manfred kaltenbacher department of sensor technology ... · overview: piezoelectricity manfred...
TRANSCRIPT
Overview: Piezoelectricity
Manfred Kaltenbacher
Department of Sensor Technology, University Erlangen-Nuremberg
Outline• Department of Sensor Technology• Basics
• Piezoelectric effect• Piezoelectric equations• Piezoelectric materials
• Finite Element Formulation• Weak form• Spatial and time discretization• Solvers for the algebraic system of equations
• Material parameter determination• Experimental methods• Invers scheme
Location
DepartmentProf. Dr.-Ing. Reinhard Lerch
SecretaryC. Salley-Sippel
Simulation/DesignPD Dr. M. Kaltenbacher
AdministrationB. Melberg
MeasurementPD Dr. M. Kaltenbacher
Dr. A. Sutor
G. Link
A. Sutor
K. BauderM. Pelz
J. StrobelL. BahrM. GüntherM. Meiler
B. Baffoun
TechnologyDr. A. Sutor
N. BretzM. Bezdek
T. HegewaldA. Streicher
U. BollertM. Escobar
C. Hahn
M. MohrT. Lahmer
Research GroupPD Dr. B. Kaltenbacher
A. Hauck
E. Leder
Overview: Piezoelectricity
• Basics
• Finite Element Formulation
• Material Parameter Determination
Piezoelectric Effect
• Direct effect (sensor)
• Indirect effect (actuator)
Governing Equations
• Constituitive equations
• Piezoelectric materials can be subdivided in the followingthree categories
• Single crystals, like quartz
• Piezoelectric ceramics like barium titanate or lead zirconate
• Polymers like PVDF (polyvinylidenfluoride)
Tensors for 6mm Crystal Class
Polarization / Strain versus Electric Field Intensity
Overview: Piezoelectricity
• Basics
• Finite Element Formulation
• Material Parameter Determination
Coupled Equations (I)
• Mechanical field (Navier‘s equation)
• Electrostatic field (Maxwell‘s equations)
Coupled Equations (II)
• Constituitive equations
• Coupled equations
• Boundary conditions
Finite Element Formulation (I)• Weak form: Find such that
for any
• Spatial approximation Nodal shape function(local support)
Finite Element Formulation (II)
• Semidiscrete Galerkin formulation:
• Introduced damping via Rayleigh model:
Finite Element Formulation (III)
• Time discretization: Newmark method
• Choice of integration parameters:• Explicit: Stability depends on mesh size, material parameters
makes just sense for piezoelectic-structure interactionexplicit/implicit splitting
• Implicit: 2nd order accurate
Algebraic Solver (I)
• Static case
• Harmonic case
Neagtiveeigenvalues
Algebraic Solver (II)
• GMRES-solver (General Minimal Residual)
• ILDL(k)-preconditioner (Incomplete LDL-decomposition with fill-in level k)
7
6
5
4
3
2
1
1
0
0no precond
k = 1k = 2k = 3k = 4k = 5
0 5 10 15 20 25 30Iteration number
1001011E-11E-21E-31E-41E-51E-61E-7
2-no
rm o
f res
idua
l
Algebraic Solver (III)
• Dependency of iteration number on problem size
10
30
50
70
90
A B C D
n
k = 1k = 2
A: 36.519 B: 77.696 C: 300.243 D: 618.403
Overview: Piezoelectricity
• Basics
• Finite Element Formulation
• Material Parameter Determination
Simplification to the one-dimensional case, direct relation betweenresonance frequencies and coefficients
State of the Art
• Test samples with special geometries: (IEEE Standard)
• Example: thickness resonantor
Identification of Material Parametersby Simulation of the Full System
Find material tensors
c , e , εfrom measured impedance
E S
Equipment for characterization of linear and nonlinear material properties
Combined measurement methods for accuratepiezoelectric material parameters
linear nonlinearelectricalimpedance
pulse response
mechanicaldisplacement
force
acousticalpulse echoe
Impedance / gain-phase analyzer
Ritec SNAP: two 5kW-pulse amplifiers with receivers
measurements
differential fibreinterferometer
500W CW RF-amplifier
100kN materialstesting machine
Measurement setupAutomated setup for impedance measurement
Contacting phase
- X-positioning of the spring contactpair Lc-Lp for contact force
- Testing contact resistance withconstant current
sample
Hc
Hp
Lc
Lplinear stage
Measuring sequence
- Contacting phase for theshort/open circuit
- Measurement for calibration
- Contacting phase for thepiezo sample
- Material measurement(V0=1Veff)
Auto balancing bridge
virtual ground
Material configuration
7 mm
7 mm32.5 mm
layers:200
material: the same as the bulk samples
not within the IEEE range because width > 5 * thickness is not fulfilled
Finite element model
Bulk samples– PZT disc (radial and thickness mode)thickness: 0.43 mm, radius: 6.35 mm– PZT strip (transversal mode)thickness: 0.43 mm, length: 11.03 mm, width: 2.44 mm
Device sample: stack actuator of a CR-injector application
12.70 mm
thickness: 0.43 mm
Results (1)
PZT disc – fitted impedance curves
2 3 4 5 6 7 8
x 106
100
101
102
|Z|
Hz
MessungApproximationAusgang
0 1 2 3 4 5 6
x 105
100
101
102
103
104
105
Hz
|Z|
MessungApproximationAusgang
measurementforward simulation with fitted material parametersforward simulation with IEEE material parametersdata for the vector of measurements
radial mode thickness mode
100
101
102
(MHz)8765432
|Z| (Ω)
100 200 300 400 500(kHz)
104
105
100
101
102
103
|Z| (Ω)
y
0.8 1 1.2 1.4 1.6 1.8 2
x 105
102
103
104
MessungApproximationAusgang
Hz
|Z|
|Z| (Ω)
104
103
102
(MHz)1.00.8 1.2 1.4 1.6 1.8
Results (2)
PZT strip – fitted impedance curves
y
transversal mode 11.03 mm
2.44 mm
thickness: 0.43 mm
measurementforward simulation with fitted material parametersforward simulation with IEEE material parametersdata for the vector of measurements
Results (3)
Stack actuator (based on results of raw material)
2 3 4 5 6 7 8
x 104
10-2
10-1
100
101
102
Frequency (Hz)
|Z| (
Ohm
)Impedance Stack, 200 Layers
Measurement
Simulation
Applications
• Medical diagnostic, nondestructive testing
Acoustic lens
Focal areaUltrasonic beam
Transducer element
Backing
Scanning direction
Matching layer
Applications
• Surface acoustic wave devices (mobile phones, television)
Puls compression filter (43 MHz)
Resonator (1 GHz)
Origin: Siemens
Sensor for wheel pressure
WLAN
Applications
• High intensity ultrasound: e.g. lithotripsy
Applications
• High intensity ultrasound: e.g. cleaning
Applications
• Stack actuators (common-rail injection systems)
Inner electrodes
Single ceramic layer
Thickness: 30-200µmNumber : till 1000 layers
Thank you foryour attention