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Vibration and cooling performances of piezoelectric cooling fan: numerical and experimental investigations

In this paper, the vibration and cooling performances of the piezoelectric cooling fan are studied. The finite element and experimental methods are adopted for the analyses. The natural frequency, mode shape, flapping amplitude, and cooling performance are discussed for the primary design. The numerical results have good agreement with the experimental measurements. For the cooling purpose, the piezoelectric cooling fan has to work under the natural frequency. The aspect ratio 2:3 is the optimal geometry of the fan blade.


Introduction
As shown in Fig. 1, the piezoelectric cooling fan uses the flapping blade to make the air flow for the electronic cooling. It is quite different from the traditional rotating cooling fan. Using the piezoelectric actuator, the piezoelectric effect makes the cyclic deformation so that the blade can vibrate and flap. Under the natural frequency, the piezoelectric cooling fan can perform the maximum flapping displacement and air flow.
In the past references [1][2][3][4][5][6], it is concluded that the piezoelectric cooling fan consumes lower electric power. Also, it has good cooling performance for the small-size electronic devices. Undoubtedly, the piezoelectric cooling fan is a good cooling solution for many electronic products. Recently, detail researches have been finished by using the fluid mechanics and flow analysis [7][8][9]. In Ref. [7], at peak skewness, the vortex behind the phase leading blade is 101% larger than its counterpart. Evenly matched vortices between the two blades are optimal for generating peak mass transfer [7]. In Ref. [9], it was found that the propagation of the side vortex is a key factor in determination of the flow pattern. Based on the numerical results, it was found that whether the side vortex propagates or not is an important factor in determining three-dimensional flow pattern around the piezoelectric fan [9].
In this paper, the vibration and cooling performances of the piezoelectric cooling fan will be studied. The numerical and experimental methods are adopted for the analyses. The natural frequency, mode shape, flapping amplitude, and cooling performance will be discussed for the primary design. Based on the vibration mechanics and temperature reduction, the present study will find the optimal geometry of the fan blade and associated conditions.

Definition of research
The geometry and photo of the piezoelectric cooling fan are shown in Fig. 2 and 3. It contains two main parts: the blade and piezoelectric actuator. The dimensions of the rectangular blade (W b , L b , t b ) are variables and will be studied for the vibration and cooling performances.
In Fig. 4, the detail geometry of the bimorph piezoelectric actuator is illustrated. All dimensions are constant values. The piezoelectric material type is PZT-5H, i.e. a kind of the piezoelectric ceramic. The Parrows define the poling directions. Three electrodes are attached to the piezoelectric material. Due to relatively thin value, the thickness of the thin-film electrode is ignored in the numerical analysis. As shown in Fig. 4, the piezoelectric material is actuated by the electric field between two electrodes. When the voltage difference (V 2 -V 1 ) is applied on both electrodes, the piezoelectric actuator deforms and bends due to the electric field and poling direction. For making the cyclic deformation, the alternative current (AC) is applied on two thin-film electrodes as V 1 = V amp sin(2πft) V. In addition, the copper electrode is grounded (V 2 = 0 V). In above equation, the parameters f and t are the AC frequency and time, respectively. Thr AC amplitude is The electro-mechanical piezoelectric behavior is ruled by the constitutive equation under the Cartesian coordinate where T, S, D, E, c, e and ε are the stress, strain, electric displacement, electric field, elastic constant, piezoelectric constant, and permittivity, respectively. In Eq. (1), the poling direction of the piezoelectric material is along the x 3 -axis.
The piezoelectric material is PZT-5H. Two materials, PET and PC plastics, are used to make the blade. Table 1 and 2 list all material data for the numerical simulations.

Numerical method
In this study, the numerical method is the finite element method. Also, the software ANSYS is employed. In Fig.  5 piezoelectric effect can be simulated. In ANSYS, the modal analysis is used to calculate the natural frequencies and mode shapes of the vibration bahaviors.

Experimental method
In Figs. 6-8, the experimental equipments for the flapping amplitude and cooling performance of the piezoelectric cooling fan are shown. The AC power drives the piezoelectric cooling fan so that the air flow can be produced for the cooling process. The laser displacement sensor and thermo-meter are used to obtain the data of the flapping amplitude (δ t ) and cooling performance (temperature reduction of the heatsink). The distance between the blade and heatsink is 10 mm.

Vibration behaviours
In this section, the dimensions of the PET blade are W b =10 mm, L b =60 mm, and t b =0.25 mm. The natural frequency is determined according to numerical modal analysis and experimental maximum flapping amplitude. In Fig. 9 and 10, the finite element and experimental results show the mode shapes and natural frequencies of the piezoelectric cooling fan. Both numerical and experimental values are almost the same. It confirms the good accuracy of the research methods. Also, the finite element method can predict the vibration behaviour of the piezoelectric cooling fan before the real cooling system is established.
The maximum flapping amplitude occurs under the natural frequency, i.e. the resonance condition. The larger flapping amplitude makes larger air flow and better cooling performance.  According to Fig. 10, the flapping amplitude of the firstmode vibration is larger than that of the second-mode. In this study, the first-mode flapping amplitude δ t (as shown in Fig. 6 and 10a) is adopted for the electronic cooling. Also, the amplitude δ t is obtained under the first-mode natural frequency and V amp =100 V.

Flapping amplitude
The variations of δ t with different geometric properties are shown in Fig. 11 and 12. The wider, shorter and thicker blades have smaller δ t . The larger flapping amplitude makes larger air flow and better cooling performance. The amplitude δ t is an important value for the piezoelectric cooling fan design.

Cooling performance
In Fig. 7 and 8, it shows the experimental configuration for the cooling performance. To prevent from environmental disturbance, the transparent structure covers the heat source and piezoelectric cooling fan. The temperature at the heatsink bottom is measured by the thermo-meter. Figure 13 shows the typical temperature history. During t= 0~600 s, the DC power and heater provide the thermal energy and temperature rise from T i to T max . At t=600 s, the piezoelectric cooling fan begins to work under the first-mode natural frequency. The steady-state temperature T ss is obtained at t=2000 s. The temperature reduction ∆T of the heatsink is defined as T max −T ss . The larger value of ∆T expresses the better cooling performance.
In Table 3~6, the ∆T values of different blades are listed. Four cases: 46.8×70 mm, 40×60 mm, 33.4×50 mm, and 27×40 mm have largest ∆T values, i.e. best cooling performance. These optimal cases have the same geometric property: L b /W b ≈ 2/3. Table 3. Cooling performances.  Table 4. Cooling performances.  Table 5. Cooling performances.  Table 6. Cooling performances.   Table 4. When L b /W b ≈ 2/3, it shows the largest ∆T value in each curve. The wider blade makes larger air flow. Shorter, thicker and stiffer blades have higher natural frequency. The above reasons dominate the cooling performance.

Conclusions
The vibration and cooling performances of the piezoelectric cooling fan have been studied in this paper. The natural frequency, mode shape, flapping amplitude, and temperature reduction have been obtained. The numerical results have good agreement with the experimental measurements. As a result, the piezoelectric cooling fan has to work under the natural frequency. The aspect ratio 2:3 (L b /W b ≈ 2/3) is the optimal geometry of the fan blade for the cooling purpose.