Resarch methodology

1. INTRODUCTION 

In recent years, energy harvesting from ambient vibration [I and human motion [2] has received both considerable industrial and academic interest due to advances in micro-electronic technology leading to an increased computation efficiency and reduced power consumption of wireless sensors and portable electronic devices. In addition to environmental benefits associated with limiting the disposal of traditional batteries, energy harvesting technologies [3] provide a great promising of autonomous and self-powered electronic devices for safety monitoring, structure-embedded diagnosis and medical implants. The narrowband issues of linear resonant piezoelectric energy harvesters have motivated several research groups to develop the nonlinear monostable [4], bistable [5] and tristable [6] approaches to enhance frequency bandwidth and output power. The theoretical analysis and experimental verification of those nonlinear energy harvesters have been extensively investigated under harmonic and stochastic excitations [7-9]. For the realistic excitation, Green [2] numerically analyzed the efficiency of nonlinear energy harvesting from human motion and Cao [10] applied the time-varying potential bistable energy harvester to human motion to demonstrate its better performance than the linear one. However, tristable energy harvesting performance has not yet been evaluated under realistic excitations induced by human motions. Therefore, the paper employs tristable magnetic coupled piezoelectric cantilever to harvest energy from human walking and running. Based on the characteristics of human motion, theoretical model of nonlinear tristable energy harvester with time-varying potential energy function is established. And experiment results show that the tristable energy harvester exhibits better performance than the linear one when applied to harvesting energy from human walking and running. 

2. ELEC TROMECHANICAL MODEL 

The magnetic coupled piezoelectric energy harvester with external magnets is illustrated in Fig.1 (a). The configuration consists of a stainless steel substrate, two symmetric PZT-51 piezoelectric layers at the root, tip magnet attachments and two external magnets. 

Tristable energy harvester can be obtained by adjusting the parameters h, d and a.When harvester is applied to harvesting energy from human motion , the lower limb swing motion will drive the cantilever to swing a certain angle (shown in Fig.1 (b) which results in a time-varying potential energy function due of the beam. On these conditions, the electromechanical model of the nonlinear piezoelectric energy harvesters with time-varying potential energy function can be given by the following equation: 

Where m is the equivalent mass and c is the equivalent damping. 0 is the equivalent electromechanical coupling coefficient, Cp is the equivalent capacitance of the piezoelectric materials, R is the load resistance, v(t) is the voltage across the electrical load, x() is tip displacement of the harvester in the transverse direction, B(t) is the swing angle of the human leg and al) is the external excitation. (x, B)) is the time-varying potential energy function described as the integral of nonlinear restoring force depending on structural parameters and the swing angle Bt) shown in Fig.1 (b). It is found that the time-varying potential energy function mainly attributes to the gravity effect under different sway angles where the magnetic force similar B 0. Therefore, the restoring force of the nonlinear harvester can be approximated by 

Where Fis the restoring force for B 0. The time-varying potential energy function in Equation. (1) is: 

In this paper it is assumed that the clockwise angle is positive otherwise negative.

3. EXPERIMENTAL VERIFICATION 

In the experiment, the energy harvester is tied to human leg for harvesting energy from human motion as shown in Fig.2. An acceleration sensor (CXL04GP3) and an angle sensor (BWD-VG100) are used to collect the acceleration and swing angle data. A displacement sensor (HL-GI) is applied to measure the tip displacement of the cantilever. All the measured data are acquired by an oscilloscope (MSOX3052A) with 10 M2 resistance. The cantilever is made of stainless steel of 90x10x0.27 mm3. Two PZT-51 have dimension of 12x10x0.6 mm3. All the magnets used in the experiment are NdFeB cylinder magnets and the endmost ones have the dimension of 8x6x4 mm3 while the external magnets have diameter of 25 mm, and has the dimension thickness of 5 mm.

A tristable energy harvester (TEH) with three stable equilibrium points is adjusted to harvest energy from human motion and the traditional linear energy harvester (LEH) is used to compare. In the experiment, the restoring forces of the cantilever are measured by the system Mark-10 and the fitted curve is plotted in Fig. 3 while the corresponding potential energy functions are illustrated in Fig.4. The asymmetry in the potential energy function can be viewed as due to imperfections caused by the evenly distributed material and structure or eccentricity of magnetic force. 

In the experiment, the nonlinear restoring forces of tristable harvester at different swing angle+11 and +31o are measured to demonstrate the time-varying potential energy function and the corresponding potential energy functions are plotted in Fig. 5 and Fig. 6. When the swing angle is negative, the left potential well depth increase while the right one becomes shallow and in this condition the potential well in the middle does not disappear. When the swing angles are 11o and 31°, the left potential well depth decreases while the right increases gradually. Moreover, the potential well in the middle disappears when the swing angle is 31°. Furthermore, larger swing angle has greater influence on the potential well than small angle. Obviously, when the tristable harvester is applied to human limb, the swing motion will greatly increase the harvesting efficiency.

One participant (weight: 63Kg; Height: 175cm) asked to walk or run at the speed of 4-9 km/h on treadmill the motion acceleration, swing angle, output voltage and tip displacement. The acceleration and swing angle data for speed 5 km/h are shown in Fig.7. It can be seen the amplitude of the acceleration reach about 2g and it exhibits maximum value when the foot strikes the treadmill. For the swing motion, the lower limb swing about 60° to backward and 15° to the forward. experimental results show that the acceleration and swing angle range increase with the increasing of the motion speed. The tip displacement and voltage response as well as the frequency spectrum at the speed of 5 km/h are illustrated in Fig.8. The tristable harvester could travels across the potential well frequently and does large amplitude inter-well motion between the three stable equilibrium points because of the leg swing motion strike, thus generates large output voltage. Furthermore, frequency spectrum in Fig.8 shows that the response frequency ranges from 4 Hz to 8 Hz which is probably due to the nonlinear restoring force. The average output power of the tristable and linear energy harvesters different motion speed are shown in Fig.9. It can be found that the tristable energy harvester performs better than the linear one at any motion speed. Further, the average output power increases with the increasing of the motion speed and the maximum average output power of the tristable energy harvester is 16.38uW.

4. CONCLUSION 

The electromechanical model of the tristable energy harvester with time-varying potential energy function is proposed based on the characteristics of human motion. Detailed restoring forces of the tristable energy harvester under different swing angles are measured and the corresponding potential energy functions are obtained. Further, a measurement system is setup to collect the acceleration, swing angle as well as the voltage data generated during human motion, experimental results under various motion speeds show that the tristable energy harvester exhibits better performance than the linear one for harvesting vibration energy from human walking or running. 

ACKNOWLEDGEMENTS 

This research is supported by National Natural Science Foundation of China (Grant No. 51421004, 51575426), National Key Scientific Instrument and Equipment Development Project (No: 2012YQ03026101), Program for New Century Excellent Talents in University (Grant No. NCET-12-0453), and Fundamental Research Funds For the central universities of China (Grant No. CXTD2014001).