determining limitations in the ability of the abaqus
TRANSCRIPT
Determining Limitations in the Ability of the ABAQUS Commercial
Finite Element Analysis Program to Accurately Predict Piezoelectric
Strain Behavior in Actuation DevicesTRACE: Tennessee Research and
Creative TRACE: Tennessee Research and Creative
Exchange Exchange
Spring 4-2004
Determining Limitations in the Ability of the ABAQUS Commercial Determining Limitations in the Ability of the ABAQUS Commercial
Finite Element Analysis Program to Accurately Predict Finite Element Analysis Program to Accurately Predict
Piezoelectric Strain Behavior in Actuation Devices Piezoelectric Strain Behavior in Actuation Devices
Christina Marie Spencer University of Tennessee - Knoxville
Follow this and additional works at: https://trace.tennessee.edu/utk_chanhonoproj
Recommended Citation Recommended Citation Spencer, Christina Marie, "Determining Limitations in the Ability of the ABAQUS Commercial Finite Element Analysis Program to Accurately Predict Piezoelectric Strain Behavior in Actuation Devices" (2004). Chancellor’s Honors Program Projects. https://trace.tennessee.edu/utk_chanhonoproj/797
This is brought to you for free and open access by the Supervised Undergraduate Student Research and Creative Work at TRACE: Tennessee Research and Creative Exchange. It has been accepted for inclusion in Chancellor’s Honors Program Projects by an authorized administrator of TRACE: Tennessee Research and Creative Exchange. For more information, please contact [email protected].
Name: Cb v\ n OeL S~V1CW
College: £ V~ I!'\«( f j f\~ Department: fv\ .echrul l ccJl F:1culry Yremor. 1),1 A T, 80. k-e .
PROJECT TITLE: 0eleyw) ,/\ if\) LID)! k b !.Nl~ ttl ±0..0
; , )
B-c. ~"\Q.V1QY I . A Ch({07L' ~. vI ces [ have reV1ewed this c omple~ed senior honors ilies is wiili thIS srudem IDd cemfy that it is J. projec~
comrnensur::ue with honors level underg::r:I.;uate rese:lfch In ,hIS neld.
Signed: _ ""/~~ . FJc:liry :V(enror
Comme~H::i (Oprrona!):
-0
DETERMINING LIMITATIONS IN THE ABILITY OF THE ABAQUS COMMERCIAL FINITE ELEMENT ANALYSIS PROGRAM TO
ACCURA TELY PREDICT PIEZOELECTRIC STRAIN BEHAVIOR IN ACTUATION DEVICES
Reviewed by
NASA Langley Research Center March 31st, 2004
NASA-USRP Mentor Dr. Robert Bryant Advanced Materials and Processing Branch
University of Tennessee Mentor Dr. AJ. Baker Department of Mechanical, Aerospace, and Biomedical Engineering
ABSTRACT In order to better predict the actuation capabilities of piezoelectric materials, a series of tests was performed on piezoelectric material PZT SA and compared with computational results performed using ABAQUS, a commercial finite element analysis package. These experiments consisted of applying voltages to basic PZT SA ceramic plates and PZT SA ceramic plates with varying thicknesses of brass plates attached to the top of the ceramic. A range of voltages was applied under quasi-isostatic conditions and the resulting strain was measured at the top and bottom of the actuator using commercial thin film strain gages. The comparisons of experimental results to ABAQUS predicted results show how accurate a commercial finite element analysis package is with respect predicting the behavior of piezoelectric materials. By looking at these comparisons, deficiencies in ABAQUS and other similar programs can be recognized, and ways to overcome these limitations can be developed. Such limitations include the variation of piezoelectric constants with applied voltage, piezoelectric hysteresis effects, and capturing the surface strain in the plate from bending effects. Overcoming these deficiencies will allow for faster and more accurate predictions of the geometry and type of material needed for the more efficient use of piezoelectric actuators.
INTRODUCTION The study of piezoelectric materials dates back to 1880 when they were discovered by Jaques and Pierre Curie. Their discovery that some crystals became electrically charged when a mechanical strain is applied to the crystal is known as the piezoelectric effect. Since this discovery, testing and development of these piezoelectric materials has led to the application of the piezoelectric effect in many different generators and transducers. The inverse piezoelectric effect, the deformation of these same crystals when they are exposed to an electric field, has also been used in a variety of sensors and actuators.
