Note: A valve-type piezoelectric reciprocating pump with secondary resonant vibrator Yu Ting Ma, Ce Wang, Xin Tao Yan, and Zhi Hua Feng
Citation: Rev. Sci. Instrum. 87, 016104 (2016); doi: 10.1063/1.4940412 View online: http://dx.doi.org/10.1063/1.4940412 View Table of Contents: http://aip.scitation.org/toc/rsi/87/1 Published by the American Institute of Physics
REVIEW OF SCIENTIFIC INSTRUMENTS 87, 016104 (2016)
Note: A valve-type piezoelectric reciprocating pump with secondary resonant vibrator Yu Ting Ma,1 Ce Wang,1 Xin Tao Yan,1 and Zhi Hua Feng2
1
CAS Key Lab of Bio-Medical Diagnostics, Suzhou Institute of Biomedical Engineering and Technology, Chinese Academy of Sciences, Suzhou, Jiangsu 215163, China 2 Department of Precision Machinery and Precision Instrumentation, University of Science and Technology of China, Hefei, Anhui 230026, China
(Received 18 August 2015; accepted 10 January 2016; published online 20 January 2016) A valve-type piezoelectric diaphragm pump using secondary resonant vibrator is introduced in this paper. The secondary resonant vibrator, which is mainly composed of a first vibrator and a second vibrator, is used to coordinate the frequency incompatibility between piezoelectric elements and check valves. The intermittent vibration of the first vibrator excites the resonant vibration of the second vibrator. The diaphragm in the pump chamber moves with the second vibrator, resulting in chamber volume and pressure variations. Control circuit capable of frequency tracking is designed. Vibration displacement and flow rate changing with driving voltage amplitude, frequency, and backpressure are studied in experiments. The flow rate of a prototype driven by voltage of 712 Vpp is 13.94 ml/min at secondary resonant frequency of 6 Hz. C 2016 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4940412]
Valve-type reciprocating displacement piezoelectric pumps utilize check valves to regulate flow direction, and the pump chamber is controlled by piezoelectric actuators. It is favorable that the pump works at resonant frequency of the chamber, which magnifies volume change and output power. But the mechanical membranes or flaps often used in check valves show a serious lag in frequency response, making it difficult to work with piezoelectric actuator synchronously.1,2 Compared with passive check valves, piezoelectric active valves3,4 increase the operating frequency of the pump, but in high frequency pumping, it is not easy to coordinate operation of pump vibrator and valve vibrator. And the valve control system is complex and difficult in integrated design. Using MEMS technology to produce new check valves5,6 with excellent high frequency characteristics is an alternative way, but these microvalves often have complex design, difficult manufacturing, high cost, and short life time. The incompatibility of valve and actuator has become a constraint to performance improvement of reciprocating displacement piezoelectric pumps. Large numbers of experiments and theoretical analysis prove that the higher the operating frequency of the piezoelectric element, the higher is its power density. Therefore, we believe that the frequency converter is a solution to the frequency incompatibility problem, which allows piezoelectric element to work with high power density, and allows the valve to work effectively. This note proposes a novel piezoelectric reciprocating pump with secondary resonant vibrator to complete the frequency converting. Besides, the pump can be separated into reusable actuator and disposable chamber, so it can achieve low-cost and contamination-free liquid delivery. A sectional view of the designed pump is shown in Fig. 1. The vibrator of the pump is comprised of the first vibrator and the second vibrator. Two rectangular piezoelectric sheets attached to a metal rod symmetrically serve as the first vibrator. 0034-6748/2016/87(1)/016104/3/$30.00
One end of the metal rod is clamped by the pump shell and the other end is free. A small piece of piezoelectric sheet is adhered to the metal rod serving as a vibrating sensor. The second vibrator consists of a metal ring that is put around the free end of the rod, and a coupler that connects the metal ring and pump diaphragm. For better performance, the bottom side surface of the metal rod is polished to be flat, which is beneficial to force transmission between piezoelectric sheets and metal rod. The inner radius of metal ring should be a little larger than the outer radius of metal rod. The coupler is supposed to transport the vertical deformation and force, so it should have large stiffness in vertical direction and be flexible in horizontal plane to facilitate smooth movement of the metal ring. One cycle of liquid transport is composed of two steps. First, the two piezoelectric elements are excited to push the metal rod to swing at its first bending resonant frequency. The metal ring is driven by rod to move downwards, as shown in Fig. 1(a). The diaphragm becomes convex and the pump chamber volume is increased, and the working liquid flow into pump chamber from inlet valve under negative pressure. Second, the metal rod stops swinging, so the diaphragm recovers to original state by elastic force and press working liquid out of the chamber through outlet valve, as shown in Fig. 1(b). With the two steps cycled, the working liquid can be continuously transported. By adjusting the intermittent excitation and suppression of the vibration of metal rod, resonant vibration of the second vibrator and a large output can be expected. The working frequency of check valve is equal to the vibrating frequency of the second vibrator, which is much lower than that of the piezoelectric elements, which is equal to the fundamental bending resonant frequency of the first vibrator. There are two reasons for the second vibrator to move downward during the absorbing period. One is the downward
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FIG. 1. Sectional view of the designed pump: (a) absorbing mode and (b) discharging mode.
