Patent Publication Number: US-2023151867-A1

Title: Shock Isolators Utilizing Multiple Disc Springs

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a divisional of U.S. patent application Ser. No. 16/900,167 filed on Jun. 12, 2020 by Terrence Lee Schneider entitled, “Shock Isolators Utilizing Multiple Disc Springs” which claims priority to U.S. Provisional Application No. 62/861,296 filed on Jun. 13, 2019 by Terrence Lee Schneider, entitled “Shock Isolation Device Utilizing Multiple Disc Springs”, both of which are incorporated herein by reference as if reproduced in their entirety. 
    
    
     TECHNICAL FIELD OF THE DISCLOSURE 
     The present disclosure relates to shock isolation devices, more specifically to shock isolators comprising a plurality of disc springs. 
     BACKGROUND 
     Shock may be defined as a transient condition where a single impulse of energy produced by a force is transferred to a system in a short period of time and with large acceleration. 
     The reduction of shock may be achieved by the use of isolators which results in the storage of the transient shock energy within the isolator and the subsequent release of the energy over a longer period of time by physical deflection of the isolator. Therefore, an effective shock isolation system receives and releases shock energy over a period of time greater than what would have been observed had a resilient isolator not been applied. 
     High levels of acceleration are typically a detriment to the performance of a system for a variety of reasons. Moreover, humans and equipment can be harmed if various thresholds of acceleration are exceeded. Thus, improvements in mechanical isolation systems to mitigate shock transmitted to humans and equipment is of interest. 
     The design of an ideal shock isolator would be one that imparts no more than a desired threshold level of acceleration to a structure or mass, while keeping the deflection to do so to a minimum. Designing such an optimal shock isolator entails two conflicting goals: low acceleration transmission and low isolator deflection. Low transmission of acceleration to a mass or body typically requires significant deflection. But this can pose a problem in many practical applications since geometric limitations usually require minimizing deflection in the isolating device. For example, the use of a stiff spring may keep the deflection of an isolator low, but will result in a high amount of acceleration transmitted from the base to the mass. 
       FIG.  1    presents a load-deflection graph  100  of an ideal shock isolator. Axis  102  represents deflection and axis  104  represents load (or force). The load-deflection graph  100  is considered to be ideal because a maximum deflection  106  experienced by the isolator represents the minimum deflection required to isolate a mass from given shock force while transmitting to the isolated structure no more than a threshold acceleration of a maximum load  108  divided by a mass m of the isolated structure. 
     Such an ideal shock isolator is infinitely stiff for zero relative deflection but provides isolation at a constant load for higher deflections. When a structure isolated by an ideal shock isolator experiences a shock force to the ideal shock isolator, a response such as the load-deflection graph  100  prevents the structure from experiencing more than the threshold level of acceleration while minimizing the relative deflection required to do so. 
     SUMMARY 
     In a first embodiment, a shock isolator includes an axial compression element (ACE), a first disc spring, a disc spring system, and an annular stand-off. The first disc spring is mechanically coupled to the ACE, is coaxial with the ACE, and is configured to be deflected by the ACE. The first disc spring has a non-linear load-deflection response. The disc spring system is coaxial with the first disc spring and has a first side facing the first disc spring and a second side mechanically coupled to a mass to be isolated from a shock load. The disc spring system is configured to be deflected by the first disc spring and has a linear load-deflection response. The annular stand-off is mechanically coupled to the mass and to an outer edge of the first disc spring. The annular stand-off is coaxial with the first disc spring. 
     In a second embodiment, a shock isolator includes an ACE, a first disc spring, a first annular stand-off, a second disc spring, and a second annular stand-off. The first disc spring is mechanically coupled to the ACE, is coaxial with the ACE, and is configured to be deflected by the ACE. The first disc spring has a first non-linear load-deflection response. The first annular stand-off is mechanically coupled to an outer edge of the first disc spring and is coaxial with the first disc spring. The second disc spring is coaxial with the first disc spring, is configured to be deflected by the first disc spring, and has a second non-linear load-deflection response. The second annular stand-off is mechanically coupled to an outer edge of the second disc spring, to the first annular stand-off, and to a mass to be isolated from a shock load. The first annular stand-off and the second annular stand-off are configured to hold the first disc spring and the second disc spring in a spaced apart parallel configuration. The second annular stand-off is coaxial with the second disc spring. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a more complete understanding of this disclosure, reference is now made to the following brief description, taken in conjunction with the accompanying drawings in which like reference numerals indicate like features. 
         FIG.  1    presents a load-deflection graph of an ideal shock isolator. 
         FIG.  2    presents a cross-section view of a disc spring. 
         FIG.  3    presents a load-deflection graph of a non-linear disc spring. 
         FIG.  4    presents a load-deflection graph of a shock isolator of a first type according to the disclosure. 
         FIG.  5    presents a load-deflection graph of a shock isolator of a second type according to the disclosure. 
         FIG.  6    presents an exploded cross-section view of a shock isolator of the first type according to the disclosure. 
         FIG.  7    presents an assembled cross-section view of the shock isolator of  FIG.  6   . 
         FIGS.  8 - 11    present detail views of elements of the shock isolator of  FIG.  6   . 
         FIGS.  12 A-B  through  16 A-B present configurations and load-deflection graphs of the shock isolator of  FIG.  6    under increasing amounts of deflection. 
         FIG.  17    presents an exploded cross-section view of a shock isolator of the second type according to the disclosure. 
         FIGS.  18 A-B  present detail cross-section views of the first and second annular stand-offs of the shock isolator of  FIG.  17   . 
         FIG.  19    presents a hidden line plan view of the annular stand-off of the shock isolator of  FIG.  17   . 
         FIGS.  20 A-B  through  23 A-B present configurations and load-deflection graphs of the shock isolator of  FIG.  17    under increasing amounts of deflection. 
         FIG.  24    presents a cross-section view of a third shock isolator system according to the disclosure. 
