Villingen-Sckwennigen, Germany. Abstract

Transcription

1 Coupled field calculations of a micromachined flow sensor with differentfiniteelement analysis programmes S. Messner, N. Hey, H.E. Pavlicek Hahn-Schickard Society, Institute for Micro- and Information Villingen-Sckwennigen, Germany Abstract A resonant silicon microstructure with electrothermal excitation and resistive detection with NiCr strain gauges is used for fluid sensor application. Sensor features like thermal fluid-structure interactions and dynamic properties are investigated by finite element analysis. Coupled calculations of structure mechanical and fluid mechanical interactions are undertaken. The different programmes ANSYS and FIDAP are connected by implemented interfaces. 1 Introduction The complexity of micro-electro-mechanical systems (MEMS) with several physical phenomena of excitation, transducing and detection requires the consideration of the coupled field interactions for those phenomena [1]. As an example, we model a resonant silicon beam microstructure with electrothermal excitation and resistive detection by NiCr strain gauges for application as a flow sensor. Sensor features will be investigated by finite element analysis (PEA), especially thermal fluid-structure interactions and dynamical behaviour. The sensitivity of frequency against fluid flow is to be optimized. To analyse the resonance frequency dependence of the gas fluid velocity the fluid mechanical model has to be coupled with the structure mechanical model. The temperature distribution due to the flow delivers the stress within the sensor structure which influences the resonance frequency of the system. At present there is no single commercial software tool available for the necessary coupled calculations. Therefore, the different programmes ANSYS and FIDAP are connected by implemented interfaces. Structure model data from ANSYS are used for the calculation of velocity and temperature field with

2 114 Microsystems and Microstructures FIDAP. Cooling of the sensor by ambient fluid flow is calculated. The temperature distribution serves for a static analysis in ANSYS to determine the mechanical stress. A modal analysis of the stressed structure follows to calculate eigenfrequencies and eigenmode shapes for different temperature loads. The influence of certain modeling parameters is investigated. 2 Sensor principle The resonant sensor principle is based on the dependence of the eigenfrequency of a resonant structure on a physical parameter (e.g. pressure, force, temperature, etc.). Variation of stress in the resonator or a change of inertia caused by mass coating shifts the eigenfrequency of the resonator. In figure 1 the resonant sensor principle is illustrated schematically for a resonator with electrothermal excitation and resistive detection. The oscillator circuit controls the excitation signal depending on the resonator signal. As a result the sensor is always kept in resonance. The resonator signal is compared with a reference frequency by a frequency counter which leads to a digital output signal. The main advantages of the resonant sensor principle are high resolution and sensitivity as a result of the high mechanical quality factor and the quasidigital output signal. x = temperature force pressure etc. mechanical resonator heatings electro thermal excitation heating impulses nnn St-reaonator strain gauges oscillator circuit f(x) frequency counter resistive detection digital output Figure 1: Schematical illustration of the resonant sensor principle by means of a beam resonator with electrothermal excitation and resistive detection.

3 Microsystems and Microstructures 115 In this special case a resonant flow sensor based on a thermal effect is examined. The heating and detecting resistors placed on the resonator cause a warm-up of the resonating structure. However, since this is fixed to the silicon frame the thermal expansion of the resonating structure is disabled causing stress in the structure. Because of a fluid flow the sensor is cooled and therefore the stress and consequently the resonance frequency changes. Thus the resonance frequency is depending on the fluid flow. The main part of the sensor consists of a 50 im thick, 1 mm wide and 10 mm long silicon beam. The silicon frame of the beam is of 380 \im thickness and is very stiff compared to the beam. An isolation layer of silicon dioxide exists on the top suface of the sensor. The electrical wires and resistors will not be considered in the simulation because their influence on the mechanical behaviour of the sensor is negligible. However, the ceramic substrate, the sensor is mounted on, has to be taken into consideration. 3 Structure mechanical analysis The investigation is build up by a step by step analysis from a simple to a more complex model. Therefore, at first we create a structure mechanical model to understand the thermal behaviour of the sensor due to a constant and homogeneous temperature distribution. The general-purpose finite element analysis (FEA) programme ANSYS is used to create a simple 2-dimensional model including the silicon beam and frame, the silicon dioxide layer and the ceramic substrate. Figure 2 shows the resonance frequency of the first vibration mode depending on the temperature and the strain gauge power, respectively. Analytical, FEA and experimental data are compared snnn i i - -i i j NL 3000^ i ^-^ 2000^ :j Q "j 0 10 strain gauge power [mw] {;. */ X V temperature difference [K] Figure 2: Resonance frequency of the first vibration mode depending on temperature difference and strain gauge power, respectively. A experimental, FEA and analytical data are compared.

