Abstract:
Methods and systems for providing space tethers for limiting the dynamic response of structures are disclosed. In one embodiment, a method for limiting the dynamic response of a structure having a base member and a substructure projecting outwardly from the base member includes coupling a first end of an elongated flexible tether to the substructure at a first location spaced apart from the base member; and coupling a second end of the elongated flexible tether to the base member at a second location spaced apart from the substructure, the tether being configured to be in a non-taut configuration when the substructure moves within a design volume with respect to the base member, the tether being further configured to be in a taut position when the substructure displaces to a limit of the design volume.

Description:
FIELD OF THE INVENTION 
       [0001]    The invention relates to methods and systems for utilizing space tethers on structures, and more specifically, to methods and systems for providing space tethers for limiting the dynamic response of structures. 
       BACKGROUND OF THE INVENTION 
       [0002]    Satellite transport into space has become a commonplace occurrence as reliance in satellite based technology continues to expand. Satellites may be launched into space in cargo holds of spacecraft or on top of rockets. Often, satellites contain large and lightweight structures such as antennas which cannot sustain high loads or high displacement during launch into space or during ground tests prior to launch. Once in orbit, satellites must be able to sustain thermal distortions without adversely affecting the satellite&#39;s functionality. 
         [0003]    To overcome displacement and high load stresses on satellite structures, designers often add additional reinforcements to the structure, extra material, beams, securing braces, or padding to assure structural integrity of the satellite&#39;s structures during launch. However, such additional reinforcements may detrimentally affect the mission performance. For example, heavy reinforcements contribute additional mass to the payload of the spacecraft and thus increases cost. Once in orbit satellites must be capable of operating under exposure to thermal distortions. Additional reinforcement structures may interfere with the satellite&#39;s thermal distortions and may adversely affect the lightweight structure&#39;s position and operation. Reinforcement structures which are removed in space, such as by pyrotechnic launch locks, are problematic as they often require additional processes, complexity, mass, and cost to the launch mission. 
         [0004]    The launch and transport of satellites into space only requires a short period of time in comparison to the entire lifespan of the satellite in orbit. During the launch phase, the satellite&#39;s structure must be capable of sustaining high loads without incurring damage, therefore dynamic displacements must be limited. During the remainder of the satellite&#39;s mission, while the satellite is in orbit, the satellite&#39;s operation may be significantly improved by the absence of redundant load paths (e.g., reinforcement structures) and minimized loads caused by thermal distortions. 
         [0005]    Therefore, there exists a need for improved methods and systems for limiting the dynamic response of structures during the launch phase of space transport, while minimizing redundant constraints on lightweight satellite structures that experience thermal distortions while in orbit. 
       SUMMARY 
       [0006]    Embodiments of methods and systems for providing space tethers for limiting the dynamic response of structures are disclosed. Embodiments of methods and systems in accordance with the present disclosure may advantageously improve operation and reliability of structures subjected to high stresses during space launch and thermal distortions while in space. 
         [0007]    In one embodiment, a method for limiting the dynamic response of a structure having a base member and a substructure projecting outwardly from the base member includes coupling a first end of an elongated flexible tether to the substructure at a first location spaced apart from the base member; and coupling a second end of the elongated flexible tether to the base member at a second location spaced apart from the substructure, the tether being configured to be in a non-taut configuration when the substructure moves within a design volume with respect to the base member, the tether being further configured to be in a taut position when the substructure displaces to a limit of the design volume. 
         [0008]    In another embodiment, a system includes a structure including a base member; a elongated structure coupled at one end to the base member; and an elongated flexible tether attached to the base member and at least one of the elongated structure and base member, the tether configured to be in a non-taut configuration when the substructure moves within a design volume with respect to the base member, the tether being further configured to be in a taut position when the substructure displaces to a limit of the design volume. 
         [0009]    In a further embodiment, a method of dampening dynamic response of a space structure includes determining the structure predicted deformation during a mission; determining a design volume for allowable dynamic response of the structure during the mission; configuring an elongated flexible tether suitable for coupling between two attachment locations on the structure, including determining at least two attachment points on the structure for the tether; determining a tether design length, the design length configured to provide a non-taut tether configuration when the structure is within the design volume; and attaching the tether to the structure. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0010]    Embodiments of the invention are described in detail below with reference to the following drawings. 