force applied to the metal ring. As shown in Figs. 2(a) and 2(c), when the metal rod moves away from the central balance position to one side (forward period), downward force is applied to the metal ring. Although both upward and downward displacements are presented on the rubber diaphragm, the chamber volume is increased. On the contrary, when the metal rod moves back to central balance position (backward period), upward force is applied to the metal ring, and the chamber volume is decreased, as shown in Figs. 2(b) and 2(d). However, there is a gap between metal ring and rod, which means that the upward force is applied with shorter period than downward force. Or there is no upward force applied to metal ring if the size of gap is equal to the vibration amplitude because metal rod and ring make no contact during backward period with proper initial position. The second reason is the low response of the rubber diaphragm. When the metal rod moves back to central position, the metal ring cannot return to its original axial position if metal rod and ring make no contact (no upward force is applied), so its axial position is unchanged during this period. Therefore, an accumulated downward displacement of the metal ring is obtained after several vibrating cycle of the metal rod. After the first vibrator stop vibrating, there is enough time for the rubber diaphragm to recover, so the metal ring moves upwards driven by elasticity. A prototype pump was fabricated and investigated. The complete mechanical structure and a photograph of the assembled pump are shown in Fig. 3. The check valves were made by a PDMS (Polydimethylsiloxane) thin film sandwiched between two valve seal plates with grooved channels.7 A spring with stiffness of 125 kg/m was chosen as the coupler. The total
FIG. 2. The displacement of second vibrator in axial direction at different stages of vibration, and the supposed applied force is 100 N.
Rev. Sci. Instrum. 87, 016104 (2016)
size of the pump prototype was 30 mm × 30 mm × 77 mm. The detailed material properties and dimensions of the pump components are listed in Table I. The second vibrator moves along the axis of tube, so the bending resonant frequency of the metal tube is changing during the absorbing period. It is preferred for the driving circuit to automatically track the resonant frequency and achieve stable operation of the pump. Meanwhile, in order to increase the efficiency of the pump, it is better for the tube to start and stop vibration quickly. The above functions are enabled by the driving circuit shown in Fig. 4. Vin is the voltage signal from piezoelectric sensor. The metal tube was excited by a square waveform and the sensing signal is sinusoidal waveform with almost 90◦ phase shift, as shown in Fig. 4(b). The dynamic character of the vibrators was investigated using FEM simulation. The simulated first bending resonant frequency of the first vibrator without load was 1.84 kHz and the measured one was 1.724 kHz. The simulated first bending resonant frequency of the first vibrator with metal ring attached to the free end was 1.405 kHz and the measured one was 1.374 kHz. The measured resonant frequency of the first vibrator with second vibrator connected presented lower frequency of 1.337 kHz, which means that the second vibrator turns out to be a larger load than single metal ring. If the pump was filled with liquid, the measured resonant frequency of the first vibrator could be lower, which was 1.238 kHz and caused by liquid load. Besides, the simulated resonant frequency of the second vibrator without liquid load was 22 Hz.
FIG. 3. Photograph of a prototype pump. TABLE I. Dimensions and material properties of the pump components. Components Metal ring Coupler Metal tube Rubber diaphragm Piezoelectric sheets Piezoelectric sensor
Material
Steel Rubber PZT-4
Dimension (mm) Φ7 × Φ3.99 × 2.5 Φ8 × 10 Φ3.96 × 55 Φ12 × 0.1 15 × 3 × 0.4 3 × 3 × 0.4
FIG. 4. (a) Design of control circuit and (b) driving waveform.