         FIG.  25    presents a cross-section view of a fourth shock isolator system according to the disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     A novel shock isolator is described which can approach this ideal behavior by providing isolation at a constant load over a chosen range of deflection. In some embodiments, the device consists of two different geometries of disc springs, each of which as individual springs, exhibit significantly different load-deflection behavior: a first disc spring exhibits non-linear load-deflection behavior (having a meta-stable region which enables “snap-through” of the disc) and a disc spring system comprising one or more disc springs exhibits linear load-deflection. When combined in series as a shock isolation system, the sum of their properties approach ideal shock isolation by exhibiting a constant load over a specific range of deflection, key to efficient shock isolation. 
     The meaning of “linear” and “non-linear” disc springs is a technical definition known in the industry. It is based on a disc&#39;s load-deflection profile. This profile is a function of a disc&#39;s free height-to-thickness ratio (h/t) (free height meaning the distance the disc can compress before it is in a flat configuration). A disc described as having linear load-deflection behavior (or linear “force-deflection” or “load-displacement” behavior), may have a range of height/thickness ratios in which the disc&#39;s load-deflection behavior is not exactly linear but is considered substantially linear. For purposes of this disclosure, discs with an h/t ratio greater than zero but less than the square root of 2 (i.e. 0&gt;h/t&lt;√{square root over (2)}) are considered linear, and discs with an h/t ratio greater than or equal to the square root of 2 are considered non-linear. 
       FIG.  2    presents a cross-section view of a disc spring  200  that may be used in shock isolators according to the disclosure. The disc spring  200  has a frusto-conical shape that includes a top  210  and a skirt  212 . Dimension  202  is D e , an external diameter of the disk. Dimension  204  is D i , an inner diameter of the disk. Dimension  206  is t, a material thickness of the disk. Dimension  208  is h, a free height of the disk (which may alternatively be referred to as h 0 ). The dimensions of the disc spring  200  may be referred to as a geometry of the disc spring  200 . 
     In some embodiments of shock isolators according to the disclosure, the top  210  includes an aperture having a diameter equal to D i , as shown in  FIG.  2   . In other embodiments, the top  210  comprises a solid planar surface having a diameter equal to D i . In some such embodiments, the solid planar top surface includes an aperture having a diameter less than D i . In still other embodiments of shock isolators according to the disclosure, disc springs may include slots or notches extending from an aperture in the top  210  radially toward the outer edge of the disc spring  200  (which may be referred to as diaphragm disc springs). 
     In yet other embodiments of shock isolators according to the disclosure, the skirt  212  of the disc spring  200  may have a trapezoidal cross-section or a curved cross-section. In still other embodiments of shock isolators according to the disclosure, rather than having a frusto-conical shape, the disc spring  200  may have a curved cross-section across its width. Such curved springs may include central apertures, which may include slots or notches as described above. 
     In general, the load-deflection performance of disc springs can be tailored to particular applications by controlling the disc springs&#39; value of h/t. As described above, a spring with h/t≥√{square root over (2)} exhibits non-linear load-deflection behavior, and a spring with h/t&lt;√{square root over (2)} exhibits linear load-deflection behavior. 
       FIG.  3    presents a load-deflection graph  300  of a non-linear disc spring that may be used in shock isolators according to the disclosure. Axis  302  represents deflection and axis  304  represents load. This convention of the horizontal axis representing deflection and the vertical axis representing load will be used throughout this disclosure. The dotted line  306  indicates a load-deflection curve of the non-linear disc spring, showing a percent (%) of load to flat (from 0 to 200%) absorbed by the disc spring as it is deflected from 0 to 200% of flat. The disc spring begins as concave in a first direction at 0% deflection; at 100% deflection, the disc spring is flat; and at 200% deflection, the disc spring is concave in a second direction, opposite to the first direction. 
     The non-linear disc spring exhibits “snap-through” or inversion during axial compression as it deflects through its flat, bi-stable instability region. A solid line indicates the instability region  308  of the load-deflection curve, where the disc spring is reversing from concave in the first direction to concave in the second direction. The non-linear disc spring is characterized as “bi-stable”, because its load response to increasing deflection increases in a stable manner prior to and after the snap-through instability zone, but decreases in the instability region  308 . 
     The geometry of the non-linear disc spring determines a deflection range of the snap-through instability zone—i.e., the amount of deflection at which the instability zone begins and the amount of deflection at which the instability zone ends. The deflection range may be controlled by selecting desired values for one or both of the free height and/or a ratio of the outer diameter to inner diameter of the non-linear disc spring. Additionally, the geometry of the non-linear disc spring determines a load range of the instability zone—i.e., an amount of load at which the instability zone begins and an amount of deflection at which the instability zone ends. The load range may be controlled by selecting desired value(s) for any or all of the thickness, the inner diameter, and/or the outer diameter of the non-linear disc spring. 
       FIG.  4    presents a load-deflection graph  400  of a shock isolator of a first type according to the disclosure. The shock isolator of the first type is described in more detail below with reference to  FIGS.  6 - 16 B . The shock isolator of the first type includes two different geometries of disc springs, each geometry exhibiting significantly different load-deflection behavior. A disc spring of a first geometry exhibits non-linear behavior having a bi-stable region in which snap-through occurs during axial compression of the spring, as shown by a load-deflection curve  402 . A disc spring system comprising one or more disc springs of a second geometry exhibits linear load-deflection behavior, as shown by a load-deflection curve  404 . The combined geometries of the disc springs of a disc spring system comprising two or more disc springs may be referred to as a geometry of the disc spring system. In some embodiments, two disc springs are placed in series (i.e., “back-to-back” or having concave sides facing toward each other) to yield a linear load-deflection behavior upon axial compression when contacted by the first disc spring from above. Combined in series as a shock isolation system, the sum of the properties of all disc springs causes the shock isolator of the first type to produce a combined load-deflection curve  406 , which includes a constant load region  408  of deflection providing a constant load, resulting in more efficient shock isolation. 
     The constant load region  408  is characterized by a deflection range over which the shock isolator absorbs the constant load. The deflection range extends from the minimum deflection to the maximum deflection at which the shock isolator absorbs the constant load. The deflection range of the constant load region  408  corresponds to the instability region of the non-linear disc spring. The constant load region  408  is also characterized by a load value, or a value of load that the shock isolator absorbs in the constant load region  408 . 
