Abstract:
A microelectromechanical vibration isolation system includes a microelectromechanical structure having a plurality of fin apertures etched therethrough, and a plurality of fins each disposed within a respective one of the plurality of fin apertures and spaced apart from the microelectromechanical structure so as to define a fluid gap therebetween. The fluid gap is configured to provide squeeze film damping of vibrations imparted upon the microelectromechanical structure in at least two dimensions. The system further includes a frame surrounding the microelectromechanical structure, and a plurality of springs each coupled to the microelectromechanical structure and to the frame. The plurality of springs is configured to support the micromechanical structure in relation to the frame.

Description:
BACKGROUND 
     Conventional techniques for isolating objects from vibration include large systems having metal springs, shock absorbers, rubber gaskets, metal mesh springs, oil- or grease-filled dampers, or friction dampers. One disadvantage of the prior techniques is that they utilize macroscopic elements that are large and unsuitable for use in highly compact (e.g., micro-scale) applications. Another disadvantage is that the performance of some conventional dampers is sensitive to temperature variations due to the inherent viscous properties of oil, grease, and polymers. Therefore, these conventional dampers can only achieve critical damping within a narrow range of temperatures, and may be inoperable in temperatures outside of that narrow range. Polymer-based dampers have a further disadvantage in that the polymer can take a permanent set (e.g., the polymer structure doesn&#39;t return to its reference position when stress is removed), which, if forming part of a vibration-isolation support structure, can upset the orientation of the supported objects. Other types of dampers that are based on sliding friction or springs can exhibit undesirable hysteresis characteristics. 
     SUMMARY 
     Aspects and embodiments are directed to vibration isolation systems and methods for very small (e.g., micro-scale) objects. One aspect includes a microelectromechanical (MEMS) vibration isolation system (VIS) configured to decouple an instrument package or module (e.g., an Inertial Measurement Unit or IMU) from shock and vibration. In one embodiment, the VIS is configured such that the instrument module can be mounted to the VIS. The VIS can be configured to use squeeze film damping for critically damping vibrations imparted externally and/or by the instrument module. For example, a microelectromechanical structure, including a platform for mounting the instrument package thereto, can include a plurality of fin apertures. A plurality of fins can each be disposed within a respective one of the fin apertures and spaced apart from the microelectromechanical structure so as to define a fluid gap therebetween. The fluid gap can be configured to provide squeeze film damping of vibrations imparted upon the microelectromechanical structure in at least two dimensions, as discussed further below. In one embodiment, the fins and gaps are formed by etching slots into a single silicon substrate. The fins and gaps may be simultaneously batch produced. 
     According to one embodiment, a microelectromechanical vibration isolation system includes a microelectromechanical structure having a plurality of fin apertures etched therethrough, a plurality of fins each disposed within a respective one of the fin apertures and spaced apart from the microelectromechanical structure so as to define a fluid gap therebetween, a frame surrounding the microelectromechanical structure, and a plurality of springs each coupled to the microelectromechanical structure and to the frame. The fluid gap is configured to provide squeeze film damping of vibrations imparted upon the microelectromechanical structure in at least two dimensions. The springs are configured to support the micromechanical structure in relation to the frame. 
     In one embodiment, the damping ratio can be between 0.2 and 0.7 and the stiffness of the springs can be substantially equal in three translation dimensions. 
     In one embodiment, the fluid gap may be a first fluid gap. The system may include a substrate mounted adjacent to and spaced apart from the microelectromechanical structure so as to define a second fluid gap between the microelectromechanical structure and the substrate. The second fluid gap may be configured to provide additional squeeze film damping of the vibrations in at least one dimension. In another embodiment, each of the fins may be coupled to the substrate and extend outwardly therefrom. In yet another embodiment, the microelectromechanical structure may include at least one damping region opposing at least a portion of the second fluid gap. The damping region may be free of fin apertures. 
     In one embodiment, the substrate may be approximately 50 to 1000 microns thick. 
     In another embodiment, each of the fins may be coupled to the frame and extend outwardly therefrom toward the micromechanical structure. 
     In one embodiment, the system may include an enclosure surrounding the micromechanical structure. The fluid gap may be a first fluid gap. The micromechanical structure may include at least one damping region spaced apart from at least a portion of the enclosure so as to define a second fluid gap therebetween. The second fluid gap may be configured to provide additional squeeze film damping of the vibrations. The damping region may be free of fin apertures. 