The development of these new products requires significant amounts of testing and analysis. The need to accurately predict experimental results using commercial finite element analysis (PEA) programs is widely recognized because of the benefits accurately predicted results will produce. Once a type of material can be modeled using FEA, the need to perform actual experiments and the high cost associated with these experiments can be limited. The need to use a commercial FEA program arises when dealing with companies and manufacturers that want fast results that can be shared among colleagues using similar programs.
Currently, most FEA work in piezoelectric modeling has been done using computer code written specifically for the chosen experiment. While this provides more accurate results, it is not practical when trying to determine geometry of complex actuators for larger systems without performing experiments. Conversely, the piezoelectric options in PEA programs like ABAQUS are vastly oversimplified and do not accurately predict the experimental results needed to replace testing.
PROBLEM The NASA Morphing project is developing a new type of airplane wing that could use piezoelectric actuators. This theoretical wing would have small holes in the downwind side of the wing, allowing gas to be expelled from the wing when desired. This idea has many aeronautical advantages, however it has some disadvantages. One disadvantage is that the
1
device required to open and close the hole would prevent the wing from being a wet wing and would also change the interior structure of the wing. If a piezoelectric actuator could be used instead of this device, the wet wing and structure of the wing would still be feasible options for
the project.
Because of the obvious benefits of the piezoelectric actuator to this project, this study was completed in order to better understand how accurate ABAQUS results are and if the inaccuracies could be accounted for using FEA techniques. If a somewhat accurate prediction of a piezoelectric actuator can be developed, considerable time and money can be saved when determining what size and type of piezoelectric actuator would work best for this wing.
METHOD OF SOLUTION In order to establish exactly what the ABAQUS program can predict and what it's limitations are, a series of experiments were performed, and the same experiments were modeled using ABAQUS software. This was done in order to establish the differences between the experimental results and the ABAQUS predicted results. By comparing the two sets of results , the limitations in the ABAQUS software become apparent. Once these shortfalls are recognized, ways to vary the ABAQUS input to supply the desired output can be created.
A series of experiments were performed in order to understand where each problem with the ABAQUS modeling program occurs. For example, the first experiment was a simple piezoelectric plate with an electric field applied to it. By finding the differences in ABAQUS predicted and experimental results for this simple experiment and accounting for them, one step of the actuator modeling has been complete. When moving to a more complicated actuation device, the variation in the predicted and experimental results can be limited because the variations in a simple piezoelectlic plate have already been accounted for.
I. Simple Piezoelectric Plate Test The first test performed was on a lead zirconate titanate (PZT) piezoelectric plate. Transparent graph paper was used to align a Micromeasurements precision strain gage in the center on the top of the plate. The strain gage was attached using M-Bond 200 adhesive and a lOOg weight was set on top of the strain gage while the glue dried. Strain gauge solder telminals were also attached to the plates on either side of the strain gauge, offset from the gage to avoid interference.
Next, lead wires were soldered to the solder terminals. One black and one white wire were soldered to one of the terminals, and one red wire was soldered to the other terminal. Lastly, a red wire was applied to the top of the plate and a black wire applied to the bottom of the plate using silver epoxy. These wires act as electrodes to apply the electric field across the plate. The plate was then placed in an oven to cure the epoxy. Once the epoxy was dry and the instrumentation of the plate was complete, the plate was poled by attaching the red and black wires to an amplifier and running a direct current of appropriate magnitude through the plate.
This instrumentation and poling process was completed for two plates, Plate 1 and Plate 2, poling plate 1 at 1200 V and plate 2 at 2400 V. Plate 1 measured 4xlxO.015 inches and Plate 2 measured 3.375x2.25xO.03 inches. Once the plates were instrumented, Plate 1 was hooked up to
2
a Model 3800 Wide Range Strain Indicator from Vishay Instruments Division, SIN 150658. Next, the plate was set on a small ceramic block to allow the plate to be level. The red and black wires attached to plate 1 were connected to a Trek PZD2000 High Voltage Amplifier by the high voltage output and the ground output, respectively. The amplifier input was attached to an Agilent 33120A Frequency Generator.
To run the experiment, the frequency generator was set to output a sine wave at 0.1 Hz. The High Z option on the generator was set. The alternating current was applied at 100-1200 V in 100 V increments. For each voltage, the strain indicator was set to zero, the amplifier turned on, and the frequency increased from minimum voltage to the desired voltage. Strain readings were taken using an Agilent datalogger, and then the voltage was decreased and the amplifier turned off. The strain indicator was re-zeroed, and the process was repeated. After Plate 1 was finished, Plate 2 was tested using the same process but the final voltage was 2400 V instead of 1200 V, as Plate 2 is twice the thickness of Plate 1.
