Independent nonlinearity tuning of planar spring via geometrical design for wideband vibration energy harvesting

Accepted Manuscript Title: Independent nonlinearity tuning of planar spring via geometrical design for wideband vibration energy harvesting Authors: Shi Sun, Xuhan Dai, Zaichun Feng, Guifu Ding, Xiaolin Zhao PII: DOI: Reference:

S0924-4247(17)31105-6 https://doi.org/10.1016/j.sna.2017.10.045 SNA 10411

To appear in:

Sensors and Actuators A

Received date: Revised date: Accepted date:

15-6-2017 25-9-2017 17-10-2017

Please cite this article as: Shi Sun, Xuhan Dai, Zaichun Feng, Guifu Ding, Xiaolin Zhao, Independent nonlinearity tuning of planar spring via geometrical design for wideband vibration energy harvesting, Sensors and Actuators: A Physical https://doi.org/10.1016/j.sna.2017.10.045 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Independent nonlinearity tuning of planar spring via geometrical design for wideband vibration energy harvesting Shi Suna, Xuhan Daia, *, Zaichun Fengb, Guifu, Dinga and Xiaolin Zhaoa, * a

National Key Laboratory of Science and Technology on Micro/Nano Fabrication,

School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai 200240, People's Republic of China b

Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, MO 65211, USA

* Corresponding authors. E-mail address: [email protected] (X.Dai), [email protected] (X.Zhao)

Highlights: 1. Nonlinearity tuning can be realized through sophisticated geometrical design. 2. Nonlinear stiffness coefficient can be designed independently. 3. Both simulation and experiment validate the tuning method. 4. Working bandwidth of the output voltage can be tuned from 37Hz to as wide as 75Hz. 5. The tuning method is compatible with MEMS batch fabrication process.

Abstract This paper reports a novel nonlinearity tuning method through sophisticated geometrical design for wideband energy harvesting application. By carefully controlling the thickness to length ratio of the planar spring beams, the nonlinear stiffness coefficient can be intentionally and precisely adjusted, while the linear stiffness coefficient can be kept unchanged. Thanks to the different effects on the linear and nonlinear parts, both the resonant frequency of the linear part and the bandwidth range of nonlinear vibration can be designed separately. As a proof of concept, MEMS-based electromagnetic vibrational energy harvesters employing the independent nonlinearity tuning method have been designed and fabricated. Both simulation and experiment were conducted to validate our method. At the acceleration of 0.5g, the micro-fabricated device is able to tune the operating bandwidth of the output voltage from 37Hz to as wide as 75Hz. This design can easily tune the length and thickness of the spring beams without changing the volume of the whole energy harvester device, which is compatible with MEMS batch fabrication process.

Key words: Electromagnetic energy harvesting; Nonlinearity tuning; Geometrical design; Planar spring; Micromachining; MEMS

1. Introduction Recently the rapid development of internet of things (IoT) has led to growing demand of wireless sensors. Power source may become the main obstacle that hinders their low-cost and large-scale application. Vibration energy harvesters, which are capable of converting ambient kinetic energy into electrical energy, have attracted much attention due to their potential as alternatives to traditional electrochemical batteries [1, 2]. Typical vibration energy 1

harvesters mainly employ the piezoelectric [3-5], electrostatic [6-8] and electromagnetic [9-13] transduction mechanisms. Electromagnetic energy harvesters are preferred in some applications owing to its relatively low output impedance, high output current and power density. Linear resonant structure suffers from narrow bandwidth issues. If the excitation frequency of the ambient vibration shifts slightly, the output power of the energy harvester would drop drastically. Unfortunately, some of environmental vibrations occur with a broadband frequency and could vary with time (e.g. car engine)[14]. Thus, researchers have been seeking new approaches to overcome this limitation [15, 16], including resonant frequency tuning [17, 18], multimodal energy harvesting [19, 20], electrical tuning [21, 22] and nonlinear design [23], which contains mono-stable [24-33] and bi-stable nonlinearity [34]. Nonlinear effect can cause the frequency response curves to bend in order to create wider operating bandwidth. The frequency response curve is dependent on both linear and nonlinear stiffness of the vibration system. However, for physical realizations of most nonlinear vibration energy harvesters, the linear and nonlinear stiffness coefficients cannot be tuned independently, which will influence the practical application to the targeted ambient vibrations. Taking the magnets tuning mechanism as an example, when the distance between the magnets is changed, both the linear and nonlinear stiffness coefficients change simultaneously [23]. In order to tune the linear stiffness and nonlinear stiffness coefficients separately, Dai et al. [35] proposed a topology method to keep the linear stiffness coefficient constant while tuning the nonlinear stiffness coefficient. Boisseau et al. [36] designed and simulated nonlinear H-shaped springs to achieve the similar outcome. Xie et al. [37] proposed a novel frequency-tunable nonlinear electromagnetic energy harvester, where tuning frequency was realized by changing the stretch length of the elastic strings via adjustable screws. In this work, we propose a novel systematic geometrical design methodology via tuning thickness to length ratio of the planar spring for tuning linear and nonlinear stiffness coefficient separately. Our proposed geometrical design method has good compatibility with MEMS fabrication. This design can easily tune the length and thickness of the spring beams without changing the volume of the whole energy harvester device. It is convenient to adjust the frequency response range to match the vibration frequency spectrum. The content of this paper is organized as follows. Section 2 describes the design and modeling of this work, including a brief introduction on the basic electromagnetic vibration energy harvester, how to use the geometrical design method to tune the nonlinearity independently, and static and dynamic analyses. Section 3 describes the experimental validation including the fabrication process and characterization method. Section 4 provides the test results and discussions. Final section gives the conclusions.