     In one embodiment, the system may include a plurality of electrical contacts disposed upon the microelectromechanical structure. In another embodiment, each of the springs may be coupled to a respective one of the electrical contacts. In yet another embodiment, the plurality of electrical contacts may include at least one bump bond pad. In yet another embodiment, the plurality of electrical contacts may be a first plurality of electrical contacts. The system may include a second plurality of electrical contacts disposed upon the frame, each of the second plurality of electrical contacts being electrically coupled to a respective one of the first plurality of electrical contacts. 
     In one embodiment, the microelectromechanical structure may be configured to support an instrument module thereupon. The electrical contacts may be configured to be electrically coupled to the instrument module. 
     In one embodiment, the fluid gap may contain a gas, such as nitrogen or neon. In another embodiment, the fluid gap may contain an oil or a grease. In yet another embodiment, the fluid gap may be between approximately 2 and 250 microns wide. 
     In one embodiment, the system may be configured to occupy a volume of approximately 10 cubic millimeters or less. 
     In one embodiment, at least one of the fins may be concentric with another one of the fins. In another embodiment, the springs may include at least one folded spring. In yet another embodiment, the springs may be configured to provide damping of at least some of the vibrations. 
     According to one embodiment, a microelectromechanical vibration isolation system includes a microelectromechanical structure having a plurality of recesses etched therein, a frame surrounding the microelectromechanical structure, means for coupling the microelectromechanical structure to the frame such that the micromechanical structure is supported in relation to the frame, and means for damping vibrations imparted upon the microelectromechanical structure including a plurality of damping structures each disposed within a respective one of the recesses. 
     In one embodiment, the damping structures may be oriented substantially perpendicular to a plane of the microelectromechanical structure. In another embodiment, the damping structures may be oriented substantially parallel to a plane of the microelectromechanical structure. In yet another embodiment, the damping structures may include at least one squeeze film damper. In yet another embodiment, the squeeze film damper may include a gas, such as nitrogen. 
     In one embodiment, the damping structures may include at least one spring coupled to the microelectromechanical structure and to the frame. 
     According to one embodiment, a method of making a vibration isolation apparatus includes etching a plurality of fin apertures into a substrate wafer to form a first portion of the substrate wafer having a plurality of fin structures disposed within respective ones of the plurality of fin apertures. The fin apertures form a fluid gap between the fin structures and a second portion of the substrate wafer. 
     In one embodiment, the method may include etching a frame aperture into the substrate wafer to form a frame configured to surround the second portion of the substrate wafer. In another embodiment, the method may include etching, in the substrate wafer, a plurality of suspension beams for coupling the second portion of the substrate wafer to the frame. In yet another embodiment, the method may include disposing a plurality of first electrical contacts on the second portion of the substrate wafer and a plurality of second electrical contacts on the frame, and coupling each of the first electrical contacts to a respective one of the second electrical contacts using the suspension beams. In yet another embodiment, the method may include injecting a gas, such as nitrogen or neon, into the fluid gap. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Various aspects of at least one embodiment are discussed below with reference to the accompanying figures, which are not intended to be drawn to scale. The figures are included to provide illustration and a further understanding of the various aspects and embodiments, and are incorporated in and constitute a part of this specification, but are not intended as a definition of the limits of the invention. In the figures, each identical or nearly identical component that is illustrated in various figures is represented by a like numeral. For purposes of clarity, not every component may be labeled in every figure. 
       In the figures: 
         FIG. 1A  is a cross-sectional profile view of one example of a vibration isolation system in accordance with aspects of the invention; 
         FIG. 1B  is a cross-sectional profile view of another example of a vibration isolation system in accordance with aspects of the invention; 
         FIG. 2A  is a top view of the vibration isolation system of  FIG. 1 ; 
         FIG. 2B  is a more detailed top view of a portion of the vibration isolation system of  FIG. 2A ; 
         FIG. 2C  is a side cross-sectional view of one example of a spring of the vibration isolation system of  FIG. 1 ; 
         FIG. 2D  is a graph illustrating stiffness as a function of vertical length of the spring corresponding to examples of the spring of  FIG. 2C , in accordance with aspects of the invention; 
         FIG. 3  is a cross-sectional perspective view of one portion of the vibration isolation system of  FIG. 1A ; 
         FIG. 4A  is a top view of one example of a vibration isolation system in accordance with aspects of the invention; 
         FIG. 4B  is a more detailed top view of a portion of the vibration isolation system of  FIG. 4A ; and 
         FIG. 5  is a top view of another example of a vibration isolation system in accordance with aspects of the invention. 
     
