Design, Modeling, and Experiment of a Piezoelectric Pressure


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DESIGN, MODELING, AND EXPERIMENT OF A PIEZOELECTRIC PRESSURE SENSOR BASED ON A THICKNESS-SHEAR MODE CRYSTAL RESONATOR Thanh Tuong Pham
Thesis Prepared for the Degree of MASTER OF SCIENCE
UNIVERSITY OF NORTH TEXAS May 2017
APPROVED: Haifeing Zhang, Major Professor Phillip R. Foster, Committee Member Shuping Wang, Committee Member Enrique Barbieri, Chair of the Department of
Engineering Technology Costas Tsatsoulis, Dean of the College of
Engineering Victor Prybutok, Vice Provost of the Toulouse
Graduate School

Pham, Thanh Tuong. Design, Modeling, and Experiment of a Piezoelectric Pressure Sensor based on a Thickness-Shear Mode Crystal Resonator. Master of Science (Engineering Technology), May 2017, 71 pp., 2 tables, 56 figures, 37 numbered references.
This thesis presents the design, modeling, and experiment of a novel pressure sensor using a dual-mode AT-cut quartz crystal resonator with beat frequency analysis based temperature compensation technique. The proposed sensor can measure pressure and temperature simultaneously by a single AT-cut quartz resonator. Apart from AT-cut quartz crystal, a newly developed Langasite (LGS) crystal resonator is also considered in the proposed pressure sensor design, since LGS can operate in a higher temperature environment than ATcut quartz crystal. The pressure sensor is designed using CAD (computer aided design) software and CAE software - COMSOL Multiphysics. Finite element analysis (FEA) of the pressure sensor is performed to analyze the stress- strain of the sensor’s mechanical structure. A 3D printing prototype of the sensor is fabricated and the proposed sensing principle is verified using a force-frequency analysis apparatus. Next to the 3D printing model verification, the pressure sensor with stainless steel housing has been fabricated with inbuilt crystal oscillator circuit. The oscillator circuit is used to excite the piezo crystal resonator at its fundamental vibrational mode and give the frequency as an output signal. Based on the FEA and experimental results, it has been concluded that the maximum pressure that the sensor can measure is 45 (psi). The pressure test results performed on the stainless steel product shows a highly linear relationship between the input (pressure) and the output (frequency).

Copyright 2017 by
Thanh Tuong Pham
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ACKNOWLEDGEMENT First, I would like to express my thanks, sincere gratitude, and appreciation to my Major Professor, Dr. Haifeng Zhang, for his instruction, great support, and motivation to accomplish my thesis. He consistently allowed this paper to be my own work, but steered me in the right the direction whenever he thought I needed it. Second, I also truly express my thanks to Committee members Dr. Phillip R. Foster and Dr. Shuping Wang for their guidance and invaluable comments on this thesis. Next, I would like to give special thanks Dr. Suresh Kaluvan - a member in Dr. Zhang’s lab, other members in the lab, friends, and ETEC department staff for their support during the time I worked on my thesis. Finally, I would like to thank you my family members for their encouragement, physical and mental support. This thesis could not be accomplished without their contributions.
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TABLE OF CONTENTS

Page

ACKNOWLEDGEMENT ..................................................................................................................... iii

LIST OF TABLES ...............................................................................................................................vi

LIST OF FIGURES ............................................................................................................................vii

CHAPTER 1 INTRODUCTION ............................................................................................................ 1

CHAPTER 2 LITERATURE REVIEW .................................................................................................... 4

2.1 Pressure Measurement and Pressure Sensor .................................................................. 4

2.2 Piezoelectric Material and Piezoelectric Effect................................................................ 9

2.2.1 Piezoelectric Material ............................................................................................... 9

2.2.2 Piezoelectric Effect.................................................................................................. 11

2.3 AT-Cut Quartz and Langasite Piezoelectric Material ..................................................... 12

2.3.1 AT-Cut Quartz Piezoelectric Material ..................................................................... 12

2.3.2 Langasite Piezoelectric Material ............................................................................. 13

2.4 Bulk Acoustic Wave (BAW), Surface Acoustic Wave (SAW), and Modes of Vibration .. 14

2.5 Force-Frequency Effect on Crystal Resonator................................................................ 16

2.6 Application of Quartz, Langasite Crystal on Pressure Sensor ........................................ 19

2.7 Temperature and Resonance Frequency Relation on Crystal Resonator ...................... 19

2.8 Dual-Mode and Temperature Compensation ................................................................ 21

CHAPTER 3 EXPERIMENT METHODOLOGY ................................................................................... 22 3.1 Experiment on Force-Frequency Effect of Crystal Resonator........................................ 22

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3.1.1 Experiment Procedure ............................................................................................ 22 3.1.2 Experiment Results ................................................................................................. 25 3.2 Pressure Sensor Housing Design .................................................................................... 27 3.2.1 Operation Principle of the Presssure Sensor .......................................................... 27 3.2.2 Preliminary Design by CAD (Computer Aided Design) Software ............................ 28 3.2.3 Finite Element Analysis (FEA) of the Pressure Sensor ............................................ 31 3.3 3D Printing Prototype..................................................................................................... 38 3.4 Experiment on 3D Printing Prototype ............................................................................ 38 3.5 Design and Fabrication of Pressure Sensor with Stainless Steel Housing ..................... 40 3.6 Experiment on Pressure Sensor with Stainless Steel Housing ....................................... 43 3.7 Crystal Oscillator Circuit Design ..................................................................................... 47 3.8 Beat Frequency Experiment ........................................................................................... 48 CHAPTER 4 CONCLUSION AND FUTURE RESEARCH...................................................................... 54 APPENDIX A DESIGN DRAWINGS OF PRESSURE SENSOR ............................................................. 55 APPENDIX B DESIGN DRAWINGS OF ALL-LANGASITE STRUCTURE............................................... 64 REFERENCES .................................................................................................................................. 67
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LIST OF TABLES