2. Design and modeling 2.1 Basic electromagnetic energy harvester model The schematic design of the nonlinear electromagnetic energy harvester is shown in Figure 1. The electromechanical system is composed of two main systems. One is mechanical system (mass-spring-damper) and the other one is electrical system (coils and external load). The key component of our energy harvester is the MEMS-based nickel guided-beam structure, which determines the working bandwidth of our energy harvester system. The NdFeB magnet (2×2×1 mm3, 30 mg) with a vertical magnetization is mounted on the central platform of the planner spring as proof mass, which can provide magnetic field. The MEMS-based two-layer copper coils (linewidth of 12 μm, coil gap of 18 μm, single coil thickness of 15 μm, inner side length of 0.706 mm, outer side length of 2.5 mm and 30 turns for each layer) are located at bottom of the harvester. The center of the coils is aligned to the center of the magnet to maximize the flux gradient. The SU-8 spacer (300 μm) is used to define the air gap between the magnet and coils. When the magnet is vibrating relative to the coils, the induced voltage can be generated in the coil according to Faraday’s law of induction.

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Figure 1. (a) 3D schematic and (b) cross-section of the proposed electromagnetic energy harvester. The vibration model of the energy harvester can be modeled as a spring-mass-damper system with single degree of freedom and the equivalent model is demonstrated in Figure 2. The governing equation of the mechanical system can be expressed as the following second order differential equation

mz  dz  kz  kn z 3  mF cos(t ),

(1)

where m is the moving mass, d is the damping constant, k is the linear stiffness, kn is the nonlinear stiffness, z is the relative displacement of the mass with respect to the fixed base, and F =Y  is the excitation amplitude of the base. 2

If k > 0, systems with kn > 0 are called hardening systems, which result in the frequency response curves bending toward right to broaden the bandwidth [23]. The frequency response has hysteresis depending on the direction of varying the frequency due to the fact that two stable solutions are viable for some frequencies. The major limitation of the monostable nonlinear system is that it can not always work on the high energy state. For hardening systems, frequency up sweep (i.e. going from low towards high frequencies) can capture the high-energy attractor hence improves the bandwidth. In addition, a momentary perturbation would be required if low-energy branch manifests. Using harmonic balance method[37], the amplitude of the vibration can be related to the input excitation by the following equation 2

 k 3 kn 3  d 2 2 2  m    A  4 m A   ( m  A)  y .   

(2)

There are either one or three real solutions of the equation depending on the excitation frequency. In the condition of three solutions, the solutions represent respectively the high energy state, the low energy state and the unstable state.

Figure 2. Equivalent electromechanical model of the electromagnetic energy harvester.

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2.2 Spring design and independent nonlinearity tuning