Finally, the same experiment was modeled using ABAQUS. A plate of the same dimensions was created using C3D20E elements. The plate was constrained by pinning one comer, which allowed for no movement of that comer. The edge the comer belonged to was then fixed in the 1 and 3 directions, allowing no movement in either direction. The opposite edge was also fixed in the 3 direction, simulating the flat surface the plate was resting on.
Edge conslrained in the 1 and 3 directions
Figure 1: ABAQUS Constraints for Simple Piezoelectric Plate Test
II. PZT -Brass Actuator After the first test was completed and the experimental and predicted results compared, another experiment was performed. This experiment used three PZT plates and attached a brass plate of varying thickness to the top of each PZT plate. The PZT plates used in this experiment had dimensions of 2.5xO.80xO.0080 inches, and the brass plates measured 2xO.80xO.00l, 0.003, or 0.005 inches. The same instrumentation and testing process was used, but before applying the strain gages a brass plate was attached to the top of the PZT plate. This was done using 3M
3
double stick tape 9461P. The strain gages were then applied to both the top (brass) and bottom (PZT) of the actuator. The poling voltage was 640 V, and the maximum alternating current applied was 400 V.
For the ABAQUS model, the same constraints as applied in the simple piezoelectric plate test were used. The brass plates were attached using the *TIE constraint, which ties the PZT plate surface to the tape surface, and the tape surface to the brass surface.
III. THUNDER Actuator After the second test was completed, a test of the more complicated THUNDER actuator was performed. The experiment used a THUNDER actuator comprised of a stainless steel layer, glue, piezoelectric plate, glue, and a thin aluminum layer. The instrumentation and testing process was the same as used in the previous two tests, except that four strain gages were applied to both the top and the bottom of the THUNDER actuator, as shown below.
Figure 2: Top of THUNDER Actuator with Strain gages applied
The THUNDER actuator was then modeled using ABAQUS. Because of modeling complications, the glue and aluminum layers were not modeled, only the stainless steel and PZT layers. The boundary conditions were applied as in previous experiments. In order to simulate the bent form of the THUNDER actuator, a force was applied to the center of the actuator before applying a voltage across the actuator. The set up is shown below.
4
DISCUSSION
I. Simple Piezoelectric Plate Test As shown below, the difference between the ABAQUS predicted results and the experimental results for this simple piezoelectric plate test consist of three main problems: the hysteresis loop in the experimental results, a shift in the experimental results, and the overall slope of the strain versus electric field plot.
-- Experimental ~- Abaqus ---4.- Abaqus Exp D31
Plate 1 ~ 150 -,----------------, E <0
b T'-
X -c .~
Electric Field (x10"3 Vim)
b T'-
X -c
~ -60 +---~--~--~-----I
Electric Field (x10"3 Vim)
Figure 4: Simple Piezoelectric Plate Test Results at 200 Volts Peak to Peak
Because the slope of these plots is the piezoelectric constant D31, the difference in the slope can be accounted for by using the experimental D31 for the ABAQUS program. This is shown by the red in Figure 4. The shift in the experimental results is probably due to residual strain induced by the poling of the plates. This and the hysteresis loop are not easily accounted for, however the ABAQUS results would give a general idea of the PZT plates induced strain.
5
II. PZT -Brass Actuator The strain versus electric field data for each actuator (0.001, 0.003, and 0.005 inch brass plates) is shown below. When completing the ABAQUS simulation, the experimental piezoelectric constant D31 was used in order to better match the experimental data.
-- Experimental ~ ABAOUS
~ 200 T"""
~ -1000 -500 0 500 1000
Electric Field (x10"3 Vim)
E 80 60
-40 ..... -en -60 0 .....
Electric Field (x10"3 Vim)
Figure 5: PZT·Brass Actuator Test Results at 200 Volts Peak to Beak for a Brass Thickness of 0.001 inches
-- Experimental ABAOUS
~ 200 T"""
X 0 -c 'n; -200 ..... -en 0 -400 ..... .2 ~ -1000 -500 0 500 1000
Electric Field (x10"3 Vim)
~
Electric Field (x10"3 Vim)
Figure 6: PZT·Brass Actuator Test Results at 200 Volts Peak to Beak for a Brass Thickness of 0.003 inches
6
~ 200 ..- x 0 --c
.(ij -200 ..... -(/) 0 -400 ..... u ~ -1000 -500 0 500 1000
Electric Field (x1 ()1\3 Vim)
E -E co < 0 ..- x --c
.(ij ..... -(/) 0 ..... u ~
60 40 20 o
Electric Field (x10"3 Vim)
Figure 7: PZT-Brass Actuator Test Results at 200 Volts Peak to Beak for a Brass Thickness of 0.005 inches
The main shortfalls of the ABAQUS program concerning these Brass-PZT actuators are the inability of ABAQUS to capture even the direction at the top of the actuator's strain and the inability of ABAQUS to show the increased strain and therefore the increased piezoelectric constant D31 for the bottom of the actuator. Upon closer inspection of this effective D31 for the experimental and ABAQUS results, the ABAQUS effective D31 is virtually the same as the actual D31. The experimental D31, however, increases dramatically which causes the increased strain in the material.
