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Calculating a piezo flexural resonator
ACUM 2014, Nürnberg
Qualification Laboratory Regensburg
Mechanical Simulation – Finite Element Method
Public
Qualification Laboratory Regensburg
Mechanical Simulation – Finite Element Method
Welcome
5 June 2014
2 Jürgen Heine, © Continental AG
A few words to introduce myself
Name: Jürgen Heine
Company / Continental, QL RBG
Department: Reliability Engineering / Simulation
Responsibility: Central Service Mechanical Simulation,
Finite Element Method
FEM-areas: structural analysis linear and non-linear
static and dynamic
stationary and transient
fatigue, magneto static, thermal, creep etc.
Contact: Osterhofener Str. 14
93055 Regensburg
Phone +49 941 790 5860
Fax +49 941 790 99 5860
Email [email protected]
Public
Qualification Laboratory Regensburg
Mechanical Simulation – Finite Element Method
Content
5 June 2014
3 Jürgen Heine, © Continental AG
Continental Corporation
- Overview
- Central Service Mechanical Simulation
Calculating a piezo flexural resonator
- APDL commands for material definition, load and results
- restrictions for voltage results and work around
- ACT (Application Customization Toolkit) for piezo
Public
Qualification Laboratory Regensburg
Mechanical Simulation – Finite Element Method
Continental Corporation Overview 2013
5 June 2014
4 Jürgen Heine, © Continental AG
Chassis & Safety 22%
Powertrain 19%
Interior 20%
Tires 28%
ContiTech 11%
Sales by division in %
Status: December 31, 2013
› Since 1871 with headquarters in Hanover, Germany
› Sales of €33.3 billion
› 177,762 employees worldwide
› 300 locations in 49 countries
Public
Qualification Laboratory Regensburg
Mechanical Simulation – Finite Element Method
Continental Corporation Five Strong Divisions
5 June 2014
5 Jürgen Heine, © Continental AG
Chassis &
Safety
Vehicle Dynamics
Hydraulic
Brake Systems
Passive Safety &
Sensorics
Advanced Driver
Assistance Systems
(ADAS)
Powertrain
Engine Systems
Transmission
Hybrid Electric
Vehicle
Sensors &
Actuators
Fuel Supply
Interior
Instrumentation &
Driver HMI
Infotainment &
Connectivity
Body & Security
Commercial Vehicles
& Aftermarket
Tires
PLT, Original
Equipment
PLT, Repl. Business,
EMEA
PLT, Repl. Business,
The Americas
PLT, Repl. Business,
Asia Pacific
Comercial Vehicle
Tires
Two Wheel Tires
ContiTech
Air Spring Systems
Benecke-Kaliko
Group
Compounding
Technology
Conveyor Belt
Group
Elastomer Coatings
Fluid Technology
Power Transmission
Group
Vibration Control
BU activities R&D
BU activities Production
in Regensburg located Division-Heads
in Regensburg located Business Unit-Heads
Public
Qualification Laboratory Regensburg
Mechanical Simulation – Finite Element Method
Data & Facts
Qualification Laboratories / EMC* & Reliability Services Reliability by design
5 June 2014
6 Jürgen Heine, © Continental AG
Performance EMC/Reliability-Engineering
› Design and concept analysis
› Components choice under EMC/REL-Aspects
› Simulation
› Risk Analysis
› Design guidelines
› Test plan creation (QV)
› Acoustic and Vibration measurement in the vehicle (NVH)
Performance EMC/Reliability-Laboratory
› DIN EN ISO IEC 17025 accredited Reliability laboratory
› EMC/Reliability tests and DV-/PV-EMC tests
› Automotive-specific tests
› Business overlapping service provider for all projects
› Development and setup of operational life span and EMC
loadboxes
EMC - Laboratory and Engineering
Commissioning 1996
Area (sqm) 1,600
Staff members 36
Reliability - Laboratory and Engineering
Commissioning 1984
Area (sqm) 2,400
Staff members 35
* EMC - Electromagnetic Compatibility
Public
Qualification Laboratory Regensburg
Mechanical Simulation – Finite Element Method
Examples
5 June 2014
7 Jürgen Heine, © Continental AG
Daily work:
detect the natural frequencies on
injector-pipes, pump-pipe, bench-pipes
etc.
qualitative analysis, detailed
interpretation - insight into how the
values of stress and strain in the vias
are change during temperature cycles,
especially for maximums and by
comparison of different via diameters,
PCB-thickness and thickness of copper
coating
reaction force and stress in the PCB
resulting from e. g. temperature load,
especially on critical components or screw
joints. Also modes, frequency and
acceleration response, resulting stress
and strain due to vibration load.
