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Computer Simulated Transient Analysis of a Polyimide V-Groove Leg
Actuator with Serpentine Heater for a Walking Micro-Robot
Ritesh A Khire, Satish G. Kandlikar, Wayne W. Walter
Department of Mechanical Engineering, Rochester Institute of Technology, Rochester, N.Y., USA.
[email protected], [email protected], [email protected]
ABSTRACT
A computer-simulated model for transient
heat and deflection analysis was developed for the
serpentine type heater actuator to be used for a
walking micro -robot. Some differences between
the simulated and experimental results reported by
T. Eberfors at the Royal Institute of Technology,
Sweden, were noted in the low frequency domain.
A need for an active cooling mechanism was
identified. The heater location and the power
supplied to each V groove needs to be optimized so
that all V-grooves participate equally in the
actuation process. The role of thermal conductivity
and wall temperature has been investigated. A
number of issues have been identified which
require future work.
INTRODUCTION
This shrinkage property of polyimide and its
compatibility with standard silicon processes make
the fabrication of this actuator achievable.
Although the details about the fabrication
technique used are beyond the scope of this paper,
in short, the fabrication involves standard silicon
processes like KOH etching, sputtering, LPCVD,
lithography etc.
In the work done by Ebefors, two types of
heaters were mounted on the actuator. The first was
a “serpentine heater”, in which aluminum was used
both as a conducting and resistance-heating
element. The heaters, located inside the trenches,
had a smaller width of aluminum and the
conductors (contacts) had a larger width. The
second heater type was a “polysilicon heater”,
located between two trenches. The contacts in this
case are still aluminum [4]. Figure 1 shows the
schematic of a serpentine heater type actuator.
Heater
Insects can be considered as the
inspiration behind the development of microrobotics. Using high-speed video photography and
computer simulations, traits of insects such as the
cockroach have been analyzed [1,2]. One of the
important locomotion requirements of a microrobot is large out-of-plane deflection of the
actuators forming its legs. Few actuators have been
developed for out-of-plane motion [3]. This paper
describes the transient computer simulations done
on a polyimide V-groove leg actuator for a walking
micro -robot, to investigate the optimal transfer of
heat.
This actuator was fabricated and tested by
T. Ebefors et al. [4] at the Royal Institute of
Technology, Sweden. The principle of actuation is
based on the thermal expansion of polyimide inside
a V-groove by an electrical heater. The out-ofplane orientation of the leg is due to the thermal
shrinkage of polyimide when cured. Due to the
larger absolute contraction length at the top of the
V-groove as compared to the bottom, the actuator
(cantilever beam) attached to the V-grooves curls
out of the plane, forming a freestanding leg [5].
Contacts
Pads
Polyimide inside V groove
After
Curing
Silicon Wafer
Before Curing
Figure 1: Schematic of Serpentine heater.
It is important to note that Figure 1 is just
a schematic representation of the system. For
accurate dimensions and details about the device,
the reader is encouraged to refer to the PhD thesis
of T. Ebefors [4].
This paper deals with the transient
analysis of the above actuator done using ANSYS
5.6. The assumptions made in the model will be
discussed later in a section on model development.
The simulation results were compared with the
published experimental data by T. Ebefors [6]. We
found that the results of the simulation match with
the experimental data in the high frequency
domain. This confirms the validity of the
assumptions made in the model being used for
further simulations at the Rochester Institute of
Technology (RIT) to understand the heat transfer
process.
effect of convection, the entire length of the
actuator was modeled. Figure 2 shows the model of
the actuator.
NOMENCLEATURE
?
c
k
?x
d
L
Density (kg/m3 )
Specific Heat (kJ/kg ºK)
Thermal Conductivity (W/m ºK)
Average element length (m)
Deflection in vertical direction (m)
Length of actuator up to center (m)
OBJECTIVE OF THE WORK
The objective of the present work is to:
(1) develop an FEM model for transient analysis of
the actuator, (2) validate the model by comparing
the simulation results with the published
experimental data, (3) understand the transient
phase of the heat transfer for further optimization
of the system, and (4) identify the role of
conduction and convection in the heat transfer
process. The future objective is to understand the
micro scale heat transfer and identify any
differences with the classical solution.
