Thermal Sensing and Actuation Part 2

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Thermal Sensing and ActuationPart 2

• EE485A Lecture
• October 8, 2008

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Thermal Expansion

• Volumetric expansion coefficient (TCE), a, the
  ratio between the relative change in volume and
  the temperature variation (ppm/K)

• Linear expansion coefficient the change of only
  one dimension of an object due to temperature
  variation,

• The volumetric and linear expansion coefficients
  are related by

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Thermal Bimetallic Effect
t1
t2
w1
w2
L
For a1 The radius of curvature of the arc is given by
The angle (in radians) associated with an arc of
length L and radius r is given by
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Thermal Bimetallic Effect, cont.

• Once the radius of curvature is found, the
  vertical displacement is found from

q
r
r cos(q)
d r - r cos(q)
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Exercise

• Calculate the radius of curvature and
  displacement for a bimorph cantilever made up of
  aluminum and silicon nitride heated to 20 C
  above room temperature. The width of both layers
  is 20 mm and the length is 100 mm. The silicon
  nitride is 1 mm thick and the aluminum is 0.5 mm
  thick. E 250 GPa for silicon nitride and 70
  GPa for aluminum. The thermal expansion
  coefficients of aluminum and silicon nitride are
  a2 25 ppm/C and a1 3 ppm/C, respectively.

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Exercise continued

• Now allow the silicon nitride to extend for an
  additional 100 mm beyond the aluminum. Determine
  the total deflection at the tip of the cantilever.

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Sample Application
Cilia array for micromanipulation, Bohringer,
Donald, Kovacs, Suh (U. Washington) Uses layers
of Polyimide engineered for different
CTEs Fingers curl up 120 mm out of
plane Thermal actuation used to flatten cilia,
electrostatic power used to hold cilia flat.
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Actuators with a Single Material

• Using geometry to cause differential heating

Luo, Flewitt and Milne, University of Cambridge
Hot arm
Cool arm

• Using a bent beam

http//john.maloney.org/thermal_actuation.htm
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Thermal Couples

• Two wires of dissimilar materials joined at a
  single point.
• Work function difference results in
  temperature-sensitive voltage difference
• Voltage change for temperature change given as
  Seebeck coefficient.
• as DV/DT (specific to material combination)
• Several types (E, J, K, T, R, S) in common use,
  see p. 172.
• Thermal pile
• multiple thermal couples connected end to end
  with hot and cold junctions aligned
• More sensitive than single thermal couple
• Micromachined thermal couples have been made
  using Ni and W with a sensitivity of 22 mV/K

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Thermal Resistors

• Electrical resistors where the resistance depends
  on temperature
• aR temperature coefficient of resistance (TCR)
• Quick exercise A thermal resistor is 2 kW at
  room temperature and has a TCR of 100 ppm/C.
  Predict the resistance at 50 C above room
  temperature.

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Characterizing Thermal Resistors

• Self-heating the current and voltage used to
  interrogate the resistor value can heat the
  resistor up.

I
R
TCR
Ohms Law
TCR 0
TCR 0
TCR
V
P
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Application Examples

• Accelerometer using differential heat loss under
  acceleration (see Case 5.4)
• Hot-wire anemometer (see Case 5.6) as flow
  increases, heat transfer from the wire increases.
  By monitoring the amount of power required to
  keep the wire at constant temperature one can
  measure flow rate.
• Infrared sensor using bimetallic structure coated
  with material the absorbs IR light (see Case 5.8)
• Cantilevers for data storage and retrieval (see
  Case 5.9)