Power Enhancement of Piezoelectric Transformers by Adding Thermal Pad

Transcription

1 P P P P P In P They Power Enhancement of Piezoelectric Transformers by Adding Thermal Pad a,b a,b b,c b,d Y. H. SuP P, Y. P. LiuP P, D. Vasic*P P, F. CostaP a PDepartment of Engineering Science & Ocean Engineering, National Taiwan University, Taipei, Taiwan; b PLab. SATIE, ENS Cachan, 9435 Cachan, France; c PUniversité de Cergy-Pontoise, Neuville/Oise, France d PIUFM, Université Paris Est Créteil (UPEC), Place du 8 mai 1945, St Denis, France * dejan.vasic@satie.ens-cachan.fr ABSTRACT It is well known that power density of piezoelectric transformers is limited by mechanical stress. The power density of 3 piezoelectric transformers calculated by the stress boundary can reach 330 W/cmP P. However, no piezoelectric transformer has ever reached such a high power density in practice. The power density of the piezoelectric transformer is 3 limited to 33 W/cmP Ptypically. This fact implies that there is another physical limitation in piezoelectric transformer. In fact, it is also known that piezoelectric material is constrained by vibration velocity. Once the vibration velocity is too large, the piezoelectric transformer generates heat until it cracks. To explain the instability of piezoelectric transformer, we will first model the relationship between vibration velocity and resulting heat by a physical feedback loop. It will be shown that the vibration velocity as well as the heat generation determines the loop gain. A large vibration velocity and heat may cause the feedback loop to enter into an unstable state. Therefore, to enhance the power capacity of piezoelectric transformer, the heat needs to be dissipated. In this paper, we used commercial thermal pads on the surface of the piezoelectric transformer to dissipate the heat. The mechanical current of piezoelectric transformers can move from 0.38A/W to 0.97A/9W at a temperature of 55 C experimentally. It implies that the power capacity possibly increases 3 times in the piezoelectric material. Moreover, piezoelectric transformers that are well suited in applications of high voltage/low current becomes also well suited for low voltage/high current power supplies that are widely spread. This technique not only increases the power capacity of the piezoelectric transformer but also allows it to be used in enlarged practical applications. In this paper, the theoretical modeling will be detailed and verified by experiments. Keywords: piezoelectric transformer, power capacity, power density 1. INTRODUCTION Compared with a electromagnetic transformer, piezoelectric transformers (PT) have several inherent advantages such as better efficiency, low profile, no EMI radiation, high power density, and easier for mass production. Accordingly, PTs are good substitutes of electromagnetic transformers especially in high voltage/low current application, such as electronic ballasts or backlight inverters. Considering the case of the large current (>1A), the piezoelectric transformer is easily unstable or even breakdown with temperature rises because of the overdeveloped internal losses. In fact, the internal heat generation in piezoelectric transformers can represent the internal losses in the steady-state. Since the internal loss as well as the heat generation is the physical limitation of the piezoelectric transformers, several researches focus on modeling and explaining the internal loss of the piezoelectric transformer at high power condition. Uchino et al. were first divided the internal loss of the piezoelectric transducers into three parts: dielectric losses, mechanical losses and piezoelectric losses and model the loss in the equivalent circuit. [1]-[3] PAlbareda et al. found that the dissipation resistance [4] increases proportionally to the square of the vibration velocity near the resonance frequency of the PT.P PTheir models both implied that the temperature rise increases with the vibration velocity significantly, and the output current of the piezoelectric transformer is thus limited. To dissipate the heat efficiently, a ring-dot-shape piezoelectric transformer with [5] a central hole was proposed for better thermal radiation.p this ring-dot-shape piezoelectric transformer, it has more uniform temperature distribution, larger output power and better efficiency. On the other hand, Shao et al. adopted the [6] contact heat transfer to dissipate the heat in order to heighten the power density of piezoelectric transformers.p Active and Passive Smart Structures and Integrated Systems 01, edited by Henry A. Sodano, Proc. of SPIE Vol. 8341, 83411U 01 SPIE CCC code: X/1/$18 doi: / Proc. of SPIE Vol U-1

