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Dielectric loss and thermal effect in high power piezoelectric systems
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Dielectric loss and thermal effect in high power piezoelectric systems Tianyue Yang a , Yuanfei Zhu a , Shiyang Li a , Dawei An a , Ming Yang a,∗ , Wenwu Cao b,∗ a b
Department of Instrument Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China Department of Mathematics and Materials Research Institute, The Pennsylvania State University, University Park, PA 16802, USA
a r t i c l e
i n f o
Article history: Received 2 June 2019 Received in revised form 9 October 2019 Accepted 6 November 2019 Available online xxx Keywords: Dielectric loss Thermal effect High power piezoelectric
a b s t r a c t Temperature rise is the main limiting factor that affects the performance of high power piezoelectric systems. Significant decrease of electromechanical conversion efficiency near the series resonance frequency results in more serious heating, which cannot be explained by the classical model. To understand the loss and heating mechanisms of transducers under actual operation conditions, we have systematically studied the dielectric loss. A series resistance is proposed in the equivalent circuit model to characterize the influence of dielectric loss. The active power and temperature rise of the transducer are measured under different conditions. Experimental results verify that our model can accurately quantify both mechanical and dielectric losses, and clarify that the dielectric loss is mainly responsible for the decrease of the efficiency and the thermal effect of the piezoelectric stack. Different from previous researches, we indicate that the dielectric loss is mainly related to the input current but not the applied voltage. This investigation could guide the design and control of high power piezoelectric systems. © 2019 Elsevier B.V. All rights reserved.
1. Introduction High power piezoelectric systems (HPPSs) are widely used for various purposes, such as cleaning, welding, cutting, cavitation, and actuation [1–5]. The main challenge is that high mechanical power density is usually accompanied by considerable heat generation. As the temperature rise could degrade the performance of lead zirconate titanate (PZT) piezoelectric ceramic, this thermal restriction is usually the main limiting factor of performance and stability in HPPSs [6–8]. To characterize the loss and heating effect, an accurate electromechanical equivalent circuit model is crucial [9]. Classical equivalent circuit models, such as the Butterworth-Van Dyke (BVD) model, are widely used in piezoelectric transducers [10,11]. Generally, piezoelectric transducers are excited at the series resonance frequency (f s ) to keep mechanical resonant mode [12]. However, researchers discover that the electromechanical conversion efficiency decreases greatly near fs in HPPSs [13,14]. Hence, the BVD model cannot characterize all of the major losses in HPPSs [15]. Beside the mechanical loss characterized by the BVD model, different losses, such as piezoelectric, elastic and dielectric losses, are also proposed to describe piezoelectric ceramic [13,16,17]. But as a whole vibrator assembly, electromechanical characteristics of an ultrasonic transducer are very different from that of a single
∗ Corresponding authors. E-mail addresses: [email protected] (M. Yang), [email protected] (W. Cao).
piezoelectric ceramic piece [18]. Umeda et al. find a series resistor type of loss in a Langevin transducer based on the electrical transient response [19]. Then they introduce a series resistor representing the loss of force factor and a parallel resistor characterizing the dielectric loss into the BVD equivalent circuit model [20]. But Uchino et al. suggest that the mechanical loss and the dielectric loss are the considerable losses in a piezoelectric transducer, and the former forms the main loss at fs whereas the latter dominates at the parallel resonance frequency (f p ) [13]. They also propose two different equivalent circuit models of a piezoelectric transducer at fs and fp , respectively [21]. In order to avoid the inconsistency in the topology of equivalent circuits, Tao et al. propose a phenomenological efficiency model presenting an empirical relationship between the loss variation and driving frequency by measuring the mechanical quality factor Qm [14]. Although this model can help understand the mechanism of efficiency enhancement, but the loss mechanisms remain unclear, neither do the thermal impact factors. In order to quantify the losses and investigate the thermal impact factors in HPPSs. We analyze the dielectric, piezoelectric and mechanical components conjunctively to deduce the equivalent circuit model. An additional series resistor, which characterizes the dielectric loss, is proposed to improve the BVD equivalent circuit model. An HPPS, as shown in Fig. 1, which contains a widely used DUKANE 20 kHz 3300 W piezoelectric transducer, is used to verify the proposed model. The active power is measured between fs and fp under actual operation conditions. In addition, the temperature rise of the transducer is measured by a FLUKE thermal
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Please cite this article as: T. Yang, Y. Zhu, S. Li et al., Dielectric loss and thermal effect in high power piezoelectric systems, Sens. Actuators A: Phys., https://doi.org/10.1016/j.sna.2019.111724
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Fig. 1. Structure of an HPPS.
velocity are vectors represented by bold letters. For normal operation conditions, the Butterworth model is sufficient to characterize the mechanical properties of an HPPS [22].
2.2. The dielectric model
Fig. 2. (a) Structure of the Butterworth model. (b) Dielectrics equivalent circuit.
