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Ronny Calixto Carbonar iEmílio Car los Nelli Silva
DESIGN OF MULTI-ACTUATED PIEZOELECTRIC MICRO-TOOLS USING THE
TOPOLOGY OPTIMIZATION METHOD
DESIGN OF MULTI-ACTUATED PIEZOELECTRIC MICRO-TOOLS USING THE
TOPOLOGY OPTIMIZATION METHOD
Department of Mechatronics and Mechanical Systems EngineeringEscola Politécnica da Universidadede São Paulo - Brazil
Outline
Introduction to Micromanipulator Concept
Objective and Motivation
Topology Optimization Based on “CAMD” Approach
Formulation of the Micromanipulator Design Problem
Examples
Conclusions and Future Work
Introduction to Micromanipulator Concept
Objective and Motivation
Topology Optimization Based on “CAMD” Approach
Formulation of the Micromanipulator Design Problem
Examples
Conclusions and Future Work
Multi-Actuators Concept
Multi-flexible structure (compliant mechanism) actuated by two or more piezoceramics to generate uncoupled output displacements and
forces in different directions and specified points
Multi-flexible structure (compliant mechanism) actuated by two or more piezoceramics to generate uncoupled output displacements and
forces in different directions and specified points
• Amplify piezoceramic output displacement
• Change displacement direction• Provide stiffness (grabbing force)
Examples of Micromanipulators:
Multi-flexible structureMulti-flexible structure
Coupling Structure
Coupling Structure
Mechanical Transform
Mechanical Transform
Applications: microsurgery tools, MEMS, nanotechnology equipment, lens positioner for interferometers, electronic microscopy instruments
PiezoceramicsPiezoceramics
XY micromanipulatorobject
Motivation
Piezoelectric micro-actuators design is very complex since it is necessary to design a compliant mechanism that will generate
uncoupled movements when actuated by different piezoceramics.
Piezoelectric micro-actuators design is very complex since it is necessary to design a compliant mechanism that will generate
uncoupled movements when actuated by different piezoceramics.
Thus, it is difficult to design by using trial and error approaches
Thus, it is difficult to design by using trial and error approaches
Optimization MethodsOptimization Methods
Multi-Actuators Design
For each piezoceramic:• output displacement • blocking force
For each piezoceramic:• output displacement • blocking force
It depends on the distribution of
stiffness, flexibility in the coupling structure
it depends on topology!
It depends on the distribution of
stiffness, flexibility in the coupling structure
it depends on topology!
Design can be achieved
by using topology
optimization
Design can be achieved
by using topology
optimization
Multi-Actuators Design
Problem: coupling movementsProblem: coupling movements
x
y
∆y
∆xundesired ∆x
undesired ∆y
Objective
Changing couplingstructuretopology
Changing couplingstructuretopology
Novel designs of piezoelectric multi-actuators are obtained for different
applications
Novel designs of piezoelectric multi-actuators are obtained for different
applications
holes
To apply topology optimization based on “continuous approximation of material distribution” for designing the multi-flexible structure of piezoelectric multi-actuators
To apply topology optimization based on “continuous approximation of material distribution” for designing the multi-flexible structure of piezoelectric multi-actuators
object
?
Topology Optimization Procedure
Optimum topology
Mater ial Model for Topology Optimization
Continuous Approximation of Material Distribution (CAMD)Continuous Approximation of Material Distribution (CAMD)
x2
x1
Ω
solid (full material)
porous(intermediate material)
air(no material)
t
CouplingStructure
1
1y2
y1 unit cell
θa
b
PZT
Continuous distribution of material along the design domain is obtained by interpolating FE node density values inside each element.
