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The resonance vibration properties of a bimorph flexural piezoelectric ultrasonic transducer for distance measurement
Materials Science and Engineering B99 (2003) 316 /320 www.elsevier.com/locate/mseb
The resonance vibration properties of a bimorph flexural piezoelectric ultrasonic transducer for distance measurement XiaoBing Hu, LongTu Li, XiangCheng Chu *, ZhiLun Gui Department of Materials Science and Engineering, State Key Laboratory of New Ceramics and Fine Processing, Tsinghua University, Beijing 100084, People’s Republic of China Received 14 June 2002; received in revised form 10 October 2002
Abstract In this paper, a bimorph flexural piezoelectric ultrasonic transducer (PUT) with improved design principles for distance measurement was discussed. The profiles of vibration modes of PUT have been measured by laser Doppler interferometry and compared with finite element analysis (FEA) results. The results show the measurement modes and FEA calculated ones are well matched. The combination and comparison between FEA and advanced measurement tools have provided much help to the design and fabrication of PUT. # 2002 Published by Elsevier Science B.V. Keywords: Resonance vibration; Laser Doppler interferometry; Piezoelectric ultrasonic transducer (PUT); Finite element analysis (FEA)
1. Introduction Piezoelectric ultrasonic transducers (PUTs) are now widely used in distance sensing, medical imaging, and other applications. In relatively low frequency applications such as air acoustics, large displacement and deformation are often required, which is often far beyond the range reachable by ceramics materials. In order to overcome this problem, for the application of airborne distance sensing, a bimorph flexural structure is usually suggested. The maximum operation frequency is limited by the attenuation of sound waves in the air, which increases as the operation frequency increases, and is usually below 100 kHz for sensing distances up to 3 m. The operation frequencies also depend on the physical properties of the materials and transducer structure parameters. Theoretical predictions of the resonance frequencies are very desirable for design and engineering of this kind of transducer. The ultrasonic performance of such a transducer, such a directivity of their beam and sound pressure at axial direction
* Corresponding author. Tel.: /86-10-6278-6189; fax: /86-106277-1160 E-mail address: [email protected] (X. Chu).
strongly depends on the vibration profiles of the transducer. More significantly, experimental researches of dynamic surface vibration are valuable because ultrasonic pressure generated by a transducer depends not only on the vibration amplitude but also on the phase relationships between different surface areas. The purpose of this study was to research the vibration behavior and structure performance relationship of this transducer.
2. Model The inner structure and equivalent model of resonant parts of PUT are shown in Fig. 1. A thin plate PMNPNN-PZT piezoelectric ceramic was used as the exciting part [1], that is, it served as the converter between electric power and mechanic power. Therefore, the construction of a bimorph flexural PUT consists of two steps: making a high quality piezoelectric ceramic disk and assembling it to a housing. Poled piezoelectric ceramic was electroded by printing silver ink on both sides. Then it was attached into inner side of the bottom of metal housing by epoxy (Fig. 1a). The equivalent model of resonant parts of PUT was shown in Fig. 1b. The thickness of ceramic disk and housing bottom was
0921-5107/02/$ - see front matter # 2002 Published by Elsevier Science B.V. PII: S 0 9 2 1 - 5 1 0 7 ( 0 2 ) 0 0 5 6 2 - 7
X. Hu et al. / Materials Science and Engineering B99 (2003) 316 /320
317
Fig. 1. Schematic images of the inner structure of PUT (a) and equivalent model (b).
0.7 and 0.6 mm, respectively, and the nominal thickness of silver ink and epoxy were negligible in the model. The diameter of ceramic disk and housing bottom was 10.0 and 12.4 mm, respectively. The model could be simplified into an equivalent composite thin disk with fixed boundary. According to the theory of thin disk, the equation of the motion for the composite thin disk with fixed boundary is [2]: 94 j
12r(1 s2 ) @ 2 j Eh2
@t2
0
(1)
where E is Young’s modulus, s is Poisson’s ratio, j is the surface particle out-of-plane displacement, h is the thickness of the disk. Combined with the boundary conditions, Eq. (1) can be numerically calculated by computer once the parameters are determined.The resonance frequencies are: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi m20n h E f0n (2) 2 4pa 3r(1 s2 ) The corresponding resonance frequencies are: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h E f01 0:469 2 a 3r(1 s2 ) 6:306 2 f02 f01 3:89f01 3:196
(3) (4)
The function of the symmetric vibration profiles is: m J (m ) m (5) j¯0 (r) A0 J0 0n r 0 0n I0 0n r I0 (m0n ) a a Combined the specific cases, the first-order, secondorder symmetric vibration profiles are: 3:196 3:196 r 0:0555I0 r (6) j¯01 (r) A01 J0 a a 6:306 6:306 r 0:00252I0 r (7) j¯02 (r) A02 J0 a a j¯/(r, 8 ) is the distribution function of the resonant vibration.
