Design and Analysis of a Triple Axis Thermal Accelerometer

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1 Design and Analysis of a Triple Axis Thermal Accelerometer DINH Xuan Thien a and OGAMI Yoshifumi b Ritsumeikan University, Nojihigashi, Kusatsu, Shiga Japan a thien@cfd.ritsumei.ac.jp, b y_ogami@cfd.ritsumei.ac.jp Keywords: Thermal accelerometer, buoyancy flow, MEMS. Abstract. In this paper, the authors propose a triple axis MEMS based thermal accelerometer and analyze its sensitivity and response. Thermal accelerometers detect acceleration by measuring the deflection of a heat plume in a microchamber. Usually, the heat plume is created by a heater on the top of a microcavity. By the use of computational fluid dynamics, the measurement ability of the sensor was analyzed for different positions of the heater. The results showed that the conventional designs where the heater located at the cavity center could measure only two components of acceleration vector, since the large cross-sensitivity between vertical and horizontal measurements cannot be avoided. In contrast, in our novel design, the heater formed a wide loop rounding the cavity center so that the mutual effects of these measurements were significantly reduced. For instance, the cross sensitivities were less than 5 % for acceleration up to g applied to any directions. Furthermore, with the new position of the heater a frequency bandwidth at 3 db of 7 Hz was obtained with applying a sinusoidal acceleration. Introduction Recently, inertial sensors with multi-axis measurement ability are required since this ability allows reducing energy consumption and high precision. In general, vibratory accelerometers using a suspended proof mass can measure simultaneously three components of acceleration vector because the proof mass can move in three directions [ 5]. However, the vibratory accelerometers have the disadvantages such as multi step and complicated fabrication process. The tiny bridges which are used to hold the proof mass are fragile then cannot suffer a high shock. Furthermore, the efforts to remove the squeeze film effect between the proof mass and accelerometer structure requires a complex package. Alternatively, thermal accelerometers eliminate these drawbacks because they avoid using solid proof mass. Their operation is based on the displacement of a hot air bubble generated by a heated wire in an enclosed chamber under acceleration. Various gas and liquid media have filled in the chamber [6 9] to improve the sensitivity of this type of accelerometers. Nevertheless, the developed thermal accelerometers can measure only two components of acceleration vector. Recently, a principle for a triple axis accelerometer has been proposed []. However, there is no discussion if this principle is efficient or not. In this study, we design a new structure that can be used as a triple-axis acceleration sensor. The design of the sensor is driven from the thermal fluid analysis. The sensitivity of the sensor is then investigated by computational fluid dynamics. Finally, the response of the sensor under sinusoidal acceleration is analyzed. The design Basically, thermal acceleration sensors measure acceleration through the deflection of a heat bubble generated by a heater on the top of a microcavity as the principle shown in Fig.. For convenience, T denotes temperature at the normal state a = (,, g) and T is temperature at the accelerated state a = (a x, a y, a z g), respectively, where g is the earths surface gravity. In the case without acceleration, the distribution of T (i.e. T ) is symmetrical, therefore the different temperature between X -detector and X 2 -detector is zero, T X =. Obviously, in this case, T Z = T - T at /3/$3. 23 IEEE 295

2 T between the detectors Z-detectors is also zero. In the case with X-acceleration, the symmetrical distribution of T is deviated, so the temperatures of the detectors X and X 2 are different, i.e. T X. Similarly, in the case with Z-acceleration, T Z is different from zero. Conversely, from these different temperatures T X and T Z, the accelerations a x and a z are attained. (c) a x = a x a z = a z detectors T z T x Substrate Heater Cavity X detector X 2 detector Z detector Z 2 detector Figure. The principle to measure acceleration in thermal accelerometer. The schematic design of the sensor. The principle to measure horizontal X-acceleration. (c) The principle to measure vertical Z-acceleration. In the conventional thermal accelerometers, the heater is suspended at the center of the microcavity, therefore, the temperature detectors are only possible to locate around the heater as in Fig. 2. As shown in Fig. 2, the temperature difference T X is much larger than T Z in the whole area, i.e. < x/l <, where we are able to place the X-detectors and Z-detectors. It implies that Z-detector will sense T X largely than T Z for any its location. In the other words, the cross talk of X acceleration to Z-measurement is very high. Thus, the conventional design is applicable for dual-axis measurement ability. Centered heater T x T z detector Heater - Figure 2. The configuration of the conventional sensor. The radial distribution of the difference in temperature between the detectors. In our new design as shown in Fig. 3, the heater is formed a wide ring and therefore the temperature detectors are possible to locate both inside and outside of the heater ring. Figure 3 plots T X and T Z for < x/l <. The figure shows that T X is small and T Z is large inside the heater ring < x/l < where indicates the location of the heater. In contrast, T X is large and T Z is small outside the heater ring, < x/l <. Therefore, it is obvious that locating Z-detectors inside the heater ring and X-detectors outside the heater ring can reduce significantly the cross talk between x/l /3/$3. 23 IEEE 296