     For a particular application, a desired load value and a desired deflection range of the constant load region  408  (also referred to as the “plateau load” region) can be obtained by selecting a number and combination of discs, disc materials, and disc geometries used in the shock isolator of the first type—predominantly, but not solely, by controlling the non-linear disc load-deflection curve  402 . An area under the combined load-deflection curve  406  is equivalent to a total energy absorbed by the shock isolator of the first type. 
     Because the first type of shock isolator includes both a non-linear disc spring (which experiences 200% deflection) and a set of linear disc springs (which experience 100% deflection), the scale of the horizontal deflection axis has been relabeled in  FIGS.  4  and  12 B- 16 B . The scale for the non-linear load-deflection curve  402  is 0, 50, 100, 150, and 200. The scale for the linear load-deflection curve  404  is 0, 25, 50, 75, and 100. 
       FIG.  5    presents a load-deflection graph  500  of a shock isolator of a second type according to the disclosure. The shock isolator of the second type is described in more detail below with reference to  FIGS.  17 - 23 B . The shock isolator of the second type includes two non-linear disc springs in a spaced-apart parallel configuration. A first of the two disc springs is deflected by an applied load into its snap-through region, at which point it makes contact with a second of the two disc springs. As more load is applied, both disc springs absorb the applied load, until the first disc spring is fully deflected, at which point the second disc spring is partially through its snap-through region. The non-linear behavior of the first disc spring is shown by dotted line  502 , and the non-linear behavior of the second disc spring is shown by dotted line  504 . The combination of disc springs in the shock isolator of the second type produces a combined load-deflection curve  506 , which includes a region  508  of deflection providing a constant load, resulting in more efficient shock isolation. 
     For a particular application, a desired load value and a desired deflection range (as defined with reference to the constant load region  408 ), of the constant load region  508  can be obtained by selecting the number and combination of discs, disc materials, disc geometries, and vertical spacing of the discs (to control at what point the second disc spring begins deflecting) used in the shock isolator of the second type. As described for the combined load-deflection curve  406 , the area under the combined load-deflection curve  506  is equivalent to a total energy absorbed by the shock isolator of the second type. 
     Because the shock isolator of the second type includes two non-linear disc springs, two scales appear on the horizontal deflection axis in  FIGS.  5  and  20 B- 23 B . The first non-linear disc spring experiences 200% deflection, which is represented in a first scale of the axis. The second non-linear disc spring experiences less than 200% deflection and its percentage of deflection is represented in a second scale of the axis. 
     One benefit of shock isolators of both the first and second types according to the disclosure is that they provide greater area under the shock isolator load-deflection curve as compared to either a linear or non-linear disc spring. The area under the load-deflection curve represents work energy absorbed by the shock isolator. A shock isolator according to the disclosure has a plateau region and is more effective regarding total absorbed energy. The plateau region also represents storage of the transient shock energy within the isolator, allowing the subsequent release of the energy over a longer period of time by physical deflection of the isolator. Shock loads above the load plateau are also mitigated within the deflection range of the plateau, which improves the isolation of structures from detrimental shock impulses. 
       FIG.  6    presents an exploded cross-section view of a shock isolator  600  of the first type according to the disclosure. The shock isolator  600  comprises an axial compression element (ACE)  602 , an alignment collar  604 , a first disc spring  606 , a disc spring system  618  comprising a second disc spring  608  and a third disc spring  610 , an annular stand-off  612 , and an elastomer gasket  614 . The shock isolator  600  is mechanically coupled by the annular stand-off  612  to a mass  616  to be isolated from a shock load. The mass  616  is not an element of the shock isolator  600 . 
     The ACE  602  is a rigid component configured to receive the shock load and transfer the shock load to the first disc spring  606  via the alignment collar  604 . The first disc spring  606  is a disc spring having a non-linear load-deflection response and is mechanically coupled by an outer edge to the annular stand-off  612 . The outer edge of the first disc spring  606  rests on the elastomer gasket  614 . In an unloaded configuration of the shock isolator  600 , a convex side of the first disc spring  606  faces the second disc spring  608 . 
     The second and third disc springs  608  and  610  are a pair of series-mounted disc springs that comprise a disc spring system  618 , mounted with their concave sides facing toward each other and with their outer rims in contact with each other. Each of the second and third disc springs  608  and  610  have a linear load-deflection response, as does the disc spring system  618 . The second disc spring  608  forms a first side of the disc spring system  618 . The third disc spring  610  forms a second side of the disc spring system  618 . In the unloaded configuration of shock isolator  600 , the first side of the disc spring system  618  faces and is spaced apart from the first disc spring  606 . The second side of the disc spring system  618  is mechanically coupled, via the alignment collar  604 , to the mass  616 . 
     As described above, in other embodiments the disc spring system  618  may comprise a single disc spring or more than two disc springs. In such embodiments having a single disc spring, the disc spring may be oriented with either its concave or its convex face toward the first disc spring  606 . In such embodiments having three or more disc springs, the disc springs are coupled in series and the topmost disc spring may have either its concave or its convex face toward the first disc spring  606 . 
       FIG.  7    presents an assembled cross-section view of the shock isolator  600  of  FIG.  6   . The alignment collar  604  is inserted into central apertures of the first disc spring  606 , the second disc spring  608 , and the third disc spring  610  and holds those elements in a coaxial alignment. The outer edge of the first disc spring  606  is received in a recess in an inner side of the annular stand-off  612  and holds the annular stand-off  612  and the elastomer gasket  614  in a coaxial alignment with the other elements of the shock isolator  600 . As the shock isolator  600  is placed under an increasing axial load, the alignment collar  604  compresses while maintaining coaxial alignment of the other elements of the shock isolator  600 . 
     In some embodiments, the top of the first disc spring  606  (as oriented in  FIG.  7   ) has a D i  and an aperture larger than the D i  of the second disc spring  608 . In such an embodiment, the first disc spring  606  may not sufficiently depress the second and third disc springs  608  and  610  to produce the constant load region  408  described with reference to  FIG.  4   . In such embodiments, a flat, rigid circular plate with an aperture (similar to a washer) may be positioned horizontally between the first disc spring  606  and the second disc spring  608 . The circular plate has an outer diameter greater than the D i  of the first disc spring  606  and an aperture with a diameter configured to accept the alignment collar  604  and be held in coaxial alignment of the other elements of the shock isolator  600 . The dimensions of the circular plate are selected to produce a shock isolator having a constant load region such as the constant load region  408 . 