2 P Then, includes P and and increases claimed that their proposed mechanism gives excellent performance even though the contact interface may produce additional friction heat. In this paper, we start from observing the relationships between the equivalent dissipation resistances and the input voltages at different temperatures to establish a theoretical-phenomenological model. The proposed model can explain the relationship between vibration velocity and generated heat of the piezoelectric [7] transformer.p we added commercial thermal pads and thermoelectric cooling modules on the piezoelectric transformer to dissipate the heat and it is revealed that the power capacity increases almost 3 times in the piezoelectric material. In the following, the theoretical model will be detail in the section and will be verified by the simulation and experiments in chapter 3.. THEORETICAL ANALYSIS OF MULTI-LAYER PIEZOELECTRIC TRANSFORMER.1 Equivalent circuit of piezoelectric transformers with nonlinear resistance When the constitutive equations of the piezoelectric material are derived, quadratic and cubic terms are typically neglected. However, these terms may decrease the quality factor of the piezoelectric material. More specifically, the mechanical resistance RRmR both low excitation resistance RR0R nonlinear resistance RRNLR. RRmR=RR0R+RRNL (1) [4] According to Albareda s nonlinear model of piezoelectric transducersp P, RRNLR is a function of mechanical current irmrp P: RRNLR= α irmrp () The mechanical nonlinearity increases the mechanical resistance. The increment of the mechanical resistance is a function of the square mechanical current irmrp a coefficient α that characterizes the material nonlinearity. The increment of the losses influences the transfer power of the PT and limits the power density. To analyze the working characteristic of piezoelectric transformer with high vibration level, a nonlinear equivalent circuit should be used. In figure 1, we introduce the nonlinear resistance RRNLR in the classical equivalent circuit with the parameters LRmR, CRmR, RR0R, CR1R, CRR, and N, which determined by the dimensional parameters and material properties of the piezoelectric transformers. In this paper, the operating frequency is set near the resonant frequency, so the effect of the dielectric losses is small and can be neglected. Therefore, we assume that the heat is only generated from mechanical loss PRm-lossR. Figure 1. Nonlinear equivalent circuit of piezoelectric transformer It can be seen that the power losses PRPTlossR in the piezoelectric transformer are strongly dependent on the mechanical current in Figure 1, i.e. irmrp PRRmR. Based on the experimental observation, the mechanical resistance RRmR with the temperature rise. To indicate this characteristics in the theoretical model, the nonlinear resistance RRNL Rcan be characterized as a temperature-dependent resistance through the coefficient α, i.e. α(t C). On the other hand, we also observe that the temperature may also increase with the losses increase experimentally. It implies that a positive feedback may exist between the losses and the temperature rise. This is the underlying reason that the losses may increase unstably in the high vibration level. To have the larger output power, the mechanical resistance should be insensitive to the temperature rise. The best case is that the coefficient α is independent of temperature α(t C).. Control loop of the energy loss and output power The energy losses of the piezoelectric transformer are usually transfers into thermal energy, which leads to the temperature rise of the piezoelectric transformer. Then, as mentioned in last section, the mechanical resistances increase with temperature rise as shown in figure (see the black arrows). However, there are two tendencies with increasing mechanical resistances RRmR. First, the power loss increases with increasing mechanical resistance to form a positive Proc. of SPIE Vol U-

3 decreases, feedback loop. On the other hand, considering the voltage across the piezoelectric transformer is controlled as a constant, the current flowing through RRmR to form a negative feedback loop. The black arrows in figure shows the physical loop mentioned above in the piezoelectric transformers without any cooling device. In addition, after applying the heat transfer equipment (HTE), another physical loop in the piezoelectric transformers is established..the function of the HTE is to reduce coefficient α. According to equations (1) and (), the mechanical resistance decreases with the HTE and then the mechanical loss decrease as shown in the blue arrow. In such a condition, the output power is increasing immediately. Considering the voltage across the PT is a constant, there is another new positive feedback loop (the red line in figure ), which can be viewed that the passing current capacity of the piezoelectric transformers is increased. Based on the control loop of the piezoelectric transformer, the relationships between RRmR RRNLR, irmr, temperature rise, energy loss and output power can be described clearly. Figure. Energy loss control loop of the piezoelectric transformers.3 Measurement of the Parameters and Temperature-Dependent Resistance RRNLR in the Equivalent Circuit Except for RRNLR, the other equivalent circuit parameters of PT could be measured by the impedance analyzer Agilent 4194A. The equivalent circuit employed for measurement is shown in figure 3(a) as compared with the equivalent circuit of PT in figure 3(b). We used the piezoelectric transformer provided by Eleceram Technology Co., Ltd., Taiwan. It is a multi-layer rectangular transformer with circular electrodes. The properties and parameters of the specimen are given in table 1. (a) (b) Figure 3. (a) Equivalent circuit employed by the impedance analyzer (b) Equivalent circuit of PT To obtain the parameters of the equivalent circuit, we applied the methods shown in table by using the impedance analyzer. The relationships between the different equivalent circuits are listed in table. It is revealed that we could derive these parameters by connecting the input terminal and output terminal in short circuit respectively. The experimental results measured by the impedance analyzer are listed in table 3. It should be noted that RR0 Ris measured at room temperature (5 C). Proc. of SPIE Vol U-3