/
The finite element analysis (FEA) of the resonant parts of PUT was conducted by ANSYS 6.0. The piezoelectric module VM175 for the analysis of the threedimensional piezoelectric vibration was adopted, one of the mechanical force which fixed the housing bottom flank boundary and one of the electrical potential or charge in the thickness were specified as the boundary conditions. The PMN-PNN-PZT piezoelectric ceramic showed Kp of 0.697, d33 of 644pC/N, o33 of 3318, Qm of 18.1 and tg d of 1.92e-2. The profiles of the first-order and second-order resonant modes were computed by FEA method, which are shown in Fig. 2.
3. Experimental The surface out-of-plane vibration displacement distributions associated with the various piezoclectrically excitable resonance frequencies of the PUT were measured systematically by use of a specially developed laser vibrometer (OFV3001S/OFV-056, Polytec, Waldbronn, Germany). The function generator is HP 3325B. The conductance spectrum was measured by HP 4194A. Resonance frequencies of the PUT were measured by the laser vibrometer. Two different measurement methods can be conducted by the laser vibrometer; single point detection and area scanning. Resonance frequencies of the vibrations can be measured by single point detection, and the modal shapes by area scanning. A 12 V sine wave AC electric voltage was applied to the piezoelectric ceramic disk, and the laser beam was perpendicularly incident on the sound emission surface of the PUT. During single point detection, with the changing of the driving frequency of the applied field, the frequency response of the out-of-plane displacement (or velocity) of that point can be measured. Resonance occurs when the displacement (or velocity) reaches a maximum. Two resonance modes were observed at 40.0 and 153.0 kHz, respectively, which are shown in Fig. 3. They are the first-order and second-order symmetric resonant modes. The conductance spectrum is shown in Fig. 4. Although the resonant frequencies in the conductance spectrum have a little difference from those in the displacement spectrum, they are almost the same.
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X. Hu et al. / Materials Science and Engineering B99 (2003) 316 /320
Fig. 2. Modal shapes with displacements at each resonance.
preselected surface area and the vibration profile of the area can be mapped out. Shown in Fig. 5a and b are the surface displacement profiles at first-order and secondorder symmetric resonant modes.
4. Discussion
Fig. 3. Frequency response of out-of-plane displacement.
Fig. 4. Measured input conductance of the transducer.
It was obvious since the impedance has very close relationship with the mechanical resonance mode. For an airborne PUT, experimental information about the surface vibration amplitude is very important because they directly affect the radiated sound pressure and the ultrasound beam patterns. This surface vibration profile can be measured by using the area scanning mode of the laser vibrometer. In this mode, the frequency of the applied electric field is usually fixed at a resonance frequency. The laser beam can scan a
As discussed above, Eqs. (6) and (7) can give the outof-plane displacement amplitude of the PUT. We can also get the experimental results from the laser scanning images. To verify the calculation results, the changes of surface displacement amplitude have been plotted. Normalizing the surface position, with 0 and 1 representing the clamped edges and 0.5 representing the center point. Since at the first-order symmetric resonance frequency, the surface can generate strong sound pressure in the air, it was used at the practical use and thoroughly studied. Fig. 6 is the comparison of measured and calculated displacement distributions at the first-order resonance frequency. The voltage response of the displacement amplitude at the central point (normalized position /0.5) was also measured, as shown in Fig. 7. According to the Eqs. (3) and (4), Figs. 2 and 5, the numerical and FEA calculated, and measured resonance frequencies in this work were compared, which are shown in Table 1. From Table 1, the numerical calculated and FEA calculated results are nearly consistent with that of measurement. The surface vibration profile of the PUT has important effects on the performance of the transducer such as sound pressure and beam patterns. In this paper, both experimental and theoretical studies of surface vibration profiles are presented. Theoretical calculation predicted the displacement amplitude profiles, which can be verified by the laser vibrometer. As is shown in Fig. 6, it is obvious that the calculation model can provide fairly good prediction of the displacement peak positions (about 6% discrepancy). However, the experimental results show lower amplitude than the calculated because of the following reasons. First, the backing materials has a little clamping effect on the
X. Hu et al. / Materials Science and Engineering B99 (2003) 316 /320
319
Fig. 5. Surface displacement amplitudes. Table 1 Numerical and FEA calculated, and measured resonance frequencies
Numerical calculated FEA calculated Measured
Fig. 6. Comparison of measured and calculated displacement profiles.