infrared camera to verify the thermal effects of the mechanical and dielectric losses in the HPPS. Furthermore, the model is also verified under a typical loading condition. 2. Fundamental models and properties of an HPPS 2.1. The Butterworth model The mechanical properties of a vibrator can be characterized by the Butterworth model [10], as shown in Fig. 2(a). The applied force F and the vibration speed v are equivalent to the voltage U and the current I, respectively. The mechanical resistance Rm , the mass m and the mechanical stiffness s analogous to the electrical R, L and C, respectively. For periodic vibrators, the voltage, current, force, and
Piezoelectric ceramics have high dielectric properties and they behave as typical capacitors when the operating frequency is far from their resonances. The characteristics of dielectrics can be represented by an equivalent circuit as shown in Fig. 2(b), where Ri is the insulation resistance that characterizes the ability to isolate leakage current; Cs stands for geometric capacitance, which is the capacitance with non-polarized dielectric materials in between the electrodes; Cd and Rd represent the polarization capacitance and the equivalent polarization loss resistance, characterizing the capacitance and the resistance generated by the dielectric dipole rotation phenomenon [23]. Normally, the insulation resistance can be estimated under a DC voltage [23]. Considering applying about maximum applied peak voltage of 2.0 kV with an electric field strength of 3.5 kV/cm to the ceramic under the actual operation condition, the insulation resistance measurement of the HPPS utilizes a 2.5 kV tramegger. The result verifies that the insulation resistance Ri is larger than 5 G. On the other hand, the relative permittivity of the piezoelectric ceramic PZT-8 is about 1000 in audio frequency range [22]. So this equivalent circuit model can be simplified to a polarization resistance Rd and a polarization capacitance Cd in series for an HPPS. Meanwhile, for piezoelectric ceramic, the static capacitance C0 is regarded as a constant in audio frequency range [11], so Cd ≈ C 0 .
2.3. The piezoelectric properties Polarization is the essential property of piezoelectric ceramic. Polarization domains in piezoelectric ceramic are composed of a large number of dipoles with the same direction, and the dipoles can be affected by two factors directly. First, a deformation x at the polarization direction of the piezoelectric ceramic stack changes the dipole moments and generates polarization electric field, forming a macroscopic piezoelectric polarization voltage Up across the two electrodes. Second, a piezoelectric applied voltage Ue affects the dipoles and generates a piezoelectric force F, which makes the ceramic tend to deform. For a longitudinal transducer, the two
Please cite this article as: T. Yang, Y. Zhu, S. Li et al., Dielectric loss and thermal effect in high power piezoelectric systems, Sens. Actuators A: Phys., https://doi.org/10.1016/j.sna.2019.111724
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partial voltage Ue and the latter overcomes the dielectric loss, as shown in Eq. (4). UT = Ue + IT Rd
(4)
Then, from Eqs. (3) and (4), an equation can be derived Ue = −U p + Ud
(5)
Considering Eqs. (1) and (5) and the polarized charge Q , equations can be deduced as shown in Eqs. (6) and (7). C0 d33
(6)
dQ dUe C0 = C0 +v dt dt d33
(7)
Q = Ud C 0 = Ue C0 + x IT =
Third, as a forced vibrator, the mechanical properties of an HPPS can be equivalent to a series RLC circuit according to the Butterworth’s model [10]. Based on Eqs. (2) and (7), we can establish the electromechanical coupling relationships as shown in Eq. (8), and introduce the series equivalent mechanical branch to the electrical circuit model. Then the equivalent circuit model of an HPPS can be built as shown in Fig. 3(b). Here, the voltage, current, force, and velocity are vectors represented by bold letters. Ue =
Fd33 C0 ; I1 = v C0 d33
(8a,b)
4. Experiments 4.1. Verification of the proposed model The proposed model is verified under an actual operation vibration amplitude in the commonly used driving frequency range from fs to fp . The equivalent mechanical resistance R1 of the HPPS consists of the equivalent mechanical loss resistance Rm and the equivalent load resistance RL , as shown in Eq. (9). R1 = Rm + RL
Fig. 3. (a) Electrical model of piezoelectric ceramic. (b) Equivalent circuit model of an HPPS.
relationships can be described by Eqs. (1) and (2). Here, d33 is the longitudinal piezoelectric constant. 1 Up = x d33
(1)
C0 d33
(2)
F = Ue
3. Derivation of the equivalent circuit model Considering the dielectric and piezoelectric properties, an equivalent circuit model of an HPPS can be built in three steps. First, the inner voltage Up superposes with the external voltage UT , and excites the dielectric polarization jointly, as shown in Eq. (3). UT + Up = Ud + IT Rd
(3)
Here, IT is the input current, and Ud is the dielectric polarization voltage. According to this relationship, the electrical model of piezoelectric ceramic can be built as shown in Fig. 3(a). Second, the applied voltage can be divided into two parts, one affects the mechanical deformation and the other affects the electric displacement. The former drives piezoelectric excitation via
(9)
Since HPPSs usually have low mechanical loss and narrow resonance frequency band [22], there exist relationships as shown in Eqs. (10) and (11) at no load condition. 1 ωs C0 R1 fr ≈ fs =
(10) 1
2
L1 C1
; fa ≈ fp = 2
1
(11a,b) C C
L1 C 0+C1 0
1
Here, the resonance frequency fr and the anti-resonance frequency fa are two electrical zero phase points. Furthermore, due to the Nyquist characteristics of piezoelectric transducer, I T ,r , the input current at fr and U T ,a , the applied voltage at fa have approximate relationships with I 1 : I T ,r ≈ I 1 ; U T ,a ≈ −
I1 jωs C0
(12a,b)
Based on the analysis above, an experiment is performed on the HPPS with a 7.8 cm2 plastic welding horn as shown in Fig. 1. A KEYENCE LK-H008 laser vibrometer is used to detect the vertical vibration amplitude of the horn. The horn is excited to 55 m which is a typical amplitude used in ultrasonic welding [22], corresponding to an almost constant vibration velocity of 3.43 m/s. Therefore, I1 is constant in this experiment according to Eq. (8b). In a typical sandwich transducer, ring-shaped silver plated piezoelectric ceramic pieces and metal electrodes are pre-pressure at 3000∼3500 N/cm2 . Therefore, the conductive electrodes are in good contact with the piezoelectric ceramic pieces. In this HPPS, the
Please cite this article as: T. Yang, Y. Zhu, S. Li et al., Dielectric loss and thermal effect in high power piezoelectric systems, Sens. Actuators A: Phys., https://doi.org/10.1016/j.sna.2019.111724
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According to our proposed model, the loss of the HPPS can be estimated as shown in Fig. 4(b). The result shows that the estimated values are similar to the measured values within an error of 5 %. The experimental results show a significantly increase of loss as the driving frequency approaching fs . Our proposed model considers the mechanical loss to be constant in an HPPS, which occupies major component of the total loss at fp . Besides, the large input current closed to fs dramatically increases the dielectric loss, which becomes non-negligible. Thus, the model proposes a series resistive type of dielectric loss in an HPPS, which differs from a constant dielectric loss tangent used by others.