           [0011]      FIG. 1  is a plan view of a method or system of space tethers for limiting the dynamic response of a structure in accordance with an embodiment of the invention; 
           [0012]      FIGS. 2   a - 2   c  are schematic views of mission phases of a space tether configuration in accordance with an embodiment of the invention; 
           [0013]      FIG. 3  is a schematic of a launch phase of a space tether configuration in accordance with an embodiment of the invention; 
           [0014]      FIG. 4  is a schematic of a method or system of space tethers for limiting the dynamic response of a structure in accordance with another embodiment of the invention; and 
           [0015]      FIG. 5  is a chart illustrating the dynamic response of a structure subjected to launch conditions in accordance with an embodiment of the invention. 
       
    
    
     DETAILED DESCRIPTION 
       [0016]    Methods and systems for providing space tethers for limiting the dynamic response of structures are described herein. Many specific details of certain embodiments of the invention are set forth in the following description and in  FIGS. 1 through 5  to provide a thorough understanding of such embodiments. One skilled in the art, however, will understand that the present invention may have additional embodiments, or that the present invention may be practiced without several of the details described in the following description. 
         [0017]      FIG. 1  illustrates an overall environment  100  of methods and systems for providing space tethers for limiting the dynamic response of structures in accordance with an embodiment of the invention. The environment  100  includes a structure  102 . The structure  102  may be any space payload that includes a substructure  104 , which undergoes dynamic response during transport to space. In one embodiment, the structure  102  may be a satellite. Alternatively, the structure  102  may be experiment apparatus, spacecraft, space station supplies, space exploration apparatus, or other structures that are transported into space and undergo dynamic response during transport to space. 
         [0018]    As previously described, the structure  102  includes substructures  104 . Substructures may be booms, antennas, wings, or any other protrusion from a structure  102  that is subjected to dynamic responses during transport to space which may cause damage to the substructure. For example, during the launch phase of a spacecraft, the spacecraft experiences large vibrational forces, particularly during the phase between initiation of the launch engines (e.g., rockets) and the first few minutes of flight. During the launch phase, the spacecraft payload, including the structure  102  and substructure  104  are subjected to the vibrations experienced by the spacecraft. These vibrations may result in the dynamic response of a substructure  104 , such as by oscillating back and forth. The substructure  104  may bend, deform, or fracture from the dynamic response if the substructure  104  is not restrained and therefore may compromise the integrity of the substructure  104  or structure  102  and potentially lead to the failure or inoperability of a portion of the structure  102  or any part thereof (e.g., substructure  104 , instrument  106 , etc.). 
         [0019]    In some embodiments, the substructure  104  includes an instrument  106 . The instrument  106  may be located at the opposite end of the substructure  104  away from the structure  102 , however other configurations are contemplated. In one embodiment, the instrument  106  may be a camera. Other instruments  106  may be configured with the substructure  104  to facilitate communication and observation with the structure while it is deployed in orbit, such as a sensor or antenna. The instrument  106  may be attached to the substructure or integrally formed with the substructure  104 . The instrument  106  may further increase the dynamic response of the substructure during vibrations experienced during the launch phase of the spacecraft. For example, the instrument  106  may include additional mass, which when subjected to vibrational forces will propagate dynamic responses experienced by the substructure  104 . 
         [0020]    With continued reference to  FIG. 1 , the environment  100  includes at least one tether  108 . The tether  108  may be any type of member, limited to withstanding tensile forces, that can translate between a non-taut state (e.g., slack) to a taut state. For example, the tether  108  may be a cable, wire, string, chain, cord, or the like. In one embodiment, the tether  108  may be comprised of braided Kevlar. In another embodiment, the tether  108  may be comprised of a strand of steel wire. 