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FIG. 7. Relationship between flow rate and backpressure.
FIG. 5. Relationship between flow rate, second vibrator displacement, and second vibrating frequency (a) with water and (b) without water.
Pump performance was investigated by experiments at room temperature. Figure 5(a) shows the relationship between flow rate, second vibrator displacement, and second vibrating frequency. The driving voltage was 712 Vpp at first bending resonant frequency of vibrating tube with load of 1.238 kHz. It was at second vibrating frequencies of 3 Hz and 6 Hz that outputted the largest displacement of 1.432 mm and largest flow rate of 13.94 ml/min, respectively. In comparison, the second vibrator displacement reaches 1.8 mm at resonant frequency of 20 Hz with no load, as shown in Fig. 5(b). It is reasonable for the resonant amplitude and frequency to drop because of water load and damping. As the system has a low Q due to frictional contact, vibration amplitude is not greatly amplified at second resonant frequency, so the frequency concerning the largest flow rate is not consistent to the frequency that outputs the largest vibrating amplitude. Figure 6 shows the relationship between driving voltage amplitude, flow rate, second vibrator displacement, and output voltage of piezoelectric sensor. The driving voltage was set at first resonant frequency of 1.238 kHz and second resonant frequency of 6 Hz. The flow rate, vibrating amplitude, and sensing voltage are all linear to the applied voltage amplitude. A flow rate of 13.94 ml/min can be obtained at a driving voltage of 712 Vpp. There is no flow detected below 460 Vpp as the
metal tube could not provide vibrating amplitude large enough to drive the metal ring. Figure 7 shows the relationship between flow rate and back pressure measured at resonant frequency of the pump under 712 Vpp. The flow rate nearly linearly decreases with the backpressure. The efficiency of frequency converting of the vibrator can be accessed by ( f 1 × A1)/( f h × Ah), where f l and f h are the resonant frequency of second vibrator and the first vibrator without load, respectively; Al and Ah are the vibration amplitude of the second vibrator and the first vibrator without load. The efficiency of this prototype is (20 × 1.8)/(1238 × 0.25) = 11.6%. In conclusion, we have demonstrated a pump using secondary resonant vibrator to coordinate the frequency incompatibility between piezoelectric actuator and check valves. The pump chamber is disposable for use in medical application such as drug delivery which disallows cross contamination. Experiment results show that the piezoelectric actuator of the pump works at above 1 kHz while the check valve works below 20 Hz. The maximum flow rate of 13.94 ml/min and maximum back pressure of 1.5 kPa are obtained when the pump is driven with 712 Vpp at second resonant frequency of 6 Hz. Future work will focus on a mechanism to complete secondary resonant vibration without friction contact, to increase efficiency of frequency converting. The authors would like to acknowledge the financial support from Project No. 51305439 supported by National Natural Science Foundation of China and Project No. BK20141205 supported by National Natural Science Foundation of Jiangsu Province of China. 1M. Hsiao-Kang, H. Bo-Ren, L. Cheng-Yao, and G. Jhong-Jhih, Int. Commun.
Heat Mass Transfer 35(8), 957–966 (2008). Zhang, J. Kan, G. Cheng, H. Wang, and Y. Jiang, Sens. Actuators, A 203, 29–36 (2013). 3D. G. Lee, S. W. Or, and G. P. Carman, J. Intell. Mater. Syst. Struct. 15(2), 107–115 (2004). 4A. Doll, M. Wischke, H. J. Schrag, A. Geipel, F. Goldschmidtboeing, and P. Woias, Microelectron. Eng. 84(5-8), 1202–1206 (2007). 5C. Chiang-Ho and T. Yi-Pin, Microsyst. Technol. 19(11), 1707–1715 (2013). 6M. Seong, K. P. Mohanchandra, Y. Lin, and G. P. Carman, Proc. SPIE 6932, 69322F (2008). 7X. Y. Wang, Y. T. Ma, G. Y. Yan, and Z. H. Feng, Smart Mater. Struct. 23(11), 115005 (2014). 2Z.