4.2. Influence of the losses on thermal effect
Fig. 4. Under the vibration amplitude of 55 m, (a) Variations of the applied voltage and the input current with the driving frequency. (b) Relationship between the loss power and the driving frequency.
Table 1 Parameters in the proposed model of the HPPSs. Application
I 1 (Arms )
C 0 (nF)
C 1 (nF)
L1 (mH)
R m ()
R d ()
Welding Cutting
2.66 3.00
18.93 18.93
0.2683 0.1308
240.3 477.8
9.45 9.48
7.26 6.34
metal resistance is negligible, which is less than 0.01 measured by the impedance bridge at 20 kHz. The applied voltage UT , the input current IT and the active power are recorded at different driving frequencies between fr and fa . Here, the active power equals to the total loss power PL under no load condition. Fig. 4(a) shows a significant increase of UT and the decrease of IT as the driving frequency increases from fr to fa . According to Eqs. (11) and (12), I1 , C0 , C1 and L1 are deduced, as shown in Table 1. In Fig. 4 (b), PL is measured 10 times per group. According to Eq. (13), Rm and Rd are solved based on the related experimental data and listed in Table 1. PL = Pd + Pm = IT2 Rd + I12 Rm
(13)
In some HPPSs, like in the ultrasonic cutting systems, which work under high vibration amplitude and continuous conditions, the transducers are seriously influenced by heating. To clarify the thermal effects of the mechanical and dielectric losses, an experiment is conducted in an ultrasonic cutting system. The ultrasonic horn of the former welding system is converted to a 10-inch rubber cutter. At a typical cutting amplitude of I1 = 3.00A (effective value), the parameters of the cutting system are measured, as shown in Table 1. In the experiment, the HPPS is cool down to 24.0◦ (±0.1◦ ) before operations. Three different operation conditions are maintained for 90 s with I1 being kept constant at 3.00 A. The thermal fields of the transducer are measured by a FLUKE Ti20 thermal imager. The thermal images of the transducer are shown in Fig. 5. The left image shows even heating of the transducer at fp , where the maximum temperature rise is 6.0◦ . But the middle image shows concentrated heating at the piezoelectric stack with the maximum temperature rise of 31.0◦ when exciting at fs . According to Eq. (13), 85.3 W mechanical loss is estimated at both fp and fs , and an extra 57.1 W dielectric loss at fs . Results indicate that the mechanical loss is evenly distributed and may be relatively concentrated at the piezoelectric stack-metal interface and the flange. The temperature rise is homogeneous and the heat is easily diffused through metal structures. On the contrary, the dielectric loss only affects the piezoelectric stack. Due to the low thermal conductivity of piezoelectric ceramic, temperature rise caused by the dielectric loss is concentrated and intensive. Seriously, the piezoelectric stack is the most heat sensitivity part of a transducer [7], but the dielectric loss at fs rises the temperature up to 55.0◦ through only 90 s operation. As the transducer under test has a temperature limit of 82◦ , large dielectric loss has a high risk affecting normal operation of the piezoelectric system. These results indicate that the dielectric loss has a much more pronounced thermal effect on piezoelectric stack than the mechanical loss at the series resonance. Furthermore, an experiment under a typical high load operation condition is conducted. The cutter is immersed into water to simulate the load and the driving frequency is tracked near fp . Active power of the HPPS reaches about 1.5 kW. The right image in Fig. 5 shows the temperature rise under a typical high load operation condition with the maximum temperature rise of 12.2◦ at the piezoelectric stack. Considering a 1.34 A input current under this high load operation condition, the dielectric loss is estimated to be 11.4 W according to our model. This measured temperature rise agrees well with our theoretical prediction. In the last experiment, the temperature rise under high load condition is still lower than that under no load condition near fs due to the much lower input current. It suggests the feasibility of the proposed model under loading conditions, and on the other hand, it clarifies why the driving HPPSs near fp could significantly reduce the temperature rise of the piezoelectric stacks.
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Fig. 5. Thermal images of the transducer under different frequencies and load conditions with I1 of 3.00 A.
5. Conclusion
This work is sponsored by the National Natural Science Foundation of China (Grant No. 81571831 and Grant No. 51575344) and Shanghai Medical Instrumentation Science Foundation of China (Grant No. 19441903300).
