Abstract:
An energy harvesting cantilever formed from multiple curved sections, with each curved section wrapped within the prior curved section but in an opposing direction, is the proposed solution to the problems described above. Such an energy harvesting cantilever favors bending over torsion, can be manufactured at a small scale, and will generate useful electrical energy with low frequency inputs.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
       [0001]    This application is a non-provisional application related to U.S. patent application Ser. No. 62/307,618, filed Mar. 14, 2016, the disclosure of which is hereby incorporated by reference. 
     
    
     FIELD 
       [0002]    This invention relates to the field of energy harvesters and sensors, in particular a micro-scale vibration-based energy harvester. 
       BACKGROUND 
       [0003]    Energy comes in many forms. Some forms are more obvious than others, such as the thermal energy of hot coffee, or the electrical energy that runs our homes and offices. 
         [0004]    Less obvious as a form of energy is vibration, which is a form of mechanical energy. Vibration comes in the form of sound, the shaking of machinery, or the invisible radio frequencies around us. 
         [0005]    Sources of energy, among others, include the following:
       Vibration of equipment or the motion of a human;   Oscillation of a magnetic field; and   Cyclical motions present in nature.       
 
         [0009]    The energy from these sources can be made more useful, or measurable, by converting the mechanical vibrational energy into electrical energy. Such a conversion between types of energy is performed by an energy harvester. The harvester can also be considered a sensor, as it can sense mechanical energy and relay the energy as a proportional electrical output. The harvester can also be a type of transducer as it converts one form of energy into another. 
         [0010]    The harvester can also be operated in reverse—electrical energy applied to the same device creates mechanical motion, and thereby making the same device an actuator too. Henceforth, for simplicity and clarity, energy harvester will be synonymous with “sensor” or “transducer.” 
         [0011]    Existing energy harvesters are unable to harvest low-frequency vibrations without the use of a tip mass, or without sacrificing compactness. 
         [0012]    What is needed is a micro-scale energy harvester that can harvest low-frequency vibrations, while maintaining a small form factor. 
       SUMMARY 
       [0013]    A sensing or energy harvesting cantilever formed from multiple curved sections, with each curved section wrapped within the prior curved section but in an opposing direction, is the proposed solution to the problems described above. Such an energy harvesting cantilever favors bending over torsion, can be manufactured at a small scale, and will generate useful electrical energy under low frequency inputs. 
         [0014]    A sensor or energy harvester, as described below, operates best at a particular frequency. The closer the vibration is to the ideal, or natural, frequency of the harvester, the more efficient the energy generation. Most naturally-occurring sources of vibration have a low frequency, defined herein as at or less than 100 Hz, where Hz is hertz, or one cycle per second. 
         [0015]    The energy harvesters disclosed herein are referred to as micro-scale harvesters due to their small size of no greater than a cube &lt;1 mm, with the cantilever of the harvester in the range of tens to hundreds of microns, or less, in width. The disclosed harvester can be scaled down to the micron and nanometer scales. 
         [0016]    Historically, such small-scale energy harvesting devices have been inductive or electromagnetic in design. But such designs cannot be produced at scales below 5 mm because of limitations in the ability to miniaturize the magnets and electrical coils used for construction. 
         [0017]    To overcome the scale restrictions of inductive and electromagnetic designs, piezoelectric is the preferred construction. The piezoelectric device is comprised of piezoelectric materials sandwiched between metallic electrodes constructed of, for example, platinum. 
         [0018]    The drawback of cantilevered vibrational devices is that as size is decreased, frequency increases, and the resulting device is no longer a low-frequency harvester. The addition of a tip mass reduces the frequency, but limits the range of acceleration. The result is a decrease in the amount of force that the cantilever can withstand before stress causes breakage. 
         [0019]    As an additional drawback, shrinking the harvester size limits the maximum power conversion due to the reduced size of the cantilever on which resides the piezoelectric element. Increasing the area of the piezoelectric element is a means by which the energy conversion can be increased. 
         [0020]    The preferred solution to both the problem of high frequency and low piezoelectric area is to increase the beam length of the cantilever. But increases in beam length result in increases to overall size of the energy harvester. 
         [0021]    The fundamental frequency of a simple cantilever beam is calculated as 1/2π√{square root over (k/m)} where k is the stiffness, proportional to width*thickness 3 /length 3 , and m is the mass, proportional to width*thickness*length. When the dimensions are reduced to micron-scale dimensions, the natural frequency of a simple cantilever increases to frequencies greater than larger cantilevers. The result is difficultly achieving low natural frequencies using micron-scale harvesters. 
         [0022]    As discussed above, the drawback of a straight beam is the size of the resulting structure. Thus, curving the beam is a potential solution to fitting a longer beam in a smaller area. 
         [0023]    By curving the beam, a longer length of cantilever can be fit into a smaller space. Such curved structures include spiral cantilever beams. But a pure spiral shape causes excessive torsion, or twisting, over its length, has high displacement and bending at rest (leading to a structure that protrudes out of plane of the device) and is thus highly susceptible to breakage. Spiral harvesters generate less voltage after a certain number of spiral turns due to voltage cancelation from torsion. 
         [0024]    A superior solution to a pure spiral shape is a circular pattern where the beam wraps back on itself, switching from a clockwise path to a counter-clockwise path. This shape creates deflection that favors bending over torsion, thereby increasing the efficiency of the resulting device. 
         [0025]    Data collected during testing supports the theory, showing that the circular zigzag pattern can produce resonance frequencies consistent with other shapes, but with superior voltage generation characteristics. 
         [0026]    Table 1 below shows harvester shapes with modeled and actual resonance frequencies. 
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Deep RIE (Reactive Ion Etch) Silicon only MEMS structures 
               
