Procedia Engineering 5 (2010) 597–600
Procedia Engineering www.elsevier.com/locate/procedia
Procedia Engineering 00 (2010) 1–4
Proc. Eurosensors XXIV, September 5-8, 2010, Linz, Austria
Advanced Simulation Tool for the Design of Sensors and Actuators M. Kaltenbacher∗ Applied Mechatronics, Alps-Adriatic University Klagenfurt, Austria Sensor Technology, Friedrich-Alexander University Erlangen-Nuremberg, Germany
Abstract Sensors, actuators, and sensor-actuator systems are often based on the mutual interaction of physical fields, e.g., the mechanical field with the electromagnetic field. The accurate modeling of such transducers leads to so-called multi-field problems, which are described by a system of non-linear partial differential equations. These systems cannot be solved analytically and thus numerical calculation schemes have to be applied. Therewith, we have developed the simulation tool CFS++ (Coupled Field Simulation in C++) based on the Finite Element (FE) method, which is capable of efficiently solving the arising partial differential equations. The program is applicable for simulating capacitive micromachined transducers, piezoelectric transducers, electromagnetic and magnetomechanical sensors and actuators. It also contains models for (aero-)acoustics and ultrasound transducers. Furthermore, we offer advanced material models including hysteretic behaviors. c 2010 Published by Elsevier Ltd. Open access under CC BY-NC-ND license.
Keywords: Finite Element Method, Coupled Field Simulation, Virtual Prototyping 1. Introduction Although in the last years many commercial numerical simulation tools have been developed and are on the market, there is still a strong need for appropriate tools capable to simulate multi-field problems. An implementation of a new partial differential equation (PDE) or physical coupling between PDEs into a commercial software, e.g. using provided interfaces via user routines, results in most cases in very inefficient numerical schemes. For this reason, we have decided to develop our own tool, tuned to sensor and actuator applications using latest numerical algorithms. The result of our effort is CFS++, which has been developed within the last ten years. In the following, we will discuss the general structure of our simulation tool, our development environment, the current capabilities and advanced features. 2. Structure of CFS++ and Programming Environment From the beginning, the main focus was and still is on numerical schemes for solving the arising systems of PDEs within multi-field problems. Therewith, we have no capabilities concerning geometric modeling, mesh generation or post-processing. Instead, we provide interfaces to obtain the appropriate input data from a number of pre-processors1 , as well as to write different file formats to feed a variety of post-processors2 . ∗ Corresponding
author. Tel.: +43 463 2700 3562; fax: +43 463 2700 3698. Email address:
[email protected] (M. Kaltenbacher)
c 2010 Published by Elsevier Ltd. Open access under CC BY-NC-ND license. 1877-7058 doi:10.1016/j.proeng.2010.09.180
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2.1. Data I/O and Class Structure To obtain the necessary input information for our numerical simulation tool, certain input files need to be provided: • Mesh and field data: This data provides the coordinates and mesh topology of all 3D (volume), 2D (surface/interface) and 1D (interface) elements. Due to the fact, that all elements are tagged with unique ids, we can differ between different physical regions where different material properties may be applied, interfaces for the specification of couplings as well as surfaces within the computation. In addition to the mesh information also field information may be read as input to a simulation (e.g. source terms). By default, this data is stored in the hierarchical file format HDF5 [1]. Additionally, we support file formats of a number of external pre-processors and numerical codes1 . • Physical problem description: We use the XML-format for this task, as it is a standardized, easily extendable and human-readable file format. By specifying schemas [2] for our expected input formats, it is possible to validate input files written by humans as well as automatically generated ones. The following list shows the main commands for the coupling section within a piezoelectric-acoustic example. Table 1: XML input file listing for piezoelectric-acoustic coupling
1 2 3 4 5 6 7
8 9 10 11 12 13 14
...
...
• Material data: The XML-file format is also used for the material description allowing for automatic processing entries with 3rd party tools as well as integrity checking. Concerning the result data, our standard file format is again HDF5. This enables us to do chained simulations, since the output of a simulation may be used as an input for a subsequent simulation. We may also use third-party tools like Matlab in this chain, due to the fact that the HDF5 format is supported by many codes. Furthermore, we provide many specific input- and output-file formats to allow the use of different pre- and post-processing tools2 .
n
1 1 -singlePDEs -couplings
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Mechanic PiezoCoupling
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-integrators
-integrators
ElecPDE -integrators
MechPDE -integrators
AcousticPDE
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Piezo Elec PiezoInt
MechAcouInt
LaplaceInt
ElastInt
LaplaceInt
MassInt
MassInt
MechAcou
Assemble BilinearForm +CalcElementMatrix()
-integrators -algsys
AlgebraicSystem
Figure 1: Class structure for the piezoelectric-acoustic coupled PDEs (left) and resulting linear system (right).
