View
8
Download
0
Category
Preview:
Citation preview
N. Mahmoodi1, C. J. Anthony1
1 University of Birmingham, School of Mechanical Engineering, Edgbaston, Birmingham, B15 2TT, UK
Air Damping Simulation of MEMS Torsional Paddle
Excerpt from the Proceedings of the 2014 COMSOL Conference in Cambridge
A MEMS torsional paddle (Figure 1) can be considered as
a potential device for bio/chemical sensing [1]. The Quality
Factor (QF) is inversely proportional to energy loss of the
resonator and can determine the sensitivity.
The effect of geometrical parameters on the behavior of
the MEMS torsional resonator was investigated. It was
shown that by changing these parameters the quality
factor could be enhanced which consequently could have
significant results on the sensitivity of the sensor. The
fabrication of the resonator by Focused ion beam would
be the next step to verify these results.
[1] Boonliang, B. , et al. , "A focused-ion-beam-fabricated micro-paddle
resonator for mass detection." Journal of Micromechanics and
Microengineering 18(1), (2008)
device thickness) on air damping and Quality factor of the
torsional paddle are investigated using COMSOL
Multiphysics® 4.4.
The Fluid-Structure Interaction interface was used.
2-D model was developed. Angular displacement
𝜃(𝑡) = 𝜃0 sin 𝜔𝑡 is applied on opposite sides to
produce the moment (Figure 3).
Fluid is in continuum regime and classified as a laminar
and incompressible fluid.
Time domain analysis was performed.
Figure 3. Applying angular
displacement
Power loss
• 𝑃𝑙𝑜𝑠𝑠 𝑡 = (𝑑𝑎𝑚𝑝𝑖𝑛𝑔 𝑡𝑜𝑟𝑞𝑢𝑒. 𝜔)
Energy loss
• 𝐸𝑙𝑜𝑠𝑠 = 𝑃𝑙𝑜𝑠𝑠(𝑡)𝑇
0
Quality factor
• 𝑄 = 2𝜋𝐸𝑛𝑒𝑟𝑔𝑦 𝑠𝑡𝑜𝑟𝑒𝑑
𝐸𝑛𝑒𝑟𝑔𝑦 𝑙𝑜𝑠𝑠=
𝐼𝜃𝑚𝑎𝑥𝜔𝑛2
𝑇𝑚𝑎𝑥
Figure 2. Steps to calculate the
Quality factor
ρ𝜕𝒖𝑓𝑙𝑢𝑖𝑑𝜕𝑡
=
𝛻. [−𝑝𝑰 + µ 𝛻𝒖𝑓𝑙𝑢𝑖𝑑 + 𝛻𝒖𝑓𝑙𝑢𝑖𝑑𝑇
+ 𝑭
𝜌𝛻. 𝒖𝑓𝑙𝑢𝑖𝑑 = 0
−𝛻. 𝜎 = 𝑭𝑣
Figure 4. Eigenfrequency and air flow distribution around the paddle (length×width
×thickness=10×8×0.2μm3 ),(a,b) anchors at the centre, (c,d) anchors offset from the
centre.
(b)
(d)
Q=127
Q=95 f=1.37 (MHz)
f=2.01 (MHz)
(a)
(c)
Figure 5. (a) phase difference between the
damping torque and angular velocity, (b) sine
and cosine components of damping torque
Figure 6. (a) Damping coefficient
versus angular velocity, (b) damping
torque versus angular velocity
0
5E-16
1E-15
1.5E-15
2E-15
2.5E-15
0 10000 20000 30000 40000
Dam
pin
g d
rag
to
rqu
e
(N.m
)
Angular velocity (rad/s)
2.E-20
3.E-20
4.E-20
5.E-20
6.E-20
0 20000 40000 60000
Dam
pin
g c
oe
ffic
ien
t (N
.m.s
)
Angular velocity (rad/s)
(a)
(b)
L (µm) t (nm) f (MHz) T(max) (N.m) D (N.m.s) QF
1 200 2.86 8.03E-16 4.47E-20 170
2.5 200 2.01 5.31E-16 4.21E-20 127
5 200 1.47 3.48E-16 3.75E-20 105
1 500 6.33 2.36E-15 5.92E-20 712
2.5 500 4.50 1.47E-15 5.19E-20 578
5 500 3.34 9.57E-16 4.56E-20 488
Table 1. Summarized simulation results (L=anchors’ length, t=thickness, f=resonance
frequency, T(max)=damping torque, D=damping ratio, Q=quality factor
L (µm) t (nm) Sensitivity
(Hz/fg)
2.5 (asymmetric) 200 5.58
2.5 200 8.17
2.5 500 10.88 0
1000
2000
3000
4000
5000
6000
0.E+0 2.E+6 4.E+6 6.E+6Maxim
um
dis
pla
cem
en
t (p
m)
Frequency (Hz)
Unloadedresonator
Resonator withadded mass (100pg)
Q=578
Table 2. Summarized sensitivity value for
paddle
Figure 7. Response curve for loaded
and unloaded micro paddle
-4.E-15
-3.E-15
-2.E-15
-1.E-15
0.E+00
1.E-15
2.E-15
3.E-15
4.E-15
2.22E-07 3.22E-07 4.22E-07
Da
mp
ing
to
rqu
e(N
.m)
Time(s)
Cos component
Sin component
Total damping torque
-4E-15
-3E-15
-2E-15
-1E-15
0
1E-15
2E-15
3E-15
4E-15
2.22E-07 5.22E-07 8.22E-07 1.12E-06 Time (s)
Angular velocity*10^-15 (rad/s)
Total damping torque (N.m)(a)
(b)
Prediction of the
QF is important
for optimization
and precise
dynamic performance
analysis of such a
sensor. In this study the
geometrical effect (anchors’
length, position and
Introduction
Figure 1. MEMS Torsional paddle
Results
Computational method
Refrence
Conclusion
𝜃(𝑡)
−𝜃(𝑡)
Recommended