a multi-functional cantilever for energy scavenging from...

A MULTI-FUNCTIONAL CANTILEVER FOR ENERGY SCAVENGING FROM VIBRATIONS

M. Wischke, P. Woias

Laboratory for Design of MEMS Department of Microsystems Engineering (IMTEK), University of Freiburg, Germany

Abstract: To overcome the drawbacks of battery technology in embedded sensors, environmental energy is scavenged to power MEMS systems. Piezoelectric materials and electromagnetic set-ups are widely spread to transduce vibrations into electrical energy. This paper presents the merging of a piezoelectric with an electromagnetic transducer. The resulting hybrid energy generator shows a higher power density and an enhanced power output. Two power sources within one system feature different interconnection possibilities, and two different optimal load resistances. Key Words: energy harvesting, vibration energy scavenging, piezoelectric, electromagnetic 1. INTRODUCTION

The progress in the recent past brought along a growing request for a more “intelligent” environment. Modern buildings, for example, feature a technical equipments, e.g. to incorporate the outside weather conditions to achieve a pleasant climate inside, and furthermore, to decrease the building’s power consumption. Beside the improvement of comfort, the safety of critical infrastructure such as bridges and tunnels is of vital importance. Hence, many different sensors are patched into urban infrastructures. In general, these sensors can be considered as devices using external energy to gather information of the environment and transmit them. Due to the great efforts in wireless communication the data transmission requires a decreasing amount of space and energy. Instead, the power feed-in appears challenging since a wired supply is too extensive for reconditioned systems or wide area networks. An ambitious solution is that each sensor node supplies itself by gathering energy from its environment.

Among the ambient energy sources, vibrations are favorable as they are present in almost every building and in machines with rotating parts. By far the best suited transducers to retrieve energy from mechanical vibrations are piezoelectric and electromagnetic setups, as worked out in [1]. Up to now, each principle is always employed in a separate system. The following sections present the merging of both principles into one hybrid generator, which combines the advantages of both principles and features multi-functionality. 2. DESIGN & FABRICATION

Generally, piezoelectric materials are integrated in cantilever structures [2-4] with a tip mass. Under

acceleration, the cantilever is bent due to inertia forces, and charge can be extracted from the piezoelectric material. In the electromagnetic setup [5, 6], a coil (or magnet) is fixed at a suspension. Again, inertia forces lead to an oscillation with respect to the static magnet (or coil). In the piezoelectric layout, the tip mass material itself is functionless, only its mass is important to tune the resonance frequency and enlarge the tip amplitude. The suspension in the electromagnetic layout serves as mounting for the oscillator, but features no material functionality. Replacing in each layout the parts without functional material with functional ones creates a hybrid piezoelectric electromagnetic generator. A schematic setup is shown in Figure 1.

Fig. 1: Schematic setup of the hybrid generator.

Due to the functional principles involved, the voltage of the piezoelectric part is in phase with the tip displacement, whereas the output from the electromagnetic part is in phase with the tip velocity. With this p/4-phase shift, four power maxima are deserved per period, furnishing the power more evenly over the time.

Tab. 1: Material properties of the two PZT ceramics.

The cantilevers are fabricated in our proven piezo-polymer-composite technology [7], where a two

Type s11 [m2/N] d31 [C/Vm] e t [µm]

PZT A 14.2*10-12 -315*10-12 4500 260

PZT B 16*10-12 -290*10-12 4000 200

Proceedings of PowerMEMS 2008+ microEMS 2008, Sendai, Japan, November 9-12, (2008)

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Fig. 2: Piezoelectric bimorph cantilever and electromagnetic parts before assembling.

compound epoxy resin is cast onto the piezo-ceramic in a PDMS mold. For a benchmark of the output power, two different PZT ceramics were used here. The essential material properties are shown in Table 1. The basic unimorph cantilever is 20 mm long, 5 mm wide and has a total thickness of 500 µm. As structural improvement [8], cantilevers with a varying width have been fabricated. Neglecting the cantilever’s own weight, this trapezoidal shape equilibrates the strain across the beam length. The PZT area is equal in both layouts. In order to increase the output from the piezoelectric part, bimorph cantilevers with both ceramics types and with constant and varying width were manufactured (length 20 mm, 0.6mm thick). The cylindrical coils are self-made from a 50 µm copper wire with 500, 750 and 1000 windings. The inner coil diameter is 2.2 mm, the coil height 1.5 mm, and the outer diameter depends on the number of windings. In the experimental setup, cylindrical NdFeB magnets, 2.0 mm in diameter and in height, and with a residual induction of 1.17 Tesla are used. All components (before assembling) are depicted in Figure 2.