3 T between the detectors X-measurement and Z-measurement. The physics behind this phenomenon is that the buoyancy flow due to a z in the region just above the cavity center is high when the heater forms a loop, thus temperature here varies sensitively with a z. Looped heater T x T z detector detector Heater Heater - - x/l Figure 3. The configuration of the present sensor. The radial distribution of the difference in temperature between the detectors. Simulation In order to capture the density temperature dependence due to large temperature change, the conservative law of mass, momentum, and energy for a compressible fluid are employed to describe the thermo fluidic phenomena in the accelerometer, which can be expressed as follows: t + (u) = () ut + u(u) = p + (u) (2) c p Tt + u( c p T) = (T) (3) where u, p are velocity and pressure of the fluid flow., c p,, and are density, specific heat, viscosity, and thermal conductivity of the fluid. a is acceleration vector. The term represents the momentum source due to the change of fluid density. To close the equations, we assume that the working fluid obeys the ideal gas law for compressible flows as p RT / M w (4) with R is universal gas constant, M w is gas molecular weight. The sensor is decomposed into a hexagonal mesh. The flow parameters on this mesh then are obtained by computational fluid dynamics package, Fluent ANSYS Inc., which uses Volume Finite Method to discrete the governing equations. The SIMPLEC method was adopted for pressure velocity coupling and all spatial discretizations were performed using the second order center scheme. The heaters are simulated as a solid zone with constant heat generation rate. Results and Discussions The optimal positions for the temperature detectors were discussed in our previous work [9]. Most output of the sensor relies on the dependence of the detector resistance to its temperature as R R ( (T T )) (5) ref ref where R and R ref are the resistances of the detector at temperature T and refered temperature T ref, respectively. The coefficient is temperature coefficient of resistance TCR /3/$3. 23 IEEE 297

4 T x ( C) T x ( C) If the used Wheatstone bridge is supplied at constant voltage E, the output of the sensor G is given by G Rref E R R w ref T for R = R ref (T T ref ) << R w + R ref, where R w is known resistance. For horizontal measurement, T in Eq. 6 is the temperature difference between detector X and X 2, T x = T x T x2. For vertical measurement, T is the temperature of the Z detector between the accelerated state with a z and normal state, T z = T za T z. The reference resistance R ref, known resistance R w, and are determined independently on the variation of acceleration. Therefore, for convenience, we discuss the sensitivity of the sensor through T x and T z. Sensitivity of the sensor. We discuss only the measurements of x and z components of acceleration because of the equivalence between the measurements of x and y components. To consider the cross effect between the vertical and horizontal measurements, i.e., the effects of a x to T z and of a z to T x, we simulate for a x = g to g and a z = g to g in combined manner. Figure 4 plots the variation of temperature differences T x with a x for different a z. We observe that T x varies linearly with a x up to a x = 2 g with the sensitivity T x /a x ~.29 C/g, and then starts curving as a parabolic curve with increasing a x. As shown in the zoom in view of Fig. 4, the effect of a z on T x is within 5 % in comparison with T x at a z = g for a z up to 3 g. (6) a z = g a z = 2 g a z = 3 g a z = 2 g a x (g) a x (g) Figure 4. Variation of temperature difference between detectors X and X 2 with acceleration applied to x axis for different a z. Plot for a x ranging from to g. Plot for a x ranging from to 2 g. The error bar represents 5% of T x at a z = g. Similar to Fig. 4, Fig. 5 plots the variation of temperature differences T Z with a z for different a x. It shows that T z increases linearly with a z up to a z = 2 g with the sensitivity T z /a z ~.62 C/g. In the other region of the curve, the relation becomes nonlinear in a parabolic form. Since a x is greater than g, the increase in T Z due to the increasing a x is larger 5% in comparison with T z at a x = g as shown in Fig. 5. By using linear least square technique, we can formulate the change of T x and T z as function of a x and a z in the range of g to g as T.29a.2 a g x x z T.2a.62 a g z x z Eq. 7 represents the dominant effect and of a x and neglected effect of a z on T x, and in contrast, the significant effect of a z and neglected effect of a x on T z. (7) /3/$3. 23 IEEE 298