    
    
     DETAILED DESCRIPTION 
     Aspects and embodiments relate generally to vibration isolation systems and methods, and more particularly, systems and methods of isolating small instrument packages and other small objects from external vibration and shock. An example of a small object is an inertial measurement unit (IMU), which may include accelerometers, gyroscopes and/or magnetometers. Due to its small mass and weak springs, the IMU can be particularly sensitive to shock and vibration, which can result in errors in the output of the IMU or breakage. For example, if the IMU is used for navigation based on acceleration and rotation, vibration can affect motion measurements. Therefore, it is desirable to isolate the IMU from externally-imparted vibrations. 
     Due to the small size of the objects being isolated, and the isolation system itself, some embodiments can be classified as microelectromechanical systems (MEMS). One embodiment includes a MEMS-based VIS for isolating small objects from external vibration and shock. Another embodiment includes a MEMS-based VIS configured to prevent small vibrating objects from transmitting energy to the surrounding environment. 
     As discussed above, some conventional vibration damping techniques utilize macroscopic machined springs, damping elements, polymer supports, or oil/grease to isolate a system from the surrounding environment. Each of these techniques has disadvantages that are overcome by various embodiments. For instance, one embodiment includes small MEMS elements, which enables the VIS to be much more compact than conventional damping systems. Another embodiment uses silicon springs, which have no hysteresis. Yet another embodiment utilizes gas damping, which has a much smaller temperature variation of viscosity than conventional techniques that use oil or grease. Gas viscosity is proportional to the square root of absolute temperature and is independent of pressure and density over a wide range of temperature. 
     Aspects and embodiments discussed herein are not limited in their application to the details of construction and the arrangement of components set forth in the following description or illustrated in the drawings. The embodiments described herein are capable of being practiced or carried out in various ways. Also, the phraseology and terminology used herein is for the purpose of description and should not be regarded as limiting. The use of “including,” “comprising,” or “having,” “containing,” “involving,” and variations thereof herein, is meant to encompass the items listed thereafter and equivalents thereof as well as additional items. 
     As used herein, the terms “squeeze film” and “squeezed film” refer to a type of hydraulic or pneumatic damper for damping vibratory motion of a moving component with respect to a fixed component. Squeezed film damping occurs when the moving component is moving perpendicular and in close proximity to the surface of the fixed component (e.g., between approximately 2 and 50 micrometers). The squeezed film effect results from compressing and expanding the fluid (e.g., a gas or liquid) trapped in the space between the moving plate and the solid surface. The fluid has a high resistance, and damps the motion of the moving component as the fluid flows through the space between the moving plate and the solid surface. 
       FIGS. 1A and 1B  are cross-sectional profile views of two examples of a VIS  100 ,  400 , according to at least one embodiment. As shown in the example of  FIG. 1A , an instrument module  110 , which is not necessarily included in this embodiment, can be mounted on a floating platform  112 . Electrical interconnects (not shown) from the instrument module  110  can be brought to the bottom surface of the module  110 , where bump bonds  114  or other types of electrical contacts electrically interconnect the instrument module  110  and the floating platform  112 . The VIS  100  includes a frame  116  surrounding at least a portion of the floating platform  112 , to which one or more electrical interconnects  118  are connected. The electrical interconnects  118  may be connected to an external device (not shown), including, but not limited to, a power supply, a processor, or other electronic device. Examples of electrical interconnects include wires, pins, bumps, traces, etc. As will be discussed below in further detail with respect to  FIG. 2A , the electrical interconnects  118  can be electrically connected to the bump bonds  114 , enabling electrical signals to travel between the instrument module  110  and the external device through the electrical interconnects  118  and the bump bonds  114 . 
