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)

ronny@usp.br ecnsilva@usp.br

(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)