Page

Table 1: Maximum Force Applied on Crystal ................................................................................ 37

Table 2: Force-Frequency Relation ............................................................................................... 40

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LIST OF FIGURES

Page

Figure 1: Pressure sensor using diametric force application (Hewlett Packard)............................ 6

Figure 2: Structures where external hydrostatic pressure applies planar stress patterns in a

TSMR disc via a cylindrical shell ...................................................................................................... 7

Figure 3: Pressure sensor using uniaxial stress (Schlumberger)..................................................... 7

Figure 4: Components of the all-langasite sensor structure .......................................................... 8

Figure 5: Unit cell of quartz [16] ................................................................................................... 10

Figure 6: Direct piezoelectric effect [16] ...................................................................................... 11

Figure 7: Inverse piezoelectric effect at applied electric field [16] .............................................. 11

Figure 8: Typical cuts of quartz crystal [18] .................................................................................. 13

Figure 9: Modes of vibration of quartz resonator [21]................................................................. 15

Figure 10: Isometric view of an AT-cut quartz crystal resonator ................................................. 16

Figure 11: Illustration of force application and azimuth angle ψ [29] ......................................... 17

Figure 12: Force sensitivity coefficients in resonators of different materials and cuts [31] ........ 18

Figure 13: Block diagram of the temperature compensation ...................................................... 21

Figure 14: 3D isometric view (a) and front view (b) of the force loading device ......................... 22

Figure 15 Pictorial representation of the force loading device .................................................... 23

Figure 16: Photo of experiment setup .......................................................................................... 24

Figure 17: Definition of azimuth angles ψ for the experiment .................................................... 25

Figure 18: Force-frequency relation graph at different azimuth angles ψ obtained from

LabVIEW ........................................................................................................................................ 26

Figure 19: The curve Kf of a quartz resonator from the experiment vs. peer’s curve Kf.............. 27

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Figure 20: Mounting methods for TSMR using either a two-point mount or a three or four-point mount [21] .................................................................................................................................... 28 Figure 21: Dimensions and section view of the pressure sensor ................................................. 29 Figure 22: Detailed view and side view B of the pressure sensor ................................................ 29 Figure 23: Section isometric view (a) and exploded view (b) of the pressure sensor.................. 30 Figure 24: Subdomains (a, b, c, d) of the analyzed assembly model............................................ 31 Figure 25: Boundaries (a, b, c, d) of the analyzed assembly model ............................................. 32 Figure 26: Mesh analysis of the analyzed assembly model .......................................................... 33 Figure 27: Stress vs. diametric dimension of the crystal resonator ............................................. 34 Figure 28: FEA result of stress on a diametric section of the assembly model ............................ 35 Figure 29: FEA result of displacement on the assembly model.................................................... 35 Figure 30: FEA result of displacement on a diametric section of the assembly model ............... 36 Figure 31: Linear relationship between the inlet pressure and force applied on the crystal ...... 37 Figure 32: Prototype of the pressure sensor fabricated by a 3D printer ..................................... 38 Figure 33: (a) Mounting and electrical connection of the crystal, and (b) Fundamental resonance frequency graph of the crystal when the applied force is 0 N ..................................................... 39 Figure 34: (a) Force applied on the box, (b) Force-frequency graph............................................ 40 Figure 35: Section view of the assembly of the designed pressure sensor.................................. 41 Figure 36: Detail views of the assembly of the designed pressure sensor................................... 41 Figure 37: Bill of material of pressure sensor assembly ............................................................... 41 Figure 38: Mounted crystal on one end cap (holder) ................................................................... 42 Figure 39: Stainless steel pressure sensor final assembly ............................................................ 42
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Figure 40: Final assembly of the pressure sensor with stainless steel housing ........................... 43 Figure 41: Diaphragm of the resonance frequency measurement .............................................. 43 Figure 42: Resonance frequency measurement on mounted crystal .......................................... 44 Figure 43: Schematic diaphragm of the pressure measurement experiment setup ................... 44 Figure 44: Pictorial diaphragm of the pressure measurement experiment setup ....................... 45 Figure 45: Pressure measurement experiment and graph result................................................. 46 Figure 46: Fabricated crystal oscillator circuit .............................................................................. 46 Figure 47: Pressure measurement result of the designed pressure sensor ................................. 47 Figure 48: Designed crystal oscillator circuit ................................................................................ 48 Figure 49: Fabricated crystal oscillator circuit .............................................................................. 48 Figure 50: Diagram of the experiment setup on temperature vs. frequency .............................. 49 Figure 51: Photos of the experiment set up for beat frequency vs. temperature ....................... 50 Figure 52: Crystal resonator mounting and connection in the ceramic box ................................ 50 Figure 53: 3*fundamental frequency and 3rd overtone frequency vs. temperature in quartz... 51 Figure 54: 3*fundamental frequency and 3rd overtone frequency vs. temperature in LGS ....... 52 Figure 55: Beat frequency vs. temperature of quartz .................................................................. 52 Figure 56: Beat frequency vs. temperature of LGS....................................................................... 53
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Design, Modeling, and Experiment of a Piezoelectric Pressure