     A frustopyramidal central portion of the ACE  602  has a defined angle and height that are chosen to prevent the central portion protruding beyond the thickness of the first disc spring  606  and making contact with the second disc spring  608 . The defined angle may be chosen based upon a thickness of the first disc spring  606  and/or a diameter of a central aperture of the first disc spring  606 —which can vary depending on the application. The defined angle may fall into a range of angles between a maximum value and a minimum value. The ACE  602  is seated into the aperture of the first disc spring  606  (via the alignment collar  604 ) and stays positioned there during compression of the discs in the shock isolator  600 . In some embodiments of the shock isolator  600 , the flat apex of the frustopyramidal central portion of the ACE  602  is wide enough to mechanically couple with a portion of the top surface of the first disc spring  606  surrounding its central aperture, rather than being seated into the aperture of the first disc spring  606 . 
     In various embodiments, the ACE  602  is rigid and configured to be rigid and transfer shock loads to the other elements of the shock isolator  600 . The ACE  602  is further configured to transfer shock loads without experiencing permanent deformation upon removal of the shock loads. In some embodiments, the ACE  602  comprises organic polymer plastic, which may be thermoplastic or thermosetting. In some such embodiments, the ACE  602  is molded into shape while soft and then set into a final rigid form. In some such embodiments, the ACE  602  comprises unreinforced organic polymer plastic. In other such embodiments, the ACE  602  comprises a composite organic polymer plastic material, reinforced with particles (metallic or non-metallic), discontinuous fibers, or continuous fibers. Suitable reinforcement fiber types include metal, carbon, glass. Other reinforcement fiber types include Kevlar, nylon, polyethylene, and other suitable polymers. 
     In some embodiments, the ACE  602  comprises a metal having isotropic properties (i.e., mechanical, thermal or physical properties equivalent in all directions). In other embodiments, the ACE  602  comprises a hybrid composite material that includes layers (or discrete plies) of different materials such as various combinations of metallic layers and composite layers. Such hybrid composite materials may be referred to as FMLs (Fiber Metal Laminates). Such laminates include discrete layers in various combinations including metallic layers intermixed with layers of composite plies that may be carbon, glass, or polymer fiber-reinforced composite materials. 
     The alignment collar  604  is configured with a degree of rigidity and thickness to maintain coaxial alignment of the disc springs  606 ,  608 , and  610  while also being configured to contract to a shorter length during compression of the disc springs from applied shock loads. Suitable materials for fabrication of this component would include plastic made from a wide range of organic polymers, either thermoplastic or thermosetting, that can be molded into shape while soft and then set into a final semi-rigid form. Such plastics may be unreinforced or increased in rigidity with reinforcement additives. Reinforcement examples may include particles (metallic or non-metallic) or discontinuous fibers. 
     In some embodiments, the alignment collar  604  comprises organic polymer plastic, which may be thermoplastic or thermosetting. In some such embodiments, the alignment collar  604  is molded into shape while soft and then set into a final semi-rigid form. In some such embodiments, the alignment collar  604  comprises unreinforced organic polymer plastic. In other such embodiments, the alignment collar  604  comprises a composite organic polymer plastic material, reinforced with particles (metallic or non-metallic) or discontinuous fibers. Suitable reinforcement fiber types include metal, carbon, and glass. Other reinforcement fiber types include Kevlar, nylon, polyethylene, and other suitable polymers. 
     The annular stand-off  612  is configured with a degree of rigidity sufficient to contain and support the first disc spring  606  at its base but also having a degree of flexibility to allow for insertion of the first disc spring  606  into the annular stand-off  612  (as described with reference to  FIG.  9   ). In some embodiments, the annular stand-off  612  comprises organic polymer plastic, which may be thermoplastic or thermosetting. In some such embodiments, the annular stand-off  612  is molded into shape while soft and then set into a final semi-rigid form. In some such embodiments, the annular stand-off  612  comprises unreinforced organic polymer plastic. In other such embodiments, the annular stand-off  612  comprises a composite organic polymer plastic material, reinforced with particles (metallic or non-metallic) or discontinuous fibers. Suitable reinforcement fiber types include metal, carbon, and glass. Other reinforcement fiber types include Kevlar, nylon, polyethylene, and other suitable polymers. 
     In some embodiments, the annular stand-off  612  comprises a metal having isotropic properties (i.e., mechanical, thermal or physical properties equivalent in all directions). In such embodiments, the annular stand-off  612  may be fabricated in two parts to allow the annular stand-off  612  to be assembled around the first disc spring  606 , rather than the first disc spring  606  being inserted into the annular stand-off  612   
       FIGS.  8 - 11    present detail views of elements of the shock isolator  600  of  FIG.  6   .  FIG.  8    presents a hidden line plan view of the ACE  602 . 
       FIG.  9    presents a cross-section view of the annular stand-off  612  and the elastomer gasket  614 . A recess  902  in an inner side of the annular stand-off  612  is configured to receive an outer edge of first disc spring  606 . The recess  902  is configured with a height that exceeds a height of the elastomer gasket  614  by an amount  904 . The amount  904  is selected to be slightly less than a material thickness t of the first disc spring  606 . Once the first disc spring  606  is inserted into the recess  902 , the elastomer gasket  614  is in in compression and operates to retain the first disc spring  606  in the recess  902 . In some embodiments, an upper edge  908  of the annular stand-off  612  is flexible and configured to allow insertion of the first disc spring  606  into the recess  902 . In other embodiments, the annular stand-off  612  is fabricated in two parts and assembled around the first disc spring  606 . The annular stand-off  612  has a base height  906  that is selected to be high enough to allow full snap-through deflection of the first disc spring  606  (as shown in  FIG.  16 A ). The base height  906  is also selected (in conjunction with the material and thickness of the elastomer gasket  614 ) to cause the first disc spring  606  to contact the second disc spring  608  at full compression of the elastomer gasket  614 . 
       FIG.  10    presents a plan view of the elastomer gasket  614 .  FIG.  11    presents a hidden line plan view of annular stand-off  612 . A dotted line  1102  indicates an inner wall of the recess  902 . 