sensor assembly - stress and
strain at all parts due to
traction forces in different
directions at the main power
supply line
design study - stress and strain
at a mounting clip, comparison
of designs
stress on PCB/components
during pressfit insertion (plug
pins)
card bending test1, aim of
analysis was an
estimation of stress and
strain levels on PCB to
estimate the risk of solder
damage under bending
test condition.
mechanical design of bracket -
spectrum analysis / fatigue
calculation
vibration fixtures - weakness of critical modes
deformation, reaction force, stress, strain, tightness (sealing), temperature distribution,
modes, resonance frequencies, harmonic response, system behavior, fatigue …….
deformation, force/ pressure, temperature,
acceleration (sinus sweep/PSD) …
Public
Qualification Laboratory Regensburg
Mechanical Simulation – Finite Element Method
Examples
5 June 2014
8 Jürgen Heine, © Continental AG
removing Cu-Oxid by melting on
with laser, calculate heating around
laserpoint
stress, strain, relaxation and
strain creep behavior of
solder joints during
temperature cycling,
comparison of slow and rapid
temperature change
shunt – deformation due
to power dissipation
VISHAY / KOA /
ISABELLENHÜTTE
NOx-sensor - deformation in connector
pin area due to temperature load
several analyses - deformation due to
temperature change (-40°C - 140°C), stress in
sensors / thermal transient analysis -
temperature during soldering of sensors,
deformation of solder points, bonding process
Special tasks:
complex assemblies, solder-creep, multiphysics, magnetostatic, piezo
coil– magnetostatic
field, e.g. magnetic flux
density, transient
magnetic fields
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Qualification Laboratory Regensburg
Mechanical Simulation – Finite Element Method
Piezo
5 June 2014
9 Jürgen Heine, © Continental AG
Blei-Zirkonat-Titanat
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Qualification Laboratory Regensburg
Mechanical Simulation – Finite Element Method
Measurement
5 June 2014
10 Jürgen Heine, © Continental AG
Measurement results to following values:
Frequency: ~ 14.000 – 14.600Hz
Amplitude: ~ 6µm (max.)
Voltage: ~ 12,0 - 14,6V (max., hanging free)
Public
Qualification Laboratory Regensburg
Mechanical Simulation – Finite Element Method
Model
5 June 2014
11 Jürgen Heine, © Continental AG
Harmonic response / frequency response
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Qualification Laboratory Regensburg
Mechanical Simulation – Finite Element Method
Material Data Sheet
5 June 2014
12 Jürgen Heine, © Continental AG
Public
Qualification Laboratory Regensburg
Mechanical Simulation – Finite Element Method
Material Matrices
5 June 2014
13 Jürgen Heine, © Continental AG
Example: Material matrices for PZT
elastic compliance or stiffness piezoelectric
stress or strain
permittivity at constant
stress or strain
elastic compliance
Piezoelectric stress
permittivity at constant stress
Public
Qualification Laboratory Regensburg
Mechanical Simulation – Finite Element Method
Material Data via EXCEL-Sheet
5 June 2014
14 Jürgen Heine, © Continental AG
TB,PIEZ,matid,,,1
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Qualification Laboratory Regensburg
Mechanical Simulation – Finite Element Method
Material Input
5 June 2014
15 Jürgen Heine, © Continental AG
esel,s,mat,,matid !select all elements with actual mat ID
*get,enum,elem,,count !get number of selected elements
*dowhile,enum !change all elements to type 226 (186+40)
*get,etyp,elem,elnext(0),attr,type ! PIEZOELECTRIC AXISYMMETRIC ELEMENT TYPE
*get,enam,etyp,etyp,attr,enam
et,etyp,enam+40,1001
esel,u,type,,etyp
*get,enum,elem,,count
*enddo
alls
mpdel,all,matid !delete all mat data and temp
tdel,all,matid
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Qualification Laboratory Regensburg
Mechanical Simulation – Finite Element Method
Material Input
5 June 2014
16 Jürgen Heine, © Continental AG
/PREP7
mp,dens,matid,RHO
mp,rsvx,matid,RESIS ! resistivity
mp,LSST,matid,17e-3 ! dielectric loss tangent
TB,ANEL,matid,,,1 ! ANISOTROPIC ELASTIC COMPLIANCE MATRIX
TBDA,1,S11,S13,S12