4 NRpR = ρrmr = QRmR = P and P and P are P are Table 1. Picture, size and material properties of the PT PT size : mm*mm*4.5mm Input section Output section No. of layers 4 No. of layers 4 Thickness 0.5mm Thickness 0.5mm (0.5*4=mm) (0.5*4=mm) Input inductance 51 μ H Operating frequency 94.3 khz Material properties (PZT-QA, ELECERAM TECHNOLOGY Co., Ltd., Taiwan): Isolation No. of layers 1 Thickness 0.5mm (0.5*1=0.5mm) Unstable temperature of PT 55 C KRpR= 0.58 is the electromechanical coupling coefficient 00 is the frequency constants of the plane vibration (khz mm) dr33r = 30 10P dr31r = P the piezoelectric constants (m VP P) 1 1 YR33R = 30 10P YR31R = P the elastic constants (N mp P) is the density (g cmp P) ν = 0.16 is Poisson s ratio 1800 is the mechanical quality factor S ε = is the permittivity at constant strain condition, i.e. constant S (F m 1) 33 E s 11 = is the compliance constant under the constant electric field, i.e. constant E Table. Relationships between Figure 3(a) and 3(b) Output terminal (short) Input terminal (short) R RR0 - L LRm - CRa CRm - CRb CR1 CR Table 3. The experimental result obtained by impedance analyzer frr fra RR0 LRm CRm CR1 CR N Temperature (KHz) (KHz) (Ω) (mh) (nf) (nf) (nf) (-) C According to the equivalent circuit in figure 4, we know that. IRoutR=NiRmR, (3) PRRmR, (4) PRinR= irmrp Combining equations (3) and (4), the following equation can be derived: RRNLR = PRinR/( IRoutR/N)P P-RR0R, (5) To obtain the nonlinear resistance RRNL Rin equation (5), we can measure the temperature-independent resistance (RR0R) and parameter N by the impedance analyzer first. Then, obtain the temperature-dependent resistance (RRNLR) by measuring the output short current IRoutR. In this paper, to observe the nonlinear resistance RRNLR in different vibration level, the output short current IRoutR and input power PRinR were measured with increasing input voltage VRinR. The experimental values and simulation values of RRNLR are shown in figure 5. Proc. of SPIE Vol U-4

5 P for Figure 4. The method of shortening the output terminal to measure the mechanical current and nonlinear resistance RNL(Ohm) PT- Simulation resutls PT temperature 36 C PT temperature 8 C PT temperature 49 C PT- Experimental resutls PT temperature 55 C I m (A rms) Figure 5. Characteristics between the square of mechanical current and the RRNLR at different temperatures.4 Increasing output power of the PT To increase the output power of the PT, we can control the temperature through the coefficient α. In this research, the coefficient α was reduced by the high-quality cooling devices, including the thermal pad, radiator and thermoelectric cooling module. Once α is reduced by the heat cooling device, both the values of temperature-dependent resistance RRNLR and mechanical loss PRm-lossR can be reduced in the same mechanical current condition. Specifically, a smaller coefficient α leads to a smaller mechanical loss at a constant stable operating temperature of the PT. Based on the decreases of mechanical losses and RRNLR by applying high-quality cooling devices, output power can be increased in this study. Figure 6 shows three different cooling methods to control the coefficient α, which includes: (a) Air cooling without any cooling device, (b) Contacted heat transfer equipment (HTE) (c) HTE and thermoelectric cooling module The HTE is a aluminum box was mounted onto a radiator, which served as a heat sink and provided an additional surface area of 16 cmp cooling. In the third type of experimental setup, a pair of thermoelectric cooling modules was also mounted onto the radiator and thermal pad. Proc. of SPIE Vol U-5