First-order (kHz)
Second-order (kHz)
39.3 42.8 40.0
153.0 148.8 153.0
tical model in this work assumed perfect clamped at the round edge. However, it was found that even with a well-designed mechanical clamped system, this clamping condition was still not perfectly satisfied. Not only is the surface vibration amplitude important, but also the phase relationship between different areas can strongly affect the generated sound pressure. The laser vibrometer can take a snapshot of the surface vibration at any moment of a driving circle and can also export the animated files. From Fig. 6, we can see that, under a driving electric field, all points at the surface move toward the same direction at any moment of time. This in-phase vibration profile can generate a strong ultrasound wave in the air. From Fig. 7, we can see that the displacement amplitudes at the central point are linear with the input AC voltage.
Fig. 7. Voltage response of the displacement amplitudes at the central point.
5. Conclusion
surface, which was assumed to be free from any mechanical clamping in the calculation, also reduced the overall vibration amplitude. Secondly, the theore-
This paper describes a type of PUT with improved design principles to measure distance. High-performance low-sintering piezoelectric ceramics based on PMN-PNN-PZT were adopted. The numerical and
320
X. Hu et al. / Materials Science and Engineering B99 (2003) 316 /320
finite element analysis of their resonant modes were analyzed. A laser scanning vibrometer has been used to measure the displacement amplitude profiles of their resonant mode. It is greatly helpful to us to design and analyze transducers.
References [1] Z. Gui, H. Hu, L. Li, et al., Solid State Phenomena 25 and 26 (1992) 309 /316. [2] Y. Xue, Acoustic and Electronic Engineering 58 (2000) 10 /15.
The resonance vibration properties of a bimorph flexural piezoelectric ultrasonic transducer for distance measurement XiaoBing Hu, LongTu Li, XiangCheng Chu *, ZhiLun Gui Department of Materials Science and Engineering, State Key Laboratory of New Ceramics and Fine Processing, Tsinghua University, Beijing 100084, People’s Republic of China Received 14 June 2002; received in revised form 10 October 2002
Abstract In this paper, a bimorph flexural piezoelectric ultrasonic transducer (PUT) with improved design principles for distance measurement was discussed. The profiles of vibration modes of PUT have been measured by laser Doppler interferometry and compared with finite element analysis (FEA) results. The results show the measurement modes and FEA calculated ones are well matched. The combination and comparison between FEA and advanced measurement tools have provided much help to the design and fabrication of PUT. # 2002 Published by Elsevier Science B.V. Keywords: Resonance vibration; Laser Doppler interferometry; Piezoelectric ultrasonic transducer (PUT); Finite element analysis (FEA)
1. Introduction Piezoelectric ultrasonic transducers (PUTs) are now widely used in distance sensing, medical imaging, and other applications. In relatively low frequency applications such as air acoustics, large displacement and deformation are often required, which is often far beyond the range reachable by ceramics materials. In order to overcome this problem, for the application of airborne distance sensing, a bimorph flexural structure is usually suggested. The maximum operation frequency is limited by the attenuation of sound waves in the air, which increases as the operation frequency increases, and is usually below 100 kHz for sensing distances up to 3 m. The operation frequencies also depend on the physical properties of the materials and transducer structure parameters. Theoretical predictions of the resonance frequencies are very desirable for design and engineering of this kind of transducer. The ultrasonic performance of such a transducer, such a directivity of their beam and sound pressure at axial direction
* Corresponding author. Tel.: /86-10-6278-6189; fax: /86-106277-1160 E-mail address: [email protected] (X. Chu).
strongly depends on the vibration profiles of the transducer. More significantly, experimental researches of dynamic surface vibration are valuable because ultrasonic pressure generated by a transducer depends not only on the vibration amplitude but also on the phase relationships between different surface areas. The purpose of this study was to research the vibration behavior and structure performance relationship of this transducer.
