How to get the linearity in frequency response of piezoelectric transducer?

- October 26, 2022 at 4:06 pm
  
  safiana
  Subscriber
  
  I am trying to model a piezoelectric sensor in ANSYS and I would like to get the frequency response of the sensor to calculate its usable frequency range and linearity. I first tried using harmonic analysis through the mode superposition method. I get a frequency response that includes the natural frequency and a linear range can be obtained through this plot. But I realized, this method is not accurate because the resistant element (CIRCU94) is ignored in the mode superposition method (please correct me if I am wrong). By changing the resistance value, the amplitude does not change. We need to have resistance to model charge dissipation, otherwise this open circuit voltage that does not properly change with excitation frequency won't give me an accurate frequency range and linearity. Please see the following plot:
  
  Then I used full harmonic analysis which I could see the effect of resistance in my voltage. But my expecation was that at least for low frequencies in the frequency response I see nonlinear behavior, and once the frequency increases, a more linear behavior in the voltage should be observed like this:
  
  But what I get from the full harmonic analysis is this for low frequencies up to 500 Hz:
  
  I am sure over frequencies like 20 Hz there must be almost a linear voltage amplitude.
  I attached my code for mode superposition and full harmonic. Can anyone check where I am making a mistake? or this is correct? The bottom of the PZT sensor is fixed, and excitation is from the top. The middle disc is PZT and I selected the top node at the end of the code to easily get results for this node.
  
  I hope someone can help me soon because I need to report this simulation very soon. Thank you in advance, everyone!
  Mode superposition:
  finish
  /clear
  
  /PREP7
  et,1,solid226,0
  keyopt,1,1,1001
  allsel
  
  /com Stiffness
  TB, ANEL, 1 , 1 , 0
  TBDATA, 1, 1.327E+5 , 0.866E+4 , 0.856E+4
  TBDATA, 7, 1.327E+5 , 0.856E+4
  TBDATA, 12, 1.192E+5
  TBDATA, 16, 2.12E+4
  TBDATA, 19, 2.12E+4
  TBDATA, 21, 2.99E+4
  
  /com Piezo matrix
  TB,PIEZ,1,,,1
  TBDATA, 3, -1.86e-10
  TBDATA, 6, -1.86e-10
  TBDATA, 9, 4.00e-10
  TBDATA, 11, 6.17e-10
  TBDATA, 13, 6.17e-10
  
  /com Permittivity
  tb,DPER,,,,1 ! Relative permittivity at const
  tbdata,1,1852,1852,1751
  TB,DPER,1,,,1852,1852,1751,1
  EMUNIT, EPZRO, 8.85E-15
  MP, DENS, 1 , 7.8e-9
  
  !==============================================
  et,2,solid185
  MP,EX,2,350e3
  MP,PRXY,2,0.22
  MP,DENS,2,3.9e-9
  MP,BETD,2,1e-4
  !==============================================
  CYL4,0,0,2.5, , , ,1.5
  BLC4,0,-1.25,7.1,2.5,1.5
  VSBV, 2, 1
  CYL4,0,0,2.5, , , ,1.5
  vglue,all
  k,21,0,0,1.5
  csys,4
  wpcsys,-1,0
  kwpave,21
  CYL4,0,0,1.5, , , ,2
  k,,0,0,2
  kwpave,26
  CYL4,0,0,1.5, , , ,1.5
  csys,4
  wpcsys,-1,0
  save
  !==============================================
  Type,2
  Mat,2
  esize,0.3
  SMRT,1
  vsweep,2
  vsweep,4
  vsweep,3
  
  Type,1
  Mat,1
  vsweep,1
  save
  !================================================
  DA,7,all,0
  DA,18,all,0
  
  lsel,s,,,39,42
  DL,all,,ux,0
  DL,all,,uy,0
  allsel
  
  asel,s,,,1
  lsla,s
  ksll,s
  nsla,s
  nsll,a
  nslk,a
  !D,all,volt,0
  cp,next,volt,all
  *get,n_ground,node,0,num,min
  allsel
  
  asel,s,,,2
  lsla,s
  ksll,s
  nsla,s
  nsll,a
  nslk,a
  cp,next,volt,all
  *get,n_supply,node,0,num,min
  allsel
  