4 116 Microsystems and Microstructures The characteristic of figure 2 has a cusp. Starting with the resonance frequency at a temperature difference of 0 K the frequency decreases with increasing temperature difference because internal compressive stress builds up due to the disabled thermal expansion of the beam. When a critical stress value is reached the beam buckles and on further increasing temperature difference the resonance frequency increases. This occurs because the net compressive stress over the cross-section of the beam is reduced and internal tensile stress becomes more dominant. The calculated curves are in good agreement with experimental data. The relation between heat power and temperature difference was determined to AT = P [2]. The experimental data are determined by operating the sensor with electrothermal excitation, with constant strain gauge power and without air flow. The frequency is detected optically by a laser vibrometer. Based on the mathematical approach of [3] the analytical model used here is derived by [2]. In figure 3 the deflection of the beam depending on the temperature difference and the strain gauge power, respectively, is depicted. FEA and experimental data are compared and show good agreement. Starting with a temperature difference of 0 K nearly no deflection of the beam can be recognized until the buckling temperature is reached. Going beyond the buckling temperature the deflection of the beam increases immediately. The experimental data are acquired by operating the sensor with constant strain gauge power without air flow and detecting the deflection by an optical measurement setup. strain gauge power [mw] deflection [ftm] I j 50 i 40 i * 01 - > 0 A.. f. 1.. F A I, * L * r * *.* r temperature difference [K] Figure 3: Beam deflection depending on temperature difference and strain gauge power, respectively (A experimental and FEA data). In order to check the results of the 2-dimensional model and to estimate the influence of temperature dependent anisotropic material properties a 3- dimensional model is created. In addition the torsion modes of the beam can be calculated. Because of the anisotropic material properties the resonance frequency of the first vibration mode in the 2-dimensional model is about 12 % higher than in the 3-dimensional model [3].

5 Microsystems and Microstructures Fluid dynamic analysis The computational fluid dynamics (CFD) programme FIDAP is used to calculate a 2-dimensional model of the temperature distribution in the sensor caused by an air flow. Figure 4 shows schematically the arrangement of the sensor in a flow pipe used for numerical and experimental examinations [5]. The sensor is mounted on a ceramic substrate and placed in the centre of the flow pipe. The ceramic substrate is mounted on two metallic pins which, however, are not considered in the simulation. For simulation purposes the heating resistors and the strain gauges are regarded as three single heat sources. At the two spots where the ceramic substrate is supported heat sinks are defined. flow pipe heat sinks sensor air flow ceramic substrate Figure 4: Schematical illustration of the sensor arrangement used for fluid dynamical simulation. Knowledge of the exact thermal boundary conditions for this arrangement is not possible. Therefore, the temperature distribution at the top surface of the sensor was detected by a thermographic system in order to adapt the simulation results to the measured values by variation of the thermal boundary conditions. The influence of the heat sinks is examined by regarding two extreme cases: a) fixing all nodal temperatures at the heat sink to 20 C ; b) defining no heat sink. The calculation of the velocity-dependent temperature distribution of the sensor consists of two steps. First, the velocity field is calculated independent of the temperature field. In the second calculation step the temperature field is determined from the calculated velocity field. In figure 5 the velocity field and the associated temperature field is illustrated. The initial velocity at the pipe inlet in this case is 0.6 m/s and no heat sinks are considered. The inlet temperature of the air is defined to 20 C which is also the constant temperature at the flow pipe edge.