Another interesting feature of the experimental data is the fact that the slope of the strain versus electric field plot at the top of the actuator is in the opposite direction for the 0.001 inch brass plate actuator as it is in the 0.003 and 0.005 inch brass plate actuators. This is probably because the 0.001 inch brass plate is so thin that the piezoelectric material is stretching the brass, where in the other two actuators, the brass is thick enough to induce actuation. This theory is supported by the fact that the slope of the strain versus electric field plot is less in the 0.001 inch actuator than in the 0.003 and 0.005 inch actuators.
7
E Bottom of Actuator (PZT) u·c> -C\I u..-
0..---- --------,
::::<fJ We o
Electric Potential (Volts)
E u·c> -C\I u..- ~b OT"" N x Q)- O:::T""
('t)
20
o
-20
Electric Potential (Volts)
Figure 8: PZT -Brass Actuator Effective Piezoelectric Constant for a Brass Thickness of 0.005 inches
III. THUNDER Actuator Experimental Results of the THUNDER Testing are shown in Appendix 1. Because of time constraints, successful ABAQUS modeling of the THUNDER device was not achieved at the time of this report.
CONCLUSION From these initial results, it is clear that more work needs to be done to achieve a successful model of piezoelectric materials using ABAQUS. While it is clear that the ABAQUS program does not present an ideal representation of piezoelectric materials, it can be modified to present more accurate results. This study has identified the most significant problems of ABAQUS modeling of piezoelectric materials in relation to the strain measurements of piezoelectric actuators. They are as follows: piezoelectric hysteresis loops, the strain shift caused by poling of piezoelectric materials, the increased effective piezoelectric constant in a simple piezoelectric actuator, and the strain measurements on the top of a simple piezoelectric actuator.
Some if not all of these problems with ABAQUS can be overcome using various modeling techniques. For example, an initial strain based on the poling of the material could be applied to the material in order to account for the strain shift caused by poling of piezoelectric materials. More experimental studies of simple actuators could yield a formula to determine how much to increase the effective piezoelectric constant by to obtain similar stress results. Other methods could be employed to simulate hysteresis loops and to obtain accurate results for the strain on the top of a simple piezoelectric actuator.
8
REFERENCES
"Load characterization of high displacement piezoelectric actuators with various end conditions." Sensors and Actuators April 2001. 19-24
"Piezoelectric strain in lead zierconate titante ceramics as a function of electric field, frequency, and dc bias." Journal of Applied Physics. 15 July 2003. Volume 94, number 2,1155-1162
Wanders, l.W. Piezoelectric Ceramics. Eindhoven; N.V. Philips, April 1991
9
Thunder Wafer Instrumentation
Top Gage 1 (Uppe, Left) Gage 2;;:::: Gage 3 Uppe, Right
~I I Gage 4 (Lower Left)
Bottom (plate flipped horizontally)
Gage 5 (Upper Left) Gage 7 (Upper Right)
Test 2: 100 V with 150 DC Bias 100V, 150 DC Bias
0.0001 -,------------ - --- --- -------------,
Y = 1.6607E-ll x + 3.2009E-0
0.00005 r==~;;;;;;;;;;;~;;;;;;;;~:::_.~Y~-=~9~.36~1~0~E-~'2~X~+~2.~466;5E~-05~ o y = -5.065OE-12x + 1.2783E-05
4 0 500000 600000 700000 800000 900000 1 OOOOOOy = \ 'BWg_ 121 22~e888~:(J -0.00005 -\-_ ________________ --'-.....:..:::::..:=:.::..c=-:...:..:==::....::..=j
-0.0002
-0.00025
-0.0003
Bottom Upper Lelt (transverse) - Bottom Upper Rig,t
Top Upper Left (transverse) - Top Upper Rig,t - Bottom Lower Left - Bottom Center - Top Lower Left
y = -8.0069E-llx - 3.1943E-
y = -1.3911E-1Ox - 5.2621E-05
f------------- --- - - --l - To Center
4 5 6 7
Determining Limitations in the Ability of the ABAQUS Commercial Finite Element Analysis Program to Accurately Predict Piezoelectric Strain Behavior in Actuation Devices
Recommended Citation
Exchange Exchange
Spring 4-2004
Determining Limitations in the Ability of the ABAQUS Commercial Determining Limitations in the Ability of the ABAQUS Commercial
Finite Element Analysis Program to Accurately Predict Finite Element Analysis Program to Accurately Predict
Piezoelectric Strain Behavior in Actuation Devices Piezoelectric Strain Behavior in Actuation Devices
Christina Marie Spencer University of Tennessee - Knoxville
Follow this and additional works at: https://trace.tennessee.edu/utk_chanhonoproj
Recommended Citation Recommended Citation Spencer, Christina Marie, "Determining Limitations in the Ability of the ABAQUS Commercial Finite Element Analysis Program to Accurately Predict Piezoelectric Strain Behavior in Actuation Devices" (2004). Chancellor’s Honors Program Projects. https://trace.tennessee.edu/utk_chanhonoproj/797
This is brought to you for free and open access by the Supervised Undergraduate Student Research and Creative Work at TRACE: Tennessee Research and Creative Exchange. It has been accepted for inclusion in Chancellor’s Honors Program Projects by an authorized administrator of TRACE: Tennessee Research and Creative Exchange. For more information, please contact [email protected].