FIG. 6. Relationship between driving amplitude, flow rate, second vibrator amplitude, and output voltage of piezoelectric sensor.
Citation: Rev. Sci. Instrum. 87, 016104 (2016); doi: 10.1063/1.4940412 View online: http://dx.doi.org/10.1063/1.4940412 View Table of Contents: http://aip.scitation.org/toc/rsi/87/1 Published by the American Institute of Physics
REVIEW OF SCIENTIFIC INSTRUMENTS 87, 016104 (2016)
Note: A valve-type piezoelectric reciprocating pump with secondary resonant vibrator Yu Ting Ma,1 Ce Wang,1 Xin Tao Yan,1 and Zhi Hua Feng2
1
CAS Key Lab of Bio-Medical Diagnostics, Suzhou Institute of Biomedical Engineering and Technology, Chinese Academy of Sciences, Suzhou, Jiangsu 215163, China 2 Department of Precision Machinery and Precision Instrumentation, University of Science and Technology of China, Hefei, Anhui 230026, China
(Received 18 August 2015; accepted 10 January 2016; published online 20 January 2016) A valve-type piezoelectric diaphragm pump using secondary resonant vibrator is introduced in this paper. The secondary resonant vibrator, which is mainly composed of a first vibrator and a second vibrator, is used to coordinate the frequency incompatibility between piezoelectric elements and check valves. The intermittent vibration of the first vibrator excites the resonant vibration of the second vibrator. The diaphragm in the pump chamber moves with the second vibrator, resulting in chamber volume and pressure variations. Control circuit capable of frequency tracking is designed. Vibration displacement and flow rate changing with driving voltage amplitude, frequency, and backpressure are studied in experiments. The flow rate of a prototype driven by voltage of 712 Vpp is 13.94 ml/min at secondary resonant frequency of 6 Hz. C 2016 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4940412]
Valve-type reciprocating displacement piezoelectric pumps utilize check valves to regulate flow direction, and the pump chamber is controlled by piezoelectric actuators. It is favorable that the pump works at resonant frequency of the chamber, which magnifies volume change and output power. But the mechanical membranes or flaps often used in check valves show a serious lag in frequency response, making it difficult to work with piezoelectric actuator synchronously.1,2 Compared with passive check valves, piezoelectric active valves3,4 increase the operating frequency of the pump, but in high frequency pumping, it is not easy to coordinate operation of pump vibrator and valve vibrator. And the valve control system is complex and difficult in integrated design. Using MEMS technology to produce new check valves5,6 with excellent high frequency characteristics is an alternative way, but these microvalves often have complex design, difficult manufacturing, high cost, and short life time. The incompatibility of valve and actuator has become a constraint to performance improvement of reciprocating displacement piezoelectric pumps. Large numbers of experiments and theoretical analysis prove that the higher the operating frequency of the piezoelectric element, the higher is its power density. Therefore, we believe that the frequency converter is a solution to the frequency incompatibility problem, which allows piezoelectric element to work with high power density, and allows the valve to work effectively. This note proposes a novel piezoelectric reciprocating pump with secondary resonant vibrator to complete the frequency converting. Besides, the pump can be separated into reusable actuator and disposable chamber, so it can achieve low-cost and contamination-free liquid delivery. A sectional view of the designed pump is shown in Fig. 1. The vibrator of the pump is comprised of the first vibrator and the second vibrator. Two rectangular piezoelectric sheets attached to a metal rod symmetrically serve as the first vibrator. 0034-6748/2016/87(1)/016104/3/$30.00
One end of the metal rod is clamped by the pump shell and the other end is free. A small piece of piezoelectric sheet is adhered to the metal rod serving as a vibrating sensor. The second vibrator consists of a metal ring that is put around the free end of the rod, and a coupler that connects the metal ring and pump diaphragm. For better performance, the bottom side surface of the metal rod is polished to be flat, which is beneficial to force transmission between piezoelectric sheets and metal rod. The inner radius of metal ring should be a little larger than the outer radius of metal rod. The coupler is supposed to transport the vertical deformation and force, so it should have large stiffness in vertical direction and be flexible in horizontal plane to facilitate smooth movement of the metal ring. One cycle of liquid transport is composed of two steps. First, the two piezoelectric elements are excited to push the metal rod to swing at its first bending resonant frequency. The metal ring is driven by rod to move downwards, as shown in Fig. 1(a). The diaphragm becomes convex and the pump chamber volume is increased, and the working liquid flow into pump chamber from inlet valve under negative pressure. Second, the metal rod stops swinging, so the diaphragm recovers to original state by elastic force and press working liquid out of the chamber through outlet valve, as shown in Fig. 1(b). With the two steps cycled, the working liquid can be continuously transported. By adjusting the intermittent excitation and suppression of the vibration of metal rod, resonant vibration of the second vibrator and a large output can be expected. The working frequency of check valve is equal to the vibrating frequency of the second vibrator, which is much lower than that of the piezoelectric elements, which is equal to the fundamental bending resonant frequency of the first vibrator. There are two reasons for the second vibrator to move downward during the absorbing period. One is the downward
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FIG. 1. Sectional view of the designed pump: (a) absorbing mode and (b) discharging mode.