         [0021]    The tether  108  is configured in environment  100  in a position to limit the dynamic response of the substructure  104  during the launch phase while remaining in a non-taut state during the rest of the substructure&#39;s  104  operation (i.e., space mission). For example, a substructure  104  with tethers  108  is limited to dynamic response within a volume defined by the length of the tether  108 . The tether  108  may be arranged in a variety of configurations to limit the dynamic response. In one embodiment, the tether  108  may be affixed between the structure  102  and the substructure  104 . The tether  108  may be fastened to another object or itself by knots, fasteners, connectors, or any other fastening means. In an alternative embodiment, the tether may be affixed to an instrument  106 . It is also contemplated that the tether  108  may limit the dynamic response of the substructure  104  during the launch phase without being attached to the substructure  104  or the instrument  106 . For example, the tether  108  may be affixed between two different attachment points on the structure  102  such that the tether  108  limits the dynamic response of the substructure during the launch phase of the space transport of the structure  102 . In yet another embodiment, the tether  108  may be affixed to a secondary tether  402 , as depicted in  FIG. 3 . 
         [0022]      FIGS. 2   a,    2   b,  and  2   c  illustrate a tether configuration during three phases  200   a,    200   b,    200   c  of a mission of the structure  102  in accordance with an embodiment of the invention. The three phases  200   a,    200   b,    200   c  depict a tether configuration including a single tether  108   a,    108   b,    108   c.  Although only one tether configuration is depicted, other tether configurations are contemplated, such as utilizing two or more tethers  108 . The first phase  200   a  depicts the tether configuration on earth prior to launch. The second phase  200   b  depicts the tether configuration when the structure  102  is in orbit in space after a relatively short period of time (e.g., one week) when the tether and structure have been subjected to the space environment and have reached a static deformation state. The third phase  200   c  depicts the tether configuration at the end of the operating mission of the structure  102 . For example, the structure  102  may be designed to operate in space for 15 years, therefore in such instance the third phase  200   c  would represent the tether configuration at the end of the 15 year mission. Each phase will be discussed in turn with further detail. 
         [0023]    With reference to the first phase  200   a  in  FIG. 2   a,  the tether  108   a  is depicted as non-taut as configured between the structure  102  and the substructure  104   a  (or alternatively the instrument  106 ). In this phase, the tether  108   a  is subjected to the atmospheric conditions on earth such as temperature, pressure, and humidity. Under the earth&#39;s possible range of atmospheric conditions, the tether  108   a  may have a minimum length (TE min ) and a maximum length (TE max ). The length of the tether may vary between TE min  and TE max  due to changing atmospheric conditions, including those experienced during the early stages of the launch phase, as described above. 
         [0024]    In the second phase  200   b  in  FIG. 2   b,  the tether  108   b  is again depicted as non-taut as configured with the structure  102 . In the second phase  200   b,  the tether  108   b  is subjected to the conditions of space (e.g., temperature, radiation, pressure, humidity, etc.) after the conditions have stabilized and the structure is not undergoing deformation because of a transition between the atmospheric condition variations between earth and space. For example, the structure&#39;s orbit in space does not contain any of the water contained in the atmosphere near earth. Additionally, the tether  108   b  may be exposed to radiation, large temperature variations, and other conditions that affect the length of the tether  108   b.  Therefore, the length of the tether  108   a  in the first phase  200   a  may change (e.g., shrink) to a new length of the tether  108   b  in the second phase  200   b  when subjected to the space conditions because the tether  108   a  may dry out when initially reaching space until the tether  108   b  has finished adjusting to the conditions of space and reaches a static deformation state. The tether may reach the second length, the initial length in space (TS i ) with a minimum length TS i,min  and maximum length TS i,max . For simplicity sake, the tether reaches static deformation at t(min), where t(min) may be an hour, day, week, month, or any other amount of time whereas the tether reaches its static deformation state. Similarly, substructure  104   b  may experience deformation upon the introduction of the conditions of space, therefore changing in shape from the state on earth of the substructure  104   a,  in the first phase  200   a.    