Name: Cb v\ n OeL S~V1CW
College: £ V~ I!'\«( f j f\~ Department: fv\ .echrul l ccJl F:1culry Yremor. 1),1 A T, 80. k-e .
PROJECT TITLE: 0eleyw) ,/\ if\) LID)! k b !.Nl~ ttl ±0..0
; , )
B-c. ~"\Q.V1QY I . A Ch({07L' ~. vI ces [ have reV1ewed this c omple~ed senior honors ilies is wiili thIS srudem IDd cemfy that it is J. projec~
comrnensur::ue with honors level underg::r:I.;uate rese:lfch In ,hIS neld.
Signed: _ ""/~~ . FJc:liry :V(enror
Comme~H::i (Oprrona!):
-0
DETERMINING LIMITATIONS IN THE ABILITY OF THE ABAQUS COMMERCIAL FINITE ELEMENT ANALYSIS PROGRAM TO
ACCURA TELY PREDICT PIEZOELECTRIC STRAIN BEHAVIOR IN ACTUATION DEVICES
Reviewed by
NASA Langley Research Center March 31st, 2004
NASA-USRP Mentor Dr. Robert Bryant Advanced Materials and Processing Branch
University of Tennessee Mentor Dr. AJ. Baker Department of Mechanical, Aerospace, and Biomedical Engineering
ABSTRACT In order to better predict the actuation capabilities of piezoelectric materials, a series of tests was performed on piezoelectric material PZT SA and compared with computational results performed using ABAQUS, a commercial finite element analysis package. These experiments consisted of applying voltages to basic PZT SA ceramic plates and PZT SA ceramic plates with varying thicknesses of brass plates attached to the top of the ceramic. A range of voltages was applied under quasi-isostatic conditions and the resulting strain was measured at the top and bottom of the actuator using commercial thin film strain gages. The comparisons of experimental results to ABAQUS predicted results show how accurate a commercial finite element analysis package is with respect predicting the behavior of piezoelectric materials. By looking at these comparisons, deficiencies in ABAQUS and other similar programs can be recognized, and ways to overcome these limitations can be developed. Such limitations include the variation of piezoelectric constants with applied voltage, piezoelectric hysteresis effects, and capturing the surface strain in the plate from bending effects. Overcoming these deficiencies will allow for faster and more accurate predictions of the geometry and type of material needed for the more efficient use of piezoelectric actuators.
INTRODUCTION The study of piezoelectric materials dates back to 1880 when they were discovered by Jaques and Pierre Curie. Their discovery that some crystals became electrically charged when a mechanical strain is applied to the crystal is known as the piezoelectric effect. Since this discovery, testing and development of these piezoelectric materials has led to the application of the piezoelectric effect in many different generators and transducers. The inverse piezoelectric effect, the deformation of these same crystals when they are exposed to an electric field, has also been used in a variety of sensors and actuators.
The development of these new products requires significant amounts of testing and analysis. The need to accurately predict experimental results using commercial finite element analysis (PEA) programs is widely recognized because of the benefits accurately predicted results will produce. Once a type of material can be modeled using FEA, the need to perform actual experiments and the high cost associated with these experiments can be limited. The need to use a commercial FEA program arises when dealing with companies and manufacturers that want fast results that can be shared among colleagues using similar programs.