force applied to the metal ring. As shown in Figs. 2(a) and 2(c), when the metal rod moves away from the central balance position to one side (forward period), downward force is applied to the metal ring. Although both upward and downward displacements are presented on the rubber diaphragm, the chamber volume is increased. On the contrary, when the metal rod moves back to central balance position (backward period), upward force is applied to the metal ring, and the chamber volume is decreased, as shown in Figs. 2(b) and 2(d). However, there is a gap between metal ring and rod, which means that the upward force is applied with shorter period than downward force. Or there is no upward force applied to metal ring if the size of gap is equal to the vibration amplitude because metal rod and ring make no contact during backward period with proper initial position. The second reason is the low response of the rubber diaphragm. When the metal rod moves back to central position, the metal ring cannot return to its original axial position if metal rod and ring make no contact (no upward force is applied), so its axial position is unchanged during this period. Therefore, an accumulated downward displacement of the metal ring is obtained after several vibrating cycle of the metal rod. After the first vibrator stop vibrating, there is enough time for the rubber diaphragm to recover, so the metal ring moves upwards driven by elasticity. A prototype pump was fabricated and investigated. The complete mechanical structure and a photograph of the assembled pump are shown in Fig. 3. The check valves were made by a PDMS (Polydimethylsiloxane) thin film sandwiched between two valve seal plates with grooved channels.7 A spring with stiffness of 125 kg/m was chosen as the coupler. The total
FIG. 2. The displacement of second vibrator in axial direction at different stages of vibration, and the supposed applied force is 100 N.
Rev. Sci. Instrum. 87, 016104 (2016)
size of the pump prototype was 30 mm × 30 mm × 77 mm. The detailed material properties and dimensions of the pump components are listed in Table I. The second vibrator moves along the axis of tube, so the bending resonant frequency of the metal tube is changing during the absorbing period. It is preferred for the driving circuit to automatically track the resonant frequency and achieve stable operation of the pump. Meanwhile, in order to increase the efficiency of the pump, it is better for the tube to start and stop vibration quickly. The above functions are enabled by the driving circuit shown in Fig. 4. Vin is the voltage signal from piezoelectric sensor. The metal tube was excited by a square waveform and the sensing signal is sinusoidal waveform with almost 90◦ phase shift, as shown in Fig. 4(b). The dynamic character of the vibrators was investigated using FEM simulation. The simulated first bending resonant frequency of the first vibrator without load was 1.84 kHz and the measured one was 1.724 kHz. The simulated first bending resonant frequency of the first vibrator with metal ring attached to the free end was 1.405 kHz and the measured one was 1.374 kHz. The measured resonant frequency of the first vibrator with second vibrator connected presented lower frequency of 1.337 kHz, which means that the second vibrator turns out to be a larger load than single metal ring. If the pump was filled with liquid, the measured resonant frequency of the first vibrator could be lower, which was 1.238 kHz and caused by liquid load. Besides, the simulated resonant frequency of the second vibrator without liquid load was 22 Hz.
FIG. 3. Photograph of a prototype pump. TABLE I. Dimensions and material properties of the pump components. Components Metal ring Coupler Metal tube Rubber diaphragm Piezoelectric sheets Piezoelectric sensor
Material
Steel Rubber PZT-4
Dimension (mm) Φ7 × Φ3.99 × 2.5 Φ8 × 10 Φ3.96 × 55 Φ12 × 0.1 15 × 3 × 0.4 3 × 3 × 0.4
FIG. 4. (a) Design of control circuit and (b) driving waveform.