     In one embodiment, the frame  116  is coupled to a substrate  120 , which has a fixed position with respect to the floating platform  112  (e.g., the substrate  120  may be mounted to an enclosure). Several damping fins  122  may be coupled to the substrate  120 . In one embodiment, the frame  116  and/or damping fins  122  are etched from a single silicon substrate (e.g., an SOI wafer which may include the substrate  120 ) using a micromachining process, which may be batch fabricated. At least some of the damping fins  122  are used to produce a squeezed film effect between the substrate  120  and the floating platform  112 . Such damping fins  122  may be narrow with respect to the surrounding portions of the floating platform  112 . Other damping fins and/or other portions of the floating platform  112  (e.g., including the out-of-plane damping regions  134  described below with respect to  FIG. 2A ), may be wider than the narrow fins  112  to damp motion in the vertical direction (e.g., normal to the substrate  120 ). In one embodiment, the substrate  120  can be approximately 50 to 1000 microns thick. It is to be appreciated that the substrate  120  is not used in some embodiments, and that the damping fins  122  may, for example, be mounted to the frame  116  or the floating platform  112  instead of the substrate  120 , such as shown in the example VIS  400  of  FIG. 1B  and discussed further below with respect to  FIGS. 4A and 4B . 
     Referring to  FIG. 1B , although the instrument package  110  is shown mounted to a central floating platform  112 , it is to be understood that the roles of the frame  116  and central platform  112  could be reversed, e.g., the frame  116  can equally well serve as the floating platform  112  while the floating platform  112  can be mounted to an external package. Furthermore, through-silicon vias (TSV&#39;s)  150  may be utilized to bring electrical connections from one side of the silicon frame or floating platform  112  to the other side, as shown in  FIG. 1B . 
       FIGS. 2A and 2B  are exemplary top views of the VIS  100  of  FIG. 1A , according to one embodiment. For clarity, the instrument module  110  is not shown. The floating platform  112  is attached to the frame  116  by a plurality of springs  124  that may also function as electrical interconnects to the instrument module  110  through the bump bonds  114 . One end of each spring  124  is coupled to a respective bump bond  114  on the floating platform  112 , and the other end of each spring  124  is coupled to a wire-bond  126  or other type of electrical contact mounted to the frame  116 . The springs  124  are configured to support the floating platform  112  with respect to the frame  116  and provide at least some vibration damping. A dielectric layer (not shown) covers the surface of the frame  116 , springs  124  and floating platform  112 , providing dielectric isolation between the metal electrical pads  126  and  114  and the silicon frame and platform. 
     In one embodiment, the springs  124  are folded springs.  FIG. 2C  shows a top view of one example of a folded spring. The folded springs  124  are designed to provide substantially equal spring constants in three dimensions (e.g., X, Y and Z). Because, in some embodiments, the springs  124  can be configured to resonate at approximately 300 to 500 Hz, most vibration and shock, which typically occurs at higher frequencies, is rejected. 
     Referring again to  FIGS. 2A and 2B , the damping fins  122  are inserted into corresponding fin apertures  128  of the floating platform  112  to provide damping in the X and Y directions (i.e., in the plane of the floating platform  112 ). This is shown in further detail in  FIG. 3 , which is a cross-sectional profile view of one portion of the VIS  100  including the damping fins  122 , the substrate  120 , the floating platform  112  and the fin apertures  128 . The fin apertures  128  can be formed, for example, using deep reactive ion etching to create narrow gaps  130  between the floating platform  112  and the damping fins  122 . For example, the aspect ratio between the height h of the damping fins  122  and the width w of the gaps  130  may be between approximately 10 to 1 and 100 to 1, which creates a high squeeze film damping coefficient. In one embodiment, the gaps  130  on any side of the damping fins  122  are approximately the same width as the damping fins  122  (e.g., between about 2 and 50 microns wide). 
     In one embodiment, the gaps  130  are filled with a gas, such as nitrogen or neon, to provide squeeze film damping between the damping fins  122  and the floating platform  112  in at least the X and Y directions. In addition to X and Y damping, the damping fins  122  may dampen motion in the vertical Z direction when the gas is squeezed out or sucked into the gaps  130  through a separation  132  between the floating platform  112  and the substrate  120 . In the embodiment of  FIG. 3 , the damping fins  122  are straight. In other embodiments, the damping fins can be formed in other shapes, such as concentric rectangles or circles. 
     Referring back to  FIGS. 2A and 2B , the floating platform  112  may include one or more out-of-plane damping regions  134  that are free of fin apertures  128  (e.g., the out-of-plane damping regions are solid) and do not contain any damping fins  122 . Out-of-plane squeeze film damping (i.e., damping in the Z direction) may be achieved, at least partly, in gaps between the out-of-plane damping regions  134  and the substrate  120 . 
