterfly.		this is the reason the gyro is called the butterfly.
	Since the structure is manufactured using an anisotropic wet-etch process, the connecting beams are slanted.		Since the structure is manufactured using an anisotropic wet-etch process, the connecting beams are slanted.
	This makes it possible to keep all electrodes, both for capacitive excitation and detection, confined to one layer beneath the two wing pairs.		This makes it possible to keep all electrodes, both for capacitive excitation and detection, confined to one layer beneath the two wing pairs.
	The excitation electrodes are the smaller dashed areas shown in ~~<xr id="fig2"/>~~.		The excitation electrodes are the smaller dashed areas shown in Fig. 2.
	The detection electrodes correspond to the four larger ones.		The detection electrodes correspond to the four larger ones.
	By applying DC-biased AC-voltages to the four pairs of small electrodes, the wings are forced to vibrate in anti-phase in the wafer plane.		By applying DC-biased AC-voltages to the four pairs of small electrodes, the wings are forced to vibrate in anti-phase in the wafer plane.
	This is the excitation mode.		This is the excitation mode.
	As the structure rotates about the axis of sensitivity (see ~~<xr id="fig2"/>~~), each of the masses will be affected by a Coriolis acceleration.		As the structure rotates about the axis of sensitivity (see Fig. 2), each of the masses will be affected by a Coriolis acceleration.
	This acceleration can be represented as an inertial force that is applied at right angles with the external angular velocity and the direction of motion of the mass. The Coriolis force induces an anti-phase motion of the wings out of the wafer plane.		This acceleration can be represented as an inertial force that is applied at right angles with the external angular velocity and the direction of motion of the mass. The Coriolis force induces an anti-phase motion of the wings out of the wafer plane.
	This is the detection mode. The external angular velocity can be related to the amplitude of the detection mode, which is measured via the large electrodes.		This is the detection mode. The external angular velocity can be related to the amplitude of the detection mode, which is measured via the large electrodes.
Line 40:		Line 40:
	This will prove helpful in testing the model based Kalman signal processing algorithms that are being designed for the '''butterfly gyro'''.		This will prove helpful in testing the model based Kalman signal processing algorithms that are being designed for the '''butterfly gyro'''.

	The structural model of the gyroscope has been done in [http://www.ansys.com/ ANSYS] using quadratic tetrahedral elements (SOLID187, see ~~<xr id="fig3"/>~~).		The structural model of the gyroscope has been done in [http://www.ansys.com/ ANSYS] using quadratic tetrahedral elements (SOLID187, see Fig. 3).
	The model shown is a simplified one with a coarse mesh as it is designed to test the model reduction approaches.		The model shown is a simplified one with a coarse mesh as it is designed to test the model reduction approaches.
	It includes the pure structural mechanics problem only. The load vector is composed from time-varying nodal forces applied at the centers of the excitation electrodes (see ~~<xr id="fig2"/>~~).		It includes the pure structural mechanics problem only. The load vector is composed from time-varying nodal forces applied at the centers of the excitation electrodes (see Fig. 2).
	The amplitude and frequency of each force is equal to <math>0.055 \mu N</math> and <math>2384 Hz</math>, respectively.		The amplitude and frequency of each force is equal to <math>0.055 \mu N</math> and <math>2384 Hz</math>, respectively.
	The Dirichlet boundary conditions have been applied to all degree of freedom of the nodes belonging to the top and bottom surfaces of the frame.		The Dirichlet boundary conditions have been applied to all degree of freedom of the nodes belonging to the top and bottom surfaces of the frame.
	The output nodes are listed in Table 2 and correspond to the centers of the detection electrodes (see ~~<xr id="fig3"/>~~).		The output nodes are listed in Table 2 and correspond to the centers of the detection electrodes (see Fig. 3).
	The structural model		The structural model