         [0025]    In the third phase  200   c  in  FIG. 2   c,  the tether  108   c  depiction remains non-taut as configured with structure  102 . In this phase, the structure  102  is at the end of its mission operation. During the duration of the mission, the structure  102 , including any substructures  104   c  may become deformed. A deformation, bend, or other structural change in the substructure  104   c  may be caused by the conditions in space, such as temperature change or prolonged exposure to radiation. These conditions are typically predictable, thus the amount of potential deformation may be calculated for a substructure  104   c  subjected to the space environment during a mission. The important characteristic of the third phase  200   c  is the tether  108   c  configuration between the structure  102  and the deformed substructure  104   c,  whereas the tether  108   c  remains in a non-taut configuration. Throughout the transition from the second phase  200   b  to the third phase  200   c,  the tether  104   b,    104   c  remains in a non-taut configuration and therefore does not interfere with the operation of the substructure  104   b,    104   c  and any instrument  106 . 
         [0026]      FIG. 3  depicts a launch phase  300  of a space tether configuration. During the launch phase  300 , the spacecraft (not shown) and its payload, including structure  102  and substructure  104 , are subjected to vibrational forces, particularly during the early stages of the launch of the spacecraft. During the launch phase  300 , the structure  102  may undergo large vibrational forces which may be caused by the rocket thrusting forces of the spacecraft, the effect of gravity on any payload, turbulence during flight, or other physical factors, which cause the spacecraft (and any payload such as structure  102 ) to experience vibrations. During these vibrations, the substructure  104  may undergo dynamic responses to the vibrations, such as to cause the substructure  104  to oscillate  302 . For example, the range of positions of the substructure  104  subjected to a dynamic response may oscillate  302  from a first position of the substructure  104 ( 1 ) to a second position of the substructure  104 ( 2 ), whereas the tether  108  moves from a first tether position  108 ( 1 ) to a second tether position  108 ( 2 ), respectively. In the first tether position  108 ( 1 ), the tether  108 ( 1 ) is taut and limits further dynamic motion of the substructure  104 ( 1 ) from the non-vibration position of the substructure  104 . The tether restricts the dynamic response of the substructure outside of a predetermined design constraint volume (the maximum dynamic response of substructure  104 ). In the second tether position  108 ( 2 ), the tether  108 ( 2 ) is non-taut and thus the substructure  108 ( 2 ) is unrestrained by the tether  108 ( 2 ). The tether  108 ( 2 ) is non-taut because the tether is limited to tensile forces. 
         [0027]    In one embodiment, a single tether  108  may meet the design requirements of limiting the dynamic response of a substructure  108 . Alternatively, other tethers may be attached to the substructure  104  and/or structure  102  (or other fixtures) to limit the dynamic response of the substructure  104  in other ranges of motion. For example, in  FIG. 1 , two tethers  108  are utilized to limit the dynamic response of the substructure  102 . When the tethers are correctly configured on the structure and/or substructure, the substructure  104  will not experience a dynamic response causing operational failure or permanent deformation of the substructure  104  or structure  102 . Further, any attached instrument  108 , such as a camera or communication device, will be protected from damage or failure when subjected to dynamic responses by the substructure  104  constrained by the tether  108 , such as damage from colliding with other structures within the launching vehicle, including the structure  102  and other substructures  104  attached to structure  102 . 
         [0028]    In order to provide the functionality as described in the  FIGS. 2 and 3 , the tether  108  is desirably configured to a proper design initial length. A number of factors must be considered to determine the initial length of the tether  108 . The combined expansion, shrinkage, and deformation experienced by the tether  108 , the substructure  104 , and the structure  102  (if the tether is attached to the structure  102 ). Additionally, if multiple tethers  108  are utilized in the design, all tethers  108  must be considered for length changes during the elapse of all three phases discussed above (i.e., the mission duration). 
         [0029]    In one embodiment, the length of the tether  108  at t max  (at the end of the mission) must be greater than the maximum shrinkage of the tether during the elapsed mission plus the distance between the tether&#39;s  108  attachment locations at the end of the operating mission, thus ensuring the tether  108  is in a non-taut configuration throughout orbital phase of the mission. Further, this ensures that the tether  108  does not introduce environmentally-induced distortions into the substructure  104  or structure  102 , such as by resisting an environmentally-induced deformation of the substructure  104 . Environmentally-induced distortions may damage the operation of the structure  102  or substructure  104 . For example, internal components, such as wires, mechanisms, etc. may be damaged if they cannot deform in accordance with the substructure  104 . 