[12] X. Liu, A.I. Colli-Menchi, J. Gilbert, D.A. Friedrichs, K. Malang, E. Sánchez-Sinencio, An automatic resonance tracking scheme with maximum power transfer for piezoelectric transducers, IEEE Trans. Ind. Electron. 62 (2015) 7136–7145. [13] K. Uchino, S. Hirose, Loss mechanisms in piezoelectrics: how to measure different losses separately, IEEE Trans. Ultrason. Ferroelec. Freq. Control 48 (2001) 307–321. [14] Y. Tao, X. Dong, H. Shekhani, C. Li, Y. Maida, T. Tou, et al., Driving an inductive piezoelectric transducer with class E inverter, Sens. Actuators A:Phys 261 (2017). [15] Y. Zhuang, S.O. Ural, A. Rajapurkar, S. Tuncdemir, A. Amin, K. Uchino, Derivation of piezoelectric losses from admittance spectra, J. Appl. Phys. 48 (1-6) (2014), 041401. [16] W. Shi, H.N. Shekhani, Z. Hui, M. Jie, Y. Yu, K. Uchino, Losses in piezoelectrics derived from a new equivalent circuit, J. Electroceram 35 (2015) 1–10. [17] X. Dong, M. Majzoubi, M. Choi, Y. Ma, M. Hu, J. Long, et al., A new equivalent circuit for piezoelectrics with three losses and external loads, Sens. Actuators A: Phys. 256 (2017). [18] Y. Wang, X. Lin, J. Li, S. Huang, C. Xin, Effect of structural parameters and stability of constituent materials on the performance of 1–3 spherical crown piezocomposite and transducer, Sens. Actuators A: Phys. 278 (2018) 18–24. [19] M. Umeda, K. Nakamura, S. Ueha, The measurement of high-power characteristics for a piezoelectric transducer based on the electrical transient response, J. Appl. Phys. 37 (1998) 5322–5325. [20] M. Umeda, K. Nakamura, S. Ueha, Effects of vibration stress and temperature on the characteristics of piezoelectric ceramics under high vibration amplitude levels measured by electrical transient responses, J. Appl. Phys. 38 (1999) 5581–5585. [21] K. Uchino, J.H. Zheng, Y.H. Chen, X.H. Du, J. Ryu, Y. Gao, et al., Loss mechanisms and high power piezoelectrics, J. Mater. Sci. 41 (2006) 217–228. [22] Z. Yundian, Sandwich Piezoelectric Transducers and Their Applications, Science Press, Beijing, 2006. [23] Walter, Dielectric Physics, Beijing: Higher Education Press, 1957.
References
Biographies
In conclusion, the polarization loss is the major part of the dielectric loss, which is non- negligible in HPPSs. An equivalent circuit model is deduced, which introduces an additional resistor characterizing the dielectric loss. This model infers that the dielectric loss is mainly related to the input current but not the applied voltage, which is very different from previous models. Experiments conducted under actual operation conditions verify that our improved equivalent circuit model can accurately quantify both the mechanical and dielectric losses within 5 % accuracy. Moreover, we find that the dielectric loss has a much greater thermal effect on the piezoelectric stack than the mechanical loss in HPPSs, and also find a significant thermal improvement near the parallel resonance frequency. The proposed model could be very useful for the design and control of ultrasonic actuators, especially under high vibration amplitude and continuous operation applications, such as in the ultrasonic cutting system. Acknowledgements
[1] M.R. Rani, K. Prakasan, R. Rudramoorthy, Studies on thermo-elastic heating of horns used in ultrasonic plastic welding, Ultrasonics 55 (2015) 123–132. [2] M. Carboni, Failure analysis of two aluminium alloy sonotrodes for ultrasonic plastic welding, Int. J. Fatigue 60 (2014) 110–120. [3] X.G. Jiang, X.B. Zhu, C.Y. Wong, D.Y. Zhang, D.X. Geng, Theory of series inductance matching to transducer at premechanical resonance zone in ultrasonic vibration cutting, IEEE Trans. Ind. Electron. 66 (2019) 3019–3029. [4] H.W. Baac, T. Lee, J.G. Ok, T. Hall, L.J. Guo, Dual-frequency focused ultrasound using optoacoustic and piezoelectric transmitters for single-pulsed free-field cavitation in water, Appl. Phys. Lett. 103 (2013) 4. [5] D. An, M. Yang, X. Zhuang, T. Yang, F. Meng, Z. Dong, Dual traveling wave rotary ultrasonic motor with single active vibrator, Appl. Phys. Lett. 110 (2017). [6] K. Shinekumar, S. Dutta, High-temperature piezoelectrics with large piezoelectric coefficients, J. Korean Inst. Electr. Electron. Mater. Eng. 44 (2015) 613–622. [7] P.M. Weaver, T. Stevenson, T. Quast, G. Bartl, T. Schmitz-Kempen, P. Woolliams, et al., High temperature measurement and characterisation of piezoelectric properties, J. Mater. Sci.-Mater. Electron. 26 (2015) 9268–9278. [8] J. Zheng, S. Takahashi, S. Yoshikawa, K. Uchino, J.W.C.D. Vries, Heat generation in multilayer piezoelectric actuators, J. Am. Ceram. Soc. 79 (2010) 3193–3198. [9] M. Al Ahmad, A.M. Elshurafa, K.N. Salama, H.N. Alshareef, Determination of maximum power transfer conditions of bimorph piezoelectric energy harvesters, J. Appl. Phys. 111 (2012) 4. [10] S. Butterworth, On electrically-maintained vibrations, Proc. Phys. Soc. Lond. 27 (1914) 410–424. [11] K.S.V. Dyke, The piezo-electric resonator and its equivalent network, Proc. Inst. Radio Eng. 16 (1928) 742–764.