             
          
           
               
                   
                 Resonance (kHz) 
                   
               
             
          
           
               
                   
                 Harvester shape 
                   
                 Model 
                 Actual 
               
               
                   
                   
               
             
          
           
               
                   
                 4 turn Circular Spiral 
                   
                 6.065 
                 6.71 
               
               
                   
                 3 turn Circular Spiral 
                   
                 12.637 
                 13.413 
               
               
                   
                 3 turn Circular Zigzag 
                   
                 12.938 
                 13.406 
               
               
                   
                 2 turn Circular Zigzag 
                   
                 34.07 
                 38.688 
               
               
                   
                 3 arc Circular cantilever 
                 long arc 
                 20.644 
                 20.787 
               
               
                   
                   
                 middle arc 
                 44.747 
                 45.063 
               
               
                   
                   
                 short arc 
                 76.514 
                 77.37 
               
               
                   
                 2.5 turn Square Spiral 
                   
                 16.825 
                 15.45 
               
               
                   
                 2 turn Square Spiral 
                   
                 40.345 
                 36.19 
               
               
                   
                 3 beam Linear Zigzag 
                   
                 28.883 
                 33.13 
               
               
                   
                 5 beam Linear Zigzag 
                   
                 13.464 
                 13.55 
               
               
                   
                   
               
             
          
         
       
     
         [0027]    Table 2 shows frequency, voltage, and power measurements for 4 and 5 turn circular zigzag shaped cantilevers. The shapes were constructed from single-layer piezoelectric sheets; unimorph construction, which is one active layer and one inactive layer; and bimorph construction, which is two active layers. An active layer is a piezoelectric layer, whereas an inactive layer, or passive layer, is a material that does not generate electricity, such as silicon. 
         [0000]    
       
         
               
             
               
               
               
               
             
               
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 d31 mode Microwater jet Piezos 
               
             
          
           
               
                   
                 Sheet 
                 Unimorph 
                 Bimorph 
               
               
                   
                   
               
             
          
           
               
                 Frequency (Hz) +/−3 
                   
                   
                   
               
               
                 dB 
               
               
                 4 turn Circular Zigzag 
                 52.71 +/− 1   
                 64.0 +/− 2.5 
                 89.3 +/− 5.7 
               
               
                 5 turn Circular Zigzag 
                 43.25 +/− 0.5 
                 37.75 +/− 4.25 
                 67.74 +/− 4.97 
               
               
                 Voltage (Voc, V) 
               
               
                 4 turn Circular Zigzag 
                 0.138 
                 0.567 
                 1.842 
               