     In one embodiment, a combination of damping provided by the springs  124  and the gas-based squeeze film damping between the floating platform  112 , the damping fins  122  and the substrate  120  provides near critical damping over a wide temperature range (e.g., between approximately −40 and 125 degrees Celsius). The springs may be designed for a wide range of suspension natural frequencies using known closed-form equations or equivalent finite element calculations.  FIG. 2D  is a graph illustrating stiffness as a function of the length of one example of a beam of the spring  124  of  FIG. 2C . Line  210  shows stiffness along the x axis; line  212  shows stiffness along the y axis; line  214  shows stiffness along the z axis; and line  216  shows stiffness as a function of (x+y)/2. For an assumed beam thickness or substrate thickness of 100 microns (z direction), a beam width of 20 microns, and a 150 micron segment length L x , stiffness is plotted as a function of segment length L y  (see  FIG. 2D ). Because the in-plane springs can consist of two orthogonal sets, the x axis and y axis stiffness may be set equal to one another. From  FIG. 2D , the z axis stiffness of the spring  124  equals the average x and y stiffness of the spring  124  when the segment length L y  equals approximately 400 microns. By selecting the number of beams, the desired stiffness and, hence, resonant frequencies can be selected. In one embodiment, the damping ratio can be between 0.2 and 0.7 and the stiffness of the spring  124  can be substantially equal in all three translation dimensions (i.e., x, y, and z). A point of three-axis equal spring stiffness is indicated at  200  in  FIG. 2D . 
       FIG. 4A  is a top view of one example of the VIS  400  (as shown in  FIG. 1B  in cross section), according to another embodiment.  FIG. 4B  is a more detailed view of a portion of the VIS  400  of  FIG. 4A . The VIS  400  includes a frame  416  surrounding at least a portion of a floating platform  412 . A plurality of wire bonds  426  or other types of electrical contacts are mounted to the frame  416  and electrically connected to one or more electrical interconnects (not shown). The electrical interconnects may be connected to an external device (not shown), including but not limited to a power supply, a processor, or other electronic device. 
     In contrast to the embodiment of  FIGS. 2A and 2B , the VIS  400  of  FIGS. 4A and 4B  achieves in-plane damping (e.g., in the X and Y directions) without the use of a substrate layer to support damping fins. Instead, a plurality of damping fins  422  are coupled to and protrude from the frame  412  into a plurality of fin apertures  428 , which are formed in the floating platform  412 . These are shown in  FIGS. 4A and 4B  as feather-like regions with fins angled at approximately 45 degrees. 
     The floating platform  412  is attached to the frame  416  by a plurality of springs  424  that also function as electrical interconnects to the instrument module via the bump bonds  414 . One end of each spring  424  is coupled to a respective bump bond  414  on the floating platform  412 , and the other end of each spring  424  is coupled to one of the wire-bonds  426  mounted on the frame  416 . The springs  424  support the floating platform  412  and provide some vibration damping. In one embodiment, the springs  424  can be folded beam structures having 45 degree beams configured to provide equal spring constants in the X and Y directions. In another embodiment, a plurality of out-of-plane limit stops (not shown) can be mounted to the floating platform  412 . For example, the out-of-plane limit stops may include one or more hooks for coupling the instrument package to the floating platform  412 . The out-of-plane limit stops may be used to restrain the instrument package during high acceleration normal to the floating platform  412 . 
     An instrument module (not shown) can be mounted on the floating platform  412 , although it should be understood that the instrument module is not necessarily part of this embodiment. Electrical interconnects from the instrument module can be brought to the bottom surface of the instrument module, where bump bonds  414  or other types of electrical contacts mounted on the floating platform  412  electrically connect the instrument module to the floating platform  412 . 
     In one embodiment, out-of-plane damping (e.g., damping in a direction orthogonal to the floating platform  412 ) can be achieved by squeeze film damping between a portion of the floating platform  412 , such as indicated at  440 , and an external package (not shown) that encloses the entire VIS  400  and instrument module. 
