FEM Analysis of a 2D Frame with a combination of Beam and Bar Elements

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Project Number PS 1.3 Development of a Smart
Materials Based Actively Conformable Rotor
Airfoil PIs Prof. Farhan Gandhi
Prof. Mary Frecker
Graduate Student Andrew Nissly Penn State
University 2005 NRTC RCOE Program Review May 3-4,
2005
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Background/ Problem Statement

• Develop analysis and design method for
  conformable rotor airfoil
• achieve significant deformation required to
  reduce rotor vibration at N/rev
• can be viewed as the successor to rotor blade
  trailing-edge flaps
• advantage integral structure (no hinges,
  linkages, etc.)

Deformable skin
Conformable Airfoil
Trailing Edge Flap

• Technical Barriers
• Smart actuation must have required authority
  (under airloads) and bandwidth
• weight, volume, and power constraints
• Airfoil cross-section traditionally designed NOT
  to undergo any deformation
• a fundamental change in design philosophy is
  required for conformable airfoil
• reduction in cross-section stiffness is required
  
• Large local surface strains in the skin due to
  shape change require novel materials
• Highly-specialized sandwiched composite skins

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• Task Objectives
• Develop design methodology for a conformable
  (controllable camber)
• rotor airfoil using a passive substructure and
  a limited number of actuators
• Meet specified trailing edge deflection
  
  (camber)
• Withstand aerodynamic loads
• Consider volume (weight) constraint

Concept presented at 2004 review

• Approach
• Shape optimization starting with passive
  structure of predetermined topology actuated by
  limited number of piezo actuator elements
• max trailing edge vertical deformation (camber)
  while withstanding airloads
• FEA-based optimization method, gradient-based
  solution method

• Expected Research Results or Products
• Develop new design methodology and obtain
  solution(s)
• Demonstrate feasibility of a smart-materials
  based conformable rotor airfoil
• controllable camber
• flexible skin sections to allow large local
  strains
• Develop a thorough understanding of the physical
  issues in this design
• Build and evaluate demonstration prototype

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Numerical Testbed

• Rotor Airfoil (NACA 0012)
• Chord length C 1.66 ft (50 cm)
• Maximum Thickness 12 chord
• Rigid Spar from LE to 25 Chord
• Only aft portion is actuated and flexible
• High EI, low EA skin

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Conformable Airfoil Actuation Mechanism
Active Vertical Members (Actuators)
Point Moves up-down as actuators extend/shrink
A Cellular Truss Mechanism
Passive Linkage
Left active member restrained in vertical
position exaggerated rotation of right active
member
Deformed Configuration
-- Top Skin Extends -- Bottom Skin Shrinks
Accumulation of rotation, Build-up of camber
Array of such units along the airfoil chord ?
Limited number of actuators required, Easy to
Build
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Design Domain Parameterization

• Shape Optimization
• Thickness of passive elements
• 0 lt tlower lt ti lt tupper

ti

• Passive Material Area Constrained to of Amax

-V (Contraction)
Piezoelectric Elements
Passive Elements
V (Extension)
Skin Elements
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Optimization Problem

• Objective function
• Maximize Tip Deflection (TD) under actuation
  load
• Minimize deflection under air load
• Air load unchanged with changes in airfoil shape
• Two objective functions considered

TD
J1 Tip Deflection (TD)
J2 wT K w Strain Energy (SE)
Kw fair
Single-criteria objective function Max (J) J1
TD
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Sample Optimized Geometry Comparison of Two
Objective Functions
TD Objective Function
Ratio Objective Function
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Comparison Of Objective Functions Actuation
Deflection

• DActuation ? with ? Amax using the TD objective
  function
• DActuation ? with ? Amax using the Ratio
  objective function
• DAirload ? with ? Amax for both objective
  functions

Actuation Deflection (mm)
Airload Deflection (mm)
X/Y ()
X/Y ()
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Effect of Actuator Thickness

• DActuation ? with ? actuator thickness for both
  objective functions
• Increase in DActuation is smaller for the TD
  objective function because the passive structure
  is less rigid and the actuators are already
  operating close to their free strain
• DAirload ? slightly with ? actuator thickness
  for both objective functions

Actuation Deflections
Deflection (mm)
Ratio Objective Function
TD Objective Function
Airload Deflections
Actuator Thickness (mm)
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Discussion Conclusions

• Choice of optimal design
• Ratio objective function gives solutions with
  very low airload deflections.
• TD objective function solutions have a higher
  airload deflection, however the actuation
  deflection is considerably higher
• Displacement of 68 mm under actuation achieved
  using four compliant mechanism units
• 18-22 change in lift (calculated using X-FOIL)