               
                 5 turn Circular Zigzag 
                 0.196 
                 0.639 
                 1.294 
               
               
                 Power (μW) 
               
               
                 4 turn Circular Zigzag 
                 1.02  
                 5.466 
                 52.89 
               
               
                 5 turn Circular Zigzag 
                 1.288 
                 7.232 
                 18.88 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
             
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 d33 mode Piezo MEMS with Chevron electrodes 
               
             
          
           
               
                   
                 Silicon 
               
               
                   
                   
               
             
          
           
               
                   
                 Frequency (Hz) 
                   
               
               
                   
                 4 turn Circular Zigzag 
                 31.47 
               
               
                   
                 5 turn Circular Zigzag 
                 28.66 
               
               
                   
                 Voltage (Voc, V) 
               
               
                   
                 4 turn Circular Zigzag 
                 0.68 
               
               
                   
                 5 turn Circular Zigzag 
                 1.06 
               
               
                   
                 Power (μW) 
               
               
                   
                 4 turn Circular Zigzag 
                 4.15 
               
               
                   
                 5 turn Circular Zigzag 
                 13.15 
               
               
                   
                   
               
             
          
         
       
     
         [0028]    With this background, the energy sensing and harvesting cantilever will be described in detail. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0029]    The invention can be best understood by those having ordinary skill in the art by reference to the following detailed description when considered in conjunction with the accompanying drawings in which: 
           [0030]      FIG. 1  illustrates a schematic view of a straight beam. 
           [0031]      FIG. 2  illustrates a schematic view of a curved beam. 
           [0032]      FIG. 3  illustrates a schematic view of a first embodiment. 
           [0033]      FIG. 4  illustrates a schematic view of a second embodiment. 
           [0034]      FIG. 5  illustrates a schematic view of a third embodiment. 
           [0035]      FIG. 6 a    illustrates a cross-sectional view of a piezoelectric beam of a first type. 
           [0036]      FIG. 6 b    illustrates a cross-sectional view of a piezoelectric beam of a second type. 
           [0037]      FIG. 7 a    illustrates an isometric view of a piezoelectric beam of a first type. 
           [0038]      FIG. 7 b    illustrates an isometric view of a piezoelectric beam of a second type. 
           [0039]      FIG. 8  illustrates a curved beam with a standard electrode pattern. 
           [0040]      FIG. 9  illustrates a schematic view of a chevron electrode pattern. 
           [0041]      FIG. 10  illustrates a schematic view of the first embodiment with a chevron electrode pattern. 
           [0042]      FIG. 11  illustrates a schematic view of the second embodiment with a chevron electrode pattern. 
       
    
    