       FIG. 5  is a top view of another example of a VIS  500 , according to one embodiment. The VIS  500  is similar to the VIS  400  of  FIG. 4A  in that it achieves in-plane damping using a single layer wafer. The VIS  500  includes a frame  516  surrounding at least a portion of a floating platform  512 . A plurality of wire bonds  526  or other types of electrical contacts are mounted to the frame  516  and electrically connected to one or more electrical interconnects (not shown). The electrical interconnects may be connected to an external device (not shown), including but not limited to a power supply, a processor, or other electronic device. Through silicon vias (TSV&#39;s)  150  (see  FIG. 1B ) may be used to bring electrical signals from one side of the VIS  400  to the other side. 
     Similar to the embodiment of  FIG. 4A , the VIS  500  of  FIG. 5  achieves in-plane damping (e.g., in the X and Y directions) without the use of an additional substrate layer to support damping fins. Instead, a plurality of damping fins  522  are coupled to and protrude from the frame  512  into a plurality of fin apertures  528  formed in the floating platform  512 . The damping fins  522  are shown in  FIG. 5  as orthogonal (straight) beams. Depending on their arrangements, one or more groups of damping fins  522  may be configured to provide damping in the X direction, and one or more other groups of damping fins  522  may be configured to provide damping in the Y direction. 
     The floating platform  512  is attached to the frame  516  by a plurality of springs  524  that also function as electrical interconnects to the instrument module via the bump bonds  514 . One end of each spring  524  is coupled to a respective bump bond  514  on the floating platform  512 , and the other end of each spring  524  is coupled to one of the wire-bonds  526  mounted on the frame  516 . The springs  524  support the floating platform  512  and provide some vibration damping. In one embodiment, the springs  524  can be folded beam structures having orthogonal beams, as discussed above with reference to  FIG. 2C . In another embodiment, a plurality of out-of-plane limit stops (not shown) can be mounted to the floating platform  512 . For example, the out-of-plane limit stops may include one or more hooks for coupling the instrument package to the floating platform  512 . The out-of-plane limit stops may be used to restrain the instrument package during high acceleration normal to the floating platform  512 . 
     An instrument module (not shown) can be mounted on the floating platform  512 , although it is to be understood that the instrument module is not necessarily part of this embodiment. Electrical interconnects from the instrument module can be brought to the bottom surface of the instrument module by TSV&#39;s  150 , where bump bonds  514  or other types of electrical contacts mounted on the floating platform  512  electrically connect the instrument module to the floating platform  512 . 
     In one embodiment, as discussed above, gas-based squeeze film damping can be used to critically damp the floating platform (e.g., floating platform  112  of  FIG. 2A  or floating platform  412  of  FIG. 4A ) and the instrument module mounted thereon. Some examples of gases that may be used include nitrogen, which is readily available, and neon, which has a viscosity 78% greater than nitrogen. Gas viscosity is proportional to the square root of absolute temperature, and is independent of pressure and density over a wide range. For example, in a temperature range from −25 degrees C. to +80 degrees C., there may be a 19% change in viscosity (+/−10% from nominal). Such a change in viscosity will have a minimal effect on a critically damped system, thus enabling the system to perform well over a relatively wide temperature range. By contrast, it is appreciated that many non-gaseous fluids, such as oil, have a very large change in viscosity (e.g., greater than 10:1) over the −25 degree C. to +80 degree C. temperature range. A viscosity change of this magnitude can render a critically damped isolation system inoperable except within a narrow temperature range. Therefore, the use of many non-gaseous fluids can lead to undesirable damping characteristics, particularly in very small-scale applications. However, it will be appreciated that in some systems that are not required to work over a large temperature range, damping by use of an oil or grease may be utilized. 
     In one embodiment, damping in the X and Y directions can be achieved by inserting many narrow damping fins  120  into the floating platform  112 , such as shown in  FIG. 2A . By the use of deep reactive ion etching, narrow gaps with aspect ratio of 10-100 can be achieved, leading to high damping coefficients. Consider, for instance, isolator suspension natural frequencies of approximately 300 and 500 Hz, which are typical for applications where the sensor (e.g., an accelerometer) bandwidth is approximately 50 to 100 Hz. Several exemplary damping results, in accordance with one embodiment, are shown in Table 1 below. 
     