1 Supported 2 Supported
pre-processors and CFD codes: ANSYS Classic, GiD, Gmsh, OpenFOAM, FASTEST, ANSYS-CFX post-processors: ANSYS, GiD, Gmsh, GMV, VTK, ParaView
Acou
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The whole software is written in C++ and we exploit its class concept without loosing numerical performance by using techniques like e.g. expression templates. The goal was and still is thatour numerical simulation tool CFS++ can be easily extended for any new PDE, any new physical coupling as well as new types of finite elements (e.g, discontinuous finite elements). The flexibility of our program structure is demonstrated by the coupled piezoelectricacoustic problem (ref. Fig. 1). In Fig. 1 the resulting linear system, as well as the involved classes are depicted. The main class DirectCoupledPDE holds references to the three involved single field problems, as defined by the derived SinglePDE objects of type ElecPDE, MechPDE and AcouPDE. Each PDE defines the BilinearForms and passes it to the Assemble class, which performs the loop over all the involved elements. To arrive at the fully coupled system, derived instances of the class Coupling define the mutual coupling between each two PDEs (here PiezoCoupling and MechAcouCoupling). In the assembly phase, all element matrices of the BilinearForm instances get passed to the AlgebraicSystem. 2.2. Development Environment Concurrent development of a large software project by several programmers requires an advanced development environment. For this purpose, we utilize the following tools: • SVN: Subversion is a free/open source version control system, which manages files, directories, and the changes made to them over time. It facilitates the recovery of older versions and the concurrent management of different developing branches [3]. • CFSDEPS: When developing a general purpose finite element code a lot of external libraries (e.g. BLAS, LAPACK, ARPACK, Metis) have to be included. If more than the standard GNU compiler suite should be supported it is almost certain that incompatibilities with pre-built system libraries will arise. Therefore we decided to build all our dependencies in an automated script based manner. The scripts fetch the sources from the web, unpack them, perform checksum checks, patch, configure, build and install the libraries. • CMake Build System: CMake is a family of platform independent tools designed to build, test and package software [4]. Instead of writing Makefiles or autoconf/automake scripts on Unix or Visual Studio projects on Windows, one just needs to maintain platform independent configuration files from which CMake will generate the previously mentioned projects for the native build environments. • CTest: In order to keep the quality of a software project high, it is imperative to perform automated tests, which we specify in the same simple CMake syntax. • CDash: This is an open source, web-based software testing server, which aggregates, analyzes and displays the results of software testing processes submitted from different clients [5]. We use it to gather information about nightly builds on various platforms to track errors, e.g. which are platform-dependent (e.g. 32 bit vs. 64 bit). • Trac: This tool is an enhanced wiki and issue tracking system for software development projects. Therewith, we can discuss different issues, fix upcoming development steps by assigning tickets, browse the Subversion repository and look at the changes been made between different versions, [6]. 3. Capabilities and Features As mentioned, our main focus is on an efficient simulation tool for the development of sensors, actuator and sensoractuator-systems. Therewith, we have concentrated on FE formulations for electromagnetics, mechanics, acoustics, thermal and fluid flow. Furthermore, we have currently realized the following couplings: electromagnetics - mechanics - acoustics (electrodynamic loudspeaker, electromagnetic valve, electric power transformer, see, e.g., [7] and Fig. 3), piezoelectricity (ultrasound array, surface acoustic wave devices, stack actuators, see, e.g. [8]), electrostatics mechanics - acoustics (capacitive micro-machined ultrasound transducers, mirror systems and microphones, see, e.g. [9] and Fig. 2), fluid flow - mechanics - acoustics (flow-induced sound , human phonation, see, e.g., [10]). Most of the implemented algorithms are described in [11]. Concerning special features, we may mention higher order finite elements (p-FEM) and spectral finite elements (s-FEM) [12, 13], non-matching grid techniques (Mortar FEM) [14], micro-macro-modeling by homogenization [15],
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advanced material models including hysteresis [16], inverse schemes for the precise determination of material parameters [17], and topology optimization [18].
