Shock and Vibration

Volume 2015, Article ID 216353, 10 pages

http://dx.doi.org/10.1155/2015/216353

## Performance Analysis of Wind-Induced Piezoelectric Vibration Bimorph Cantilever for Rotating Machinery

School of Mechanical and Electrical Engineering, China University of Mining & Technology, Xuzhou, Jiangsu 221116, China

Received 15 January 2015; Revised 7 April 2015; Accepted 7 April 2015

Academic Editor: Alicia Gonzalez-Buelga

Copyright © 2015 Gongbo Zhou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Harvesting the energy contained in the running environment of rotating machinery would be a good way to supplement energy to the wireless sensor. In this paper, we take piezoelectric bimorph cantilever beam with parallel connection mode as energy collector and analyze the factors which can influence the generation performance. First, a modal response theory model is built. Second, the static analysis, modal analysis, and piezoelectric harmonic response analysis of the wind-induced piezoelectric bimorph cantilever beam are given in detail. Finally, an experiment is also conducted. The results show that wind-induced piezoelectric bimorph cantilever beam has low resonant frequency and stable output under the first modal mode and can achieve the maximum output voltage under the resonant condition. The output voltage increases with the increase of the length and width of wind-induced piezoelectric bimorph cantilever beam, but the latter increasing amplitude is relatively smaller. In addition, the output voltage decreases with the increase of the thickness and the ratio of metal substrate to piezoelectric patches thickness. The experiment showed that the voltage amplitude generated by the piezoelectric bimorph cantilever beam can reach the value simulated in ANSYS, which is suitable for actual working conditions.

#### 1. Introduction

With the continuous development of measurement and control technology of large mechanical and electrical equipment, the wireless sensors are widely used in the equipment monitoring system. Compared with the wired sensor, wireless sensors take the place of the wired communication cable with the help of wireless communication technology and substitute the portable power like battery for the wired power. As the wireless sensors can work without physical connection, it can be applied in the condition detection of middle-low-speed rotating machinery. In the process of practical application, the wireless communication module can avoid frequent maintenance, but the batteries need to be replaced frequently, especially in the detection of stress and vibration which has a large amount of data. Therefore, obtaining the energy contained in the running environment of rotating machinery to supplement energy to the battery and prolong the working life of the nodes is one of the problems that needs to be solved urgently.

Wind energy is a kind of typical energy in running environment of large mechanical and electrical system like mine hoist. For example, when rotary machine is working, there will be a certain relative velocity between rotary machine and air, resulting in the flowing air. So if the wind energy harvesting device is placed on the rotator, the wind energy can be collected in real time to power the wireless sensor nodes.

At present, the research on micro wind power generation technology is mainly divided into four categories: micro wind turbine generator, micro bellows generator, micro electromagnetic wind generator, and wind-induced piezoelectric energy harvesting device. Among these devices, the most mature and most commonly used one is the traditional wind power turbine technology, but under the condition of a small size, its power generation efficiency will decrease due to the increasing influence of the bearing friction loss and the decrease of the leaf area [1, 2]; micro bellows generator has a higher power output when the wind speed is high (>5.5 m/s), but the power output is very low when the wind speed is low (<3.5 m/s); besides, it makes a lot of noise in the working process [3]; micro electromagnetic wind generator is reliable and the mechanical damping is small. But under the condition of low-speed wind, the efficiency of the generator will be influenced by the weight of the magnet [4]; wind-induced piezoelectric energy harvesting device is cheap, easy to install, sensitive to the low-speed wind and also has a high efficiency of electromechanical conversion, small volume, light weight, compact structure, low magnetic permeability, and almost no heat loss [5]. Thus wind-induced piezoelectric energy harvesting technology is very suitable for the wireless sensors system.

The key point that influences the power generation efficiency of the wind-induced piezoelectric vibration energy harvesting device is the performance of energy collector. As the cantilever support mode can produce the biggest flexure coefficient and compliance coefficient [6], and the bent vibration frequency of the cantilever beam is usually lower than its longitudinal vibration frequency when it works as a shaft or its torsional vibration frequency when it works as an axle; besides, it can be motivated easily; most energy collectors choose the cantilever beam as their structure [7]. In addition, the wireless sensor nodes can work with a low voltage and the voltages generated by the two piezoelectric layers are the same; however, the current generated by piezoelectric bimorph is very low; thus parallel connection mode is often adopted to improve generator current in piezoelectric bimorph energy harvesting device. So this paper takes piezoelectric bimorph cantilever beam with parallel connection mode as energy collector and analyzes the factors that can influence the generation performance of the wind-induced piezoelectric vibration bimorph cantilever beam (WPB) by adopting the finite element method.

#### 2. Related Works

Researchers have done a lot of works on piezoelectric vibration generator and made tremendous achievements. Priya et al. have manufactured a small generator [8] by using piezoelectric devices, which can provide up to the power of 50 mW for the wireless sensor nodes by increasing the number of piezoelectric bimorph in windmill. Tang and Zuo [9] proposed a spring-quality system generator model of double degree of freedom and calculated the maximum output power of the model; Arafa et al. [10] confirmed its feasibility by experiment. Challa et al. [11] and Xu et al. [12] established piezoelectric cantilever vibration generator model, respectively, from the perspective of adjusting the resonance frequency and broadening bandwidth. Sodano et al. [13] and DuToit et al. [14] built discrete mathematic model of piezoelectric vibration generator distributed-parameter system using the Rayleigh-Ritz discrete formula, but the methods simplify electromechanical coupling in the beam equation into viscous damping, and cannot consider resonance phenomena. Abd El-Mageed et al. [15] and Kiwata et al. [16] have conducted several experiments on energy harvester utilizing flow-induced vibration; however, the flow is liquid and not many literatures are focused on other flows like wind.

#### 3. Theory Model of Modal Response

Piezoelectric bimorph cantilever belongs to Bernoulli-Euler beam as its thickness is far less than its length. Before building the theory model of modal response [17], this paper assumed a group of variables: the linear density of WPB , the bending stiffness of WPB ( is the Young modulus of WPB and is product of inertia that cross section to neutral axle of WPB), the length from each point to the origin , the base lateral displacement , and the base rotational displacement . The modal response satisfies the following ordinary differential equation:where denotes the order undamped natural frequency of WPB, is the damping ratio of WPB, and is each order generalized force of PWB. And the damping ratio satisfies the following equation:then, the damping ratio can be expressed as follows:where denotes the viscous air damping coefficient, is the strain rate damping coefficient, is the strain rate damping ratio, and is viscous air damping ratio. The strain rate damping coefficient and the viscous air damping coefficient can be expressed asEach order generalized force of PWB composed of inertia force and damping exciting force can be expressed as And the inertia force and damping exciting force can be expressed aswhere , .

Finally, by using Duhamel integral, modal response can be expressed aswhere is damping natural vibration frequency.

#### 4. Finite Element Modeling for WPB

##### 4.1. Parameters of the Model

The structure of WPB is shown in Figure 1. Piezoelectric ceramic PZT-5 is used as piezoelectric layer on both sides, and the intermediate is metal plate. Nickel alloy is selected as the metal layer and the mass block. The reference dimension of the WPB selected in this paper is shown as follows. The length, width, and thickness of the piezoelectric patches are 77 × 42 × 0.1 mm. So does the metal layer.