         [0030]    The initial length of the tether  108  may also include additional factors. For example, the design length of the tether  108  will preferably not permit the tether  108  to become taut at any time during the structure&#39;s  102  mission in orbit. Additionally, the tether  108  will preferably not become taut during any phase of the transport from earth into space, except where the tether  108  is taut from counter-acting dynamic response forces due to vibration in the launch phase. Therefore, the length and deformation of the tether  108 , substructure  104 , and any other structures or tethers in connection with the tether  108  may be analyzed for expansion, shrinkage, and deformation in order to select the proper tether  108  length for use prior to launch. Further, the above consideration must be kept in mind when designing and determining the attachment points of the tether  108 , therefore enabling a designer to position an appropriate length of tether  108  in relation to the substructure  104  to prevent critical dynamic response which results in deformation, damage, failure, or other undesirable consequences of the substructure  104 , any instrument  106 , and the structure  102 . 
         [0031]      FIG. 4  illustrates an overall environment  400  of methods and systems for providing space tethers for limiting the dynamic response of structures in accordance with an embodiment of the invention. The environment  400  includes a structure  102 , such as a satellite. Structure  102  further includes a substructure  104  extending from the surface of the structure  102 , such as a boom or antenna. The substructure  104  may further include an instrument  106 . The instrument  106  may be integrally formed with the substructure  104  or attached to the substructure  104 , such as by bolts and nuts, welds, or other attachment means. Further, environment  400  includes at least one primary tether  108 . The primary tether  108  may be a cable, wire, string, chain, cord, or the similar deformable structure, which can undergo tensile forces but is ineffective for providing compressive forces. 
         [0032]    Additionally, a secondary tether  402  may be included in environment  400 . The secondary tether  402  may provide further support for the primary tether  108  or the substructure  104  when the substructure  104  is subjected to dynamic responses such as by launch vibrations. The secondary tether  402  may be attached to the primary tether  108  at an attachment point  404 , such as by a fastener, knot, or other connection. Alternatively, the secondary tether  402  may be attached to the substructure  104  or structure  102 . The function of the secondary tether  402  may be either for providing additional strength to the primary tether  108  relating to control of the dynamic response of the substructure  104 , or to restrain the primary tether  108  within a volume or range of motion when the primary tether is non-taut, such that the primary tether  108  will not interfere with other substructures, wings, solar panels, antennas, tethers, or other protrusions from the structure  102 . For example, when the substructure  104  is subjected to dynamic responses, such as in  FIG. 3 ,  104 ( 1 ),  104 ( 2 ), the primary tether  108  is non-taut and may interfere with other protrusions of the structure  102  by becoming entangled with such other protrusions. Therefore, a secondary tether  402  may be included to restrain the primary tether  108  within a design volume such that the primary tether  108  cannot become entangled or otherwise interfere with other protrusions from the structure  102 . 
         [0033]    In another embodiment of the invention, a motion control member  406  may be included in the tether configuration. For example, the motion control member  406  may be a biasing device and/or dampening device. In one embodiment, the motion control member  406  is a dampening device that reduces the impact force exerted on the substructure when the tether  108  (including the motion control member  406 ) becomes taut. In another embodiment, the motion control member  406  is a biasing device such as a coil spring. The motion control member  406  may be located within a tether  108 ,  402  or configured with a tether connection point such as to act between a tether  108 ,  402  and the structure  102  or substructure  104 . Further, additional motion control members  406  may be utilized in any advantageous configuration, such as in series or in parallel configuration with one another. 
         [0034]      FIG. 5  is a chart  500  illustrating vibration of a structure experiencing launch conditions. Chart  500  includes an axis  502  representing zero displacement over a period of time. Plotted on chart  500  are two different exemplary curves: an unrestricted substructure curve (“unrestricted curve”)  504  and a tethered substructure curve (“tethered curve”)  506 . The unrestricted curve  504  represents the oscillation of a substructure (such as  FIG. 1 ,  106 ) subjected to vibrational forces, such as those experienced during the launch phase of a spacecraft. The unrestricted curve  504  is the dynamic response of a substructure without restraining features such as tethers. The shape of the unrestricted  504  is continuous and smooth. For example, the unrestricted curve  504  may be substantially similar to a sinusoidal curve. 