0)( ExEH pρ=
( ) ( )= =
nnodes
iII N
1
xx ρρ
“SIMP” model
Reduces checkerboard
problem
PZT
x1
x3
Maximize output displacement
(U1)
Maximize output displacement
(U1)
Max (mean transduction)
Maximize blocking
force
Maximize blocking
force
Min (mean compliance)
trade-off
body
12 Qtφ
u3
PZT
U3
U1
Q1
F2=1
φ2
U3 t F3
F3=-1
Formulation of the Optimization Problem
Minimize undesired
displacement (U4)
Minimize undesired
displacement (U4)
Min (mean transduction)
14 Qtφ
Q1
U1(undesired) F4=1
For each piezoceramic:
Objective Function
Combining optimization problems:
Maximize:
MultiobjectiveFunction involving all mean compliancesand mean transductions
Subject to:
10 min <≤< nρρΩ Ω≤ s
=
Q
FU
KK
KK
U
UUUt
Flow Char t of the Optimization Procedure
Initializing anddata input
Initializing anddata input
Calculating (FEM)Mean Transduction
and Mean Compliance
Calculating (FEM)Mean Transduction
and Mean Compliance
Calculating objective function and constraints
Calculating objective function and constraints
Initially
Converged?Plotting resultsPlotting results
Calculating sensitivity
Calculating sensitivity
Optimizing (SLP) with respect to ρ
Optimizing (SLP) with respect to ρ
Updating mater ial distr ibution (design
var iables)
Updating mater ial distr ibution (design
var iables)
Final Topology
N
Y
PZT
PZT
Example - XY nanopositioner
∆uA
Aluminum
x
y With coupling Minimizing coupling
deformed
undeformed
(symmetry constraint)
ϕ
11φ
21φ
%35=Ω s
Excitation by voltage
u/ucoupled=11,3u/ucoupled=11,3 u/ucoupled=111,2u/ucoupled=111,2AFM tip support
Example - XY nanopositioner
With coupling Minimizing coupling
u/ucoupled=2,0u/ucoupled=2,0 u/ucoupled=55,1u/ucoupled=55,1
(symmetry constraint)
Excitation by voltage
∆uA
Aluminum
x
y
11φ
21φ
3 0 %sΩ =
deformed
undeformed
Load Cases for Piezoceramic (1)
Calculation of mean
compliance
Calculation of mean
transductionfor y
displacement(undesired)
Calculation of mean
transductionfor x
displacement
Aluminum
F21=1
Aluminum
Q11
A
Aluminum Aluminum
F31=- F2
1F4
1=-F21=1
A A
Example – Piezoelectr ic Gr ipper
Q11
Q12
Q13Aluminum
Optimal topologies ( )Optimal topologies ( )%30=Ω s
FEM verification of interpreted resultFEM verification of interpreted result
X movement Y movement Jaw movement
Minimizing couplingMinimizing coupling
Example – Four-piezo micromanipulator
Optimal topology ( )Optimal topology ( )%35=Ω s
X movement Y movement Open/close movement
Q11
Q12
Q13
Q14 Aluminum
PZT
PZT
PZT PZ
T1
3
Rotation movement
Results – Actuator Piezoelectr icConsidering:• V = 20%;• 2000 finite elements;• p = 3.0;• w = 0.8;• d1 = 1 µC/m2.
PZT
Design DomainDesign Domain Optimal TopologyOptimal Topology
Deformed of Optimal TopologyDeformed of Optimal TopologyManufactured
Actuator
Manufactured Actuator
Conclusions and Future Work
• Design of novel and complex microtoolscan be achieved by applying Topology Optimization Method which is a systematic method that allows us to design complex micromanipulators with uncoupled movements and good performance in a short term;• Continuous density approach seems to be more robust and provided more clear results than a previous implementation based on the homogenization design method.
• Design of novel and complex microtoolscan be achieved by applying Topology Optimization Method which is a systematic method that allows us to design complex micromanipulators with uncoupled movements and good performance in a short term;• Continuous density approach seems to be more robust and provided more clear results than a previous implementation based on the homogenization design method.
• Manufacturing and testing of prototypes in meso and micro scale (MEMS);
• Manufacturing and testing of prototypes in meso and micro scale (MEMS);
Acknowledgments
Centro Nacional de Desenvolvimento Científico e Tecnológico
Laboratór io Nacional de Luz Síncrotron(Laboratório de Microfabricação)
[email protected] [email protected]
(Doctoral Scolarship)
F2=1
φ2
PZT
Formulation of Mean Transduction
Applied chargeApplied charge
Dummy tractionDummy traction
L2(u1,φ1) Displacement at region Γt2 due to the input electrical charge at the electrode.
L2(u1,φ1) Displacement at region Γt2 due to the input electrical charge at the electrode.
Q1
U1
PZT
Mean transduction: L2(u1,φ1)= U1 t F2 = φ2 t Q1
Formulation of the Optimization Problem
Piezoelectric micromanipulator load cases
Case 1(Maximize
outputdisplacement)
Case 2(Maximizeblocking
force)
Case 3(Minimize undesired
displacement)