Optimal design of a flexural actuator

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Optimal design of a flexural actuator

• by
• Vasamsetti Rajesh Kumar
• Under the guidance of Rajab Challoo

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OVERVIEW

• Introduction
• Actuator Design
• Design Problem
• Lowest Weight and Power
• Conclusion

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Introduction

• Actuators embrace a size range from nanometers to
  meters, with electrical, magnetic, thermal or
  pneumatic input signals
• They use a thermal input signal to generate
  motion
• Such actuation is relatively simple, yet enables
  three-dimensional linear or rotary motion.

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• Here the lightweight actuator concept is
  presented and the associated design problem is
  stated.
• The complete temperature history of the SMA face
  sheets upon heating and cooling is obtained.
• An analysis is then performed to find the minimum
  weight that achieved
• (i) a specified displacement
• (ii) a restraining moment
• (iii) assures no failure, and
• (iv) operates within a power budget.

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Actuator Design

• Actuator comprises a triangular corrugated core
  with shape memory alloy (SMA) faces.
• It is clamped at one end and free at the other
  end.
• We fix a light weight beam which must flex over a
  displacement against restraining springs and
  dashspots as shown in the figures.

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• For actuators with dimensions in the
  centimeter-to-meter range, the core comprises
  corrugated polymer where as for micro scale
  devices, silicon is chosen as the core.
• A triangular corrugation has been chosen for the
  core because of 2 reasons
• a) It offers no rotational resistance when
  comprised of fiction less pinned joints.
• b) When attached to the face sheets, the
  triangulated configuration has exceptional
  bending stiffness.

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Fig. 2. Non-dimensional transverse shear
stiffness of corrugated panel as function of
corrugation angle.
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• The top SMA face sheet is heated to temperature T
  by transmitting an electric current while the
  bottom sheet and core are maintained below finish
  temperature Tf.
• As the temperature increases, the peak
  temperature of the top face crosses the finish
  temperature Tf and heating is stopped.
• Now cooling is initiated and the curve bend
  downwards.

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Fig. 3. Schematic of heating and cooling curves
of top and bottom faces during one
full cycle.
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Design Problem

• The power consumed by the actuator is given by
• The power is converted into heat in a spatially
  uniform manner and is consumed by three
  mechanisms.
• Temperature increase of the face sheet relative
  to the initial temperature
• Convective heat transfer
• Phase transformation

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• Under these assumptions, the temperature
  variations of the face sheet w.r.t time and
  position is as follows
• To obtain solution for this we consider two
  boundary conditions Type-I and Type-II
• Type-I where both ends of cantilever remain at
  ambient
• Type-II only attached end is ambient and the
  free end is thermally insulated

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Type I boundary condition

• Initial conditions are
• T(x,0)T0 T(0,t)T0 and T(L,t)T0.
• The solution is given by

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Fig. 4.
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Type II boundary conditions

• Initial conditions are
• T(0,t)T0 and dT(L,t)/dt0.
• All the solution in Type II is similar to that of
  Type I except that L is replaced by 2L.

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Fig. 5.
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Fig. 6. Schematic of face temperature and tip
deflection with time.
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• Operational frequency
• The operational frequency is largely limited by
  the efficiency of cooling.
• The frequency can be increased by reducing the
  face thickness d or by increasing the heat
  transfer coefficient h.
• Electro Mechanical power consumption
• With in a full thermal cycle the heat needed to
  raise the temperature of faces is
• End deflection
• Upon heating the length of top face is
  reduced and the bottom face does not stretch
  or contract causing the beam to bend upwards.

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Lowest weight and power

• The initial goal is to minimize the actuator
  weight. To achieve this we have to overcome six
  constraints
• minimum deflection
• Power consumption
• Face yielding
• Core member yielding
• Face buckling
• Core member buckling.

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Fig. 9. Selection map for acceptable dimensions
subjected to the constraints
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conclusion

• It has been shown that cantilever actuators
  consisting of SMA face sheets and triangular
  corrugated cores can be designed to operate
  against large restraining moments at relatively
  low weight relative to competing concepts.
• The triangular corrugation is attractive owing to
  its minimal rotational/bending resistance and
  high transverse shear stiffness

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References

• Allen, H.G., 1969. Analysis and Design of
  Structural Sandwich Panels. Pergamon Press,
  Oxford.
• Allen, H.G., Bulson, P.S., 1980. Background to
  Buckling. McGraw-Hill Ltd., London.

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• Thank you

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• Questions
• ?