Thermal actuators
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Transcript of Thermal actuators
Thermal actuators Give qualitative and quantitative descriptions
of the three modes of heat transfer. Explain the behavior of a hot arm actuator,
both qualitatively and quantitatively, based on our simplified lumped element model.
A generic thermal actuator
Inside the actuator energy has been converted to the thermal mode.
Thermal energy moves from regions of high temperature to low temperature. This is called heat transfer.
electrical input
mechanical output (motion)
waste thermal energy
Thermalactuator
TH TLQ
The three modes of heat transfer
Conduction
TH TL
Convection (Conduction + advection)
Radiation
Both require a material medium
Does not require a material medium
Working equations of the three modes
TH TL
Conduction
A
T1
T2
Q
Q
thR
TT
A
dTT
Q 2121
R
ee
A
dee
i 2121
T1 T2e1
e2
Material κ (W/m·K = [ॐ·m]-1)
Copper
Styrofoam
Silicon
401
0.04
148
Ad
TT
21
thR
TT 21
Working equations of the three modes
TH TL
Convection
Q
Convection Fluid h (W/m2·K = [ॐ·m2]-1)
Natural Gas
Natural Liquid
Forced Gas
Forced Liquid
10-1000
20-250
100-20,000
)( 21 TThAthR
TT 21
surface area A at Ts
moving fluid at T∞
Q
T1
T2
thRhA
1
2-20
Working equations of the three modes
TH TL
Radiation
Q
Material ε
Polished Al
Black paint
Skin
Si
0.98
0.90
0.67
4
SAT
surface area A at Ts
Q
0.04
Perfect blackbody
4
SAT
Non-ideal surface
)( 44surrS TTAQ
Small object completely surrounded by large surface
Q surrounding surface at Tsurr
Repaso del actuador térmico
Actuador térmico (brazo caliente)
Actuador térmico hecho de poli silicio
~ 200 μm
Actuador térmico
Como funciona el actuador
i
+e-
Modelo sencillo de actuador térmico
mechanical output (motion)
voltage
waste thermal energy
Thermalactuator
electrical input
tip deflection
+e-
ωtip
ωtip = f(e)Our goal:
Te toca a ti
Ideas on modeling
List some ideas about how you might create such a model. What physical concepts would you use? What simplifications would you make?
• Assume actuator has only two arms (hot arm and cold arm) each with only
one temperature
• The actuator is at steady state with a continuous electrical input being
dissipated in the two electrical resistances created by the hot arm and the cold
arm.
• All the stress is initially experienced by the hot arm, which can be calculated in a
way similar to thermal mismatch stress.
• The hot arm stress causes a bending moment in the cold arm, the deflection of
which can be calculated using standard beam bending theory. (Bernoulli beam
bending)
)( TThA cconv
)( TThA hconv
Modelo sencillo de actuador térmico
+ eh -
- ec +
I+e-
L
hot arm at Th
cold arm at Tc
Ac
Ah
D
side view
Q
Q
W
Perimeter, P
Modelo sencillo de actuador térmico
+ eh -
- ec +
i+e-
L
hot arm at Th
cold arm at Tc
Ac
Ah
D
side view
Perimeter, P Te toca a ti
Find the voltage drops across the hot arm and cold arm (eh and ec) in terms of the input voltage (e), the resistivity of the actuator material (ρ), and its geometry.
eRR
Re
ch
hh
eALAL
AL
ch
h
)/()/(
)/(
h
h A
LR
eAA
A
ch
c
eAA
Ae
ch
hc
cc A
LR
Modelo sencillo de actuador térmico
+ eh -
- ec +
i+e-
L
hot arm at Th
cold arm at Tc
Ac
Ah
D
side view
Perimeter, P Te toca a ti
Find the temperatures the hot arm and cold arm (Th and Tc) in terms of the input voltage (e), the resistivity of the actuator material (ρ), its geometry, and the heat transfer coefficient (h).
Q
Q
W
)( TThA hconv
)( TThA cconv
hieh
h
R
e 2
TeAA
A
Lh
AT
ch
c
h
hh
2
2
2P
)( TThAQ hconv
A = PL
TeAA
A
Lh
AT
ch
h
c
cc
2
2
2P
Modelo sencillo de actuador térmico
ωtip
Hot arm thermal stress σ
D
Induced bending moment M ≈ DσAh
x
Hot arm is initially at T∞, and is then heated to Th. What is the thermal strain?
What about the cold arm?
Cold arm is much thicker than hot arm. So let’s assume both experience the same actual strain. Which one?
h )( TThT
c )( TTcT
εboth = εh or εc ?
The ______ ______ experiences two pieces of strain – one due to thermal expansion and another extra piece due to the fact that it is hooked to the ______ ______.
hot armcold arm
h )( TThT extra c )( TTcT
Modelo sencillo de actuador térmico
ωtip
Hot arm thermal stress σ
D
Induced bending moment M ≈ DσAh
x
Solve for this extra piece of strain, εextra.
How would you model the stress/strain in the hot arm? What would the relation for strain be, then? Is the arm in tension or compression?
)( hcT TT extra
E
)( hcT TTE
Modelo sencillo de actuador térmico
dx
ds
x
ω
R
θ
dθ
Rdds
Rdx
d 1
For small deflections dx ≈ ds, hence dx ≈ Rdθ. So
For small deflections tan(θ) ≈ θ.
Rdx
d 12
2
dx
d
EI
M
dx
d
2
2EI
M
R
1
Can also show
Beam bending relations
Modelo sencillo de actuador térmico
ωtip
Hot arm thermal stress σ
D
Induced bending moment M ≈ DσAh
x
This gives us an expression for the deflection as a function of the length, x.
EI
AD
EI
M
dx
d h2
2
Integrate this expression from x = 0 to x = L to get the tip deflection, ωtip.
EI
LAD htip 2
2
222
2 ch
h
c
c
ch
c
h
hhTtip AA
AA
AA
AA
Ih
eAD
PP
Finally, substitute expressions for σ and the temperatures to complete our model.
¡E no está!
convQ
convQ convQ
Modelo un poco más complejo
Add a third resistor for the flexure:
Modelo un poco más complejo
Electrical resistances of the arms given by
Allow for a temperature dependence of resistivity, ρ = ρ(T):
Modelo un poco más complejo
Comparison to the model of Huang and Lee (1999)
Q. A. Huang and N. K. S. Lee, “Analysis and design of polysilicon thermal flexure actuator,: J. Micromech. Microeng., vol. 9, pp. 64–70, 1999
our model
Modelo un poco más complejo
Mechanical model
EI
xM
dx
xd )()(2
2
x
62
1 320 hh
hh
VLLM
EI
6
22
1
62
1
33
22
32
fcf
fcfc
f
c
fff
fc
LLLV
LLLH
PM
EI
VLLM
EI
Modelo un poco más complejo
Comparison to data
Lc = 120 μmLh = 240 μm
Lc = 180 μmLh = 240 μm
Modelo un poco más complejo
Comparison to data
E = 150 GPa E = 10 Pa
Lc = 120 μmLh = 240 μm
Lc = 120 μmLh = 240 μm