Tianyue Yang received his B.Eng. degree in electrical engineering from Shanghai Jiaotong University, Shanghai, China. From 2012–2015, he received the M. Eng. degree in automotive engineering from Tongji University, Shanghai, China. Since 2015 he has been studying for Ph.D. in the Department of Instrument Science and Engineering in Shanghai Jiaotong University. His research interests are in electrical control, high power ultrasonic. Yuanfei Zhu received his B.Eng. degree in measurement control and instrument from Hebei University of Technology, Tianjin, China. From 2010–2014, he received the M. Eng. degree in instrument science and technology from Hebei University of Technology, Tianjin, China. Since 2017 he has been studying for Ph.D. in the Department of Instrument Science and Engineering in Shanghai Jiaotong University. His research interests are in ultrasonic device driver and control, artificial organs. Shiyang Li is currently an associate professor in Department of Instrument Science and Engineering, Shanghai Jiaotong University, China. He received M. Eng. degree in circuit and system from Zhengzhou University, Zhengzhou, China, and a PHD degree at the Department of Instrument Science and Engineering, Shanghai Jiaotong University, China, respectively, in 2005, 2008. His research interests include the measurement of piezoelectric material, design and optimization of piezoelectric ultrasonic motors. Dawei An received his B.Eng. degree in mechanical engineering from Henan University of Science and Technology, Luoyang, China. From 2008–2011, he received the M. Eng. degree in mechanical manufacturing and automation from Chongqing University, Chongqing, China. Since 2014 he has been studying for Ph.D. in the Department of Instrument Science and Engineering in Shanghai Jiaotong University. His research interests are in ultrasonic actuators design and their medical application.
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Ming Yang is currently a professor in the Department of Instrument Science and Engineering of Shanghai Jiaotong University, Shanghai, China. He received a B. Eng. degree in automatic detection from Northeast Heavy Machinery Institute (Yanshan University), Qiqihaer, China, and a M. Eng. degree in electrical magnetic measurement from Xian Jiaotong University, Xian, China, and a Ph.D. degree in precision instrumentation from Tianjin University, Tianjin, China, respectively, in 1985, 1990, 1996. From 1996–1998, he was a postdoctoral researcher in the Research Center of Ultrasonic Motor in Nanjing University of Aeronautics and Astronautics, Nanjing, China. He was a research fellow in the School of Mechanical Engineering, University of Leeds, Leeds, UK, from 2002 to 2005. His research interests include ultrasonic motors and their medical application, measurement, and instrumentation.
Wenwu Cao is currently a professor in Department of Mathematics and Materials Research Institute, The Pennsylvania State University, University Park, USA. He received a Ph.D. degree in Physics from the Pennsylvania State University in 1987. He worked for one and a half years at the Materials Research Laboratory of Penn State as a Research Associate. In 1989, he went to The Laboratory of Atomic and Solid State Physics, Cornell University for one year to further pursue theoretical study on martensitic phase transitions. In 1990, he came back to Penn State as a research faculty. His joint appointment with the Mathematics Department started in the fall of 1995. His research interests include ferroelectric materials and their applications, design of ultrasonic devices using computer simulations.
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Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna
Dielectric loss and thermal effect in high power piezoelectric systems Tianyue Yang a , Yuanfei Zhu a , Shiyang Li a , Dawei An a , Ming Yang a,∗ , Wenwu Cao b,∗ a b
Department of Instrument Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China Department of Mathematics and Materials Research Institute, The Pennsylvania State University, University Park, PA 16802, USA
a r t i c l e
i n f o
Article history: Received 2 June 2019 Received in revised form 9 October 2019 Accepted 6 November 2019 Available online xxx Keywords: Dielectric loss Thermal effect High power piezoelectric
a b s t r a c t Temperature rise is the main limiting factor that affects the performance of high power piezoelectric systems. Significant decrease of electromechanical conversion efficiency near the series resonance frequency results in more serious heating, which cannot be explained by the classical model. To understand the loss and heating mechanisms of transducers under actual operation conditions, we have systematically studied the dielectric loss. A series resistance is proposed in the equivalent circuit model to characterize the influence of dielectric loss. The active power and temperature rise of the transducer are measured under different conditions. Experimental results verify that our model can accurately quantify both mechanical and dielectric losses, and clarify that the dielectric loss is mainly responsible for the decrease of the efficiency and the thermal effect of the piezoelectric stack. Different from previous researches, we indicate that the dielectric loss is mainly related to the input current but not the applied voltage. This investigation could guide the design and control of high power piezoelectric systems. © 2019 Elsevier B.V. All rights reserved.
1. Introduction High power piezoelectric systems (HPPSs) are widely used for various purposes, such as cleaning, welding, cutting, cavitation, and actuation [1–5]. The main challenge is that high mechanical power density is usually accompanied by considerable heat generation. As the temperature rise could degrade the performance of lead zirconate titanate (PZT) piezoelectric ceramic, this thermal restriction is usually the main limiting factor of performance and stability in HPPSs [6–8]. To characterize the loss and heating effect, an accurate electromechanical equivalent circuit model is crucial [9]. Classical equivalent circuit models, such as the Butterworth-Van Dyke (BVD) model, are widely used in piezoelectric transducers [10,11]. Generally, piezoelectric transducers are excited at the series resonance frequency (f s ) to keep mechanical resonant mode [12]. However, researchers discover that the electromechanical conversion efficiency decreases greatly near fs in HPPSs [13,14]. Hence, the BVD model cannot characterize all of the major losses in HPPSs [15]. Beside the mechanical loss characterized by the BVD model, different losses, such as piezoelectric, elastic and dielectric losses, are also proposed to describe piezoelectric ceramic [13,16,17]. But as a whole vibrator assembly, electromechanical characteristics of an ultrasonic transducer are very different from that of a single
∗ Corresponding authors. E-mail addresses: [email protected] (M. Yang), [email protected] (W. Cao).