       FIGS.  12 A-B  through  16 A-B present configurations and load-deflection graphs of the shock isolator  600  of  FIG.  6    under increasing amounts of deflection.  FIG.  12 A  shows a first loaded configuration of the shock isolator  600 . An axial shock load  1202  has been applied to the ACE  602  along an axis of deflection  1230 , causing the first disc spring  606  to compress the elastomer gasket  614 . The first disc spring  606  has not begun deflecting but, due to the compression of the elastomer gasket  614 , an inner portion of the concave side of the first disc spring  606  has come into contact with an inner portion of the convex side of the second disc spring  608 . 
     As described above, in some embodiments no elastomer gasket  614  is included in the shock isolator  600  and the base height  906  of the annular stand-off  612  is selected to cause the first disc spring  606  to contact the second disc spring  608  in an unloaded configuration.  FIG.  12 A  presents an unloaded configuration of such an embodiment. 
       FIG.  12 B  presents a load-deflection graph  1210  for the shock isolator  600  in the first loaded configuration (or the shock isolator  600  having no elastomer gasket  614  in the unloaded configuration). A dotted line  1212  indicates a combined linear load-deflection response of the disc spring system  618 . A dotted line  1214  indicates a non-linear load-deflection response of the non-linear first disc spring  606 . Icon  1216  indicates a current combined deflection of the disc spring system  618 . Icon  1218  indicates a current deflection of the first disc spring  606 . The icons  1216  and  1218  indicate that there is zero deflection in the configuration shown in  FIG.  12 A . The icons  1216  and  1218  are individually distinguishable in  FIGS.  13 B and  15 B . 
       FIG.  13 A  shows a second loaded configuration of the shock isolator  600  (or a first loaded configuration of the shock isolator  600  having no elastomer gasket  614 ). An axial shock load  1302  (greater than the axial shock load  1202  of  FIG.  12 A ) has been applied to the ACE  602 , which has caused the first disc spring  606  and the disc spring system  618  to deflect over a distance that is equal to 50% deflection to flat of the first disc spring  606  and 25% deflection to flat of the disc spring system  618 . The inner portion of the concave side of the first disc spring  606  has applied force to the inner portion of the convex side of the second disc spring  608 , causing the second disc spring  608  to deflect. Further, the outer rim of the second disc spring  608  has applied force to the outer rim of the third disc spring  610 , causing the third disc spring  610  to deflect. 
       FIG.  13 B  presents a load-deflection graph  1310  for the shock isolator  600  in the configuration shown in  FIG.  13 A . The icon  1216  indicates 25% deflection to flat of the disc spring system  618  and the icon  1218  indicates 50% deflection to flat of the first disc spring  606 . Further deflection of the first disc spring  606  will take it into its instability region. 
       FIG.  14 A  shows a third loaded configuration of the shock isolator  600  (or a second loaded configuration of the shock isolator  600  having no elastomer gasket  614 ). An axial shock load  1402  (greater than the axial shock load  1302  of  FIG.  13 A ) has been applied to the ACE  602 , which has caused the first disc spring  606  and the disc spring system  618  to deflect over a distance that is equal to 100% deflection to flat of the first disc spring  606  and 50% deflection to flat of the disc spring system  618 . 
       FIG.  14 B  presents a load-deflection graph  1410  for the shock isolator  600  in the configuration of  FIG.  14 A . The icon  1216  indicates 50% deflection to flat of the disc spring system  618  and the icon  1218  indicates 100% deflection to flat of the first disc spring  606 . 
       FIG.  15 A  shows a fourth loaded configuration of the shock isolator  600  (or a third loaded configuration of the shock isolator  600  having no elastomer gasket  614 ). An axial shock load  1502  (greater than the axial shock load  1402  of  FIG.  14 A ) has been applied to the ACE  602 , which has caused the first disc spring  606  and the disc spring system  618  to deflect over a distance that is equal to 150% deflection to flat of the first disc spring  606  and 75% deflection to flat of the disc spring system  618 . The first disc spring  606  has snapped-through (or inverted). 
       FIG.  15 B  presents a load-deflection graph  1510  for the shock isolator  600  in the configuration shown in  FIG.  15 A . The icon  1216  indicates 75% deflection to flat of the disc spring system  618  and the icon  1218  indicates 150% deflection to flat of the first disc spring  606 . 
       FIG.  16 A  shows a fifth loaded configuration of the shock isolator  600  (or a fourth loaded configuration of the shock isolator  600  having no elastomer gasket  614 ). An axial shock load  1602  (greater than the axial shock load  1502  of  FIG.  15 A ) has been applied to the ACE  602 , which has caused the first disc spring  606  and the disc spring system  618  to deflect over a distance that is equal to 200% deflection to flat of the first disc spring  606  and 100% deflection to flat of the disc spring system  618 . No further deflection of the shock isolator  600  is possible because the second and third disc springs  608  and  610  are flattened against the mass  616  and prevent further deflection of the first disc spring  606 . 
       FIG.  16 B  presents a load-deflection graph  1610  for the shock isolator  600  in the configuration shown in  FIG.  16 A . The icon  1216  indicates 100% deflection to flat of the disc spring system  618  and the icon  1218  indicates 200% deflection to flat of the first disc spring  606 —indicating that the first disc spring  606  has further inverted from the fourth loaded configuration shown in  FIG.  15 A . 
     While  FIGS.  12 A-B  through  16 A-B describe the shock load being applied to the ACE  602  and the mass  616  to be isolated from the shock load being mechanically coupled to the annular stand-off  612 , it will be understood that the shock isolator  600  is reversible. The shock load may be applied to the annular stand-off  612  and the mass  616  mechanically coupled to the ACE  602 . 