6 (a) (c) (b) Figure 6. (a) Air cooling without any cooling device (b) Heat transfer equipment (HTE) (c) HTE and thermoelectric cooling module. 3. SIMULATIONS, EXPERIMENTAL RESULTS AND DISCUSSIONS 3.1 Experimental setup Experimental setups were shown in figure 7. The half-bridge circuit was used to drive the vibration of the PT. The frequency of the half-bridge circuit is controlled by the connected function generator. The input inductance was set at 51μH with the switching frequency set at 94.3 khz to achieve soft switching conditions. In this study, we used a multilayer rectangular-type piezoelectric transformer working in planar vibrating mode. The experimental data of the PT specimen is shown in table 1. Furthermore, a DC power supplies the thermoelectric cooling module in the HTE device to cool down the system. The specification of the thermoelectric cooling module is shown in table 4. A temperature sensor was used to obtain the temperature variation of PT at different driving conditions. Three different cooling devices as shown in figure 6 were used to verify the mechanical losses and nonlinear resistance R NL. In such an experimental setup, we can clearly compare the relationships between the value of α, mechanical resistance, mechanical current, temperature, PT losses and output power. R Figure 7. Experimental setup Proc. of SPIE Vol U-6 R

7 Table 4. Experimental data of the thermoelectric cooling module specimen Thermoelectric cooling module size : 40mm*40mm*3.8mm Maximum intensity 8.4A Number of pairs N 14 Maximum power 8.1W Maximum temperature 80 C Maximum voltage 15.7V Manufacturer code AND RS Operating voltage.5v Operating current 0.7A Operating input power 1.75 W 3. Effect of temperature on the equivalent circuit parameters To explain the relationship between vibration velocity (mechanical current irmr) and generated heat of the piezoelectric transformer, the coefficient α is determined by measuring the mechanical current and resistance RRNLR as well as the temperature rise for the three experimental setups as shown in figure 6. The variation of mechanical current and PT temperature are obtained by applying different input voltages as shown in figure 8 and figure and thermoelectric cooling module Im (A rms) Vin (V rms) Figure 8. Characteristics between mechanical current and input voltage Temperature( ) and thermoelectric cooling module Vin (V rms) Figure 9. Characteristics between temperature and input voltage Proc. of SPIE Vol U-7

8 is and The simulation software PSIM is also used to verify the experimental results in comparison with the model. The relationships between mechanical current and temperature in different cooling methods is shown in figure Simulation results of PT Simulation results of PT with radiator Simulation results of PT with radiator and thermoelectric cooling module Experimental resultsof PT with radiator and thermoelectric cooling module Im (A rms) Temperature( ) Figure 10. Characteristics between mechanical current and temperature In figure 8 and figure 10, it can be seen that mechanical current increases with input voltage and temperature. Through applying the heat transfer equipment (HTE), the passing current of the piezoelectric transformers can increase from 0.38A/W to 0.97A/9W at the temperature of 55 C as shown in figure 10. At the 5 55 C temperature range, mechanical currents which were measured from the heat transfer equipment based experimental setup increased almost three times more than the single PT experimental setup. In addition, utilizing the impedance analyzer and the method of shortening the output terminal discussed in chapter., the relationship between RRmR mechanical current is shown in figure 11. Rm(Ohm) Simulation results of PT Simulation results of PT with radiator Simulation results of PT with radiator and thermoelectric cooling module and thermoelectric cooling module 55 PT limit temperature 55 PT limit temperature 55 PT limit temperature Im (A rms) Figure 11. Characteristics between mechanical resistance RRm Rand mechanical current In figure 11, it is clear that the resistance RRmR efficiently decreased by applying the heat transfer equipment (HTE) at the constant mechanical current. In addition, the mechanical losses PRm-losRRsR and RRmR can be related as: Proc. of SPIE Vol U-8