TBDA,7,S33,S13
TBDA,12,S11
TBDA,16,S44
TBDA,19,S44
TBDA,21,S66
TB,PIEZ,matid,,,1 ! PIEZOELECTRIC STRAIN MATRIX
TBDA,2,D31
TBDA,5,D33
TBDA,8,D31
TBDA,10,D15
TBDA,15,D15
TB,DPER,matid,,,1 ! DIELECTRIC REL PERMITTIVITY AT CONST STRESS
TBDA,1,EP11,EP33,EP11
/COM, -- MATERIAL MATRICES (POLAR AXIS ALONG Y-AXIS): Mechanical APDL INPUT
/COM,
/COM, [s11 s13 s12 0 0 0 ] [ 0 d31 0 ] [ep11 0 0 ]
/COM, [s13 s33 s13 0 0 0 ] [ 0 d33 0 ] [ 0 ep33 0 ]
/COM, [s12 s13 s11 0 0 0 ] [ 0 d31 0 ] [ 0 0 ep11]
/COM, [ 0 0 0 s44 0 0 ] [d15 0 0 ]
/COM, [ 0 0 0 0 s44 0 ] [ 0 0 d15]
/COM, [ 0 0 0 0 0 s66] [ 0 0 0 ]
/COM, COMPLIANCE COEFFICIENTS, M2/N
S11=1.6E-11 !sE11
S12=-7.7E-12 !sE12
S13=-6.9E-12 !sE13
S33=1.8E-11 !sE33
S44=4.52E-11 !sE44
S66=5.15E-11 !sE66
/COM, PIEZOELECTRIC STRAIN COEFFICIENTS, C/N
D15=5.5E-10 !d15
D31=-1.95E-10 !d31
D33=4.6E-10 !d33
/COM, REL PERMITTIVITY AT CONSTANT STRESS
EP11=1650 !KT11 senkrecht zur Polungsrichtung
EP33=1850 !KT33 in Polungsrichtung
/COM, DENSITY, KG/M3
RHO=7900
/COM, RESISTIVITY, ohm
RESIS=1E12
Public
Qualification Laboratory Regensburg
Mechanical Simulation – Finite Element Method
Boundary Condition / Load
5 June 2014
17 Jürgen Heine, © Continental AG
/prep7
*do,i,1,3
cmsel,s,piezo%i% !select voltage areas
cp,next,volt,all !couple voltage areas
nf%i%=ndnext(0) !master node nf1-nf3
d,nf%i%,volt,arg%i% !voltage to master node as defined
*enddo
allsel
! Command for load definition, insert after boundary condition
! define boundary condition
! define components (areas) for electric potential
! Argumente arg1, arg2 … are defining the potential values
! ddel,nf1,volt
! ddel,nf2,volt
ddel,nf3,volt ! delete potential definition -> RESULT area
outres,erase
outres,all,all
/solu
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Qualification Laboratory Regensburg
Mechanical Simulation – Finite Element Method
Results - Deformation
5 June 2014
18 Jürgen Heine, © Continental AG
Public
Qualification Laboratory Regensburg
Mechanical Simulation – Finite Element Method
Frequency Response
5 June 2014
19 Jürgen Heine, © Continental AG
Public
Qualification Laboratory Regensburg
Mechanical Simulation – Finite Element Method
Results Definition
5 June 2014
20 Jürgen Heine, © Continental AG
set,1
my_volt11=volt(nf1) !Voltage at master node 1
my_volt21=volt(nf2)
my_volt31=volt(nf3)
Command to get the voltage for a pre-defined set!
! define components (areas) for electric potential
Public
Qualification Laboratory Regensburg
Mechanical Simulation – Finite Element Method
Problems With Voltage Results
5 June 2014
21 Jürgen Heine, © Continental AG
Evaluation depends on frequency and phase angle
Result print for frequency response depends on
stress, strain, deformation or acceleration
not on VOLT!
Maximum VOLTAGE are not necessarily occur on maximum stress, strain etc.
Own evaluation with imaginary values -> APDL Command
Public
Qualification Laboratory Regensburg
Mechanical Simulation – Finite Element Method
/post26
alls
nsol,2,node(0,3e-4,0),VOLT ! In Variable 2 Ergebniswerte VOLT ueber Zeit einlesen
prcplx,1 ! Komplexer Zahlenbereich eingestellt
prvar,2
!Tabelle mit Ampl-Phase als spg-phase-tabelle.txt im Solververzeichnis speichern
/output,spg-phase-tabelle,txt
prcplx,1
prvar,2
/output
!max Spannung als Variable
VGET,zeit,1, ,0
VGET,real_werte,2, ,0 !Real
VGET,imag_werte,2, ,1 !Imaginaer
VGET,calc1_werte,2, ,0 !Real
VGET,calc2_werte,2, ,1 !Imaginaer
!Aus imaginär und real teil muß die Amplitude berechnet werden a=sqrt(b^2+c^2)
*voper,calc1_werte(1,1),real_werte(1,1),mult,real_werte(1,1) !Realwerte quadrieren
*voper,calc2_werte(1,1),imag_werte(1,1),mult,imag_werte(1,1) !Imaginärwerte quadrieren
*voper,calc1_werte(1,1),calc1_werte(1,1),add,calc2_werte(1,1) !Addition der quadrierten Werte
*vfun,calc1_werte(1,1), sqrt,calc1_werte(1,1) !Wurzel aus .. -> Amplitude
*voper,calc2_werte(1,1),imag_werte(1,1),ATN2,real_werte(1,1) !arctan aus imag/real
*voper,calc2_werte(1,1),calc2_werte(1,1),mult,180 !für Grad *180 / PI
*voper,calc2_werte(1,1),calc2_werte(1,1),div,3.141592654
!Mit *vscfun ermittle ich erst den Maximalwert und die Zeile in der der Maximalwert steht.