6 118 Microsystems and Microstructures a) resonanter Stroemungssensor GMS/HSG-IMIT CONTOUR SPEED PLOT LEGEND E E E E E+00 4I26E E E+00 87IIE E+00 MINIMUM MAXIMUM.OOOOOE+00.9I696E+00 b) resonanter Stroemunqssensor GMS/HSG-IMIT CONTOUR TEMPERATURE PLOT LEGEND.2029E+02.2I62E E E IE E E E E E*02 MINIMUM MAXIMUM.19625E I8E+02 Figure 5: a) Flow velocity (inlet velocity is 0.6 m/s). b) Temperature distribution caused by flow velocity (temperatures depicted in C). 5 Coupledfieldanalysis The dependence of resonance frequency on the flow velocity of the sensor (sensor characteristic) is determined by coupling the fluid dynamical and the structure mechanical simulation as shown in figure 6. Geometry, material data, mesh and boundary conditions (e.g. velocities, temperatures, etc.) are defined using ANSYS. Then the complete FE-model is transfered to FIDAP by a special interface programme called ANSFED. In FIDAP the fluid dynamical calculation for different initial velocities is carried out as presented above. The calculated temperature distributions are transfered back to ANSYS by an interface implemented in FIDAP. This special interface allows to write nodal values of e.g. temperature on a file readable by ANSYS. In ANSYS a structure mechanical simulation with the temperature distribution received by FIDAP is performed to get the mechanical stresses of this loadcase. Therefore, new mechanical boundary conditions (e.g. clamping of the sensor) have to be defined. With this thermal induced stress distribution the eigenfrequency is calculated. As a result, the eigenfrequency of the sensor due to different initial velocities of air at the flow pipe inlet can be calculated which leads to the sensor characteristic depicted in figure 7. To estimate the influence of thermal boundary conditions, two different characteristics with and without heat sink at the bottom of the ceramic substrate are compared.

7 Microsystems and Microstructures 119 1v,(x=0) interface ANSYS/FIDAP interface FIDAP/ANSYS ANSYS model generation: - geometry - meshing - material properties - boundary conditions mechanical thermal model data FIDAP fluid dynamics: - calculation of velocity field v(x) - calculation of temperature field T(x.v(*)) nodal temperatures T ANSYS mechanical analysis: - calculation of mechanical stresses (static analysis) - calculation of eigenfrequency shift due to the mechanical stresses (modal analysis) 1 resonance frequencies f, Figure 6: Flow chart of the coupledfieldcalculations. I temperature # " without heat sink " with heat sink * : 6000 i ^ LO flow velocity [m/s] Figure 7: Resonance frequency depending on the flow velocity. Increasing velocity causes decreasing temperature. The calculated sensitivity of the sensor without heat sink amounts to about 2500 Hz/ms"* and is in fact much higher than the sensitivity with heat sink of about 130 Hz/ms~*. The largest frequency change takes place in the velocity range between 0 and 1 m/s because of the large gradient of temperature in this range. In both cases (with and without heat sink) the temperature range is above the critical buckling temperature and therefore the sensor characteristic is not affected by buckling.

8 120 Microsystems and Microstructures 6 Summary We simulated a resonant micromachined flow sensor with two different finite element analysis programmes. After description of the sensor principle we presented the structure mechanical analysis. With ANSYS we determined the dependence of the resonance frequency on the strain gauge power. The occuring buckling effect was discussed. Analytical and experimental data were in good agreement with FEA. With a 2-dimensional model in FIDAP we calculated the temperature distribution around the sensor caused by an air flow. The influence of the boundary conditions of the heat sinks was examined. Finally, we investigated the dependence of resonance frequency on the velocity field by coupling the fluid dynamical and structure mechanical programmes. The concrete procedure for linking the two different programmes was described with respect to different boundary conditions. FEA based modeling and calculation could be verified by electrical and optical measurements of thermal activated statical deflections, temperature dependent frequency behaviour and sensitivity of real sensors. Our 2-dimensional simulation results agreed reasonably with analytical calculations and experimental results. Discrepancies between simulation and experimental results were caused by simplification of certain boundary conditions. References 1. Pavlicek, H., Wachutka, G. & al. CAD Tools for MEMS, UETP- MEMS Course, FSRM, Switzerland, Bartuch, H., Biittgenbach, S., Fabula, Th. & Weiss, H. Resonante Silizium-Sensoren mit elektrothermischer Anregung und DMS in Metalldunnfilmtechnologie, pp. 17 to 24, SENSOR 93 Proceedings, Nuremberg, Germany, 1993, ACS Organisations GmbH, Wunstorf, Geijselaers, H.J.M. & Tijdeman, H. The dynamic mechanical chracteristics of a resonating microbridge mass-flow sensor, Sensors and Actuators A, 1991,29, Messner, S. Finite Elemente Berechnung der Fluid-Struktur-Wechselwirkung bei einem mikromechanischen Stromungssensors, Thesis, University of Stuttgart / HSG-IMIT, Villingen-Schwenningen, Germany, Wiedemann, M.-C. Entwicklung von Anregungsschaltungen fur frequenzanaloge Sensoren, Thesis, Fachhochschule Kiel, Germany, 1993