Fuel Intake B in T
Return Spring
2
Housing
Coil Stroke Gap Armature Valve Needle
Coil Armature
Magnetic Saturation
1
Injection Nozzle 0
Figure 2: CMUT: snap-in computation
Figure 3: Magnetic valve: setup and magnetic field
Acknowledgement Among many scientists, who have contributed to CFS++, I want to acknowledge S. Reitzinger (support in the design phase), M. Hofer (forms class), M. Mohr (algebraic system and XML-structure), T. Lahmer (inverse schemes), former Ph.D. students E. Zhelezina (first implementations), M. Escobar (aeroacoustics), G. Link (fluid flow and coupling to mechanics) and current Ph.D. students A. Hauck (revision of class structure, p-FEM, gFEM), S. Triebenbacher (non-matching grids, aeroacoustics, CFSDEPS, CMake environment), F. Wein (optimization), J. Grabinger (non-matching grids, aeroacoustics), A. H¨uppe (s-FEM), S. Z¨orner (fluid-structure-acoustic). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18]
The HDF group, http://www.hdfgroup.org/. XML Schema, http://en.wikipedia.org/wiki/XML Schema. Subversion: The Standard in Open Source Version Control, http://svnbook.red-bean.com/. K. Martin, B. Hoffman, An Open Source Approach to Developing Software in a Small Organization, IEEE Softw. 24 (1) (2007) 46–53. doi:http://dx.doi.org/10.1109/MS.2007.5. CDash, http://www.cdash.org/. Trac, http://trac.edgewall.org/. M. Rausch, G. Gebhardt, M. Kaltenbacher, H. Landes, Computer-aided design of clinical resonance imaging scanners by coupled magnetomechanical-acoustic modeling, IEEE Transactions on Magnetics 41 (1) (2005) 72–81. T. Hegewald, B. Kaltenbacher, M. Kaltenbacher, R. Lerch, Efficient modeling of ferroelectric behavior for the analysis of piezoceramic actuators, Journal of Intelligent Material Systems and Structures 19 (2008) 1117–1129. M. Kaltenbacher, R. Lerch, G. Link, Numerical Modeling of Capacitive Micromachined Transducers, in: Computational Methods for Coupled Problems in Science and Engineering, CD-ROM Proceedings, CINME, ECCOMAS Santorini, Greece; 25.-27.05.2005, 2005. G. Link, M. Kaltenbacher, M. Breuer, M. D¨ollinger, A 2d finite-element scheme for fluid-solid-acoustic interactions and its application to human phonation, Computer Methods in Applied Mechanics and Engineering 198 (2009) 3321–3334. M. Kaltenbacher, Numerical Simulation of Mechatronic Sensors and Actuators, 2nd Edition, Springer, Berlin, 2007. A. H¨uppe, M. Kaltenbacher, Higher order finite element methods for acoustic field problems in the time domain, in: Proceedings of WAVE 09, 2009. G. Cohen, A. Hauck, M. Kaltenbacher, T. Otsuru, Different types of finite elements, in: S. Marburg, B. Nolte (Eds.), Computational Acoustics of Noise Propagation in Fluids, Springer-Verlag, Berlin Heidelberg, 2008, Ch. 2, pp. 57–88, iSBN 978-3-540-77447-1. S. Triebenbacher, Applications of the mortar fem in elasto-acoustics and flow induced noise computations, Acta Acustica(accepted for publication). A. Hauck, T. Lahmer, M. Kaltenbacher, Enhanced homogenization technique for magnetomechanical systems using the generalized finite element method, COMPEL 28 (4) (2009) 935–947. M. Kaltenbacher, B. Kaltenbacher, T. Hegewald, R. Lerch, Finite element formulation for ferroelectric hysteresis of piezoelectric materials, Journal of Intelligent Material Systems and Structures(to be published). B. Kaltenbacher, T. Lahmer, M. Mohr, M. Kaltenbacher, PDE based determination of piezoelectric material tensors, European Journal of Applied Mathematics 17 (2006) 383–416. F. Wein, M. Kaltenbacher, E. B¨ansch, G. Leugering, F. Schury, Topology optimization of a piezoelectric-mechanical actuator with single- and multiple-frequency excitation, International Journal of Applied Electromagnetics and Mechanics 30 (2009) 201–221.