     The shock isolator  600  is of the first type of shock isolator according to the disclosure, previously described with reference to  FIG.  4   . The combined load-deflection curve  406 , representative of the combined load-deflection curve of the shock isolator  600  (or the shock isolator  600  having no elastomer gasket  614  and a base height  906  of the annular stand-off  612  that is selected to cause the first disc spring  606  to contact the second disc spring  608  in an unloaded configuration), is presented in  FIG.  4   . The first disc spring  606  has an h/t ratio of approximately √{square root over (5)}, however other embodiments of the first type of shock isolator may use a first disc spring  606  with a height-to-thickness ratio of another value greater than or equal to √{square root over (2)}, resulting in a non-linear load-deflection curve different than the non-linear load-deflection response as shown by dotted line  1214  shown in  FIG.  12 B . Similarly, while the second and third disc springs  608  and  610  have an h/t ratio of approximately zero, other embodiments of the first type may have linear disc springs (as defined herein) with values of h/t that are greater than zero but less than √{square root over (2)}. Such linear disc springs would exhibit a load-deflection curve different than the combined linear load-deflection response shown in dotted line  1212  shown in  FIG.  12 B . The load-deflection curve for such linear disc springs would have some curvature and not be ‘linear’ in the conventional sense of the term. Still other embodiments may have only a single linear disc spring or three or more disc springs. Any of these differences in other embodiments could result in a combined load-deflection curve different than the load-deflection curve  406  shown in  FIG.  4   . 
     Still other embodiments of shock isolators of the first type according to the disclosure may have other changes to elements of the shock isolator  600 . In some embodiments, no elastomer gasket  614  is included. In some such embodiments, the annular stand-off  612  has a base height  906  that is selected to cause the first disc spring  606  to contact the second disc spring  608  in an unloaded configuration. Such embodiments will exhibit the load-deflection curve  406  shown in  FIG.  4   . 
     Two other embodiments having changes to elements of the shock isolator  600  will exhibit a combined load-deflection curve different than the load-deflection curve  406  shown in  FIG.  4   . In both the following embodiments, the non-linear first disc spring  606  begins deflecting before the linear disc spring system  618  begins deflecting. As such, the load-deflection curve  402  of the first disc spring  606  will be as shown in the load-deflection graph  400 , but the load-deflection curve  404  of the disc spring system  618  will be shifted to the right, indicating that deflection of the disc spring system  618  begins after deflection of the first disc spring  606 . This will result in a change to the combined load-deflection curve  406 , including a shift to the right of the deflection range of the constant load region  408  and, in some embodiments, a change in the load value of the constant load region  408 . 
     In one such embodiment, the annular stand-off  612  has a base height  906  that is selected to be sufficiently high to cause, in response to an initial load, the elastomer gasket  614  to fully compress and the first disc spring  606  to deflect by a first amount before the first disc spring  606  contacts the second disc spring  608 . In response to an additional load, both the first disc spring  606  and the disc spring system  618  deflect, the first disc spring  606  deflecting by a second amount and causing the disc spring system  618  to deflect by a third amount. 
     In another such embodiment, no elastomer gasket  614  is included and the annular stand-off  612  has a base height  906  that is selected to configure the first disc spring  606  to be spaced apart from the second disc spring  608  in an unloaded configuration. In response to an initial load, the first disc spring  606  deflects by a first amount before the first disc spring  606  contacts the second disc spring  608 . In response to an additional load, both the first disc spring  606  and the disc spring system  618  deflect, the first disc spring  606  deflecting by a second amount and causing the disc spring system  618  to deflect by a third amount. 
       FIG.  17    presents an exploded cross-section view of a shock isolator  1700  of a second type according to the disclosure. The shock isolator  1700  includes non-linear first and second disc springs  1702  and  1704 , and rigid first and second annular stand-offs  1706  and  1708 . When the shock isolator  1700  is assembled (as shown in  FIG.  20 A ), the first disc spring  1702  is mounted in the first annular stand-off  1706  and the second disc spring  1704  is mounted in the second annular stand-off  1708 . The second annular stand-off  1708  is mechanically coupled to a mass  1712  to be isolated from a shock load. 
     In some embodiments, one or both of the first and second disc springs  1702  and  1704  rest on elastomer gaskets within the corresponding first and second annular stand-offs  1706  and  1708 , similar to the elastomer gasket  614  described with reference to  FIG.  6   . Elastomer gaskets may be used to improve a durability of the first and second disc springs  1702  and  1704 , especially where the disc springs have experienced multiple shock events. The elastomer gaskets may cushion a portion of the shock energy transferred to discs that are thin and/or are fabricated from a material that is less ductile than a metal and less able to absorb the tensile and compressive forces that occur while the disc is deflecting under a shock load. 
     In applications where a weight of the shock isolator  1700  is an important design criterion, the first and second disc springs  1702  and  1704  may be fabricated from fiber-reinforced polymer composite materials, which can be sensitive to the rate of strain associated with shocks, suggesting the use of elastomer gaskets to reduce the degree of shock loading directly experienced by such disc springs. The weight of the shock isolator  1700  may be reduced even further by using an elastomer gasket under only the first disc spring  1702 , as that is the spring that receives the initial shock load. 
       FIGS.  18 A-B  present detail cross-section views of the first and second annular stand-offs  1706  and  1708  of the shock isolator  1700  of  FIG.  17   .  FIG.  18 A  present a detail exploded cross-section view. The first annular stand-off  1706  is designed to stack on the second annular stand-off  1708 . The first annular stand-off  1706  includes a pin protrusion  1802  extending from a lower surface and the second annular stand-off  1708  includes a corresponding cavity  1804  in an upper surface that is configured to receive the pin protrusion  1802 . Such pins and cavities may be spaced in corresponding positions radially around the first and second annular stand-offs  1706  and  1708 , respectively, to secure and coaxially align the first and second annular stand-offs  1706  and  1708  when stacked. In other embodiments, the lower surface of the first annular stand-off  1706  includes an annular ring protrusion and the upper surface of the second annular stand-off  1708  includes a corresponding annular slot in the upper surface. Still other embodiments may include other structures suitable to secure and coaxially align the first and second annular stand-offs  1706  and  1708 , preventing them from moving relative to each other perpendicularly to an axis of deflection when stacked. 