piezoelectric ceramic piece [18]. Umeda et al. find a series resistor type of loss in a Langevin transducer based on the electrical transient response [19]. Then they introduce a series resistor representing the loss of force factor and a parallel resistor characterizing the dielectric loss into the BVD equivalent circuit model [20]. But Uchino et al. suggest that the mechanical loss and the dielectric loss are the considerable losses in a piezoelectric transducer, and the former forms the main loss at fs whereas the latter dominates at the parallel resonance frequency (f p ) [13]. They also propose two different equivalent circuit models of a piezoelectric transducer at fs and fp , respectively [21]. In order to avoid the inconsistency in the topology of equivalent circuits, Tao et al. propose a phenomenological efficiency model presenting an empirical relationship between the loss variation and driving frequency by measuring the mechanical quality factor Qm [14]. Although this model can help understand the mechanism of efficiency enhancement, but the loss mechanisms remain unclear, neither do the thermal impact factors. In order to quantify the losses and investigate the thermal impact factors in HPPSs. We analyze the dielectric, piezoelectric and mechanical components conjunctively to deduce the equivalent circuit model. An additional series resistor, which characterizes the dielectric loss, is proposed to improve the BVD equivalent circuit model. An HPPS, as shown in Fig. 1, which contains a widely used DUKANE 20 kHz 3300 W piezoelectric transducer, is used to verify the proposed model. The active power is measured between fs and fp under actual operation conditions. In addition, the temperature rise of the transducer is measured by a FLUKE thermal
https://doi.org/10.1016/j.sna.2019.111724 0924-4247/© 2019 Elsevier B.V. All rights reserved.
Please cite this article as: T. Yang, Y. Zhu, S. Li et al., Dielectric loss and thermal effect in high power piezoelectric systems, Sens. Actuators A: Phys., https://doi.org/10.1016/j.sna.2019.111724
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Fig. 1. Structure of an HPPS.
velocity are vectors represented by bold letters. For normal operation conditions, the Butterworth model is sufficient to characterize the mechanical properties of an HPPS [22].
2.2. The dielectric model
Fig. 2. (a) Structure of the Butterworth model. (b) Dielectrics equivalent circuit.
infrared camera to verify the thermal effects of the mechanical and dielectric losses in the HPPS. Furthermore, the model is also verified under a typical loading condition. 2. Fundamental models and properties of an HPPS 2.1. The Butterworth model The mechanical properties of a vibrator can be characterized by the Butterworth model [10], as shown in Fig. 2(a). The applied force F and the vibration speed v are equivalent to the voltage U and the current I, respectively. The mechanical resistance Rm , the mass m and the mechanical stiffness s analogous to the electrical R, L and C, respectively. For periodic vibrators, the voltage, current, force, and
Piezoelectric ceramics have high dielectric properties and they behave as typical capacitors when the operating frequency is far from their resonances. The characteristics of dielectrics can be represented by an equivalent circuit as shown in Fig. 2(b), where Ri is the insulation resistance that characterizes the ability to isolate leakage current; Cs stands for geometric capacitance, which is the capacitance with non-polarized dielectric materials in between the electrodes; Cd and Rd represent the polarization capacitance and the equivalent polarization loss resistance, characterizing the capacitance and the resistance generated by the dielectric dipole rotation phenomenon [23]. Normally, the insulation resistance can be estimated under a DC voltage [23]. Considering applying about maximum applied peak voltage of 2.0 kV with an electric field strength of 3.5 kV/cm to the ceramic under the actual operation condition, the insulation resistance measurement of the HPPS utilizes a 2.5 kV tramegger. The result verifies that the insulation resistance Ri is larger than 5 G. On the other hand, the relative permittivity of the piezoelectric ceramic PZT-8 is about 1000 in audio frequency range [22]. So this equivalent circuit model can be simplified to a polarization resistance Rd and a polarization capacitance Cd in series for an HPPS. Meanwhile, for piezoelectric ceramic, the static capacitance C0 is regarded as a constant in audio frequency range [11], so Cd ≈ C 0 .
2.3. The piezoelectric properties Polarization is the essential property of piezoelectric ceramic. Polarization domains in piezoelectric ceramic are composed of a large number of dipoles with the same direction, and the dipoles can be affected by two factors directly. First, a deformation x at the polarization direction of the piezoelectric ceramic stack changes the dipole moments and generates polarization electric field, forming a macroscopic piezoelectric polarization voltage Up across the two electrodes. Second, a piezoelectric applied voltage Ue affects the dipoles and generates a piezoelectric force F, which makes the ceramic tend to deform. For a longitudinal transducer, the two
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partial voltage Ue and the latter overcomes the dielectric loss, as shown in Eq. (4). UT = Ue + IT Rd
(4)
Then, from Eqs. (3) and (4), an equation can be derived Ue = −U p + Ud
(5)
Considering Eqs. (1) and (5) and the polarized charge Q , equations can be deduced as shown in Eqs. (6) and (7). C0 d33
(6)
dQ dUe C0 = C0 +v dt dt d33
(7)
Q = Ud C 0 = Ue C0 + x IT =
Third, as a forced vibrator, the mechanical properties of an HPPS can be equivalent to a series RLC circuit according to the Butterworth’s model [10]. Based on Eqs. (2) and (7), we can establish the electromechanical coupling relationships as shown in Eq. (8), and introduce the series equivalent mechanical branch to the electrical circuit model. Then the equivalent circuit model of an HPPS can be built as shown in Fig. 3(b). Here, the voltage, current, force, and velocity are vectors represented by bold letters. Ue =
Fd33 C0 ; I1 = v C0 d33
(8a,b)
4. Experiments 4.1. Verification of the proposed model The proposed model is verified under an actual operation vibration amplitude in the commonly used driving frequency range from fs to fp . The equivalent mechanical resistance R1 of the HPPS consists of the equivalent mechanical loss resistance Rm and the equivalent load resistance RL , as shown in Eq. (9). R1 = Rm + RL
Fig. 3. (a) Electrical model of piezoelectric ceramic. (b) Equivalent circuit model of an HPPS.