  d,n_ground,volt,0
  !======= CONTACT ==========
  /COM, CONTACT PAIR CREATION - START
  CM,_NODECM,NODE
  CM,_ELEMCM,ELEM
  CM,_KPCM,KP
  CM,_LINECM,LINE
  CM,_AREACM,AREA
  CM,_VOLUCM,VOLU
  /GSAV,cwz,gsav,,temp
  MP,MU,1,
  MAT,1
  MP,EMIS,1,7.88860905221e-31
  R,3
  REAL,3
  ET,3,170
  ET,4,174
  R,3,,,1.0,0.1,0,
  RMORE,,,1.0E20,0.0,1.0,
  RMORE,0.0,0,1.0,,1.0,0.5
  RMORE,0,1.0,1.0,0.0,,1.0
  RMORE,,,,,,1.0
  KEYOPT,4,4,0
  KEYOPT,4,5,0
  KEYOPT,4,7,0
  KEYOPT,4,8,0
  KEYOPT,4,9,0
  KEYOPT,4,10,0
  KEYOPT,4,11,0
  KEYOPT,4,12,5
  KEYOPT,4,14,0
  KEYOPT,4,18,0
  KEYOPT,4,2,0
  KEYOPT,3,5,0
  KEYOPT,4,1,5
  ! Generate the target surface
  ASEL,S,,,17
  CM,_TARGET,AREA
  TYPE,3
  NSLA,S,1
  ESLN,S,0
  ESLL,U
  ESEL,U,ENAME,,188,189
  NSLE,A,CT2
  ESURF
  CMSEL,S,_ELEMCM
  ! Generate the contact surface
  ASEL,S,,,1
  CM,_CONTACT,AREA
  TYPE,4
  NSLA,S,1
  ESLN,S,0
  NSLE,A,CT2 ! CZMESH patch (fsk qt-40109 8/2008)
  ESURF
  ALLSEL
  ESEL,ALL
  ESEL,S,TYPE,,3
  ESEL,A,TYPE,,4
  ESEL,R,REAL,,3
  /PSYMB,ESYS,1
  /PNUM,TYPE,1
  /NUM,1
  EPLOT
  ESEL,ALL
  ESEL,S,TYPE,,3
  ESEL,A,TYPE,,4
  ESEL,R,REAL,,3
  CMSEL,A,_NODECM
  CMDEL,_NODECM
  CMSEL,A,_ELEMCM
  CMDEL,_ELEMCM
  CMSEL,S,_KPCM
  CMDEL,_KPCM
  CMSEL,S,_LINECM
  CMDEL,_LINECM
  CMSEL,S,_AREACM
  CMDEL,_AREACM
  CMSEL,S,_VOLUCM
  CMDEL,_VOLUCM
  /GRES,cwz,gsav
  CMDEL,_TARGET
  CMDEL,_CONTACT
  /COM, CONTACT PAIR CREATION - END
  APLOT
  !*
  !*
  /COM, CONTACT PAIR CREATION - START
  CM,_NODECM,NODE
  CM,_ELEMCM,ELEM
  CM,_KPCM,KP
  CM,_LINECM,LINE
  CM,_AREACM,AREA
  CM,_VOLUCM,VOLU
  /GSAV,cwz,gsav,,temp
  MP,MU,1,0
  MAT,1
  MP,EMIS,1,7.88860905221e-31
  R,4
  REAL,4
  ET,5,170
  ET,6,174
  R,4,,,1.0,0.1,0,
  RMORE,,,1.0E20,0.0,1.0,
  RMORE,0.0,0,1.0,,1.0,0.5
  RMORE,0,1.0,1.0,0.0,,1.0
  RMORE,,,,,,1.0
  KEYOPT,6,4,0
  KEYOPT,6,5,0
  KEYOPT,6,7,0
  KEYOPT,6,8,0
  KEYOPT,6,9,0
  KEYOPT,6,10,0
  KEYOPT,6,11,0
  KEYOPT,6,12,5
  KEYOPT,6,14,0
  KEYOPT,6,18,0
  KEYOPT,6,2,0
  KEYOPT,5,5,0
  KEYOPT,6,1,5
  ! Generate the target surface
  ASEL,S,,,2
  CM,_TARGET,AREA
  TYPE,5
  NSLA,S,1
  ESLN,S,0
  ESLL,U
  ESEL,U,ENAME,,188,189
  NSLE,A,CT2
  ESURF
  CMSEL,S,_ELEMCM
  ! Generate the contact surface
  ASEL,S,,,11
  CM,_CONTACT,AREA
  TYPE,6
  NSLA,S,1
  ESLN,S,0
  NSLE,A,CT2 ! CZMESH patch (fsk qt-40109 8/2008)
  ESURF
  ALLSEL
  ESEL,ALL
  ESEL,S,TYPE,,5
  ESEL,A,TYPE,,6
  ESEL,R,REAL,,4
  /PSYMB,ESYS,1
  /PNUM,TYPE,1
  /NUM,1
  EPLOT
  ESEL,ALL
  ESEL,S,TYPE,,5
  ESEL,A,TYPE,,6
  ESEL,R,REAL,,4
  CMSEL,A,_NODECM
  CMDEL,_NODECM
  CMSEL,A,_ELEMCM
  CMDEL,_ELEMCM
  CMSEL,S,_KPCM
  CMDEL,_KPCM
  CMSEL,S,_LINECM
  CMDEL,_LINECM
  CMSEL,S,_AREACM
  CMDEL,_AREACM
  CMSEL,S,_VOLUCM
  CMDEL,_VOLUCM
  /GRES,cwz,gsav
  CMDEL,_TARGET
  CMDEL,_CONTACT
  /COM, CONTACT PAIR CREATION - END
  