       FIG.  18 B  presents a detail assembled cross-section view of the first and second annular stand-offs  1706  and  1708 . The first annular stand-off  1706  has been stacked on the second annular stand-off  1708 , with the pin  1802  received in the cavity  1804 . A recess  1806  in the first annular stand-off  1706  is configured to receive an outer edge of the first disc spring  1702 . A recess  1808  in the second annular stand-off  1708  is configured to receive an outer edge of the second disc spring  1704 . The dimensions of the first and second annular stand-offs  1706  and  1708  are selected so that a distance  1810  between a bottom surface of the recess  1806  and a bottom surface of the recess  1808  provides a separation between the first disc spring  1702  and the second disc spring  1704  that is configured to cause the first disc spring  1702  to contact the second disc spring  1704  at a desired amount of deflection of the first disc spring  1702 . When elastomer gaskets are used in one or both of the recesses  1806  and  1808 , the distance  1810  is measured from the top of the elastomer gasket or the bottom surface of the recess, as appropriate. 
     As described for the annular stand-off  612  of the shock isolator  600 , an upper edge  1812  of the first annular stand-off  1706  may be flexible, to enable insertion of the first disc spring  1702  into the first annular stand-off  1706  and to ensure retention of the first disc spring  1702  in the first annular stand-off  1706 . In some embodiments, the second annular stand-off  1708  includes a similar flexible upper edge. In other embodiments, the second annular stand-off  1708  includes no upper edge and the lower surface of the first annular stand-off  1706  forms an upper surface of the recess  1808  and ensures retention of the first disc spring  1702  in the first annular stand-off  1706 . 
       FIG.  19    presents a hidden line plan view of the first annular stand-off  1706  of the shock isolator  1700  of  FIG.  17   . A dotted line  1902  indicates an inner wall of the recess  902 . 
       FIGS.  20 A-B  through  23 A-B present configurations and load-deflection graphs of the shock isolator  1700  of  FIG.  17    under increasing amounts of deflection.  FIG.  20 A  shows an assembled cross-section view of the shock isolator  1700  in an unloaded configuration, with the addition of an ACE  1714 . An outer edge of the first disc spring  1702  is mechanically coupled to the first annular stand-off  1706  and an outer edge of the second disc spring  1704  is mechanically coupled to the second annular stand-off  1708 . The second annular stand-off  1708  is mechanically coupled to the first annular stand-off  1706  and to the mass  1712 . The first and second annular stand-offs  1706  and  1708  are configured to hold the first and second disc springs  1702  and  1704  in a spaced-apart parallel configuration. The first and second disc springs  1702  and  1704  and the first and second annular stand-offs  1706  and  1708  are coaxially mounted. 
     As described for the ACE  602  of the shock isolator  600 , the ACE  1714  has a frustopyramidal central portion with a defined angle and height that are chosen to prevent the central portion protruding beyond the thickness of the first disc spring  1702  and making contact with the second disc spring  1704 . The defined angle may be chosen based upon a thickness of the first disc spring  1702  and/or a diameter of a central aperture of the first disc spring  1702 —which can vary depending on the application. The defined angle may fall into a range of angles between a maximum value and a minimum value. The ACE  1714  is seated into the aperture of the first disc spring  1702  and stays positioned there during compression of the discs in the shock isolator  1700 . In some embodiments of the shock isolator  1700 , the flat apex of the frustopyramidal central portion of the ACE  1714  is wide enough to mechanically couple with a portion of the top surface of the first disc spring  1702  surrounding its central aperture, rather than being seated into the aperture of the first disc spring  1702 . 
       FIG.  20 B  presents a load-deflection graph  2010  for the shock isolator  1700  in the unloaded configuration. A dotted line  2012  indicates a non-linear load-deflection response of the first disc spring  1702 . A dotted line  2014  indicates a non-linear load-deflection response of the second disc spring  1704 . Icon  2016  indicates that the first disc spring  1702  is not deflected in the unloaded configuration. Icon  2018  indicates that the second disc spring  1704  also is not deflected in the unloaded configuration. 
     As described above with reference to  FIG.  5   , because the shock isolator  1700  includes two non-linear disc springs, two scales appear on the horizontal deflection axes in  FIGS.  20 B,  21 B,  22 B, and  23 B . The first non-linear disc spring experiences 200% deflection, which is represented in a first scale of the axis. The second non-linear disc spring experiences approximately 0% to 120% deflection and its percentage of deflection is represented in a second scale of the axis. 
       FIG.  21 A  shows a first loaded configuration of the shock isolator  1700 . An axial shock load  2102  has been applied to the ACE  1714  along an axis of deflection  2130 , causing the first disc spring  1702  to deflect over a distance that is equal to 100% deflection to flat. In embodiments where the first disc spring  1702  rests on a first elastomer gasket, the first elastomer gasket fully compresses before the first disc spring  1702  begins to deflect to flat. The first disc spring  1702  has come into contact with the second disc spring  1704  and caused the second disc spring  1704  to deflect over a second distance, which is less than the first distance. In embodiments where the second disc spring  1704  rests on a second elastomer gasket, the second elastomer gasket fully compresses before the second disc spring  1704  begins to deflect. 
       FIG.  21 B  presents a load-deflection graph  2110  for the shock isolator  1700  in the first loaded configuration. Icons  2016  and  2018  are superimposed in the center of the load-deflection graph  2110 , indicating that the first disc spring  1702  is at 100% deflection, while the second disc spring  1704  is about 20% deflected. 
       FIG.  22 A  shows a second loaded configuration of the shock isolator  1700 . An axial shock load  2202  (greater than the axial shock load  2102  of  FIG.  21 A ) has been applied to the ACE  1714 , causing the first disc spring  1702  to deflect by an additional second distance, deflecting past flat. The first disc spring  1702  has caused the second disc spring  1704  to deflect by the same second distance, deflecting to flat. 
       FIG.  22 B  presents a load-deflection graph  2210  for the shock isolator  1700  in the second loaded configuration. Icons  2016  and  2018  are again superimposed in the load-deflection graph  2210 , indicating that the first disc spring  1702  is about 180% deflected, and the second disc spring  1704  is 100% deflected. 
       FIG.  23 A  shows a third loaded configuration of the shock isolator  1700 . An axial shock load  2302  (greater than the axial shock load  2202  of  FIG.  22 A ) has been applied to the ACE  1714 , causing the first disc spring  1702  to deflect by an additional third distance, deflecting to fully inverted. The first disc spring  1702  has caused the second disc spring  1704  to deflect by the same third distance, deflecting to a partially inverted configuration. 