relationships can be described by Eqs. (1) and (2). Here, d33 is the longitudinal piezoelectric constant. 1 Up = x d33
(1)
C0 d33
(2)
F = Ue
3. Derivation of the equivalent circuit model Considering the dielectric and piezoelectric properties, an equivalent circuit model of an HPPS can be built in three steps. First, the inner voltage Up superposes with the external voltage UT , and excites the dielectric polarization jointly, as shown in Eq. (3). UT + Up = Ud + IT Rd
(3)
Here, IT is the input current, and Ud is the dielectric polarization voltage. According to this relationship, the electrical model of piezoelectric ceramic can be built as shown in Fig. 3(a). Second, the applied voltage can be divided into two parts, one affects the mechanical deformation and the other affects the electric displacement. The former drives piezoelectric excitation via
(9)
Since HPPSs usually have low mechanical loss and narrow resonance frequency band [22], there exist relationships as shown in Eqs. (10) and (11) at no load condition. 1 ωs C0 R1 fr ≈ fs =
(10) 1
2
L1 C1
; fa ≈ fp = 2
1
(11a,b) C C
L1 C 0+C1 0
1
Here, the resonance frequency fr and the anti-resonance frequency fa are two electrical zero phase points. Furthermore, due to the Nyquist characteristics of piezoelectric transducer, I T ,r , the input current at fr and U T ,a , the applied voltage at fa have approximate relationships with I 1 : I T ,r ≈ I 1 ; U T ,a ≈ −
I1 jωs C0
(12a,b)
Based on the analysis above, an experiment is performed on the HPPS with a 7.8 cm2 plastic welding horn as shown in Fig. 1. A KEYENCE LK-H008 laser vibrometer is used to detect the vertical vibration amplitude of the horn. The horn is excited to 55 m which is a typical amplitude used in ultrasonic welding [22], corresponding to an almost constant vibration velocity of 3.43 m/s. Therefore, I1 is constant in this experiment according to Eq. (8b). In a typical sandwich transducer, ring-shaped silver plated piezoelectric ceramic pieces and metal electrodes are pre-pressure at 3000∼3500 N/cm2 . Therefore, the conductive electrodes are in good contact with the piezoelectric ceramic pieces. In this HPPS, the
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According to our proposed model, the loss of the HPPS can be estimated as shown in Fig. 4(b). The result shows that the estimated values are similar to the measured values within an error of 5 %. The experimental results show a significantly increase of loss as the driving frequency approaching fs . Our proposed model considers the mechanical loss to be constant in an HPPS, which occupies major component of the total loss at fp . Besides, the large input current closed to fs dramatically increases the dielectric loss, which becomes non-negligible. Thus, the model proposes a series resistive type of dielectric loss in an HPPS, which differs from a constant dielectric loss tangent used by others.
4.2. Influence of the losses on thermal effect
Fig. 4. Under the vibration amplitude of 55 m, (a) Variations of the applied voltage and the input current with the driving frequency. (b) Relationship between the loss power and the driving frequency.
Table 1 Parameters in the proposed model of the HPPSs. Application
I 1 (Arms )
C 0 (nF)
C 1 (nF)
L1 (mH)
R m ()
R d ()
Welding Cutting
2.66 3.00
18.93 18.93
0.2683 0.1308
240.3 477.8
9.45 9.48
7.26 6.34
metal resistance is negligible, which is less than 0.01 measured by the impedance bridge at 20 kHz. The applied voltage UT , the input current IT and the active power are recorded at different driving frequencies between fr and fa . Here, the active power equals to the total loss power PL under no load condition. Fig. 4(a) shows a significant increase of UT and the decrease of IT as the driving frequency increases from fr to fa . According to Eqs. (11) and (12), I1 , C0 , C1 and L1 are deduced, as shown in Table 1. In Fig. 4 (b), PL is measured 10 times per group. According to Eq. (13), Rm and Rd are solved based on the related experimental data and listed in Table 1. PL = Pd + Pm = IT2 Rd + I12 Rm
(13)
In some HPPSs, like in the ultrasonic cutting systems, which work under high vibration amplitude and continuous conditions, the transducers are seriously influenced by heating. To clarify the thermal effects of the mechanical and dielectric losses, an experiment is conducted in an ultrasonic cutting system. The ultrasonic horn of the former welding system is converted to a 10-inch rubber cutter. At a typical cutting amplitude of I1 = 3.00A (effective value), the parameters of the cutting system are measured, as shown in Table 1. In the experiment, the HPPS is cool down to 24.0◦ (±0.1◦ ) before operations. Three different operation conditions are maintained for 90 s with I1 being kept constant at 3.00 A. The thermal fields of the transducer are measured by a FLUKE Ti20 thermal imager. The thermal images of the transducer are shown in Fig. 5. The left image shows even heating of the transducer at fp , where the maximum temperature rise is 6.0◦ . But the middle image shows concentrated heating at the piezoelectric stack with the maximum temperature rise of 31.0◦ when exciting at fs . According to Eq. (13), 85.3 W mechanical loss is estimated at both fp and fs , and an extra 57.1 W dielectric loss at fs . Results indicate that the mechanical loss is evenly distributed and may be relatively concentrated at the piezoelectric stack-metal interface and the flange. The temperature rise is homogeneous and the heat is easily diffused through metal structures. On the contrary, the dielectric loss only affects the piezoelectric stack. Due to the low thermal conductivity of piezoelectric ceramic, temperature rise caused by the dielectric loss is concentrated and intensive. Seriously, the piezoelectric stack is the most heat sensitivity part of a transducer [7], but the dielectric loss at fs rises the temperature up to 55.0◦ through only 90 s operation. As the transducer under test has a temperature limit of 82◦ , large dielectric loss has a high risk affecting normal operation of the piezoelectric system. These results indicate that the dielectric loss has a much more pronounced thermal effect on piezoelectric stack than the mechanical loss at the series resonance. Furthermore, an experiment under a typical high load operation condition is conducted. The cutter is immersed into water to simulate the load and the driving frequency is tracked near fp . Active power of the HPPS reaches about 1.5 kW. The right image in Fig. 5 shows the temperature rise under a typical high load operation condition with the maximum temperature rise of 12.2◦ at the piezoelectric stack. Considering a 1.34 A input current under this high load operation condition, the dielectric loss is estimated to be 11.4 W according to our model. This measured temperature rise agrees well with our theoretical prediction. In the last experiment, the temperature rise under high load condition is still lower than that under no load condition near fs due to the much lower input current. It suggests the feasibility of the proposed model under loading conditions, and on the other hand, it clarifies why the driving HPPSs near fp could significantly reduce the temperature rise of the piezoelectric stacks.