       
         
               
             
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Damping Calculations for Small Inertial Measurement Unit Suspension. 
               
             
          
           
               
                   
                   
                   
                 Example 1 
                 Example 2 
               
               
                 Descriptor 
                 Units 
                 Symbol 
                 10 mm{circumflex over ( )}3, Si 
                 10 mm{circumflex over ( )}3, Si 
               
               
                   
               
               
                 PROOF MASS 
                   
                   
                   
                   
               
               
                 material 
                   
                   
                 silicon 
                 silicon 
               
               
                 length (shortest dimension) 
                 m 
                 lm 
                 3.00E−03 
                 3.00E−03 
               
               
                 width 
                 m 
                 wm 
                 4.00E−03 
                 4.00E−03 
               
               
                 thickness 
                 m 
                 tm 
                 8.33E−04 
                 8.33E−04 
               
               
                 hole diameter 
                 m 
                 dm 
                 0 
                 0 
               
               
                 density 
                 kg/m{circumflex over ( )}3 
                 rhom 
                 2330 
                 2330 
               
               
                 thermal expansion coefficient 
                 1/K 
                 alpham 
                 2.50E−06 
                 2.50E−06 
               
               
                 proof volume 
                 m{circumflex over ( )}3 
                 Vp 
                 1.00E−08 
                 1.00E−08 
               
               
                 proof mass 
                 kg 
                 mp 
                 2.33E−05 
                 2.33E−05 
               
               
                 Design acceleration 
                 g 
                 gdes 
                 5 
                 5 
               
               
                 design frequency-no rebalance 
                 Hz 
                 fdes 
                 300.00 
                 500.00 
               
               
                   
                 rad/s 
                 wdes 
                 1.88E+03 
                 3.14E+03 
               
               
                 required throw 
                 m 
                 gmin 
                 1.38E−05 
                 4.97E−06 
               
               
                 designed gap 
                 m 
                 gapdes 
                 1.38E−05 
                 4.97E−06 
               
               
                 Gas Damping on IMU 
                   
                   
                   