!Danach lese ich noch die Zeit und den Realwert aus.
*VSCFUN,i_max,MAX,calc1_werte(1,1)
*VSCFUN,zeile,LMAX,calc1_werte(1,1)
max_zeit_=zeit(zeile,1)
max_ampl_=calc1_werte(zeile,1)
max_phas_=calc2_werte(zeile,1)
APDL Skript – Voltage Evaluation
5 June 2014
22 Jürgen Heine, © Continental AG
/com,+++++++++++++++++++++++++++++++++++
/com, max bei f=%max_zeit_%
/com, Real = %max_ampl_% Phase = %max_phas%
/com,+++++++++++++++++++++++++++++++++++
my_max_zeit=max_Zeit_
my_max_ampl=max_ampl_
my_max_phas=max_phas_
/show,png
!/gropt,logy,on
/axlab,x,FREQ HZ
/axlab,y,VOLT V
/color,curve,red,1
/title,Amplitude
plvar,2
plcplx,1
/title,Phase
/axlab,y,Phasenwinkel
/gropt,logy,off
plvar,2
/show,term
generate graph
Public
Qualification Laboratory Regensburg
Mechanical Simulation – Finite Element Method
APDL Skript - Results
5 June 2014
23 Jürgen Heine, © Continental AG
Public
Qualification Laboratory Regensburg
Mechanical Simulation – Finite Element Method
APDL Skript - Results
5 June 2014
24 Jürgen Heine, © Continental AG
Public
Qualification Laboratory Regensburg
Mechanical Simulation – Finite Element Method
ACT – Install And Use
5 June 2014
25 Jürgen Heine, © Continental AG
Customer Portal – zip-File Download
Installing from WB Project page:
1. Select the “Install Extension …” option
2. It will open a file dialog to select a “*.wbex” file
3. The extension is installed
ACT - Application Customization Toolkit
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Qualification Laboratory Regensburg
Mechanical Simulation – Finite Element Method
ACT – Material Data
5 June 2014
26 Jürgen Heine, © Continental AG
mp,rsvx,matid,RESIS
mp,LSST,matid,17e-3
RESISTIVITY, ohm
electric loss tangent
7,91662E-9 / 8,854E-12 =
894,129
Public
Qualification Laboratory Regensburg
Mechanical Simulation – Finite Element Method
ACT – Material Data
5 June 2014
27 Jürgen Heine, © Continental AG
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Qualification Laboratory Regensburg
Mechanical Simulation – Finite Element Method
ACT – Boundary Condition
5 June 2014
28 Jürgen Heine, © Continental AG
voltage includes coupling!!!
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Qualification Laboratory Regensburg
Mechanical Simulation – Finite Element Method
ACT – Boundary Condition
5 June 2014
29 Jürgen Heine, © Continental AG
voltage coupling for
voltage output area !!!
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Qualification Laboratory Regensburg
Mechanical Simulation – Finite Element Method
ACT - Results
5 June 2014
30 Jürgen Heine, © Continental AG
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Qualification Laboratory Regensburg
Mechanical Simulation – Finite Element Method
General Findings
5 June 2014
31 Jürgen Heine, © Continental AG
Check element size – mesh should be fine enough!
Position and size of solder joints are significantly for
resonance frequency and damping!
Silver conductive has clearly influence to results (stiffness, damping)!
System damping are a main factor for voltage results!
Resistance of piezo material (RESIS) has no (or less) influence to results!
Public
Qualification Laboratory Regensburg
Mechanical Simulation – Finite Element Method
Common Notes
5 June 2014
32 Jürgen Heine, © Continental AG
Be careful with the unit system!
Define coupled voltage areas with master node!
Dynamic analysis - all contacts bounded (linear)!
Check material data in case of strange results!
Use ACT with English language (WB/Tools/Option/Regional and Language Options)
ACT is a Beta option
Include Stiffness matrix in matdat area
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Qualification Laboratory Regensburg
Mechanical Simulation – Finite Element Method
Thank you!
33
5 June 2014
Jürgen Heine, © Continental AG