Fig. 3: Cantilever element with force and moment resultants. 3. MODELING For their characterization, the cantilevers are fixed with their base to a shaker. A cantilever element with force and moment resultants is shown in Figure 3. From the balance of forces and moments, the motion ),( txυ can be expressed by:

2

2

4

4

tA

xEI

∂∂−=

∂∂ υδυ

. (1)

Tab. 2: Characteristics of all cantilever layouts. This time and position dependent differential equation can be solved with Bernoulli’s function:

)()(),( tTxXtx =υ . (2)

Using a trigonometric approach for the time function, expression (1) can be transformed into a differential equation with derivatives with respect to space only. This equation can be solved by:

⎟⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛+

⎟⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛=

xl

SinhCxl

SinC

xl

CoshCxl

CosCxX

λλ

λλ

43

21)( (4)

Applying the boundary conditions for a fixed-free cantilever generates, after some calculations, the expression (5) that defines the first eigenvalue l of the oscillating structure. Assuming no damping, the first eigenfrequency w (6) is equal to the basic resonance frequency of the cantilever.

)()(1 λλ CoshCos=− (5)

AEI

l δλω 2

2

= (6)

EI is the cantilever’s bending stiffness, dA the mass resultant of inertia, l the cantilever length. Table 2 shows the calculated and measured values.

Fig. 4: Equivalent electro-mechanical circuit of a piezoelectric transducer.

PZT Layout fR [Hz] calculated Q

A unimorph, rectangular 412 404 43

A unimorph, trapezoidal 612 600 56

A bimorph, rectangular 715 755 40

A bimorph, trapezoidal 1101 1113 58

B unimorph, rectangular 420 397 46

B unimorph, trapezoidal 616 602 54

B bimorph, rectangular 722 740 36

B bimorph, trapezoidal 1105 1110 52


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The electro-mechanical behavior of the piezoelectric transducer, disregarding all nonlinear effects, can be described by the equivalent circuit depicted in Figure 4. The secondary part forms the mechanical part of the piezo, which is stimulated by the velocity

=u& I2. The primary part, coupled via the inductor to the mechanical part, embodies the electric behavior. The voltage V of the piezo can be described by:

( ) uXcjR

RuCpRV

Load

LoadLoad && αα

+==

1|| . (7)

The phase shifts of this expression are written as equation (8). Taking the phase of the velocity u& as reference (=0°), the phase of V is only affected by the phase shift of the impedance Z (9). In the case an of open circuit, (RLoadØ¶) V is shifted by 90° to the induced voltage.

—V=—Z+—u& (8)

—V=— )( LoadRα -— )1( XcjRLoad+ (9)

With a decrease of the resistance load the phase shift decreases until it reaches zero for the short circuit case (RØ0). If so, the piezoelectric voltage is in phase with velocity u& and the voltage from the coil. Figure 5 shows the transducer characteristics as a function of the load resistance. As RLoad impacts the current I1 it influences via the transformer the mechanical behavior. Electrical resistance loading leads to a higher mechanical stiffness of the cantilever, which increases the resonance frequency. This is synonymic to a lower velocity and oscillating amplitude.

Fig. 5: Phase, amplitude and output power versus load resistacne. 4. EXPERIMENTAL RESULTS The cantilever’s resonance frequency and output power were determined on a shaker that was driven with a sinusoidal input signal. The acceleration, the tip deflection as well as the output voltage were

Fig. 6: Output power and optimal load resistance of coils with different numbers of windings. recorded with a oscilloscope with phase measurement capabilities. The peak acceleration was kept constant to 1 g (9.81 m/ss) during all measurements. First, the basic resonance frequencies and the quality factors Q are determined (Table 2). The presented values are the averages of five characterized devices each per layout. For the analysis of the output power, all eight cantilever types were combined with the three coil sizes. Figure 6 shows the resulting output power of a trapezoidal unimorph cantilever of PZT type B with different coil sizes. Also the output power of a bimorph cantilever with different electrical interconnections between the piezoelectric layers and the inductor were investigated (Figure 7).