Currently, most FEA work in piezoelectric modeling has been done using computer code written specifically for the chosen experiment. While this provides more accurate results, it is not practical when trying to determine geometry of complex actuators for larger systems without performing experiments. Conversely, the piezoelectric options in PEA programs like ABAQUS are vastly oversimplified and do not accurately predict the experimental results needed to replace testing.
PROBLEM The NASA Morphing project is developing a new type of airplane wing that could use piezoelectric actuators. This theoretical wing would have small holes in the downwind side of the wing, allowing gas to be expelled from the wing when desired. This idea has many aeronautical advantages, however it has some disadvantages. One disadvantage is that the
1
device required to open and close the hole would prevent the wing from being a wet wing and would also change the interior structure of the wing. If a piezoelectric actuator could be used instead of this device, the wet wing and structure of the wing would still be feasible options for
the project.
Because of the obvious benefits of the piezoelectric actuator to this project, this study was completed in order to better understand how accurate ABAQUS results are and if the inaccuracies could be accounted for using FEA techniques. If a somewhat accurate prediction of a piezoelectric actuator can be developed, considerable time and money can be saved when determining what size and type of piezoelectric actuator would work best for this wing.
METHOD OF SOLUTION In order to establish exactly what the ABAQUS program can predict and what it's limitations are, a series of experiments were performed, and the same experiments were modeled using ABAQUS software. This was done in order to establish the differences between the experimental results and the ABAQUS predicted results. By comparing the two sets of results , the limitations in the ABAQUS software become apparent. Once these shortfalls are recognized, ways to vary the ABAQUS input to supply the desired output can be created.
A series of experiments were performed in order to understand where each problem with the ABAQUS modeling program occurs. For example, the first experiment was a simple piezoelectric plate with an electric field applied to it. By finding the differences in ABAQUS predicted and experimental results for this simple experiment and accounting for them, one step of the actuator modeling has been complete. When moving to a more complicated actuation device, the variation in the predicted and experimental results can be limited because the variations in a simple piezoelectlic plate have already been accounted for.
I. Simple Piezoelectric Plate Test The first test performed was on a lead zirconate titanate (PZT) piezoelectric plate. Transparent graph paper was used to align a Micromeasurements precision strain gage in the center on the top of the plate. The strain gage was attached using M-Bond 200 adhesive and a lOOg weight was set on top of the strain gage while the glue dried. Strain gauge solder telminals were also attached to the plates on either side of the strain gauge, offset from the gage to avoid interference.
Next, lead wires were soldered to the solder terminals. One black and one white wire were soldered to one of the terminals, and one red wire was soldered to the other terminal. Lastly, a red wire was applied to the top of the plate and a black wire applied to the bottom of the plate using silver epoxy. These wires act as electrodes to apply the electric field across the plate. The plate was then placed in an oven to cure the epoxy. Once the epoxy was dry and the instrumentation of the plate was complete, the plate was poled by attaching the red and black wires to an amplifier and running a direct current of appropriate magnitude through the plate.
This instrumentation and poling process was completed for two plates, Plate 1 and Plate 2, poling plate 1 at 1200 V and plate 2 at 2400 V. Plate 1 measured 4xlxO.015 inches and Plate 2 measured 3.375x2.25xO.03 inches. Once the plates were instrumented, Plate 1 was hooked up to
2
a Model 3800 Wide Range Strain Indicator from Vishay Instruments Division, SIN 150658. Next, the plate was set on a small ceramic block to allow the plate to be level. The red and black wires attached to plate 1 were connected to a Trek PZD2000 High Voltage Amplifier by the high voltage output and the ground output, respectively. The amplifier input was attached to an Agilent 33120A Frequency Generator.
To run the experiment, the frequency generator was set to output a sine wave at 0.1 Hz. The High Z option on the generator was set. The alternating current was applied at 100-1200 V in 100 V increments. For each voltage, the strain indicator was set to zero, the amplifier turned on, and the frequency increased from minimum voltage to the desired voltage. Strain readings were taken using an Agilent datalogger, and then the voltage was decreased and the amplifier turned off. The strain indicator was re-zeroed, and the process was repeated. After Plate 1 was finished, Plate 2 was tested using the same process but the final voltage was 2400 V instead of 1200 V, as Plate 2 is twice the thickness of Plate 1.
Finally, the same experiment was modeled using ABAQUS. A plate of the same dimensions was created using C3D20E elements. The plate was constrained by pinning one comer, which allowed for no movement of that comer. The edge the comer belonged to was then fixed in the 1 and 3 directions, allowing no movement in either direction. The opposite edge was also fixed in the 3 direction, simulating the flat surface the plate was resting on.