9 can P (RR0R+α P RRmR, PRm-lossR =irmrp (7) From equation (7), mechanical losses PRm-lossR is also decreased by applying the heat transfer equipment (HTE) at the same mechanical current value. It is evident that the HTE successfully reduces the energy dissipation of the PT. Moreover, the relations between coefficient α, temperature and RRmR be derived from the statistics of figures 10 and 11 shown above. In figure 1, it is shown that the coefficient α of the PT-only experimental setup is much larger than the others in the same temperature condition. 350 Simulation results of PT Simulation results of PT with radiator Simulation results of PT with radiator and thermoelectric cooling module and thermoelectric cooling module α Temperature( ) Figure 1. Characteristics between loop gain α(t ) value and temperature Owing to the fact that the coefficient α is proportional to the mechanical resistance and mechanical losses, the mechanical losses P m-lossr and α can be related as: PRm-lossR =irmrp irmrp P), (8) It is clear that large coefficient α leads to high PT losses at the same mechanical current. To enhance the power capacity of the piezoelectric transformer, the heat must be dissipated using heat transfer devices to decrease the coefficient α as shown in figure 13. α and thermoelectric cooling module Im (A rms) Figure 13. Characteristics between loop gain α(t ) value and mechanical current Proc. of SPIE Vol U-9

10 It should be noted that all of the parameters are measured in stable working conditions, which is about 10 min after applying the input voltage in each experimental setups. 3.3 Results of the enhanced output power and efficiency of PT by applying HTE In figure 14, the measured results show that the largest output power of HTE used for PT can move from 3.43 W to 9.9 W at the temperature of 55 C with 47 Ohm load value. The output power was increased at least three times when the load was varied from 10 to 330 Ohm. PT 55 Operting Temperature Limit PT PT with Radiator PT with Radiator and Thermoelectric Cooling Module Output Power(W) Load ( Ω ) Figure 14. Results of output power in different heat transfer structures Furthermore, all specimens remained at good efficiency (70%+) when the load was varied from 10 to 100 Ohm at the PT limit temperature of 55 C. The experimental results are also shown in figure 15. PT 55 Operting Temperature Limit PT PT with Radiator PT with Radiator and Thermoelectric Cooling Module 0.9 Efficiency Load ( Ω ) Figure 15. Results of efficiency in different heat transfer structures 4. CONCLUSION In this paper, the cooling method was used to enhance the output power of piezoelectric transformers. According to the experimental results, all specimens remained a satisfactory efficiency even at temperature 55 C. By applying HTE, the ability of heat dissipation becomes better. The passing current of the piezoelectric transformers can increase from 0.38A/W to 0.97A/9W and the maximum output power of the piezoelectric transformers can also increase from 3.43W to 9.9 W at specific temperature. On the other hand, we proposed a measured method to obtain the equivalent circuit of piezoelectric transformers, especially the temperature-dependent mechanical resistance, in the conditions of high temperature and high power. This study clearly indicates that it is possible to enhance the performance of the piezoelectric transformer by decreasing the loop gain α(t ) value. Moreover, the output current of the piezoelectric transformer in our design also increases, which implies that this technique, allows the piezoelectric transformer to be Proc. of SPIE Vol U-10

11 used in low voltage-high current applications. References [1] S. Hirose, M. Aoyagi, Y.Tomikawa, S. Takahashi, and K. Uchino, High power characteristics at a antiresonance frequency of piezoelectric transducers, Ultrasonics. Papers 34, 13-17(1996). [] K. Uchino, J. Zheng, A. Joshi, Y. H. Chen and S. Yoshikawa, High power characterization of piezoelectric materials, Journal of Electroceramics, 33-40(1998). [3] K. Uchino, and S. Hirose, Loss mechanisms in piezoelectrics: how to measure different losses separately, IEEE Trans. Ultrason. Ferroelectr. Freq. Control (001) [4] A. Albareda, P. Gonnard, V. Perrin, R. Briot, and D. Guyomar, Characterization of the mechanical nonlinear behavior of piezoelectric ceramics IEEE Trans. Ultrason. Ferroelectr. Freq. Control (000) [5] I. Kim, M. Kom, S. Jeong, J. Song, and V.V. Thang, Piezotransformer with ring-dot-shape for easy heat radiation and high efficiency power Applications of Ferroelectrics (ISAF/PFM), 1-6(000) [6] W.W. Shao, Z.H. Feng, J.W. Xu, C.L. Pan and Y.B. Liu, Radiator heightens power density of piezoelectric transformers, Electronics Letters, (010). [7] S. Tashiro, M. Ikehiro and H. Igarashi, Influence of temperature rise and vibration level on electromechanical properties of high-power piezoelectric ceramics, Jpn. J. Appl. Phys. Papers 36, (1997). Proc. of SPIE Vol U-11