         [0035]    The tethered curve  506  represents the dynamic response oscillation of a substructure subjected to vibrations forces when restricted by a tether (such as  FIG. 1 ,  108 ). Although chart  500  only represents the tethered curve  506  of a substructure with a single tether, more tethers may be used to limit the dynamic response of the substructure. Line x  508  represents the limit of positive displacement of the substructure permitted by the tether. For example, when the substructure begins to experience dynamic response, the substructure may flex, bend, or deform away from the tether fastening point (e.g., in the positive x direction). While the tether is non-taut, the substructure may continue to experience varying displacement from axis  502 . Once the tether becomes taut, such as when the tether curve  506  intersects line x  508 , the tether is subjected to tensile forces which restrict the substructures deformation past line x  508 . Next, the substructure begins to reduce displacement, thus the tethered curve  506  returns toward axis  502 . The substructure continues its directional motion (dynamic response), thus the tethered curve  506  moves toward line −x  510 . When the tethered curve  506  intersects line −x  510 , it continues until the dynamic response energy is fully dissipated by the substructure and the substructure and tethered curve  200   c  begin to oscillate back toward axis  502 . It should be appreciated that if a second tether were connected to the substructure in an equivalent, but opposite, position then the corresponding tethered curve (not shown) may be restrained from surpassing line −x  510  in the negative displacement direction. 
         [0036]    The operation of the tether  108  during the launch phase is further explained below with reference to  FIG. 5  and  FIG. 3 . The net effective damping force is defined to be the equivalent viscous damping force needed in a linear model of the substructure  104  without a tether to approximate the nonlinear behavior of the substructure  104  when a tether  108  is present. The tether configuration increases the net effective damping force by utilizing nonlinear aspects of two sets of mode shapes that describe the dynamic behavior and transfer of energy from modal coupling. First, the tether  108  constrains the substructure  104  in dynamic motion only when the dynamic motion creates enough displacement in the substructure  104 ( 1 ) to make the tether  108 ( 1 ) taut. The taut tether  108 ( 1 ) only limits the displacement of the substructure  104  in a single linear direction, while all other displacement directions of the substructure  104  are unrestrained. 
         [0037]    This one-direction constraint creates an unsymmetric boundary condition that is described mathematically with two different sets of equations of motion. Mathematically, the substructure  104  has a first set of vibration mode shapes when the tether  108  is non-taut and second set of vibration mode shapes when the tether  108  is taut. Sinusoidal resonance dynamic motion of a structure typically occurs when the mode shapes are identical for both directions of motion (e.g., curve  504  in  FIG. 5 ). The tether configuration described herein creates two separate sets of mode shapes. First, any large displacement dynamic motion caused by sinusoidal excitations is dramatically reduced because a true resonance response is not possible with the disclosed tether configuration. Therefore, the lack of a true resonance response in the nonlinear behavior of the structure with tethers  108  requires an increase in the net effective damping force in a completely linear model of the substructure  104  without tethers  108  to approximate and bound the nonlinear, transient behavior. Second, the tether  108  creates conditions where energy is transferred from lower frequency modes to higher frequency modes. 
         [0038]    When the tether  108  becomes taut, it creates an impulse-function input (i.e., shock impact) as depicted in  FIG. 5  at location  512  along the tethered curve  506 . An impulse-function input excites all modes of a substructure  104 . The energy for the input is generated from the low frequency modes of vibration when the tether  108  is slack and is transferred to all of the higher frequency modes of the substructure  104  when the tether  108  is taut. This modal coupling from the tether  108  results in an energy transfer from the lower frequency modes to the higher frequency modes, which dissipate the energy more quickly as they vibrate at an increased rate. Therefore, the nonlinear modal coupling behavior of the substructure  104  with tethers  108  requires an increase in the net effective damping force in a completely linear model of the (lower frequency) substructure  104  without tethers  108  in order to approximate and bound the nonlinear, transient behavior. 
         [0039]    While preferred and alternate embodiments of the invention have been illustrated and described, as noted above, many changes can be made without departing from the spirit and scope of the invention. Accordingly, the scope of the invention is not limited by the disclosure of these preferred and alternate embodiments. Instead, the invention should be determined entirely by reference to the claims that follow.