  !============================================================
  /prep7
  ET,7,CIRCU94
  R,5,1, , , , ,
  RMORE, , , , , ,
  RMORE, , , ,
  type,7
  real,5
  E,n_ground,n_supply
  !============================================================
  /solu
  ANTYPE,2
  MODOPT,LANB,50
  EQSLV,SPAR
  MODCONT,ON
  MXPAND,50, , ,0,,YES
  SFA,12,1,PRES,1/7.069
  LUMPM,0
  PSTRES,0
  MODOPT,LANB,50,0,4e10, ,OFF
  /solu
  SOLVE
  finish
  !============================================================
  
  !===========================================================
  /solu
  ANTYPE,3
  HROPT,MSUP, , ,0
  HROUT,ON
  LUMPM,0
  HROPT,MSUP,all, ,0
  HROUT,ON,OFF,0
  LVSCAL,1,1
  
  HARFRQ,0,4e5,
  NSUBST,4e2,
  KBC,1
  !BETAD,1e-6,
  DMPRAT,0.03
  MDAMP,1, , , , , , ,
  SOLVE
  
  save,pzt_harmonic,db
  finish
  save
  /SOLU
  EXPASS,1 ! Harmonic Analysis Expansion Pass
  NUMEXP,ALL,0,4e5,0 ! Frequency range
  HREXP,ALL,
  SOLVE
  
  nsel,s,,,n_supply
  
  Full harmonic analysis:
  finish
  /clear
  
  /PREP7
  et,1,solid226,0
  keyopt,1,1,1001
  allsel
  
  /com Stiffness
  TB, ANEL, 1 , 1 , 0
  TBDATA, 1, 1.327E+5 , 0.866E+4 , 0.856E+4
  TBDATA, 7, 1.327E+5 , 0.856E+4
  TBDATA, 12, 1.192E+5
  TBDATA, 16, 2.12E+4
  TBDATA, 19, 2.12E+4
  TBDATA, 21, 2.99E+4
  
  /com Piezo matrix
  TB,PIEZ,1,,,1
  TBDATA, 3, -1.86e-10
  TBDATA, 6, -1.86e-10
  TBDATA, 9, 4.00e-10
  TBDATA, 11, 6.17e-10
  TBDATA, 13, 6.17e-10
  
  /com Permittivity
  tb,DPER,,,,1 ! Relative permittivity at const
  tbdata,1,1852,1852,1751
  TB,DPER,1,,,1852,1852,1751,1
  EMUNIT, EPZRO, 8.85E-15
  MP, DENS, 1 , 7.8e-9
  
  !==============================================
  et,2,solid185
  MP,EX,2,350e3
  MP,PRXY,2,0.22
  MP,DENS,2,3.9e-9
  MP,BETD,2,1e-4
  !==============================================
  CYL4,0,0,2.5, , , ,1.5
  BLC4,0,-1.25,7.1,2.5,1.5
  VSBV, 2, 1
  CYL4,0,0,2.5, , , ,1.5
  vglue,all
  k,21,0,0,1.5
  csys,4
  wpcsys,-1,0
  kwpave,21
  CYL4,0,0,1.5, , , ,2
  k,,0,0,2
  kwpave,26
  CYL4,0,0,1.5, , , ,1.5
  csys,4
  wpcsys,-1,0
  save
  !==============================================
  Type,2
  Mat,2
  esize,0.3
  SMRT,1
  vsweep,2
  vsweep,4
  vsweep,3
  