Edge conslrained in the 1 and 3 directions
Figure 1: ABAQUS Constraints for Simple Piezoelectric Plate Test
II. PZT -Brass Actuator After the first test was completed and the experimental and predicted results compared, another experiment was performed. This experiment used three PZT plates and attached a brass plate of varying thickness to the top of each PZT plate. The PZT plates used in this experiment had dimensions of 2.5xO.80xO.0080 inches, and the brass plates measured 2xO.80xO.00l, 0.003, or 0.005 inches. The same instrumentation and testing process was used, but before applying the strain gages a brass plate was attached to the top of the PZT plate. This was done using 3M
3
double stick tape 9461P. The strain gages were then applied to both the top (brass) and bottom (PZT) of the actuator. The poling voltage was 640 V, and the maximum alternating current applied was 400 V.
For the ABAQUS model, the same constraints as applied in the simple piezoelectric plate test were used. The brass plates were attached using the *TIE constraint, which ties the PZT plate surface to the tape surface, and the tape surface to the brass surface.
III. THUNDER Actuator After the second test was completed, a test of the more complicated THUNDER actuator was performed. The experiment used a THUNDER actuator comprised of a stainless steel layer, glue, piezoelectric plate, glue, and a thin aluminum layer. The instrumentation and testing process was the same as used in the previous two tests, except that four strain gages were applied to both the top and the bottom of the THUNDER actuator, as shown below.
Figure 2: Top of THUNDER Actuator with Strain gages applied
The THUNDER actuator was then modeled using ABAQUS. Because of modeling complications, the glue and aluminum layers were not modeled, only the stainless steel and PZT layers. The boundary conditions were applied as in previous experiments. In order to simulate the bent form of the THUNDER actuator, a force was applied to the center of the actuator before applying a voltage across the actuator. The set up is shown below.
4
DISCUSSION
I. Simple Piezoelectric Plate Test As shown below, the difference between the ABAQUS predicted results and the experimental results for this simple piezoelectric plate test consist of three main problems: the hysteresis loop in the experimental results, a shift in the experimental results, and the overall slope of the strain versus electric field plot.
-- Experimental ~- Abaqus ---4.- Abaqus Exp D31
Plate 1 ~ 150 -,----------------, E <0
b T'-
X -c .~
Electric Field (x10"3 Vim)
b T'-
X -c
~ -60 +---~--~--~-----I
Electric Field (x10"3 Vim)
Figure 4: Simple Piezoelectric Plate Test Results at 200 Volts Peak to Peak
Because the slope of these plots is the piezoelectric constant D31, the difference in the slope can be accounted for by using the experimental D31 for the ABAQUS program. This is shown by the red in Figure 4. The shift in the experimental results is probably due to residual strain induced by the poling of the plates. This and the hysteresis loop are not easily accounted for, however the ABAQUS results would give a general idea of the PZT plates induced strain.
5
II. PZT -Brass Actuator The strain versus electric field data for each actuator (0.001, 0.003, and 0.005 inch brass plates) is shown below. When completing the ABAQUS simulation, the experimental piezoelectric constant D31 was used in order to better match the experimental data.
-- Experimental ~ ABAOUS
~ 200 T"""
~ -1000 -500 0 500 1000
Electric Field (x10"3 Vim)
E 80 60
-40 ..... -en -60 0 .....
Electric Field (x10"3 Vim)
Figure 5: PZT·Brass Actuator Test Results at 200 Volts Peak to Beak for a Brass Thickness of 0.001 inches
-- Experimental ABAOUS
~ 200 T"""
X 0 -c 'n; -200 ..... -en 0 -400 ..... .2 ~ -1000 -500 0 500 1000
Electric Field (x10"3 Vim)
~
Electric Field (x10"3 Vim)
Figure 6: PZT·Brass Actuator Test Results at 200 Volts Peak to Beak for a Brass Thickness of 0.003 inches
6
~ 200 ..- x 0 --c
.(ij -200 ..... -(/) 0 -400 ..... u ~ -1000 -500 0 500 1000
Electric Field (x1 ()1\3 Vim)
E -E co < 0 ..- x --c
.(ij ..... -(/) 0 ..... u ~
60 40 20 o
Electric Field (x10"3 Vim)
Figure 7: PZT-Brass Actuator Test Results at 200 Volts Peak to Beak for a Brass Thickness of 0.005 inches
The main shortfalls of the ABAQUS program concerning these Brass-PZT actuators are the inability of ABAQUS to capture even the direction at the top of the actuator's strain and the inability of ABAQUS to show the increased strain and therefore the increased piezoelectric constant D31 for the bottom of the actuator. Upon closer inspection of this effective D31 for the experimental and ABAQUS results, the ABAQUS effective D31 is virtually the same as the actual D31. The experimental D31, however, increases dramatically which causes the increased strain in the material.