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Fig. 5. Thermal images of the transducer under different frequencies and load conditions with I1 of 3.00 A.
5. Conclusion
This work is sponsored by the National Natural Science Foundation of China (Grant No. 81571831 and Grant No. 51575344) and Shanghai Medical Instrumentation Science Foundation of China (Grant No. 19441903300).
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In conclusion, the polarization loss is the major part of the dielectric loss, which is non- negligible in HPPSs. An equivalent circuit model is deduced, which introduces an additional resistor characterizing the dielectric loss. This model infers that the dielectric loss is mainly related to the input current but not the applied voltage, which is very different from previous models. Experiments conducted under actual operation conditions verify that our improved equivalent circuit model can accurately quantify both the mechanical and dielectric losses within 5 % accuracy. Moreover, we find that the dielectric loss has a much greater thermal effect on the piezoelectric stack than the mechanical loss in HPPSs, and also find a significant thermal improvement near the parallel resonance frequency. The proposed model could be very useful for the design and control of ultrasonic actuators, especially under high vibration amplitude and continuous operation applications, such as in the ultrasonic cutting system. Acknowledgements
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Tianyue Yang received his B.Eng. degree in electrical engineering from Shanghai Jiaotong University, Shanghai, China. From 2012–2015, he received the M. Eng. degree in automotive engineering from Tongji University, Shanghai, China. Since 2015 he has been studying for Ph.D. in the Department of Instrument Science and Engineering in Shanghai Jiaotong University. His research interests are in electrical control, high power ultrasonic. Yuanfei Zhu received his B.Eng. degree in measurement control and instrument from Hebei University of Technology, Tianjin, China. From 2010–2014, he received the M. Eng. degree in instrument science and technology from Hebei University of Technology, Tianjin, China. Since 2017 he has been studying for Ph.D. in the Department of Instrument Science and Engineering in Shanghai Jiaotong University. His research interests are in ultrasonic device driver and control, artificial organs. Shiyang Li is currently an associate professor in Department of Instrument Science and Engineering, Shanghai Jiaotong University, China. He received M. Eng. degree in circuit and system from Zhengzhou University, Zhengzhou, China, and a PHD degree at the Department of Instrument Science and Engineering, Shanghai Jiaotong University, China, respectively, in 2005, 2008. His research interests include the measurement of piezoelectric material, design and optimization of piezoelectric ultrasonic motors. Dawei An received his B.Eng. degree in mechanical engineering from Henan University of Science and Technology, Luoyang, China. From 2008–2011, he received the M. Eng. degree in mechanical manufacturing and automation from Chongqing University, Chongqing, China. Since 2014 he has been studying for Ph.D. in the Department of Instrument Science and Engineering in Shanghai Jiaotong University. His research interests are in ultrasonic actuators design and their medical application.
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Ming Yang is currently a professor in the Department of Instrument Science and Engineering of Shanghai Jiaotong University, Shanghai, China. He received a B. Eng. degree in automatic detection from Northeast Heavy Machinery Institute (Yanshan University), Qiqihaer, China, and a M. Eng. degree in electrical magnetic measurement from Xian Jiaotong University, Xian, China, and a Ph.D. degree in precision instrumentation from Tianjin University, Tianjin, China, respectively, in 1985, 1990, 1996. From 1996–1998, he was a postdoctoral researcher in the Research Center of Ultrasonic Motor in Nanjing University of Aeronautics and Astronautics, Nanjing, China. He was a research fellow in the School of Mechanical Engineering, University of Leeds, Leeds, UK, from 2002 to 2005. His research interests include ultrasonic motors and their medical application, measurement, and instrumentation.
Wenwu Cao is currently a professor in Department of Mathematics and Materials Research Institute, The Pennsylvania State University, University Park, USA. He received a Ph.D. degree in Physics from the Pennsylvania State University in 1987. He worked for one and a half years at the Materials Research Laboratory of Penn State as a Research Associate. In 1989, he went to The Laboratory of Atomic and Solid State Physics, Cornell University for one year to further pursue theoretical study on martensitic phase transitions. In 1990, he came back to Penn State as a research faculty. His joint appointment with the Mathematics Department started in the fall of 1995. His research interests include ferroelectric materials and their applications, design of ultrasonic devices using computer simulations.
Please cite this article as: T. Yang, Y. Zhu, S. Li et al., Dielectric loss and thermal effect in high power piezoelectric systems, Sens. Actuators A: Phys., https://doi.org/10.1016/j.sna.2019.111724