MODEL DEVELOPMENT
ANSYS 5.6 was used to develop the
model. For generating the mesh “coupled field”
“Plane 13” elements were used. This is a two
dimensional quadratic element with a maximum of
four degrees-of-freedom per node. Displacements
UX and UY, in the x and y directions, respectively,
and temperature were selected as degrees of
freedom per node. The element behavior was set as
“plain strain” which refers to no heat transfer in the
z direction [7]. The dimensions and material
properties were obtained from the Eberfor’s thesis
report [4, 6].
The model was simplified using the
following assumptions: (1) all the material
properties were assumed to remain constant over
the operating temperature range, (2) the out-ofplane curling of the actuator was neglected (thus
the actuator beam was assumed to remain in the
plane of wafer as a straight beam), and (3) the top
and bottom edge dimensions of the V-grooves were
reduced as per the shrinkage coefficient (~ 45% for
curing temperature 350ºC [6]). To identify the
Figure 2: Model of the actuator showing
polyimide inside the V-grooves
Since the modeling was done in two
dimensions, the supplied power was converted into
an equivalent heat generation rate by dividing the
total power by the product of the volume of the
aluminum heater times the number of V-grooves.
For calculating the volume of the heater, the
thickness of the aluminum was assumed to be
uniform (1.5 micron) [4,6]. For the contacts, our
two dimensional model would assume the width of
the contact to be equal to the width of the structure,
which would decrease the resistance to the heat
flow of the contacts. To correct for this, the thermal
conductivity of the aluminum forming the contact
was scaled down by multiplying it by the ratio of
the actual width of the contact to the entire width
of the structure.
Further simplification was done by
neglecting the oxide layer deposited inside the
trenches to act as an electrical insulator, and on top
of the wafer to act as a masking layer for etching
the V-grooves. Since the power was converted into
an equivalent heat generation rate for this
simulation, it was reasonable to neglect it. The
various regions forming the beam were attached
(glued) to each other before meshing. By dividing
all the lines forming the model into appropriate
portions, uniform meshing (mapping) was
obtained.
Aluminum
Heater
Silicon
Contact
Polyimide
Figure 3: Meshed Model (3 V groove model)
Transient analysis was done for one heat
cycle. The cycle was divided into three steps.
Figure 4 shows the graphical representation of
these time steps. The first step is applied for a very
small time of (~1e-8 sec). This step defines the
initial boundary conditions of the system. These
initial boundary conditions include: (1) the left wall
of the actuator was restrained from having
displacements in the x and y directions, (2) a heat
sink was created at the same edge by enforcing a
constant temperature (20 ºC), and (3) convection
was applied on the top and bottom surfaces of the
actuator.
In the second step, the heat generation rate
was applied to the aluminum heaters inside the
trench. In order to accommodate various losses, the
heat generation rate was truncated by 5%. All other
Figure 5: Comparison of different time step
values for 90 mW, 10 Hz, and 1 V-groove
In the third step, the heat generation rate
was equated to zero, which represents the cooling
period.
RESULTS
The three V-groove configuration was
first simulated with convection applied at the top
and bottom surface of the system (h=20 W/m2 °C),
and then with no convection applied (h=0 W/m2
°C). Figure 6 shows the comparison of results
obtained from the two simulations.
Figure 4: Load steps in one heat cycle
boundary conditions applied in the first step were
used. The time sub-step was calculated using the
Fourier number given in the following equation
[7]:
∆t =
ρc(∆x) 2
K
(1)
For micro systems, the average element length is of
the order 1e-6 m, which leads to an extremely
small time sub-step (~1e-8 sec.). When a simple
system of only one V-groove was simulated for
this time step, ANSYS stopped the simulation after
1e-4 seconds. The same behavior was observed for
a time step equal to 1e-7 and 1e -6 sec.
Figure 5 shows the comparison of
different time sub-step values. The simulation
stopped at point ‘A’ on the graph for time step
values from 1e-8 to 1e-6 sec. Also it can be seen
from the graph that results nearly match for a time
step equal to 1e-4 sec and 1e-5 sec. As a result, for
faster simulation, a time sub-step value was taken
as 1e-4 sec.
Figure 6: Effect of convection on the
heat transfer process
It is apparent that the output does not
change even if convection is neglected.