2. Model The inner structure and equivalent model of resonant parts of PUT are shown in Fig. 1. A thin plate PMNPNN-PZT piezoelectric ceramic was used as the exciting part [1], that is, it served as the converter between electric power and mechanic power. Therefore, the construction of a bimorph flexural PUT consists of two steps: making a high quality piezoelectric ceramic disk and assembling it to a housing. Poled piezoelectric ceramic was electroded by printing silver ink on both sides. Then it was attached into inner side of the bottom of metal housing by epoxy (Fig. 1a). The equivalent model of resonant parts of PUT was shown in Fig. 1b. The thickness of ceramic disk and housing bottom was
0921-5107/02/$ - see front matter # 2002 Published by Elsevier Science B.V. PII: S 0 9 2 1 - 5 1 0 7 ( 0 2 ) 0 0 5 6 2 - 7
X. Hu et al. / Materials Science and Engineering B99 (2003) 316 /320
317
Fig. 1. Schematic images of the inner structure of PUT (a) and equivalent model (b).
0.7 and 0.6 mm, respectively, and the nominal thickness of silver ink and epoxy were negligible in the model. The diameter of ceramic disk and housing bottom was 10.0 and 12.4 mm, respectively. The model could be simplified into an equivalent composite thin disk with fixed boundary. According to the theory of thin disk, the equation of the motion for the composite thin disk with fixed boundary is [2]: 94 j
12r(1 s2 ) @ 2 j Eh2
@t2
0
(1)
where E is Young’s modulus, s is Poisson’s ratio, j is the surface particle out-of-plane displacement, h is the thickness of the disk. Combined with the boundary conditions, Eq. (1) can be numerically calculated by computer once the parameters are determined.The resonance frequencies are: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi m20n h E f0n (2) 2 4pa 3r(1 s2 ) The corresponding resonance frequencies are: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h E f01 0:469 2 a 3r(1 s2 ) 6:306 2 f02 f01 3:89f01 3:196
(3) (4)
The function of the symmetric vibration profiles is: m J (m ) m (5) j¯0 (r) A0 J0 0n r 0 0n I0 0n r I0 (m0n ) a a Combined the specific cases, the first-order, secondorder symmetric vibration profiles are: 3:196 3:196 r 0:0555I0 r (6) j¯01 (r) A01 J0 a a 6:306 6:306 r 0:00252I0 r (7) j¯02 (r) A02 J0 a a j¯/(r, 8 ) is the distribution function of the resonant vibration.
/
The finite element analysis (FEA) of the resonant parts of PUT was conducted by ANSYS 6.0. The piezoelectric module VM175 for the analysis of the threedimensional piezoelectric vibration was adopted, one of the mechanical force which fixed the housing bottom flank boundary and one of the electrical potential or charge in the thickness were specified as the boundary conditions. The PMN-PNN-PZT piezoelectric ceramic showed Kp of 0.697, d33 of 644pC/N, o33 of 3318, Qm of 18.1 and tg d of 1.92e-2. The profiles of the first-order and second-order resonant modes were computed by FEA method, which are shown in Fig. 2.
3. Experimental The surface out-of-plane vibration displacement distributions associated with the various piezoclectrically excitable resonance frequencies of the PUT were measured systematically by use of a specially developed laser vibrometer (OFV3001S/OFV-056, Polytec, Waldbronn, Germany). The function generator is HP 3325B. The conductance spectrum was measured by HP 4194A. Resonance frequencies of the PUT were measured by the laser vibrometer. Two different measurement methods can be conducted by the laser vibrometer; single point detection and area scanning. Resonance frequencies of the vibrations can be measured by single point detection, and the modal shapes by area scanning. A 12 V sine wave AC electric voltage was applied to the piezoelectric ceramic disk, and the laser beam was perpendicularly incident on the sound emission surface of the PUT. During single point detection, with the changing of the driving frequency of the applied field, the frequency response of the out-of-plane displacement (or velocity) of that point can be measured. Resonance occurs when the displacement (or velocity) reaches a maximum. Two resonance modes were observed at 40.0 and 153.0 kHz, respectively, which are shown in Fig. 3. They are the first-order and second-order symmetric resonant modes. The conductance spectrum is shown in Fig. 4. Although the resonant frequencies in the conductance spectrum have a little difference from those in the displacement spectrum, they are almost the same.