       FIG.  23 B  presents a load-deflection graph  2310  for the shock isolator  1700  in the third loaded configuration. Icon  2016  indicates that the first disc spring  1702  is at full 200% deflection. Icon  2018  indicates that the second disc spring  1704  is at about 120% deflected. 
     The shock isolator  1700  is of the second type of shock isolator according to the disclosure, previously described with reference to  FIG.  5   . The combined load-deflection curve  506 , representative of the combined load-deflection curve of the shock isolator  1700 , is presented in  FIG.  5   . Both the first and second disc springs  1702  and  1704  have an h/t ratio of approximately √{square root over (5)}, however other embodiments of the second type of shock isolator may use disc springs with height-to-thickness ratios of other values greater than or equal to √{square root over (2)}, resulting in non-linear load-deflection curves different than the responses  2012  and  2014  shown in  FIG.  20 A  and a different combined load-deflection curve than the combined load-deflection curve  506  shown in  FIG.  5   . While the first and second disc springs  1702  and  1704  have approximately equal h/t ratios and load-deflection curves, other embodiments may use disc springs having h/t ratios and load-deflection curves that are not the same, resulting in non-linear load-deflection curves different than the responses  2012  and  2014  shown in  FIG.  20 A  and a different combined load-deflection curve than the combined load-deflection curve  506  shown in  FIG.  5   . 
     As described for the shock isolator  600 , the shock isolator  1700  is also reversible. The shock load may be applied to the second annular stand-off  1708  and the mass  1712  mechanically coupled to the ACE  1714  in such a reversed application. 
       FIG.  24    presents a cross-section view of a third shock isolator system  2400  according to the disclosure. The shock isolator system  2400  includes a rod  2420  extending through a shock isolator  2600  (similar to the shock isolator  600  described with reference to  FIGS.  6 - 16 B ) and a plate  2422  into a mass  2416  to be isolated from a shock load. The rod  2420  is fixedly mounted to the mass  2416 . In some embodiments, the rod  2420  is fabricated as a part of the mass  2416 . 
     The shock isolator  2600  and the plate  2422  surround and are free to slide along a longitudinal axis  2430  of the rod  2420 . The longitudinal axis  2430  is also an axis of deflection of the shock isolator  2600  and the shock isolator system  2400 . When a shock load is applied to the shock isolator  2600 , a distance  2424  between the plate  2422  and the mass  2416  may change. A coil spring or some other device for absorbing force or shock may be positioned between the plate  2422  and the mass  2416 . When the coil spring or other device has a higher stiffness than the shock isolator  2600 , the shock isolator  2600  may absorb an initial shock load, before beginning to compress the coil spring or other device. 
       FIG.  25    presents a cross-section view of a fourth shock isolator system  2500  according to the disclosure. The shock isolator system  2500  includes a rod  2520  extending through a shock isolator  2700  (similar to the shock isolator  1700  described with reference to  FIGS.  17 - 23 B ) and a plate  2522  into a mass  2516  to be isolated from a shock load. The rod  2520  is fixedly mounted to the mass  2516 . In some embodiments, the rod  2520  is fabricated as a part of the mass  2516 . 
     The shock isolator  2700  and the plate  2522  surround and are free to slide along a longitudinal axis  2530  of the rod  2520 . The longitudinal axis  2530  is also an axis of deflection of the shock isolator  2700  and the shock isolator system  2500 . When a shock load is applied to the shock isolator  2700 , a distance  2524  between the plate  2522  and the mass  2516  may change. A coil spring or some other device for absorbing force or shock may be positioned between the plate  2522  and the mass  2516 . When the coil spring or other device has a higher stiffness than the shock isolator  2700 , the shock isolator  2700  may absorb an initial shock load, before beginning to compress the coil spring or other device. 
     In some embodiments, one or more shock isolators according to the disclosure may be mounted between an outer shell of a helmet and an inner shell of the helmet, to isolate the inner shell and the head of a person wearing the helmet from shock loads applied to the outer shell. As noted above, shock isolators according to the disclosure are reversible and may be mounted in either orientation relative to the outer shell and inner shell of the helmet. 
     In other embodiments, one or more shock isolators according to the disclosure may be mounted in the sole of a shoe or boot to protect the wearer&#39;s foot from shocks applied to the sole. Shock isolators according to the disclosure may be mounted in protective clothing, padding, shields, or the like, such as shin guards, forearm pads, elbow pads, knee pads, thigh pads, chest pads, and other types of padding used in football, hockey, baseball, mountain biking, motorcycling, or other sporting activities. Shock isolators according to the disclosure may be mounted in police and military protection gear. Shock isolators according to the disclosure may provide improvements in shock and vibration damping in snow boards, skate boards, skis, and other planar sporting equipment. Shock isolators according to the disclosure may be used in side-wall panels, bumpers and other structural elements of commercial and military vehicles for protection against impacts by objects and/or shock waves due to impulse energies transmitted by explosive events. 
     Suitable materials for disc springs in shock isolators according to the disclosure include (i.e., are not limited to):
         Metals: Metallic discs having isotropic properties (mechanical, thermal or physical properties equivalent in all directions).   Orthotropic Composites: Composites that are orthotropic (e.g., have mechanical, thermal or physical properties that are directional, based on the orientations of reinforcement at the individual ply level). Suitable orthotropic composites may involve two kinds of components: a matrix and one or more types of reinforcements to the matrix.
           Matrix examples for disc springs include polymeric matrices (thermoplastic and thermosetting polymers) and metal matrices.   Reinforcement examples include particles (metallic or non-metallic), discontinuous fibers and continuous fibers. Fiber types include metal, carbon, glass and/or polymeric (e.g. Kevlar, nylon, polyethylene, and other suitable polymers).   
           Hybrid Composites: Composites that include layers (discrete plies) of different materials such as various combinations of metallic layers and composite layers. Such hybrid composites may be referred to as FMLs (Fiber Metal Laminates). Such laminates include discrete layers in various combinations including metallic layers with composite plies that may be carbon, glass, or polymer fiber-reinforced composite materials. Another suitable hybrid composite is an elastomer layer combined as a discrete ply within an FML, or a Polymer Composite Laminate (PCL).