Accordingly, for all further simulations, convection
was neglected.
Figure 7 shows the comparison of
experimental results versus the simulated values
for the three V-groove configuration. The bending
angle was calculated using the following formula:
−1  δ 
θ = sin  
 L
(2)
heated the most. Similar behavior was observed in
the case of the 3V groove configuration.
Figure 7: Comparison of Simulated
values with experimental data for 3 V
It can be seen from the graph that
simulated values agree with the experimental data
for the high frequency domain. Differences in the
low frequency domain will be addressed in the
Parametric Analysis and Discussion sections,
which follow. A similar analysis was done for the
four V-groove configuration. Figure 8 shows the
comparison of results.
Figure 9: Temperature evolution at the
center of the V- grooves in the 4 Vgroove configuration
PARAMETRIC ANALYSIS
Effects of various parameters were
simulated. The following trends were obtained:
Effect of convection: As can be seen from Figure
6, convection plays a very limited role in the heat
transfer process, for this actuator. Similar behavior
was observed when the heat transfer coefficient
was increased to h=100 W/m2 C. This observation
leads to the conclusion that an effective cooling
mechanism is required for the actuator.
Figure 8: Comparison of Simulated values
with experimental data for 4 V-grooves
When experiments were done on the
actuator, it was observed that the outermost Vgroove gets heated more as compared to the
innermost V-groove [5]. A similar behavior was
also observed in the simulation. Figure 9 shows the
simulated temperature evolution at the center point
of the top edge of the V-groove. It can be seen that
the temperature in the last V-groove is maximum
among the four. This is primarily due to the inner
V-groove acting as a thermal insulator, which heats
up the outer V-grooves. The last V-groove gets
Effect of conductivity of silicon: The simulation
was run for three different thermal conductivity
values of silicon. Figure 10 shows the comparison
of simulation results for 3 V grooves. As the
conductivity of silicon is reduced, the deflection
increases, as a result of increased polyimide
heating. It can be seen that the variation in
conductivity value causes a small change in
deflection at higher frequencies, but at lower
frequencies, the magnitude of change is increased.
Effect of conductivity of polyimide: The effect of
thermal conductivity variation of polyimide is
shown in Figure 11. When the conductivity of
polyimide is increased, the deflection value
increases. This is consistent with the increased
heating of polyimide. This increase in deflection is
nearly constant over the frequency range.
Effect of wall temperature: For the analysis done
previously in Figures 7 and 8, the left wall
temperature was enforced at a constant value of
20ºC. But from the steady state analysis done on
the polysilicon heater by Ebefors, the wall
temperature rises to 33.75ºC [4]. Figure 12 shows
the effect of linearly increasing wall temperature
from 20ºC to 35ºC over the period of 150 ms
(settling time obtained experimentally [6]). Figure
12 shows better agreement with experimental
results as compared to Figure 7. The trend of the
simulation results is more consistent with the
experimental data at lower frequencies. A similar
trend was observed for the 4 V-groove
configuration also.
Figure 10: Effect of silicon conductivity.
Figure 11: Effect of change in
polyimide conductivity.
Figure 12: Effect of change in wall
temperature.
DISCUSSION
The curves of deflection vs. frequency are
consistent with the experimental data for
frequencies of 40 Hz and above. The difference is
more in the 3 V-groove configuration as compared
to the 4 V-groove configuration for frequencies
between 20 and 40 Hz (see Figures 7 and 8). Since
the same power is distributed in each case, the
power per groove is more in the 3 V-groove
configuration. As more power is dissipated per Vgroove here, the temperature rise in each V groove
is higher. Since for this analysis, the material
properties have been assumed to remain constant
with temperature, the difference is more in the case
of the 3 V-groove configuration.
From Figure 6 it is seen that convection
plays a very little role in case of heat dissipation.
This leads to the conclusion that an active cooling
mechanism will be required for dissipating the
entire heat during the cooling cycle. Failure to
remove all the heat may result in little deflection
over the time period. Further simulation will be
required for optimizing the heat transfer.