  Type,1
  Mat,1
  vsweep,1
  save
  !================================================
  DA,7,all,0
  DA,18,all,0
  
  lsel,s,,,39,42
  DL,all,,ux,0
  DL,all,,uy,0
  allsel
  
  asel,s,,,1
  lsla,s
  ksll,s
  nsla,s
  nsll,a
  nslk,a
  !D,all,volt,0
  cp,next,volt,all
  *get,n_ground,node,0,num,min
  allsel
  
  asel,s,,,2
  lsla,s
  ksll,s
  nsla,s
  nsll,a
  nslk,a
  cp,next,volt,all
  *get,n_supply,node,0,num,min
  allsel
  
  d,n_ground,volt,0
  !======= CONTACT ==========
  /COM, CONTACT PAIR CREATION - START
  CM,_NODECM,NODE
  CM,_ELEMCM,ELEM
  CM,_KPCM,KP
  CM,_LINECM,LINE
  CM,_AREACM,AREA
  CM,_VOLUCM,VOLU
  /GSAV,cwz,gsav,,temp
  MP,MU,1,
  MAT,1
  MP,EMIS,1,7.88860905221e-31
  R,3
  REAL,3
  ET,3,170
  ET,4,174
  R,3,,,1.0,0.1,0,
  RMORE,,,1.0E20,0.0,1.0,
  RMORE,0.0,0,1.0,,1.0,0.5
  RMORE,0,1.0,1.0,0.0,,1.0
  RMORE,,,,,,1.0
  KEYOPT,4,4,0
  KEYOPT,4,5,0
  KEYOPT,4,7,0
  KEYOPT,4,8,0
  KEYOPT,4,9,0
  KEYOPT,4,10,0
  KEYOPT,4,11,0
  KEYOPT,4,12,5
  KEYOPT,4,14,0
  KEYOPT,4,18,0
  KEYOPT,4,2,0
  KEYOPT,3,5,0
  KEYOPT,4,1,5
  ! Generate the target surface
  ASEL,S,,,17
  CM,_TARGET,AREA
  TYPE,3
  NSLA,S,1
  ESLN,S,0
  ESLL,U
  ESEL,U,ENAME,,188,189
  NSLE,A,CT2
  ESURF
  CMSEL,S,_ELEMCM
  ! Generate the contact surface
  ASEL,S,,,1
  CM,_CONTACT,AREA
  TYPE,4
  NSLA,S,1
  ESLN,S,0
  NSLE,A,CT2 ! CZMESH patch (fsk qt-40109 8/2008)
  ESURF
  ALLSEL
  ESEL,ALL
  ESEL,S,TYPE,,3
  ESEL,A,TYPE,,4
  ESEL,R,REAL,,3
  /PSYMB,ESYS,1
  /PNUM,TYPE,1
  /NUM,1
  EPLOT
  ESEL,ALL
  ESEL,S,TYPE,,3
  ESEL,A,TYPE,,4
  ESEL,R,REAL,,3
  CMSEL,A,_NODECM
  CMDEL,_NODECM
  CMSEL,A,_ELEMCM
  CMDEL,_ELEMCM
  CMSEL,S,_KPCM
  CMDEL,_KPCM
  CMSEL,S,_LINECM
  CMDEL,_LINECM
  CMSEL,S,_AREACM
  CMDEL,_AREACM
  CMSEL,S,_VOLUCM
  CMDEL,_VOLUCM
  /GRES,cwz,gsav
  CMDEL,_TARGET
  CMDEL,_CONTACT
  /COM, CONTACT PAIR CREATION - END
  APLOT
  !*
  !*
  /COM, CONTACT PAIR CREATION - START
  CM,_NODECM,NODE
  CM,_ELEMCM,ELEM
  CM,_KPCM,KP
  CM,_LINECM,LINE
  CM,_AREACM,AREA
  CM,_VOLUCM,VOLU
  /GSAV,cwz,gsav,,temp
  MP,MU,1,0
  MAT,1
  MP,EMIS,1,7.88860905221e-31
  R,4
  REAL,4
  ET,5,170
  ET,6,174
  R,4,,,1.0,0.1,0,
  RMORE,,,1.0E20,0.0,1.0,
  RMORE,0.0,0,1.0,,1.0,0.5
  RMORE,0,1.0,1.0,0.0,,1.0
  RMORE,,,,,,1.0
  KEYOPT,6,4,0
  KEYOPT,6,5,0
  KEYOPT,6,7,0
  KEYOPT,6,8,0
  KEYOPT,6,9,0
  KEYOPT,6,10,0
  KEYOPT,6,11,0
  KEYOPT,6,12,5
  KEYOPT,6,14,0
  KEYOPT,6,18,0
  KEYOPT,6,2,0
  KEYOPT,5,5,0
  KEYOPT,6,1,5
  ! Generate the target surface
  ASEL,S,,,2
  CM,_TARGET,AREA
  TYPE,5
  NSLA,S,1
  ESLN,S,0
  ESLL,U
  ESEL,U,ENAME,,188,189
  NSLE,A,CT2
  ESURF
  CMSEL,S,_ELEMCM
  ! Generate the contact surface
  ASEL,S,,,11
  CM,_CONTACT,AREA
  TYPE,6
  NSLA,S,1
  ESLN,S,0
  NSLE,A,CT2 ! CZMESH patch (fsk qt-40109 8/2008)
  ESURF
  ALLSEL
  ESEL,ALL
  ESEL,S,TYPE,,5
  ESEL,A,TYPE,,6
  ESEL,R,REAL,,4
  /PSYMB,ESYS,1
  /PNUM,TYPE,1
  /NUM,1
  EPLOT
  ESEL,ALL
  ESEL,S,TYPE,,5
  ESEL,A,TYPE,,6
  ESEL,R,REAL,,4
  CMSEL,A,_NODECM
  CMDEL,_NODECM
  CMSEL,A,_ELEMCM
  CMDEL,_ELEMCM
  CMSEL,S,_KPCM
  CMDEL,_KPCM
  CMSEL,S,_LINECM
  CMDEL,_LINECM
  CMSEL,S,_AREACM
  CMDEL,_AREACM
  CMSEL,S,_VOLUCM
  CMDEL,_VOLUCM
  /GRES,cwz,gsav
  CMDEL,_TARGET
  CMDEL,_CONTACT
  /COM, CONTACT PAIR CREATION - END
  