318
X. Hu et al. / Materials Science and Engineering B99 (2003) 316 /320
Fig. 2. Modal shapes with displacements at each resonance.
preselected surface area and the vibration profile of the area can be mapped out. Shown in Fig. 5a and b are the surface displacement profiles at first-order and secondorder symmetric resonant modes.
4. Discussion
Fig. 3. Frequency response of out-of-plane displacement.
Fig. 4. Measured input conductance of the transducer.
It was obvious since the impedance has very close relationship with the mechanical resonance mode. For an airborne PUT, experimental information about the surface vibration amplitude is very important because they directly affect the radiated sound pressure and the ultrasound beam patterns. This surface vibration profile can be measured by using the area scanning mode of the laser vibrometer. In this mode, the frequency of the applied electric field is usually fixed at a resonance frequency. The laser beam can scan a
As discussed above, Eqs. (6) and (7) can give the outof-plane displacement amplitude of the PUT. We can also get the experimental results from the laser scanning images. To verify the calculation results, the changes of surface displacement amplitude have been plotted. Normalizing the surface position, with 0 and 1 representing the clamped edges and 0.5 representing the center point. Since at the first-order symmetric resonance frequency, the surface can generate strong sound pressure in the air, it was used at the practical use and thoroughly studied. Fig. 6 is the comparison of measured and calculated displacement distributions at the first-order resonance frequency. The voltage response of the displacement amplitude at the central point (normalized position /0.5) was also measured, as shown in Fig. 7. According to the Eqs. (3) and (4), Figs. 2 and 5, the numerical and FEA calculated, and measured resonance frequencies in this work were compared, which are shown in Table 1. From Table 1, the numerical calculated and FEA calculated results are nearly consistent with that of measurement. The surface vibration profile of the PUT has important effects on the performance of the transducer such as sound pressure and beam patterns. In this paper, both experimental and theoretical studies of surface vibration profiles are presented. Theoretical calculation predicted the displacement amplitude profiles, which can be verified by the laser vibrometer. As is shown in Fig. 6, it is obvious that the calculation model can provide fairly good prediction of the displacement peak positions (about 6% discrepancy). However, the experimental results show lower amplitude than the calculated because of the following reasons. First, the backing materials has a little clamping effect on the
X. Hu et al. / Materials Science and Engineering B99 (2003) 316 /320
319
Fig. 5. Surface displacement amplitudes. Table 1 Numerical and FEA calculated, and measured resonance frequencies
Numerical calculated FEA calculated Measured
Fig. 6. Comparison of measured and calculated displacement profiles.
First-order (kHz)
Second-order (kHz)
39.3 42.8 40.0
153.0 148.8 153.0
tical model in this work assumed perfect clamped at the round edge. However, it was found that even with a well-designed mechanical clamped system, this clamping condition was still not perfectly satisfied. Not only is the surface vibration amplitude important, but also the phase relationship between different areas can strongly affect the generated sound pressure. The laser vibrometer can take a snapshot of the surface vibration at any moment of a driving circle and can also export the animated files. From Fig. 6, we can see that, under a driving electric field, all points at the surface move toward the same direction at any moment of time. This in-phase vibration profile can generate a strong ultrasound wave in the air. From Fig. 7, we can see that the displacement amplitudes at the central point are linear with the input AC voltage.
Fig. 7. Voltage response of the displacement amplitudes at the central point.
5. Conclusion
surface, which was assumed to be free from any mechanical clamping in the calculation, also reduced the overall vibration amplitude. Secondly, the theore-
This paper describes a type of PUT with improved design principles to measure distance. High-performance low-sintering piezoelectric ceramics based on PMN-PNN-PZT were adopted. The numerical and
320
X. Hu et al. / Materials Science and Engineering B99 (2003) 316 /320
finite element analysis of their resonant modes were analyzed. A laser scanning vibrometer has been used to measure the displacement amplitude profiles of their resonant mode. It is greatly helpful to us to design and analyze transducers.
References [1] Z. Gui, H. Hu, L. Li, et al., Solid State Phenomena 25 and 26 (1992) 309 /316. [2] Y. Xue, Acoustic and Electronic Engineering 58 (2000) 10 /15.