The simulated values differ from the
experimental values at lower frequencies. This
deviation may be explained due to following
reasons:
1) Although the shape of the polyimide is
assumed to be a perfect V, in actual practice the
shape of the experimental V may not be the same,
causing dimensional differences. One of the
reasons for this shape difference in the
experimental V is due to the presence of the
aluminum contact, which expands at the high
curing temperature of polyimide (as opposed to
shrinkage in polyimide). As a result, the actual
shrinkage pattern will be different than assumed.
2) Constant material properties were
assumed over the temperature range. As the
frequency is reduced, the temperature increases
inside the system since the heating time is longer.
Therefore, at lower frequencies the assumption of
constant material properties rather than temperature
dependent properties will induce more error.
3) The inner most V-groove acts as a heat
insulator, thereby causing higher temperatures in
the outer V- grooves (see Figure 9). This higher
temperature increases the resistance of the heating
element of the outer V-groove, causing higher
power generation inside the outer V- groove. This
results in the outermost V-groove contributing
more to the total deflection. For this analysis, equal
power generation in all V-grooves was assumed.
Therefore, at lower frequencies, the simulated heat
supplied to the outermost V groove is less than the
actual value. The power generation inside each Vgroove needs to be changed over time, to correct
this error.
4) Increasing the wall temperature over
time gives better results than the constant
temperature assumption (see Figure 12). Rather
using a linear temperature rise, as was done here,
perhaps a exponential rise may prove to be more
effective.
5) Due to the thermal expansion
coefficient mismatch between polyimide and
aluminum, residual stresses get developed in the
structure after curing, which have been neglected
in the modeling.
6) As reported by T. Ebefors, the data
acquisition
system
used
had
significant
uncertainties [4]. Deviations as high as +/- 0.25º
can be involved in the measurement system.
CONCLUSIONS
A computer-simulated model for transient
heat and deflection analysis was validated for the
serpentine heater case in the high frequency
domain. Some differences between the simulated
and experimental results reported by T. Eberfors
were noted in the low frequency domain. A need
for an active cooling mechanism was identified as
convection plays a small role in the heat transfer
process. It was also observed that all the V grooves
do not contribute equally to the actuation process.
Thus, the heater location and the power supplied to
each V groove needs to be optimized, so that all Vgrooves participate equally in the actuation
process. The role of various parameters (thermal
conductivity and wall temperature) has been
investigated. A number of issues have been
identified which require future work.
FUTURE WORK
The following issues are scheduled for further
investigation:
1) Temperature dependent material properties.
2) Coupled electrical-thermal effects.
3) Wall temperature effects employing an
exponential function.
4) Optimal heater location.
5) Residual stress effects.
6) Development of an active cooling mechanism.
7) Fabrication and test of a leg actuator prototype
(currently in progress at RIT).
REFERENCES
[1]. S. Laksanacharoen, A.J. Pollack, G.M.
Nelson, R.D. Quinn and R.E. Ritzmann
“Biomechanics and Simulations of a
Cricket for Microrobot Design,” IEEE
International Conference on Robotics and
Automation, San Francisco, USA, April
24-28, 2000.
[2]. T. Ebefors, J. U. Mattsson, E. Kalvesten,
and G. Stemme, “A Walking Silicon
Micro-Robot,” The 10th Int. Conference
on Solid-State Sensors and Actuators
(Transducers ’99), Sendai, Japan, June
1999, pp 1202-1205.
[3]. P. Kladitis, V. Bright, K. Harsh, and Y.C.
Lee, “Prototype Microrobots for Micro
Positioning in a Manufacturing Process
and Micro Unmanned Vehicles,” Proc. of
IEEE 12th Int. Conference on MicroElectro-Mechanical Systems (MEMS’99),
Orlando, USA, 1999,pp. 570-575.
[4]. T. Ebefors, “Polyimide V-Groove Joints
for Three – Dimensional Silicon
Transducers – Exemplified Through a 3-D
Turbulent Gas Flow Sensor and Microrobotic
Devices,”
thesis
report,
Department of Signals, Sensors, and
Systems, Royal Institute of Technology
(KTH), SE-100 44 Stockholm, Sweden.
[5]. T. Ebefors, E. Kalvesten, and G. Stemme,
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Microstructures,” Journal of Micromech
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[6]. T. Ebefors, E. Kalvesten, and G. Stemme,
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– part 1” for Release 5.6, Nov 1999.
ANSYS® is a registered trademark of SAS
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