| In recent years,with the rapid development of wireless sensor networks,vibration energy harvesting technology is rising to provide energy for the low-power wireless sensors with a more efficient and environmental friendly manner.Piezoelectric vibration energy harvester is a new type of micro-scale electromechanical device that can convert the vibration energy into the electricity.Its goal is mainly to replace the chemical batteries to provide power for the low power electronic devices.Due to the green,pollution-free and simple structure,it has become a research hotspot.The occurrence of vibration in the environment is random,and the traditional harvester only has a large power output near the natural frequency point of the structure.In order to broaden the effective working band of the harvester and improve its working efficiency,it is one of the more effective solutions to realize the bi-stable or multi-stable energy harvester by using the nonlinear jump characteristics of the nonlinear structure between multiple steady-state solutions.At present,the nonlinear tri-stable piezoelectric vibration energy harvester has been widely concerned because of its wide and shallow potential well characteristics,and excellent energy harvesting performance.However,the potential well of a typical tri-stable piezoelectric vibration harvester(TPEH)is symmetric about the central equilibrium position,and the depth and width of the potential well are fixed with the structure.The improvement of the output performance of the tri-stable harvester was limited by this characteristic severely,especially for the low excitation level,or even failure.In order to solve this problem,in this paper,a tri-stable piezoelectric vibration energy harvester with asymmetric variable potential well is presented.Based on the point magnetic charge method and Lagrange function,its nonlinear magnetic force and distributed parameter dynamics model of the system are established.The effects of the distance between magnets,acceleration,spring stiffness and other parameters on the system potential are simulated and analyzed,as well as its dynamic response characteristics,then the static equilibrium bifurcation and dynamic bifurcation characteristics of the system are studied,and based on the harmonic balance method,the influence of system parameters on system output response is studied.Finally,to verify the results,a system experimental platform is established.The results show that under the appropriate spring stiffness,the energy collector can reduce the potential energy well,easier jump into the inter-well movement,and enhance the energy harvesting efficiency.This paper studies as follows:1.The research and development status of piezoelectric energy harvesting technology and some existing problems are introduced,and then the basic theoretical knowledge related to the research content of this paper is described,such as piezoelectric effect and piezoelectric equation.In order to solve the problem of low collection efficiency of the energy harvester under low excitation level and improve the adaptability of the harvester in practical application,A tri-stable piezoelectric vibration energy harvester with asymmetric variable potential well(TPEH-K)is constructed by a piezoelectric cantilever beam with a magnet at the end and a pair of external magnets which can change with the spring stretching and compression.When the harvester is excited by the external environment,the magnetic force between the end magnet of the cantilever beam and the external magnets changes,causing the two springs to have stretching or compression movement and rotation movement in the horizontal direction,thus changing the distance between the end magnet and the external magnets,resulting in an asymmetric potential well that changes with time.Based on the point magnetic charge method,the nonlinear magnetic force model of TPEH-K asymmetric and variable potential well harvester is established,and the influence of system parameters such as magnet spacing and spring stiffness on the static bifurcation characteristics of the system,potential well and nonlinear magnetic force is simulated and analyzed.The results show that the tension and compression of spring is the main factor to produce asymmetric and variable potential well,and changing the spring stiffness can make the depth of asymmetric potential well shallow;Adjusting the horizontal distance between magnet pairs can change the distribution position of stable and unstable static equilibrium points and realize the transition from mono-stable to multi-stable motion state.2.Based on the energy method and Lagrange equation,the electromechanical coupling nonlinear dynamic model of the asymmetric variable potential well multi-stable piezoelectric energy harvester is established.The influence of magnet spacing,acceleration and spring stiffness on the system potential is simulated and analyzed,as well as the influence on the dynamic response characteristics.Furthermore,the dynamic characteristics of the spring oscillation system are deeply studied to optimize the spring stiffness provide theoretical reference for improving the efficiency of energy harvester.In addition,in order to prove that TPEH-K has better energy harvesting performance,TPEH-K is compared with TPEH in terms of dynamic output response.The results show that TPEH-K can achieve large vibration and generate higher output voltage(2.1V)and wider output frequency band(0～4.5Hz)at a lower excitation level(A=8m/s~2)when the spring stiffness k=900N/m,while TPEH-K only has 0.2V and 2.5～4Hz output voltage and frequency band,and it requires A=10m/s~2 to cross the limit of potential barrier for large amplitude vibration.3.In order to further study the nonlinear dynamic response characteristics of TPEH-K,the harmonic equation of TPEH-K is established based on the harmonic balance method.First,the steady-state response solution of the system and its stability analysis are derived.Then,the influence of parameters such as spring displacement,magnet spacing d and d_g,acceleration A and damping on the output response of the energy harvester is analyzed,and the impedance characteristics of the system are explored.It is found that the nonlinear characteristics of the system attenuate with the increase of distance d;Increasing the acceleration amplitude and reducing the damping coefficient can effectively increase the amplitude of the high energy inter-well vibration of the harvester,broaden its effective working frequency band,and improve the acquisition performance.4.Based on the proposed theoretical model,an experimental prototype of the harvester model is developed,and the simulation theoretical analysis of the asymmetric system is fully verified by experiments.The results show that TPEH-K is more conducive to improving the dynamic response output and frequency band width under the appropriate spring stiffness(k=900N/m).Compared with TPEH,TPEH-K has a lower excitation threshold,making it easier to achieve large inter-well oscillation and generate higher output voltage. |
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