                   
               
               
                 gas viscosity 
                 N-s/m 2   
                 mu 
                 3.10E−05 
                 3.10E−05 
               
               
                 single plate damping 
                 N-s/m 
                 _c1x 
                 4.00E−02 
                 8.57E−01 
               
               
                 damping ratio-1 plate 
                 — 
                 zeta1x 
                 0.46 
                 5.85 
               
               
                 Air Damping on Fins 
                   
                   
                   
                   
               
               
                 machining aspect ratio 
                 — 
                 nm 
                 25 
                 25 
               
               
                 % fraction of area for one direction 
                 — 
                 fdamp 
                 0.25 
                 0.25 
               
               
                 depth fin-width of damper 
                 m 
                 tfin 
                 3.45E−04 
                 1.24E−04 
               
               
                 damping gaps per axis 
                 — 
                 ndamp 
                 36 
                 101 
               
               
                 damping for one in-plane direction 
                 N-s/m 
                 _c3x 
                 4.08E−02 
                 1.15E−01 
               
               
                 damping ratio-ndamp damping 
                 — 
                 zeta3x 
                 0.46 
                 0.78 
               
               
                 gaps 
                   
                   
                   
                   
               
               
                 include resistance of end flow 
                 N-s/m 5   
                 Rfin 
                 5.29E+08 
                 4.64E+09 
               
               
                   
                 N-s/m 
                 _c4x 
                 4.59E−02 
                 1.31E−01 
               
               
                 damping ratio with end flow 
                 — 
                 zeta4x 
                 0.52 
                 0.89 
               
               
                 resistance 
               
               
                   
               
             
          
         
       
     
     For example, if a 5 g acceleration is input to the VIS  100 , the proof mass (as listed in Table 1) may be free to move approximately 14 or 5 micrometers for the 300 and 500 Hz frequencies, respectively. This dimension of movement may be used to determine the gap size (e.g., the distance between the squeeze damping surfaces of the floating platform  112  and one of the fins  122 . 
     If a micromachining aspect ratio of 25 to 1 (i.e., fin height h to gap width w) (see  FIG. 3 ) is assumed, the fin height h, which is the dimension perpendicular to the substrate  120  of  FIG. 1 , can be determined. With wider gaps, higher fins can be constructed. The results of Table 1 were achieved under the assumption that 25% of the 3×4 mm 2  chip area is available for lateral damping and that the fin thickness is approximately the same as the gap between fins. Also, the calculations of Table 1 assume that 25% of the plate area is devoted to squeeze film vertical damping. Neon is assumed as the fill gas. 
     In one embodiment, a VIS has a damping ratio between 0.2 and 0.7 and the spring stiffness is substantially equal for the three translation motions (i.e., in three dimensions). 
     For the 500 Hz, 5 micrometer case in Table 1, the calculated damping ratios for the vertical (zeta1×) and horizontal (zeta4×) directions may be, for example, 6 and 0.9, respectively. By reducing the length or width of the vertical damper and the number of horizontal damping fins, the desired damping ratios can be achieved. For the 300 Hz, 14 micrometer case, the damping ratios for the vertical (zeta1×) and horizontal (zeta4×) directions may be, for example, 0.5 and 0.5. According to one embodiment, the damping gap is inversely proportional to the bandwidth squared, and the damping effect is inversely proportional to the gap cubed; hence, there is a large difference between vertical damping in the 5 and 14 micrometer movement examples above. The fin width can be determined by the aspect ratio. With narrower gaps, for example, the fin width is smaller; thus, the damping ratio is proportional to the isolator natural frequency. 
     Having thus described several aspects of at least one embodiment, it is to be appreciated various alterations, modifications, and improvements will readily occur to those skilled in the art. Such alterations, modifications, and improvements are intended to be part of this disclosure, and are intended to be within the scope of the invention. Accordingly, the foregoing description and drawings are by way of example only, and the scope of the invention should be determined from proper construction of the claims and their equivalents.