     DETAILED DESCRIPTION 
       [0043]    Reference will now be made in detail to the presently preferred embodiments of the invention, examples of which are illustrated in the accompanying drawings. Throughout the following detailed description, the same reference numerals refer to the same elements in all figures. 
         [0044]    Referring to  FIG. 1 , a schematic view of a straight beam is shown. 
         [0045]    For a better understanding of the benefits of the disclosed invention, a discussion of a typical beam is helpful. Beam  20 , has a fixed end  12  affixed at anchor  10 . The free end  14  is free to deflect in response to vibration. 
         [0046]    Beam at rest  20   a  shows the beam  20  location under no load, and beam deflected  20   b  shows the beam  20  in a deflected position in response to a load. Beam length L is the total distance from the anchor  10  to the tip of the free end  14 . Deflection distance d is a measurement of the amount of free end  14  deflection, and t b  is a measurement of the thickness of beam  20 . The combination of L, t b , and d affect the quantity of energy generated by the deflection. An increase in any of these three variables results in an increase of generated energy. 
         [0047]    Referring to  FIG. 2 , a schematic view of a curved beam is shown. 
         [0048]    Again shown are anchor  10 , fixed end  12 , and free end  14 . By virtue of its shape, the curved beam  20  can fit a greater length L into a smaller space. 
         [0049]    But with the shape of a single, continuous curve, the curved beam  10  creates a new problem of excessive torsion, or twisting. A load applied to the beam  20 , even the load of only the beam&#39;s weight, results in a continuous increase in torsion, or twisting, along the entire length of the beam  20 . The piezoelectric composition of the beam  20  cannot convert torsion into useful energy, thus the continuous spiral shape, or circular spiral shape, is inefficient. 
         [0050]    The solution to the excessive torsion problem is to have the beam turn back on itself, creating multiple shorter beams rather than a single continuous beam. The result is that the deflection manifests as bending rather than twisting, increasing the beam energy conversion efficiency. 
         [0051]    Referring to  FIG. 3 , a schematic view of a first embodiment is shown. 
         [0052]    The beam  20  has a circular zigzag shape. The segments, or turns, of the beam  20  are curved, taking the form of circles or arcs. But rather than an ever-decreasing diameter, as that of the circular spiral shape in  FIG. 2 , the turns are of a consistent diameter. At the end of each beam the shape changes direction, or zigzags, at a reversal  16 , moving to a larger or smaller diameter, and thus beginning an additional turn or beam segment. 
         [0053]    The beam  20  of the energy harvesting cantilever  1  starts at fixed end  12 , which is connected to anchor  10 . Beam  20  continues along length L, the beam  20  including multiple reversals  16  along its length before reaching free end  14 . The result is a beam  20  of an increased length L as compared to a straight beam, while maintaining a diameter D that is a fraction of beam length L. 
         [0054]    A reversal  16  is a point at which the beam changes direction by substantially 180 degrees, resulting in a subsequent path that is parallel to the previous portion of the beam  20 . The result is a series of nested parallel curves of decreasing diameter until the beam  20  reaches the free end  14 . 
         [0055]    The reversals  16  in the first embodiment include hard or sharp corners  18 . This type of corner maximizes the area of the beam  20 , and thus maximizes the area of piezoelectric material available for energy conversion. 
         [0056]    The first embodiment shown in  FIG. 3  has four turns or bands. Shown are first turn  51 , second turn  52 , third turn  53 , and fourth turn  54 . 
         [0057]    Embodiments with four or five turns are preferred, but other numbers of turns are anticipated. 
         [0058]    Referring to  FIG. 4 , a schematic view of a second embodiment is shown. The second embodiment of the energy harvesting cantilever  1  is similar to the first embodiment, but with the addition of a fifth turn  55 . 
         [0059]    As described above regarding  FIG. 3 ,  FIG. 4  discloses a circular zig zag shape. 
         [0060]    The reversals  16  in the second embodiment are also hard or sharp corners  18 . This type of corner maximizes the area of the beam  20 , and thus maximizes the area of piezoelectric material available for energy conversion. 
         [0061]    Referring to  FIG. 5 , a schematic view of a third embodiment is shown. 
         [0062]    The reversals  16  in the third embodiment are soft or rounded corners  18 . This type of corner reduces stress concentrations at the reversal  16 , but does reduce the area of piezoelectric material available for energy conversion. 
         [0063]    Referring to  FIG. 6   a,  a cross-sectional view of a piezoelectric beam of a first type is shown. 
         [0064]    The illustrated configuration is referred to as a d 31  mode. In this mode, the piezoelectric layer  40  is sandwiched between a positive electrode  30  and a negative electrode  32 . The layers are bonded to a layer of silicon or electrically passive substrate  42 . Deflection causes current flow  36  in the piezoelectric layer  40  from negative electrode  32  to positive electrode  30 . 
         [0065]    The thickness of the piezoelectric layer  40  is t pe  and the thickness of the silicon  42  is t s . 