5 T ( C) T z ( C) T z ( C) T z ( C) a x = g a x = g a x = 5 g a x = 2 g a z - g (g) a z - g (g) Figure 5. Variation of temperature difference between accelerated state and normal state at Z detector with a z for different a x. Plot for a z ranging from to g. Plot for a z ranging from to 2 g. The error bar represents 5 % of T z at a x = g. Response of the sensor. The response of the sensor is simulated under a sinusoidal acceleration a x and a z as a Asin(2 ft) (8) It should be noted that the amplitude A of a z is referred at the earths gravity and A = 2 g, while A = g for a x. Since the detector has typical thermal diffusivity of -4 m 2 /s and length of 3-4 m, the response of the detector resistance to the change of its temperature is up to ( 5 Hz). In our present study, the sensor is investigated under frequency of ( Hz). Consequently, the transient response of the sensor is dominated by the fluid response X X t x f Figure 6. Time dependent temperature at detector X and X 2 for a x = g sin(2ft) and at detector Z for a z = 2 g sin(2ft). Frequency f = Hz. Figure 6 and 6 plot the time dependent temperature at X and X 2, and at Z detector for Hz, respectively. The temperatures at X and X 2 detectors are in 8 phase shifted, since the detector X and X 2 are located in opposite sides of the heat plume generated by the heater. At any temperature detectors, the variations of temperature complete one cycle with t f =. This implies that at this frequency, the sensor responds well with oscillating acceleration. The response of the sensor is shown in Fig. 7. The sensor frequency bandwidth at 3 db is about 7 Hz. This frequency is higher than reported in [9], which is represented by the black dotted line, because the detectors are located a distance above the open surface of the cavity where the air can response easier than at the cavity surface. t x f /3/$3. 23 IEEE 299

6 2log(T x x /T xmax xmax ) ) 2log(T x /T xmax ) Frequency (Hz) Frequency (Hz) Figure 7. The response of the sensor with sinusoidal acceleration. Summary The sensitivity and response of a triple axis thermal accelerometer was numerically studied. The sensor was simulated in the state that both vertical and horizontal acceleration are applied simultaneously. Therefore, the mutual effect between the vertical and horizontal measurements was explicitly investigated. The output of the sensor is linear with acceleration with the slope of.29 C/g for horizontal measurement and of.62 C/g for vertical measurement, and cross sensitivities are less than 5 %, for acceleration within g. Finally, a frequency bandwidth at 3 db of 7 Hz was obtained with applying a sinusoidal acceleration. Acknowledgment This work was partially funded by Grant in Aid for Scientific Research (C) References. U.A. Dauderstadt, P.M. Sarro and P.J. French: Sens. Actuators A Vol. 66 (998), p A. Partridge, J. K. Reynolds, B.W. Chui, E.M. Chow, A.M. Fitzgerald, L. Zhang, N.I. Maluf and T.W. Kenny: Microelectromech. Syst. Vol. 9 (2), p E. Belloy, A. Sayah and M.A.M. Gijs: Microelectromech. Syst. Vol. (22), p R. Toda, N. Takeda, T. Murakoshi, S. Nakamura and M. Esashi: Microelectromech. Syst. 5 th IEEE International Conf. (22), p T. Denison, K. Consoer, W. Santa, M. Hutt and K. Mieser: IMTC 27, IEEE (27), p. 6. X.B. Luo, Z.X. Li, Z.Y. Guo and Y.J. Yang: Heat Mass Transfer Vol. 38 (22), p S. Billat, H. Glosch, M. Kunze, F. Hedrich, J. Frech, J. Auber, H. Sandmaier, W. Wimmer and W Lang: Sens. Actuators A Vol (22), p K.M. Liao, R. Chen and B.C.S Chou: Sensor Actuator A Vol. 3 3 (26), p F. Mailly, A. Giani, A. Martinez, R. Bonnot, P. Temple Boyer and A. Boyer: Sensor Actuator A Vol. 3 (23), p Y. Hua, L. Jiang, Y. Cai, A. Leung and Y. Zhao: US Patent 83 A (27) /3/$3. 23 IEEE 3

Effect of the Detector Width and Gas Pressure on the Frequency Response of a Micromachined Thermal Accelerometer

Micromachines 2011, 2, 167-178; doi:10.3390/mi2020167 OPEN ACCESS micromachines ISSN 2072-666X www.mdpi.com/journal/micromachines Article Effect of the Detector Width and Gas Pressure on the Frequency