Figure 3. (a) Schematic model of guided-beam spring, and (b) nonlinear effects in fixed-guided beams. The frequency response of the vibrating system depends on the linear stiffness k and nonlinear stiffness kn. Geometric design methodology can be used to achieve the desired linear and nonlinear stiffness. Therefore, the resonant frequency and working bandwidth can be controlled. In order to achieve different bandwidth through tuning spring hardening effect, the linear stiffness k can be kept unchanged and the nonlinear stiffness can be tuned by adjusting the dimension of the spring. The guided-beam spring adopted in this work is presented in Figure 3(a), which consists of four evenly distributed thin and long beams to provide a restoring force. The beam is with length L, width b and thickness e. A similar spring structure is reported by Marinkovic et al. [33] for piezoelectric energy harvesting and Mallick et al. [28] for macro-scale electromagnetic energy harvesting. One end of each of the four beam arms is fixed, while other ends of beams are connected pairwise. This gives rise to a fixed-guided configuration where nonlinear behavior arises. The guided-beams can insure the spring moves up and down without rotation. For analytical modeling of the nonlinear spring force, a simplified model of the fixed-guided spring beam is used, as shown in Figure 3(b). The end of the beam (y = 0) is fixed, and the other end (y = L) is guided. Therefore, the possibility of any twisting movement of this single beam in other directions can be neglected. In this model, the components of spring force due to bending and stretching are obtained respectively. Combining both components of bending and stretching, the total spring restoring force is obtained analytically. [28]

F  Fb  Fs  E

be3 18 be (x)  E 3 (x)3 , 3 L 25 L

(3)

where x is the displacement at the guided end, Fb is the bending component of the force, and Fs is the stretching component due to tension force of elongation. Therefore, the force-displacement characteristic can be modeled as a hardening spring and is expressed as

F = kx+kn x3 .

(4)

For a four beams spring, the linear stiffness k and nonlinear stiffness kn can be approximated by

k

4Ebe3 ， L3

kn 

(5)

72 Ebe 25 L3

(6)

Therefore, geometrical dimension including length, width and thickness can be adjusted to determine the linear stiffness and nonlinear stiffness. Meanwhile, the relationship between k and kn can be expressed by thickness e as 4

kn 18 1  k 25 e2

(7)

The nonlinear stiffness coefficient is inversely proportional to thickness of the spring’s beam, while linear stiffness coefficient is kept constant by proportional changing the thickness and length. Therefore, the nonlinear stiffness coefficient can be tuned independently. To adjust nonlinear effects, we designed four kinds of guided-beam springs with the same configuration, as seen in Figure 4. The parameters of the designed springs are demonstrated in the figure. All kinds of the springs have the same beam width of 80 μm. The thickness and length of the beams are different, but thickness to length ratio remains the

4Ebe3 same (e/L = constant). Therefore, springs have the same linear coefficient ( k  keeps unchanged). According L3 to

kn 18 1 , as linear stiffness coefficient keeps unchanged, the nonlinear stiffness coefficient can be determined  k 25 e2

by the thickness of the beams. Therefore, one can tune the nonlinearity independently to obtain the desired vibrating frequency response. This design can easily tune the length and thickness of the spring beams without changing the volume of the whole energy harvester device.

Figure 4. Four kinds of guided-beam springs with different thickness and length but same thickness-length ratio. 2.3 Static validation with FEA To validate the analytical results by FEA, the commercially available software COMSOL Multiphysics has been employed. Figure 5 shows force displacement of analytical calculation and FEA results by COMSOL, which show the same trend for the four kinds of guided-beam springs. Table 1 lists both analytical and FEA stiffness coefficients of the planar springs. With proportional decreasing the thickness and the length of the spring’s beams, the nonlinear stiffness increases while it influences little on the linear stiffness. It is noted that there is a little difference between the COMSOL and analytical results. The discrepancy is reasonable and it can be explained by that the analytical equation is a simplified model and the COMSOL considers the entire structure in finite-sized elements and numerically calculates higher-order terms.

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Figure 5. Force-displacement of (a) analytical calculation and (b) FEA results by COMSOL.

Table 1. Design parameters and FEA results of four kinds of guided-beam springs.

Ⅰ Ⅱ Ⅲ Ⅳ

E

b

L

e

Modulus

width

length

thickness

GPa

μm

mm

μm

e/L

k

kn

(analytical)

(analytical)

N/m

3

N/m

k

kn

(FEA)

(FEA)

N/m 10

Eigenfrequency (FEA)

3

N/m

Hz 10

70.024

165

80

2.0

10

0.005

6.6

4.75×10

13.0

3.25×10

165

80

2.2

11

0.005

6.6

3.93×1010

12.6

2.73×1010

69.877

165

80

2.5

12.5

0.005

6.6

3.04×1010

11.5

2.15×1010

69.669

6.6

10

10.3

10

69.356

165

80

3.0

15

0.005

2.11×10

1.53×10

2.4 Modal analyses and frequency response Modal analyses performed by COMSOL are used to determine the vibration modes of the system. Figure 6 shows the shape and resonant frequency of the primary vibration mode. It can be found that all of the four kinds of spring-mass resonant frequency structure vibrate at resonant frequency of ~70 Hz. This is consistent with the static analyses that our method used to tune nonlinear coefficients influences little on the linear stiffness.