  !============================================================
  /prep7
  ET,7,CIRCU94
  R,5,1e6, , , , ,
  RMORE, , , , , ,
  RMORE, , , ,
  type,7
  real,5
  E,n_ground,n_supply
  !============================================================
  /solu
  ANTYPE,2
  MODOPT,LANB,50
  EQSLV,SPAR
  MODCONT,ON
  MXPAND,50, , ,0,,YES
  !!!!!!!!!!!!!!!!!!!!!!!!!!!!SFA,12,1,PRES,1/7.069
  LUMPM,0
  PSTRES,0
  MODOPT,LANB,50,0,4e10, ,OFF
  /solu
  SOLVE
  finish
  !============================================================
  /solu
  asel,s,,,12
  nsla,s
  nsel,r,loc,x,-0.25,0.25
  nsel,r,loc,y,-0.25,0.25
  *get,n_force,node,0,num,min
  allsel
  f,n_force,fz,-1
  !===========================================================
  /SOL
  ANTYPE,3
  HROPT,FULL
  HROUT,ON
  LUMPM,0
  EQSLV, ,0,
  PSTRES,0
  HARFRQ,0,500,
  NSUBST,100,
  KBC,0
  DMPRAT,0.1
  MDAMP,1, , , , , , ,
  solve
  
  vsel,s,,,1
  eslv,s
  nsle,s
- November 8, 2022 at 4:34 pm
  
  wrbulat
  Ansys Employee
  
  Hi there,
  I have not yet tested your code and I don't see the post processing commands used to create the xy plots you sent so I'm not sure exactly what they're plots of, but I made one possibly significant observation. You used a KBC,0 command in your full harmonic response calculation. This linearly ramps excitation over the frequency sweep. So the z component force you applied to n_force is ramped from zero to -1 over the frequency range. Does using KBC,1 (which will step the force to its full value starting at the beginning frequency in your sweep) give the response you expect?
  --Bill