         [0066]    Referring to  FIG. 6   b,  a cross-sectional view of a piezoelectric beam of a second type is shown. 
         [0067]    The illustrated configuration is referred to as a d 33  mode. In this mode, the piezoelectric layer  40  is directly affixed to the layer of silicon or electrically passive substrate  42 . Deflection causes current flow  36  in the piezoelectric layer  40  from negative electrode  32  to positive electrode  30 , but in this configuration the electrodes  30 / 32  are both affixed to the same surface of the piezoelectric layer  40 . Each of these ‘planar’ electrodes  30 / 32  have a width w, and a gap between electrodes of g. 
         [0068]    As above, the thickness of the piezoelectric layer  40  is t pe  and the thickness of the silicon  42  is t s . 
         [0069]    Referring to  FIG. 7   a,  an isometric view of a piezoelectric beam of a first type is shown. 
         [0070]    The illustrated configuration is referred to as d 31  mode. The beam  20  includes a positive electrode  30 , negative electrode  32  with piezoelectric layer  40  between. The beam  20  is affixed at anchor  10 . 
         [0071]    A beam  20  constructed with d 31  mode electrodes may be curved without a loss of functionality because the electrodes  30 / 32  are continuous sheets. Thus, an in-plane curve does not affect the electrode shape. 
         [0072]    Referring to  FIG. 7   b,  an isometric view of a piezoelectric beam of a second type is shown. 
         [0073]    The illustrated configuration is referred to as d 33  mode. With this isometric view, the positive electrodes  30  and negative electrodes  32  are shown in their interdigitated pattern. An interdigitated pattern is similar to that created by two hands in a single plane, the fingers interlocking with each other without contact. With a straight beam  20 , the width w of each electrode and gap g are consistent. 
         [0074]    The beam  20  is affixed at anchor  10 . 
         [0075]    A beam  20  constructed with d 33  mode electrodes, when curved, no longer operates efficiently because the electrodes  30 / 32  are individual protrusions. When curved in-plane, the gaps become inconsistent and affect function. 
         [0076]      FIG. 8  illustrates a curved beam with a standard electrode pattern. As shown, the curvature of the beam affects the pattern of the electrodes  30 / 32 . While the electrode width w remains consistent, the gap g does not. Instead, some gaps, such as g 1 , are greater than other gaps, such as g 2 . The result is inconsistent voltage generation, non-uniform poling of the piezoelectric between the electrodes and potential for electrical shorting and piezoelectric breakdown across the narrower gaps. 
         [0077]    Referring to  FIG. 9 , a schematic view of a chevron electrode pattern is shown. 
         [0078]    The chevron electrode pattern bends each electrode  30 / 32 , or the finger-shaped protrusions of each electrode  30 / 32 , across the centerline of the beam  20 , resulting in consistent gaps g and electrode widths  2 . 
         [0079]    Referring to  FIG. 10 , a schematic view of the first embodiment with a chevron electrode pattern is shown. 
         [0080]    The first embodiment of the energy harvesting cantilever  1  with chevron electrode pattern is shown, this embodiment including first turn  51 , second turn  52 , third turn  53 , and fourth turn  54 . 
         [0081]    Also visible are the chevron-shaped electrodes associated with each turn. Specifically, positive electrode  30  and negative electrode  32 . The connections between the electrodes  30 / 32  of each turn are also shown. 
         [0082]    The electrodes  30 / 32  may be linked to each other in succession, forming a daisy chain arrangement leading to the outermost turn, here the first turn  51 . Or the electrodes  30 / 32  of each turn  51 / 52 / 53 / 54  may be individually connected to the external power measurement device. 
         [0083]    Referring to  FIG. 11 , a schematic view of the second embodiment with a chevron electrode pattern is shown. 
         [0084]    The second embodiment of the energy harvesting cantilever  1  with chevron electrode pattern is shown, this embodiment including first turn  51 , second turn  52 , third turn  53 , fourth turn  54 , and fifth turn  55 . 
         [0085]    Also visible are the chevron-shaped electrodes associated with each turn. Specifically, positive electrode  30  and negative electrode  32 . The connections between the electrodes  30 / 32  of each turn are also shown. 
         [0086]    As above, the electrodes  30 / 32  may be linked to each other in succession, forming a daisy chain arrangement leading to the outermost turn, here the first turn  51 . Or the electrodes  30 / 32  of each turn  51 / 52 / 53 / 55  may be individually connected to the external power measurement device. 
         [0087]    Equivalent elements can be substituted for the ones set forth above such that they perform in substantially the same manner in substantially the same way for achieving substantially the same result. 
         [0088]    It is believed that the system and method as described and many of its attendant advantages will be understood by the foregoing description. 
         [0089]    It is also believed that it will be apparent that various changes may be made in the form, construction, and arrangement of the components thereof without departing from the scope and spirit of the invention or without sacrificing all of its material advantages. The form herein before described being merely exemplary and explanatory embodiment thereof.