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FIG. 7. Relationship between flow rate and backpressure.
FIG. 5. Relationship between flow rate, second vibrator displacement, and second vibrating frequency (a) with water and (b) without water.
Pump performance was investigated by experiments at room temperature. Figure 5(a) shows the relationship between flow rate, second vibrator displacement, and second vibrating frequency. The driving voltage was 712 Vpp at first bending resonant frequency of vibrating tube with load of 1.238 kHz. It was at second vibrating frequencies of 3 Hz and 6 Hz that outputted the largest displacement of 1.432 mm and largest flow rate of 13.94 ml/min, respectively. In comparison, the second vibrator displacement reaches 1.8 mm at resonant frequency of 20 Hz with no load, as shown in Fig. 5(b). It is reasonable for the resonant amplitude and frequency to drop because of water load and damping. As the system has a low Q due to frictional contact, vibration amplitude is not greatly amplified at second resonant frequency, so the frequency concerning the largest flow rate is not consistent to the frequency that outputs the largest vibrating amplitude. Figure 6 shows the relationship between driving voltage amplitude, flow rate, second vibrator displacement, and output voltage of piezoelectric sensor. The driving voltage was set at first resonant frequency of 1.238 kHz and second resonant frequency of 6 Hz. The flow rate, vibrating amplitude, and sensing voltage are all linear to the applied voltage amplitude. A flow rate of 13.94 ml/min can be obtained at a driving voltage of 712 Vpp. There is no flow detected below 460 Vpp as the
metal tube could not provide vibrating amplitude large enough to drive the metal ring. Figure 7 shows the relationship between flow rate and back pressure measured at resonant frequency of the pump under 712 Vpp. The flow rate nearly linearly decreases with the backpressure. The efficiency of frequency converting of the vibrator can be accessed by ( f 1 × A1)/( f h × Ah), where f l and f h are the resonant frequency of second vibrator and the first vibrator without load, respectively; Al and Ah are the vibration amplitude of the second vibrator and the first vibrator without load. The efficiency of this prototype is (20 × 1.8)/(1238 × 0.25) = 11.6%. In conclusion, we have demonstrated a pump using secondary resonant vibrator to coordinate the frequency incompatibility between piezoelectric actuator and check valves. The pump chamber is disposable for use in medical application such as drug delivery which disallows cross contamination. Experiment results show that the piezoelectric actuator of the pump works at above 1 kHz while the check valve works below 20 Hz. The maximum flow rate of 13.94 ml/min and maximum back pressure of 1.5 kPa are obtained when the pump is driven with 712 Vpp at second resonant frequency of 6 Hz. Future work will focus on a mechanism to complete secondary resonant vibration without friction contact, to increase efficiency of frequency converting. The authors would like to acknowledge the financial support from Project No. 51305439 supported by National Natural Science Foundation of China and Project No. BK20141205 supported by National Natural Science Foundation of Jiangsu Province of China. 1M. Hsiao-Kang, H. Bo-Ren, L. Cheng-Yao, and G. Jhong-Jhih, Int. Commun.
Heat Mass Transfer 35(8), 957–966 (2008). Zhang, J. Kan, G. Cheng, H. Wang, and Y. Jiang, Sens. Actuators, A 203, 29–36 (2013). 3D. G. Lee, S. W. Or, and G. P. Carman, J. Intell. Mater. Syst. Struct. 15(2), 107–115 (2004). 4A. Doll, M. Wischke, H. J. Schrag, A. Geipel, F. Goldschmidtboeing, and P. Woias, Microelectron. Eng. 84(5-8), 1202–1206 (2007). 5C. Chiang-Ho and T. Yi-Pin, Microsyst. Technol. 19(11), 1707–1715 (2013). 6M. Seong, K. P. Mohanchandra, Y. Lin, and G. P. Carman, Proc. SPIE 6932, 69322F (2008). 7X. Y. Wang, Y. T. Ma, G. Y. Yan, and Z. H. Feng, Smart Mater. Struct. 23(11), 115005 (2014). 2Z.
FIG. 6. Relationship between driving amplitude, flow rate, second vibrator amplitude, and output voltage of piezoelectric sensor.