Fig. 7: Different interconnections of the piezoelectric layers, and in parallel with the inductor. 6. DISCUSSION Figure 5 clearly shows that the piezoelectric part and the electromagnetic part have a significantly different optimal load resistance. With a higher number of windings, the inner impedance of the coil increases and hence the optimal load increases too. However, there is still a dip in the power between the two


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generator parts. In the case of a bimorph cantilever, the piezoelectric layer can be connected in parallel. Doing this the output voltage is halved, but the electric capacitance and the inner impedance are doubled. Hence the optimal load is decreased from 200 kW to 70 kW without affecting the power output (see Figure 7). In the same diagram it can be seen, that parallel connected piezos in a parallel connection to the coil (a) lead to the highest output compared to the in series connected piezos with the parallel coil (b) and the pure coil (c). In summary, the parallel connection of the piezoelectric layers in a bimorph cantilever is beneficial for the power output. However, the piezoelectric and electromagnetic generator parts should be used separately to extract all power and benefit from the two optimal load resistances. The comparison between the unimorph and bimorph cantilever design of PZT A is plotted in Figure 8. As the inducted voltage is regulated by tB ∂∂ / it is evident that the unimorph design generates more electromagnetic power. This is due to the higher tip velocity which in turn results from the lower resonance frequency. With the higher stiffness, the bimorph exhibits a much higher resonance frequency and, consequently, a much smaller tip velocity. Therefore the electromagnetic power output is negligible compared to the increased piezoelectric output, which originates from the higher strain in the stiffer layout.

Fig. 8: Comparison between the output power of a unimorph (top) and a bimorph (bottom) cantilever. Here a trade-off has to be found between the strain in the piezo and the velocity of the magnet, in order to maximize the extractable power from both generator parts. An easy strategy to meet both requirements is to increase the tip mass by using a larger magnet. Due to the fixed-free condition of the cantilever, its tip moves along a parabolic track. The magnet will therefore dip into the coil with a certain inclination which reduces the electromagnetic coupling. With a pre-set

inclination of the coil this problem will vanish. The cantilever layout with varying width shows a higher resonance frequency (Table 2) compared to the rectangular shape. Accordingly, the tip velocity and the electromagnetic output power are smaller. Thus the trapezoidal shape yields no advantage concerning the output power, but requires a more complicated fabrication. The variations between measured and calculated results in Table 2 originate from inaccuracy in the fabrication. As the two PZT ceramic types show no important difference, the results are not presented here. 6. CONCLUSION With the presented design of a hybrid piezoelectric-electromagnetic generator the power output was increased up to 150% compared to a single unimorph piezoelectric cantilever (see Figure 8 top). It was shown that the parallel connection of the piezos in a bimorph layout is beneficial and the different generator parts should be tapped separately. With its two optimal load resistances, the improved power output, and the different frequency layouts the hybrid generator is capable of supplying wireless sensors with energy from ambient vibrations. Numerical analysis will be adopted to optimize the design and electromagnetic coupling to enhance the performance of the next generation of harvester. REFERENCES [1] S. Roundy, P. K. Wright, J. M. Rabaey, “Energy Scavenging for Wireless Sensor Networks”, Kluwer Academic Publishers, 2003 [2] E. M. Yeatman, P. D. Mitcheson, A. S. Holmes, “Micro-engineered devices for motion energy harvesting”, Proc. of IEDM’07, Washington, USA, pp. 375-378, 2007 [3] E. K. Reilly, E. Carleton, P. Wright, “Thin film piezoelectric energy scavenging system for long term medical monitoring”, Proc. of BSN’06, Boston, USA, pp. 38-41, 2006 [4] W. J. Choi, Y. Jeon, J.-h. Jeong, R. Sood, S. G. Kim, “Energy harvesting MEMS devices based on thin film piezoelectric cantilvers”. J. of Electroceramics, Vol. 15, pp. 543-548, 2006 [5] P. Glynne-Jones, M. J. Tudor, S. P. Beeby, N. M. White, “An electromagnetic, vibration-powered generator, for intelligent sensor systems”, J. of Sensor and Actuators A, Vol. 110, pp. 344-349, 2004 [6] E. Koukharenko, S. P. Beeby, M. J. Tudor, N. W. White, T. O’Donnell, C. Saha, S. Kilkarni, S. Roy, “Mircoelectromechanical systems virbration powered electromagnetic generator for wireless sensors application”, Microsyst. Technol., Vol. 17, pp. 1071-1077, 2006 [7] C. Friese, F. Goldschmidtboeing, P. Woias, “Piezoelectric Microactuators in Polymer-Composite Technology”, Proc. of Transducers’03, Boston, USA, pp. 1007-1010, 2003 [8] F. Goldschmidtboeing, P.Woias, “Characterization of different beam shapes for piezoelectric energy harvesting”, J. Micromech. Microeng., in press, 2008


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