A study on performance improvement of MEMS hair flow
sensors by parametric amplification
H. Droogendijk and G. J. M. Krijnen
MESA
+Research Institute, University of Twente
P.O. Box 217, 7500 AE, Enschede, The Netherlands
Keywords: cricket hair, bio-inspired, flow sensor, parametric amplification
Inspired by crickets and its perception for flow phenomena (figure 1), artificial hair flow sensors have been developed successfully in our group[1]. Improvement of fabrication methodologies have led to better perfor-mance, making it possible to detect and measure flow velocities in the range of sub-mm/s [2]. To improve the performance of these sensors even further, we will make use of non-linear effects. In nature a wide range of such effects exist (filtering, parametric amplification, etc.) and can give a rise in sensitivity, dynamic range and selectivity.
Here, we consider parametric amplification, which is adaptation of the sensor performance. By controlling the mechanical properties of the hair sensory system in time, a dynamical system with non-linear properties can be obtained. Carr et al.[3] showed that with the right choice of parameters the input is amplified. Generally, with a well-defined configuration one can achieve filtering and selective gain of the system.
To determine how this principle can be used in our bio-inspired hair sensor, we consider the second-order dif-ferential equation describing its behavior (figure 3), where J is the moment of inertia, R the torsional resistance,
Sthe torsional stiffness and T the drag torque due to oscillating air flow:
Jd
2α
d t2 + R dα
d t + S(t)α = T0cos(ω0t) (1)
Normally the torsional stiffness is given by a spring constant S0. Now, we electrostatically modulate the
torsional spring stiffness of the system in time (see figure 4):
S(t) = S0−1 4U 2 0 d2C dα2− 1 4U 2 0cos(2ωst+ 2θs) d2C dα2 (2)
With the appropriate pump amplitude U0, frequencyωs and phaseθs we are able to improve the gain of
the flow velocity input signal, which is confirmed by numerical simulations in MATLAB (figure 5). Especially by pumping with the same frequency and the double frequency of the incoming flow, significant gain of the signal can be obtained.
In conclusion, by introducing non-linear effects to our artificial hair sensory system, we have indicated para-metric amplification to be a useful mechanism to improve the performance of these sensors.
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Corresponding author: H. Droogendijk, University of Twente, MESA+ Research Institute, P.O. Box 217, 7500 AE, Enschede, The Netherlands, E-mail: h.droogendijk@utwente.nl, Tel:+31 (0)53 489 4029 , Fax: +31 (0)53 489 3343.
References
[1] M. A. Dijkstra, J. J. J. van Baar, R. J. Wiegerink, T. S. J. Lammerink, J. H. de Boer, and G. J. M. Krijnen. “Artificial sensory hairs based on the flow sensitive receptor hairs of crickets”. Journal of Micromechanics
and Microengineering, 15:S132–S138, July 2005. ISSN 0960-1317.
[2] C. M. Bruinink, R. K. Jaganatharaja, M. J. de Boer, J. W. Berenschot, M. L. Kolster, T. S. J. Lammerink, R. J. Wiegerink, and G. J. M. Krijnen. “Advancements in technology and design of biomimetic flow-sensor
arrays”. In 22nd IEEE International Conference on Micro Electro Mechanical Systems (MEMS 2009), Sorrento,
Italy, number CFP09MEM-USB, pages 152–155, Piscataway, January 2009. IEEE Computer Society Press. [3] D. W. Carr, S. Evoy, L. Sekaric, H. G. Craighead, and J. M. Parpia. “Parametric amplification in a torsional
microresonator”. Applied Physics Letters, 77(10):1545–1547, September 2000.
[4] T. Shimozawa, T. Kumagai, and Y. Baba. “Structural scaling and functional design of the cercal wind-receptor hairs of cricket”. J. of Comp. Physiol. A, 183:171–186, 1998.
Figure 1: Flow perception by crickets (SEM pictures courtesy of Jérôme Casas, Université de Tours).
Figure 2: MEMS hair flow sensors.
Air flow T(t) J R S y L θ(t)
Figure 3: Model of a flow sensing hair[4].
Vacos(ωat)
Upcos(ωpt+ θp) Upcos(ωpt+ θp)
Figure 4: Modulating the torsional spring stiffness in time. 1 0 1 0 0 1 0 0 0 1 . 0 1 . 1 1 . 2 1 . 3 1 . 4 1 . 5 H a l f a i r f l o w f r e q u e n c y G a in P u m p f r e q u e n c y ( H z ) G a i n v s . p u m p f r e q u e n c y A i r f l o w f r e q u e n c y
Figure 5: Analysis for variable flow frequencies.