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Figure 6. Eigenfrequency and shape of the primary vibration mode. The frequency response of the nonlinear vibration system depends on the linear and nonlinear stiffness coefficients. For electromagnetic energy harvesting, both relative displacement and velocity are meaningful quantity for output performance. Figure 7 shows displacement and velocity frequency response of the harvesters with four kinds of springs at the acceleration of 5m/s2. It can be seen that, while the linear stiffness is kept constant and nonlinear stiffness increase, the resonant frequency shifts toward right and the bandwidth of the displacement frequency response is broadened.

Figure 7. Dynamic responses calculated with stiffness fitted by COMSOL results: (a) overview of displacement response; (b) enlarged view of displacement response; (c) overview of velocity response; and (d) enlarged view of 7

velocity response.

3. Experimental validation The guided-beam springs of nonlinear electromagnetic energy harvester were fabricated using low cost micromachining technique, which is based on convenient multilayer electroplating processes. Positive photoresist (AZ 4620) was used as a mold and sacrificial layer. Electroplated nickel was selected as the structural material of the present device, which has better mechanical property than silicon with brittleness under large vibration. The properties of electroplated nickel can be adjusted through the electroplating solution compositions and the optimization of electroplating conditions. The composition of the solution is Ni[NH2SO3]2 (600 g·L-1), H3BO3 (25 g·L-1), NiCl2·6H2O (10 g·L-1), the conditions are PH 4.0, temperature 40℃ and current density 1.3A·dm-2. The stylus profiler (Dektak XT, Bruker, USA) was used to monitor the entire manufacturing process. The thickness was controlled by the photoresist mold and electroplating time. The micro fabrication process of the nickel guided-beam spring is shown in Figure 8(a) and described as follows: (A) The glass substrate was cleaned by ultrasonic clean process. (B) The sacrificial layer photoresist was spin coated onto the substrate and baked. (C) Chromium/copper (Cr/Cu) seed layer was sputtered on the photoresist. (D) The mold layer photoresist for electroplating was spin coated onto the seed layer and baked. (E) The photoresist was patterned by exposure and development. (F) Nickel of guided-beam structure was electroplated. (G) Another mold layer photoresist for adding-layer was spin coated and baked. (H) The photoresist was patterned by exposure and development. (I) Nickel of adding-layer was electroplated. (J) Acetone was used to remove photoresist. (K) Ammonia/peroxide solution was used to remove the seed layer. (L) Finally, the nickel guided-beam spring was completed released. The photograph of samples of four kinds of springs is shown in Figure 8(b) and the prototype harvester is shown in Figure 8 (c).

Figure 8. (a) Micro fabrication process flow, (b) the samples of the four kinds of springs and (c) the enlarged view of 8

the prototype harvester. The experimental setup system used for characterization of dynamic performance is shown in Figure 9. The harvester device including the magnet, spring, SU-8 spacer and coil was assembled and mounted on the shaker to observe their displacement and output voltage frequency response to input vibrations. The shaker (SINOCERA JZK-5) was driven by the data acquisition (DAQ) card of NI USB-6356 through a power amplifier (SINOCERA YE5871A). The base vibration was measured by the charge amplifier (SINOCERA YE5858) through the accelerometer (SINOCERA CA-YD-107) with feedback. The displacement of the harvester device under vibration condition was measured by the laser displacement detector (Keyence LK-G30). The signals from the charge amplifier, displacement detector, and output of the electrical signal from the harvester device were recorded by the DAQ card. All the instruments were connected by the DAQ card to the PC where LabVIEW software coordinated the signals generation and measurement. In the experiment, the excitation frequency was swept up in the range of 200 ~ 650 Hz at excitation acceleration of 5m/s2.

Figure 9. Block diagram of the experimental setup for the controlled vibration system.

4. Results and discussions Figure 10 shows the experimental frequency response of the nonlinear energy harvesters. Figure 10 (a) shows the displacement frequency response of the nonlinear spring, and Figure 10 (b) shows the RMS output voltage frequency response of the devices. A similar trend is observed for the displacement and voltage frequency response. When conducting frequency-up sweep, the frequency response curves bend toward right and suddenly drop down from the peak, which show typical jump-down phenomenon of hardening system. It can be seen that, consistent with the results of calculation, with proportional decreasing the thickness and the length of the spring’s beams, the jump-down frequency shift regularly toward right and the operating bandwidth is broadened.