Best choice is an airfoil optimized using the TD
objective function where the deflections due to
the airloads are constrained by an upper limit.
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Prototype design
Wire EDM Machining

• Main Structure 6061-T6 Aluminum (Fatigue
  Strength 95 MPa)
• 10 PICA-Thru Piezo Stack Actuators P-010.20H

Pro-Engineer Model
Prototype Part
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Actuator Selection
Physik Instrument Tubular Piezo Stack Actuator
P-010.20H Length 27 mm, OD 10 mm, ID 5
mm Blocking Force 1800 N Max Voltage 1000
V Advertised Displacement at 1000 V 30
µm Measured Displacement at 1000 V 25-30 µm
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ANSYS Finite Element Analysis
Active Elements

• Maximum Stress in Flexures
• 35 MPa lt 95 MPa Fatigue Strength
• Predicted Deflections
• MATLAB Code 5.6 mm
• ANSYS 4.0 mm

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Skin Design Camber under Actuation Loads
Moment applied at this section
   
   
M 200 N-m/m span
(Low actuation load)
Deformations due to aerodynamic loads lt 1o
Decrease skin EA ? more camber Change in EI ?
less effect (unless baseline EI was very high)
aEI
Skin bubbling
aEA
EI increased by factor of 10 EA reduced by factor
of 100
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Camber under Moderate Actuation Loads
M1 400 N-m/m span
M2 800 N-m/m span
aEI
aEI
Deformations due to aerodynamic loads lt 1o
Buckling boundary under actuation loads
SBB
SBB
aEA
aEA
If skin has low EA, as actuation load increases,
need higher EI to avoid buckling
If EA reduced by factor of 50, and EI increased
by factor of 600 Camber of 3o for M1 Camber of
6o for M2
Camber due to air loads lt 1o
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Skin Design Conclusions
Process used is analogous to inverse design What
should the properties of the skin be? .such
that -- global (camber) deformations under air
load are not excessive -- local deformations due
to surface pressure are not significant (no
skin bubbling) -- local sections do not buckle
under actuation loads -- actuation forces are not
excessive for a desired camber The process
followed gives us EA, EI, and max strain specs We
can then go about designing a composite skin
using these specs
Low Modulus (silicone) face-sheets
Spacer Flex-Core (Foam?)
Composite Skin has low EA, but high EI, and can
undergo high max strains
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• Accomplishments since the last (2004) review
• Shape optimization of series of compliant
  mechanisms within airfoil
• - Examined effects of passive material
  constraint, mechanism geometry, and actuator
  thickness
• Started construction of a bench-top model
• Optimized skin properties to avoid buckling and
  localized transverse deflections under surface
  pressure loading while keeping actuation
  requirements low

• Planned Accomplishments for the remainder of 2005
• Complete prototype and conduct bench-top test
• Optimization using dynamic analysis

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• Technology Transfer Activities
• Paper accepted for publication in the 2005 AHS
  Forum 61 Proceedings
• Presented paper at 2004 ASME Design Engineering
  Technical Conference, Salt Lake City, Utah
• Presented paper at The 15th International
  Conference on Adaptive Structures and
  Technologies, October, 2004, Bar Harbor, Maine

• Recommendations at 04 review
• The task is a tough problem and shows
  potential, but needs to look at skin structures
  as to whether it is practical.  It is appreciated
  to pay attention to last year comments.  The task
  is unique, however potential payoff or
  practicality is debatable.

• Actions Taken
• Completed comprehensive study of optimal skin
  properties
• Completed detailed design of practical design
• Demonstration prototype has been constructed and
  will be evaluated in the lab under quasi-static
  and dynamic operating conditions

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Overall Accomplishments of Task 1.3

• Developed finite element models and optimization
  algorithms for trailing edge camber control
• Topology optimization
• Geometry optimization
• Concurrent optimization
• Calculated Lift/Drag increment of optimized
  designs using XFOIL
• Developed a shape optimization method for simpler
  design
• Studied flexible skin designs
• Developed practical actuation system
• Built prototype and bench-top testing

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Forward Path

• Demonstrated that a controllable camber airfoil
  can be designed and fabricated.
• Controllable camber, as a rotor morphing concept,
  is ready to move to CRI (formerly RITA) or other
  6.2 type activity.  The lessons learned and
  experiences gained can be used in industry-type
  development and testing activities.
• The lessons learned on how to design structures
  compliant to actuation loads, stiff to
  aerodynamic loads, with deformable skins, and
  requiring modest actuation efforts, should be
  applied to other rotor morphing concepts.
• Of particular interest to us (and we will propose
  as an RCOE renewal task) is the use of bistable
  mechanisms for control of blade twist and blade
  chord in the outboard regions. Bistable
  mechanisms provide large stroke with small
  actuation effort.