Another interesting feature of the experimental data is the fact that the slope of the strain versus electric field plot at the top of the actuator is in the opposite direction for the 0.001 inch brass plate actuator as it is in the 0.003 and 0.005 inch brass plate actuators. This is probably because the 0.001 inch brass plate is so thin that the piezoelectric material is stretching the brass, where in the other two actuators, the brass is thick enough to induce actuation. This theory is supported by the fact that the slope of the strain versus electric field plot is less in the 0.001 inch actuator than in the 0.003 and 0.005 inch actuators.
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E Bottom of Actuator (PZT) u·c> -C\I u..-
0..---- --------,
::::<fJ We o
Electric Potential (Volts)
E u·c> -C\I u..- ~b OT"" N x Q)- O:::T""
('t)
20
o
-20
Electric Potential (Volts)
Figure 8: PZT -Brass Actuator Effective Piezoelectric Constant for a Brass Thickness of 0.005 inches
III. THUNDER Actuator Experimental Results of the THUNDER Testing are shown in Appendix 1. Because of time constraints, successful ABAQUS modeling of the THUNDER device was not achieved at the time of this report.
CONCLUSION From these initial results, it is clear that more work needs to be done to achieve a successful model of piezoelectric materials using ABAQUS. While it is clear that the ABAQUS program does not present an ideal representation of piezoelectric materials, it can be modified to present more accurate results. This study has identified the most significant problems of ABAQUS modeling of piezoelectric materials in relation to the strain measurements of piezoelectric actuators. They are as follows: piezoelectric hysteresis loops, the strain shift caused by poling of piezoelectric materials, the increased effective piezoelectric constant in a simple piezoelectric actuator, and the strain measurements on the top of a simple piezoelectric actuator.
Some if not all of these problems with ABAQUS can be overcome using various modeling techniques. For example, an initial strain based on the poling of the material could be applied to the material in order to account for the strain shift caused by poling of piezoelectric materials. More experimental studies of simple actuators could yield a formula to determine how much to increase the effective piezoelectric constant by to obtain similar stress results. Other methods could be employed to simulate hysteresis loops and to obtain accurate results for the strain on the top of a simple piezoelectric actuator.
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REFERENCES
"Load characterization of high displacement piezoelectric actuators with various end conditions." Sensors and Actuators April 2001. 19-24
"Piezoelectric strain in lead zierconate titante ceramics as a function of electric field, frequency, and dc bias." Journal of Applied Physics. 15 July 2003. Volume 94, number 2,1155-1162
Wanders, l.W. Piezoelectric Ceramics. Eindhoven; N.V. Philips, April 1991
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Thunder Wafer Instrumentation
Top Gage 1 (Uppe, Left) Gage 2;;:::: Gage 3 Uppe, Right
~I I Gage 4 (Lower Left)
Bottom (plate flipped horizontally)
Gage 5 (Upper Left) Gage 7 (Upper Right)
Test 2: 100 V with 150 DC Bias 100V, 150 DC Bias
0.0001 -,------------ - --- --- -------------,
Y = 1.6607E-ll x + 3.2009E-0
0.00005 r==~;;;;;;;;;;;~;;;;;;;;~:::_.~Y~-=~9~.36~1~0~E-~'2~X~+~2.~466;5E~-05~ o y = -5.065OE-12x + 1.2783E-05
4 0 500000 600000 700000 800000 900000 1 OOOOOOy = \ 'BWg_ 121 22~e888~:(J -0.00005 -\-_ ________________ --'-.....:..:::::..:=:.::..c=-:...:..:==::....::..=j
-0.0002
-0.00025
-0.0003
Bottom Upper Lelt (transverse) - Bottom Upper Rig,t
Top Upper Left (transverse) - Top Upper Rig,t - Bottom Lower Left - Bottom Center - Top Lower Left
y = -8.0069E-llx - 3.1943E-
y = -1.3911E-1Ox - 5.2621E-05
f------------- --- - - --l - To Center
4 5 6 7
Determining Limitations in the Ability of the ABAQUS Commercial Finite Element Analysis Program to Accurately Predict Piezoelectric Strain Behavior in Actuation Devices
Recommended Citation