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Figure 10. (a) Displacement and (b) output voltage amplitude of frequency response with acceleration of 5m/s2. Table 2 lists the values of resonant frequency, bandwidth and amplitude of the displacement and RMS voltage frequency response. At the acceleration of 0.5g, the micro-fabricated device is able to tune the operating bandwidth of the output voltage from 37Hz to as wide as 75Hz. Parameters of the electromagnetic energy harvesters, such as coil and magnet size, air gap and electrical load, are not optimized. Larger coil with optimized number of turns, stronger magnetic field with optimized magnet size, smaller air gap and matched electrical load could result in better performance of the devices. However, as we focused on the output parameters of resonant frequency and working bandwidth in current study, such design and fabrication optimization is not further considered. From the results we have obtained, one can demonstrate that the independent nonlinearity tuning has been implemented successfully on the four prototypes, which indicates a promising design strategy for tuning the resonant frequency and working bandwidth to match different ambient frequency. Table 2. Performance of displacement and RMS output voltage

Ⅰ Ⅱ Ⅲ Ⅳ

Resonant frequency(Hz) 605 536 489 435

Displacement Bandwidth(Hz)

Amplitude(μm)

184 141 100 86

132 147 169 207

Resonant frequency(Hz) 605 536 489 435

Output Voltage Bandwidth(Hz) 75 54 40 37

RMS Voltage(mV) 15.8 18.4 21.0 24.4

5. Conclusions The possibility of systematic geometric design methodology for tuning of the non-linear vibration inside MEMS harvesters has been investigated in this work. Compared with other frequency and bandwidth tuning method of the nonlinear energy harvester system, it is very convenient to tune the resonant frequency and bandwidth by changing the geometrical dimension, which is suitable for batch fabrication. For the first time, through controlling the thickness-length ratio of the planar spring beams, its linear stiffness coefficient can be kept constant and the nonlinear stiffness coefficient can be intentionally tuned. In this way, the resonant frequency and range of nonlinear vibration can be designed separately. Bandwidth can be broadened around specific frequency with proportional decreasing the thickness and the length of the spring’s beams. For energy harvesting application, that means the working bandwidth of the device could be adjusted to better match different ambient frequency for higher-efficiency energy conversion. Both simulation and experiment were conducted to validate our method. At the acceleration of 0.5g, the 10

micro-fabricated device is able to tune the operating bandwidth of the output voltage from 37Hz to as wide as 75Hz.

Acknowledgements The authors would like to thank supports from the National Natural Science Foundation of China (No. 51375311).

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Biographies Shi Sun received the B.Sc. degree from Nanchang University, Nanchang, China, in 2009. He received the M.Sc. degree from South China University of Technology, Guangzhou, China, in 2013. He is currently working toward the Ph.D. degree in electronics science and technology at School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, China. His research interests include the design, simulation, and fabrication of MEMS/NEMS devices. Xuhan Dai received the B.Sc. degree from Yanshan University, Qinhuangdao, China, in 1994. He received the M.Sc. and the Ph.D. degree from Zhejiang University, Hangzhou, China, in 1997 and 2000, respectively. Now he is an associate professor of the National Key Laboratory of Science and Technology on Micro/Nano Fabrication, School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, China. His research interests include the design, simulation and fabrications of the MEMS/NEMS devices. Zaichun Feng is a Professor of mechanical and Aerospace Engineering at the University of Missouri, Columbia, MO, USA. His current research interests include the design and fabrication of micro gyroscopes, cell electrochemical sensors, microfluidic channels for cell sorting, polymer-derived ceramic heat flux sensor arrays, capacitive power harvesters and nonlinear dynamics. He has conducted research on design, modeling, and fabrication of MEMS devices and micro sensors funded by NSF, NIH, and U.S. Army PEO. He is a fellow of ASME. Guifu Ding received the B.Sc. and the M.Sc. degree from Fudan University, Shanghai, China, in 1984 and 1987, respectively. He is now a professor and the vice-director of the National Key Laboratory of Science and Technology on Micro/Nano Fabrication, School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, China. His main research interests include the nano materials and the design, simulation and fabrications of the MEMS/NEMS devices. Xiaolin Zhao received his B.Sc. degree from Shanghai Tech University, Shanghai, China, in 1975. He is currently a professor and director of the National Key Laboratory of Micro/Nano Fabrication Technology, School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, China. His current research interests include the design, simulation, and fabrication of microelectromechanical system devices, and microfabrication technologies for non-silicon devices.

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